steel construction 01/2014 free sample copy

Steel ConstructionDesign and Research

– Simplifi ed FE analysis for slab fi re design with membrane action– 3D component method for modelling beam/column joints– Strength/stiffness of screws/rivets in shear in metal member/sheeting

joints– Shenzen Airport Terminal 3 – structure and façade– Steel design and construction for oil sands industry in Canada– Orthotropic steel bridges in Germany– The setting-out of the NiGRES Tower– Wind forces on hyperbolic lattice towers

1Volume 7Februar 2014ISSN 1867-0520

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HALFEN GmbH • Liebigstrasse 14 • 40764 Langenfeld • GermanyTel.: +49 (0) 2173 970-9020 • Fax: +49 (0) 2173 970-450 • www.halfen.com

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Content

Steel Construction1

Articles

01 Martin Stadler, Martin Mensinger Simplified finite element analyses for fire design of slabs including membrane

action

08 Markku Heinisuo, Henri Perttola, Hilkka Ronni A step towards the 3D component method for modelling beam-to-column joints

14 Thomas Misiek, Saskia Käpplein Strength and stiffness of shear-loaded fastenings for metal members and sheeting

using fastening screws and rivets

Reports

24 Thorsten Helbig, Florian Scheible, Florian Kamp, Roman Schieber Engineering in a computational design environment – New Terminal 3

at Shenzhen Bao’an International Airport, China

32 Osama Bedair Modern steel design and construction in Canada’s oil sands industry

41 Heinz Friedrich Orthotropic steel bridges in Germany

48 Ekaterina Nozhova Between geometry and craft: the setting-out of the NiGRES Tower

56 Matthias Beckh, Rainer Barthel Wind forces on hyperbolic lattice towers

Regular Features

40 News59 ECCS news61 Announcements

A4 Products & Projects

Shenzhen Airport’s Terminal 3 is one of the largest buildings in the world designed with parametrically controlled digital tools and has an annual capacity of 24 million passen-gers. In a close collaboration between Massimiliano Fuksas Architects in Rome and the engineers of Knippers Helbig in Stuttgart, specific solutions were developed to provide sufficient structural integrity for the space structure, which is clad by the outer and inner façade layers (see report pp. 24–31).

(© Leonardo Finotti)

Volume 7February 2014, No. 1ISSN 1867-0520 (print)ISSN 1867-0539 (online)

Wilhelm Ernst & SohnVerlag für Architektur und technische Wissenschaften GmbH & Co. KGwww.ernst-und-sohn.de

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Journal for ECCS members

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A4 Steel Construction 7 (2014), No. 1

Products & Projects

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Expansion Joints for bridges must not only allow for safe and comfortable driving, but be durable and waterproof. Leaking units lead to serious and very costly longterm corrosion da-mages to the structures.

The steel profile design used for many decades for Expansion Joints with elastomer profiles have performed less advantageous.Difficult installation, frequent leakage, danger of fatigue and lack of ride comfort have led to the development of elastic asphaltic plug joints in the 90ies.Unfortunately, they did not meet the expectations. They are relatively easy to install and have a high level of driving com-fort. But the possible expansion movements are extremely low. They are prone to cracking and material squeezing and their life span is very short.Reisner & Wolff Engineering therefore developed a plastic compound based on polyurethane in cooperation with the world’s biggest chemical construction materials producer. This material covers all the requirements of Expansion Joints: POLYFLEX® PU.This material is exceptionally stretchable and extremely age resistant, highly durable and resistant to weathering and chemi-cals. The two components of the material can be mixed cold. Slopes and upturns are no problem due to the high viscosity during installation. The materials temperature range of applica-tion covers all climate zones. The reaction forces depend only slightly on temperature.If the bridge is expanding a block of this material, it may become detached from the adjoining road pavement. This is prevented by means of a perforated steel angle, which takes over all reaction forces and horizontal traffic loads.If the bridge is pressing a block of this material, there may be bulging. This is prevented by cast-in stabilizers.Thus, the patented POLYFLEX® Expansion Joints are able to permanently cope with large movements. The traffic loads are dissipated without any noise, free of fatigue or maintenance with maximum ride comfort.There is no rutting. Due to low height, the design is also perfect for steel bridges with low pavement thickness.Extensive investigations for verification of performance includ-ing permanent water tightness and long life span have led to the

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Further information:RW Sollinger Hütte GmbH, Auschnippe 52, 37170 Uslar, Germany, Tel. +49 (0)5571 – 305-0, Fax +49 (0)5571 – 305-26, [email protected], www.rwsh.deFig. 1. Steel Expansion Joint with rubber profile

Fig. 2. Stabilizers prevent bulging

Fig. 3. POLYFLEX® at the test rig of Technical University of Munich (© RW Sollinger Hütte)

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Ruukki to invest € 2.5 million in steel construction research during 2014–2017

The framework agreement for a Steel Construction Excellence Center is was recently signed in Hämeenlinna, Finland. Besides Ruukki, the other parties to the agreement are HAMK University of Ap-plied Sciences, Tavastia Vocational Col-lege, the City of Hämeenlinna, Häme De-velopment Centre Ltd and Tampere Uni-versity of Technology. The parties will jointly contribute an estimated more than € 6 million to steel construction research and teaching during the next four years.

Ruukki’s aim in the project is to promote research and development and to thus strengthen competence and training in new technologies at the vocational col-lege and university level. At the same time, the aim is to strengthen the interna-tional research network in the field. Ruukki will contribute around € 2.5 mil-lion to the steel construction research and development project during 2014–2017. Ruukki will conclude separate coopera-tion agreements with actors in the Hä-meenlinna region and with Tampere University of Technology. A similar agreement currently under preparation in the Seinäjoki region will be included

and thus also secure continued funding for the Research Centre of Metal Struc-tures in Seinäjoki and the research pro-fessorship in steel structures. “Ruukki aims to increase steel construction re-search and development to create new competence, which it is important to ensure at all levels of education. New technologies in steel construction en-able, for example, more energy- and ma-terial-efficient structures and functional-ities integrated into structures,” explains Toni Hemminki, Chief Strategy Officer at Ruukki. The agreement will strengthen 15 years of partnership between Ruukki and HAMK University of Applied Sciences in the product development of coated steel sheets and in the research and test-ing of steel structures. New competence will be built at HAMK’s Sheet Metal Centre, which will expand activities to cover an increasingly more significant share of R&D within steel construction.

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1© Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co. KG, Berlin · Steel Construction 7 (2014), No. 1

Articles

DOI: 10.1002/stco.201310033

Simplifications to finite element models are the subject of this article. These simplifications form part of a new method for the fire design of concrete and composite slab systems with partly unprotected secondary steel beams, taking into account tensile membrane action. Internal forces can be determined with the simplified model and cross-section design procedures can be ap-plied to calculate the required reinforcement amount equivalent to ambient temperature. The FE model is simplified by replacing the thermal analysis with a substitute thermal loading. Non-linear material behaviour is taken into account via a reduced model stiffness, which allows an efficient linear elastic calculation. The new method presented therefore enables the simple and efficient design of slab systems for fire.

1 Introduction

Composite slab systems can survive a fire even if some of the secondary steel beams are unprotected against heating. Large deformations allow membrane forces to be activated in the slabs and wider spans to be bridged. In the literature [1], this loadbearing behaviour is called membrane action. The utilization of membrane action has enormous economic potential since a large amount of the costly fire protection can be avoided.

Several design methods are available, including mem-brane action, but none satisfies all the requirements of a safe and economic design. The Eurocode [2] allows designers to use advanced calculation models, including non-linear finite element analyses. These models are most exact and unlim-ited, but also complicated, prone to faults and time-consum-ing. There are two main reasons for these problems: (1) two separate simulations (thermal and mechanical) have to be performed, and (2) complex non-linear material laws have to be included.

Simple calculation models can be applied more quickly and more efficiently. However, the models currently avail-able (e.g. [3], [4]) include assumptions that have to be revised. For example, so far no satisfactory approach has been pub-

Simplified finite element analyses for fire design of slabs including membrane action

Martin Stadler*Martin Mensinger

lished for determining the maximum allowable vertical deformation of a slab, although in all the current simple calculation models this is essential in order to predict the loadbearing capacity. The models available also neglect im-portant aspects such as the interaction with adjacent slab panels. This can lead to the formation of large cracks, cause loss of integrity and possibly loss of structural resist-ance. Such cracks and integrity failures occurred in one of the Munich fire tests on membrane action [5], [6], [7], as shown in Fig. 1.

A new design procedure has therefore been developed [8] which is based on advanced calculation models but is radically simplified to enable efficient application. This pa-per presents the simplifications made to the numerical model of the slabs. The whole design procedure, including the de-sign of the edge beams, the detailed theoretical background and validation via fire tests can be found in [8]. On the one hand, simple functions for determining a substitute thermal loading are presented which avoid the need for a specific thermal analysis. On the other, the stiffness of the mechan-ical finite element model is determined before the analysis in order to be able to use linear material laws. This enables short computing times by avoiding the iteration involved in non-linear solution procedures. Internal forces can be cal-culated with this simplified numerical model and cross-sec-tion design procedures equivalent to those for ambient temperature can be applied.

Received 2 May 2013, revised 1 July 2013, accepted 23 July 2013 * Corresponding author:

e-mail [email protected] Fig. 1. Crack near intermediate beam in a Munich fire test

05_001-007_Mensinger (033)_cs6_2sp.indd 1 03.02.14 11:27

M. Stadler/M. Mensinger · Simplified finite element analyses for fire design of slabs including membrane action

2 Steel Construction 7 (2014), No. 1

and no elongation or shortening of the neutral axis and will therefore be called thermal curvature.

If eq,subs and kq,subs are applied to any beam, they will cause the same deformations as a real temperature distri-bution qreal would do in the beam originally considered. The height and stiffness of the beam can be arbitrary, only the length must be the same. The reason for this is that the overall elongation u, caused by eq,subs, and the deflection in the middle of the beam wm, caused by kq,subs, only depend on the length � of a beam as shown in Eqs. (1) and (2). This means that the stiffness of a structure can be determined separately from the deformations caused by temperature changes.

u = eq,subs · � (1)

wmsubs=

κθ, · �

8 (2)

For finite element programs in which direct input of ther-mal strain and curvature is not possible, these values can be easily transformed into temperature loadings. With an arbitrarily chosen coefficient of thermal expansion aT, the uniform temperature increase Dqunif can be calculated with Eq. (3), and the temperature gradient between the top and bottom surfaces of the slab Dqgrad with depth h is obtained using Eq. (4).

∆θε

αθ

unifsubs

T

= ,

(3)

∆θκ

αθ

gradsubs

T

h= , ·

(4)

Formulas for the thermal elongation e(q) of concrete as a function of temperature are given in EN 1994-1-2, 3.3.2 [2]. The temperature-dependent Young’s modulus of concrete is slightly more difficult to determine. In the Eurocodes, Young’s moduli for concrete are only available for ambient temperature. For elevated temperatures, only stress-strain curves are given, no Young’s moduli. These stress-strain curves exhibit no linear character from zero strain. In or-der to obtain the same results in numerical simulations with the full stress-strain curves and the method in this paper, the same stiffness has to be used. Young’s modulus therefore has to be derived from the non-linear stress-strain

2 Design procedure

The new design procedure is very similar to the procedures that are commonly used for ambient temperature. Only the ultimate limit state, just before the loadbearing capacity is reached, is considered. The slab is modelled with simple shell elements and the steel beams with beam elements, connected together with coupling elements. Linear-elastic material behaviour is used for both the slab and the beams. Loads are applied to the finite element model and internal forces are calculated. Cross-section design procedures can be applied with these forces to determine the amount of reinforcement required in the slab. Such procedures are given in EN 1992-1-2, Annex B [9], for concrete slabs and in EN 1994-1-2, Annex D [2], for composite slabs. In contrast to the procedures for ambient temperature, an additional temperature load has to be applied to the slabs and beams to take into account thermal elongation and a geometric non-linear calculation has to be performed so that membrane forces can be activated.

Shell elements have to be used for modelling the slabs. Simpler plate elements are not sufficient since the finite ele-ments have to be able to take into account membrane forces. Concrete slabs are modelled with their actual depth. The depth of composite slabs can be assumed to be the effective thickness heff given in EN 1994-1-2, Annex D [2]. Orthotropic behaviour of composite slabs can be neglected since the loads are mainly transferred by axial forces and the axial stiffness is almost identical in both directions.

The heating has three main effects on the structure: thermal elongation, reduction in stiffness and decrease in material strength. The thermal elongation is taken into ac-count through a substitute thermal loading, which is ex-plained in the next section. The stiffness reduction is con-sidered with a reduced Young’s modulus for the numerical model as explained in section 4. The lower material strength is included in the cross-section design procedures of the Eurocodes.

3 Substitute thermal loading3.1 Derivation

A distribution of high temperatures qreal inside a cross-sec-tion has effects as shown in Fig. 2. It causes thermal elon-gation, which can be expressed by thermal strains e(q), and it reduces the stiffness expressed by the Young’s modulus E(q). If the thermal elongation is restrained, stresses will occur in the cross-section, which will be called non-linear thermal stresses snonl(q). These stresses can be calculated by multiplying E(q) by e(q). The stress distribution can be split into a linear part sq,lin and a curvilinear part of self- equilibrating stresses sq,self. The fictitious linear stress dis-tribution sq,lin causes the same deformations in a beam as the real stress distribution snonl(q). The self-equilibrating stresses sq,self do not cause any deformation and can there-fore be neglected. The linear stress distribution sq,lin can again be split. To start with, a Young’s modulus Esubs is re-moved from the equation by division. Then the remaining strains are split into a constant part eq,subs and a linear part kq,subs with zero-crossing at the neutral axis of the cross-sec-tion. The thermal strain eq,subs causes only elongation in a beam and no bending, whereas kq,subs causes only bending

Fig. 2. Derivation of the substitute thermal loading according to [8]



3Steel Construction 7 (2014), No. 1

lus kE,q = Ec,q/Ec,20 can be calculated. These are tabulated for a range of temperatures in Table 2. The values in both tables are only valid for normal-weight concrete with sili-ceous aggregates.

3.2 Concrete slabs

The substitute thermal loading for concrete slabs can be determined analytically. The real temperature distribution qreal for the standard fire can be taken, for example, from EN 1992-1-2, Fig. A.2 [9], or calculated by simple one-dimen-sional thermal analyses with finite elements. Temperatures are determined for several discrete points over the slab depth and spreadsheet software is used for the integrations that follow using the trapezoidal rule. The non-linear stress dis-tribution snonl(q) can be integrated over the cross-section to generate a fictitious thermal normal force Nq and bend-ing moment Mq:

(6)N dA E z z dz

E

nonlh

h

A

c

θ σ θ θ ε θ= ( ) = ( ) ( ) =

=

−( )∫∫ , · ,/

/

,

2

2

2002

2

k z z dzEh

h

,/

/

· ,θ ε θ( ) ( )−∫

M z dA E k z znonlA

n c Eh

h

θ θσ θ ε θ= ( ) = ( ) ( )( ) −∫ · · ,, ,

/

/

202

2

∫∫ · z dzn

(7)

where h is the slab depth and zn is the distance from the neutral axis of the hot cross-section. These forces would occur in a beam whose deformations are restrained against both elongation and bowing. Applied to unrestrained beams, they cause the same deformation as the real temperature distribution. Both forces act at the neutral axis of the cross- section as it is commonly defined in engineering mechanics. The neutral axis of a rectangular cross-section with uniform stiffness lies at the centre of the cross-section. If Young’s modulus changes non-uniformly, as in heated slabs, the stiffness becomes non-uniform and the neutral axis moves. The distance of the neutral axis from an arbitrary location can be calculated using Eq. (8):

aES

EA

E z z dz

E z dzzn

y h

h

h

h=

( )( ) =

( )( )

−

−

∫θ

θ

θ

θ

, ·

,

/

/

/

2

2

2

//

,/

/

,/

/

·

22

2

2

2

∫∫∫

=( )

( )−

−

k z z dz

k z dz

Eh

h

Eh

h

θ

θ

(8)

Once the thermal normal force and bending moment are known, the substitute thermal strain and curvature can be determined. For the determination of the required bending stiffness (Ely)q, it is important that zn is again the distance from the neutral axis of the hot cross-section.

(9)εε θ

θθ

θ

θ

θ

,

,/

/

,

· ,subs

Eh

h

E

N

EA

k z z dz

k z= ( ) =

( ) ( )( )

−∫ 2

2

ddzh

h

−∫ /

/

2

2

curves. For ambient temperature, an approach can be found in EN 1992-1-1, 3.1.5 [10]. The secant modulus is used, where the secant intersects the stress-strain curve at 40 % of the compressive strength. This approach is adopted in this pa-per as shown in Fig. 3.

An equation for the compression part of the stress-strain curve of concrete under elevated temperature is given in EN 1992-1-2, 3.2.2.1 [9]. If the stress is set to s = 0.4 fc,q, an equation can be found to determine the corresponding strain e0.4fcq:

(5)3

2

0.4 00.4fc

c1,0.4fc

c1,

ε

ε +εε

− =θ

θθ

θ

From Eq. (5) it can be seen that the strain at the intersection point does not depend on the concrete strength, instead only depends on the temperature, expressed by the value ec1,q, which is tabulated in EN 1992-1-2, Table 3.1 [9]. Young’s moduli for a range of concrete strength classes at 20 °C are given in Table 1. Since Eq. (5) is independent of the concrete strength, reduction factors for Young’s modu-

Fig. 3. Young’s modulus of concrete under elevated tempera-tures according to [8]

Table 1. Young’s moduli of concrete at 20 °C according to the non-linear stress-strain curves of EN 1992-1-2 according to [8]

fc,20 [N/mm²] 20 25 30 35 40

Ec,20 [N/mm²] 11884 14855 17826 20797 23768

Table 2. Reduction factor for Young’s modulus of concrete under elevated temperature according to [8]

qc [°C] 20 100 200 300 400 500

kE,q [–] 1.000 0.625 0.432 0.304 0.188 0.100

qc [°C] 600 700 800 900 1000 1100

kE,q [–] 0.045 0.030 0.015 0.008 0.004 0.001




(12)κθ,subsw=

( )8

22�

The method described in this section allows a substitute thermal loading to be determined for any kind of cross-sec-tion. As for concrete slabs, it only depends on slab depth and fire scenario. The approaches in this and the previous section can be used to validate each other. It can be shown that both methods lead to the same results [8].

3.4 Approximation functions

As described above, the substitute thermal loading only depends on slab depth and fire scenario. If the standard fire is used for the fire scenario, curves for every fire resistance class can be determined as a function of the slab depth. Approximation functions can be fitted to these curves, which allows the substitute thermal loading to be calcu-lated very easily. Simple power functions can be found for concrete slabs as shown in Eqs. (13) and (14). The same functions can be used for composite slabs in the longitudi-nal direction if the slab depth is replaced by the effective thickness according to EN 1994-1-2, Annex D [2]. In the transverse direction, a correction term b has to be included, which depends on the fire resistance class and whether steel sheeting with open or re-entrant troughs is used.

ε βθ,subs effbb h= 1

2

(13)

(14)κ βθ,subs effb

eff

b h

cm h cm

=

≤ ≤

34

10 20

where:heff slab depth of concrete slabs and effective thick-

ness of composite slabs according to EN 1994-1-2, Annex D [1]

b = 1.0 for concrete and composite slabs in the longitudinal direction

= c1t + c2 for composite slabs in the transverse direction

t time considered in [min] of fire resistance classb1 to b4 coefficients given in Table 3c1 and c2 coefficients given in Table 4

(10)κ

ε θθ

θ

θ

θ,

,/

/

,

· , ·subs

y

E nh

h

E

M

EI

k z z z dz

k= ( ) =

( ) ( )−∫ 2

2

θθ z z dznh

h ( )−∫ ·

/

/2

2

2

The substitute thermal strain and curvature only depend on the slab depth and the temperature distribution in the cross-section. They are independent of concrete strength classes. The temperature distribution only depends on the depth of the slab and the fire scenario. If the standard fire is used for the fire scenario, the only remaining parameter is the slab depth. This correlation allows very simple ta-bles, diagrams and approximation functions for eq,subs and kq,subs to be determined. Such functions are derived in sec-tion 3.4 for both concrete and composite slabs.

3.3 Composite slabs

Determining the substitute thermal loading is more difficult for composite slabs. The thermal expansion is orthotropic due to different cross-sections in the longitudinal and trans-verse directions. The substitute thermal strains and curvature therefore need to be determined separately for both direc-tions. Furthermore, the temperature distribution in the cross-sections changes permanently within a slab. A two-di-mensional integration over the cross-sectional area has to be performed in order to determine the thermal forces Nq and Mq plus the cross-section properties EA, ESy and Ely. The integration over a polygon has to be carried out using numer-ical methods. The area has to be split into sub-areas, like finite elements, with constant temperatures. These sub- areas can be summed up to approximate the integration. The cross-section already needs to be modelled with finite elements to deter-mine the temperature distribution. It is reasonable to use the FE program for the integrations too, instead of reading out the temperatures and integrating with spreadsheet software.

For these reasons, the substitute thermal loading for composite slabs is determined with FE models in this paper. The procedure will be demonstrated on a slab with unit width as shown in Fig. 4. As a first step, a thermal analysis is performed to obtain the temperature distribution in the slab. The FE model is changed from thermal to mechanical and the temperature field from the thermal analysis is ap-plied to the mechanical model. In a second step, the location of the resulting neutral axis is identified as shown in Fig. 4 (top). For this calculation, the material in the model only has a temperature-dependent Young’s modulus, no thermal elon-gations. A force F is applied at the end of the beam with a variable distance az from the bottom of the slab. The dis-tance az is varied iteratively until no vertical deformation w occurs. This distance azn is then the location of the resulting neutral axis. This procedure requires a normal force that acts on the neutral axis of a beam and is known to cause no bending moment and therefore no deflection. In a third step, the force is removed and thermal elongation is included in the material model. With the resulting elongation u and ver-tical deformation w of the beam on the neutral axis, as shown in Fig. 4 (bottom), the substitute thermal loadings can be calculated with Eqs. (11) and (12):

εθ,subsu=�

(11)

Fig. 4. Model for determining the substitute thermal loading of composite slabs according to [8]




area of reinforcement in the slab. In addition to the bond strength, the cracking is mainly influenced by the rein-forcement ratio. This can be seen in Fig. 5. In the upper part of Fig. 5, the bar has a high reinforcement ratio. The first crack occurs when the tensile strength of the concrete fct is reached. The whole load then has to be taken by the reinforcement, which leads to a strain peak in the reinforce-ment at the crack. Further tensile forces are transferred from the reinforcement at the crack to the uncracked concrete by the bond between them. As soon as the bond reaches the tensile strength of the concrete, the next crack occurs. The bar is further tensioned and all cracks develop until the concrete cannot reach its tensile strength at a further loca-tion.

The lower part of Fig. 5 shows a lightly reinforced con-crete bar. Here, the first crack also occurs when the tensile strength of the concrete is reached. Again, at the crack the whole force has to be taken by the reinforcement. However, the admissible force in the reinforcement Ns = Asfy is smaller than the force that is required to induce the first crack Ncr = Acfct. The induced force Nind therefore drops to Ns. The reinforcement in the crack is not able to transfer enough force into the concrete in order to induce a second crack since Ns < Ncr. If the bar is tensioned further, the first crack opens, the reinforcement in the crack yields and finally ruptures at its ultimate strength fu. If the force required to induce the first crack is even higher than the ultimate strength of the reinforcement, the reinforcement may rup-ture as soon as the first crack occurs. This kind of brittle failure is usually supposed to be avoided since it happens suddenly and without warning. The method presented in this paper is therefore only valid if sufficient reinforcement is available to enable a distributed crack pattern and to avoid brittle failure. This can be assured if a minimum reinforce-ment ratio is used, as introduced later on in this paper. This minimum reinforcement also avoids the situation of the first cracks opening widely and the slab failing in terms of integrity.

Tension stiffening effects are taken into account in the method presented here, with the following assumptions:– The whole slab is in tension as described above.– Only the top reinforcement is considered for determin-

ing the resulting stiffness.– The bottom reinforcement in concrete slabs becomes

very soft since it reaches a very high temperature; the contribution it makes to the stiffness can therefore be neglected.

– The steel sheeting of composite slabs also becomes very soft due to high temperatures and it possibly debonds from the concrete; its contribution to the stiffness can also be neglected.

– The concrete around the top reinforcement remains cold; tension stiffening can therefore be taken into ac-count with assumptions for ambient temperature.

– The amount of reinforcement available is such that it does not yield due to the internal forces determined.

– The amount of reinforcement available is sufficient for transferring the cracking force caused by the tensile strength of the concrete and for developing a distributed crack pattern.

– To determine the resulting stiffness with tension stiffening, it is assumed that the reinforcement just reaches its yield strength.

4 Stiffness reduction

Material non-linearities are the main reasons for the long computing times and convergence problems in advanced finite element models. These non-linear material laws are replaced in the method presented here by linear material laws with reduced stiffness. Material non-linearities have only one effect on a finite element formulation: they reduce the stiffness of the element expressed through its stiffness matrix. If the resulting stiffness is known before the simula-tion, it can be reduced simply by reducing the Young’s modulus when the model is set up.

In a fire, the stresses in a slab decrease with its stiff-ness. On the one hand, larger deformations are possible with a lower stiffness, which leads to smaller membrane forces. This behaviour can be compared with the behaviour of ropes, where a larger catenary sag leads to smaller tensile forces for a similar loading. On the other hand, large re-straint forces occur in a slab during a fire which decrease with the stiffness. The design procedure presented there-fore takes into account the smallest possible stiffness at the ultimate limit state.

For concrete and composite slabs with partly unpro-tected secondary beams it can be assumed – in the case of fire – that the stiffness of the slab is governed by the axial stiffness. The bending stiffness is very small since the depth of the slab is very small compared with the span, and the concrete cracks. Furthermore, the large deformations gen-erate a membrane system whose tensile stiffness has a greater effect than the bending stiffness. In addition, al-most the whole slab is under tension due to tensile mem-brane action and restrained thermal elongation of the edge beams and unprotected secondary beams. The stiffness reduction of a slab is caused by two effects: (1) softening of the concrete due to heating and (2) cracking of the con-crete. It can be shown [8] that the softening of the concrete can be simplified and taken into account by a reduction factor kE,q,mean, which is the reduction factor for Young’s modulus determined from the temperature at the centre of the cross-section.

The reduction in stiffness due to concrete cracking is referred to as tension stiffening in the literature [11]. The concrete around a reinforcing bar cannot crack completely; some parts remain uncracked and increase the stiffness of a slab. The cracking behaviour depends decisively on the

Table 3. Coefficients for determining the substitute thermal loading according to [8]

b1 b2 b3 b4

R30 31.91 –1.485 3867 –1.924

R60 89.09 –1.630 4976 –1.845

R90 136.3 –1.641 4889 –1.744

Table 4. Coefficients for composite slabs in transversal direc-tion according to [8]

Profile type c1 c2

re-entrant trough 0.0038 0.47

open trough 0.0019 0.96




The tensile strength of concrete varies statistically over a broad range. Therefore, a mean value fctm is usually used, e.g. in Eurocode 2, for determining a minimum rein-forcement area for brittle failure. The German National Annex to EN 1992-1-1 specifies that the effective tensile strength fct,eff should be at least 3.0 N/mm2. This value roughly corresponds to concrete class C30/37 and takes into account that, in reality, lower concrete classes in par-ticular often have a higher strength than required. This work follows this line of reasoning. The same is true for the effective Young’s modulus of concrete Ec,eff, and a mini-mum value should again be used. In this work the value for concrete class C30/37 is proposed. The coefficient b1, which takes into account the duration of the loading, is set to 0.25 here since no values for the case of fire are availa-ble. For concrete slabs, the effective thickness heff is similar to the slab depth.

The effective tension area Act,eff is assumed on the basis of Eurocode 2 [10] as shown in Fig. 7. The origin is explained in detail in [11]. Generally, the height of the tension area is 2.5 times the distance of the reinforcement from the ten-sioned surface d1. For membrane action, the effective ten-sion area needs to be enhanced. For example, if the upper reinforcement is placed very close to the top surface of the slab, the effective tension area would be very small. The larger the effective tension area is, however, the higher are the resulting stiffness of the slab and the resulting internal forces. Therefore, the worst case is a tension area as large as possible. This area should cover at least half the effec-tive depth but it cannot be larger than the effective depth.

The assumptions for determining the resulting Young’s modulus above are only valid if the amount of reinforce-ment available is large enough to transfer the cracking force caused by the tensile strength of the concrete and to develop a distributed crack pattern. In order to ensure this, a minimum reinforcement area As,min is required. The fol-lowing equation can be derived by assuming that the min-

Given these assumptions, tension stiffening approaches for ambient temperature can be used. The following ap-proaches are based on the book by Zilch and Zehetmaier [11] and DIN-Fachbericht 102 [12]. Fig. 6 shows the stress-strain curves and the meaning of the symbols.

The following equation can be derived for calculating the resulting stiffness of a slab related to cross-sectional area and depth heff:

E kf

f

E

f

EE

cmII

E meany c

y

st

ct eff

s c eff

s

, , ,,

,

θ θ

ρ

βρ

=

− +1EE

f

Ec eff

ct eff

e eff,

,

,

−

−

1

(15)

where:

(16)ρcs

c

s

eff

AA

Ab h

= =·

(17)ρc effs

ct eff

s

ct eff

AA

Ab h,

, ,·= =

(18)h dh

hct effeff

eff, ,= ≥ ≤2 521

f f N mmct eff ctm, . /= ≥ 3 0 2 (19)

E E N mmc eff cm, /= ≥ 33000 2 (20)

Fig. 5. Cracking behaviour of a rein-forced concrete bar with high (top) and low (bottom) reinforcement ratios on the basis of [11]

Fig. 6. Tension stiffening on the basis of [11]

Fig. 7. Effective tension area according to [8]




[2] EN 1994-1-2. Eurocode 4: Design of composite steel and concrete structures – Part 1-2: General rules – Structural fire design, German version, Dec 2010.

[3] Bailey, C. G.: Membrane action of unrestrained lightly rein-forced concrete slabs at large displacements. Engineering Structures 23 (2001), pp. 470–483.

[4] Cameron, N. J. K., Usmani, A. S.: New design method to de-termine the membrane capacity of laterally restrained com-posite floor slabs in fire. Part 1: Theory and method. The Structural Engineer, vol. 83, No. 19 (2005), pp. 28–33.

[5] Mensinger, M., Schaumann, P., Stadler, M., Sothmann, J.: Nutzung der Membranwirkung von Verbundträger-Decken- Systemen im Brandfall (Utilization of membrane action for the design of composite beam-slab systems in fire). DASt-Forschungsbericht 2012 (due for publication).

[6] Mensinger, M., Schaumann, P., Stadler, M., Sothmann, J.: Membranwirkung von Verbunddecken bei Brand – Experi-mentelle Untersuchungen (Membrane action of composite slabs in fire – experimental investigations). Stahlbau 80 (2011), No. 8, pp. 561–565.

[7] Stadler, M., Mensinger, M., Schaumann, P., Sothmann, J.: Munich fire tests on membrane action of composite slabs in fire – test results and recent findings. Proc. of Int. Conf., Appli-cations of Structural Fire Engineering, Prague, 2011, pp. 177–182.

[8] Stadler, M.: Design of composite slab systems in case of fire using simplified finite element analyses. Diss., Technische Uni-versität München, 2012.

[9] EN 1992-1-2. Eurocode 2: Design of concrete structures – Part 1-2: General rules – Structural fire design, German ver-sion, Dec 2010.

[10] EN 1992-1-1. Eurocode 2: Design of concrete structures – Part 1-1: General rules and rules for buildings, German ver-sion, Jan 2011.

[11] Zilch, K., Zehetmaier, G.: Bemessung im konstruktiven Be-tonbau: Nach DIN 1045-1 (Fassung 2008) und EN 1992-1-1 (Eurocode 2). Springer Verlag, Berlin, 2010.

[12] DIN-Fachbericht 102. Betonbrücken. Mar 2009.

Keywords: membrane action; composite slabs; simple design method

Authors:Martin Stadler, Technische Universität München, Chair of Metal Structures,Arcisstr. 21, 80333 Munich, Germany, e-mail: [email protected]

Martin Mensinger, Technische Universität München, Chair of Metal Structures, Arcisstr. 21, 80333 Munich, Germany, e-mail: [email protected]

imum reinforcement just reaches its yield strength fy when the first crack occurs:

(21)AA

f

fE

E

sct eff

y

ct eff

s

c eff

,min,

, ,

=− +1

In practice, during the design of concrete and composite slab systems, an initial calculation should be performed using a slab stiffness determined with the minimum reinforcement area. If the amount of reinforcement required for the internal forces is larger than the minimum reinforcement, a second calculation with a higher stiffness needs to be performed.

5 Conclusions

The simplifications presented for numerical models are the key elements in a new fire design method for concrete and composite slabs with partly unprotected secondary beams, including membrane action. Due to the simplifications, no thermal analysis is necessary and no non-linear material laws have to be included. This means the method can be applied with ordinary finite element programs and no spe-cialized software is required. The design procedure is sim-ilar to ambient temperature design methods, which can increase the user acceptance in practice. The method pre-sented follows the specifications of the Eurocodes. It can therefore be applied in every country that has adopted the Eurocodes. Since internal forces and the amount of rein-forcement required can be determined at every location in the slab, the method presented here prevents gaping cracks and integrity failure anywhere in a slab. The failure criterion in this method is defined as under ambient temperature, with yielding of the reinforcement, crushing of the concrete or shear failure of the slab at any location. However, the amount of reinforcement determined with this method is higher than the amount usually necessary in composite slabs for ambient temperature, especially above intermedi-ate beams between two slab panels. The use of membrane action nonetheless helps the composite structures to be built more economically than with classical fire design methods. In addition, the method presented in this paper helps con-crete and composite slabs to be designed simply, efficiently and safely for the case of fire.

References

[1] Mensinger, M., Schaumann, P., Stadler, M., Sothmann, J.: Membranwirkung von Verbunddecken bei Brand – Stand der Technik (Membrane action of composite slabs in fire – state of research). Stahlbau 79 (2010), No. 4, pp. 298–305.


Articles

DOI: 10.1002/stco.201300001

8 © Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co. KG, Berlin · Steel Construction 7 (2014), No. 1

A step towards the 3D component method for modelling beam-to-column joints

Markku Heinisuo*Henri PerttolaHilkka Ronni

This paper deals with the component method for the structural de-sign of steel joints in the 3D modelling of loads. The essential fea-tures of the method are presented in terms of the local and global analysis model. There is a discussion about the location of the local joint model, the definition of generalized joint displacements and the generic nature of the method. The proposed method is verified for a beam-to-column joint. Verification is carried out by a detailed 3D non-linear finite element analysis of a single joint. Other results in the literature are discussed briefly. One of the new components used in 3D modelling is introduced here. The pro-posed 3D component method seems to work rather well for mo-ment resistances of joints in both ambient and fire conditions. Ini-tial rotational stiffness needs to be studied more. Validation of the 3D component method is continuing with experiments on the end plate splice joints of rectangular tubular structures.

1 Introduction

The component method for the structural analysis of steel and aluminium joints has been developed over the last few decades. The method is presented in Eurocodes [1, 2]; it allows the definition of the stiffnesses and resistances of joints in 2D cases for ambient and fire conditions. Compre-hensive literature on the component method can be found in [3, 4 and 5], for example.

The component method for analysing joints in 3D was proposed in [6]. It was first applied to bolted base joints in [7]. The construction of the 3D component method for the bolted end plate joint of the rectangular tubular member shown in Fig. 1 is described as an introduction. The joint may be loaded by axial force and bending moments about the weak axis y or the strong axis z. The behaviour of the joint in terms of its resistance, stiffness and ductility can be analysed through this 3D model in a condition such that the resistances and stiffnesses of the components can be determined. Where the tension components are con-cerned, this is possible by using the same rules as given in Eurocodes [1] and [2] for 2D models, provided the bolts are located inside the flange lines marked EC in Fig. 1.

If the bolts are located at the corners of the end plate, however, it is necessary to define a tension component not included in the standards. At the corner, the behaviour of the end plate in bending differs profoundly from that ex-pected with end plates inside the flange lines. The associ-ated yield line mechanisms are presented in [8]. Both types of these tension components are of course applicable in 3D component analysis irrespective of whether the exter-nal loading is associated with strong-axis, weak-axis or bi-axial bending.

The tension components are located at the mid-points of the bolts. All parts of the connected members are di-vided into three sections of equal width. The mid-points of these sections are the locations of the potential compres-sion components. They are supposed to be absolutely rigid on the member side, as is assumed in [1] and [2] for corre-sponding compression components associated with entire flanges. The compression resistances of these components are calculated by multiplying their area by the yield strength of the connected member. As in the case of ten-sion components, the compression components can be used irrespective of whether the external loading is associ-ated with strong-axis, weak-axis or biaxial bending. The 3D component model of the joint in Fig. 1 is constructed ac-cording to the rules of [6]. This means that potential ten-sion or compression components are connected to the member axis with rigid links at the end (cross-section) of the member. The components at the other ends of rigid links can be interpreted as tension-only or compres-sion-only springs describing the strongly non-linear charac-ter of potential components. Thus, the tension component is active only in tension and the compression component, in turn, active only if compressed. Linear elastic–ideal plas-tic behaviour is assumed for all active tension and com-pression components in this study.

In principle, the global analysis of the entire frame reveals which potential components are active, i.e. which of them transfer the forces. It is also necessary to check whether the resistances of the active components are ex-ceeded. In other words, the premises of the global solution should be in compliance with the local joint models. With non-symmetrical joints, the mean of the rotational stiffness may be used to linearize the global analysis [7], but this option should be used with caution. In some cases the joint may be considered frictionless, without pretension and initial gaps at the potential contact surfaces. In these

Received 4 April 2013,revised 16 October 2013,accepted 4 December 2013* Corresponding author:

e-mail: [email protected]

06_008-013_Heinisuo_(001)_cs6.indd 8 03.02.14 11:27

M. Heinisuo/H. Perttola/H. Ronni · A step towards the 3D component method for modelling beam-to-column joints


behaviour of the member outside the joint. The generalized displacements not only form a link between Vlasov beam theory and joint analysis, but can be exploited when the results of the 3D finite element analysis (FEA) of the joints are converted to compare them with the results achieved by the (2D or 3D) component method.

The generic nature of the component method is also present in 3D. This enables automatic generation of the local joint analysis model although the joint layout and dimensions may vary. It is then possible to use the product model of steel structures [12] systematically as basic data when creating a joint model. This significantly enhances integrated steel design.

Let us next consider a beam-to-column joint as an ex-ample of the application of the 3D component method. Test results for the joint under strong-axis bending for both ambient and fire conditions are available in [13]. The joint consists of two UB 254x102x22 beams (grade 43) con-nected to one UC 152x152x23 column (grade 43) with flush end plate joints and six M20 bolts (grade 8.8) per joint. A non-linear FEA of a joint was conducted with the ABAQUS program. The FE model used was validated by tests in [14]. The FEA results were used in order to evalu-ate the results obtained by the proposed 3D component model in the example. Other cases in the literature are also discussed briefly.

2 Beam-to-column joint

The joint considered is shown in Fig. 2 and detailed infor-mation about it is given in [14]. An FE model of the joint was created using ABAQUS/CAE and the analysis was performed, consistently, by ABAQUS/Standard [15]. Eight-

cases (so-called linear contact problems), simplified algo-rithms may be used in a global analysis [9]. Sometimes ten-sion bolts may act in groups, requiring more iterations. The division of the parts of members into three sections for potential compression components is coarse. It was shown in [10] that a division into 3–10 sections does not markedly affect the results. Thus, it is recommended to have a local joint analysis model of moderate size. Three sections are typically enough. The local joint model is at the end of the connected member, as proposed in [5], not at the mid-line of the column as in [1] and [2], nor at the mid-plane of the end plate as in [11]. The local joint model is connected to the global analysis model of the connected member at this point. If the Vlasov beam element is used in the analysis of the members, the best way to fit measured or calculated axial joint displacements u(s) (s = coordinate along the cross-section) to the member element in the sense of the L2 norm is to use the following equations, so-called general-ized displacements [10]:

uu s dA

AN* A∫ ( )

= (1)

u s z s dA

Iy* A

z

∫ ) )( (ϕ =

⋅ (2)

u s y s dA

Iz* A

y

∫ ( ) ( )ϕ =

⋅ (3)

u s s dA

I* A∫ ( ) ( )

θ =⋅ ω

ω (4)

whereA area of cross-section of connected memberz, y, w coordinates of cross-section of memberIz, Iy moments of inertia of cross-section of memberIw inertia of sectorial coordinate of Vlasov theory

The generalized displacements and the corresponding forces (axial force N, bending moments My, Mx and secto-rial warping moment, Mθ) should be integrated over the cross-section at the end of the member. These quantities then reflect the behaviour of the joint itself and not the

Fig. 1. End plate joint and potential tension and compres-sion components of 3D com-ponent model

Fig. 2. Beam-to-column joint with strong-axis moment

06_008-013_Heinisuo_(001)_cs6.indd 9 03.02.14 11:27



node brick elements with reduced integration (C3D8R) are used for all parts, as proposed in [16]. Instead of the de-tailed modelling of the welds, the associated parts are tied to each other by the TIE constraint available in ABAQUS/Standard. This means that the translational (and rota-tional, not used here) degrees of freedoms on the associ-ated surfaces of the beam end and the end plate are con-strained to produce, in principle, the same deformation on both surfaces. The FE meshes created are shown in Fig. 3.

The interaction at the contact parts of the model was defined as surface-to-surface contact with finite sliding. The contact surfaces were: between bolt and end plate, between bolt and column flange, between end plate and column flange. The potential contact surfaces of one bolted connection are shown in Fig. 4. The master–slave pairs, i.e. the associated surfaces needed in ABAQUS for the contact analysis, were assigned as shown in Table 1. A fric-tion coefficient of 0.2 was used to determine tangential behaviour, whereas a hard contact was adopted for nor-

mal behaviour. In hard contact, the surfaces separate if the contact pressure decreases to zero (or negative). Separated surfaces come into contact when the clearance between them decreases to zero.

The contact procedure applied and the modelling of pretension in bolts and boundary conditions are presented in detail in [14]. The elastic–ideal plastic material model with a measured [13] elastic modulus and yield strength for all parts was used for ambient conditions. Thus, no decay phase was used for the material models and plastic strain (PEEQ in ABAQUS) development was followed during the analysis. In fire, the first parts of the material rules were used for all parts up to the horizontal yielding stage as shown in [16]. No decay phase was used in fire for the material models either, and a horizontal phase with con-stant stress was assumed up to large strains. This is consist-ent with the idea of following the plastic strain develop-ment in fire. Consequently, no redistribution of stresses in the joint could take place due to the decay phase of a cer-tain component. This resulted in some overestimation of the joint resistance. Redistribution of stresses was, in gen-eral, possible because of the yielding.

A thermal analysis in fire was conducted using the same FE model as in the mechanical analysis. The testing procedure used in fire was simulated by the thermal-me-chanical modelling. Load was applied first and the temper-ature then increased, which constituted a transient analy-sis.

In general, rather good consistency was observed be-tween the results based on the FE model and the tests re-sults concerning strong-axis bending. In fire, the moments of the joints estimated by ABAQUS were about 10 % larger determined at about 20 % of maximum strain when com-pared with the maximum moments obtained in the fire tests. The simulated moment–rotation relationships devel-oped much the same as the test results in the fire’s growth phase. The deformed shape of the joint given by the FEA (left) and the one observed in the test (right) are illustrated in Fig. 5. The joint was analysed using the 2D component method in strong-axis bending. The details of the calcula-tions are shown in [14]. Fig. 6 illustrates moment resistance based on the component method and four test results in fire.

The results of the component method are rather well in line with the test results when the reduction factor for steel yield strength is included in the method. End plate resistance was critical in fire both in the tests and with the

Fig. 3. Mesh patterns: a) beam, b) column, c) bolt, d) end plate

Fig. 4. Contact surfaces at one bolt

Table 1. Master and slave surfaces of contact areas

Master Surface Slave surface

Bolt Vs Column Bolt Column

Bolt Vs Endplate Bolt Endplate

Endplate Vs Column Column Endplate

Fig. 5. Simulated and observed displacements for strong-axis bending in fire

06_008-013_Heinisuo_(001)_cs6.indd 10 03.02.14 11:27



component method. The same joint was then modelled by the suggested 3D expansion of the component method and by FEA as described above. This time, a bending moment acting on both sides of the joint is associated with a weak-axis bending of the connected beam. The joint was ana-lysed with stiffener plates (10 mm, grade 43) between the column flanges at the level of the beam flanges (not shown in Fig. 7). In the 3D FE model, the stiffeners were con-nected through TIE constraints to the column flanges and web. In the suggested 3D component model, the compres-sion flange was divided into three sections of equal width, and the centre of compression was located at the mid-point of the outmost section. The potential tension compo-nents were each defined as “the end plate in bending and the bolt in tension”. Thus, the tension component was comprised of two components connected in series. Load-ing and active tension components T1, T2, T3 and active compression components C1, C2 are illustrated in Fig. 7. Fig. 8 shows the corresponding lever arm z related to the weak-axis bending.

The resistances and stiffnesses of the components were calculated using the rules of [1] and [16] in ambient and fire conditions. It should be emphasized that in this case the only new component required in the suggested 3D component model in addition to those introduced in [1] was a compression one defined as a third of the com-

pressed part (flange or web). In ambient conditions a value of 5.80 kNm was determined for a moment resistance without stiffeners and, correspondingly, 6.06 kNm with stiffeners, through the 3D component method. Consider-ing this, the component for column web bending was ne-glected, since the column web was presumed to act as a rigid part in weak-axis bending. The difference between the values resulted from the critical yield lines omitted at the column flange in the case with stiffeners. Initial rotational stiffness was Sj,ini = 1011 kNm/rad and final Sj = 505 kNm/rad. The critical component was the “column flange in transverse bending” with non-circular yield lines when in-terpreted to act in the group. Fig. 9 illustrates the moment–rotation relationship for weak-axis bending. The ABAQUS results shown as a comparison were calculated by assum-ing the stiffeners between the column flanges.

The component method results of Fig. 9 were achieved by adopting rotational stiffness Sj, which made initial stiff-ness Sj,ini = 2Sj too large compared with the FEA results explained below.

In the FE simulation of the joint considered, the max-imum load did not occur within reasonable deformations. The main reason for this is to be found in the relatively large flexibility of the end plate (with respect to the bolts). On the other hand, the structure with linear elastic–ideal plastic materials can take more loads until the plastic mechanism develops. Up to that point, the derivative of the load–displacement curve is positive due to the elastic areas left in the structure. In the case of excessive deforma-tions, it is necessary to define somehow the “practical cri-terion for the resistance”. In [14] the ABAQUS analysis was terminated when a maximum plastic strain of about

Fig. 6. Strong-axis moment resistance in fire

Fig. 7. Loading a) and active components b) for weak-axis bending

Fig. 8. Centre of compression at beam flanges

Fig. 9. Weak-axis moment–rotation relationship with 3D component method and ABAQUS in ambient conditions. Weak-axis rotation is determined as a generalized displace-ment by integrating over the cross-section of the beam end

06_008-013_Heinisuo_(001)_cs6.indd 11 03.02.14 11:27



27 % was obtained at the tip of the beam’s top flange, which represents a configuration with excessive deforma-tion. The resistance of the joint was defined at 50 mrad. In this example the corresponding value of the bending mo-ment was about 9 kNm. This value is 1.5 times larger than the moment resistance determined by the 3D component method, which is a rather reasonable result for the compo-nent method. The character of the criterion used for the moment resistance was more intuitive rather than based on strict physical reasoning.

The joint behaviour was simulated by FEA for the case without stiffeners between the column flanges as well. That made the stresses and strains at the column web crit-ical, as expected. The analysis was terminated at a moment of 2.8 kNm for similar reasons as the analysis of the joint with the stiffeners as explained above (i.e. excessive defor-mations). Finally, the same joint was analysed with weak-axis bending in fire using the ABAQUS model with stiffen-ers. About 20 % maximum plastic strains were obtained at 650 °C with a constant weak-axis moment of 6 kNm main-tained during the fire (Fig. 10).

Plastic strains were observed not only on the compres-sion side of the joint, in the beam flange and in the end plate, but also on the tension side, in the bolt shank and in the column flange. Rotation was very large, about 200 mrad, at this stage. The component method gave a 6 kNm mo-ment resistance at the ambient temperature, implying an approx. 0.35 × 6 = 2.1 kNm moment resistance at 650 °C using the reduction of [16] for the yield strength. No decay phase was assumed in the ABAQUS material models. Refer-ring to Fig. 10, the ABAQUS model means 9–34 % strains at 600–700 °C. This means that the failure of the joint hap-pens in this range and the component model result is quite reliable.

3 Discussion and conclusions

The estimates for moment resistances are on the safe side in both ambient and fire conditions based on the proposed 3D component method. Rotational stiffness needs to be studied further, especially initial rotational stiffness. Stiff-ness Sj predicts rotations rather well up to 2/3 of moment resistance. The ratio η = Sj,ini/Sj = 2 was used in the analy-sis. In the example, one new component was used for the

compressed part of the connected beam. The tension com-ponents are the same as in the 2D method. New compo-nents will be needed in other cases when the loads on the joints involve 3D actions such as biaxial bending. Other possible components associated with web bending, torsion cases, e.g. warping of joints, may be examined in similar fashion. More tests are urgently required for validating the 3D component method, which could fill one of the missing utilities in the designer’s toolbox.

Six cases were analysed in [18] using comprehensive non-linear 3D FEM models and the component method. Beam and column sizes varied. Joints were bolted in five cases and welded in one. In three cases there were no stiff-eners at the column and in three cases they were included. Ambient conditions were studied with weak-axis moments. Quite close correlations for rotational stiffness were found between the 3D component method and FEM. Variations in the compressed beam flange component were observed. It was concluded in [18] that the 3D component method works well for stiffened columns, but the performance of the model is not satisfactory for the case of an unstiffened column flange. Further studies of the behaviour of the col-umn flange in twisting and the column web in bending are needed. The proposed 3D component method works well with beam-to-column joints if the column is stiffened with horizontal stiffeners at the beam flange level in weak-axis bending. The estimated resistance of the joint is satisfac-tory in both ambient conditions and fire. Its rotational stiff-ness depends on how it is defined. Generalized displace-ments of joints are introduced. Use of Eqs. (1)–(4) is rec-ommended to invert the results obtained from FE models so that they can be compared with, for example, the results of the 3D component method. In principle, these defini-tions can be used in the treatment of the test results as well instead of the rather alternating procedures used in prac-tice in the past. This affects the measurements needed in the tests. Anyway, using the generalized displacements could be one way of comparing precisely the results achieved through different research efforts.

The general nature of the 3D component method is very similar to that of 2D methods: the rigid links are just extended to reach the potential compression or tension components situated outside of the loading plane of the 2D model. Thus, the 3D component model can resist the combined action of biaxial bending and normal force. For example, the 3D component model could offer a practical tool for the design of the column base in the corner of the skeleton. Furthermore, the designer could face plenty of problems where the 3D analysis should necessarily be taken into account. It must be pointed out that although the 3D component model of a joint was demonstrated by exploiting the 2D loading case (weak-axis bending), the essential features related to the 3D model were given. The 3D component model should of course lead to the same solution as that obtained by the 2D model when the load-ing is introduced as a two-dimensional one. This is a per-quisite when the 2D component method is extended to the 3D in the right way.

The 2D or 3D component models can be generated automatically from the product models of steel structures based on the embedded rules of the generation modules. That is essential for practising engineers because determin-

Fig. 10. Temperature vs. rotation for a weak-axis bending moment of 6 kNm

06_008-013_Heinisuo_(001)_cs6.indd 12 03.02.14 11:27



ing the stiffnesses of components and resistance checks are impossible without computers. When these models are available, the stiffnesses of joints based on their real fea-tures can be used in global analysis to ensure safety. New components are needed for the cases not included in the standards. These should be developed case by case and verified and validated with care. The proposed 3D compo-nent method may have many new applications. The most urgent need is to validate the method with tests. Bolted end plate splices for rectangular tubes have been tested in biaxial bending in ambient conditions [19] and in fire [20]. Comprehensive 3D FEM simulations and component method analyses on these problems are currently being conducted by our research team.

Acknowledgements

The financial support of E-P Liitto (Regional Council of South Ostrobothnia) and other organizations and compa-nies from the Seinäjoki Region is gratefully acknowledged.

References

[1] EN 1993-1-8, Eurocode 3: Design of steel structures – Part 1-8: Design of joints. CEN, Brussels, 2005.

[2] EN 1999-1-1, Eurocode 9: Design of aluminium structures – Part 1-1: General structural rules. CEN, Brussels, 2007.

[3] Simões Da Silva, L.: Towards a consistent design approach for steel joints under generalized loading. Journal of Construc-tional Steel Research, 2008, 64, pp. 1059–1075.

[4] Diaz, C., Marti, P., Victoria, M., Querin, O.: Review on mod-eling of joint behaviour in steel frames. Journal of Construc-tional Steel Research, 2011, 67, pp. 741–758.

[5] Heinisuo, M., Perttola, H., Ronni, H.: Component method for end plate joints, modeling of 3D frames, literature review. Steel Construction, vol. 5, No. 2, June 2012, pp. 101–107.

[6] Heinisuo, M., Laine, V., Lehtimäki, E.: Enlargement of the component method into 3D. In: Proc. of Nordic Steel Con-struction Conference, Malmö, 2–4 Sept 2009, pub. 181, LUT & SBI, pp. 430–437.

[7] Laine, V.: Teräsrungon liitosten jouston huomioon ottami-nen integroidussa suunnittelujärjestelmässä. MSc thesis, Tam-pere University of Technology, Tampere, Finland, 2008 (in Finnish).

[8] Heinisuo, M., Ronni, H., Perttola, H., Aalto, A., Tiainen, T.: End and base plate joints with corner bolts for rectangular tubular members. Journal of Constructional Steel Research, 2012, 75, pp. 85–92.

[9] Heinisuo, M., Miettinen, K. A.: Linear contact between plates and unilateral elastic supports. Mechanics of Structures and Machines, 17(3), 1998, pp. 385–414.

[10] Perttola, H., Heinisuo, M.: 3D component method for base bolt joint. In: Yardimci, N., Aydöner, A., Gures, H., Yorgun, C.

(eds.): Steel Structures: Culture & Sustainability. Turkish Con-structional Steelwork Association (TUSCA), Istanbul, 2010, pp. 361–368.

[11] Del Savio, A., Nethercot, D., Vellasco, P., Andrade, S., Mar-tha, L.: Generalized component-based model for beam-to-col-umn connections including axial versus moment interaction. Journal of Constructional Steel Research, 2009, 65, pp. 1876–1895.

[12] Heinisuo, M., Laasonen, M., Ronni, H., Anttila, T.: Integra-tion of joint design of steel structures using product model. In: Walid, T. (ed.): Proc. of International Conference on Comput-ing in Civil & Building Engineering, Nottingham University Press, Nottingham, 2010, pp. 323–324.

[13] Al-Jabri, K. S.: The Behaviour of Steel and Composite Beam-to-Column Joints in Fire. PhD thesis, Department of Civil & Structural Engineering, University of Sheffield, UK, 1999.

[14] Rueda Romero, E.: Finite element simulation of a bolted steel connection in fire using Abaqus program. MSc thesis, Tampere University of Technology, Tampere, Finland, 2010.

[15] Hibbit, Karlsson and Sorsen, Inc.: ABAQUS/Standard User’s Manual, vol. II, 2001.

[16] Hu, Y., Davison, B., Burgess, I., Plank, R.: Component Modeling of Flexible End-Plate Joints in Fire. Steel Structures, 9, 2009, pp. 1–15.

[17] EN 1993-1-2, Eurocode 3: Design of Steel Structures – Part 1-2: General Rules, Structural Fire Design. CEN, Brus-sels, 2005.

[18] Neumann, N., Buzaljko, M., Thomassen, E., Nuhic, F.: Ver-ification of design model for out-of-plane bending of steel joints connecting H or I section. In: Proc. of Nordic Steel Construction Conference, Oslo, 5–7 Sept 2012, Norwegian Steel Association, pp. 683–692.

[19] Perttola, H., Heinisuo, M.: Test Report, End Plate Joints of Steel Tubes, Biaxial and Weak Axis Bending. Tampere Univer-sity of Technology. Department of Civil Engineering. Struc-tural Engineering, research report 155, Tampere, 2010.

[20] Ronni, H., Heinisuo, M.: Test Report, End Plate Joints of Steel Tubes, Biaxial Bending in Fire. Tampere University of Technology. Department of Civil Engineering. Structural En-gineering, research report 156, Tampere, 2012.

Keywords: 3D component method; beam-to-column end plate joint; fire; Eurocodes

Authors:Professor Markku HeinisuoResearcher Henri PerttolaResearcher Hilkka Ronni

Tampere University of TechnologyDepartment of Civil EngineeringKampusranta 9 C, 60320 Seinäjoki, Finland

06_008-013_Heinisuo_(001)_cs6.indd 13 03.02.14 11:27

Articles

DOI: 10.1002/stco.201410004

14 © Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co. KG, Berlin · Steel Construction 7 (2014), No. 1

Strength and stiffness of shear-loaded fastenings for metal members and sheeting using fastening screws and rivets

Thomas Misiek*Saskia Käpplein

The paper deals with the strength and stiffness of fastenings with fastening screws or rivets in thin-walled sheeting and sections. After a brief review of the design equations given in some codes, an additional proposal is given. A further review covers the stiff-ness equations from both codes and research papers, and con-cludes with a recommendation for applications.

1 Introduction

While working on the revision to the current version of EN 1993-1-3, questions arose regarding the formulas given for the design of fastening screws loaded in shear. For ex-ample, when plotting the bearing resistance Fb,Rk over sheet thickness t of the component to be fixed, an abrupt change in the curve can be observed for different thick-nesses t1 of the supporting structure.

Furthermore, according to the English original ver-sion, the formulas given apply to self-tapping screws, but are also applied to self-drilling screws. Therefore, it was preferable to check whether these formulas (and also the ones given in EN 1999-1-4) can also be applied to self-drill-ing screws.

While doing so, the idea for a general evaluation of the design formulas for both fastening screws and rivets arose. The results are presented here.

As an introduction, some remarks are given regarding the behaviour of fastening screws loaded in shear. The test-ing procedures laid down in both the ECCS recommenda-tions [1] and EOTA documents are introduced.

Current and some older design formulas are presented and – based on a huge number of test results – some cor-rections are suggested.

Finally, some special aspects such as stiffness of fas-tenings and temperature loads are discussed.

Unfortunately, different designations apply for the connected sheets in the different codes and recommenda-tions. The most relevant for practical applications are, on the one hand, the ones given in EN 1993-1-3 and, on the other, the ones given in the European Technical Approvals (and also the draft EN 1090-4 for thin-walled structures

and several other documents). EN 1993-1-3 contains the following definitions:t thickness of thinner connected part or sheett1 thickness of thicker connected part or sheet

and use either no or Arabic numerals as indexes. It is gen-erally assumed that the thinnest sheet is next to the head of the fastening screw or rivet. If not, then t1 = t should be assumed for design.

The European Technical Approvals use the following definitions:tI thickness of sheet next to head of fastening screw or

rivet, usually the component to be fastenedtII thickness of sheet averted from head of fastening screw

or rivet

and use Latin indexes. In the following, both definitions are used because they can hardly be confused. This ensures better accuracy, especially when presenting design equa-tions from codes.

The following definitions given in the ECCS recom-mendations [2] apply:Fastener: connecting element in a fasteningFastening: interaction of fastener with surrounding ma-

terialConnection: group of (one or more) fasteners

Fig. 2 shows examples of typical fastening screws. Self-tap-ping screws require a hole to be drilled beforehand (pilot

Received 23 August 2013,revised 1 November 2013,accepted 11 October 2013* Corresponding author:

e-mail: [email protected]

Fig. 1. Bearing resistance vs. sheet thickness t for different thicknesses t1

abrupt change

07_014-023_Misiek-Kaepplein_(004)_cs6.indd 14 03.02.14 11:26

Th. Misiek/S. Käpplein · Strength and stiffness of shear-loaded fastenings for metal members and sheeting using fastening screws and rivets


a design function is structured, i. e. which parameters and failure modes have to be taken into account: The behav-iour of shear-loaded fastenings heavily depends on sheet thicknesses, ratio of sheet thicknesses, ratio of fastener di-ameter to sheet thickness and the question as to whether or not a washer is to be used.

In principle, two observations are relevant when stud-ying the effects of loads on fastenings: the elongation of the holes and the tilting of fasteners in the direction of loading. Both effects have a significant impact on stiffness and re-sistance.

Elongation of holes, or bearing failure, is the most com-mon failure mode in fastenings in thin-walled sheeting. If both connected sheets are of the same thickness, elongation of holes will most likely occur in the sheet averted from the head of the fastener: The head or washer both stabilizes and provides some friction for the sheet adjacent to the head or washer. Resistance to elongation of holes is proportional to sheet thickness, tensile strength and diameter of fastener.

Titling requires a minimum thickness of the connected sheets because otherwise elongation of holes occurs and the forces will not be that high. On the other hand, with increasing sheet thickness, the fastener is clamped into the sheet, which prevents tilting. Washers tend to stabilize the fastener and therefore may prevent tilting failure, and usu-ally lead to a stiffer fastening. With increasing deformation (usually larger than the applied deformation criterion of 3.0 mm), tensile forces in the fastener will occur, leading to an increase in force and stiffness.

In the design formulas, tilting is usually reflected in a square root approach. Current design formulas assume that tilting will most likely occur for sheet thickness ratios of unity, which cannot be proved by tests.

hole), whereas self-drilling screws have a drill point. If the drill point diameter is significantly smaller than the diam-eter of the screw, we speak of a reduced drill point. Fasten-ing screws with reduced drill point are preferably used as seam fasteners (small sheet thicknesses). Stitching screws do not require pre-drilled holes, but their application is also limited to small thicknesses (about 2 × 1.0 mm in steel and 2 × 1.5 mm in aluminium). Most of them have a seal-ing washer, one type a sealing ring. As it is quite usual, the one with the sealing ring has a mushroom head, whereas all the others shown have hexagonal heads. Other head geometries are available and applications without washers are possible. Fastening screws for metal members and sheeting are usually made of stainless steel, case-hardened steel or heat-treatable carbon steel.

Fig. 3 shows examples of rivets. Simple blind rivets are often used as seam fasteners or for fixing flashings etc. They are made of aluminium, galvanized carbon steel, stainless steel or special alloys such as Monel (nickel-cop-per alloy). Triple-claw blind rivets are used for very thin supporting structures because they have a comparatively high pull-out strength; they are usually made of aluminium. Rivets with a protruding head are used for applications with thicker sheets, where they have to compete with met-ric bolt-and-washer fastenings. Typical applications are rack structures. Rivets with a protruding head are usually made of carbon steel.

2 Loadbearing behaviour and testing

The loadbearing behaviour of shear-loaded fastenings in metal members and sheeting using fastening screws or riv-ets has to be discussed because it has an effect on the way

Fig. 2. Fastening screws: a) self-tapping screw, b) self-drill-ing screw, c) self-drilling screw with reduced drill point di-ameter, d) flow-drilling screw (stitching screw)

Fig. 3. Rivets: a) blind rivet, b) triple-claw blind rivet, c) rivet with protruding head

Fig. 4. Test setup according to [1]




for t1 ≥ 2.5 t and t > 1.00 mm2.1α = (2c)

For t < t1 < 2.5 t, α should be calculated by linear interpo-lation.

As will be seen later, this formula is the only one with an additional case distinction for a large thickness of the substructure. If t < 1.00 mm applies, α is calculated for the case t = t1. This is questionable according to the informa-tion given in section 2. The square root formulation re-flects the failure mode tilting of fastener, which will not occur if the screw is clamped into the thicker sheet of the supporting structure. Older drafts of EN 1993-1-3 did not include this additional case distinction.

For steel sheet fastenings with rivets, EN 1993-1-3 gives the following:

for t = t1

3.6 t d 2.1α = ≤

(3a)

for t1 ≥ 2.5 t2.1α = (3b)


Compared with the formulas for fastening screws given in EN 1993-1-3, the constant factor with the tilting failure mode is about 12 % higher, possibly reflecting the stabilizing effect of the closing head on the blind side.

3.3 EN 1999-1-4 for aluminium sheets

For aluminium sheets connected with self-tapping screws or rivets, EN 1999-1-4 [5] gives the following:

for t = t1

2.5 t d 1.5α = ≤

(4a)

for t1 ≥ 2.5 t1.5α = (4b)


The formulas are the same for fastening screws and rivets. Compared with EN 1993-1-3, the constant factors are about 40 % higher in EN 1993-1-3 than in EN 1999-1-4. Assuming a Hertzian contact-like mechanical model, about 70 % higher factors would apply in EN 1993-1-3. In fact, both EN 1993-1-8 and EN 1993-1-3 use the same fac-tors for bearing resistance in the design of bolted connec-tions.

3.4 DIN 18807-6 for aluminium sheets

For aluminium sheets connected with self-tapping screws or rivets, DIN 18807-6 [6] gives the following:

for t = t1

1.6 t d 1.6α = ≤ (5a)

Other possible failure modes are net section failure and shear failure of the fastener itself. Both failure modes are not discussed here, but must be checked in the design. Rivets especially have a low shear resistance.

A simple test setup for determining shear resistance is shown in Fig. 4. The setup consists of two sheet strips con-nected with one fastener. The connection is loaded at a constant rate; usually 1 mm/min and corresponding forces are measured. The test is stopped once the deformation criterion of 3.0 mm is reached. There are several reasons for the application of a deformation criterion: – If tilting occurs, tensile forces in the fasteners increase,

questioning the interaction formulas usually applied. – Elongation of holes can reduce the pull-through resist-

ance and has to be limited. For screwed fastenings with washer dw = 16 mm, it was proved that there is no sig-nificant reduction in pull-through resistance if hole elongation is limited to 3 mm [3].

After the test, hole elongations and tilting angles are meas-ured. The observed failure mode decides how to deal with temperature loads, see section 6 below.

3 Review of design formulas given in different codes3.1 General

This section provides an overview of the design formulas for shear-loaded fastenings with screws or rivets given in some codes. Net section failure and failure of the fastener itself are not covered and have to be checked separately.

In these codes, the following symbols are used for the definition of the sheets:t thickness of thinner connected part or sheett1 thickness of thicker connected part or sheet

Notwithstanding any other remarks, it is generally as-sumed that the thinnest sheet is next to the head of the fastening screw or rivet.

Most codes work with a design formula:

Ff d t

b,R,du

M

=α ⋅ ⋅ ⋅

γ (1)

The factor α changes depending on the sheet thicknesses and the thickness ratios, reflecting the different failure modes associated with them. Whereas bearing resistance is associated with a constant factor α, tilting of the fastener usually leads to a factor α depending on the ratio of sheet thickness to fastener diameter.

3.2 EN 1993-1-3 for steel sheets

For steel sheet fastenings with self-tapping screws, EN 1993-1-3 [4] gives the following:

for t = t1

3.2 t d 2.1α = ≤

(2a)

for t1 ≥ 2.5 t and t ≤ 1.00 mm

3.2 t d 2.1α = ≤ (2b)




the evaluation. In most cases the actual diameter of the fastener was available and used in the evaluation. If not, the mean diameter from the tolerance range given in the manufacturers’ specifications was used. Different test func-tions were investigated, including the functions given in the codes. For each test function chosen, the correspond-ing constant factors were calculated using the least-square approach. This leads to an equation representing the mean values. The test function showing the best correlation with the test results was chosen for further evaluation. An equa-tion rt for the characteristic values was derived by further statistical evaluation based on the ratios di of actual value rei to calculated mean value rmi (theoretical value rti multi-plied by mean value correction factor b). The variances of the independent parameters sheet thickness t, tensile strength Rm and diameter d were taken into account with Vt = 0.0195, VRm = 0.076 (for steel and aluminium, correct value for aluminium VRm = 0.059) and Vd ≈ 0.00.

4.2 Design equations

Finally, the fastenings were grouped in the following way: – Fastenings with self-drilling and self-tapping screws – Fastenings with self-drilling screws with reduced drill

point diameter and flow-drilling/stitching screws (both fastening screws deform the sheets such that additional engagement in the sheets is provided)

– Riveted fastenings

All self-drilling screws with ratio of drill point diameter to outer diameter ≤ 0.75 are regarded as self-drilling screws with reduced drill point. Following StbK-N5, but deviating from EN 1993-1-3 and EN 1999-1-4, no differentiation was made between steel and aluminium. In fact, EN 1993-1-8 and EN 1999-1-1 also include the same design formulas for bearing resistance of steel and aluminium.

In the design expressions it was always assumed that only one failure mode governs the behaviour of the spe-cific fastening. If, for example, in practice elongation of holes occurs in both connected sheets, the sheet with the minimum resistance defines the resistance of the fastening.

The corresponding parameter range is also given for all design equations. If higher parameter values occur, the design equation is applicable, but the values should be re-duced to the corresponding upper limits of the application range.

4.3 Fastenings with self-drilling and self-tapping screws

The proposed design equation for self-drilling and self-tap-ping screws is based on Johansen’s equation developed for timber fastenings [9], which provided the best results in the end. The failure modes covered are given in Fig. 5.

Failure modes irrelevant for fasteners of thin-walled sheeting and sections were not taken into account in Jo-hansen’s equations. A plastic hinge in a fastener was never observed in the tests, possibly the result of the applied de-flection limit of 3.0 mm and the thin sheets, which never provide sufficient rotational restraint but lead to tilting of the fasteners. The additional failure mode “shear failure of the fastener”, which is especially relevant for rivets, must

for t1 ≥ 2.5 t1.6α = (5b)


It is worth comparing these formulas with those in EN 1999-1-4, which have exactly the same application range.

The change in the constant factor in Eq. (5b) results from a change in the partial safety factor from gM = 1.33 in DIN 18807-6 to gM = gM2 = 1.25 in EN 1999-1-4.

3.5 StbK-N5 for steel and aluminium sheets

StbK-N5 [7] can be regarded as a “parent code” for many European codes on thin-walled structures. Contrary to the codes introduced above, StbK-N5 deals with thin-walled steel and aluminium structures. Noteworthy is the fact that just one design formula for steel and aluminium is given, which applies for both fastening screws and rivets:

Ff d t

b,R,dy

M

=α ⋅ ⋅ ⋅

γ

(6)

for t = t1

2.8 t d 1.6α = ≤

(7a)

for t1 ≥ 2.5 t1.6α = (7b)


Attention should be given to the fact that StbK-N5 uses the yield strength instead of the tensile strength. This might be the reason for the change in the constant factor in the equation.

3.6 Summary

The review of the design formulas resulted in even more questions. Changes to constant factors seem to be rather arbitrary. This might be the reason why constant factors for design formulas for steel and aluminium sheets devel-oped differently.

4 Evaluation of tests4.1 Database and statistical evaluation

All 9600 tests taken into account were performed accord-ing to [1]. This means, in particular, that a limit deforma-tion of 3.0 mm applies.

The following applies for the riveted fastenings: the mandrel of blind rivets was removed after setting; for rivets with protruding head and for triple-claw blind rivets, the mandrel was regarded as elementary to the loadbearing system and not removed.

Statistical evaluation and verification of design formu-las followed the rules of EN 1990 Annex D [8] as well as the specific recommendations of [1]. For every test, the actual material properties tensile strength and sheet thick-ness (steel sheets without zinc) were available and used in




If higher parameter values occur, the design equation is applicable, but the values should be reduced to the corre-sponding upper limits of the application range.

It should be noted that: – Neglecting the tilting term in the test function leads to

comparable results, both in correlation with test results and constant factors.

– Johansen’s equations are also suitable for providing one single set of parameters valid for all types of fastening covered in this paper and also leading to comparable results in correlation with test results and constant fac-tors.

If tests with fasteners leading to tests results of approx. rti ≥ 15.0 kN are neglected (which means in this case neglecting tests with two types of self-tapping screw) and the tilting term is ignored, then

min ;I II{ }α = α α (12)

always be checked. In the end, three failure modes remain: bearing failure in tI, bearing failure in tII and tilting, each leading to a separate α value. The minimum α value applies for the design:

Ff d t

b,R,du,I I

M2

=α ⋅ ⋅ ⋅

γ (8)

min ; ;I II tilt{ }α = α α α (9)

� 0.358 0.358f

fu,II

u,I

β = ⋅β = ⋅ (10)

1.668Iα = (11a)

�3.172t

t1.136

f t

f tIIII

I

u,II II

u,I I

α = ⋅β ⋅ = ⋅⋅

⋅

(11b)

2.8531

2 1t

t

t

t

t

t1

t

t

tilt

2 II

I

II

I

2

3 II

I

2

II

I

α =+ β

β + ⋅β ⋅ + +

+ β ⋅

− β ⋅ +

(11c)

The coefficient of correlation is 0.942 and the ratio rk/rm about 0.673. The formulas apply for: – Self-drilling and self-tapping screws made of carbon

steel or stainless steel – Diameter d = 4.2 to 10.6 mm – Pilot hole diameter according to Table 1 for self-tapping

screws – Sheets made of steel or aluminium – Sheet thicknesses tI = 0.40 to 4.00 mm and tII = 0.40 to

12.00 mm – Nominal tensile strength Rm = 180 to 805 N/mm² (In

the tests the minimum tensile strength was 200 N/mm². For harmonization with EN 1999-1-4, a minimum nom-inal tensile strength of 180 N/mm² is given here.)

– Edge distances and spacings to EN 1993-1-3 and EN 1999-1-4

Fig. 5. Failure modes according to Johansen: a) bearing fail-ure in tI, b) bearing failure in tII, c) tilting

Table 1. Pre-drilling (= pilot hole) diameter for self-tapping screws

tII [mm] 0.75 0.75 < tII ≤ 1.5 1.5 < tII ≤ 3.0 3.0 < tII ≤ 5.0 5.0 < tII ≤ 7.0 7.0 < tIId0 [mm] 4.0 4.5 5.0 5.3 5.5 5.7

Fig. 6. Comparison of calculated value according to equa-tions (8) to (11) and test results (5804 tests)

Fig. 7. Comparison of calculated value according to equa-tions (12) to (14) and test results (5804 tests, statistical evaluation based on 5514 tests)




f

fu,II

u,I

β = (17)

1.516Iα = (18a)

1.528t

t1.528

f t

f tIIII

I

u.II II

u,I I

α = ⋅β ⋅ = ⋅⋅⋅

(18b)

4.600 t dtilt,I Iα = ⋅ (18c)

3.266t

tt dtilt,II

II

IIIα = ⋅β ⋅ ⋅ (18d)

Bearing resistance and tilting resistance are calculated for each sheet; the minimum value applies. As tI = tII usually applies for these screws, the higher constant factor in the tilting term for tI reflects the stabilizing effect of the washer or head. Bearing resistance is similar for both sheets. The coefficient of correlation is 0.909 and ratio rk/rm about 0.674. The formulas apply for: – Self-drilling screws with reduced drill point diameter

and flow-drilling/stitching screws – Diameter d = 4.2 to 6.3 mm – Ratio of drill point diameter to outer diameter ≤ 0.75 – Sheets made of steel or aluminium – Sheet thicknesses tI = 0.40 to 1.50 mm and tII = 0.40 to

3.00 mm – Nominal tensile strength Rm = 180 to 805 N/mm² (In

the tests, the minimum tensile strength was 200 N/mm². For harmonization with EN 1999-1-4, a minimum nom-inal tensile strength of 180 N/mm² is given here.)



4.5 Riveted fastenings

A simple bearing resistance calculation is sufficient for riv-eted fastenings:

Ff d t

b,R,du,I I

M2

=α ⋅ ⋅ ⋅

γ (19)

min ;I II{ }α = α α (20)

f

fu,II

u,I

β = (21)

1.444Iα = (22a)

1.274t

t1.274

f t

f tIIII

I

u,II II

u,I I

α = ⋅β ⋅ = ⋅⋅

⋅ (22b)

f

fu,II

u,I

β = (13)

1.784Iα = (14a)

1.065t

t1.065

f t

f tIIII

I

u.II II

u,I I

α = ⋅β ⋅ = ⋅⋅⋅

(14b)

is obtained from the statistical evaluation. This formula is applicable over the same parameter range, see Fig. 7. Due to ease of application, this simplified formula is suggested for design.

4.4 Fastenings with self-drilling screws with reduced drill point diameter and flow-drilling/stitching screws

For these fastenings, the test function resembles the one given in the codes:

Ff d t

b,R,du,I I

M2

=α ⋅ ⋅ ⋅

γ (15)

min ; ; ;I II tilt,I tilt,II{ }α = α α α α (16)






and self-tapping screws to fastenings with self-drilling screws with reduced drill point diameter and flow-drilling/stitching screws is possible, but will lead to smaller resist-ances because αII is smaller for fastenings with self-drill-ing/tapping screws (elongation of holes in tII). But in fact this reflects the actual behaviour known from test results. The larger value of αII for fastenings with self-drilling screws with reduced drill point diameter and flow-drilling/stitching screws is due to the local deformation, especially in the supporting structure of thickness tII. The actual sheet thickness as a reference parameter gets lost.

For fastenings with self-drilling screws with reduced drill point diameter and flow-drilling/stitching screws, the common rule applies, i.e. that more calculation effort and more elaborate design formulas lead to higher resistance values. A simplified approach is to use the design formulas for fastenings with self-drilling and self-tapping screws but to allow for a further increase in αII of up to 20 %, which also includes the effect from the tilting terms.

5 Stiffness of fastenings5.1 Initial situation

Information on the stiffness of fastenings is required, for example, when designing shear diaphragms (Fig. 11) or multi-span beam systems with semi-rigid connections for taking into account the benefits from moment redistribution (Fig. 12). Current Eurocodes do not provide information about the stiffnesses of fastenings, but information can be found in several other documents. In the following, this in-formation is reproduced as far as the authors are aware of.

The coefficient of correlation is 0.983 and ratio rk/rm about 0.711. The formulas apply for: – Rivets made of aluminium, carbon steel or stainless steel – Diameter d = 4.0 to 10.0 mm – Maximum hole diameter d0 = d –0.0/+0.2 mm or

d –0.0 mm/+1.05 · d, whichever gives the greater hole diameter

– Sheets made of steel or aluminium – Sheet thicknesses tI = 0.40 to 3.00 mm and tII = 0.40 to

3.00 mm – Nominal tensile strength Rm = 180 to 405 N/mm2 (In

the tests, the minimum tensile strength was 200 N/mm2. For harmonization with EN 1999-1-4, a minimum nom-inal tensile strength of 180 N/mm2 is given here.)



It is obvious that the small values (small sheet thick-nesses) produce the high scatter and therefore have a large impact on the rk/rm ratio. If tests with rivets leading to test results rti ≥ 6.0 kN are neglected, then αI = 1.646 is ob-tained from the statistical evaluation (αII remains approx-imately the same). This formula is applicable over the same parameter range, see Fig. 10.

4.6 Conclusion and recommendation

For fastenings with self-drilling/tapping screws and riveted fastenings, a simple bearing formulation leads to a design equation showing acceptable results and a reasonable cal-culation effort. In both cases, αI is larger than αII, reflect-ing the effect of stabilization against tilting provided by the head of the fastener (screw or rivet). For fastenings with self-drilling screws with reduced drill point diameter and flow-drilling/stitching screws, the design equations are slightly more complicated, which seems to be connected more with the range of applicable sheet thicknesses than with the type of fastener. Because sheets are not so thick, the stabilizing effect of the head is not that effective. There-fore, applying the formulas for fastenings with self-drilling

Fig. 10. Comparison of calculated value according to equa-tions and test results (894 tests, statistical evaluation based on 824 tests)

Fig. 11. Diaphragm with sheeting panels (taken from [10])

Fig. 12. Moment-resisting connection between sheeting pan-els (semi-rigid)




5.3 Fastening of sandwich panels

Ref. [11] specifies an equation for screw fasteners with seal-ing washers and t = t1, as usually applies in the longitudinal joints of steel sheeting panels:

k Fv

1900 Nmm

t dv 3= = ⋅ ⋅

(24)

Fig. 13 shows the stiffness plotted against sheet thickness t = t1, showing that the values are following the same trend as given in [7].

Formulas for calculating the stiffness of fastenings for attaching steel-faced sandwich panels to a supporting steel structure are also given. Based on these formulas, it is pos-sible to derive the stiffnesses of fastenings with thickness tII so high that no tilting of the fastener can occur.

k Fv

6.93f t d

0,26 0,8 tvu

31= = ⋅

⋅ ⋅+ ⋅

(25)

This can be interpreted as the bearing stiffness of the sheet tI. Fig. 14 shows the stiffness plotted against sheet thick-ness t (assuming t1 ≥ 2.5 t).

Interestingly, for the same thickness t, the values for seam fastenings are higher than for fastenings on rather thick substructures with t1 ≥ 2.5 t. Comparing [11] and [7], it can be seen that for seam fasteners, the values with washer are higher than without washer.

5.4 ECCS Recommendation 088

The ECCS Recommendation for the design of diaphragms [12] gives values for the flexibility

s 1kv

= (26)

for different types of fastening with steel sheeting. The val-ues are cited in Table 3 and Table 4.

The corresponding values are plotted in Figs. 13 and 14, showing that for sheet thicknesses of about 0.50 to 1.00 mm, the constant value represents a good and simple approximation of the formulas given in [7].

Ref. [13] includes two additional tables with values from specific tests.

5.2 Swedish Code StbK-N5

Ref. [7] includes a formula for calculating the shear defor-mations parallel to the plane of the steel or aluminium sheeting if screw fasteners without sealing washer or rivets are used:

k Fv

k d t 10v 23= = ⋅ ⋅ ⋅

(23)

wherek2 coefficient according to Table 2

The equation is plotted in Figs. 13 and 14.

Table 2. Coefficient k2 for determining shear deformation in fastenings according to [7] (abridged)

Fastener Ratio of sheet thicknesses

t1 = t t1 = 2 t t1 ≥ 2.5 t

Self-tapping screws 1 N/mm2.5 1.3 N/mm2.5 1.5 N/mm2.5

Rivets 1 N/mm2.5 1.3 N/mm2.5 1.5 N/mm2.5

Cartridge-fired pin – 3 N/mm2.5 5 N/mm2.5

Fig. 13. Comparison of equations for calculating the stiff-nesses of seam fasteners (screws)

Fig. 14. Comparison of equations for calculating the stiff-nesses of fastening screws

Table 3. Flexibility of fastenings at longitudinal joints between sheeting panels according to [12]

Fastener Nominal diameter ss

Screw 4.1 to 4.8 mm 0.25 · 10–3 m/kNBlind rivet made of steel (including stain-less steel) or Monel

4.8 mm 0.30 · 10–3 m/kN




5.5 Aluminium sheeting

Baehre [14] gives values for the flexibility of fastenings for aluminium sheeting

s 1kv

= (27)

for different types of fastening. The values are cited in Ta-ble 5.

5.6 Recommendation

Stiffness values heavily depend on the test setup and the accuracy of the test performance. Comparing results from different test campaigns will show a relatively high scatter.

Nevertheless, the recommendation can be given to use Eq. (23) given in StbK-N5, amended by Eq. (24) if washers are used in seam fastenings or moment-resisting connections between sheeting panels. However, in some cases the constant values taken from [12] or [14] may be sufficient for design.

6 Temperature loading on fasteners

Temperature-related loads may lead to constraint shear forces acting on the fasteners. Resistance to these loads and their interaction with shear and tensile forces from external loads has to be proved in design, e.g. according to [15]. If this proof is neglected, the constraint forces must not lead to a reduction in resistance to tensile forces. A reduction in resistance to tensile forces arises from an elongation of the hole or tilting of the fastener.

For screwed fastenings with washers of diameter dw ≥ 14 mm or comparable head geometries, elongation of the hole in component I is acceptable because for screwed fastenings with washer dw = 16 mm it was proved that

there is no significant reduction in pull-through resistance [3]. Based on this observation, the following applies for the failure modes observed in the tests and the conclusions reached: – Failure mode in the test is elongation of holes in com-

ponent I. – Maximum load is reached after a minimum deformation

of 3 mm. If maximum load corresponds to a deforma-tion < 3 mm, the residual resistance Rr of the single test must be higher than the design resistance Rd (see ECCS Rec. No. 124, Fig. 2.11).

If both requirements are fulfilled, the fasteners can be used without further proof for applications where forces from restraint elongation due to temperature occur. If tests were performed with the test setup shown in Fig. 4 (type a con-nection), this conclusion is also valid for type c connec-tions (Fig. 15). For type b and type d connections, proof has to be demonstrated in design or by way of correspond-ing tests.

Table 4. Flexibility of fastenings with substructure according to [12]

Fastener Nominal diameter sp

Screw with hexagon head 5.5 to 6.3 mm 0.15 · 10–3 m/kN

Screw with hexagon head and sealing washer 5.5 to 6.3 mm 0.35 · 10–3 m/kN

Cartridge-fired pin 3.7 to 4.8 mm 0.10 · 10–3 m/kN

Fig. 15. Types of connection

Table 5. Flexibility of fastenings with aluminium sheeting according to [12]

Fastener Nominal diameter Component I Component II ss

screw 5.5 mm, pitch 1.8 mm aluminium aluminium 0.6 · 10–3 m/kN

screw 5.5 mm, pitch 2.23 mm, reduced drill point

aluminium, ti < 2.3 mm

aluminiumtii < 2.3 mm

0.4 · 10–3 m/kN


aluminium, ti < 2.3 mm

aluminiumtii ≥ 2.3 mm

0.4 · 10–3 m/kN

screw 5.5 mm, pitch 1.8 mm aluminium steel 0.5 · 10–3 m/kN


aluminium, steel 0.2 · 10–3 m/kN

Blind rivet, made of aluminium (in-cluding stainless steel) or Monel

4.8 mm aluminium aluminium 0.25 · 10–3 m/kN




[7] StbK-N5: Tunnplåtsnormen (Swedish Code for Light-Gauge Metal Structures). Stalbyggnadsinstitutet (National Swedish Committee on Regulations for Steel Structures), Stockholm, 1979.

[8] EN 1990:2002 + A1:2005 + A1:2005/AC:2010: Eurocode: Basis of structural design.

[9] Johansen, K. W.: Theory of timber connections. Mémoires AIPC/IVBH Abhandlungen/IABSE pub. 9 (1949), pp. 249–262 (http://dx.doi.org/10.5169/seals-9703).

[10] Kathage, K., Lindner, J., Misiek, T., Schilling, S.: A proposal to adjust the design approach for the diaphragm action of shear panels according to Schardt and Strehl in line with Eu-ropean regulations. Steel Construction 6 (2013), pp. 107–116.

[11] Käpplein, S., Ummenhofer, T.: Querkraftbeanspruchte Verbindungen von Sandwichelementen (Shear loaded fasten-ings of sandwich panels). Stahlbau 80 (2011), pp. 600–607.

[12] ECCS TC7: European Recommendations for the Applica-tion of Metal Sheeting acting as a Diaphragm – Stressed Skin Design. ECCS pub. No. 88, Brussels, 1995.

[13] Davies, J. M., Bryan, E. R.: Manual of stressed skin dia-phragm design. Granada Publishing Limited, St. Albans, UK, 1982.

[14] Baehre, R.: Zur Schubfeldwirkung von Aluminium-trapezprofilen (Diaphragm action of trapezoidal aluminium sheeting). Stahlbau 62 (1993), pp. 81–87.

[15] Schwarze, K., Berner, K.: Temperaturbedingte Zwängung-skräfte in Verbindungen bei Konstruktionen mit Stahl-trapezprofilen (Locally enhanced peak forces in connections of IBR sheeting due to thermal expansion). Stahlbau 57 (1988), pp. 103–114.

Keywords: thin-walled structures; screws; rivets; fastener; fas-tening; connection

Authors:Dr.-Ing. Thomas Misiek, Breinlinger Ingenieure Tuttlingen – Stuttgart, Kanalstr. 1-4, 78532 Tuttlingen, [email protected]

Dipl.-Ing. Saskia Käpplein, Versuchsanstalt für Stahl, Holz und Steine, Karlsruher Institut für Technologie, Otto-Ammann-Platz 1, 76131 Karls-ruhe, [email protected]

7 Summary and final remarks

This paper introduces design formulas from different codes for shear-loaded fastenings in thin-walled sheeting and sec-tions, some of them having limitations with regard to ap-plication or questionable constant factors. Based on a huge number of tests, design formulas eliminating this problem are given. In addition, stiffness values of fastenings loaded in shear are collected and a recommendation is given.

Notwithstanding the fact that most fastener manufac-turers have European Technical Approvals (ETAs) based on test results for their fasteners, general design formulas are still relevant because they provide design values for applications not yet tested and guidance while preparing or evaluating tests for approvals.

In any case, the application range stated by the man-ufacturer should be respected. This refers to both drilling capacity and clamping thickness, and also thickness ratios. Fixing thick sheets on thin ones will require special atten-tion with respect to the thread formation in the thin sheet and tightening torque (overtightening and ruined thread).

References

[1] ECCS TC 7: The Testing of Connections with Mechanical Fasteners in Steel Sheeting and Sections. ECCS pub. No. 124, Brussels, 2009.

[2] ECCS TC 7: The Testing of Connections in Steel Sheeting and Sections. ECCS pub. No. 21, Brussels, 1990.

[3] Klee, S., Seeger, T.: Vorschlag zur vereinfachten Ermittlung von zulässigen Kräften für Befestigungen von Stahltrapezpro-filen (Proposal for the simplified determination of admissible forces for fastenings of steel sheeting panels).TH Darmstadt, Institut für Stahlbau und Werkstoffmechanik,1979.

[4] EN 1993-1-3:2006+AC:2009: Eurocode 3: Design of steel structures – Part 1-3: General rules – Supplementary rules for cold-formed members and sheeting.

[5] EN 1999-1-4:2007+AC:2009: Eurocode 9: Design of alumin-ium structures – Part 1-4: Cold-formed structural sheeting.

[6] DIN 18807-6:1995-09: Trapezoidal sheeting in buildings – Part 6: Aluminium trapezoidal sheeting and their connections – De-termination of loadbearing capacity by calculation.


DOI: 10.1002/stco.201420014


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Shenzhen Airport’s Terminal 3 is one of the largest buildings in the world designed with parametrically controlled digital tools. These tools enabled the teams from Fuksas and Knippers Helbig to de-velop the free-form, perforated, double-skin building envelope into which a space truss structure is integrated. The inherent op-timization potential of the iterative process not only facilitated the geometrical definition of a large number of unique, non-repetitive components, but also resulted in a successive performance im-provement for the integrated structural system.In a close collaboration with the architects, specific solutions were developed to provide sufficient structural integrity for the space structure, which is clad by the façade layers. These design inter-ventions enable the mega-structure to withstand all impacting loads, such as high winds and seismic loads, without disrupting the transparency of the architects’ intended honeycomb-shaped perforations.The design process of the new Terminal 3 clearly demonstrates how parametrically controlled design tools can offer the means to design new structures and envelopes that go beyond existing typologies.

1 Introduction1.1 General

Shenzhen is among the fastest growing cities at the Pearl River Delta – one of the most productive urban zones worldwide. The first of five Special Economic Zones in China, Shenzhen has grown rapidly to become the fourth-largest metropolis in China, currently inhabited by more than 10 million people. Shenzhen Airport is among

the top 10 busiest airports in China (2012: passengers: 6th; cargo: 4th). On 28 November 2013 the new Terminal 3 took over all activities from the existing Terminals 1 and 2. The total area of Terminal 3 is approx. 450 000 m², and the airport has an annual capacity of 24 million passengers after completing the first of three phases. Subsequent phases, with remote passenger concourses, will raise the total capacity to 36, then 40 million passengers, in 2025 and 2035 respectively.

The design of the new Terminal 3 for Shenzhen Inter-national Airport followed an international competition held in 2007/2008. Massimiliano Fuksas Architects, Rome, supported by Knippers Helbig, Stuttgart, prevailed against five high-ranking teams.

Based on a masterplan study undertaken by the airport authority, the general arrangement of the building is based on a T-shaped footprint (Figure 1). The three levels of the new terminal provide independent functions: bus gates and baggage handling on the ground floor; arrivals, baggage claim, customs and immigration on the first floor; check-in and departure, with a total of 63 gates, on the second floor. The traffic centre, accounting for a quarter of the entire project, is situated in front of the terminal and hosts railway and bus stations. Facilities for long-distance, regional and airport rail services are located below ground. The follow-ing article focuses on the geometrical development and structural design of the main terminal building with its in-tegrated concourses.

1.2 Architectural concept

A “manta ray emerging from the depths of the sea, trans-formed into a bird and ascending into the sky” – this is how Massimiliano and Doriana Fuksas describe their de-sign for the new Terminal 3 [1].

The terminal building is clad by an organically shaped, double-skin envelope covering the structure. The outer and inner skins, each perforated by approx. 25 000 honey-comb-shaped openings, allows for bright but diffused and patterned natural light. The ensuing different and varying light situations and the free form of the inner skin create a lively and pleasant space for the passage from check-in to gate, which can be up to 1300 m long. Horizontal window strips 6 m high provide a visual link in the form of a pano-ramic view of the airfield. The generous spatial impression is supported by long-span structures. The 650 m long and

Engineering in a computational design environment –New Terminal 3 at Shenzhen Bao’an International Airport, ChinaThorsten HelbigFlorian ScheibleFlorian KampRoman Schieber

Fig. 1. Aerial view of airport (photo: © Leonardo Finotti)

08_024-031_Scheible (014)_Report_cs6.indd 24 03.02.14 11:25

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architectural and technical parameters in the script-based model. It is a process that clearly demonstrates how para-metrically controlled design tools can offer the means to design new structures and envelopes that go beyond exist-ing typologies.

2.2 General procedure

Once the initial concept was designed at M. Fuksas’ office using numerous clay models and studies with paper and foam-board surface models were generated within Rhino. Through several iterations, the shape and façade pattern was revised to suit basic functional requirements such as program, lighting and energy gains, and an approximation of the volume enclosed by the outer and inner skins to provide sufficient structural integrity. As a next step, the façade geometry plus the definition of all structural com-ponents were automatically generated using a script based on Rhino and RhinoScript. The script contains most of the significant technical parameters needed to generate the full set of geometry data, which creates a dataset with more than 1.45 million coordinates. In that way, one single model database became the direct link between the global geom-etry and the individual structure and façade components.

2.3 Basic geometry setting

Two major decisions guaranteed that every passenger would have an unobstructed view out over the airfield: At the competition phase it became clear that the structure should be aligned with the logic of the honeycomb façade,

305 m long terminal hall roof rests on conical columns up to 25 m high, with typical spans of 36 m (Figure 2).

The wing-like roof covers the departure hall with its check-in counters, various restaurants and shops. It sits alongside a 760 m long transverse structure containing the concourse with its departure gates. The arch-shaped con-course spans over 45 m, bulging out to a maximum of 63 m. At half its length, it opens out to form a piazza with floor slab openings, which include the 80 m wide entrances to the cross-concourses (Figure 3).

2 Process design2.1 From linear design process to interactive design

collaboration

A demanding project schedule, which required the building to be completed within five years after the outcome of the design competition, called for the development of fast-track design tools. As conventional linear design processes are inadequate for the design of such complex free-form geom-etries and the intended highly variable façade pattern in such a short time, a parametrically controlled design strategy was developed. This methodology replaces the traditional back-and-forth exchange of information so characteristic of linear design processes, with real-time modifications to

Fig. 2. Terminal building

Fig. 3. Main concourse departure level

Fig. 4. Ray system

Fig. 5. 1:100 model of a half concourse segment


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etry of the structure was then imported into appropriate FEM calculation software and the façade geometry was further processed to create individual panels and details.

2.5 Generation of façade components

The architectural intention is to create a honeycomb-shaped façade with openings that vary smoothly across the façade from fully open to almost closed (Figure 8). The application of differently sized planar hexagons – representing the in-sulating glass units – to a doubly curved surface (Figure 7) led to a concept of three-dimensional folded panels that vary in size and shape according to the geometry of the master surface. In an iterative process, numerous adapta-tions to ensure a technically feasible configuration were implemented in the numerical algorithm, such as the con-trol of sufficient joint spacings, planarity of the individual glass units, a clash check with adjacent system parts of the structure, drainage direction as well as the amount of day-light and energy gains. All technical development was linked to architectural aims such as smooth transitions be-tween open and closed panels (Figure 10). The last step was a geometric refinement that included organizing similar panels into groups of identical panels in order to reduce the number of different parts and closing off all open seams.

which meant that the structure had to follow the diagonal orientation. Otherwise, verticals and horizontals would cut through the windows. As a second aspect, a “ray” system was developed to define the geometry of the concourse section (Figure 4). The façade openings and main structure were oriented to allow horizontal views through the façade from all locations on the departure level. Passengers standing on opposite sides of the concourse on departure level are able to enjoy a vertical-oriented panoramic view towards both the airfield and the sky (Figures 5 and 6).

2.4 Master geometry

The intersection of rays and inner and outer master sur-faces created a set of reference points for the concourses. The terminal reference points were created by the vertical projection of the intended grid. The reference points served as a base for façade and structure. As a next step, offsets were generated defining the position of the structural steel nodes and individual façade layers (Figure 11). The geom-

Fig. 6. Model showing unobstructed view out and hidden structure

a) b)

c) d)

Fig. 7. a) to d) generation of panel geometry

Fig. 8. Panel types with varying aperture


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depth of the space truss configuration. The configuration of chord layers and posts follows a straightforward, fully automated algorithm, whereas additional bracing compo-nents were subjected to subsequent iterative modifications to provide locally adjusted stiffness.

In an iterative form-finding process, the distance of the master surface was increased and decreased when nec-essary or intended by the architects. A transformation tool developed in-house for the structural analysis software en-ables a direct evaluation of the impact on stresses and de-flections in the underlying steel structure. These optimiza-tion efforts minimized material consumption, which not only decreased direct costs but also significantly lowered the consumption of natural resources and emissions con-nected with the production of structural components.

3 Structural design3.1 General

Owing to the geometrical complexity and restraints, and due to the tight design and construction schedule, all the structural components for the roof were proposed in steel. Furthermore, the project benefits enormously from the wide experience gained by the Chinese steel industry in more complex projects such as the Bird’s Nest and Water-cube in Beijing and from the central axis roof constructed for the ‘Expo Boulevard’ in Shanghai.

The roof structure basically consists of a spatial frame-work with varying depth between upper and lower chord levels. Truss members are mainly circular hollow sections and the effective depth of the space truss varies from 3 to 8 m (Figure 12). Rectangular hollow sections are used in certain areas. These sections are composed of flanges and webs with a plate thickness adjusted to the local structural requirements.

3.2 Segmentation

The total size of the roof structure is approx. 1250 m long and 642 m wide.

In a close collaboration with local engineering partner BIAD, the supporting concrete main structure and the steel roof structure were divided into segments by expan-sion joints (Figure 13).

The outcome was an Excel spreadsheet containing the entire geometric information for all the 60 000 façade units of the outer and inner skins (Figure 9).

2.6 Implementation of structure geometry

Following the logic of the parametric process, master points were created with a defined offset to the inner and outer façade layers. The resulting distance is the effective beam

Fig. 9. Excel spreadsheet for coordinating aperture width of panels

Fig. 10. Population of various panel types with different aperture grades

Fig. 11. Line model of structural components

Fig. 12. Volume model of structure


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The roof of the terminal building was designed as a two-way steel truss structure. The roof is supported by col-umns at a regular spacing of about 36 m, with truss depths of 3.0–4.5 m. The steel trusses are made of circular hollow and rolled sections. The columns are pinned at the base and rigidly connected to the roof structure. Global lateral stiff-ness is provided by the network of rigidly connected col-umns. Although expansion effects due to temperature dif-ferences can be accommodated by the flexibility of the slender columns, sufficient stiffness is provided for lateral loads and accelerations due to seismic actions.

Besides the structural requirement to support the ter-minal roof to withstand vertical and horizontal loads, the columns serve as a part of the roof drainage system. Owing to the high amount of rainwater accumulating on the approx. 20 000 m2 roof surface, all columns are equipped with an internal downpipe system. The structurally effective circular hollow section with its integrated drainage system is en-closed by a conically shaped cladding.

3.3 Concourses

The concourse part of the structure extends over a total length of about 1350 m. It consists of the central main con-course and the cross-concourses. Basically, the structural system is generated by the extrusion of an arch-shaped truss with a maximum distance of 3–6 m between upper and lower chord levels. The two-hinged arch configuration transfers reaction forces caused by vertical and lateral loads on the outer perimeter line of the supporting main concrete structure at regular intervals of 18 m. This support distance corresponds to the architecturally shaped massive walls that stabilize the concourse slabs.

Bracing on the main axis stabilizes the structure effi-ciently and prevents long-wave oscillations of the system.

The honeycomb-shaped geometry of the structure does not naturally generate a super-efficient structure, since it does not provide direct load paths for in-plane loads.

Several strategies for strengthening were investigated in a collaboration between architect and engineer. The final configuration uses bracing elements located within the ar-chitecturally defined hexagonal configuration. The global transversal stiffness had to be optimized to cope with ex-treme, typhoon-level wind forces. As shown in Fig. 14, the final design option follows a basically straightforward struc-tural strategy of implementing effective bracing elements in the trapezoidal configuration set by the architecture. Fol-lowing the geometrical basic units, bracing distances of 72, 36, 18 and 9 m were investigated. Even if a 9 m distance provides per se the stiffest configuration compared with all other options, the longer distances were favoured. The ar-chitectural intention of enabling a wide, unobstructed view through the envelope and the structural logic of a culmina-tion of stiffening elements and support point led to a min-imum distance of 18 m – according to the dominant archi-tecturally shaped walls supporting the primary platform structure.

Geometrical conditions in the longitudinal direction would have allowed for reasonable space-frame trusses to span up to 36 m between the bracings. But the global trans-verse stiffness had to be adjusted to cope with extreme wind loads resulting from typhoons. This was achieved by com-paring an analysis of inherent eigenfrequencies (EF), and a regular bracing spacing of 18 m was established (Figure 15).

The transverse braces are formed by plane frame ele-ments, whereas the truss geometries follow the hexagonal structural pattern. Conflicts between the plane frame ele-ments and openings were inevitable, but were minimized by

Fig. 13. Footprint and subdivision of roof structure

Fig. 14a. Bracing spacing: 72 m Fig. 14b. Bracing spacing: 36 m Fig. 14c. Bracing spacing: 18 m1st horizontal EF: 1.2 Hz 1st horizontal EF: 1.5 Hz 1st horizontal EF: 1.8 Hz1st vertical EF: 1.8 Hz 1st vertical EF: 2.4 Hz 1st vertical EF: 2.9 Hz

Fig. 15. Position of twin bracing


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splitting the transverse braces into two parallel and identi-cal halves with a 2 m spacing, and arranging them symmet-rically at the boundaries of the hexagons. This results in reduced truss openings. The truss chords are made of rec-tangular hollow section fabricated from steel sheet. The wall thicknesses vary to suit localized structural loading. Circular hollow sections provide the diagonal braces be-tween the top and bottom chords. At the support points, the members culminate in a single bearing point (Figure 16).

3.4 Culmination of forces and movement

All loads are transferred to a central bearing shaft at the support points. The four chords and eight tubular sections which make up the roof hexagon space framework are brought together at this location.

Vertical loads culminate in massive, high-strength steel bolts, whereas longitudinal forces are resolved by custom- configured spring assemblies. Due to the complex geometry of the system and the high load concentrations, a force-op-timized steel casting was developed for the node design. The high number and repetition of the castings made them economically viable. The force-optimized moulding results in a technically favourable stress homogenization in a solid adapter fork. At the time, these adapter forks were among the largest castings ever fabricated in China (Figure 17–19).

3.5 Optimization of support conditions

Long structure segments with a length of up to 200 m were chosen in order to reduce the number of technically com-plex and expensive expansion joints. As a result, another optimization aspect, namely the limitation of longitudinal reaction forces due to seismic effects or thermal expansion, became important. To let thermal expansion occur without restraint, usually one pair of fixed bearings is chosen at a central position while all others are sliding.

One disadvantage of such a bearing situation is that the seismic forces (or other longitudinal forces) have to be transferred locally via one single pair of bearings. Further, the structure needs to be strengthened near to the fixed bearing point.

Such a local strengthening of the concrete substructure below the steel roof would have had a visible impact on the global architectural design which was not intended. In or-der to avoid this, spring bearings were chosen as an opti-mum compromise between these two controversial load scenarios and to equalize the total bearing reaction forces.

The figures 20a–c show a simplified structural system as a continuous beam on five supports. For the different bearing situations chosen, the differences in the results are shown qualitatively. The first two situations are extreme ones, showing a good behaviour for only one of the load

Fig. 16. Twin bracing and supporting joint

Fig. 17. Bracing at 18 m intervals

Fig. 18. Elevation on base detail

Fig. 19. Precast support joint


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achieved by grouping several discs in the same or opposite directions. The chosen package of disc springs for each bearing point has been arranged on both sides of the strap so that all load directions, as well as thermal expansion and contraction, can be transferred with the same properties.

Additional optimizing options can be created by using non-linear spring characteristics with either a digressive or progressive course (see curves 1 and 2 in Fig. 21). Putting digressive spring characteristics into the central part and progressive characteristics into the borders can help to avoid excessively high forces in the central part.

cases. In (a) thermal expansion does not lead to reaction forces, and in (b) seismic loads are equally distributed. High reaction forces occur in the other load case. The third situation uses a varying spring stiffness along the structure, decreasing towards the borders. It can be seen from (c) that reaction forces resulting from an earthquake can be equalized at the intermediate bearing points. However, no important thermal constraints occur at the borders.

In a similar way, optimized spring configurations can be found for each concourse part when taking into ac-count its individual length, seismic mass and friction force. The chosen spring type for Shenzhen International Airport Terminal 3 is a disc spring positioned between the bearing strap and the strap of the main bracing structure. These springs can simply be mounted on the bearing shaft.

An advantage of the disc spring is the small width and the simple way of combining several disc springs together to produce a higher or lower spring stiffness. This can be

Fig. 20. Simplified structural system with different support conditions: (a) fixed intermediate support, all others sliding, (b) all supports with identical spring stiffness, (c) supports with spring stiffnesses decreasing towards the borders

Fig. 21. Options for spring characteristics

Fig. 22. Assembly of twin bracings

Fig. 23. View on end of concourse structure


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Structural design, façade design, parametric design:Knippers Helbig Advanced Engineering, Stuttgart, GermanyArchitect of record:BIAD (Beijing Institute of Architectural Design), Beijing, ChinaGeneral Contractor:China State Construction Engineering Corporation, China

References

[1] Kaltenbach, F.: A tube? No, an event space landscape! – Ter-minal 3, Shenzhen Bao’an International Airport. Detail, No. 12, 2013, pp. 1422–1432.

[2] Knippers, J.: From Model Thinking to Process Design, Archi-tectural Design, vol. 83, No. 2, Mar/Apr 2013, pp. 74–81.

[3] Helbig, T., Kamp, F.: New Terminal 3 for Shenzhen Airport: a 1250 m long structure. IASS-APCS 2012, From Spatial Structures to Space Structures, Abstract Book, p. 439.

[4] Sofistik – ase: General Static Analysis of Finite Element Structures, SOFISTIK AG, Oberschleißheim, 2007.

[5] Knippers, J., Helbig, T.: Digital Process Chain from Design to Execution. Innovative Design + Construction, Detail Devel-opment (2012) , pp. 21–33.

Keywords: airport; computational design; free form; steel struc-ture; façade

Authors:Thorsten Helbig, Florian Scheible, Florian Kamp, Roman SchieberKnippers Helbig Advanced EngineeringTübinger Str. 12–16, 70178 Stuttgart, [email protected]

In the case of high seismic forces, the spring movement increases disproportionally (curve 2) at the central part, which leads to force redistribution to the border regions where the force increases disproportionally (curve 1). On the other hand, the progressive characteristics at the bor-ders have to keep the range of thermal expansion free of high reaction forces.

4 Construction on site

The erection of the 50 000 tonnes of steelwork began in October 2010 and ended in September 2011. The primary platform construction enabled a fast-track method. The sequential concourse erection started at the outer ends si-multaneously.

Once the prefabricated twin-bracing segments were installed, the rhomboid-shaped space structures in between the 18 m spacings were added. These intermediate parts were assembled from bar and node parts by on-site weld-ing on mobile scaffolding platforms (Figures 22–27).

Terminal and cross-concourse parts were erected by using conventional scaffolding platforms.

Project creditsClient:Shenzhen Airport (Group) Co. Ltd., ChinaArchitect:Massimiliano and Doriana Fuksas, Rome, Italy

Fig. 24. Concourse roof during construction showing relation-ship between envelope and structure

Fig. 26. Terminal roof and interior façade

Fig. 25. Main concourse, lower edge and diagonal view Fig. 27. Different assembly stages of terminal roof


DOI: 10.1002/stco.201300005


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Modern steel design and construction in Canada’s oil sands industry

Osama Bedair

Notation

G total gravity load of moduleH height of steel moduleL length of steel moduleMPa N/mm2

W width of steel moduleSPMT self-propelled module trailerSAGD steam-assisted gravity drain-

ageIv, Ih, IL vertical, horizontal and lon-

gitudinal impact force com-ponents

HP horsepowerα, β rectangular opening with sizer radius of curvatureβy circular opening spacing(σw)max maximum web stress

1 Introduction

Canada is home to the largest com-mercial oil sands industry in the world. Some 97 % of the Canadian oil sands reserves are located in three major deposits in the northern areas of Alberta province (see Fig. 1). These are the Athabasca deposits (north-east-ern Alberta), the Cold Lake deposits (north-eastern Alberta) and the Peace River deposits (north-western Al-berta). Canadian oil sands deposits cover approx. 140 000 km2 (54 000 mi2), an area larger than England, and

The continuous improvements in Canada’s oil sands industrial performance have gener-ated engineering challenges that are rarely encountered in conventional oil and gas pro-jects. Significant developments in steel construction procedures have evolved over the past few years to cope with these challenges. New design guidelines have been devel-oped to modernize structural steel design and construction procedures. These proce-dures have been successfully implemented in oil sands projects that worth billions of dol-lars. The author was involved in the design developments for these projects and would like to share with readers the difficulties and solutions used to cope with structural chal-lenges that are not addressed by North American or European codes of practice.

have reserves of approx. 1.75 trillion barrels of bitumen. The oil sands in-dustry has been a secure oil supply providing growth to the Canadian economy for a long time. The noticea-ble increase in oil prices has boosted oil sands technology. The estimated oil sands investment over the years 2006–2008 reached a record high of $19.2 billion. More than 90 oil sands projects with various sizes are operat-ing in Canada. These projects were launched concurrently by several oil sands operators with short execution durations to maximize their produc-tion rates and meet market demands. This put pressure on the engineering developments and created design,

construction and environmental chal-lenges. Both the Canadian govern-ment and the private oil sands indus-try have devoted continuous efforts to improving the efficiency of produc-tion and reducing the environmental footprint of oil sands recovery and upgrading.

Oil produced from bitumen sands is often referred to as unconventional oil or crude bitumen to distinguish it from liquid hydrocarbons produced from traditional oil wells. Oil sand material is a consolidated sandstone containing naturally occurring mix-tures of sand, clay and water (see Fig. 1) plus extremely viscous bitumen that must be treated before it can be used by refineries to produce usable fuels such as gasoline and diesel. A va-riety of procedures is currently used to recover oil sands. Each method has its own benefits and challenges in terms of production rates, surface land dis-turbance, energy use, etc.

If the oil sand is close to the sur-face, open surface mining is commonly used. Typical oil sands mining facili-ties consists of double roll crusher,

Fig. 1. Canadian oil sands deposits

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Steel Construction 7 (2014), No. 1

the surface, leaving the sand in place. Pipelines are drilled at the wellhead down to the oil sand formation as shown schematically in Fig. 3(A). The red and blue lines indicate the produc-tion and steam pipelines. The top pipe injects steam into the oil sand to liq-uefy the mixed bitumen allowing it to flow and be pumped to the surface via the bottom pipe. The SAGD recovery procedure requires the construction of well pads according to exploration recommendations. Each well pad con-tains multiple wellheads, as identified by the solid circles in Fig. 3. The cost of each well pad depends on the num-ber of wellheads used in the oil sand recovery. As an illustration, the capital cost of a well pad containing 32 well-heads is approx. $600 million. The oil production life of each pad is about six years. Each pad contains an independ-ent gathering pipeline system that ties into a distribution terminal indicated by the green rectangle. This terminal acts as a “switchboard” that turns the pipelines “on” and “off” and transports the bitumen to the upgrader.

the bitumen is separated from the sand. Once the bitumen has been re-covered, the remaining sand and clay are sent to tailing ponds. The process facilities of Fig. 2 consist of steel struc-tures supporting massive equipment and require design and analysis skills. For example, the slurry preparation unit supports equipment weighing more than 3500 t.

In situ procedures are used to re-cover deep underground oil sands de-posits. Most of the in situ bitumen and heavy oil production comes from de-posits that are buried more than 400 m below the surface. The most common in situ technique used in commercial projects is known as SAGD (steam-as-sisted gravity drainage), as illustrated in Fig. 3. Using this procedure, steam, solvents or thermal energy are used to make the bitumen flow to a point where it can be pumped via a well to

surge facility, conveyors, slurry plant (with mix box), pump houses, substa-tions and a hydrotransport pipeline, tailings, ponds, froth treatment and diluted bitumen tank farm. The initial process is performed in the materi-als-handling facilities to separate the bitumen from the sand and clay. A summary of the surface mining proce-dure is illustrated in Fig. 2. In the first step, shovels excavate the oil sands ore and place it in large trucks (Fig. 2a). Oil sand is then dumped in a double roller crusher for initial screening (Fig. 2b). Fig. 2c shows a crushing fa-cility. Oil sand is then transported us-ing conveyors (Fig. 2d) to the surge facility (Fig. 2e), then transported us-ing conveyors (Fig. 2f) to the slurry preparation unit (Fig. 2g) for further processing. The diluted slurry material is then pumped via a hydrotransport pipeline to the extraction plant where

Fig. 2. Oil sand recovery by surface mining procedure

Fig. 3. Oil sand recovery by SAGD procedure

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acceptable lateral displacement at the column base. Therefore, minimum thickness requirements must be im-posed in the project design criteria. H-Piles are more difficult to install and require very expensive splicing. Scheme (II) shows an alternative pil-ing system that can be used to support the steel frame. In this case a pedestal projects up from the pile cut-off eleva-tion to the steel level in order to in-crease the pile head area. Anchor bolts are installed prior to casting the concrete in order to connect the col-umn base plate. The cost of concrete piles is higher than steel piles; how-ever, they are required in some facili-ties to limit the lateral displacement and to avoid using multiple pile con-figurations.

The capacity of the piles depends upon the tip boundary condition and are determined using either free or fixed head conditions. The latter re-sults in a much greater lateral pile ca-pacity. However, special connection

However, concrete piles offer higher lateral and vertical capacities. Hollow steel piles have been extensively used in several projects. However, they have shown failures in some projects. The piles are designed for skin friction with partial end bearing. Accordingly, the steel structure is designed with a flexible (or moveable) support bound-ary condition.

Fig. 5 shows two schemes that are commonly used to support the steel framing in oil sands projects. In scheme (I) the steel pile is connected to the frame column using base plates. Hollow section or H-piles can be used, as shown in section B-B. A cap plate is sometimes used to increase the end bearing area at the toe of the pile. The top pile tip is normally welded to a base plate at the cut-off elevation and bolted to the base plate of the frame column as shown in sec-tion A-A. Hollow section piles are eas-ier to install; however, the stiffness at the top is weak and may result in un-

The following section illustrates structural developments and chal-lenges encountered in the design of oil sands projects. Structural steel modu-larization techniques and relocation procedures for the massive process are briefly discussed. The author was involved in many of these projects during feasibility and detailed design work. It should be noted that design rules were developed to resolve many challenges. These rules were devel-oped due to:1) the difficult project execution phi-

losophy due to economic aspects or time constraints, and

2) the absence of design guidelines in existing codes of practice [1–5].

2 Soil-structure interaction

The soil composition of oil sands con-struction sites is very weak. Generally, the first 3–4 m of the soil is composed of weak muskeg material (very soft clay). During the summer, the soil is very soft and it is even difficult to walk on the surface. As an illustration, Fig. 4 shows vehicles trapped on construc-tion sites containing muskeg soil. Therefore, engineers must pay special attention to the design of various sup-porting systems for equipment, pipe-lines or pipe-rack modules. During the winter, the temperature may drop be-low –50 °C. As a result, the soil is fro-zen and becomes very difficult to exca-vate. Furthermore, the foundation and supported steel structure must be de-signed against frost heave loads in-duced during the winter. The frozen soil in this case exerts a massive soil pressure that may displace the struc-ture in the upward direction or crack the concrete foundation. This move-ment impacts considerably the perfor-mance of the steel structure during the operating conditions and must be taken into account in the structural design. Insulation or frost cushions are used to absorb and reduce the heave pressure.

Pile foundations are used to sup-port the majority of oil sands process facilities. Piles increase the construc-tion costs dramatically and add diffi-culties in the engineering phase since the design of the structure must be integrated with the pile supports. Con-crete or steel piles are used to support oil sands facilities. The cost of steel piles is much lower than that of con-crete because they are easier to install. Fig. 5. Pile foundation system

Fig. 4. Weak soil conditions at oil sands sites

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portation weight allowance of 156 t. Therefore, large process facilities must be divided into multiple sub-modules and assembled on site.

3.1 Pipe-rack modules

Pipe-rack modules are assembled on the construction site using cranes, as illustrated in Fig. 7. The number of lifting points must be identified by the structural engineer. The modules must also be designed to accommodate the impact conditions induced during lift-ing and installation. Multi-level pipe-rack modules are lifted and stacked on top of each other. Lifting points can be positioned on the column web or the side flanges.

and requiring design verifications for several transportation modes.

Modularized oil sands facilities are fabricated off-site as small mod-ules and fitted out with piping, elec-trics, instrumentation and mechanical equipments, as shown in Fig. 6a. The fabricated steel modules are trans-ported at least 150 km to the con-struction sites on public roads. Most of the modules are transported as functionally complete units to limit construction and commissioning on site. The allowable transportation en-velope size for any prefabricated steel module must not exceed 7.3 m wide × 36 m long × 7.8 m high, as illustrated in Fig. 6. Furthermore, none of the steel modules should exceed a trans-

details are required to assure moment transfer to the pile head. Flexible sup-porting boundary conditions are used in the analysis of the steel frame dur-ing operating conditions. This results in very lengthy computer time and data preparation. If the pile is pro-jected abovegrade, the restraints should be variable through the length. The maximum allowable lateral dis-placements at the pile/column junc-tion must be limited to 6 mm. Since the stiffness of the clay till layer is not strong enough to provide a fixed end bearing to the pile, vertical restraints must be imposed in the structural analysis model. The stiffness of the springs is evaluated empirically using borehole soil samples. Furthermore, pile capacities are evaluated by com-bining the skin friction resistance and partial end bearing. In some cases sev-eral piles are required to limit the lat-eral displacements at the column base, thus complicating the analysis and the pile installation procedures.

3 Steel modularization

Steel modularization is required in most Canadian oil sands projects due to the remoteness of the sites and the harsh climate conditions. Extensive efforts were made over the past few years to develop economical and safe modularization procedures. It was found that steel modularization re-sults in substantial savings in the pro-ject cost due to:a) pronounced reduction in labour

rates,b) significant reduction in site man-

hours,c) improvements in work quality,d) increase in work productivity in

harsh weather conditions, ande) reduction in site congestion.

However, steel modularization leads to increases in the engineering man-hours needed in order to design the steel modules for lifting and transpor-tation conditions. Further, steel mod-ularization results in an increase in the steel quantity by 30–50 %. It is worth mentioning that between 2006 and 2009, several projects were launched concurrently and created a shortage of steel sections in the mar-ket. As a result, steel was fabricated in Europe and transported to Canada using several transportation schemes

Fig. 6. Steel modularization

Fig. 7. Example of pipe-rack module installation

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Pipe supports must be designed for all operating conditions. Stress analyses must be performed for large pipes and at the anchor locations. The steel shoe must allow the pipe to ex-pand and contract freely without causing excessive stresses. In the de-sign of pipe supports, the horizontal frictional forces (induced due to pipe thermal expansion) must be applied at the transverse beam top flange. These forces must act parallel to the piping run and must be combined with gravity and wind loads for both serviceability and ultimate limit states conditions.

3.2 Building modules

Building modules are assembled on steel skids and commissioned prior to their transportation to the construc-tion sites. The prefabricated buildings are placed on steel skids as illustrated in Fig. 8. Section A-A is a longitudinal section through the building and sec-tion B-B a cross-section. The dashed lines represent the equipment loca-tions. The skid contains two longitudi-nal beams bolted to transverse beams. The lifting points are also shown in the figure. The spacing of the trans-verse beams is determined by the building specification. In some cases interior equipment is attached to these beams. The steel skids must be de-signed to accommodate lifting loads as well as the jacking forces with an appropriate factor of safety. The max-imum distance between lifting lugs on building skids should not exceed 12 m. Removable lifting lugs are some-times used and are installed on the longitudinal beams as shown in detail C and section D-D. The lifting lugs are connected to the beam webs using bolted end plate connections. It is also recommended to use the same con-nection type for the transverse beams. Reinforcing plates (with radius R2) are welded around the lifting lug hole on both sides to enhance stiffness at the stress concentration regions. The lift-ing lugs are designed according to the shackle capacity of the crane. The size of the lifting hole (denoted by radius R1) must match the lifting pin size. Further, the edge distance R3 must be sufficient to prevent failures around the curved boundaries. The lifting lugs must be checked for combined ten-sion and shear block failures.

Fig. 8. Building module lifting details

Fig. 9. Example of modularized steel oil sands structure

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Fig. 10. Example of super-module Fig. 11. Mobile oil sands facility

3.3 Equipment modules

Fig. 9 shows an example of a modular-ized steel structure designed for an oil sands upgrading project. The struc-ture is composed of steel framing sur-rounding two vertical vessels. Steel platforms are connected at various levels to facilitate access for sched-uled maintenance and repairs. Two stair towers are attached at both ends to access these service platforms. Pipe and cable tray supports are connected to the steel framing at various levels. Note that the equipment on the steel platforms is omitted for clarity. The dimensions of the steel structure are 29 × 42 × 42.1 m (W × L × H) and it is separated from the two vertical ves-sels by a 300 mm gap. The steel fram-ing system is designed for operational, testing, lifting and transportation con-ditions. The height of the steel stick-built part is 14.6 m, the height of the modularized part 27.4 m.

Large scale modularization (of-ten referred to as super-modulariza-tion) was also developed in several expansions of oil sand projects. This modularization prototype minimizes the shutdown period of operating oil sands facilities during the fabrication/assembly phase. A super-module mod-ularization example is illustrated in Fig. 10. The sub-modules are assem-bled and stacked on top of each other in a laydown. Mechanical and electri-cal equipment is installed and com-missioned. The resulting massive structure is then transported to the permanent location using the self-pro-

pelled module trailer (SPMT) system. The shutdown period of the operating facility is only limited to the installa-tion of the super-module on the foun-dation. This procedure maximizes the production rate of the plant.

4 Design of mobile oil sands facilities

In some oil sands projects the process facilities are designed as “mobile” steel structures so they can be relocated as the project expands. This concept evolved over the past few years due to the substantial cost-savings. For exam-ple, it is economical to relocate the steel facilities used in SAGD (Fig. 3) from an existing well pad to a new lo-cation after completing oil production. Similarly, the concept is very effective in open mining projects (Fig. 2) for re-locating the process facilities from op-erating mining pits to new locations following mine expansions.

The oil sands facility in this case is disassembled from the foundation and transported to predetermined site locations, as illustrated in Fig. 11. Transverse steel girders are used to an-chor the facility during transportation. SPMTs are used to relocate the mas-sive structure. The number and layout of the SPMTs are determined based on the weight and location of the com-bined centre of gravity of the facility, including interior equipment, pipes

and substations. Therefore, the struc-tural design requires examination for the disassembly and reassembly proce-dures used for the mobile oil sand fa-cilities. In some cases a hydraulic jack-ing system is used to lift the facility in order to match the level of the SPMTs. The engineer in this case should iden-tify all jacking points to be used in the structural model. It is also important to specify the magnitude of the initial jacking forces to be applied at each jacking point in order to disconnect fully the supports from the concrete base. Selection of impact load factors (magnitude and direction) is very im-portant in this case to avoid any struc-tural failure that might occur during a) initial jacking, b) uphill and downhill transportation, c) application of emer-gency brakes and d) reinstallation at the new location.

The engineer must also determine whether external supports are required to restrain the movement of the steel structure during the initial jacking and transportation. The overall stability of the mobile steel structure must also be examined against overturning and slid-ing during a) transportation, account-ing for road inclination, and b) appli-cation of the emergency braking forces. The engineer must also com-pute the combined weight of structure and SPMTs during the disassembly and reassembly of each steel facility.

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pedestals must be tied to a grade beam to improve the load resistance of the foundation.

Horizontal loads induced during operation resulting from the thermal expansion or contraction of the vessel must be applied at both end supports. Bundle pull loads must also be consid-ered in the steel design. The live load associated with pulling tube bundles from shell and tube must also be calcu-lated using the larger of 1) empty bun-dle weight or 2) 10.0 kN. These forces must be applied at the centroid of the bundle body. Heat exchanger fixed and sliding supports must be designed to withstand the horizontal bundle forces. Hydrotest conditions must also be considered in the design of the steel framing. When more than one vessel is supported on an interconnected struc-ture, the forces must be computed as-suming one vessel is tested while the others are empty or operational.

6 Design loads

Oil sand facilities are designed to resist several types of loading during opera-tion, fabrication, assembly, transporta-tion and relocation. Dead loads must include equipment weight, valves, fit-tings, insulation, fireproofing, piping up to maximum operating level and also waste material build-up resulting from plant operation. If the weight at the operating level exceeds the upset conditions, then a larger value must be considered.

Steel modules must be designed to accommodate impact loads in-duced during transportation. Unfortu-nately, there are no design rules in North American codes [1–4] to pro-

This is essential for assessing the ade-quacy of the soil to bear the combined weight during relocation. An example of the transportation of a massive pro-cess facility is illustrated in Fig. 12, which uses seven SPMTs to transport the facility.

5 Heat exchanger supports

Heat exchangers and horizontal pres-sure vessels are supported either on concrete pedestals or steel framing. These vessels are supported using fixed and moveable saddles. An example of a heat exchanger support structure is shown in Fig. 13. Large support re-straints can be released using mechan-ical guides to reduce the stresses at the supports. Heat exchanger supports are designed for several operating condi-tions, including steam out, depressuriz-ing and regeneration. The axial forces are resisted by the thermal forces dur-ing operation. When considering the empty and operational conditions (in-cluding the tube bundles), the piping forces contribute almost 20 % of the overall stresses. Even for the stacked situation, the piping forces will con-tribute < 10 % to the overall stresses.

The diameter of the vessel may also change over the length. This may have impact on the support configura-tion at each end. Intermediate sup-ports may also be required to limit the displacement and the stresses at the end supports. Service platforms are sometimes required. If needed, the steel framing must be separated to eliminate any static or dynamic inter-action during operation. Further, if the equipment is supported directly on a piled foundation, the concrete

vide industrial guidelines for steel de-sign with transportation loads. There-fore, an equivalent static analysis pro-cedure was developed to approximate the impact loads induced during transportation. Common values for the vertical (Iv) and horizontal (IL) and longitudinal (Ih) components range between 1) Iv = (1.5 G – 1.75 G), 2) Ih = (0.2 – 0.3 G) and 3) IL = (0.1 – 0.3 G). Note that G is the total gravity load of the module. The im-pact loads are applied at the centre of gravity of the steel modules and act concurrently as shown in Fig. 14. To simplify the analysis, bilateral springs can be used at the supporting points to stabilize the structural model. Note that the design must account for wind loads during transportation.

Please note that most of the equipment supports are also subjected

Fig.12. Process facility being trans-ported on SPMTs Fig. 13. Example of heat exchanger support structure

Fig. 14. Impact forces acting on steel module during transportation

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the form of cracks in the structural member at an early stage of opera-tion. Therefore, regular inspection procedures are required to monitor any local damage that might occur during operation. Replacement or re-pair of these parts is very expensive due to the lengthy shutdown periods. Therefore, it is important to evaluate the influence of these penetrations during the design phase.

Graph (a) in Fig. 15 shows the in-fluence of vertical spacing βy in eleva-tion (B), with D1 = 100 mm and D2 = 250 mm. It can be seen that the maxi-mum web stress value (σw)max = 235MPa at βy = 250mm. Note that by increasing the piping spacing βy, (σw)max is reduced gradually until it reaches an asymptotic value of 150 MPa. This value is attained at βy = 500 mm. At this distance, the interac-tion between the piping penetrations is eliminated. Therefore, the distance between penetrations is at least twice the larger diameter.

Graph (b) in Fig. 15 shows the variation in the maximum web stress (σw)max with the rectangular opening depth α. The curvature r is fixed at 30 mm in this case. The web stress is computed for the three values of β = 150, 200 and 300 mm. It can be seen that in all cases (σw)max de-creases by decreasing α. For example, when β = 300 mm, (σw)max decreases from 244 to 210 MPa by reducing α from 300 to 100 mm. By reducing β to 200 mm, (σw)max decreases from 200 to 174 MPa.

8 Conclusions

Structural design procedures have a large impact on the cost of Canada’s oil sands projects. Few guidelines are available in existing codes of practice used in these projects. The paper re-viewed structural developments and challenges encountered in the design of steel oil sands facilities. Modulari-zation procedures that have been de-veloped and design guidelines were presented for the design of steel mod-ularized equipment supports and pipe-racks. The influence of structural penetrations was also discussed. Other design issues are addressed by the author in [6–10]. Further develop-ments are still underway to improve structural performance and reduce the costs of oil sands projects.

cables, ducts, etc. Fig. 15 shows a typ-ical supporting scheme commonly used to support oil sands process facil-ities. The structure is supported by three longitudinal plate girders an-chored to a common concrete pile cap. Services (indicated by the arrows) penetrate the plate girders. For illus-tration purposes, two different plate girder profiles are shown. Ele vation (A) shows a rectangular opening with size {α, β} and radius of curvature r for cable trays. Elevation (B) shows two pipe penetrations in the extreme left plate girder. The spacing between these openings is denoted by βy.

It should be noted that the pres-ence of these penetrations reduces the structural stiffness and causes a stress redistribution within the web. They may also introduce local damage in

to dynamic loads during operation. The intensity of this load varies with time and during start-up and shut-down. The structural support should also be designed to accommodate static and dynamic loads caused by dumping and storage of the oil sands material. Dynamic analyses must also be performed for all rotating equip-ment > 500 HP and reciprocating equipment > 200 HP.

7 Service penetrations

Oil sand facilities are sometimes ele-vated above grade to facilitate instal-lation and relocation procedures. Therefore, holes and cut-outs with various shapes are commonly used to allow the passage of services such as pipelines, electrical/instrumentation

Fig. 15. Influcence of structural penetrations in elevated oil sands facility

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[9] Bedair, O.: Cost-Effective Modeling Strategies for Spliced Steel Connections. Journal of Applied Mathematical Mod-elling, vol. 35 (4), 2011, pp. 1881–1892.

[10] Bedair, O.: Stability of Web plates in W-Shape Columns Accounting for Flange/ Web Interaction. Thin-Walled Struc-tures, vol. 47 (6-7), 2009, pp. 768–775.

Keywords: industrial facilities; steel mod-ules; pipe-racks; steel design; oil sands facilities

Author:Osama Bedair, PhD., P.EngEngineering Consultant, PO BOX 45577, Chapman Mills RPO, Ottawa, Canada, K2G 6S7

[5] Ziemian, R.: Guide to Stability De-sign Criteria for Metal Structures, 6th ed., John Wiley & Sons Ltd., 2010.

[6] Bedair, O.: Analysis and Limit State Design of Stiffened Plates and Shells: A World View. Journal of Applied Me-chanics Reviews, 62 (2), 2009, pp. 1–16.

[7] Bedair, O.: Stability Limit State De-sign of Box Sections Supporting Min-ing and Process Facilities. Int. Journal of Structural Engineering and Mechan-ics, 39 (5), 2011, pp. 643–659.

[8] Bedair, O.: Interaction of Multiple Pipe Penetrations Used in Mining and Petro-chemical Facilities. Journal of Thin-Walled Structures, 52, 2012, pp. 158–164.

9 References

[1] Canadian Standards Association: Limit states design of steel structures. CAN/CSA-S16-01, Mississauga, On-tario, Canada, 2007.

[2] National Research Council of Can-ada: National Building Code, Ottawa, Ontario, Canada, 2005.

[3] National Research Council of Can-ada: Alberta Building Code, Ottawa, Ontario, Canada, 2006.

[4] American Institute of Steel Construc-tion (AISC): Steel Construction Man-ual, 14th ed., AISC, Chicago, USA, 2006.

Bordeaux-red specifically requested by the artist.

There were no mechanical joints and all seams are high frequency welded. The entire scuplture was only supported by air pressure. The interior volume was approximately 75,000 m3. Inflation time took two hours. The internal air pres-sure of approximately 300 pascales was delivered by one main blower unit. The visitors were not only able to view and touch the fabric from the outside, but were also able to access the interior of the sculpture through a revolving door air lock at the entrance. The sculpture remained fully inflated for six weeks, after which it was deflated, packed and shipped back to the artist.

Anish Kapoor’s ambition for the MONUMENTA 2011 at the Grand Palais was to create an aesthetic and physical shock, a colourful experience that is poetic, meditative and stunning, measuring itself against the height and light of the Nave, an interior that some-how seems larger than the exterior.

Due to the shear size of the sculp-ture, it would have been next to impos-sible to fabricate and ship it in one

News

Hightex wins the IAA Award of Excellence for fabric art

Hightex Group plc has won the IAA Award for design excellence in specialty fabrics applications for the art installa-tion “Leviathan”, a work created by the British artist Anish Kapoor. The award was conferred on Hightex at the IFAI Specialty Fabrics Expo 2013 which took place in Orlando, Florida, USA.

“Leviathan” was exhibited at the MONUMENTA event in the Grand Pal-ais, Paris, in May 2011 and is one of the largest sculptures Kapoor has ever cre-ated. Hightex was responsible for the engineering, production and installation of the sculpture. It was made of a PVC-coated polyester membrane skin span-ning an area of more than 13,000 m2. Engineers of the company welded the sculpture, which was delivered in four pieces, into one outstanding artwork with high frequency welding. The walk-in sculpture was 100 meters long, ap-proximately 35 meters high and weighed 12 tons. It was an inflatable object, clamped only to a steel angle and the entrance arch. It was coloured in the

piece. The client, however, insisted on not having any mechanical site joints. In order to facilitate this requirement, the sculpture was manufactured in four in-dividual pieces, the largest being approx-imately 3,700 m2. In order to avoid hav-ing to move the fabric too much, the four pieces were placed at pre-calcu-lated positions within the building and unfolded.

The exhibition was the most success-ful MONUMENTA to date, attracting over 600,000 visitors during the six weeks of the exhibition.

Project detailsLocation: Paris, France Fabrics: PVC Coated Polyester by Ferrari S.A. Engineer: Aerotrope Design: Anish Kapoor, Studio Kapoor Subcontractor: Tensys Ltd.

Further information: Hightex Group plc www.hightexworld.comIndustrial Fabrics Association Internationalwww.ifai.com

Fig. 1. “Leviathan” in the Grand Palais, Paris (©Jan Cremers, Courtesy of Anish Kapoor)

Fig. 2. The inside of the “Leviathan” (©Jan Cremers, Courtesy of Anish Kapoor)

09_032-040_Bedair_(005)_cs6.indd 40 03.02.14 11:24


DOI: 10.1002/stco.201420002

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This document describes the development and state of the art of orthotropic steel bridges in Germany. Following a short historical review of the performance of orthotropic bridge decks over the last decades, the present traffic loads are described and related to the resistance of the existing structures. Based on four differ-ent hazard categories, this paper describes different retrofitting methods. Although several promising strengthening techniques are introduced and evaluated, it appears that further research is urgently required in order to improve these techniques.

1 Development, 1950–20131.1 General

Although the idea of orthotropic steel bridges was already around in 1936 [1], the significant development of steel bridges in Germany started after all the major bridges had been destroyed in World War 2. Beginning with their re-construction, orthotropic bridge deck design has been con-tinuously improved throughout the last 50 years and can nowadays be found all over the world. Today there are many different structures with significant differences re-garding both their economic efficiency and their durability. The most relevant steps in their evolution are described by the design of the following construction details:– longitudinal stiffeners (ribs)– rib wall–cross beam junction– rib–deck plate junction– deck plate

1.2 Longitudinal stiffeners (ribs)

Based on experience in shipbuilding, the longitudinal ribs for the first generation of steel bridges were in most cases designed as open stiffeners. In order to reduce the expend-iture on welding, spans were extended between the ribs. Owing to failures due to excessive local flexibility, the fol-lowing limitation was introduced and is still effective to-day:

et

≤ 25

(1)

where:e rib spacingt deck plate thickness

The development of U-shaped closed ribs for the road bridge “Weserbrücke Porta”, erected in 1954 [2], saw the appearance of a new stiffener design. Since 1960 closed ribs have been used in most cases as they have several es-sential advantages compared with open stiffeners. Longer spans (> 3.0 m) between the cross-beams allow the number of junctions to be reduced. At the same time, the number of rib–deck plate welds is decreased by 50 % in order to reduce the expenditure on materials and fabrication. Fur-thermore, the torsional stiffness of the ribs improves the local structural behaviour. Consequently, most bridges erected after 1960 have been constructed with closed ribs.

As a consequence of patent rights, different shapes of closed ribs have been used (Fig. 1). With the improvement of cold-forming techniques, closed trapezoidal ribs became predominant and represent the standard type of construc-tion from the early 1970s until today (Fig. 2).

Orthotropic steel bridges in GermanyHeinz Friedrich

a) V-section b) U-section c) Y-section(champagne-glasssection)

d) trapeziodal section with-out cope hole

e) trapeziodal section with cope hole

Fig. 1. Different shapes of closed ribs

Y-section

trapezoidal sections

U-sections

L- & T-sections

bulb sections

steel flats

V-section

longitudinal rib sections span between cross-beams

Fig. 2. History of longitudinal rib design and the corre-sponding spans between cross-beams

10_041-047_Friedrich (002)_cs6.indd 41 03.02.14 11:23

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2 Traffic loads

Traffic loads are significantly affected by numbers of heavy goods vehicles. Over the years the design load models have been consistently adapted to the increase in heavy goods traffic (Fig. 4).

In 1952 “Bridge class 60” (BK 60) was introduced as the relevant design load model: a 3-axle 60 t heavy goods vehicle represented the traffic loads sufficiently for the coming decades (Fig. 5a). Increasing traffic volumes led to this load model being replaced by “Bridge Class 60/30” (BK 60/30) in 1982 (Fig. 5b). The implementation of “DIN-Fachbericht 101” [4] in 2003 saw the introduction of the semi-probabilistic safety concept. The corresponding load model 1 (LM1) comprises a 2-axle vehicle in each of two lanes (Fig. 5c). As the latest predictions indicate a fur-ther increase in heavy goods traffic up to 2025, the next load model adaption was required. Since May 2013, Ger-man bridges have to be designed according to the “modi-fied load model” (LMM) of the Eurocode (Fig. 5d).

The load model development is illustrated in Fig. 6. It is obvious that the most significant step is from load model LM1 to LMM. The distribution of the different load mod-els from 1950 to 2010 is shown in Fig. 7. Most steel bridges erected up until the early 1980s are designed according to BK 60, newer bridges according to BK 60/30. Older bridges classified according to BK 60/30 have been recalculated. Only a few recent steel bridges correspond to LM1.

For new bridge designs, the modified load model (LMM) is the response to the rise in heavy goods traffic. The ques-tion is how to deal with the numerous older bridges, espe-cially the steel bridges. Compared with concrete bridges, steel bridges have a significantly higher traffic load to dead weight ratio and are therefore extraordinarily sensitive to any increase in traffic loads.

3 Resistance

Significant for the resistance of steel bridges are both a) their condition and b) their age. The condition of every single structure is evaluated in the course of recurrent bridge inspections based on German standard DIN 1076 “Highway Structures – Testing and Inspection” [6]. This standard comprises definite specifications in order to cal-culate a rating between 1.0 and 4.0:

1.3 Rib wall–cross beam junction

Whereas open ribs can be fed through the cross-beams rel-atively easily, a more sophisticated solution is required for closed ribs. Versions with bolted joints as well as early de-signs with ribs fitting between the cross-beams repeatedly resulted in damage. A better fatigue performance is achieved with ribs running continuously through cut-outs in the cross-beam webs.

Recently, the Y-shaped (or champagne glass-shaped) ribs that were popular in Germany up until 1976 have ex-hibited damage in numerous cases at the junction with the cross-beam. The state of the art is the trapezoidal-shaped rib running continuously through cut-outs in the cross-beams. The shape of the cut-outs normally provides a remaining opening at the flange so that only the rib webs are connected to the web of the cross-beam (Fig. 1e). The all-around welded type (Fig. 1d) is not used in Germany because of the demand-ing production tolerances.

To sum up, there is great variety in the design of rib wall–cross-beam junctions in German steel bridges. As a consequence, every construction-related damage event re-quires an individual retrofitting solution.

1.4 Rib–deck plate junction

Former design codes resulted in 3.5–4 mm thick fillet welds to connect the ribs to the deck plate. The wheel loads of today’s heavy goods vehicles cause deformations in the deck plate and, subsequently, a transmission of bending moments into the ribs. Compared with the normally 6 mm thick ribs, the thin fillet welds have a lower resisting mo-ment and are therefore the weakest link in the chain. Con-sequently, the thickness of the welds needs to be adapted to the thickness of the rib walls – especially in the case of repairs. The state of the art is to use butt welds with full penetration and a gap < 2 mm (Fig. 3).

1.5 Deck plate

The deck plate is the base for the wearing surface. Over the decades the thickness of the deck plate was adapted to the increasing traffic loads in order to reduce deformations and stress. Although a deck plate thickness of 12 mm is obligatory since 1976, there are still some steel bridges in use with 10 mm thick deck plates. However, since 2003 the deck plate of German steel bridges should be 14 mm according to DIN-Fachbericht 103 “Steel Bridges” [4] and Eurocode 3 part 2 (EN 1993-2) [5].

Fig. 3. Different kinds of weld for the rib–deck plate junction [3]

Fig. 4. Development of heavy goods vehicle traffic in Germany up until 2012 and expected values up until 2025 (BMVBS = German ministry of transport; WTR = world traffic report)


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Fig. 6. Load model development

1.0–1.4 very good condition1.5–1.9 good condition2.0–2.4 satisfactory condition2.5–2.9 adequate condition3.0–3.4 inadequate condition3.5–4.0 deficient condition

Almost 60 % of German steel bridges are rated with 2.5 or worse, which means that they need retrofitting urgently. This is especially necessary for older bridges as their con-dition deteriorates with their age (Fig. 8).

Fig. 5. Load models for road bridges

residual area lane 1 residual area lane 2 lane 1

residual area lane 3 lane 2 lane 1residual area lane 2 lane 1


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5.2 Assessment

Assessment could be a single measure but in most cases it is associated with repair or strengthening measures. Apart from the Eurocode, two guidelines are available to assist the engineer: a) the “German guideline for the reassess-ment of existing road bridges” [7] and b) the report “Assess-ment of existing steel structures: recommendations for es-timation of remaining fatigue life” [8].

The guideline includes a graded approach for evaluat-ing ultimate bearing capacity and serviceability. Based on grade 1 (assessment according to Eurocode without restric-tions on remaining service life), the other grades imply more

Whereas most steel bridges erected since the early 1990s exhibit at least a satisfactory condition, the rating becomes worse the older the structures are. Almost 50 % of the bridges built between 1980 and 1989, and more than 70 % of the steel bridges erected in the 1960s and 1970s, are rated 2.5 or worse.

4 Categorization

The big variety of different construction details has resulted in a big variety of types of damage. Nevertheless, it is possi-ble to classify the potential damage in four main categories corresponding to their location within the structure and the transfer of the traffic loads to the bearings (see Fig. 9 and Tab. 1). These categories indicate the weak points in the load path, from the bridge deck (category 1) through the stiffeners (category 2) and the cross-beams (category 3) to the main girders (category 4). Hence, these categories can be used to indicate potential fatigue hazards and should be taken into account for both a) the design of new bridges and b) the inspection and evaluation of existing bridges.

5 Retrofitting5.1 General

Various retrofitting methods for steel bridges are introduced and described in this section. However, a professional bridge inspection carried out by experienced and skilled staff is the basis for any kind of retrofitting:– assessment– repair– strengthening– replacement

Fig. 7. Load model distribution – quantity plotted against years (left) and correspond-ing areas in square metres (right)

Fig. 8. Condition rat-ing of German steel bridges (as of 2012)

Fig. 9. Details of an orthotropic bridge deck and potential damage categories


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Table 1. Examples of damage corresponding to the categories

Categories Location Figure

1Junctions with deck plate:

deck plate–stiffening girder junction

2

Junctions in longitudinal system:

stiffening girder–stiffening girder junction

stiffening girder–cross-beam junction

3

Junctions in cross-system:

cross-beam–cross bracing junction

cross-beam junctions

4

Junctions in main system:

main girder

main girder web

main girder chord

or less significant modifications (e.g. effects, partial safety factors) or restrictions (e.g. remaining lifetime, traffic).

In the report, four phases are described:– phase 1: preliminary evaluation– phase 2: detailed investigation– phase 3: expert investigation– phase 4: remedial measures

5.3 Repair

Repair measures are required in order to re-establish the original state of a damaged bridge. Regarding orthotropic

bridge decks, typical repair measures concern cracks in the welds or steel plates. Cumulative experiences are described in the German DVS Bulletin 1709 “Repair of orthotropic decks” [9]. This paper provides recommendations and prin-ciples for specific welding technologies regarding design, execution and quality assurance.

5.4 Strengthening5.4.1 General

Strengthening measures are necessary if repairs are not sufficient to generate a durable solution (due to increased fatigue effects). A sufficient remaining lifetime can only be


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guaranteed if additional measures are taken. As only a few individual solutions exist, it is not yet possible to give gen-eral advice. However, there are some ideas and research results in accordance with the categories given above. The state of the art regarding research and technology in Ger-many is summarized below.

5.4.2 Category 1

Junctions with the deck plate is the subject of category 1 (Tab. 1), where damages can occur independently of the type of ribs. As category 1 damage directly influences traffic safety and the usability of a bridge, special attention must be paid to effective strengthening methods to prevent this kind of damage. Direct strengthening of the deck plate seems to be the most promising measure in order to reduce the local stress and deflection in the attached welds. Four dif-ferent techniques are introduced here [10].

The method known as the sandwich plate system (SPS) is based on the following principle: a reinforcing plate is placed parallel to the deck plate and the resulting cavity is filled with liquid polyurethane (PU). After the curing process, the polyurethane and the two steel plates work together as a loadbearing sandwich (Fig. 10). SPS was used in a pilot project to strengthen a German road bridge in 2005. With a 50 % reduction in the local strain, this measure is regarded as very successful from a technical point of view. From an economical point of view, the first SPS application turned out to be cost-intensive. A major reason is the elevation of the gradient by 35 mm, which involves substantial costs for adapting transitions and footpaths.

The idea behind the method based on ultra-high-per-formance concrete (UHPC) is to replace the asphalt layer by a special concrete layer with a shear-resistant connection to the deck plate (Fig. 11). This technique was first devel-oped and used in the Netherlands and results in a signifi-cant reduction in the local strain [11]. Workmanship must be excellent in order to avoid cavities and provide an ade-quate evenness as well as a satisfactory skid resistance. A pilot project is currently planned for Baden-Württemberg in south-west Germany.

Externally bonded plates are directly fixed to the deck plate with epoxy. As the thickness of these reinforcing plates is only 6 mm, a standard asphalt layer can be applied on top to retain the old gradient. The success of this method de-pends on the long-term adhesion performance of the epoxy, which is currently being evaluated in the laboratories of the Federal Highway Research Institute (BASt).

HANV stands for the German expression for “porous asphalt with subsequent filling” and is based on the follow-ing principle: the asphalt layer is replaced by porous asphalt which is subsequently filled with liquid epoxy (Fig. 12). The

intention is to create an advanced material – compared with standard asphalt – that features both a) greater stiffness and deformation resistance at higher temperatures and b) better elasticity at low temperatures. However, HANV rep-resents a very new approach currently being researched and evaluated at the University of Duisburg-Essen.

5.4.3 Category 2

Junctions in the longitudinal system is the subject of cate-gory 2 (Tab. 1), where damages are normally related to a special type of orthotropic deck or a certain construction detail. As a consequence, there are many individual retro-fitting solutions for category 2 damage but no general ap-proach exists. Although a research project at the Univer-sity of Stuttgart, with the focus on champagne glass-shaped stiffeners, will be completed by the end of 2013, additional research is desirable.

5.4.4 Category 3

Junctions in the cross-system at the frame corners is the subject of category 3 (Tab. 1). Recently, the bridge over the Rhine at Leverkusen – a major bridge in the German mo-torway network – was temporarily closed to traffic for ve-hicles with a gross weight > 3.5 t after category 3 damage was detected. Permanent monitoring of the structure is now being carried out until its replacement in 2020. A strengthening strategy is expected as the result of a current research project at TU Dortmund University.

70 mm asphalt

6 mm reinformcement

30 mm polyurethane

12 mm deck plate

Fig. 10. Sandwich Plate System (SPS)

Fig. 11. Ultra-high-performance concrete (UHPC) as wearing course

Fig. 12. Sample of HANV (Hohlraum-reiches Asphalttrag-gerüst mit nach-träglichem Verguss)


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References

[1] Schaechterle, K., Leonhardt, F.: Fahrbahnen der Straßen-brücken. Erfahrungen, Versuche und Folgerungen. Die Bau-technik 16 (1938), No. 23/24, pp. 306–324.

[2] Dörnen, A.: Stahlüberbau der Weserbrücke Porta. Stahlbau 34 (1955), No. 5, pp. 97–101.

[3] Friedrich, H., Sedlacek, G., Paschen, M.: Deep Improvement of the Fatigue Behavior of Orthotropic Steel Decks with Con-sideration of the Asphalt Layer. 6th Japanese German Bridge Symposium, Munich, 2005.

[4] DIN Fachbericht 103 Stahlbrücken, Mar 2003.[5] EN 1993-2 Eurocode 3: Design of steel structures – Part 2:

Steel bridges. The European Union per Regulation 305/2011, Directive 98/34/EC, Directive 2004/18/EC.

[6] DIN 1076 Ingenieurbauwerke im Zuge von Straßen und Wegen – Überwachung und Prüfung, Berlin, 1999.

[7] Nachrechnungsrichtlinie: Richtlinie zur Nachrechnung von Straßenbrücken im Bestand. http://www.bast.de/cln_030/nn_795118/DE/Aufgaben/abteilung-b/Regelwerke/Uebersicht- Regelwerke.html, 2011

[8] Kühn, B., Lukic, M., Nussbaumer, A., Günther, H.-P., Helme rich, R. S., Kolstein, M. H., Walbridge, Herion, S., An-droic, B., Dijkstra, O., Bucak, Ö.: Assessment of Existing Steel Structures: Recommendations for Estimation of Remaining Fatigue Life, http://eurocodes.jrc.ec.europa.eu/showpublica-tion.php?id=137, JRC-report, 2008.

[9] Merkblatt DVS 1709: Instandsetzung und Verstärkung orth-otroper Fahrbahnplatten, Ausschuss für Technik, Arbeits-gruppe “Schweißen im Bauwesen”, DVS Verlag GmbH, Düs-seldorf, May 2008.

[10] Sedlacek, G., Paschen, M., Feldmann, M., Geßler, A., Stein-auer, B., Scharnigg, K.: Nachhaltige Instandsetzung und Ver-stärkung von orthotropen Fahrbahnplatten von Stahlbrücken unter Berücksichtigung des Belagssystem. BASt Schriften-reihe B, Verkehrsblatt Verlag, 2010.

[11] De Jong, F. B. P.: Renovation techniques for fatigue cracked orthotropic steel bridge decks, PhD thesis, Delft University of Technology, 2006.

Keywords: German Bridges; traffic loads; hazard categories; retrofitting methods; strengthening techniques

Author:Heinz FriedrichFederal Highway Research Institute (BASt)Department of Bridges & Structural Technology, Section for Steel Structures, Corrosion Protection, Bridge [email protected]

5.4.5 Category 4

As category 4 damages are extremely rare there is no de-mand yet for investigations of corresponding strengthening methods.

5.5 Replacement

The replacement of a bridge should be considered as a last resort if other measures are not promising or not econom-ical. A costs-benefits analysis is recommended if the costs for the retrofitting exceed 50 % of the construction costs for a new bridge. The Haseltal Bridge – a motorway bridge between Frankfurt and Würzburg – serves as an example. This structure, only 50 years old, was replaced by a new bridge at a cost of € 40 million in 2011 after a history of damage and many unsatisfactory repair and retrofitting at-tempts.

6 Conclusions6.1 Old bridges

Most old bridges are not designed for current traffic loads. In response to this problem, four different categories of poten-tial damage are available (Fig. 9). Although some promising approaches are introduced and evaluated, urgent research is required for the improvement and development of inno-vative retrofitting methods.

6.2 New bridges

New bridges should be designed according to the expected development of traffic loads in the coming decades. Special attention should be paid to the implementation of fatigue-re-sistant construction details. The configuration of two paral-lel superstructures provides the greatest flexibility for main-tenance measures during operation.

Acknowledgements

This contribution would not have been possible without the support and encouragement of many highly respected colleagues. I should like to take this opportunity to express my special thanks to all those who have given me advice and feedback during the writing of this article.


DOI: 10.1002/stco.201330035


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In 1899 Vladimir Shuchov (1853–1939), the polymath Russian engi-neer, was awarded a patent covering the principles he had de-vised for hyperbolic lattice towers. These hyperbolic towers are constructed from an assembly of straight elements connected to-gether with complex three-dimensional joints. However, their full geometry is difficult to discern from the (orthogonal) drawings still available. Until now, little was known about the technological advances that made these complex designs feasible. This paper presents an investigation into the mathematical principles and operational practices that may have been used for determining the actual geometry of individual elements for setting out and constructing the metal lattices, thus illuminating the conjunction of geometry and craft.

1 Introduction

Shuchov’s principal contribution to structural design was in the sequential development of his principles of light-weight construction – the most eminent design being that for the hyperbolic lattice tower. His hyperbolic towers are assemblies of straight elements connected together with complex three-dimensional joints. However, their full geo-metry is difficult to discern from orthogonal drawings. The subject of the patent assigned to V. G. Shuchov in 1899 was the structural principle of a lattice hyperboloid tower, and it is clear that behind the structural principle lay a highly elaborate design that included special setting-out methods for each detail and a unique sequence and method of assem-bly with a detailed sequence of steps. Until now, however, very little has been known about the precise nature of these techniques, given that they were not explicitly part of the patent documentation.

Matthias Beckh [1, 2] has thoroughly analysed the geo metry of hyperbolic surfaces, the interdependencies be-tween the key parameters and the impact on the loadbear-ing capacity of the structure. However, his description fo-cuses on a wire-like abstract model, or an outline of the structure. The important step describing precisely how the calculated dimensions were subsequently transferred to the actual metal sections, elements and details has not yet been investigated. This paper is the result of an attempt to recre-ate these “missing” methods and is based on empirical measurements of the 128 m tall NiGRES Tower (Figs. 1, 2) built in 1927–29 in Dzerzhinsk, Russia. The relative com-pleteness of its documentation [3] allows us to use the di-

Between geometry and craft: the setting-out of the NiGRES TowerEkaterina Nozhova

Fig. 2. NiGRES Tower, Dzerzhinsk, 1927-29, view from inside (photo: IDB ETH, Silke Haps, 2007)

Fig. 1. NiGRES Tower, Dzerzhinsk, 1927-29 (photo: IDB ETH, Silke Haps, 2007)

11_048-055_Nozhova (035)_cs6.indd 48 03.02.14 11:22

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H the height of the section (24 900 mm)j the rotation angle

(36°, where sin j = 0.5878, cos j = 0.8090)n the number of struts (40)

Archival research revealed that the starting point for every tower design involved prototypes in which towers were depicted as general schemes or proportional outlines. For the purposes of our calculations, we need to define ac, the projection of the generatrix onto the horizontal surface:

ac R r Rr= + − =

= + −

2 2

2 2

2

17000 12900 2 12900 17000 0

cos

· · ·

ϕ

..8090

100582600 10029

=

= =

The narrowest hyperboloid radius p lies in this case beyond the section analysed:

pRr

ac= = =sin · · .ϕ 17000 12900 0 5878

1002912853

L, the true length of the leg is

L H ac= + = + =

= =

2 2 2 224900 10029

720592600 26843 85.

Since the section has 10 rings, the strut is subdivided into 11 equal parts, which are arranged vertically at regular intervals for stability. The ring positions do not coincide with the strut overlaps. The lines marking the positions of rings on the struts would therefore be drawn at the following distances: for the first ring it would be 2440.35 (2440, fragment 1) mm; for the fifth, 12 201.75 (12 201) mm; for the ninth, 21 963.15 (21 962) mm. These match the archive drawings.

H1, the height of the narrowest radius is

H HR Rr

ac1

2

2

224900

17000 17000 12900 0 809

= − =

= −

cos

· · .

ϕ

0010029

276242

=

To reveal the interdependence of the elements and the gen-eral geometry of the tower, we will work with the first, fifth

mensions of the secondary elements for additional precision and verification.

2 Stereotomy and descriptive geometry

In construction, “stereotomy” refers to that collection of applied geometric methods used to define actual sizes and forms of individual elements that together form larger solid structures (e.g. an arch). In the past, this field also incorpo-rated, for instance, the rules used to lay out stone vaults and complicated wooden joints. In the modern era, it has under-gone a process of formalization and refinement, allied to the formal education in the “Polytechnique” schools [4]. In the first decades of the 19th century, descriptive geometry estab-lished itself as an essential technique for the engineer – a method of describing three-dimensional objects through two-dimensional projections. It was widely applied to metal structures; numerous manuals for engineers and boiler-mak-ers contained the basic plotting methods and detailed exam-ples, such as boilers, reservoirs and bridges [5, 6].

The first book on projective geometry, edited in Russia, was written by Karl Potier [7], a student of Gaspard Monge, who came to St. Petersburg in 1810 to teach at the Institute of Railway Engineers. It was originally published in French in 1816, and was translated into Russian just one year later. “Projective Geometry” by P. Galaktionov, published in 1841, was approved by the Russian Academy of Sciences and recommended for use in the military academies. The content of most of the books prepared afterwards was largely conceived as sequences of geometrical problems. Vladimir Shuchov graduated from the Moscow Poly technicum (Impe-rial Moscow Technical School), where the sound training in projective geometry as an academic and applied discipline was based on hundreds of hours of projective drawing, com-bining both abstract plotting and practical tasks. In 1929 Karl Greiner, a friend and colleague of Schuchov, edited a course of lectures [8] on metal processing in which the appli-cation of descriptive geometry to the laying-out of metal structures was just one of the matters he described; the lat-tice tower of Schuchov was briefly analysed there as an “in-teresting case”. But even this publication focuses on a pure geometrical model, not on a structure made of real sections.

3 Deriving missing methods from empirical measurements

The archive drawing depicts the inner and outer struts of the first section of the NiGRES Tower (Fig. 4) with the exact positioning of the rivet holes (up to 0.5 mm accuracy) and the precise marking-up method for the strut overlaps and ring alignments. Our task was to restore the steps used to define the dimensions of the actual elements. This meant using the initial dimensions of the tower outline to get the positions of rivet holes and the distances between the ele-ments for the whole structure, and to derive the method used to mark up elements for cutting.

4 Calculations

Five initial parameters [1, 8, 9, 10] are necessary for the calculations (Fig. 3):R the lowest ring radius (17 000 mm)r the upper ring radius (12 900 mm)

Fig. 3. Initial parameters of tower and detail of tower (author’s drawings)

11_048-055_Nozhova (035)_cs6.indd 49 03.02.14 11:22

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We will now draw the two 120 × 120 mm angles par-allel, with an offset of 10 mm for the metal gasket, and mark the positions of the rings. It is important to mention that this drawing is not a vertical projection of the detail, but rather a conventional scheme that depicts the position of both the struts towards the ring and thus helps to consider the struts as one linkage system. We take the axis of the gasket as the “basic line” of the initial outline.

The inner and outer struts are joined to the ring using angles. These sections are not right-angled, so they need to be reshaped to fit the junction. It is worth mentioning that the sections were reshaped while hot with the use of rolls or an acentric heading press – a technique widely used in boiler production. To deduce the angle, we will use the following formula:

tgH U

p R p

tg

xxµ

µ

=−

=−

1

2 2

1 2

27624 16417 7

12853 17000 12

· .

88533 1712 72 30

2 788 70 15

2 1

5 5

9

= = ° ′

= = ° ′

=

. ,

. ,

µ

µ µ

µ

tg

tg 22 5460 68 309. , µ = ° ′

and ninth rings. The constructive solution for the detail stays the same, but some dimensions within the detail vary. The radius of the ring Ux is calculated according to the following equation, where hx is the distance between the calculated ring and the narrowest radius p:

UR p

Hh p

U

x x= − +

= −

2 2

12

2 2

1

2 2

217000 12853

2762425360 3· . 66 12853

269541731 16417 7

208334932 4 144

2 2

5

+ =

= =

= =

.

.U 333 8

173730087 55 13180 79

.

. .U = =

There are 10 rings in the first section of the tower, arranged at regular intervals (24 900/11 = 2263.64 mm). So, for the first ring h1 = 27 624 – 2263.64 = 25 360.36 mm; for the fifth ring h5 = 27 624 – 5 × 2263.64 = 16 305.8 mm; for the ninth ring h9 = 27 624 – 9 × 2263.64 = 7251.24 mm.

Fig. 4. Strut templates for the first section of the NiGRES Tower (top: fragments 1, 2, 3; bottom: 4, 5, 6) (Russian State Archive of Scientific & Technical Documentation – RGANTD, Moscow, fund 166, list 1, folder 43, p. 6)

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the vertical surface and the surface of the ring. To derive this, we use the following formula:

tg EH U

U p R p

for the base ring it will be tgE

xx

x

=− −

1

2 2 2 2

0

,

==−

=−

=

H R

R p

tg E

12 2

0 2 2

27624 1700017000 12853

3 7933·

. , EE

tg E

0

1 2 2

75 15

27624 16417 7

16417 7 12853 1700

= ° ′

=−

· .

. 00 12853

3 99 75 55

5 4563 79 37

2 2

1

5 5

−=

= = ° ′

= = ° ′

. ,

. ,

E

tg E E

ttg E E9 911 199 84 55= = ° ′. ,

After we have derived these we can mark them on the sec-tion: the vertex lies on the basic line (Fig. 5). Rivet holes lie on the central axis of the angle legs. When we mark the line of the ring and then the axis line of the rivet holes, which is parallel to it at a distance of 35 mm from the edge, we see that it crosses the central axis of the angle leg at a distance different from the height mark. For the first ring, the dis-tances are approx. 21 and 51 mm, which matches the ar-chive drawing. These distances are different for each ring, and the value depends on angle Ex (Fig. 5). The numbers we derived match the numbers indicated on the archive draw-ing: compare Fig. 5 with fragments 1, 2 and 3. However, Fig. 5 indicates graphically the interdependence between Ex and these distances. The fifth ring coincides with the second strut overlap – so the junction is simpler as only the inner strut is connected to the ring and the outer strut is connected to the inner one.

As a next step, we need to define the positions of the rivet holes at the strut overlaps. At the base ring, the outer and inner struts do not start at the same point – the arrays are rotated. On the basis of the building documentation, we can define the angle of rotation (Figs. 6, 7).

It is worth mentioning that the base ring of the 128 m high NiGRES Tower in Nizhny Novgorod is polygonal (Fig. 7). This might have been chosen because the footprint was larger than the size of the average water tower plan (base radii of water towers vary from 3.2 m in Andijan (1909) to the exceptionally large 9 m in Dnepropetrowk

Fig. 6. Geometry of the tower: inner and outer struts start at the same point/rotated (author’s drawing)

Fig. 5. Tower struts and their connections to the first, fifth and ninth rings (author’s drawings)tg

H U

p R p

tg

xxµ

µ

=−

=−

1

2 2

1 2

27624 16417 7

12853 17000 12

· .

88533 1712 72 30

2 788 70 15

2 1

5 5

9

= = ° ′

= = ° ′

=

. ,

. ,

µ

µ µ

µ

tg

tg 22 5460 68 309. , µ = ° ′

The leg length of the section, indicated on the drawing, is 63 mm; ax = 63 mm · cosmx, therefore…

a1 = 63 · 0.3007 = 18.94 (19 mm, fragment 4)

a5 = 63 · 0.3379 = 21.29 (21.5 mm, fragment 5)

a9 = 63 · 0.3665 = 23.09 (23 mm, fragment 6), which matches the drawing.

Next, we need to indicate the angle of inclination Ex (the angle of the tangent to the curve at that point). This gives us the angle between the projection of the inclined strut on

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side of the inpolygon with 40 sides: AC = 2R sin 180/40 = 2669 mm.

γ= =

γ= ° ′ γ = °sin

21334.54435

0.3009,2

17 30 , 351 11

If we mark the derived numbers on the profiles, as shown in Fig. 9, we get a distance of 111 mm, which matches the archive drawing (110.5 mm, fragment 1).

Repeating the same sequence of steps for the fourth intersection, we get the following:

)

))

(

((

=° ′ − ° ′

= =

′ = ° ′ = =

′ =′λ

′ = =

=′

= =

= = = ° ′ =

= =

γ= =

γ= ° ′ γ = ° ′

z 12853cos 40 52 31 30

128530.9866

13027.5 mm

a z sin 31 30 13027.5 · 0.5225 6807

aca

sin; ac 6807

0.75629001.6

lL ac

ac26843.85 · 9001.6

1002924093.88 24094 mm,

which almost matches the drawing 24098 mm .

AB B C 24094 mm, AD R sin 31 30

17000 · 05225 8882.5

sin2

8882.524094

0.3687,2

21 35 , 43 10

4

4 4

44

44

1 1 1

4 44

If we mark the numbers on the sections again, as in the previous step, we get a distance of 88.5 mm, which fits with the archive drawing (87.5 mm, fragment 3).

To end up with the dimensions of the strut, we need to restore the development of its lower edge. We already have E0 = 75° 15′.

cossin sin

sin sin

µα ϕ α

0

17000 4 30 12900 3

=+ −( )

=

=° ′ +

R r

L

66 4 30

26843 85

0 3007 72 300

° − ° ′( )=

= = ° ′.

. ; µ

To restore the angle, we produce the following drawing (Fig. 9). Sections taken parallel with the horizontal surface will help us to build the projection of the edge of the sec-

(1930), whereas the base radius of the NiGRES Tower is 17 m) [2] and it would have been easier to control the ex-actness of a polygon (by triangulation) than the precision of a radius. The angle of rotation between the array of inner and outer struts is 9° (2a). An important characteristic of hyperboloids is the position of the strut overlaps: the points where the struts overlap lie on the radial lines; the central angles formed by these lines are multiples of a: the radial angle of the first overlap is a (4° 30′), the second 3a (13° 30′), the third 5a (22° 30′), the fourth 7a (31° 30′) (Fig. 8).

The hyperboloid radius at the point of a strut overlap is calculated with the following formula:

zp

andr ac

which gives

xx

=−( )

= − =

cos

, sin sin, s

β ϕ

β λ λ ϕ90 iin

sin

sin· .

. ,

λ ϕ

λ λ

=

= = =

rac

and12900 0 5878

100290 7561 449 8

40 52

1285340 52 4 301

° ′

= ° ′

=° ′ − ° ′

,

cos

from which

z

β

(( ) = =

′ = ° ′ =

128530 8052

15 962 5

4 30 15962 51 1

..

sin .

mm

a z ·· . .

sin; .

.

0 0785 1253 06

1253 060 75621

1

=

′ =′

′ = =aca

acλ

11657 05

26843 85 1657 0510

1

1

.

;

. · .

Lac

lac

lL ac

ac

l

=′

=′

=0029

4435 2

1

= . ,

( )which fits the drawing fragment

To define the distance between the rivet holes, we will study triangle ABC (Fig. 8). AB = BC = l = 4435 mm, AC is the

Fig. 8. Positions of strut overlaps; scheme to define the strut dimensions (author’s drawing)

Fig. 7. The base ring of the NiGRES Tower (RGANTD, Mos-cow, fund 166, list 1, folder 43, p. 3)

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Fig. 9. Details of the struts (author’s drawings)

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was specially processed. This means that even the section thickness was taken into account (Fig. 10).

The leg of the section that is not connected to the base ring is cut (hatched area in Fig. 9). This probably eased ac-cess to the rivets.

It is also important to understand the sub-dimensions of the sections that connect the strut to the ring. There are longer details, which connect the outer strut to the ring, and shorter ones, which were used to connect the inner strut to the same ring. Studying the elements in the con-struction drawings reveals that some distances (25 mm from the edge on the vertical side, 35 mm from the edge on the horizontal side) remain the same, but the distance be-tween the two rivets on the vertical side and the distance from the rivet hole to the edge of the element varies – which, accordingly, also generates the different lengths in the details.

The width of the strut is 120 mm. There is a 10 mm thick plate between the sections (Fig. 5). Depending on the angle of inclination Ex, the projection of 120 + 10/2 = 125 mm onto the surface of the ring will be different: ax′= 125/sin Ex

a

a

1

5

12575 55

1250 9699

128 9

12579 3

′ =° ′

= =

′ =° ′

sin ..

sin 77125

0 9836127 1

12584 55

1250 9961

129

= =

′ =° ′

= =

..

sin .a 55 5.

We have already calculated the radii of the first, fifth and ninth rings:

U1 = 16 417.7;

U5 = 14 433.8;

U9 = 13 180.7

These radii indicate the distance to the surface of the strut overlap. If we reduce the calculated radius on the projec-tion of the strut width, we should get the dimension of the ring:

tion on the horizontal surface; we also derive the dimen-sion of the edge projection onto the vertical surface and the dimension of its deviation. These simple steps help us to restore the cutting of the both section legs; it is impor-tant to mention that the axis line of the rivets, which con-nect the struts together, is used as a “rule line” to mark the dimensions of the strut. Its zero point lies on the intersec-tion of the axis with the edge of the section (the through-line is marked on the drawing as a dotted red line).

Because the aforementioned “rule line” with the zero mark lies on the axis that passes 50 mm from the edge, we have to use the drawing to derive the distance we need to add to the calculated L dimension, which is the length of a “rule line”, in order to get the full sizes of the outer and inner struts. For the outer strut it is L + 26.5 mm = 26843.85 + 26.5 = 26870.35 mm, which matches the draw-ing (26 874 mm). For the inner strut it is L + 15.24 mm = 26 843. 85 + 15.24 = 26 859.1 mm, which again matches the drawing (26 858 mm). The detailed drawing depicts the detail precisely and reveals that the edge of the section

Fig. 11. Section specifications showing the millimetre variations in sub-dimensions (RGANTD, Moscow, fund 166, list 1, folder 43, p. 20)

Fig. 10. Development of the lower edge of the strut (RGANTD, Moscow, fund 166, list 1, folder 43, p. 4)

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with a tolerance as large as half a millimetre, which – with regard to construction techniques – appears to have been be an unrealistic goal, but was probably the only way of controlling precision.

Normally, the marking out of sections was performed on the basis of the templates prepared by draughtsmen and engineers. However, in the case of hyperbolic towers, the method of setting-out – though it applies the standard rules of projective geometry described in the manuals – goes far beyond the standard examples, so the task here was not only to obtain the true size and form of each element, but to explain the variations on the typical element with regard to the general geometry of the structure. The setting out of Shuchov’s hyperbolic towers is a brilliant example of theo-retical engineering knowledge and practical skill applied on the construction site.

This research is done within the frames of the D-A-C-H Project „Konstruktionswissen der frühen Moderne – Schu-chovs Strategien des sparsamen Eisenbaus.“ The D-A-C-H Project unites the research groups of IDB ETH, Innsbruck University and TU Munich.

References

[1] Beckh, M., Hoheisel, M.: Form und Tragverhalten hyperbo-lischer Gittertürme. Stahlbau 79 (2010), No. 9, pp. 669–681.

[2] Beckh, M.: Hyperbolische Stabwerke. Shukhovs Gittertürme als Wegweiser in den modernen Leichtbau. Detail, Munich, 2012.

[3] Russian State Archive of Scientific and Technical Documen-tation (RGANTD), Moscow. F. 166, op. 1, d. 43.

[4] Sakarovitch J.: The teaching of stereotomy in engineering schools in France in the XVIIIth and XIXth centuries: an ap-plication of geometry, an “applied geometry”, or a construc-tion technique? In: Randelet-de Grave, P., Benvenuto, E. (eds.): Entre Mécanique et Architecture/Between Mechanics and Architecture. Birkhäuser, Basel/Boston/Berlin, 1995.

[5] Hutton, W., S.: Steam-boiler construction: a practical hand-book for engineers, boiler-makers, and steam-users. Lockwood, London, 1898.

[6] Davies, G. M.: Laying-out for boiler-makers and plate fabri-cators. Simmons-Boardman, New York, 1944.

[7] Potier, K.: Traite de géométrie Descriptive à l’usage des Eléves de l’Institut des Voyes de Communication. A. Pluchart, St. Petersburg, 1816.

[8] Greiner, K.: Kotelnoe delo [boiler-making]. Gosudarstvennoe Izdatelstvo, Moscow/Leningrad, 1929.

[9] Greiner, K.: Razmetka v kotelnom dele [laying-out for boiler-makers]. ONTI, Moscow/Leningrad, 1934.

[10] Schuchov, V., Kandeev, V., Kotliar, I.: Stalnie reservuari [steel reservoirs]. ONTI/Gosmashmetizdat, Moscow, 1934.

Keywords: Schuchov; NiGRES Tower; lattice structure; hyper-boloid; construction history; laying-out; descriptive geometry

Author:Ekaterina NozhovaInstitut für Denkmalpflege und BauforschungWolfgang-Pauli-Str. 27 HIT H 438093 Zurich Hönggerberge-mail: [email protected]

U

U

1

5

16417 7 128 9 16288 8

14433 8 127 1 1430

′ = − =

′ = − =

. . .

. . 66 7

13180 7 125 5 13055 29

.

. . .U′ = − =

This does not include minimal safety tolerances (2–3 mm) and thus fits with the archive drawing, where U1′ = 16 285 mm (diff. = 3.8 mm), U5′ = 14 304 mm (diff. = 2.7 mm), U9′ = 13 053 mm (diff. = 2.2 mm).

The width of the ring (80 mm) and construction toler-ances stay the same for all the joints, so the distance D for each case could be calculated from the following equation:

125 80 65

3

sin sinEm construction tolerance

Ex x

+ ( ) + = +

+ 55 90 25

125 80 65 35 90

tg E D

D mE E

tg

x x

xx x

−( ) + +

− + − −sin sin

−−( ) −

− = + − − −

E

D m

x 25

1250 9699

80 650 9699

35 0 2500 21 . .· . 55

108 11

109 62

112 16

1

5

9

D m

D m

D m

− =

− =

− =

.

.

.

125 80 65

3

sin sinEm construction tolerance

Ex x

+ ( ) + = +

+ 55 90 25

125 80 65 35 90

tg E D

D mE E

tg

x x

xx x

−( ) + +

− + − −sin sin

−−( ) −

− = + − − −

E

D m

x 25

1250 9699

80 650 9699

35 0 2500 21 . .· . 55

108 11

109 62

112 16

1

5

9

D m

D m

D m

− =

− =

− =

.

.

.

Construction tolerances could be derived from the draw-ings, but we can already compare the difference between the archive and calculated dimensions: on the archive drawing D5 = D1 + 1 mm, D9 = D1 + 3 mm; the calculated values are: D5 = D1 + 1.5 mm, D9 = D1 + 4 mm, which results in a minimal deviation (fragments 4, 5 and 6).

The nuances in the section sub-dimensions are subtle but crucial – for ease of handling, section specifications were in the form of tables; Fig. 11 shows an example of such a table. Here, the sections listed are those that con-nect the outer and inner struts to the ring and gaskets in the places of strut overlaps. Following the numbers in the table, we can trace minor changes present; the nature of these changes (a matter of millimetres) has been investi-gated above.

5 Conclusions

Checked against the original drawings, this investigation has successfully restored a feasible setting-out technique that might have been used in the construction of hyper-bolic structures. These results expand our understanding of how schematic dimensions were transferred to the real construction components and how the complicated three-dimensional joints were designed. It is important to men-tion that all the calculations were performed with an ac-curacy of four decimal places, as an initial trial with three did not produce satisfactory results (the divergence from the archive drawings was up to 5 mm). In reality, the details were set out, and therefore intended to be manufactured,

11_048-055_Nozhova (035)_cs6.indd 55 03.02.14 11:22

DOI: 10.1002/stco.201420007


Reports

1 Introduction

The Institute of Structural Design at the Faculty of Architecture of Techni-sche Universität München has been analysing the form and structural be-haviour of hyperbolic lattice towers in recent years. This innovative light-weight system was invented by the renowned Russian polymath and engi-neer Vladimir Shukhov and built for the first time in 1896 [1, 2]. While as-sessing the level of safety of existing Shukhov towers, one of the most diffi-cult questions has been the realistic forecasting of wind forces acting on the complex open latticework of these structures. The problem became obvi-ous when the institute joined a team of international experts in the rescue operation for the NiGRES transmis-sion line tower in 2006 [3]. When Shukhov designed and analysed his towers, he used a shielding factor to reduce the wind forces on the ring el-ements. Today, the situation is more complex. As the current European codes do not include any reduction factor for open lattice structures other than three- or four-sided space trusses, the full wind loads had to be em-ployed in the structural analysis. Since

these code-compliant wind loads led to unrealistically high forces in the structure, it was decided to study the behaviour under wind loads more thoroughly by means of wind tunnel tests. The tests were performed in the wind laboratory of Wacker Ingenieure in Birkenfeld, Germany, in 2013.

2 Wind tunnel tests on generic models

The first series of wind tunnel tests was carried out to gain a better under-standing of the distribution of forces and the overall behaviour under wind loads. Furthermore, they were in-tended to prove the suitability of the filigree models. All models were made of soldered brass sections and all of them were built to a scale of 1:50.

This series of tests comprised three generic models. A water tower designed by Shukhov for the Ukrai-nian city of Mykolaiv (formerly Niko-layev), completed in 1908, served as a blueprint for the models. The overall geometry of this tower was slightly simplified to facilitate both modelling and comparability of results. The height of the models was 50 cm, with a top diameter of 12.5 cm and a bot-tom diameter of 25 cm. Model 1 had

24 vertical members, whereas models 2 and 3 each had 48 vertical mem-bers. The latter differed only slightly in the arrangement of the supports at the bottom: in model 2 the verticals were connected in pairs at the 24 supports, in model 3 the supports for all 48 members were spaced evenly around the perimeter line (Figs. 1a–1c). Equal-leg angles with 2 mm leg thickness were used for all vertical members, thus roughly matching the 120 × 120 × 12 mm angles of the Nikolayev tower. All models had nine horizontal ring elements distributed evenly over the height of the struc-ture. Therefore, the ring elements are spaced 5 cm centre to centre in the model and thus match the 2.5 m inter-vals in reality. The ring elements were made of flat brass bars 2 mm wide.

The three generic models were tested in a boundary layer wind tun-nel with wind velocities of 9–11 m/s. At the bottom, the models were fixed to a force balance to measure the re-actions under wind load. During the tests, the exposure of the models to-wards the wind direction was varied in increments of 7.5° to measure any influence of directionality. The results of the first set of tests can be seen in

Wind forces on hyperbolic lattice towers

Matthias Beckh Rainer Barthel

Fig. 1. The models: a) series 1, model 1, b) series 1, model 2, c) series 1, model 3

a) b) c)

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segment compared with the projected side view area. It is very interesting that the measured force coefficients cdres correspond surprisingly well with the solidity ratios. The difference be-tween them varies between 2 and 5 % for all segments apart from the first one. The significantly larger difference of about 33 % in the case of the first segment can be attributed to ground effects at the bottom of the wind tun-nel. Consequently, the solidity ratio provides a reasonably fair assumption

pendently and in combination with the adjacent unit. This procedure en-sured a realistic approach flow for each segment. Unlike in the first se-ries, the models were tested this time in a uniform low-turbulence wind tun-nel to obtain more specific results. The resulting force coefficients cD can be seen in Table 2.

The subsequent wind forces on each segment can be calculated with the following formula:

F = cD A qgust (H)

where:H reference height [m]qgust (H) design gust pressure [kN/m2]A reference area, here projected

side view area [m2]

Table 3 shows the resultant wind force on each segment. Furthermore, this table also shows the solidity factor for each segment. This ratio is defined as the projected surface area of all verti-cal and horizontal members of one

Table 1 and Fig. 2 and allows us to de-duce the following: – The force coefficient c is independ-

ent of the wind direction. – The type of meshing does not have

any effect.

3 Wind tunnel tests on NiGRES transmission line tower

The main part of the study focused on the wind forces on the NiGRES trans-mission line towers. These structures, of which only one remains today, are located adjacent to the River Oka, close to Nizhny Novgorod. The Ni-GRES transmission line towers were built between 1927 and 1930 and rep-resent the most refined of Shukhov’s hyperbolic lattice towers. With a height of 130 m, the remaining tower is also the second-highest that Shukhov built – only surpassed by the Shabolovka tower in Moscow (150 m, 1919). The structure is composed of five hyper-bolic segments stacked upon each other. Each segment is 24.9 m high, ex-cept for the fifth one, which is 24.3 m.

As before, the model of the tower was made of brass sections to a scale of 1:50. For the wind tunnel tests, all segments were built individually so that they could be tested both inde-

Model 1 Model 2 Model 3

Wind Direction [°]

0 7,5 22,5 0 7,5 15 0 7,5 15

cdx 0,281 0,277 0,254 0,393 0,392 0,386 0,396 0,387 0,374

cdy –0,004 –0,038 –0,113 0,002 –0,054 –0,110 –0,026 –0,076 –0,126

cdres 0,281 0,279 0,278 0,393 0,395 0,401 0,397 0,394 0,395

Table 1. Force coefficients dependent on wind direction for towers 1–3

Force coefficient Segment

Wind direction 1 2 3 4 5

cdx 0,32 0,292 0,361 0,259 0,336

cdy –0,004 0,009 0,027 –0,004 0,012

cdres 0,32 0,292 0,362 0,263 0,336

bottom top

Table 2. Force coefficients from wind tunnel testing for the 5 segments of the NiGRES tower

Reference area [m²]

cdres [–]

Fres [kN]

Gross projected area [m2]

Solidity factor [–]

Difference [%]

1st segment 744,51 0,32 150,57 179,12 0,24 33,01

2nd segment 562,74 0,29 149,37 158,40 0,28 3,74

3rd segment 415,83 0,36 158,51 142,84 0,34 5,38

4th segment 298,80 0,26 89,51 79,90 0,27 –1,65

5th segment 194,40 0,34 78,71 67,20 0,35 –2,80

Table 3. NiGRES tower – projected area, force coefficients, and solidity factors for each segment

Fig. 3. Model of NiGRES tower

Fig. 2. Force coefficients in relation to wind direction for towers 1–3

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Fig. 4. NiGRES tower model, 3rd and 4th units

Wind tunnel Fres [kN]

to DIN 1055-4 [kN]

Difference [%] to Shukhov calcs [kN]

1st segment 150,57 206,70 –27,16 364,80

2nd segment 149,37 230,80 –35,28 292,90

3rd segment 158,51 246,50 –35,70 280,40

4th segment 89,51 156,70 –42,88 141,60

5th segment 78,71 124,40 –36,73 130,10

Table 4. NiGRES tower – comparison of the horizontal wind loads on each seg-ment according to wind tunnel testing, to the DIN 1055-4, and to Shukhov’s his-toric calculations

ing to the wind tunnel tests and ac-cording to DIN 1055-4. The forces according to the DIN standard were calculated before yet proved to be too conservative for a realistic assessment of the level of safety of the tower, as was demonstrated previously [4]. It shows that the results of the wind tun-nel are between 27 and 43 % lower than the used forces hitherto. With the observation that the solidity ratio is a fair approximation of the force co-efficient, the difference would ideally be larger, i.e. in the range of the force coefficient cf in the standard. The dif-ference can be attributed to simplifica-tions in the modelling and the con-structability of the filigree models. Thus, the main ring elements in the models had to be executed slightly larger than in the original to enable the use of independent segments.

The fact that the solidity ratio is fair design assumption for this kind of open latticework can also be ex-plained by its geometry: As an axially symmetrical structure, disadvanta-

geous exposures of members on one side of the tower will be balanced by a corresponding advantageous expo-sure on the opposite side. Further tests will have to be done to examine how the wind forces on a segment are split between vertical and horizontal members.

References

[1] Graefe, R., Gappoev, M., Pertschi, O.: Vladimir G. Šuchov – Die Kunst der sparsamen Konstruktion. DVA Verlag, Stuttgart, 1990.

[2] Beckh, M., Barthel, R., Graefe, R.: In-novation und Ästhetik – der Leichtbau-pionier Vladimir Grigorévic Šuchov. In: Detail, 2010, No. 11. pp. 1142–1148.

[3] Graefe, R., Gappoev, M.: Rettungs-aktion für Bauten in der Region Nizhny Novgorod. Stahlbau 77 (2008), H. 2, S. 99–104.

[4] Beckh, M.: Hyperbolische Stabwerke – Šuchovs Gittertürme als Wegweiser in den modernen Leichtbau. Detail Verlag, Munich, 2012.

Keywords: hyperboloid; hyperbolic; lat-tice; lightweight; Russia; Shukhov; shield-ing factor; solidity factor; tower; wind; wind tunnel test

Authors:Dr.-Ing. Matthias BeckhProf. Dr.-Ing. Rainer BarthelLehrstuhl für TragwerksplanungTU MünchenArcisstrasse 2180290 München

for the calculation of resultant wind forces with the formula given above. Table 4 lists a comparison of the resul-tant wind forces per segment accord-

12_056-058_Beckh_(007)_cs6.indd 58 03.02.14 11:21

ECCS news


Miklós Iványi †

Dr. Miklós Iványi, Professor of the Department of Structural Engineering, Pollack Mihály Faculty of Engineering, University of Pécs and formerly Profes-sor of the Department of Structural En-gineering, Budapest University of Tech-nology and Economics, Hungary, passed away unexpectedly on December 21, 2013, at his age of 73.

The international structural steelwork society mourns together with his family the loss of husband, father and grand-father, a great professor and scientist.Miklós Iványi was born in 1940 in Endrod at the southern-east part of Hungary, also grew up there and begun his education in Békéscsaba in the Vásárhelyi Pál Technical School founded and directed by his father, which made him proud of him in his whole life.He received his Civil Engineering de-gree in 1963 at the Technical University of Budapest. After completing his uni-versity studies he became an Assistant Professor at the Department of Steel Structures. In these years he continued his research on the fi eld of lateral buck-ling of beams, supervised by Professor Ottó Halász. He received his Candidate of Science degree in 1973 from the Hun-garian Academy of Science with a thesis entitled “Lateral buckling of beams tak-ing strain-hardening into account”. On this basis he also earned his PhD equiv-alent degree from the TU Budapest and he became an Associate Professor at the same Department. He continued and extended his research on various fi elds of the stability of steel structures. In 1983 he received his Doc-tor of Science degree at the Hungarian Academy of Science with a thesis entitled

“Interaction of stability and strength phe-nomena in the load carrying capacity of steel structures; role of plate buckling”. From 1984 to 2007 he was a Professor at the Department of Steel Structures at the TU Budapest (now called Budapest Uni-versity of Technology and Economics). Besides teaching and research he played signifi cant role in the managing board of the university between 1982 and 1988, where he organized the civil engineering courses in foreign languages as Deputy Rector. Between 1986 and 1999 he was the Head of the Department of Steel Structures. From 2004 until his death he was a Pro-fessor at the Pollack Mihály Faculty of Engineering, Pécs, Hungary. He played a signifi cant role in improving the edu-cation and science to University level at his faculty in Pécs. He founded the inter-nationally approved scientifi c journal called Pollack Periodica and he was in the founding member of the Breuer Marcell PhD School.Prof. Iványi had outstanding professional and social activities as the member of numerous national and international sci-entifi c organizations. From 1977 he took part in the organization of more than 30 international scientifi c conferences in-cluding the well-known Stability Collo-quia and the Bridges on the Danube Conferences. The pioneering events or-ganized by Prof. Iványi provided the fi rst scientifi c platforms for the researchers of east and west parts of Europe. Beside the scientifi c background of the conferences, he created a friendly atmosphere, inspir-ing the researchers to tighten the con-nections and to expand the technical co-operations. He had signifi cant roles in international educational and research projects with European, US and Japan universities and institutions. He was member of the editorial boards of inter-national scientifi c journals. His profes-sional activity is composed in more than 40 books and 220 scientifi c papers.The whole constructional steel society misses him. We will honour his memory.

Prof. László Dunai

Events

Eurosteel 2014

The seventh Eurosteel event will be held in 2014. The European Conference on Steel and Composite Structures will take place in Naples and the event is being organized by the Department of Struc-tures for Engineering & Architecture of the University of Naples Federico II. Past Eurosteel events have been held in

Athens (1995), Prague (1999), Coimbra (2002), Maastricht (2005), Graz (2008) and Budapest (2011).

The great participation in Eurosteel 2011 in Budapest, where about 500 del-egates from more than 40 countries from all over the world took part, confi rmed the growing interest in steel and com-posite structures.

The 2014 event in Naples will be an excellent opportunity for the communi-ties of scientists and researchers, profes-sional engineers and architects, contrac-tors and manufacturers to meet, present and discuss achievements and new ideas in this fi eld.

The online procedure for submitting abstracts is now available on the confer-ence website: www.eurosteel2014.it. All the information you need about the sub-mission procedure can be found there.

Announcements

Deutscher Stahlbautag 2014

The Deutscher Stahlbautag 2014 will be held on 29 and 30 October in Hannover. Further informations: www.bauforumstahl.de

Norwegian Steel Day 2014, 6 November

The Norwegian Steel Day 2014 will be held on 6 November in the Grand Hotel, Oslo. The programme is available at www.norskstaldag.no

Danish Nationale Steeldag 2014, 13 November

The Danish Nationale Steeldag will be held on 13 November. The programme is available at www.steelinfo.dk/dsi_steeldag.php

Technical Committees (TC) activities

TC meetings agenda

TMB – Technical Management BoardChairperson: Prof. M. Veljkovic

PMB – Promotional Management BoardChairperson: Mr. Yener Gur’es

13_059-062_ECCS_News_NEU.indd 59 03.02.14 11:21

ECCS news


TC3 – Fire SafetyChairperson: Prof. P. Schaumann Secretary: Prof. Paulo Vila Real

TC6 – Fatigue & FractureChairperson: Dr. M. Lukic Date: 15–16 May 2014, Gothenburg, Sweden

TC7 – Cold-formed Thin-Walled Sheet Steel in BuildingsChairperson: Prof. J. LangeDate: 12–13 June 2014, Istanbul, Turkey

TWG 7.5 – Practical Improvement of Design ProceduresChairperson: Prof. Bettina Brune Date: 12–13 June 2014, Istanbul, Turkey (Joint Committee TC 7)

TWG 7.9 – Sandwich Panels & Related StructuresChairperson: Dr. Thomas Misiek Date: 12–13 June 2014, Istanbul, Turkey (Joint Committee TC 7)

TC8 – Structural StabilityChairperson: Prof. H. H. Snijder Secretary: Dr. Markus KnoblochDate: 20 June 2014, Luxembourg

TWG 8.3 – Plate BucklingChairperson: Prof. U. Kuhlmann Secretary: Dr. B. Braun

TWG 8.4 – Buckling of ShellsChairperson: Prof. J. M. RotterSecretary: Prof. S. Karamanos

TC9 – Execution & Quality ManagementChairperson: Mr. Kjetil Myrhe

TC10 – Structural ConnectionsChairperson: Prof. Thomas UmmenhoferSecretary: Mr. Edwin Belder

TC11 – Composite StructuresChairperson: Prof. R. Zandonini Secretary: Prof. Graziano LeoniDate: 16 May 2014, Coimbra

TC13 – Seismic DesignChairperson: Prof. R. Landolfo Secretary: Dr. Aurel Stratan

TC14 – Sustainability & Eco-Efficiency of Steel ConstructionChairperson: Prof. Luís BragançaSecretary: Ms. Heli KoukkariDate: 30 January 2014, ArcelorMittal headquarters building, Boulevard d’Avranche, Luxembourg

TC15 – Architectural & Structural DesignChairperson: Prof. P. Cruz

TC News

TC 7

The next meetings of the Joint Commit-tee will be held in Istanbul on 12 and 13 June 2014. This will be a meeting of the whole of TC7. The Joint Committee is currently working on several documents and papers:– a document giving advice on actions

and loads on sandwich panels, bridg-ing the gap between the information given in Eurocode 1 and the special aspects of sandwich panels,

– a document dealing with the design and detailing of axially loaded panels and the point of load introduction into the thin faces,

– a guideline for the design of fasteners, including fixing on just one face, also covering detailing and applications, and

– a document dealing with point loads, with special focus on the use of solar energy systems on roofs made of sand-wich panels.

TC 11 – Composite Structures

The last meeting of TC11 was in Prague on 22 November.

TC11 is collecting contributions from members about three important topics for steel construction: shear connections, shallow flooring systems and composite frames. A comprehensive state of the art document on shear connections in com-posite elements, including features rele-vant to slim floors, is in preparation un-der the coordination of Matti Leskelä. As for the other two topics, Ulrike Kuhl-mann and Jean-François Demonceau are managing the collection of member’s contributions, which are to be published in the Steel Construction journal as sepa-rate papers. In particular, a deadline of July 2014 has been set for the final sub-mission of the papers on shallow floors.

During the meeting there were five presentations by members and invited guests:– Prof. Josef Machacek from the Czech

Technical University presented re-search activities about longitudinal shear in composite steel and concrete trusses used for bridges.

– Mr. Štepán Thöndel showed the re-sults of research carried out at the Czech Technical University into steel-concrete composite beams with deep-rib decks.

– Prof. Jean-Paul Lebet reported on the lateral torsional buckling of steel gird-ers in composite bridges.

– Mr. Quang-Huy Nguyen presented the results of research on concrete

structures reinforced with steel sec-tions.

– Prof. Luís Neves presented a docu-ment that brings together the results of a wide body of research on perfo-rated shear connectors in composite constructions.

MembershipPedro Vellasco from the State Univer-sity of Rio De Janeiro was appointed as a new member. Further, Kwok Fai Chung from the Hong Kong Polytechnic University, Jerome F. Hajjar from North-eastern University and Quang Huy Nguyen from Institut National des Sciences Appliquées were appointed as new corresponding members. TC11 now has 23 full members and 11 correspond-ing members.

Publications

P135 – EUROPEAN RECOMMENDA-TIONS ON THE STABILIZATION OF STEEL STRUCTURES BY SANDWICH PANELS

by Technical Working Group 7.9 – Sandwich Panels & Related StructuresCIB Working Commission W056 – Sandwich Panels

Sandwich panels can support steel members against flexural, torsional and lateral buckling. Sandwich panels pro-vide stiffness against displacements in the plane of the panels and against rota-tion about the transverse axis of the panels.

This document provides information on the use of sandwich panels as stabi-lizing elements for single steel members such as beams or columns. The docu-ment extends the application range of sandwich panels to construction class II according to EN 1993-1-3 and extends the use of sandwich panels to areas out-side the scope of EN 14509.


ECCS news / Announcements


This document introduces the evalua-tion of rotational stiffness and shear stiffness provided by individual sand-wich panels installed in a wall or roof of a building.

P134 – PRELIMINARY EUROPEAN RE-COMMENDATIONS FOR THE DESIGN OF SANDWICH PANELS WITH OPE-NINGS – A STATE OF THE ART REPORT

by Technical Working Group 7.9 – Sandwich Panels & Related StructuresCIB Working Commission W056 – Sandwich Panels

This report includes current information about the influence of openings on the behaviour and resistance of sandwich panels. The intention of this report is to complete the directions given in European product standard EN 14509, which studies solely complete sandwich panels and does not give any guid-ance on the design or cutting of open-ings.

This report introduces technical infor-mation such as calculation models and experimental arrangements concerning the influence of the openings as well as useful practical advice based on the ex-perience of and guidance from compa-nies. Background information covering rules, expressions and knowledge gained from practice is given in note boxes.

Announcements

The First International Conference on Infrastructure Management, Assess-ment and Rehabilitation Techniques

Location and date:Sharja, UAE, 4–6 March 2014

Information and registration:https://www2.aus.edu/conferences/ icimart14/index.html

IX International Conference of Structural Dynamics

Location and date:Port, Portugal, 30 June–2 July 2014

Information and registration:[email protected]

9th International Conference on Short and Medium Span Bridges

Location and date:Calgary, Canada, 15–18 July 2014


Footbridge 2014

Location and date:London, UK, 16–18 July

Information and registration:www.footbridge2014.com

37th IABSE Symposium

Location and date:Madrid, Spain, 3–5 September 2014


EUROSTEEL 2014Seventh European Conference on Steel and Composite Structures

Location and date:Naples, Italy, 10–12 September 2014

Information and registration:www.eurosteel2014.it

12th International Probabilistic Workshop

Location and date:Weimar, Germany, 4–5 November 2014

Information and registration:[email protected] [email protected]

5th International Congress on Construction History

Location and date:Chicago, USA, 3–7 June 2015

Information and registration:http://5icch.org/

World Steel Bridge Symposium

Location and date:Toronto, Canada, 26–28 March 2014

Information and registration:www.aisc.org

Structures Congress

Location and date:Boston, USA, 3–5 April 2014

Information and registration:www.aisc.org

The 3rd China (Guangzhou) Internatio-nal Exhibition for Steel Construction & Metal Building

Location and date:China Import & Export Fair Pazhou Complex (Area B), 12–14 May 2014

Information and registration:www.steelbuildexpo.com

International Conference on Sustain-able Development of Critical Infra-structure

Location and date:Shanghai, China, 16–18 May


CWE 2014 - sixth International Symposium on Computational Wind Engineering

Location and date:Hamburg, Germany, 8–12 June 2014

Information and registration:www.cwe2014.org

AMCM 2014 – Analytical Models and New Concepts in Concrete and Masonry Structures

Location and date:Wrocław, Poland, 16–18 June 2014

Information and registration:www.amcm2014.pwr.wroc.pl

IABSE Workshop ‘hybrid2014 by iabse.ch’

Location and date:Fribourg, Switzerland, 22–24 June 2014



www.structurae.net

A Product of

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Steel Construction 2/2014

Xiao-Ling Zhao, Amin Heidarpour, Leroy GardnerRecent Developments in High Strength Structural Hollow Sections

Ahmed Y. Elghazouli, Jeffrey A. Packer Seismic Design Solutions for Connec-tions to Tubular Members

Peter Marshall, Vul Thang Radical Proposals for Hot Spot Stress Design

Jaap Wardenier, Yoo Sang Choo, Jeffrey A. Packer, G. J. van der Vegte, W. Shen Design recommendations for axially loaded elliptical hollow sections X and T joints

G. J. van der Vegte, Jaap Wardenier Evaluation of the recent IIW – ISO (2013) strength equations for axially loaded CHS K gap joints

Pekka Ritakallio, Timo BjörkLow temperature ductility and struc-tural behaviour of cold-formed hol-low section structures, progress dur-ing the last two decades

František Wald, Becková ŠárkaThe component embedded plate in tension

The Liège-Guillemins station is a monumental “dome” of steel and glass 200 m long, covering the tracks, platforms and travel centre. This dome has a central sec-tion 73 m wide which is flanked by two impressive lateral canopies 39 and 45 m wide cantilevering over the square at the City entrance and over the passenger drop-off point at the Hillside entrance. (Source: Vallourec Deutschland GmbH)

(subject to change without notice)

F. S. K. Bijlaard, R. Abspoel Optimization of Plate Girders

Andreas Lipp, Thomas UmmenhoferInfluence of tensile chord stresses on the strength of circular hollow section joints

Nol Gresnigt, Spyros A. KaramanosResponse of Steel Tubes under Con-centrated Lateral Loads

Esther Pfeiffer, Andreas KernModern production of heavy plates for constructional application: Con-trol of production process and quality

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