steel_buildings_design_notes.pdf

Ferenc Papp Ph.D., Dr habil

Steel Buildings

DESIGN NOTES

Reviewed by Dr. Béla Verőci honorary lecturer

This work is to the scientific program of the Development of quality-oriented and harmonized R+D+I strategy and functional model at BME.

This work is supported by the New Széchenyi Plan. The rroject ID is TÁMOP-4.2.1/B-09/1/KMR-2010-0002.

2010-2011 Budapest

Ferenc Papp Steel Buildings – Design Notes

2

Practice 1

PRELIMINARY DESIGN

Written in the framework of the project TÁMOP 421.B JLK 29.

2010-2011 Budapest


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1.1 The aim of the design task The objective of the design task is the steel structure of a simple hall. The main properties of the structure are the following: - Symmetric form with duopitch roof; - Equal interval between main frames; - Equal interval between purlins; - Horizontal wall girder system, with wall columns in the end walls; - Covering system with double trapezoidal plates and heat isolation. 1.2 The initial data for the design The work starts with the preliminary design of the structure. It is based on the initial data which are determined and supplied by the architectural engineer which satisfy both the appropriate building regulations and the requirements of the owner. In the case of the present design project the initial data concerns to the outer surfaces of the flanges of the steel main frames (see Figure 1):

• Base area to be built: A [m2]; • Horizontal distance between the flanges of the main frame: b [m]; • Height of the side walls: Hw [m] • Slope of the roof: αααα [deg]

Fig.1 Initial data for the design 1.3 The theoretical parameters of the main structure The main theoretical parameters of the steel structure should be determined for the structural analysis (see Figure 2 which considers both the prismatic and the tapered members). The theoretical span of the main frame is equal to the horizontal distance between the central (reference) axes of the columns:

chL −= b

where hc is the initial height of the column section, b is the outer distance of the columns prescribed by the architectural engineer. The theoretical height of the columns is equal to the distance between the theoretical column base point and the intersectional point of the column and the beam central axis. This parameter may be calculated approximately by the following expression:

A [m2] 0.0

Hw

[m]

b [m] αααα [deg]


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Fig.2 Theoretical parameters of the main frame

2

hH b

c −= wH

where Hw is the initial height of the side walls, hb is the initial depth of the beam section. The theoretical ridge (top) point of the frame may be calculated by the following expression:

)(tg2

LHH cf α⋅+=

1.4 The number of the main frames and their interval The architectural concept has prescribed the basic area of the building (A), from which the theoretical length of the steel structure may be calculated,

bA=0d

where the parameters are defined in the Section 1.2. The required number of the main frames may be determined as following:

1c

dn 0

n +=

In the expression c denotes the interval between the main frames, where the optimal value is c=5÷7 meters. Different distance may be used in special circumstances only. The applied number na of the main frames should be an integer, which is determined on the base of the required number of frames nn. The real theoretical length between the final frames is the following (see Figure 3):

( ) c1nd a ⋅−=

Hc Hw

L/2

b/2 hc

αααα

Ht

hb

covering system

hb

hc

Hf

b/2

L/2

Hf

(a) (b)


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Fig.3 The applied number of main frames and the real theoretical length of the structure

Since the distance between the main frames is normally uniform, therefore the initial basic area (A) of the building may be kept only approximately. The real basic area can be calculated by the main parameters of the structures which were determined previously: ( ) ( )cswbfca h2bdhLA ⋅++⋅+=

where bbf [m] is the flange width of the beam section, hcsw is the depth of the column section in the end wall system (see Figure 4). It should be noted that the previous expression is valid for the structural solution illustrated in the Figure 4.

Fig.4 Structural system of the end wall 1.5 The initial cross-sectional parameters for the main frames As a matter of fact, the main frames at the end walls carry lower loads than the intermediate ones. This is why these two frames might be fabricated from weaker cross-sections. In order

purlin

beam of the frame

wall column

bbf hcsw

wall beam

d

d

c c c c


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for easy enlarging the building longitudinally in the future, these frames are suggested being as strong as the intermediate ones. The parameters of the cross-sections of the main frames are related to the span L and the height Hf. Assuming that the building to be designed is relatively low and the roof is relatively flat, i.e:

oc 15 és 5.0L

H ≤≤ α ,

and the structure is loaded only by dead load and meteorological loads, the initial types and parameters of the cross-sections may be determined as the function of the theoretical span L. Table 1 contains the suggested initial values for the cross-sectional parameters which are based on practical experiences. The used symbols of the geometrical parameters can be found in the Table 2. Tab.1 The initial sizes of the cross-sections of the main frames in the function of the span L

span L [m] type of the section size* [mm]

12÷16 hot rolled (IPE/HEA) 300÷450/200÷260 16÷24 welded I flange: 200÷300 – 16÷20

web: 400÷600 – 8÷10 24÷32 tapered I flange: 300÷340 – 16÷20

web: 800÷1200 – 6÷8 * in the case of hot rolled sections the values mean depth of the section for the lower and the upper limits of the span L; in the case of welded sections the values mean the width and thickness of the plates for the lower and the upper limits of the span L Tab. 2 The signs of the geometrical properties of the cross-sections structural member property meaning

bcf width of the flange tcf thickness of the flange hcw width of the web

column

tcw thickness of the web bbf width of the flange tbf thickness of the flange hbw width of the web

beam

tbw thickness of the web 1.6 The initial grade of material The main structural elements are normally made from S235 or S355 steel. Unless there is any previous reason to use S355 steel grade, the grade of S235 is suggested using. If it is reasonable, the initial grade of steel may be changed during the analysis and design of the structure.


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1.7 Application

1. PRELIMINARY DESIGN1.1 Initial parameters

- area to be built [m2] A 725

- width of the building [m] b 20.0

- heigth of the side walls [m] H w 7.5

- slope of the roof [deg] α 10

1.2 Initial data for the main structural members

- main frames (welded I section) column [mm]

flange b cf 240 t cf 16

web h cw 468 t cw 8

depth h c h cw 2 t cf. h c 500=

beam [mm] flange b bf 240 t bf 16

web h bw 368 t bw 6

depth h b h bw 2 t bf. h b 400=

- columns in side walls HEA160 h csw 150

- purlin Lindab Z 200 h p 200

- beams in walls Lindab C 200 h bsw 200

1.3 Theoretical properties of the structural model

- span of the frames [m]

L bh c

1000L 19.5=

- height of the columns [m]

H c H wh b

2

1

1000. H c 7.3=

- heigth of the frame [m]

H f H cL

2tan α π

180.. H f 9.019=

1.4 Number of the main frames

- prescribed length of the building [m]

d 0A

bd 0 36.25=

- interval of the frames [m] c 6.0

- required number of the frames n nd 0

c1 n n 7.042=

- applied number of the frames

n a 7

The building consists of 7 frames!1.5 Area of the bulding

- length of the building [m]

d n a 1 c. d 36=

- actual area of the building [m2]

A tény Lh c

1000d

b bf

10002

h csw

1000..

A tény 730.8=

The actual area of the building satisfies the official plan!


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1.8 Arrangement of the purlin system In our case (the building is under static loading) the purlin system and the wind bracing system may be independent ones, but they also may form a unified system. In the present phase of the design it should be determined which concept is followed:

• Concept A: Purlin system is independent to the wind bracing system • Concept B: Purlin and wind bracing members form a unified static system

In case of Concept A it is assumed that the purlin system carry the loads and effects which act directly to the roof, and it does not take part in the bracing of the building. In this case the wind bracing system is a trussed structure, which consist of two neighboring main frames, the diagonals and the longitudinal bars are placed under the purlins independently to them. In the case of Concept B the longitudinal bracing bars are replaced by the purlin system (besides the primary rule the purlins are part of the wind bracing system). Which concept to be followed in the design may be supported by the following rules and suggestions:

• Application of the Concept A may be suggested in the case of m18L ≥ , since the solution is not economical for relatively small spans with relatively low design loads and effects.

• The application of the Concept B may not be suggested for structures loaded by other considerable loads (e.g. crane load) besides the dead load and the meteorological loads.

In the framework of this design project the Lindab Z purlin is suggested for the roof system. It is a practical experience that the optimal distance between two neighboring purlins is e=1,5÷3,0 meters. The depth of the purlin may change form 200 mm to 300 mm, while the thickness from 1,5 mm to 2,5 mm. The distance is determined also by the rule that the optimal value of the angle of the bracing diagonals to the axis of the frame beam is about 45 degrees, but it is not greater than 60 degrees and not lower than 30 degrees. The suggested numbers for intermediate units are 4, 6 or 8, since the application of a half-bracing unit can be avoided by this way (see Figure 5).

Fig.5 Optimal arrangement of purlin system in term of the distance Ls

Ls≈12÷24m

Ls≈18-36m

Ls≈24-48m

Ls

Ls

Ls

Ls - distance between the ridge point of the roof and the outer point of the edge purlin in the plane of the roof system (see Figure 6)


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The practical purlin arrangement shown in Figure 6 may differ from the theoretical arrangement shown in Figure 5: (i) at the ridge double purlins are used (Figure 6a); (ii) at the edge of the roof special edge shape is used (Figure 6b). The distances denoted in Figure 6 may be calculated by the following expressions:

αα

α cos

h2

h

f wheref2

sinh

cos2

LL

bswc

bs

+=+⋅+

⋅=

where hbsw is the depth of the wall beams and g=150÷200 mm.

Fig. 6 The scheme of the practical purlin arrangement:

(a) double purlins at the ridge; (b) special shaped edge purlin

1.9 Wind bracing system The wind bracing system is shown in Figure 7. According to the Concept A (see Section 1.8) the purlin system is independent to the wind bracing system, therefore the main frames should be connected to each other by bracing bars (see the dashed lines).

Fig. 7 The wind bracing system which is independent to the purlin system

(dashed lines denote the bracing bars)

e

e g

(b)

(a)

f

Ls e


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These bars may be connected to the beams under every second purlin, close to the upper flange of them. It is noted that according to the Concept B the longitudinal bracing bars could be replaced by the purlins (see the continuous lines). 1.10 Application

1.6 Arrangement of the purlin system

- distance between the edge purlin and the theoretical point of the frame corner [mm]

f

h c

2h bsw

cos α π180

.f 456.942=

- distance between the edge beam and the ridge of the frame [mm]

L s1000 L.

2 cos α π180

..

h b sin α π180

..

2f L s 1.039104.=

- interval of purlins [mm]

four spans e4L s

4e4 2.598103.=

six spans e6L s

6e6 1.732103.=

applied spans e e4 e 2.598103.=

The e=2598 mm distance is choosen for the arrangement of the purlin system (except the last distance at the ridge) !

1.11 Covering system Two different constructions of the covering system are shown in Figure 8. In any case the external loads and effects are carried by the external trapezoidal sheet.

Fig. 8 Covering system with heat isolation and double trapezoid sheets: (a) isolation is placed between the purlins

(b) isolation is placed on the purlins

external trapezoid sheet vapour permeable leaf heat isolation (150 mm) vapour proof leaf internal trapezoid sheet

external trapezoid sheet vapour permeable leaf heat isolation (150 mm) vapour proof leaf internal trapezoid sheet

spacer members

(a) (b)


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1.12 Preliminary drawings The aim of the preliminary drawing is to establish the initial parameters of the design in drawings. The preliminary drawings are the basic documents for the structural analysis and design. Therefore, these drawings should contain all the initial parameters of the building used in the procedure of the analysis and design. These drawings should not be confused with the architectural plans and the scenario of the building. In this design project the following three drawings should be prepared (the format of the drawings is A4 or A3): • top view of the foundation and the roof structure • side views of the building • side views of the main frame. 1.12.1 Foundation and roof view (M 1:200) The building is symmetric, therefore the one half of the drawing may show the top view of the foundation, while the other half of it may show the top view of the roof. If the wind bracing system follows the Concept A (the bracing system is independent to the purlin system), the top view side of the drawing may be divided into two symmetrical parts: the upper quarter of the drawing shows the arrangement of the purlin system, while the lower quarter of the drawing shows the bars of the bracing system. The view of the foundation and the roof system is projected to the horizontal plane. The drawing gives exact answer to the following parameters: • top view of the foundation (right side of the drawing):

- theoretical span (L) - number of the frames (n) - distance between the frames (c) - arrangement and initial parameters of the columns in the side walls - scheme of the foundation

• top view of the roof structure (left side of the drawing): - arrangement and initial parameters of the purlins - arrangement and parameters of the wind bracing system.

The drawing of the top view of the foundation and the roof structure which satisfies the Sections 1.7 and 1.10 (Applications) is shown in the Figure 9. It can be seen that the bracing system follows the Concept A. Furthermore, it can be seen that the column foundations are tied up by beams, and this system works together with the concrete slab of the industrial floor. 1.12.2 Side views of the building (M 1:200) The aim of the side view drawings of the building is to give direct information about the arrangement of the wall beams and about the area and place of the openings as well. The building is symmetrical, therefore the right hand side of the drawing may show the arrangement of the openings, while the left hand side may show the arrangement of the wall beams and the bracing system. The drawing should give exact answer for the following parameters: - places and initial section of the wall beams - arrangement and initial sections of the bracing system - place and area of the openings.


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The drawing of the side view does not contain architectural sceneries, it concentrates to the above parameters. The drawing which satisfies the Sections 1.7 and 1.10 (Applications) is shown in the Figure 10. 1.12.3 Side view of the frame (cross section of the building) (M 1:100) The aim of the side view drawing of the frame is to give direct information to take the structural and load model for analysis and design. The frame is symmetrical, therefore the right hand side of the drawing may contain the general parameters, while the left hand side of it may show the theoretical parameters and the arrangement of the structural members: • general parameters (right hand side)

- distance between the outer flanges of the columns (b) - height of the facade (Hw); - slope of the roof (αααα); - height of the structure (Ht); - parameters of the column section (bcf;tcf.hcw;tcw); - parameters of the beam section (bbf;tbf.hbw;tbw); - parameters of the haunching (bhf;thf.hhw;thw); - type of the joints; - type of the column base; - layers of the covering system;

• arrangement of members and theoretical parameters (left hand side) - theoretical height of the columns (Hc); - theoretical height of the frame (Hf); - arrangement and initial section of the purlins; - arrangement and initial section of the wall beams; - length of the haunch.

The drawing which satisfies the Sections 1.7 and 1.10 (Applications) is shown in the Figure 11. It can be seen that the column foundation, the beams between the concrete blocks and the concrete slab of the industrial floor form a unified structural system.

Department of Structural Engineering BUTE Steel Buildings Draw No. 1: Preliminary drawing/Top view M 1:200 Designer Clever Student (XYZVW) Supervisor Clever Teacher assistant professor

Top view of the roof (projected to horizontal plane)

Top view of the foundation

6000 6000 6000

19500

4632

4632

10126

Purlin system

Bracing system

10236

2559

2559

2559

2559

9750

5118

4632

Bracing bars (CHS)

Bracing cross bars (L or rod section)

Lindab purlin (Z section)

Wall columns (HEA or IPE)

Fig. 9 Top view drawing of the roof and the foundation

Department of Structural Engineering BUTE Steel Buildings Draw No. 002: Preliminary drawing/Side view M 1:200 Designer Clever Student (XYZVW) Supervisor Clever Teacher assistant professor

0,0

7,900

3,600

4,600

6000 6000 6000 length of the window: 11600

18 400

3000

1200

2900

600

18 000

Arrangement of wall beams and bracing system Arrangement of openings

3000

1200

2900

600 0,0

7,900

3,600

4,600

9,650

4632 5118 5000 (door) 3600 (window)

7700

7700

Bracing bars (CHS)

Bracing diagonals (L or rod section)

Lindab wall beam (C200)

Fig.10 Side view drawing of the building

Department of Structural Engineering BUTE Steel Buildings Draw No. 003: Preliminary drawing /Side view of the frame M 1:200 Designer Clever Student (XYZVW) Supervisor Clever Teacher assistant professor

19 500/2 20 000/2

Rigid column base

Welded I section: - flanges: 240-16 - web: 468-8

Welded I section: - flanges: 240-16 - web: 368-6

Moment resistant end-plated bolted connections

9019

10390

2597

2598

2598 2447

150

3500

Covering system: - external trapezoidal sheet - vapour permeable leaf - heat insulation (150 mm) - vapour proof leaf - internal trapezoidal sheet

3000

2900

600

1200

7300 7500

9219 Purlins (Lindab Z200)

Wall beams (Lindab C200)

Haunch: - flanges: 240-20 - web: 330-6

CHS bracing members

Slope of roof: 100

Fig.11 Side view drawing of the structural frame


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Practice 2

LOADS AND EFFECTS ON THE BUILDING


2010-2011 Budapest


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2.1 General The loads and effects in general are the subject of the course of Basis of the design (BMEEOHSAT16) in the framework of the BSc education. Here the application of the general knowledge to the design of simple halls is presented. The loads and effects should be determined using the following design standards:

• EN 1991-1-1:2005 Eurocode 1: Actions on structures Part 1-1: General actions. Densities, self-weight, imposed loads for buildings (EC1-1-1);

• EN 1991-1-2:2005 Eurocode 1: Actions on structures. Part 1-2: General actions. Actions on structures exposed to fire (EC1-1-2);

• EN 1991-1-3:2005 Eurocode 1: Actions on structures. Part 1-3: General actions. Snow loads (EC1-1-3);

• EN 1991-1-4:2005 Eurocode 1: Actions on structures - General actions - Part 1-4: Wind actions (EC1-1-4);

• EN 1998-1:2005 Eurocode 8: Design of structures for earthquake resistance. Part 1: General rules, seismic actions and rules for buildings (EC8-1).

In the present phase of the design procedure we are dealing with the basic loads and effects which act on the building. The applied load cases and load combinations are discussed in the sections which are denoted to the design of the structural members. In general the following loads and effects should be taken into consideration in the case of a symmetric and duopitch building:

• dead loads; o weight of the structural members; o weight of the covering system; o other dead load type loads;

• meteorological loads and effects; o snow load; o wind effect;

• imposed loads; • seismic effect; • fire effect.

2.2 Dead loads 2.2.1 Weight of the structural members The self weight of the structural members should be taken on the base of the initial structural parameters. The evaluation should follow the specifications of EC1-1-1. The density of the steel material is 78,5 kN/m3. The dead loads which are based on the initial design parameters should not be changed unless these initial design parameters have changed considerably. The change is considerable if the effect of the change of any parameter on the design forces exceeds by 3%. If the effect of the change is at the safe side, the modification of the initial loads may be neglected. The theoretical self weight of the structural members of the frame is automatically taken into consideration by the analysis software (Axis, ConSteel, FEM-Design), but the self weight of the purlins and trapezoidal sheets or panels should be given by the designer (DimRoof). The self weights of the additional elements (stiffeners, bolts, ect.) are usually taken into consideration by 5÷10% of the theoretical self weight. 2.2.2 Weight of the covering system


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The weight of the covering system of the roof and the walls should be evaluated according to the layers specified in the preliminary drawing (see Figure 8 in Practice 1). The densities of the materials may be found in the appropriate tables of EC1-1-1. The weights structural sections (purlin, wall beam, etc.) may be found in the product information of the producers. 2.2.3 Other dead load type loads This type of loads refers to the loads which are acting regularly. Such loads are the weights of the electrical and mechanical equipments, for example the weights of lighting, climate technology. Such dead load is the weight of the earth layer of the special ‘greenroof’. These type of loads should be specified by the mechanical engineer and the architectural engineer, respectively. The applied intensity and the distribution of this type of loads should satisfy the specifications of EC1-1-1. In present design project – in lack of precise information – we can apply approximately 0,25kN/m2÷0,45kN/m2 dead load which is totally distributed on the roof. 2.2.4 Application

2. LOADS AND EFFECTS2.1 Dead loads

2.1.1 Weights of the structural members and the layers of the covering system

- external trapizoidal sheet : LTP 85 t=0.75mm [kN/m 2] q tr.ext 0.0804

- internal trapizoidal sheet: LPT 20 t=0.4mm [kN/m2] q tr.int 0.0390

- heat insulation (mineral rockwool) [kN/m2]

density [kN/m3] and thickness [m] γ iso 1.5

thickness [m] t iso 0.150

q iso t iso γ iso. q iso 0.225=

- further layers for insulation [kN/m2] q iso.other 0.100

- purlin: LINDAB Z 200 (t=2,0) [kN/m] q purlin 0.0579

- main frame: automatically considered

2.1.2 Installation loads

Installation load projected to the total area of the roof

- lightning [kN/m2] q light 0.10

- building equipments [kN/m2] q equip 0.15

- other loads [kN/m2] q other 0.20


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2.3 Meteorological loads and effects 2.3.1 Snow load 2.3.1.1 Surface snow load The snow loads on the building are determined by the specifications of EC1-1-4. In Hungary the additional specifications of the Hungarian National Annex (HNA) should be considered. The surface snow load may be calculated as follows: - persistent and transient design situations: ktei sCCs ⋅⋅⋅= µ

- exceptional design situation: Adtei sCCs ⋅⋅⋅= µ

where s snow load on the horizontal ground [kN/m2]; µi shape coefficient; Ce exposure coefficient; Ct thermal coefficient; sk characteristic value of the ground snow load [kN/m2]-ben; sAd exceptional value of the ground snow load [kN/m2]-ben. The characteristic value of the ground snow load according to the specification HNA 1.5 is the following:

+⋅=100

A125,0sk but 25,1sk ≥

where A is the height of the ground above the sea level in [m]. The exceptional value of the ground snow load according to the specifications HNA 1.2 and 1.7 is the following:

keslAd sCs ⋅=

where Cesl is the exceptional snow load factor which is 2,0. The exposure factor Ce depends on the topography: - windswept: Ce = 0,8 - normal: Ce = 1,0 - sheltered: Ce = 1,2

Windswept topography: flat unobstructed areas exposed on all sides without, or little shelter afforded by terrain, higher construction works or trees. Normal topography: areas where there is no significant removal of snow by wind on construction work, because of terrain, other construction works or trees. Sheltered topography: areas in which the construction work being considered is considerably lower than the surrounding terrain or surrounded by high trees and/or surrounded by higher construction works.

In the present design project it is assumed that the snow is not prevented from sliding off the roof, and the shape factor µi may be taken from the Table 3.


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Tab.3 Shape factor for duopitch roof (free slip of the snow) tető hajlásszöge (αααα) 0°°°° ≤ αααα ≤ 30°°°° 30°°°° < αααα < 60°°°° 60°°°° ≤ αααα

µ1 0,8 0,8(60-α)/30 0,0 The thermal coefficient Ct should be used to account for the reduction of snow loads on roofs with high thermal transmittance (> 1 W/m2K), in particular for some glass covered roofs, because of melting caused by heat loss. In the present design Ct=1,0 may be applied. In regions with possible rainfalls on the snow and consecutive melting and freezing, snow loads on roofs should be increased, especially in cases where snow and ice can block the drainage system of the roof. In the present design this effect may be neglected. 2.3.1.2 Application

2.2 Snow load

2.2.1 Snow load for the persistent design situation

- height of the building ground [m] A see 300

- charactheristic ground snow load [kN/m2] s k 0.25 1A see

100. s k 1=

s k 1.25

- exposure coefficient (normal) Ce 1.0

- thermal coefficient Ct 1.0

- shape coefficient (α<30 deg) µ 1 0.8

- ground snow load [kN/m2] s µ 1 Ce. Ct

. s k. s 1=

2.2.2 Snow load for the exceptional design situation

- exceptional snow load coefficient Cesl 2.0

- exceptional snow load [kN/m2] s Ad Cesl s k. s Ad 2.5=

- exceptional ground snow load [kN/m2] s r µ 1 Ce. Ct

. s Ad. s r 2=

2.3.2 Wind effect 2.3.2.1 Wind pressure on surfaces The effect is specified by the EC1-1-4. The wind load is the compressive or the sucking load which is caused by the wind effect. The wind load is perpendicular to the surface. The load may affect on the external and the internal surfaces as well. Besides the normal wind load the friction load of the wind effect may be considered. Any wind effect may be considered by a simplified set of loads which is equivalent to the effect of the turbulent peak velocity. The wind load belongs to the group of imposed loads. The wind effect depends on the following parameters of the building:

• dimensions; • shape; • dynamic properties.


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The external and internal wind pressure may be calculated by the following expressions:

peepe c)z(qw ⋅=

piipi c)z(qw ⋅=

where

)z(qp is the peak velocity pressure;

ie z,z is the external and internal reference heights;

pipe c,c is the external and internal pressure coefficients.

Figure 12 shows the physical direction of the wind loads in the cases of wind sucking (-) and wind pressure (+). It is noted that the summation of the wind loads should be done by these physical directions.

Fig.12 Physical direction of the wind loads in the cases of wind sucking (-) and wind pressure (+)

The reference heights may be determined using the following rules (see Figure 13): • if the height of the building (h) is not greater than the width (b) of the windward surface of

the building: hze = and ei zz = ;

• if the height of the building (h) is greater than b but it is not greater than 2b: - zone for height of b: bze = and ei zz = ;

- zone for height of (h-b): hze = and ei zz = .

Fig.13 Reference heights for plane buildings

(-) szí

(+)

b b

h

h

h ≤ b b < h ≤ 2b

ze=h b ze=b

ze=h maximum height

maximum height


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2.3.2.2 Peak velocity pressure The peak velocity pressure may be calculated by the following expression:

bep q)z(c)z(q ⋅=

where

)z(ce is the exposure factor;

bq is the basic velocity pressure.

The basic velocity pressure may be calculated as follows:

)z(v2

1q 2

bb ⋅= ρ

where the density of the air:

3m

kg25,1=ρ

and where the basic wind velocity:

0,bseasondirb vccv ⋅⋅=

According to the Hungarian National Annex (HNA) the initial basic wind velocity and the direction and season coefficients may be taken as

s

m6,23v 0,b = ; cdir=0,85 ; cseason=1,0

The exposure factor is the ratio of the peak velocity pressure to the basic velocity pressure, and it may be calculated by the following expression:

)z(c)z(c))z(I71()z(c 20

2rve ⋅⋅⋅+=

where

)z(cr is the roughness factor;

)z(c0 is the orography factor;

)z(Iv is the turbulence intensity.

The roughness factor depends on the reference height:

- if minzz < than

⋅=

0

minrr z

zlnk)z(c

- if minzz ≥ than

⋅=

0rr z

zlnk)z(c

where the terrain factor:


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07,0

II,0

0r z

z19,0k

=

where [ ]m05,0z II,0 = , see the second category (II) in the Table 4. In the expression 0z is the

roughness length and minz is the minimum height. These constants are given in the Table 4. Tab.4 Roughness lengths and minimum heights

terrain category 0z [m] minz [m]

0 Sea or coastal area exposed to the open sea 1 0,003 1 I Lakes or flat and horizontal area with negligible vegetation and

without obstacles 0,01 1

II Area with low vegetation such as grass and isolated obstacles (trees, buildings) with separations of at least 20 obstacle heights

0,05 2

III Area with regular cover of vegetation or buildings or with isolated obstacles with separations of maximum 20 obstacle heights (such as villages, suburban terrain, permanent forest)

0,3 5

IV Area in which at least 15 % of the surface is covered with buildings and their average height exceeds 15 m

1,0 10

When the average slope of the upwind terrain is less than 3°, the orography factor may be

0,1)z(c0 = .

The turbulence intensity may be calculated by the following expressions:

- if minzz < than

⋅

=

0

min0

Iv

z

zln)z(c

k)z(I

- if minzz ≥ than

⋅

=

00

Iv

z

zln)z(c

k)z(I

where the turbulence factor may be kI=1,0. The exposure factor can be calculated using the Figure 4.2 of EC1-1-4 (see the graphics below).


24

2.3.2.3 Application

2.3 Wind loads

2.3.1 Basic velocity pressure

- initial parameters specified by the Hungarian NAinitial basic velocity [m/s] v b.0 23.6

direction factor c dir 0.85

season factor c season 1.0

air density [kg/m 3] ρ 1.25

- basic velocity [m/s] v b c dir c season. v b.0

. v b 20.06=

- basic velocity pressure [kN/m 2]

q b1

2ρ. v b

2. 1

1000. q b 0.252=

2.3.2 Peak velocity pressure

- parameters for terrain category (Category III) z0 0.3

zmin 5.0

- parameter for category II [m] z0.II 0.05

- terrain factor k r 0.19z0

z0.II

0.07

. k r 0.215=

- reference height z H f z 9.019=

- roughness coefficient z zmin>

c r k r lnz

z0

. c r 0.733=

- orography coefficient (plane country, slope less than 3 degs) c 0 1.0

- turbulence coefficient (no specific rule) k I 1.0

- turbulence intensity I vk I

c 0 lnz

z0

.I v 0.294=

- exposure factor c e 1 7 I v. c r

2. c 02. c e 1.643=

q p c e q b. q p 0.413=- peak velocity pressure [kN/m2]

The peak velocity pressure can be determined or checked using the Figure 4.2 of the EN 1991-1-4:

reference height z 9.019=

terrain category: III

exposure factor by the graphics c e.graphics 1.63

peak velocity pressure [kN/m2] q p.graphics c e.graphicsq b.

q p.graphics 0.41=


25

2.3.2.4 External pressure coefficient The external pressure coefficients depend on the reference height and the size of the loaded area A, which is the area of the structure that produces the wind action in the section to be calculated. The external pressure coefficients are given for two loaded areas: - 1,pec is for area of 1.0 m2 as local coefficient;

- 10,pec is for area of 10.0 m2 as overall coefficient.

Between the two limit areas (for 1m2<A<10m2) the following interpolation may be used (see Figure 14):

Alg)cc(cc 1010,pe1,pe1,peA,pe ⋅−−=

Fig.14 Interpolation of the external pressure coefficient

In the present design project the interpolation may be neglected. For the design of the trapezoidal sheet the cpe.1 may be used, while for the design of the purlins and the main frames the cpe.10 may be used. The external pressure coefficients are given in tables. The tables for symmetric buildings with duopitch roofs are contained in the following Annexes: - Annex 1: Wind effect on vertical walls of the building - Annex 2: Cross wind effect on the roof (θ=0°) - Annex 3: Longitudinal wind effect on the roof (θ=90°)

Notes for application of the tables The tables of the external pressure coefficients have more rows (one row belongs to one slope) where there are two sub-rows (for example one “+” and one “-“ values). It is an important rule that for one roof plane (actually for the half roof) the sub-rows should not be changed. For example in the Annex 2 for roof slope of 5o there are two sub-rows which define four combinations:

Zones of the roof F G H I J

αααα=5o

cpe,10 cpe,1 cpe,10 cpe,1 cpe,10 cpe,1 cpe,10 cpe,1 cpe,10 cpe,1 1 -1,7 -2,5 -1,2 -2,0 -0,6 -1,2 -0,6 -0,6 +0,2 +0,2 2 -1,7 -2,5 -1,2 -2,0 -0,6 -1,2 -0,6 -0,6 -0,6 -0,6 3 0 0 0 0 0 0 -0,6 -0,6 +0,2 +0,2 4 0 0 0 0 0 0 -0,6 -0,6 -0,6 -0,6

The automatic use of the tables may lead to a large number of wind load cases. At the design of simple buildings the designer may select the most dangerous case by a decision based on his experience and intuition.

cpe,1 cpe,10

0,1 1,0 10,0 A(m2)


26

2.3.2.5 Application

2.3.3 External wind pressure

2.3.3.1 Cross wind (0 degree)

Initial parameters

- size of the building [m]width perpendicular to the wind direction b 0 d b 0 36=

width parallel to the wind direction d 0 b d 0 20=

height h 0 H f h 0 9.019=

η 0h 0

d 0η 0 0.451=- size factor

- size of the zones [m] e0 2 h 0. e0 18.038=

e0.4e0

4e0.4 4.51=

e0.10e0

10e0.10 1.804=

-slope of the roof (approximately) [deg] 10

Indeces used below A,B,... mark of the wall and the roof zone 0; 90 mark of the wind direction in degree

1;10 mark of the loaded area (1m2 or 10 m2)

Wind pressure on the walls

According to Annex 1:

- interpolation factor for the case of 0,25<h/d<1,0 β 0η 0 0.25

0.75β 0 0.268=

- pressure coefficients

c pe.A.0.10 1.2

c pe.B.0.10 0.8

c pe.C.0.10 0.5

c pe.D.0.10 0.7 0.1β 0. c pe.D.0.10 0.727=

c pe.E.0.10 0.3 0.2β 0. c pe.E.0.10 0.354=

- wind pressures [kN/m2]

w A.0.10 c pe.A.0.10q p. w A.0.10 0.496=

w B.0.10 c pe.B.0.10q p. w B.0.10 0.33=

w C.0.10 c pe.C.0.10q p. w C.0.10 0.207=

w D.0.10 c pe.D.0.10q p. w D.0.10 0.3=

w E.0.10 c pe.E.0.10q p. w E.0.10 0.146=

Wind pressure on the roof

Annex 2 contains the pressure coefficients for roof slope of 10 deg which were interpolated linearly between 5 and 15 degrees given by the EN 1991-1-4. For roof zones of F-G-H there are two cases: wind sucking and wind pressure.

zones of F-G-H

- wind sucking [kN/m 2] c pe.F.0.1 2.25 w F.0.1 c pe.F.0.1q p

. w F.0.1 0.929=

c pe.F.0.10 1.30 w F.0.10 c pe.F.0.10q p. w F.0.10 0.537=


27

c pe.G.0.1 1.75 w G.0.1 c pe.G.0.1q p. w G.0.1 0.723=

c pe.G.0.10 1.0 w G.0.10 c pe.G.0.10q p. w G.0.10 0.413=

c pe.H.0.1 0.75 w H.0.1 c pe.H.0.1q p. w H.0.1 0.31=

c pe.H.0.10 0.45 w H.0.10 c pe.H.0.10q p. w H.0.10 0.186=

- wind pressure [kN/m2] c pe.FGH.0 0.1 w FGH.0 c pe.FGH.0q p

. w FGH.0 0.041=

c pe.I.0.1 0.50 w I.0.1 c pe.I.0.1q p. w I.0.1 0.207=

c pe.I.0.10 0.50 w I.0.10 c pe.I.0.10q p. w I.0.10 0.207=

c pe.J.0.1 0.65 w J.0.1 c pe.J.0.1q p. w J.0.1 0.269=

c pe.J.0.10 0.4 w J.0.10 c pe.J.0.10q p. w J.0.10 0.165=

2.3.3.2 Longitudinal wind direction (90 degrees)

Initial parameters

- size of the building [m]

width perpendicular to the wind direction b 90 b b 90 20=

width parallel to the wind direction d 90 d d 90 36=

height h 90 H f h 90 9.019=

- size factor η 90h 90

d 90η 90 0.251=

- size of the zones [m]e90 2 h 90

. e90 18.038=

e90.2e 90

2e90.2 9.019=

e90.4e 90

4e90.4 4.51=

e90.5e 90

5e90.5 3.608=

e90.10e90

10e90.10 1.804=

- slope of the roof (approximately) [deg] 10

Wind pressure on the walls

According to Annex 1

- size factor β 90h 90

d 90β 90 0.251=


c pe.A.90.10 1.2

c pe.B.90.10 0.8

c pe.C.90.10 0.5

c pe.D.90.10 0.7

c pe.E.90.10 0.3


28

- wind pressures [kN/m2] w A.90.10 c pe.A.90.10q p. w A.90.10 0.496=

w B.90.10 c pe.B.90.10q p. w B.90.10 0.33=

w C.90.10 c pe.C.90.10q p. w C.90.10 0.207=

w D.90.10 c pe.D.90.10q p. w D.90.10 0.289=

w E.90.10 c pe.E.90.10q p. w E.90.10 0.124=

Wind pressure on the roof

According to Annex 3

c pe.F.90.1 2.1 w F.90.1 c pe.F.90.1q p. w F.90.1 0.868=

c pe.F.90.10 1.45 w F.90.10 c pe.F.90.10q p. w F.90.10 0.599=

c pe.G.90.1 2.0 w G.90.1 c pe.G.90.1q p. w G.90.1 0.826=

c pe.G.90.10 1.30 w G.90.10 c pe.G.90.10q p. w G.90.10 0.537=

c pe.H.90.1 1.2 w H.90.1 c pe.H.90.1q p. w H.90.1 0.496=

c pe.H.90.10 0.65 w H.90.10 c pe.H.90.10q p. w H.90.10 0.269=

c pe.I.90.1 0.55 w I.90.1 c pe.I.90.1q p. w I.90.1 0.227=

c pe.I.90.10 0.55 w I.90.10 c pe.I.90.10q p. w I.90.10 0.227=

2.3.2.6 Internal pressure coefficient

Internal and external pressures shall be considered to act at the same time (but external pressure may act without internal pressure). The internal pressure coefficient (cpi) depends on the size and distribution of the openings (windows and doors). When in at least two sides of the buildings (walls or roof) the total area of openings in each side is more than 30 % of the area of that side, the actions on the structure should not be calculated from the rules given here. For a building with a dominant face the internal pressure should be taken as a fraction of the external pressure at the openings of the dominant face. A face of a building should be regarded as dominant when the area of openings at that face is at least twice the area of openings and leakages in the remaining faces of the building considered. When the area of the openings at the dominant face is twice the area of the openings in the remaining faces, pepi c75,0c ⋅=

When the area of the openings at the dominant face is at least 3 times the area of the openings in the remaining faces, pepi c90,0c ⋅=

where cpe is the value for the external pressure coefficient at the openings in the dominant face. When these openings are located in zones with different values of external pressures an area weighted average value of cpe should be used. In the present design project we may assume that there is no dominant face and the distribution of the openings is uniform. In this case the internal pressure coefficient may be calculated as follows:


29

• if 25,0d/h ≤ - if 33,0≤µ than 35,0cpi =

- if 9,0>µ than 3,0cpi −=

- if 9,033,0 ≤< µ than µ14,1726,0cpi −=

• if 0,1d/h ≥ - if 33,0≤µ than 35,0cpi =

- if 95,0>µ than 5,0cpi −=

- if 95,033,0 ≤< µ than µ37,1802,0cpi −=

The opening ratio in the expressions may be calculated with the following term:

∑∑=

A

Anegµ

where ∑ negA is the area of openings where cpe is negative or zero and∑A is the area of all

areas. 2.3.2.7 Application

2.3.4 Internal wind pressure

2.3.4.1 Parameters of the openings

- area of openings in the side walls [m2]

width of the area of windows [m] L w.s 23.2

height of the area of windows [m] h w.s 1.2

A s L w.s h w.s. A s 27.84=

- area of openings in the end walls [m2]

windows width of the area of windows [m] L w.e 12.6

height of the area of windows [m] h w.e 1.2

A e.w L w.e h w.e. A e.w 15.12=industrial door

width of the door [m] b w.d 5.0

height of the door [m] h w.d 4.6

A e.d b w.d h w.d. A e.d 23=

A f A e.w A e.d A f 38.12=

2.3.4.2 Cross wind effect (0 degree)

- initial parameters

area of all openings [m2] A sum 2 A s A f. A sum 131.92=

area of openings with negative or zero external pressure [m2]

A neg.0 A s 2 A f. A neg.0 104.08=


30

opening ratio µ 0A neg.0

A sumµ 0 0.789=


for h/d=0.25

c pi.0.0.25 0.726 1.14µ 0. c pi.0.0.25 0.173=

for h/d=1.00 c pi.0.1 0.802 1.37µ 0. c pi.0.1 0.279=

c pi.0 c pi.0.0.25 β 0 c pi.0.1 c pi.0.0.25. c pi.0 0.202=

- wind pressure [kN/m2]

w i.0 c pi.0 q p. w i.0 0.083=

2.3.4.3 Longitudinal wind effect (90 degrees)

- initial parameters

area of openings with negative and zero external wind pressure coefficient [m2]A neg.90 A f 2 A s

. A neg.90 93.8=

opening ratioµ 90

A neg.90

A sumµ 90 0.711=

- internal pressure coefficient

for h/d<0.25 c pi.90 0.726 1.14µ 90. c pi.90 0.085=

- wind pressure [kN/m2]

w i.90 c pi.90q p. w i.90 0.035=

2.4 Imposed loads The imposed loads are specified by the EC1-1-1. The determination of the imposed loads should be based on careful examination of the design situation and extended consultations with the design partners (mechanical designer, electrical designer, etc.). The roof structures are classified into categories. The standard orders a distributed and a concentrated fictive load to every category. In the present design situation the walking on the roof is not allowed, except maintenance and repairing work, therefore the roof belongs to the category H. Table 5 shows the design imposed loads for the category H.

Tab.5 Imposed loads for roof of category H slope of roof

α distributed load

2k m

kNq

concentrated load [ ]kNQk

o10≤ 0,4 1,0 o20≥ 0 0

Notes: between the two limits linear interpolation may be used The imposed load and the snow load shall not be considered to act at the same time. Since the effect of the snow load is greater, the imposed load may be neglected in the present design. It is noted that the concentrated imposed load (Qk) may be relevant at the design of the trapezoid sheet and the purlins, but it is considered by the design software (DimRoof).


31

2.5 Seismic effect The seismic effect is specified by the EC8-1. Due to the earthquake the displacement and the acceleration of the ground is changing in time. The seismic design of the buildings is based on the consideration of the ground acceleration. The acceleration has vertical and horizontal components, but in Hungary the vertical component may be neglected. The horizontal component of the ground acceleration depends on the reference peak ground acceleration of type A ground:

gRIg aa ⋅= γ

where agR is the reference peak ground acceleration of type A ground (see Figure 15), γI is the importance factor given in Table 6. The building in the present design project may belong to importance category I or II.

Tab.6 Importance categories of buildings importance category importance factor

γγγγI I. Buildings of minor importance for public safety, e.g. agricultural

buildings, etc. 0,8

II. Ordinary buildings, not belonging in the other categories. 1,0 III. Buildings whose seismic resistance is of importance in view of

the consequences associated with a collapse, e.g. schools, assembly halls, cultural institutions etc.

1,2

IV. Buildings whose integrity during earthquakes is of vital importance for civil protection, e.g. hospitals, fire stations, power plants, etc.

1,4

Fig.15 The reference peak ground acceleration of type A ground in Hungary

2.6 Fire effect The fire effect on the building is specified by the EC1-1-2. In the present design project the standard (ISO) fire curve should be considered at the design of the main frame. The required fire resistance is 15 minutes, R15, which means of fire resistance class IV and one floor building. All the steel structural members (I sections) of the main frame are unprotected,


32

and they are imposed to fire effect at four sides. The main frame is examined for fire effect as an isolated structure, and the room which is specified by the frame is a unified fire compartment (see the Figure 16).

Fig.16 Unified fire compartment of the isolated main frame structure

2.7 Application

2.4 Imposed load

- service class of the roof: H

- slope of the roof: α=10o

- imposed loadsurface distributed load [kN/m2] q k 0.4

concentrated load [kN] Q k 1.0

2.5 Seismic effect

- importance category of the building: II.γ I 1.0- importance factor

-seismic zone: region of Esztergom, Hungary

- horizontal component of the reference peak ground acceleration [m/s 2]

a gR 1.5 [m/s2]

2.6 Fire effect

- applied temperature-time curve: standard (ISO)

- category of fire resistance: IV (simple building)

- required limit for fire resistance (R15) t fi 15 [min]

- type of the passive fire protection: "unprotected I section exposed to fire at four sides"

- fire compartment: "internal room determined by the main frame structure"

Standard fire curve Required resistance: 15 min

Unprotected


33

Annex 1 External pressure coefficient for vertical walls

(it is valid for case of h<b)

zones A B C D E

h/d

cpe,10 cpe,1 cpe,10 cpe,1 cpe,10 cpe,1 cpe,10 cpe,1 cpe,10 cpe,1 1 -1,2 -1,4 -0,8 -1,1 -0,5 0,8 1,0 -0,5

≤0,25 -1,2 -1,4 -0,8 -1,1 -0,5 0,7 1,0 -0,3

w b

d

D E

e/5

e

A B C

e/5

A B

Top view

side

h

A B C

A B

h

Side zones for e<d:

)h2;bmin(e=

Side zones for e>d:

Note In the case of rectangular building b is the width of the side which is affected by the wind, and d is the width of the perpendicular side. The wind may affect to the longitudinal side (θ=00) and to the front side (θ=900), respectively.

0


34

Annex 2 External pressure coefficients of the roof due to cross wind (θθθθ=00)

(it is valid for case of h<b)

zones F G H I J

αααα

cpe,10 cpe,1 cpe,10 cpe,1 cpe,10 cpe,1 cpe,10 cpe,1 cpe,10 cpe,1 +0,2 +0,2 +0,2 +0,2 0* -1,8 -2,5 -1,2 -2,0 -0,7 -1,2 -0,2 -0,2 -0,2 -0,2

-1,7 -2,5 -1,2 -2,0 -0,6 -1,2 +0,2 +0,2 5 +0,0 +0,0 +0,0 +0,0 +0,0 +0,0

-0,6 -0,6 -0,6 -0,6

-1,3 -2,25 -1,0 -1,75 -0,45 -0,75 -0,4 -0,65 10** +0,1 +0,1 +0,1 +0,1 +0,1 +0,1

-0,5 -0,5 -0,3 -0,3

-0,9 -2,0 -0,8 -1,5 -0,3 -0,3 -0,4 -0,4 -1,0 -1,5 15 +0,2 +0,2 +0,2 +0,2 +0,2 +0,2 +0,0 +0,0 +0,0 +0,0

* given for the case of sharp eaves of flat roof (no parapet or curved eaves) ** given by linear interpolation between slopes of α=50 and α=150

e/10 e/10

h α

w θθθθ=00

w

G H J I

F

F e/4

e/4

Ridge

b


35

Annex 3 External pressure coefficients of the roof due to longitudinal

wind (θθθθ=900) (it is valid for case of h<b)

F G H I αααα

cpe,10 cpe,1 cpe,10 cpe,1 cpe,10 cpe,1 cpe,10 cpe,1 +0,2 +0,2 0* -1,8 -2,5 -1,2 -2,0 -0,7 -1,2

-0,2 -0,2

5 -1,6 -2,2 -1,3 -2,0 -0,7 -1,2 -0,6 -0,6 10** -1,45 -2,1 -1,3 -2,0 -0,65 -1,2 -0,55 -0,55 15 -1,3 -2,0 -1,3 -2,0 -0,6 -1,2 -0,5 -0,5

* given for the case of sharp eaves of flat roof (no parapet or curved eaves) ** given by linear interpolation between slopes of α=50 and α=150

h

θθθθ=900 w

w

G

H

I

F

H

e/2

e/10

Ridge

G

F

e/4 I

e/4


36

Practice 4

DESIGN OF THE SECONDARY ELEMENTS


2010-2011 Budapest


37

4.1 General In this project the external trapezoidal sheet and the purlins as secondary elements are designed. The design of the elements of the façade is based on the same methods, therefore it is neglected. The design methods are specified by the EN 1993-1-3 Eurocode 3: Design of Steel structures Part 1-3: Cold-formed thin gauge members and sheeting (EC3-1-3). The theoretical background of this code is the objective of the MSc courses. The most important expressions used in the design are summarized in the Table 7. In the practice the direct use of the theory and methods given by the code may be neglected since the producers of the products (purlins, sheeting) supply design tables and design software. Design of the Lindab elements is supported by the DimRoof software which is suggested using in this project. The software may be safely used without any deep knowledge of theoretical background on the design of cold-formed thin gauge elements. Tab.7: Most important expressions used in design theory of cold-formed thin gauge elements (informative)

special structural properties special structural behaviors specialties in design

Large plate slenderness (b/t) Plate buckling „Shear lag” effect Flange induced buckling

Class 4 cross-sections

Partially stiffened plates

Distorsional instability Class 4 cross-sections Buckling of the stiffeners

One symmetric or no symmetric cross sections

Lateral torsional buckling Flexural-torsional buckling

Class 4 cross-sections Global instability

Relatively thin plates Relatively large initial geometrical imperfections

Plate thickness as the parameter of the design

Special connections Special structural failing modes New design methods based on tests

The loads for design of the purlins and sheeting should be calculated taking the effects of the slope of roof, the directions of the loads and the constructions into consideration by the following rules:

� dead load and snow load are gravity loads with vertical direction; � wind pressure is perpendicular to the structural plane; � design load consists of transverse loads only (the loads which are parallel with the axis

of elements may be neglected). These rules lead to the reduction of the loads (see Figure 17). It is noted that in case of relatively small (5o÷10o) slope of roof the approximation of cosα≅cos2α≅1 may be on the safe side.


38

Fig. 17 Reduction of loads

4.2 Design of the external trapezoidal sheet Figure 8 shows the alternative constructions for covering system. Both systems have external trapezoidal sheet which should be designed. 4.2.1 Structural model The structural model of the external trapezoidal sheet may be approximated by a multispan continuous beam (see Figure 18), which is perpendicular to the purlins supporting it rigidly. The reference axis of the model lies in the plane of the roof. The length c1 depends on the covering system, the length c2 is the distance between the last purlin and the ridge point (150÷200 mm).

Fig. 18 Structural model for external trapezoidal sheet

Figure 19 shows the cross-section of the beam (as 1000 mm wide part of sheet). In the case of Lindab products the cross-section is defined by the nominal depth (eg. LTP45) and the thickness of the plate (eg. t=0,5 mm).

Slope of roof: α [deg]

Ridge point Edge point

Basic load [kN/m2]

ps

Design load [kN/m2]

α2s cosp ⋅

pg

pw

αcospg ⋅

wp

Dead laod

Snow load

Wind load

Ridge point Edge of building Purlins as rigid supports

c1 c2


39

Fig. 19 Cross-section for the beam model

4.2.2 Load model The sizes of the trapezoidal sheets (external and internal) normally uniform on the whole roof. For the load model the adequate loading area (the load band with 1000 mm width) along the longitudinal direction of the roof should be found (see Figure 20). The dead load and the snow load are uniformly distributed, therefore the position of the load band does not matter. The intensity of the wind load is changing from zone to zone of the roof, therefore the maximum wind pressure (Wind Load Case 1) and the maximum wind sucking (Wind Load Case 2) should be found. The wind pressure, the dead load and the snow load may be the components of Load Combination 1, while the wind sucking and the dead load may be the components of Load Combination 2. For example, in case of 50 slope of and assuming cross wind, both of wind pressure and wind sucking occur on zone J but wind sucking occurs only on zones F and G (see Annex 2) which are greater than that on zone J. Assuming longitudinal wind there are no zones where wind pressure occurs and the maximum wind sucking may occur on zones F and G (see Annex 3). Consequently, the adequate place of the load band may be considered as it is shown in Figure 20. We have to take the conclusion that the determination of the load model needs an enthusiastic work.

Fig. 20 Adequate positions of load bands in case of wind effect

(for 50 slope of roof)

1000 mm

Depth

Plate thickness (t)

Ridge line

H

G F F

Wind direction: 0 degree

H

G

F

I

Wind direction: 90 degrees

Ridge line

J

I

wind load case 2

wind load case 1


40

In the practice we may use approximations at the load model but it should be noted that the engineer is responsible for the consequences: approximation at side of safe may lead to extra costs, while approximation at side of unsafe may be against the law. The following two load combinations may be adequate for the examination of the external trapezoidal sheet in persistent and transient design situations: Load Combination 1 („pressure load”)

- ultimate limit state (ULS): p.k.ww.wssgsup,G ppp ⋅⋅+⋅+⋅ γψγγ 0

- serviceability limit state (SLS): p.k.w.wsg ppq ⋅++ 0ψ

Load Combination 2 („sucking load”) - ultimate limit state (ULS): s.k.wwginf,G p""p ⋅+⋅ γγ

- serviceability limit state (SLS): s.k.wg p""p +

The following indices are used in the above expressions:

gp characteristic value of the uniformly distributed dead load in [kN/m];

sp characteristic value of the uniformly distributed snow load in [kN/m];

k.wp characteristic value of the non uniformly (but uniformly within a zone) distributed

wind load in [kN/m] due to cross or longitudinal wind direction, which is the relevant, and “p” denotes wind pressure, “s” denotes wind sucking. These loads can be calculated directly from the basic loads which were defined for the building (see Practice 2). The accidental snow load is neglected in this project. The following partial factors should be used: 515101351 , ,, ,, ,, wsinfG,sup,G ==== γγγγ

The following combination factor should be used: ψw.0=0,6 The ULS load combination is relevant for checking the resistances, while the SLS load combination is relevant for checking the deflections, where the suggested limit is L/150 (L is the span of sheet). 4.2.3 Design and Documentation Design of thin gauged Lindab trapezoidal sheet may be carried out using the DimRoof design software. The application of the software is described in Annex 4. Before starting design the following General Settings (design parameters) should be defined: � Function

Trapezoidal sheet belongs to “Roof” category. � Country

By option of “Hungary” we specify the Hungarian National Annex to be used. � Standard

The design is governed by the „Eurocode” standard system. � Profile

The depth of the Lindab trapezoidal sheet (LTP) may be 20 mm÷150 mm. Here the adequate depth should be selected.

� Extra Sidelap The type of the sidelap (“no”; “ 1 trough”; 2 trough” or “double”) is determined by the architectural engineer. In this project “1 trough” is suggested using.

� Default statical model Lap of sheeting should be avoided in longitudinal direction. The length of the sheets is limited by the transportability. In this project “continuous” model is suggested.


41

The Geometry (geometrical parameters) is defined by the following parameters: � Spans � Thickness of the plate (t=0.4 mm÷0.7 mm); � Type and width of the supports The Loads (parameters of loading) are defined by the following parameters: � Type of load - „U - uniform”: the load acts along the whole beam as uniformly distributed load; - „L - linear”: the load acts along a part of the beam, and/or its intensity is changing linearly; (in the first case only the intensity should be defined, in the second case the coordinates and the load intensities at the starting and end points of the loaded domain should be defined) � Load attribute - „ULS”: load to examine the resistances of element; - „SLS”: load to examine the deflection of element. It is noted that the software can take one ULS and one SLS load combinations into consideration at the same time. Both of the combinations may contain more load components (one load component is defined by one row in the table).

The analysis and check can be run by the Calculate! button. The results of ULS and SLS are given in [%]. More details of design may be available by the Relative Results and the Absolute Results buttons. If one of the results exceeds 100%, or it is less than 50-60%, the profile should be modified. The modification means change in plate thickness or/and in depth of sheet. After the modification the analysis and design should be repeated. The final result of the design may be documented by the following parameters: � Depth of the profile (eg. LTP 85) � Plate thickness (eg. t=0,75 mm) � ULS capacity in [%]; � SLS capacity in [%] (with the limit for deflections, such as L/150)

4.2.4 Application

3. DESIGN OF COVERING ELEMENTS

In the design project the external trapezoidal sheet and the purlins of the roof system are designed. Design of the wall elements is neglected.

3.1 Design of external trapezoidal sheet

3.1.1 Geometric model

The external trapezoidal sheet of the roof system is modelled by multispan beam as shown below. Parameters of the trapezoidal sheet: LTP85 t=0,75 mm.

250 2597 2597 2597 2447 150


42

3.1.2 Load model

Loads are given in [kN/m] for 1000 mm width of sheet.

3.1.2.1 Characteristic loads

- dead load (self weight of the trapizoidal sheet according to Section 2.1.1)

q dead q tr.extcos α π180

.. q dead 0.084=

- snow load (totally distributed load according to Section 2.2.1)

p snow s cos α π180

.2

. p snow 0.97=

- wind load

cross wind (wind effect according to Section 2.3.4.1)

a) wind suckingp wind.0.F.s w F.0.1 p wind.0.F.s 0.929=

p wind.0.H.s w H.0.1 p wind.0.H.s 0.31=

b) wind pressure p wind.0.FGH.p w FGH.0 p wind.0.FGH.p 0.041=

longitudinal wind (wind effect according to Section 2.3.4.2)

a) wind sucking

p wind.90.F w F.90.1 p wind.90.F 0.868=

p wind.90.G w G.90.1 p wind.90.G 0.826=

b) wind pressure: negligable

3.1.2.2 Design load combinationsPartial factors

γ G.sup 1.35 γ G.inf 1.0dead load

snow load γ s 1.5

wind effect γ w 1.5

Combination factorswind effect Ψ w.0 0.6

4,625

1,850

F - zóna

G - zóna

1,85

4,625

F - zóna

H - zóna


43

Load Combination 1 : 'Pressure effect' (signed by 'p')

Effect of gravity (dead and snow) loads is increased by wind effect on zones F and G

p p.ULS γ G.supq dead. γ s p snow

. Ψ w.0 γ w. p wind.0.FGH.p

. p p.ULS 1.599=

p p.SLS q dead p snow Ψ w.0 p wind.0.FGH.p. p p.SLS 1.074=

Load Combination 2 : 'Sucking effect' (signed by 's')

Maximum wind sucking from longitudinal wind effect Zone Fp s.ULS.F γ G.infq dead

. γ w p wind.90.F. p s.ULS.F 1.218=

p s.SLS.F q dead p wind.90.F p s.SLS.F 0.784=

Zone Gp s.ULS.G γ G.infq dead

. γ w p wind.90.G. p s.ULS.G 1.156=

p s.SLS.G q dead p wind.90.G p s.SLS.G 0.743=

3.1.2.3 Check of the limit states

External trapezoidal sheet is checked for ultimate and servicebility limit states using the DimRoof 3.3 design software. Results of the calculations:- ULS: 49% (Case 1)- SLS (with maximum deflection L/150): 36 % (Case 1)For details see the Annex.

Lindab LTP85 t=0,75mm trapezoidal sheet is adequate! (LTP45 trapezoidal sheet would be not adequate for SLS.)

4.3 Design of purlins 4.3.1 Geometrical model The structural model of the purlin may be approximated by a multispan continuous beam (see Figure 21) which is perpendicular to the main frames. The frames support the beam rigidly. The top flange of the Z purlin is restrained laterally by the trapezoidal sheet. The bottom flange may be restrained laterally, if the insulation is placed in the room of purlins (see Figure 8a). The load acts in the intersection point of the web and top flange. These sophisticated conditions are modeled by the design software.

ps.ULS.F ; ps.SLS.F

4 625

ps.ULS.G ; ps.SLS.G

pp.ULS ; pp.SLS


44

Fig. 21 Structural model for design of purlin

4.3.2 Load model The roof structure normally consists of uniformly sized purlins. The dead load and the snow load are totally and uniformly distributed, therefore that purlin should be examined which has the greatest width of loading area. The wind load acts on zones with different wind pressures, therefore the place of the maximum pressure and the maximum sucking should be found. The maximum wind pressure acts with the dead load and the snow load together (Load Combination 1), while the maximum wind sucking acts with the dead load (Load Combination 2). It is noted that all the possible load combinations should be examined carefully.

Fig. 22 Load bands for check of purlins

(valid for purlin system with uniform interval and 100 slope of roof)

Ridge line

H

G F F

H G I

Wind direction (90 deg)

Ridge line Load Combination 2/b (sucking)

Wind direction (0 deg)

Load Combination 1 (pressure)

purlin

Ridge line

H

Load Combination 2/a (sucking)

purlin

purlin

Y

Z

p [kN/m]

Main frames as supports

Effect of internal trapezoidal sheet, if there is.

Effect of external trapezoidal sheet.


45

For example, in case of 100 slope of roof and assuming cross wind, wind pressure occurs only on zones F, G and H but on the other zones wind sucking acts only (see Annex 2). Assuming longitudinal wind sucking occurs on all the zones (see Annex 3). The maximum wind sucking acts on zones F and G. In case of purlin design the internal wind effect should be considered. According to the above statements, the following load combinations should be taken into consideration (Figure 22): Load Combination 1: Load combination consists of dead load and snow load, and the effects of external wind pressure (ext.p) and internal wind sucking (int.s): ULS: ( )s.int.wp.ext.wwssgsup,G pppp +⋅⋅+⋅+⋅ γψγγ 0

SLS: ( )s.int.wp.ext.wsg pppp +⋅++ 0ψ

Load Combination 2: Load combination consists of dead load and the effects of external wind sucking (ext.s) and internal wind pressure (int.p) at zones F and G:

ULS: ( )p.int.ws.ext.wwginf,G pp""p +⋅+⋅ γγ

SLS: ( )p.int.ws.ext.wg pp""p ++

The load components used in the above load combinations may be calculated from the basic loads which were determined in Practice 2: pg uniformly distributed dead load in [kN/m]; ps uniformly distributed snow load in [kN/m]; pw distributed wind load on the actual zone due to cross or longitudinal wind effect in [kN/m], which is the relevant. Furthermore, index “ext” denotes the external wind effect, index “int” the internal one, while index “p” denotes pressure and index “s” sucking. The partial factors to be used: γG,sup=1,35; γG,sup=1,0, γS=1,5 és γw=1,5 The combination factor to be used: ψ0=0,6. The ULS load combination is relevant for checking the member resistances, while the SLS load combination is relevant for check deflection of members, where the usually used limit is L/150 (L is the span of the beam). The accidental snow load is neglected in this project. 4.3.3 Design and Documentation Design of thin gauged Lindab purlin may be carried out by the DimRoof design software. The application of the software is described in Annex 5. Before the stating of the design the following General Settings should be defined: � Function

Design of purlin belongs to the option “Z-beam”). � Country

Selecting “Hungary” use of the Hungarian National Annex is specified. � Standard

Design is governed by the „Eurocode” standard system. � Anti-seg bars

The purlins may be supported laterally by anti-seg bars at midspans in plane of roof. In this design project, due to the small slope, these bars are not used, therefore option “None” should be selected.

� Profile The depth of Lindab Z purlin may change between 100 mm and 350 mm. The initial depth should be selected here.


46

� Default static model Different static models may be used. Relatively short elements offer easy transportation, therefore the overlapped solution is suggested for using (10-10% overlapping at every support, except the second ones at the ends where it is 20%). For this the option of “Overlapped Standard” should be used.

� Lateral Support Z purlin may be supported laterally at both flanges (see Figure 8a) or at top flange (see Figure 8b). The option “Both flanges” or “Top flange” may be used.

� Sheeting Lateral restraint effect depends on the size of the trapezoidal sheet is used (Profile, Thickness).

� Screws The load carrying capacity of purlin may depend on the size and the grade of the bolts (screws) which connect the trapezoidal sheet to the purlins and the purlins to the main frames: - Plate: grade of screws which connect the trapezoidal sheet to the top flange of the purlins (“4.8” or “5.5”); - Overlap: grade of screws which connect the webs of purlins to each other close to the supports (“4.8” , “ 5.5” or “6.3” ); - Support: grade of bolt which connect the webs of the purlin to the main frame (“5.5” or “6.3” ); - Distance: distance between bolts which connect the trapezoidal sheet to the top flange of the purlins (“one/bottom” or “one/2nd bottom”).

The Geometry of the purlin should be defined by the following parameters: Spans � Length Purlins are supported by the main frames. The length of spans should be defined from the

left end to the right end of the beam. � Th.1

Plate thickness may be as follows: „1,0” – „1,2” – „1,5” – „2,0” – „2,5” Supports � L1 and L2

According to option “Overlapped Standard” the software takes 10-10% overlapping at both sides of the supports.

� Type Different types of support may be used. According to option “Overlapped Standard” the

software takes hinged (“H”) supports at the ends of the beam, and overlapped (“O” ) supports at the intermediate ones.

� Width Width of the supports should be defined by the user. For type “H” it may be the width of the flange of the frame, for type “O” it may be the distance between the bolts which connect the purlin to the stub (stub is welded to the top flange of the frame).

The loads should be defined by the following parameters. It is noted that the software can consider one ULS and one SLS load combinations at the same time. Both of the combinations may contain more load components (one load component is defined by one row in the table). � Type The software uses more types of loads. In this project we use the following types: - uniformly distributed load along the whole beam (option „U”); - linearly distributed load on a part of the beam (option „L”).


47

� Start p./End p. In case of “L” type load they are the coordinates of the start point and the end point of the

linearly distributed load, taking the direction from left to right. � Start int./End int. In case of “U” type of load it is the load intensity at the start point. In case of “L” type

load both of the start and end load intensities should be defined. � ULS/SLS

For every load component (for every row) the type of load combination should be defined (ULS for load carrying capacities, SLS for serviceability capacity calculations).

The analysis and check can be start by the Calculate! button. The results of ULS and SLS calculations are given in [%]. More details may be available by the Relative Results and the Absolute Results buttons. If one of the results exceeds 100%, or it is less than 50-60%, the profile should be modified. The plate thickness or/and the depth of the purlin may be modified. After the modification the analysis and design should be repeated. The final result of the design may be documented by the following parameters: � Depth of profile (eg. Z250) � Plate thickness (eg. t=1,5 mm) � ULS used part of capacity in [%]; � SLS used part of capacity in [%] (with the limit for deflections, such as L/150)

4.3.4 Application

3.2 Design of purlins

3.2.1 Geometric model

Purlins are modeled by a many supported beam shown below:

3.2.2 Load model

3.2.2.1 Load combinations in general

Intervals between purlins are uniform, therefore the place of the examined purlin does not matter. Wind pressure and maximum wind sucking occur at zones F and G. Consequently, the purlin next to the edge beam should be examined.

Load Combination 1: Combination for pressure loads (signed by 'p')Load Combination 2: Combination for wind sucking (signed by 's') Width of load area [m]

c Le4

1000c L 2.598=

6 000 6 000 6 000 6 000 6 000 6 000

Z 250 (t=2.5 mm)

Y

X

Z


48

3.2.2.2 Characteristic loads

Dead loadSelf weight of purlin, external trapezoidal sheet, insulation and internal trapezoidal sheet according to Section 2.1.1 in [kN/m]:

q dead c L q tr.ext q tr.int q iso q iso.other. cos α π

180.. q purlin cos α π

180..

q dead 1.194=

Snow load Totally distrubuted snow load according to Section 2.2.1 in [kN/m]:

p snow c L s. cos α π180

.2

. p snow 2.52=

Wind load Case 1: pressure due to cross wind on zones F and G

- external wind effect p wind.1.ext c L w FGH.0. p wind.1.ext 0.107=

- internal wind effect p wind.1.int c L w i.0. p wind.1.int 0.216=

Case 2: a) sucking due to cross wind on zones F and G- external wind effect

zone F p wind.2.a.F c L w F.0.10. p wind.2.a.F 1.395=

zone G p wind.2.a.G c L w G.0.10. p wind.2.a.G 1.073=

- internal wind effect: opposite to external wind effect, it is negligable b) sucking due to the longitudinal wind on zones F and G

- external wind effect zone F p wind.2.b.F c L w F.90.10

. p wind.2.b.F 1.556=

zone G p wind.2.b.G c L w G.90.10. p wind.2.b.G 1.395=

- internal wind effect: opposite to the external wind effect, it is negligable3.2.2.3 Design load combinations

Partial factorsdead load γ G.sup 1.35 γ G.inf 1.0

snow load γ s 1.5

wind load γ w 1.5

Combination factor for wind effect Ψ w.0 0.6

Load combinations for two load cases [kN/m]Load Combination 1 : Pressure effectULS p p.ULS γ G.supq dead

. γ s p snow. Ψ w.0 γ w

. p wind.1.ext p wind.1.int.

SLS p p.SLS q dead p snow Ψ w.0 p wind.1.ext p wind.1.int. p p.ULS 5.683=

p p.SLS 3.908=

pp.ULS ; pp.SLS

cL

purlin to be designed


49

Load Combination 2 : Sucking effect - longitudinal wind is dominant

zone F ULS p s.ULS.F γ G.infq dead. γ w p wind.2.b.F

. p s.ULS.F 1.118=

SLS p s.SLS.F q dead p wind.2.b.F p s.SLS.F 0.34=

zone G ULS p s.ULS.G γ G.infq dead. γ w p wind.2.b.G

. p s.ULS.G 0.877=

SLS p s.SLS.G q dead p wind.2.b.G p s.SLS.G 0.179=

3.2.2.4 Check of the limit states

Check of the ultimate and servicebility limit states was carried out by DimRoof 3.3 software: Results for pressure effect:- ULS: 71 %- SLS: 35 % (for maximum deflection of L/150)

Results for sucking effect:- ULS: 14 %- SLS: 3 % (for maximum deflection of L/150)

Details of calculation can be found in Annex.

LINDAB Z250 (t=2.5mm) purlin is adequate (Z200 would be not adequate)

ps.ULS,F ps.SLS,F ps.ULS.F ; ps.SLS.F ps.ULS,G ps.SLS.G

4625 4625


50

ANNEX 4 Design of trapezoidal sheet using DimRoof software

(User’s Manual) A4.1 Setting - download the dimroof_xx_telepités.zip file from the departmental portal (www.hsz.bme.hu/Oktatás/Magasépítési acélszerkezetek/Gyakorlat) - unzip the file and run the Dimroof_33_install.exe - send the required data to the responsible teacher - run the program using the code given by the responsible teacher A4.2 How to use the software After start and selecting language the design window appears. The window is divided into the following blocks: � General Settings � Structural Settings � Geometry � Loads � Parameters for Deflection Check � Results A4.2.1 General Settings Design of trapezoidal sheet should be carried out with general settings shown in Figure A4.1.

Fig. A4.1 Genaral settings for design of trapezoidal sheet

A4.2.2 Structural Settings In Profile box the parameters of cross-section should be defined (eg. LTP45), where the number denotes the depth of the profile. Cross-sectional parameters are available by Profile tool (see Figure A4.2).

Fig. A4.2 Cross-sectional parameters available by Profile tool


51

Position of sheet should be defined in Flange Up box, where the adequate option is “Common (narrow)”. This means that the narrower flange is positioned up. The measure of sidelap is defined in Extra Sidelap box. In our case option “1 trough” may be selected. This type of overlap ensures required waterproof. Static model can be defined in Default Static Model box. Continuous beam model is suggested for using, therefore option “Continuous” should be selected. This means that the sheet is continuous between ridge point and edge beam. These settings are shown in Figure A4.3.

Fig. A4.3 Structural Settings for design of trapezoidal sheet

A4.2.3 Geometry Firstly, we should define the parameters for Span/Length. The lengths of spans should be written into the boxes, where the stating point is the edge beam. The actual static model is drawn automatically in the graphical window (see Figure A4.4).

Fig. A4.4 Geometrical parameters with the graphics of actual model

The program fulfils the column of Th.1 automatically. The column contains the uniform plate thickness of the cross-section. The thickness can be changed by clicking on the first row and choosing the relevant thickness from the list of usable thicknesses. This thickness will appear in all the boxes. The program fulfils the column of Supports. The Width is equal to the width of flange of the purlin. The Width in the first row is greater than in the others because the width of flange of C formed edge beam is greater than the width of flange of Z formed purlin. The L1 is the length of the cantilever at the edge beam, while L2 is the distance between the ridge point and the double purlins. A4.2.4 Loads At the same time (within a run of the program) only one ULS and one SLS load combination can be considered. The program should be run more times, if more load combinations would be considered. Both of ULS and SLS loads may contain more load components. Every row in the table defines a load component for ULS or for SLS combinations. For example, Figure


52

A4.5 shows the definition of an ULS load combination which contains two load components. One of them is a totally and uniformly distributed load with 4,2 kN/m intensity, the other is a partially and uniformly distributed load with 2,5 kN/m intensity (the load starts at the edge beam and ends at 3000 mm distance).

Fig. A4.5 Definition of an ULS load combination with two components

The possible types of load components are shown in Figure A4.6. The type can be selected by clicking on the first box of the actual row. Option “U” denotes totally and uniformly distributed load, option “L” denotes partially and linearly distributed load.

Fig. A4.6 Types of load components A4.2.5 Parameters for Deflection Check Limit for deflections is not specified by Eurocodes therefore the limit should be defined by the designer. In this project deflection limit of L/150 is suggested for using (see Figure A4.7). In the Defl. type box “Maximum” option is suggested choosing. This means that maximum deflection along the span will be considered as design deflection.

Fig. A4.7 Limit values for deflection check

A4.2.6 Check First step of the check of member is the analysis. By Calculation button the program carries out the analysis and check of model. The used parts of capacities are shown in the Results boxes (see Fig. A4.8). The member may be considered being designed if the used part both of the ULS and SLS capacities are less than 100% but one of them is as close to 100% as possible. The detailed results can be available by the Relative Results and Absolute Results. Design parameters are the depth and the thickness of the trapezoidal sheet.


53

Fig. A4.8 Tools to get results of check and documents

A4.2.7 Documents Results of design should be documented. The type and form of the document should be economic in cost. It is acceptable if the student presents the design to the teacher on his/her notebook.


54

ANNEX 5 Design of purlin using DimRoof software

(User’s Manual)

General description of DimRoof software can be found in Annex 4. In this Annex specific knowledge of purlin design is described. A5.1 Settings Design of purlin can be carried out with general settings shown in Figure A5.1.

Fig. A5.1 General settings for design of purlin

A5.2 Structural Settings Size of purlin (size of the Z section) should be chosen in the Profile box (see Figure A5.2).

Fig. A5.2 Structural Settings for design of the purlin

In Default Statical Model box option “Overlapped Standard” is suggested for select on. This means that every purlin has 10-10% overlap at right and left sides of support. Overlap makes the beam being continuous and stronger at the supports. In Manufacturer box option “Hungary” should be selected. Adequate option for Lateral Support is “Top Flange”, if bottom flange is not supported by internal trapezoidal sheet. Option “Both Flanges” means that both of the flanges are supported by trapezoidal sheets. In Sheeting frame the size of the external trapezoidal sheet should be given. Frame of Screws contains details for the connection between purlin and trapezoidal sheet and between purlin and frame, as well.


55

A5.3 Geometry First, Spans/Length column should be fulfilled (see Figure A5.4). Lengths should be defined from the left end of beam to the right end. Actual static model will appear in the graphical window.

Fig. A5.4 Geometry and static model Column Th.1 is automatically fulfilled by the software. This parameter denotes the uniform plate thickness of the purlin. Thickness can be changed by clicking on the first row and choosing the relevant thickness from the list of usable ones. This thickness will appear in all the rows. The program fulfils the Supports column. Columns Type, L1 and L2 contain the parameters of type of support and the overlaps at supports. Software fulfils these columns automatically. Default overlap of the first and last purlin parts in adjacent intermediate spans is double of the usual one (20%).

Fig. A5.5 ULS and SLS loads with one component, respectively


56

A5.4 Loads At the same time (with a run of the program) only one ULS and one SLS load combination can be considered. The program should be run more times if more load combinations should be considered. Both of ULS and SLS loads may contain more load components. Every row in the table defines a load component for ULS or for SLS load combination. For example, Figure A5.5 shows a totally distributed load for ULS combination with 3,4 kN/m intensity, and a totally distributed load for SLS one with 2,6 kN/m intensity. A5.5 Parameters for Deflection Check Limit for deflections is not specified by Eurocodes, therefore the limit should be defined by the designer. In this project deflection limit of L/150 is suggested for using (see Figure A5.6). In Defl. type box option “Maximum” is suggested choosing, which means that the maximum deflection along the span is considered as design deflection.

Fig. A5.6 Settings for check of deflections

M5.6 Check First step of the check of member is the analysis. By Calculation bottom the program carries out the analysis and check of model. The used parts of capacities are shown in Results boxes (see Fig. A5.7). The member may be considered being designed if both of the ULS and SLS capacities are less than 100% but one of them is as close to 100% as possible. The detailed results can be available by the Relative Results and Absolute Results. Design parameters are the depth and the thickness of the purlin.

Fig. A5.7 Results and Documents

M5.7 Documents Results of design should be documented. The type and form of the document should be economic in cost. It is acceptable if the student presents the design to the teacher on his/her notebook.


57

Practice 5

ANALYSIS OF THE MAIN FRAME AN D DESIGN OF THE CROSS-SECTIONS


2010-2011 Budapest


58

Practice 5 ANALYSIS OF THE MAIN FRAME AND DESIGN OF THE CROSS-

SECTIONS 5.1 Design model 5.1.1 General Design model of steel structures may be created in the following steps: • Structural model • Load model • Static model The main components of the structural model: - reference axis of members - initial cross-sections - supports The main components of the load model: - system of load groups and cases - loads of load cases - design load combinations The static model (mesh) is automatically generated by the design software on the base of the structural model. The applied software may be based on 2D or 3D. The 2D based software neglect the out-of-plane deformation as well as the twisting of the members. The 2D model is used to calculate the in-plane design displacements and forces. The 3D based software may use the so called 12DOF element which neglects the warping effect, or the so called 14DOF element which takes the warping effect into consideration. The last type of software may analyse the spatial stability behaviour of the structure. The check of the stability of members may be based on in-plane forces and interaction design formula, or it may be based on out-of-plane stability analysis and general design formula (see the details in Practice 7). Table 8 assumes the above discussion. In the present design notes follows the 3D and out-of-plane model based stability checking which is summarized in the third row of the table. Tab. 8: Relationship between structural model and mechanical model as well as the applied software (informative)

structural model

type of element (mechanical

model)

DOF (degrees of freedom)

warping effect

stability analysis suggested software

in-plane (2D)

in-plane 6 no in-plane buckling AXIS

out-of-plane (3D)

out-of-plane 12 no in-plane buckling (about minor and

major axis)

AXIS FEM-Design

ConSteel spatial (3D)

out-of-plane 14 yes complex spatial ConSteel

5.1.2 Structural model The main geometry of the frame and the initial cross-sections of the structural members are known from the preliminary drawing. The aim is to create the 3D structural model which is adequate for computer analysis. The structural members of the main frame may be as follows: • Members with hot rolled profiles and short/long haunch;


59

• Members with welded profiles and long haunch; • Tapered welded members. First it is shown how to define the structural model, then how to take the equivalent geometric imperfections into consideration. Finally, it is discussed how to support the model. 5.1.2.1 Structural model of main frame composed of hot-rolled profiles The ends of the beams of main frames composed of hot-rolled profiles are normally constructed with haunch. The types of haunch are distinguished: • Short haunch • Long haunch. The short haunch is used to increase the distance between the tensioned bolts and the compressed flange of the end plated moment resistant connection. Applying short haunch the joint may be stiff and full resistant (see later in Practice 8). The short haunch may be neglected in the structural model which means that the structural members can be modeled with uniform cross-sections (see Figure 23a). Long haunch is used to increase the capacity of the joint (like at short haunch) and partially the beams. The long haunch should be considered in the structural model (see Figure 23b).

Fig. 23 Structural model of main frame: (a) with short haunch; (b) with long haunch 5.1.2.2 Structural model of main frame composed of welded profiles I and H profiles may be fabricated by welding technology. The geometric parameters (width and thickness of plates) of the welded profiles may be similar than those of the hot-rolled I and H profiles (equivalent welded sections), but the welded profiles may be constructed with thinner plates. The fabrication of welded profiles may be economical in great amount (see for

(a)

(b)

Partially non-uniform members

Uniform members


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example www.dongbusteel.co.kr/eng/product ). The creation of the structural model is based on same rules than those were described for hot-rolled profiles (see Section 5.1.2.1). 5.1.2.3 Structural model of main frame composed of tapered members The tapered members has normally relatively thin web with linear change of depth. The web plate belongs to Class 4 in bending, while the flanges belong to Class 2 or 3. The reference axis starts at the centroid of the lower end of the members. The model is centric, if the reference axis follows the centroid of the cross-sections (see Figure 24a). If the reference axis is out of the centroid, for example it is parallel with the outer vertical flange, the model is eccentric (see Figure 24b). The centric model allows more accurate analysis but it is complicated to build it up. It is easy to build up the eccentric model, but eccentric finite element should be used in the finite element model (see Section 5.2). The outer flanges of the columns should be vertical at both of the models.

Fig. 24 Structural model composed of tapered members:

(a) centric model; (b) eccentric model

5.1.2.4 Equivalent geometric imperfections Depending on the design method the equivalent geometric imperfections should be considered in the structural model. In general the equivalent geometric imperfection is given by the appropriate buckling shape (eigenvector). According to the design standard the equivalent geometric imperfection may be replaced by two components: • Global imperfection • Local imperfection The shapes of the components do not depend on the buckling shape. The global imperfection for frames is shown by Figure 25, where the inclination is

mh0 ααφφ ⋅⋅=

and

005,00 =φ

0,13

2 de

h

2hh ≤≤= αα

(a) (b)


61

+⋅=m

115,0mα

Fig.25 Global equivalent geometric imperfection

and where m denotes the number of columns (for the frame shown in the Figure m=2). The global equivalent imperfection may be neglected if

EdEd V15,0H ⋅≥

where HEd is the sum of the horizontal loads, VEd is the sum of the vertical loads. It is noted that in case of simple building the wind pressure on the walls satisfies the above condition. Equivalent horizontal load may be applied to replace the global imperfection. The equivalent load (φ⋅VEd) is shown in the Figure 26.

Fig.26 Equivalent load to replace the global equivalent imperfections

The local imperfection is defined as an initial out-of-straightness of the structural member. The shape of the out-of-straightness may be sinus half-wave or parabolic curve, where the amplitude should be taken from the Figure 27. If the structure is relatively stiff, the probable amplitude of the out-of-straightness of the member is not greater than L/800 and the reduction factor method is used to determine the buckling resistance (see Practice 7), then the local imperfection should not be used (the reduction factor contains the effect of the out-of straightness with characteristic value of amplitude). 5.1.2.5 Supports Supports are very important feature of the structural member. The right support model of the main frame is determined by the bracing system of the whole structure of the building. The supports can be defined on the base of the accepted preliminary configuration. Concerning the support model the following topics should be discussed:

φ

VEd

φ⋅VEd

h φ

e e

he ⋅= φ

e


62

buckling curve

amplitude for the out-of-straightness

e0 a0 L/350 a L/300 b L/250 c L/200 d L/150

Fig.27 Equivalent local imperfection

• Support model for column base • Supports on beams • Supports on columns • Knee bars In the discussion we assume that the structure is placed in the X-Z global system plane, consequently the support in direction which is perpendicular to the plane of structure is direction Y. Support model for column base The support model for a column base depends on the structural construction of the column base. The support is normally idealized, which means that the displacements in directions and rotations about directions are assumed being absolutely free or restrained. In more sophisticated models the support model may be assumed being semi-rigid (linearly elastic). Figure 28 illustrates the idealized support model of the simple pinned column base, while Figure 29 shows the idealized support model of the common rigid column base.

The end of the column is fixed in all the directions, and the rotation about the axis of the member is restricted. The support model (code) in ConSteel software is:

x , y , z , zz

Fig.28 Support model for simple pinned column base

e0 e0 L

(a) Structural construction (b) structural model (c) static model

x

z

y


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The end of the column is fixed in all the directions, and is restricted in all the rotations about the axes. The support model (code) in ConSteel software is:

fix

Fig.29 Support model for common rigid column base

Supports on beams The supports which are perpendicular to the plane of the examined structure (lateral supports) should be modeled realistically if spatial stability analysis are wanted to calculate on the model. In contrary the lateral supports should only ensure the running of the second order analysis. For this it is enough to support the model in the break joints and in quarters of the members. Lateral restraint (lateral support) may be ensured by the following two structural members: • Bracing bar connected to the bracing system • Purlin The places of the bracing bars are defined in the preliminary draw. The supporting effects of the purlins are illustrated in Figure 30. The purlin is normally sitting on the top flange of the frame beams but it may be assumed that they support the beam in the centroid (see Figure 31). It is a question whether all the purlins may be assumed as lateral support. There are two answers (models) for the question: Model 1 Purlin can be assumed as lateral support for the main beam that is connected to the bracing system. Figure 32 shows this situation where every second purlin is connected to the joint of the bracing system (in the figure yellow color indicates the purlins that are assumed as lateral support). Model 2 All the purlins may be assumed as lateral support, even if some of them are not connected to any joint of the main beam (see Figure 32). Model 1 leads to conservative design which is suggested flowing if the structure has large scale (considerable depth of cross sections), and it has high importance (ex. hangar, power station). Model 2 leads to economic design which is the number one rule of the mass production (decreasing costs to minimum). The theoretical background of Model 2 may be the shear stiffness of the covering system. Figure 33 illustrates this model where the covering system restraints the purlins that are not connected directly to the join of the bracing system.

(a) Structural construction (b) structural model (c) static model

x

z

y


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Fig.30 Modeling the effect of the purlins on the main beam

Fig.31 Place of the support (simplified modeling)

Fig.32 Two models to take the effect of purlins into consideration:

Model 1 (conservative); Model 2 (economical)


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Fig.33 Restraint of the purlin which is not connected to the bracing system

(Roofing in bottom view)

Supports on columns The columns are supported by the wall beams that run parallel to the plane of the main frame. The wall beams may be connected to the bracing system of the wall structure. The modeling rules of the lateral supports of columns follows the above rules that were established for the roofing. Knee bars Many times the supporting model of the main frame based on the modeling rules established above is not sufficient enough, in other words the critical load amplifier is too low (see Section 5.2.2). The critical load amplifier may be increased by more lateral support, but more times applying knee bars leads to a right solution. The knee bars are applied at the bracing members where they connect the compressed flange of the main structural member (beam, column) to the bracing member (see Figure 34). This construction may restrict the twist of the cross-section of the structural member. The knee bars may be sufficient if the buckling mode of the main structure is lateral torsional buckling (LTB). Section A6.9 of Annex 6 shows how to model the knee bars.

Purlin which is connected to the bracing system


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Fig.34 Knee bars against twist of the main member

5.1.2.6 Simplified model or full 3D structural model? Figure 35b shows the isolated model of one of the main frames of a simple building. From point of view of the model it does not matter whether purlins or bracing members supply the lateral supports. Figure 35a illustrates the full 3D model of the building structure which may be constructed with relatively few amount of work. It is a practical knowledge that this full 3D model does not supply more information for the main frame than those which is isolated (simplified model) and supported due to the effect of purlins or bracing members. The full 3D model may be useful at the design the bracing system. It is noted that the “fine tuning” of the full 3D model as well as the creation of the load model may take considerable amount of work but this model may be a sufficient design tool for engineers who have some years practice. In this design project we do not suggest using full 3D model.

Fig.35 Structural models for simple building: (a) full 3D model; (b) simplified model

(b)

(a)


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5.1.2.7 Application The example below shows the modeling of the main frame in ConSteel design software. Annex 6 describes the modeling step by step.

4. ANALYSIS AND DESIGN OF MAIN FRAME

In this design project the main frame which is situated close to the side wall is designed. The result of the design is considered being valid for all the main frames. The analysis and design is carried out with the ConSteel design software.

4.1 Design model

4.1.1 Structural model

The initial structural model of the examined main frame was created on the base of the Preliminary Draw found in Fig. 9-11 of this Design Notes. The model was constructed on the 3D modeling window of the ConSteel software:

The eccentricities of the lateral supoports were neglected in the structural model. Supports were placed on to the reference axes and in the break points. The intermediate supports on columns and beams were placed at the middle points of the members. At the intermediate supports of the beams knee bars were assumed.

4.1.2 Cross-sectional models and properties of cross-sections

The models of cross sections were developed in the ConSteel software, and the cross-sectional properties were imported from the software.

4.1.2.1 Cross-section of columns

Knee bar Knee bar


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Class of cross-section pure compression pure bending flange 1 1 web 4 1

Cross-sectional properties

- area [mm2] A c.pl 11424 A c.eff 10609

- moments of inertia [mm4] I c.y 518270000 I c.z 36884000

- sectional moduli [mm3] W c.y.pl 2296600 W c.z.pl 460800

- St. Venant inertia moment [mm4] I c.t 729500

- warping constant [mm6] I c.w 2157000000000

4.1.2.2 Cross-section of beams



- area [mm2] A b.pl 9888 A b.eff 9346

- moments of inertia [mm4] I b.y 308197000 I b.z 36870000

- sectional moduli [mm3] W b.y.pl 1677000 W b.z.pl 460800

- St. Venant inertia moment [mm4] I b.t 671166

- warping constant [mm6] I b.w 1358000000000

4.1.2.3 Cross-section of haunched beam

Haunch plates

- flange: 240-20

- web: 310-6

The cross-section of the haunched beam is approximated by an I section where the intermediate flange is neglected. The height of the cross-section is considered in the theoretical corner of the frame.


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- depth h bh 730

- area [mm2] A bh.pl 12804 A bh.eff 10501

- moments of inertia [mm4] I bh.y 1253000000 I bh.z 41472000

- sectional moduli [mm3] W bh.y.pl 3716000 W bh.z.pl 518400

- St. Venant inertia moment [mm4] I bh.t 1017000

- warping constant [mm6] I bh.w 5191000000000

4.1.3 Material properties

- grade of steel: S235

- design strength [N/mm2] f y 235

- elastic moduli [N/mm2] E 210000

- shear moduli [N/mm2] ν 0.3 GE

2 1 ν( ).G 8.077104.=

4.1.4 Particial factors

- for cross-sectional resistances γ M0 1.0 f y0f y

γ M0

- for stability resistances γ M1 1.0 f y1f y

γ M1

5.1.3 Load model 5.1.3.1 General The basic loads of the building were determined in Practice 2. Using these loads the design loads of the examined frame should be determined in this Chapter. The loads which have effect on the covering system (dead load of covering, snow load and wind load) are transmitted by the purlins as concentrated loads, see Figure 36a. If there are at least 3-4 purlins (wall beams) on the beam (column), the applied load may be considered as distributed load, see Figure 36b. In this design project distributed load is suggested applying. 5.1.3.2 Adequate frame to design The wind load on the roof is changing from zone to zone. Therefore the frames of the building have different design loads. The greatest wind effect can be found on the frames at the end walls of the building but the width of the loading area is only the half of the frame distance. Generally, it is for safe and economical design if the second frame is examined, as it is shown in Figure 37. 5.1.3.3 Load groups and load cases The design software supports the generation of the load combinations. In order to use this tool the load cases should be collected into load groups. Load group contains load cases which


70

Fig.36 Loads on the main frame transmitted as:

(a) concentrated loads; (b) distributed load

Fig.37 Adequate frame and width of loading area for design (top view of the building)

belong to same load type (ex. snow, wind) and may neglect each others in the load combinations. Load case contains load items which act together in the same time (ex. cross wind loads on the frame). In this design project the following load groups and load cases are suggested applying:

• Dead loads

o Weight of structural members (WSM) o Weight of covering system (WCS) o Installation loads (IL)

• Snow load o Totally distributed o Non symmetrically distributed (left sided) o Non symmetrically distributed (right sided)

Uniform intermediate frames

Frame at wall

Adequate frame for design

Width of loading area

(a)

(b)


71

• Wind load o windload_1 o windload_2 o windload_3 o windload_4 o …

Dead loads The weight of the members of the frame is considered by the software. The user should select the load case which will contain this load (WSM). The weight of purlins, wall beams and covering layers may be collected into an individual load case (WCS). The installation loads (equipments, lightings, and so on) can be collected into another load case (IL). In this project the following dead load cases are suggested using (see Figure 38):

o WSM: [kN/m] p s,g (loads considered by the software)

o WCS: [kN/m] qcp cc,g ⋅=

o IL: [kN/m] qcp ii,g ⋅=

where c [m] is the distance between the frames, qc [kN/m2] is the weight of the covering system, qi [kN/m2] is the installation load.

Fig.38 Model of dead loads

(where ’r’ denotes ’on roof’ and ’w’ denotes ’on wall’) Snow load The snow load is gravity load which means that it acts vertically. The basic snow load is related to 1 m2 horizontal area. The snow load cases are illustrated in Figure 39. In this design project it is enough to take the totally distributed load (Case 1) into consideration. It is noted that in cases of unsymmetrical duopitch roofs the unsymmetrical load cases may be adequate. The frame is loaded by the following totally distributed snow load:

scp 1s ⋅⋅= µ

where s [kN/m2] was determined in Practice 2, η1 is a factor given in Section 2.2.1.1. This snow load case is related to horizontal surface. The reduction of this load may be neglected for the safe, see Figure 40.

wc,qc ⋅wc,qc ⋅

i r , c q c ; q c ⋅ ⋅


72

Case 1: Totally distributed Case 2: Unsymmetrical (left) Case 2: Unsymmetrical (right)

Fig.39 Snow load cases

Fig.40 Model of totally distributed snow load

Wind load The wind may affect on the external and the internal surfaces of the building. The loads due to the wind effect may be calculated as following:

- external wind load: edse,w wcccp ⋅⋅=

- internal wind load: ii,w wcp ⋅=

where cscd is the structural factor, which is 1.0 for buildings being not higher than 15 m. In this design project it is suggested applying the following wind load cases: • Cross wind effect (θ=0°), see Annex 7 • Cross wind effect “+” internal wind effect, see Annex 8a • Longitudinal wind effect (θ=90°), see Annex 8b • Longitudinal wind effect “+” internal wind effect, see Annex 8c It can be seen that a wind load case might have more cases. The number of cases (number of design load combinations) may be reduced neglecting the non adequate load cases. Unfortunately, there are no general rules how to reduce the number of load cases. 5.1.3.4 Design load combinations Design load combinations for transient and persistent design situations (basic combinations) are given by the following expressions (EN 1990 6.4.3.2 6.10):

sc1 ⋅⋅η

µ1 µ1 0.5µ1

µ1 0.5µ1


73

∑ ∑ ⋅⋅+⋅+⋅ i,ki,0i,Q1,k1,Qj,kj,G QQG ψγγγ

where γG is the partial factor for dead loads (normally: 1,35) γQ,i partial factor for load case ’i’ (snow and wind load: 1,5) Ψ0,i combination factor for load case ’i’ (snow load: 0,5; wind load: 0,6) These load combinations can be generated by • Automatically • Engineer Generation of all the possible load combinations is supported by the software. This automatic method has some disadvantages: - second order and stability analysis (it is suggested) should be executed for all of the load combinations (superposition must not applied); - results may be reviewed difficultly; - runtime may be considerable. Method of generation by Engineer is preferred by senior engineers since using simple considerations (neglecting the non adequate load cases and combinations) the analysis may be executed and the results can be reviewed more easily. In this design project it is suggested using the two methods together: all the possible load combinations can be generated by the software, and then the inadequate load combinations may be disclosed. 5.1.3.4 Application The example below shows the creation of the load model using ConSteel design software. Annex 9 illustrates the program application, step by step.

4.2 Load model

4.2.1 Load groups and load cases

The load cases are set into the following groups: - dead loads - snow loads - wind loadsThe load cases in the snow and wind load groups disclose each other in any load combination.

4.2.1.1 Load cases in dead load group

Self weights of structural members are taken into consideration automatically by the software. Effect of roof slope is neglected. The loads of wall covering system are neglected.

Dead load of roof covering system

- load on surface [kN/m2]

q g.c q tr.ext q tr.int q iso q iso.otherq purlin

e4q g.c 0.451=

- load for beam [kN/m]

p g.c c q g.c. p g.c 2.706=


74

Installation loads

- load acting on roof [kN/m2]

q g.i q light q equip q other q g.i 0.45=

- load on beam [kN/m]

p g.i c q g.i. p g.i 2.7=

4.2.1.2 Load cases of snow load group

Unsymmetric snow load cases are neglected.Accidental snow load (accidental design state) is not examined.Effect of roof slope is neglected for safe.

- Totally distributed snow load on beam [kN/m]

p s c s. p s 6=


75

4.2.1.3 Load cases of wind load group

Wind effect is not considerable because of the given geometry of the building. After discussion of the load system the above five wind load cases are considered:- external cross wind effect (0 degree): wind sucking on zones F-G-H- external cross wind effect (0 degree): wind pressure on zones F-G-H- external and internal cross wind effects (0 degree)- external longitudinal wind effect (90 degrees)- external and internal longitudinal wind effects (90 degrees) Wind loads are calculated with c sds=1, because the height of the building is less than

15 meters.

4.2.1.3.1 Two load cases due to external cross wind effect (0 degree)

Distributed wind pressure on walls [kN/m] p w.e.D c w D.0.10. p w.e.D 1.801=

Distributed wind sucking on walls [kN/m] p w.e.E c w E.0.10. p w.e.E 0.876=

Distributed wind sucking on the roof [kN/m]p w.e.F c w F.0.10

. p w.e.F 3.222=Zones F-G-H (i) wind sucking p w.e.G c w G.0.10

. p w.e.G 2.479=

p w.e.H c w H.0.10. p w.e.H 1.115=

Zones I-J (ii) wind pressure p w.e.FGH c w FGH.0. p w.e.FGH 0.248=

p w.e.I c w I.0.10. p w.e.I 1.239=

p w.e.J c w J.0.10. p w.e.J 0.991=

Examined load area (second main frame) is covered by zones F and G, but for safe effect on zone F is considered on the load area.

Width of the zone F [m] e 0.10.F e 0.10 e 0.10.F 1.804=

Width of the zone J [m] e 0.10.J e0.10 e 0.10.J 1.804=

Models of load cases

4.2.1.3.2 External and internal cross wind effects (0 degree)

Internal wind sucking effect reinforces the second case of external cross wind effect, therefore first case is neglected.

Distributed wind pressure on wall [kN/m]p w.e.D c w D.0.10 w i.0

. p w.e.D 2.301=

Distributed wind sucking on wall [kN/m]p w.e.E c w E.0.10 w i.0

. p w.e.E 0.377=


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Distributed wind sucking and pressure on the roof [kN/m]

Zones F-G-H p w.e.FGH c w FGH.0 w i.0. p w.e.FGH 0.748=

Zones I-J p w.e.I c w I.0.10 w i.0. p w.e.I 0.739=

p w.e.J c w J.0.10 w i.0. p w.e.J 0.492=

4.2.1.3.3 Load case of the longitudinal external wind effect (90 degrees)

On examined load area (second main frame) zone B is dominant for walls, while zone H for roof.

- Distributed wind sucking load on walls [kN/m]p w.e.DE c w B.90.10

. p w.e.DE 1.983=

- Distrubuted wind sucking effect on roof [kN/m]p w.e.H c w H.90.10

. p w.e.H 1.611=

4.2.1.3.4 Load case of longitudinal external and internal wind effects

Internal wind effect is sucking effect which weaknings the external wind sucking, therefore this load case may not be relevant.

4.2.2 Load combinations

Load combinations shown below were generated by the ConSteel software. These load combinations belong to persitent design situation. Dead load in combination 12 may be favorable, therefore the partial factors were modified to 1.00.


77

5.1.4 Static model Static model may be generated by software. The generation is based on the structural model and the basic setting. The professional user may change the basic setting and by this way the main properties of the static model can be determined. One of the main properties of a beam-column model is the number of finite elements (FEs). The ConSteel software uses a general beam-column FE which has uniform cross-section. Following a simple method (so called segment method), the program distributes the tapered (or haunch) members into a set of uniform elements. Figure 41 shows the FE model of a haunch member where eccentric uniform FEs are used. The optimal number of FEs depends on the ratio of the length of the haunch and the depth of the cross-section. The model with 4 FEs leads usually acceptable results. The model with 8 FEs may be ‘exact’. Tapered members can be modeled on the same way but at least 8 FEs should be used. The segments may be placed centrically (see Figure 42a) or eccentrically (see Figure 42b). The centric model may be more exact from static point of view. The eccentric model may be easier to build up and it is closer to the world of the CAD/CAM systems but it is less exact from static point of view.

Fig.41 Static model for haunch beam using uniform segments (FEs)

5.2 Analysis 5.2.1 General During the design process analysis should be executed on the following structural models: • Conceptual model • Detailed model • Final model


78

Fig.42 Static models for tapered frame:

(a) using centric segments (b) using eccentric segments

Analysis on conceptual model is performed in the tender phase when the architectural design office launches the structural solution. The sharp race in the market requires very fast procedure for preliminary design, therefore instead of classical “hand” made calculations the more accurate computer calculation is used. In this phase it is not needed to deal with all the structural details, and only first order analysis is executed on simplified structural and load models. In this design project the preliminary draw may satisfy the requirements of the conceptual design. The structure was simple, therefore the initial cross-sections were able to determine without any analysis. It is noted that in case of more sophisticated structures the preliminary analysis and design could not have been neglected. Analysis on detailed model should be performed in the realization phase of the structure, where there are direct economical and criminal consequences of any design mistake. In this phase all the details should be examined which have any effect on the safe of the structure. The static analysis is normally executed by computer program which is usually based on finite element method. Usually second order theory is applied. It may be assumed that the structural joints are initially rigid or pinned. If any joint of the structure is semi-rigid, the effect of the initial stiffness of the joint should be built into the model. If any column base is pinned, it should be modeled by appropriate external point support. Design of joints follows the analysis and design of the cross-sections, therefore the design procedure is recursive, if there are semi-rigid joints in the structure. In this design project semi-rigid joints are not suggested designing.

(a) centric model (b) eccentric model


79

The properties of the whole structure (for example displacements and column base reactions, should be determined on the final model. The final 3D structural model should contain all the structural members which have any effect on the complex structural behavior and response. 5.2.2 Main steps of analysis The structural model is normally analyzed by computer software. Displacements are the primary result of the analysis. The displacements are shown on the 3D window as the deformation of the structural model. The displacements should be considered as fictive structural properties, unless the analysis was executed with the final cross-sections. The computer analysis may be performed in the following main steps: Step 1: Check the structural model The structural model may be checked for a simple and symmetric load case. First order analysis may be executed, and then the deformation of the structural model should be examined. By this way the most critical model mistakes (inadequate support system, false cross-sections, and so on) can be found and the model can be corrected. Step 2: Check the design model Assuming that the structural model is adequate, the full load model may be applied. First order analysis can be executed for all the relevant design load combinations. The model should have understandable deformation for all the load combinations. If any irregular behavior can be realized in the model response (ex. there is bending moment at pined joint), the structural model should be repaired. Step 3: Stability analysis (optional) Out-of-plane stability analysis of the structure requires appropriate software and design model. The software is appropriate if it uses general beam-column finite element which is able to take the warping effect into consideration (see the ConSteel). The design model is appropriate if it is 3D model and the support system satisfies the real conditions. False support system results in false stability response (false critical load amplifier). Using false critical load amplifier in design may indicate serious criminal consequences. The critical load amplifier is an important property of the structure, but the required value is not specified in the standard. Practically, for design of frames the following values may be suggested applying: • If 0,1cr ≤α , the structural is dangerous!

• If 0,20,1 cr ≤< α , the structure is very slender (it is not suggested)!

• If 0,30,2 cr ≤< α , the structure is slender but it is possible to design it in a safe way!

• If cr, α<03 , the structure is stiffness and the design can be safe (suggested value)!

The appropriate buckling mode (which belongs to the critical load amplifier) is also an important property of the structure. The buckling mode may show the weakest member (or group of members) which determines the actual value of αcr. The examination of the buckling mode may show how to change the support system to get higher αcr (to get higher performance in stability resistance). The support system can be changed by new supported points, by moving any support to more optimal place and using knee bars. If the change of the support system is not sufficient, the cross-sections should be changed (ex. using wider flanges, higher depth). It is highly suggested for junior designers discussing this problem with a senior engineer.


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Step 4: Execute full analysis Calculating design forces the options of first order or second order should be switched on. For stability analysis it is suggested asking at least 6 eigenvalues (critical load amplifiers). If the procedure suggested above is followed and any error occurs during the execution for any load combination, the probable reason is that αcr<1 (see Step 3). The structural background of this phenomenon may be found in the relative weakness of the structure and/or in the relative excessive loading. 5.2.3 Design document Relating to documentation of design there are two typical life situations. One of them is that when more engineers (or more groups of engineers) are working on the project, and they should use and or should control each other (for example one of them performs the main static calculation, the other designs the joints). In this situation full design documentation should be produced. In the other situation (mainly in case of small scale design projects where structural designer works in single) is that where there is no requirement for direct cooperation with other engineers. In this situation partial design documentation may be enough for internal use. In this design project the last situation is followed. Cooperative design work (concurrent engineering) will enforce an international standardization for documentation requirements of static analysis and design. Today it is not more than an effort, therefore there are no general rules for the content and style of the document. The basic requirement is that the results of the analysis and design should be traceable and reproducible by independent experts. This basic requirement may be satisfied by the documentation tools of the design software. The minimum content of the partial design documentation for a simple structure (like the frame of the present design project) may be the following:

• description of structural model • description of load model • partial results of analysis

The structural and the load model may be described by tables or draws produced by the software applied, or by both of them. The finite element analysis provides a great amount of data. It is enough to document some dominant results. For example the check of cross-section resistances needs the design internal forces (NEd, MEd, VEd) in some points of the structure. Therefore these forces may be collected into a simple table. Even a simple frame may have a lot of design load combinations. In this case it is enough to document the forces given by the most dominant load combination(s). There are no general method how to do this, but there are some guidelines what load combinations can be dominant:

• which gives maximum My.Ed for beams • which gives maximum My.Ed for columns, but in case of thin web (for example tapered

member) which gives maximum VEd and maximum NEd • which gives bending moment diagram closer to uniform (lower My.Ed may be

dominant if the moment distribution is uniform) According these guidelines the design forces may be documented with content as following: (A) Design force diagrams drawn by software for 2-3 dominant load combinations. (Figure 43 shows a pattern how to document a dominant bending moment diagram.)


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Fig.43 Diagram of My.Ed of Load Combination …[kNm]

(B) Design force table for check of cross-section resistances. (Figure 44 shows a pattern how to define the design force table for a simple frame.)

structural member

point

Load Combination

Ed.yM

(kNm) EdN

(kN) Ed.zV

(kN)

… K1 …

column

K2 … … K3 …

beam

K4 … * color yellow indicates the maximum value

Fig.44 Design force table for check of cross-section resistances


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The table and picture in Figure 44 show the intention of the designer: • columns will be checked at the column base and at the top of the columns; in both

cases that Load Combination is assumed being dominant which gives maximum bending moment;

• columns will be checked at the column base for shear force where that Load Combination is assumed being dominant which gives maximum shear force;

• beams will be checked at the frame corner and at the maximum moment along the member; in both cases that Load Combination is assumed being dominant which gives maximum bending moment;

• beams will be checked at the frame corner for shear force where that Load Combination is assumed being dominant which gives maximum shear force;

5.2.4 Application Analysis of the main frame was executed by the ConSteel software. The detailed application guide can be found in Annex 10. The application shown below is based on the method of partial design documentation.

4.3 Analysis

Second order analysis was executed by ConSteel software. Diagrams of stress resultants of two dominant load combinations are presented. Results of analysis may be controlled using the ConSteel model attached in the Annex.

4.3.1 Diagrams of stress resultants for Load Combination 1

- Bending moment diagram - My.Ed [kNm]

- Normal force diagram - NEd [kN]


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- Shear force diagram - Vz.Ed [kN]

4.3.2 Diagrams for stress resultants for Load Combination 4

- Moment diagram - My.Ed [kNm]

- Normal force digram - NEd [kN]

- Shear force diagram - Vz.Ed [kN]


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5.3 Design of cross-sections 5.3.1 General The aim of the cross-section design is to find the optimal structural dimensions. Dimensions of cross-sections may be optimal if they satisfy the design equations of resistances and the structure has the less cost (in this case the less weight) as possible. Design of cross-section is an iterative procedure, where the initial cross-sections are checked, the results are discussed, and some initial cross-sectional parameters may be modified. Any change in cross-sectional dimensions leads to change of the static model and the design forces as well. Theoretically, new analysis should be executed if there is any change in the model. Practically the new analysis may be neglected if the change is relatively inconsiderable. It is important to consider that the resistances of members are usually determined by reduction of the cross-sectional resistances. Therefore the cross-sections can not be designed for 100% usage of their resistances. In case of relatively stiff frames made from hot-rolled or equivalent welded profiles the usage of cross-sectional resistances can not be greater than 80-90%. In case of relatively slender frames (welded and tapered frame with large span) this limit may be 70-80%. The EC3-1-1 provides multilevel design formula to determine the resistances of cross-sections. In general the resistance of a cross-section may be determined by one of the following design formulas:

• general elastic formula (based on design stresses) • conservative interaction formula (based on design forces) • plastic interaction formula (based on design forces and plastic properties)

The theoretical background of these design formulas was the subject of the previous studies (Steel I and Steel II). 5.3.2 Choosing design formula The appropriate design formula depends on the type of the structure. Some guidelines are given below:

� Hot-rolled or equivalent welded profiles

In the present design project HEA and IPE profiles with middle depth may be applied. These cross-sections belong to Class 1 or 2 for pure bending and Class 2 or 3-4 for pure compression of the web. IPE profile may be Class 3-4 if the depth is greater than 400 mm and it is purely compressed. Frame which is composed of these types of profiles may be usually designed by plastic interaction formula where the effect of normal and shear forces reduce the bending moment resistance. Alternatively conservative interaction formula can be used (see the next paragraph).

� Welded cross-section with relatively thin web

Welded cross-sections with relatively thin webs and IPE profiles with depth is grater than 400 mm belong to Class 1 or 2, if the flanges are considered and Class 3 or 4, if the web is considered for pure compression. If the normal and shear forces are relatively low, the conservative interaction formula may be used. In this case Aeff and Wpl.y may be used together in the same formula.


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� Welded cross-sections with high depth and thin web Frames with relatively large span are usually made from welded cross-sections composed of relative slender web plate (large depth and thin plate). In this case the web of the cross-section may belong to Class 3 or 4, while the flanges belong to Class 2 or 3. This type of cross-sections can be designed by the general elastic formula where the effect of shear stresses is considered. The pure normal stresses can be calculated with elastic cross-sectional properties of the nominal and the effective cross-section, respectively. The effective cross-sectional properties are suggested calculating by software tool which assumes the interaction of the normal stresses due to pure axial force and due to pure bending moment (see the ConSteel/Section module).

5.3.3 Application The application shown below illustrates the ‘hand’ design of the cross-sections and compares the results with those are given by the ConSteel software. Annex 11 contains the application guide on how to use the ConSteel program designing cross-sections.

4.4 Design of cross-sections

4.4.1 Relevant cross sections and design forces

Relevant cross-sections to design- Section K1: cross-section of column at columnbase- Section K2: cross-section of column at frame corner- Section K3: cross-section of beam at frame corner- Section K4: cross-section of beam at maximum positive bending moment

Design forces of relevant cross-sections, see 4.3.1-2. member cross-section LC design forces

moment [kNm] normal force [kN] shear force [kN] column K1 4 M K1.y.Ed 354.36 N K1.Ed 179.66 V K1.Ed 116.73

K2 4 M K2.y.Ed 491.76 N K2.Ed 170.99 V K2.Ed 114.25

beam K3 4 M K3.y.Ed 469.56 N K3.Ed 142.20 V K3.Ed 148.56

K4 4 M K4.y.Ed 177.91 N K4.Ed 115.75 V K4.Ed 4.18


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4.4.2 Design of cross-secctions

Checking shear force effect- maximum design shear force [kN] V max.Ed V K3.Ed V max.Ed 148.56=

- minimum design shear area [mm2] A min.V h bw t bw. A min.V 2.208103.=

- pure shear resistance [kN] V min.Rd A min.Vf y0

3

. 1

1000.

V min.Rd 299.576=

Maximum design shear force does not excced 50% of shear resistance of web anywhere, Vmax.Ed<0.5Vmin.Rd ,

therefore effect of shear force may be neglected in any case.

Beam and column cross-sections are related to Class 4 for pure compression and Class 1 for pure bending. Therefore conservative interaction formula is used. Effective cross-sectional area is used for pure compression and plastic moduli for pure bending.

Dimensional factors (change kN to N and kNm to Nmm)β N 1000 β M 1000000

Column Section K1

η K1β N N K1.Ed

.

A c.eff f y0.

β M M K1.y.Ed.

W c.y.pl f y0.

η K1 0.729= Adequate!

Column Section K2

η K2β N N K2.Ed

.

A c.eff f y0.

β M M K2.y.Ed.

W c.y.pl f y0.

η K2 0.98= Adequate, but too much!

Beam Section K3

η K3β N N K3.Ed

.

A bh.eff f y0.

β M M K3.y.Ed.

W bh.y.pl f y0.


Beam Section K4

η K4β N N K4.Ed

.

A b.eff f y0.

β M M K4.y.Ed.

W b.y.pl f y0.


Usage of resistance of the cross-section at top of the column excedes 90% as a practical limit. Instead of reinforcment of column cross-section design bending moment is taken at the buttom flange of the haunch beam, where thecolumn has realistic cross-section.- decreasing of bending moment

∆ M h bhh b

2

M K2.y.Ed M K1.y.Ed

1000 Hc.

. ∆ M 61.431=

- reduced design bending moment

M K2.y.Ed.red M K2.y.Ed ∆ M M K2.y.Ed.red 430.329=

- Column Section K2

η K2β N N K2.Ed

.

A c.eff f y0.

β M M K2.y.Ed.red.

W c.y.pl f y0.


The initial cross-sections are adequate!


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Cross-section checking was executed by the ConSteel software too (see the picture berlow). Results are basically the same than those of the hand calculation.

4.4.3 Applied cross-sections

Column section flange width [mm] 240thickness [mm] 16

web width [mm] 368thickness [ mm] 6

Beam section flange width [mm] 240thickness [mm] 16

web width [mm] 468thickness [mm ] 8

Haunch flange width [mm] 240thickness [m m] 16

web width [mm] 300thickness [mm] 6


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Annex 6 Structural modeling with ConSteel software

(application guide) A6.1 Installation The install file of the ConSteel design software can be downloaded from the www.consteel.hu portal. The software shouldbe be installed on the User’s computer. First the ConSteel_install_”dátum”.exe file should be executed when the ConSteelKey0.bin file will be created by the software. This file and the required data should be sent to the ConSteel Software Company ([email protected]). In some days the Company will send back the ConSteelKey.bin software key which can be added to the main folder of the software. A6.2 Starting The program can start by the ConSteel.exe. On the ConSteel Startup panel the ‘Create new model’ option may be selected, and then the Model name (1) can be defined, see Figure A6.1.

Fig. A6.1 Create new model Using OK the 3D model window will appear. The short description of the main modeling tools can be available by F1. A6.3 Setting 3D modeling window First dimensions of the modeling raster may be defined (2). For example, at 19,5 meters span 20000 may be written into the Size box (3), see Figure A6.2.

Fig.A6.2 Setting modeling raster

1

2

3


89

To actualize the setting Enter should be used (or the panel should be closed). By this way the size of raster will be 20 meters (while the density will remain 1000 mm and the step 250 mm). A6.4 Setting initial cross-sections The Section table of the new model is empty, therefore the first step is to define the initial cross-sections. First the Structural members label (4) should be selected, secondly the Section administration tool (5). In case of hot-rolled cross-section „From Library” option (6), in case of welded cross-sections „Macro section” option (7) should be used, see Figure A6.3.

Fig.A6.3 Selecting cross-section category

After selecting cross-section category the appropriate parameter panel will appear where the type of cross-section (8) should be defined (actually it is „Welded I”). Clicking on Next the parameter table appears where the geometrical parameters of the cross-section should be defined (9), see Figure A6.4.

Fig.A6.4 Setting type and geometrical parameters for cross-section

„Name” (10) and „Material” (11) of the cross-section may be defined on the top part of the panel. Using Create the cross-section will be placed into the Section table of the actual model, see Figure A6.5.

4

7

8

9

10

5

6

11


90

Fig.A6.5 Section table with actually defined cross-sections All the cross-sectional properties may be available if the cross-section is selected in the Section table (12) and the Properties… is used, see Figure A6.6. The program uses two different cross-sectional models in the same time. The General Solid Section model (13) supplies only elastic properties, while the Elastic Plate Segment model (14) supplies plastic properties as well.

Fig.A6.6 Cross-sectional properties

A6.5 Create columns The first step of the structural modeling is the ‘erection’ of the two columns. Selecting the Structural member label (15) and the Column tool (16) the column definition panel will appear, where the height (17) and the cross-section (18) of the column should be determined (normally the default values of the other parameters are adequate). The columns may be placed in the global X-Z plane with the base points, see Figure A6.7. The position of a column can be defined by coordinates also. For this the column should be positioned such a way that Y=Z=0, and then the X button should be pushed, and the actual X coordinate should be written into the data box which can be found below the modeling window (19), see Figure A6.8. The action is closed by Enter, and the column will appear in the graphics. The form and the view of the visualization can be changed by the tools (20) found at left hand side of the window, see Figure A6.9.

12

13 14


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Fig.A6.7 Erecting columns

M6.8 ábra: Column position defined by coordinates

Fig.A6.9 Change visualization A6.6 Create beam The next step of the modeling is the ’erection’ of the beam. Selecting the Structural member label and the Beam tool (21) the panel of beam definition will appear, where the cross-section (22) should be selected (normally the default values of the other parameters are adequate). Using the left hand side mouse button the beginning and the end of the beam should be defined (in the example these points are the tops of the columns), see Figure A6.10. In order

15

17

18

19

20

16


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to get the symmetric duopitch roof the beam should be refracted at middle. For this the raster may be moved into the plane of the frame (23 , 24), see Figure A6.11, and then shifting to the Geometry label (25) and using the Refract selecting line element tool (26) the middle (ridge) point may be moved into the right position. The Z coordinate of the ridge point can be defined also in the control row (27) which is found below the modeling window, see Figure A6.12.

Fig.A6.10 Erecting beam

Fig.A6.11 Shift the raster into the plane of the frame

22

24

23

21


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Fig. A6.12 Refract the beam

After modeling the columns and the beam it is suggested shifting the raster into the original position (28) and saving the model (29) with version number _01, see Figure A6.13.

Fig.A6.13 Shift the raster into original position and save the model A6.7 Create haunch Selecting the Structural member label and the Haunch tool (30) the haunch panel will appear, where the geometrical parameters should be defined. Following the tips of the program the beginning point (31) and the direction (32) of the haunch should be defined on

25 26

27

28 29


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the actual structural member (for example on the beam). The direction can be defined by any get point on the member, see Figure A6.14. New haunch can be created by new definition of beginning point and direction.

Fig.A6.14 Create haunch M6.8 Create point support First the support model of the column bases is defined. According to the preliminary draw the column bases are rigid. Selecting the Structural member label and the Point support tool (33) the point support panel will appear, where the ‘Fix’ option should be selected (34). If the column base is pinned, the option should be ‘x,y,z,zz’. Following the tips of the panel the base points of the model should be selected by the mouse (35), see Figure A6.15.

Fig.A6.15 Create fix (pinned) column base supporting model

30

31

32

33

35 35

34


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In the next step the intermediate supports in global direction Y are created. These supports are placed at the purlins and wall beams or at the bracing bars. These places are determined in the preliminary draw. Point support may be set at any get point which is defined on the structural member. There are two ways to define get points:

• Dividing member into number n uniform parts. • Dividing member into parts with d uniform length.

The required option can be selected in the function row found below the model window, see Figure A6.16. The option can be changed by a click on the actual option sign. The new set of these options (‘d’ or ‘n’) can be fixed by Enter.

Fig.A6.16 Create get points on member (n: number of parts; d: relative distance in [mm])

Using setting above the get points with red color will appear on the structural member when the cursor is moved close to one of the ends of it. On the point support panel the ‘y’ option (support in global direction Y) should be selected. The support model can be placed at the get points by a click on it. In the case of the example n=2 get point system was used. The lateral supports were placed into the breakpoints and into the middspan points of the members, see Figure A6.17. This support model approximates the real construction which is established in the preliminary draw.

Fig.A6.17 Structural model with lateral point supports

(at middspan with knee bar effect, see Section A6.9) A6.9 Create lateral support with knee bar effect The critical load amplifier (see Section 7.3.2) may be increased by knee bars which can be used along the structural members. In the example this type of support is used at middspan points of the beams. Selecting the Structural member label and the Point support tool the point support panel will appear, where the ‘New support” button should be used (36). By this operation the Definition point support panel will appear, where the New button should be used. After this the automatically generated ‘Name of support model’ may be changed (37) and the ‘y’ and ‘Rx’ degrees of freedoms should be switched as ‘Fix’ and the others as ‘Free’


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(38). This means that the point will be supported in direction y and in rotation about x axis of the local system of the structural member, see Figure A6.18. Using the Apply button the support model will be created and it can be placed on the points of the structural members. Before placing the support the coordinate system should be shifted from ‘global’ to ‘local’ (39), see Figure A6.19. It is noted that the transversal pin of the support symbol should be perpendicular to the axis of the structural member (40).

Fig.A6.18 Create lateral point support with knee bar effect

Fig.A6.19 Place lateral support with knee bar effect

36

37

38

40 39


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Annex 7 External pressure coefficient for cross wind effect

(h/d<0,25; α=50 ; A>10m2 )

Case 1

Case 2

Case 3

Case 4

Megjegyzés: A fenti értékeket a ( pqc ⋅ ) –vel megszorozva megkapjuk a szélhatásból származó vonal

menti megoszló terheket.

cpe,10=+0,8 cpe,10=-0,3

cpe,10=-1,7;-1,2 cpe,10=-0,6

cpe,10=+0,2 cpe,10=-0,6

cpe,10=+0,8 cpe,10=-0,3

cpe,10=-1,7;-1,2 cpe,10=-0,6

cpe,10=-0,6 cpe,10=-0,6

cpe,10=+0,8 cpe,10=-0,3

cpe,10=-0,6 cpe,10=-0,6

cpe,10=+0,8 cpe,10=-0,3

cpe,10=+0,2 cpe,10=-0,6


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Annex 8

(a) Internal pressure coefficient for cross wind effect (h/d<0,25 ; α=50 ; A>10m2 )

(b) External pressure coefficient for longitudinal wind effect (h/d<0,25 ; α=50 ; A>10m2 )

(c) Internal pressure coefficient for longitudinal wind effect (h/d<0,25 ; α=50 ; A>10m2 )

Notes: Coefficients given above times ( pqc ⋅ ) provide the wind loads distributed on the structural

members of the frame.

+cpi,0

+cpi cpe,10,B=-0,8 cpe,10,B=-0,8

cpe,10,H=-0,7 cpe,10,H=-0,7

+cpi,90


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Annex 9 Load modeling with ConSteel software

(application guide) A9.1 Load groups and load cases The structural model defined in Annex 6 is considered. Selecting the Load label (1) and the Load cases and groups option (2) the Load definition panel appears, see Figure A9.1. (Load case: group of loads where the loads act together and in same time; Load group: group of load cases where the load cases may enclose each other in any load combination.)

Fig.A9.1 Set and rename of a load group

Fig.A9.2 Set new load case

1

2

3

4

5

6


100

In case of new design model the left hand side table contains one load group and one load case generated by the program. First the name of the default load group should be changed to the actual name (presently ‘Dead loads’) (3), and then using Apply the name of the default load case can be changed to the actual name (presently ‘weights’) (4). If the are more load cases in the actual load group, the New load case (5) and the Name option (6) can be used to define a new one, see Figure A9.2. New load group can be defined by New (7). Before this action the load type should be selected (8). For example the name of the new load group is ‘Snow loads’ (9) and the type of the load group is ‘Meteorological’, see Figure A9.3.

Fig.A9.3 Set new load group According to the actual load model (defined previously) all of the load groups and load cases should be defined, see Figure A9.4.

Fig.A9.4 Completed structure for the actual load model

7

8

9


101

Finally, the theoretical weight of the structure is generated by the program, and it should be added to one of the load cases. To do this the ‘Load case including self weight’ box found at bottom of the panel should be opened and the appropriate load case can be selected (10), see Figure A9.5. Closing the load definition panel by OK the structure of the load model is determined. In the next step the load cases should be fulfilled with concrete design loads.

Fig.A9.5 Select load case which will include the self weight of the structure

A9.2 Set of design loads The structure of the load model was set in Section A9.1. Here it will be shown how to set the design loads of the load cases. First the actual load case should be selected (11). Loads set on the model will be contained by selected actual load case as far as the actual load case is changed to another one, see Figure A9.6.

Fig.A9.6 Select load case to define design loads The paragraphs below describe how to set concrete loads for a load case:

Distributed load on structural member - in global directions Selecting the Loads label (12) and the Line load option (13) the Load parameter panel appears, where the starting and end intensities of the line load should be written into the appropriate boxes (14). The line load can be set on a structural member by a click (15), see Figure A9.7. Distributed load on a part of the structural member - in global directions Selecting the Load label (16) and the Line load option (17) the Load parameter panel appears, where the Draw option (18) should be selected, see Figure A9.8. The starting and end load intensities should be written into the appropriate boxes (19) and the starting (20) and end (21) points of the load should be selected on the loaded member. The points can be selected by get points setting on the member, see Section A6.8.

10

11


102

Fig.A9.7 Set line distributed load on structural member in global directions

Fig.A9.8 Set line load distributed on a part of the member

12 13

14

15

16 17

19

20

21

18


103

Set loads in local system of the member Basically the loads are assumed acting in the [X,Y,Z] global directions. There are loads (for example wind load) which are perpendicular to the structural member. These loads may be set in the local system of the member. The local system can be chosen by the ’Local coordinate system’ option (22), see Figure A9.9. In the local system direction X coincides with the axis of the member, directions Y and Z are the main axes of the cross-section.

Fig.A9.9 Set local system for loads

M9.3 Set load combinations The structure of the load model and the design loads of the load cases are given. The next step is to define the design load combinations. Selecting the Loads label (23) and the Load combination option (24) the Load combinations panel appears where the Automatic generation of load combinations option (25) should be selected. The relevant design situation(s) should be chosen on the appeared panel. For example to check the cross-sections the ‘Load combinations in persistent and transient design situations (6.10)’ option (26) should be selected, see Figure A9.10.

Fig.A9.10 Automatic generation of the design load combinations

22

23 24

25

26


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The panel should be closed by Apply , and then all the possible load combinations will appear in the table, see Figure A9.11. Any load combination might be cleared (27), and new combinations may be defined (28). The factors of the combinations might be changed (29).

Fig.A9.11 Automatically generated design load combinations and tools for modification

27 28

29


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Annex 10 Analysis with ConSteel software

(application guide) M10.1 Check structural model Before analysis for all the design load combinations the design model should be controlled. Selecting the Analysis label (1) and the Analysis parameters option (2) the Set analysis parameters panel appears, where only the First order analysis option (3) should be switched on, see Figure A10.1.

Fig.A10.1 Set analysis

Shifting to the Load combination label (4) and switching all of the load combinations off (5), and selecting the Load cases label (6), where one of the load cases which contains symmetrical effects should be switched on, see Figure A10.2. Using Apply and Calculation the deformed model will appear on the graphics. The method how to discuss the results of the

Fig.A10.2 Selecting load case with symmetrical effects to control the structural model

1 2

3

4

5 5

6


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analysis is described in the Paragraph A10.2. If any problem is realized in the response of the structural model, a senior engineer (presently the supervisor) should be involved into repairing the model. M10.2 Discussion of model response When the analysis is performed the deformed geometry appears in the graphics. The scale of the deformation may be changed by the Scale roller (7), see Figure A10.3.

Fig.A10.3 Scaling deformed geometry

The content of the graphics can be defined by the following selections: • Type of analysis (first order, second order, buckling, …), (8) • Load case or Load combination (9) • Category of response (deformation, design forces, reactions, …), (10) • Type of draw (diagram, color, …), (11)

Using appropriate content of graphics the deformed geometry should be examined. The guidelines for examination may be the follows: - if the load is symmetric, the deformed geometry should be symmetric too, - if the load acts in the plane of the frame, the deformed model should be remained in-plane, - maximum deflection should be realistic, - deformed geometry should be realistic from engineering point of view. As the next step, the in-plane My.Ed bending moment diagram (12) may be examined, see Figure A10.4. The guidelines for examination may be the follows: - at pinned column base the bending moment should be zero, - break/jump in bending moment diagram may occur only at concentrated load/moment, - maximum bending moment should be realistic, - shape of moment diagram should be realistic from engineering point of view.

7 8 9 10 11


107

Fig.A10.4 Select content for graphics

M10.3 Execute analysis If the model control is negative, the complex analysis can be executed. Switching all the load cases off and all the load combinations on, see Paragraph A10.1-2, and then the first order analysis can be executed. If there is no error message, the second order analysis (13) may be switched on and the analysis may be executed again, see Figure A10.5.

Fig.A10.5 Set option of second order analysis

If there is error message, it can be concluded that the structure is too weak and/or the load is too high for the structure. Assuming that the load model is adequate (there are no duplicated loads which cover each other on the graphics, and so on…), and the support system is also adequate (all the supports established which are located on the structural model in the preliminary draw) the structural should be reinforced. If there is no error message, the analysis can be considered being completed, and the design forces can be documented. M10.4 Document design forces Comprehensive description of the document tools and making full static document are not the objectives of this teaching material. The aim of this paragraph is to shown how to create a picture with specified content in order to copy it into another (Word or Mathcad) document. In the first step the dominant load combinations should be selected from the Table of cross-sectional resistances. The table can be available selecting the Global check label (14) and the Global resistance option (15). Cross-section check (16) and Second order analysis (17) options should be switched on, see Figure A10.6. The cross-sectional check will be executed by Calculation according to the setting. The results are shown by color graphics and in tables as well, see Figure A10.7. In the table the utilizations of resistances are shown in the last

12

13


108

column (18) and the appropriate load combinations in the fourth column (19), see Figure A10.7. The most dominant load combinations can be selected from the table. In this design project it is satisfactory to document the design force diagrams of the most dominant two or three load combinations. More details how to check of cross-sectional resistances can be found in Annex 11.

Fig.A10.6 Setting for examination of cross-sectional resistances

Fig.A10.7 Table of the utilization of the cross-sectional resistances

M10.5 Document pictures In this paragraph it is shown how to document a picture. For example the My,Ed bending moment diagram which belongs to the Load Combination 4 and which was computed by 2nd order analysis will be documented. The diagram can be scaled by the Grapics zoom (20). Any ordinate of the diagram can be visualized by a click on the appropriate point of the diagram using right hand side button of mouse. Selecting the Marker option (21) the value of the diagram will be fixed to the diagram (22), see Figure A10.8. The required number of markers can be fixed to the diagram, see Figure A10.9.

14

15

16 17

18 19


109

Fig.A10.8 Visualization values for the diagram

Fig.A10.9 Bending moment diagram with appropriate number of values

The diagram can be saved by the following way. Selecting the Document label (23) and the Create snapshot from current state option (24) the Create snapshot… panel appears where the Name of the picture (25) and the Dimension of picture (26) can be set. The size of the text on the picture may be changed by the Letter size option (27), see Figure A10.10. The diagram should be completed and placed into the frame draw by dashed lines, and the picture can be saved by Create (or Modify ) into the picture folder. Selecting the Handling of figures option (28) the content of picture folder appears, where the actual picture may be selected (29) and using the Save selected picture into file option (30) the picture can be saved as a file into the selected folder (31) with specified file name (32) and format (33), see Figure A10.11.

20

21

22


110

Fig.A10.10 Creating picture which can be saved into the picture map

Fig.A10.11 Selecting picture from picture folder and saving it as a file

23 24

25

26

27

28

30

29

31

32 33


111

Annex 11 Design of cross-sections by ConSteel software

(application guide) Paragraph A10.4 presents how to Check cross-sectional resistances by the ConSteel software. Utilization of resistances is shown by color graphics and in table, see Figure A11.1.

Fig.A11.1 Visualization of cross-sectional resistances by graphics and in table ConSteel software allows analyzing the results more deeply. Selecting the actual cross-section by right hand side mouse button on the graphics or in the table (1), and choosing the Calculate section option (2), see Figure A11.2, the window of Section module appears, see Figure A11.3.

Fig.A11.2 Selection of actual cross-section for examination in deep

1

2


112

Fig.A11.3 Detailed information about the check of cross-sectional resistance It is known that Eurocode 3 defines different design equations for determining cross-sectional resistances. These equations may be the follows:

‘General elastic resistance’ – theoretically this formula is allowed using for all the cross-sections, but design may be uneconomical for Class 1 and 2; ‘Pure resistances’ – pure resistance formulas should be used in case of interaction of forces too; ‘Plastic interaction resistance’ – this formula is valid for Class 1 and 2 cross-sections; the base of the formula is the bending resistance which should be reduced by the effects of the normal force and the shear force, if it is necessary (this formula ensures economic design); ‘Conservative interaction resistance’ – this formula my be valid for all the classes providing the shear force can be neglected; in the parts of the formula related to pure compression and pure bending the cross-sectional properties given for the appropriate pure effects may be used (ex. if the cross-section is related to Class 4 for pure compression and Class 2 for pure bending, Aeff and Wpl might be used in the appropriate parts of the formula).

ConSteel software selects the adequate formula, but it may be controlled by the engineer. According to Figure A11.4 the plastic interaction formula is the valid (3) for the actual case. The table shows all the design parameters of the formula. For example it can be seen that both of the normal force (4) and shear force (5) effects are allowed neglecting in the given situation. The decision of the software (what design formula is dominant) may be changed by the engineer. For example the designer may consider the conservative interaction formula as the base of the design. Figure 11.5 shows the table of parameters (6) for this case. Utilization of cross-sectional resistances computed by a selected formula can be visualized for the whole model too. For this the Box of categories (7) should be opened and the actual category (ex. ‘Conservative interaction resistance’ (8)) may be selected, see Figure11.6. This selection will be valid for all the cross-sections of the model. ConSteel software determines a unified effective cross-sectional model for Class 4 cross-sections. The considered normal stress distribution is the sum of the normal stresses due to the axial force and the bending moment. Therefore the result may differ from the result of the hand calculation where there are different effective cross-sectional models for pure compression and for pure bending moment.


113

Fig.11.4 Parameters of plastic interaction resistance formula

Fig.11.5 Parameters of conservative interaction resistance formula

Fig.A11.6 Utilization of cross-sectional resistances of the whole model based on selected design formula

(actually the conservative interaction formula is selected)

3

6

5 4

7

8


114

Practice 7

GLOBAL STABILITY RESISTANCE OF THE FRAME


2010-2011 Budapest


115

7.1 General Global stability resistance of the structural members of the frame can be performed by elastic design method using one of the following methods:

Method of reduction factor In this method in-plane or spatial static model is applied, where the phenomena of lateral torsional buckling and flexural torsional buckling is not examined. The design model does not include the equivalent imperfections but may include real geometric imperfections if their effects are considerable. The structural members or the parts of them can be examined (simple method). Alternatively the members or the frame may be examined comprehensively (general method). Determination of the buckling lengths or the critical forces should be based on the behaviour of the structural. Annex 12 illustrates the application of the method.

Method of equivalent geometric imperfection In this method spatial static model should be applied, where the design model includes the effect of torsion (warping). The design model includes the equivalent geometric imperfections. The cross-sectional resistances should be computed on design forces given by second order analysis. The cross-sectional resistances include the effect of the global instability. Annex 13 illustrates the application of the method.

Method of partial equivalent geometric imperfection In this method in-plane or spatial static model is applied, where the phenomena of the lateral torsional buckling and the flexural torsional buckling are not examined. The design model includes the global equivalent geometric imperfection but neglects the local. The structural members or the parts of them are examined by the method of reduction factor. As buckling lengths The buckling lengths of the members may be equal to the structural lengths. Annex 14 illustrates the application of the method.

The expressions used above are defined as follows:

Elastic design method Design forces are computed by linear elastic analysis (where elastic material law is applied). The method allows using plastic cross-sectional properties in the design formulas. Design model Design model consists of a structural model and a load model. The structural model is the virtual model of the real structure. The load model is the virtual model of the specified loads and effects of the structure. Static model Static model is generated from the design model following the conditions of the method of analysis. Static model may determine the type of the model response, such as in-plane, out-of-plane or spatial behaviour. Equivalent geometric imperfections Equivalent geometric imperfection is local if the structural member has a specified initial out-of-straightness, and it is global if the structural member has a specified initial inclination. The effect of the equivalent imperfections is equal to the effect of the reduction factor used in the method of reduction factor. Second order analysis Second order analysis takes the effect of the structural deformation in the equilibrium equations into consideration. Basically the idea of small displacements is used. The analysis leads to non-linear problem from mathematical point of view. Global instability The stability behaviour of the structure (or structural member) is global if the whole structure or a part of it (ex. one of the bars of a truss) takes a global buckling mode, such as flexural, flexural-torsional or lateral torsional buckling, or interaction of them. The ‘global’ indicates that the buckling mode does not include local buckling phenomena, for example local plate buckling.


116

In the design practice mostly the method of reduction factor is used. The method of equivalent geometric imperfection is suggested using for senior engineers who have the experience. The method of partial equivalent geometric imperfection is normally used in preliminary design. Within the method of reduction factor the following two methods can be used: � Method of equivalent members (simple method)

The design forces are computed on in-plane or spatial design model, where the instability responses are neglected. The stability resistance formulas (ex. interaction formulae) are applied on equivalent structural members isolated from the design model and supported appropriately. The details of this method are discussed in the Paragraph 7.2.

� General method The calculation of the design forces and the elastic stability analysis are performed on spatial static model which includes the effect of torsion (warping). Any software can be applied which uses general beam-column finite element method (14 DOF FE method). The support system of the design model should be based on the real conditions of the structure (see Paragraph 5.1.2.5). The general design formulae examines the structure as a ‘super member’. The details of this method are discussed in the Paragraph 7.3.

7.2 Method of equivalent members (simple method) 7.2.1 Interaction design formulae The stability resistance of uniform members with double symmetric cross sections should be checked by the interaction design formulae, where a distinction is made for: – members that are not susceptible to torsional deformations, e.g. circular hollow sections or sections restraint from torsion; – members that are susceptible to torsional deformations, e.g. members with open cross- sections and not restraint from torsion. The interaction formulae is based on the modelling of simply supported single span members with end fork conditions and with or without continuous lateral restraints, which are subjected to compression forces and end moment in-plane:

(1) 1fW

Mk

fAN

1M

yyLT

Ed,yyy

1M

yy

Ed ≤⋅⋅

⋅+⋅⋅γ

χγ

χ

(2) 1fW

Mk

fAN

1M

yyLT

Ed,yzy

1M

yz

Ed ≤⋅⋅

⋅+⋅⋅γ

χγ

χ

where NEd is the design compression force; My,Ed is the maximum design moment about y-y axis (including the moment due to

the shift of the centroidal axis of Class 4 cross-sections); χy , χz , χLT are the reduction factors due to flexural buckling about y-y and z-z axes, and

due to lateral torsional buckling;


117

kyy , kzy are the interaction factors; A , Wy are the cross-sectional properties due to the class of the cross-section (plastic,

elastic or effective); fy is the characteristic design strength; γM1 is the partial safety factor. The kyy and kzy interaction factors have been derived from two alternative approaches. Method 1 was developed by the so called ‘French-Belgian’ group. The method provides a continuous design curve between the cross-sectional and the stability resistances but the expressions are basically complicated and no understandable. Method 2 was developed by the so called ‘German-Austrian’ group. The method provides simple and understandable expressions but the results are less sophisticated. Method 2 is used for simple ‘hand’ design, while Method 1 may be used by software tools. The expressions of Method 2 can be found in the Annex 15. It is easy to realise that no one of the beams or columns of the frame satisfies the conditions of the interaction formulae. For example, if the column of the frame is taken as an equivalent member with simple fork supports at the ends, at least two basic conditions is not satisfied: (i) the column is elastically supported at top; (ii) the column is supported intermediately by wall beams (or bracing members). The problem may be solved by the wider meaning of the interaction formulae. The formulae consists of three pure buckling modes, such as the flexural buckling about y-y axis, the flexural buckling about z-z axis, and the lateral torsional buckling. It is allowed to take different equivalent members for these pure buckling modes. The engineer is responsible for the use of the interaction formulae in wide meaning. Determination of the χy , χz and χLT reductions factors using the wide meaning of the interaction formulae is illustrated in the following paragraphs. 7.2.2 In-plane buckling (χy) 7.2.2.1 Buckling of columns The in-plane slenderness of the column may be determined by the stability analysis of the frame. The slenderness can be calculated using buckling length factor or critical force: - Slenderness due to buckling length factor

The buckling length factor of the columns of any simple frame may be found in the literature, see Figure 45. The duopitch roof structure may be modelled by the simple portal frame model shown in the figure.

Fig.45 Slenderness due to buckling length factor

yχ

H

F

L

Io; Ao

Ig ( ) ( )

( ) ( )2y

2y

6c017.06c35.01

:keret befogott

6c02.06c4.14

:keret csuklós

ααυ

ααυ

+⋅−+⋅+=

+⋅++⋅+=

Fix (clamped) frame:

Pinned frame:

2.0AL

I4 10

HI

LIc 2

o

g

o ≤⋅

⋅=≤⋅⋅= α ( ) y.cr

yy2

y

y2

y.cr N

fA

H

EIN

⋅=

⋅⋅

= λυπ


118

- Slenderness due to critical force The slenderness of the column may be determined by global stability analysis of the

appropriate model. The numerical procedure is illustrated in the Figure 46. (a) design model (b) analysis (design forces)

(c) analysis (buckling) (d) slenderness

7.2.3 Out-of-plane buckling (χz) The out-of-plane stability responses of the columns and the beams are similar. The members are supported laterally by purlins or wall beams, optionally by bracing members. Out-of plane flexural buckling mode may develop between two neighbouring lateral supports in form of half sinus curve. The equivalent members (buckling lengths) are the parts of the examined member located between two lateral supports. It is more complicated problem if the lateral supports have considerable eccentricity (for example in case of high web depth with lateral support at the tensioned flange of the I section). In this situation the out-of-plane flexural buckling mode and the lateral torsional buckling mode can not be independent phenomena (see Paragraph 7.2.4). In the lack of more exact stability analysis method (such as general method), the equivalent member of the LTB problem may be used for the flexural buckling problem. This means that the appropriate buckling length may be longer than the distance between two lateral supports. This conservative design method is for the safe. The examples of Paragraphs 7.2.5.1 and 7.2.5.2 illustrate the design method. 7.2.4 Lateral torsional buckling (χLT) Lateral torsional buckling mode may develop between two neighbouring lateral supports where the cross-sections are restrained in rotation around the axis of the member (fork support). Fork support can be taken into consideration in two cases: - the lateral support is placed at the compressed flange, see Figure 47; - knee bars support the compressed flange, see Figure 34.

EdN

crαcr

yy

max,Edcrcr

N

fA

NN

⋅=

⋅=

λ

α

yχ

Fig.46 Slenderness due to critical force


119

Fig.47 Equivalent member for the beam at the frame corner: the second lateral support can be

considered as fork support since the support is placed at the compressed flange; (a) structural model with lateral supports

(b) equivalent member for the beam

7.2.5 How to determine the equivalent members for columns (buckling lengths) Figure 48 shows the column structure which has pinned supports at the ends. The column is supported laterally at the middle cross-section and loaded by vertical concentrated force and concentrated moment at top. Let’s determine the equivalent members for the global stability check of the column with different cross-sections. 7.2.5.1 HEA300 section

The lateral support at the middle cross-section of the column may be considered as fork support due to the following reasons: (i) the torsional stiffness of the HEA300 profile is relatively high; (ii) the eccentricity of the lateral support is relatively low.

Fig.48 Equivalent members of the column made from HEA300

(example for fork lateral support)

(a)

(b)

Structural and load model Analysis Equivalent members Checking


120

However, the column is not sensitive to the flexural torsional and the lateral-torsional buckling. In this case the global stability of the column may be examined by two equivalent members: (1) part of the column between the top and the middle supports; (2) part of the column between the middle of the column and the column base. It is noted, that in this example the structural models of the two equivalent members coincide and the normal force is uniform, but the moments are higher on the upper part. Consequently it is enough to examine the upper equivalent member, see Figure 48..

7.2.5.2 IPE600 section

The lateral support at the middle cross-section of the column can not be considered as fork support due to the following reasons: (i) the torsional stiffness of the IPE600 profile is relatively low; (ii) the eccentricity of the lateral support is relatively high. Consequently the column is sensitive to the flexural torsional and the lateral-torsional buckling modes. In this case the global stability resistance of the column may be examined on the equivalent member as the whole member (the equivalent member is the member itself), see Figure 49. It is noted that a knee bar construction at the middle of the column may lead to previous example, see the Paragraph 7.5.2.1.

Fig.49 Equivalent member of the column made form IPE600 (example for no fork lateral support)

7.2.5.3 Frames The columns and beams of the frame structure may have more equivalent members. Figure 50 shows a frame model where the lateral supports are fork supports due to knee bars construction. Let’s determine the equivalent members.

The parts of the structural members denoted by yellow colour are the equivalent members for the global stability check of the frame. The solution may be explained as follows: - rotation of cross-sections at the lateral supports are restrained due to the knee bars constructions;

Structural and load model Analysis Equivalent member Checking


121

Fig.50 Equivalent members for global stability check of the frame supported by fork lateral

supports

Fig.51 Reduction factors for the examination of the O1 equivalent member

O1

G1 G2

cry αν vagy ( )

ycr.y

yy

2y

y2

cr.yEdcrcr.y

N

fA

H

EIN vagy NN

χλ

νπ

α

⇒⋅

=

⋅⋅

=⋅=

( ) ( )

LTcr

yyLTz

cr.z

yz

z

tcr.z

z

w

cr.z

zcr

cr.z

zcr.z

M

fW

N

fA

EI

GIL

I

I

L

EICM

L

EIN

χλχλ

πππ

⇒⋅

=⇒⋅

=

⋅⋅+⋅⋅⋅=⋅=

2

2

2

2

12

2

My

In-plane buckling

Out-of-Plane buckling and LTB

Design model Analysis

Equivalent members Global stability check

Fork lateral supports

O1


122

- maximum design bending moment of the columns is found on the O1 equivalent member; - maximum design bending moment of the beams is found on the G1 equivalent member; - design bending moment diagram closed to constant is found on the G2 equivalent member. It is noted that in case of fix column bases the bottom part of the column (O2) should be examined too. Figure 51 illustrates the main steps of the examination of the O1 equivalent member.

7.2.6 Members with changing cross-section Structural members with changing cross-sections may not be checked correctly by the interaction formula and the equivalent members. Approximate check may be performed following the design idea described below. The cross-section of the member is changing due to the following structural reasons: � Short haunched members � Long haunched members � Tapered members 7.2.6.1 Short haunched members The effect of the short haunch of beam to the critical forces can be neglected, see Figure 52b. Assuming that the increasing of the stiffened part of the beam is relatively higher than the increasing of the design moment, the interaction design formula may be evaluated at the end of the haunch, see Figure 52a.

Fig.52 Global stability check of haunched beam

7.2.6.2 Long haunched and tapered members The effect of the long haunch should be taken into consideration in the global stability analysis. As a draft approximation the global stability analysis may be performed with an equivalent cross-section as following:

• if the length of the haunch is equal to about the length of the examined equivalent member, the depth of the equivalent cross-section is equal to the mean depth, see Figure 53a;

• if the length of the haunch is definitely shorter than the length of the equivalent member, the depth of the equivalent cross-section may be equal to the cross-section at the 1/3 haunch depth, see Figure 53.b.

The intermediate flange of the equivalent I cross-section may be neglected. The design interaction formula should be performed at the real cross-section which has the maximum utilization for cross-sectional resistance. The tapered members may be examined by the concept of mean depth of cross-section.

Adequate cross-section to check the global stability

(b) (a)


123

Fig.53 Equivalent cross-section for global stability analysis of the haunched equivalent

member: (a) mean depth concept; (b) 1/3 haunch depth concept 7.2.7 Application The example below shows the global stability examination of the frame using the design interaction formulae and the equivalent member concept. This examination may be preformed by the ConSteel software too. The application guide can be found in the Annex 16.

4.5 Global stabilty resistance

The global stability resistance of the frame is examined with the design interaction formula as well as the general method. The examination based on the interaction design formula is presented for the columns only. It is noted that the examionation should be extended to the whole structure in the actual design project.

4.5.1 Examination of resistance of columns with design interaction formula

4.5.1.1 Basic assumptions

In the global stability analysis of columns the following assuptions are followed:- the reduced slenderness for the in-plane buckling is determined due to the global stability analysis of the main frame;- at the inermediate points of the columns offset lateral supports are applied;- rotation of the column shape at the supports is restrained by the offset supports, therefore the out-of-plane buckling and the LTB can be examined for the O1 upper part and the O2 top part.

4.5.1.2 In-plane buckling

buckling length [mm] cI c.y L.

I b.y H c.

c 4.492=

α4 I c.y

.

1000 L.( )2 A c.pl.

α 4.772104.=

υ y 1 0.35 c 6α.( ). 0.017 c 6α.( )2. υ y 1.493=

L cr.y υ y 1000. H c. L cr.y 1.09 104.=

critical forcce [N] N cr.yπ 2

E. I c.y.

L cr.y2

N cr.y 9.04 106.=

reduced slenderness λ y

A c.eff f y.

N cr.yλ y 0.525=

mean depth cross-section

cross-section at 1/3 depth haunch

(b)

(a)


124

reduction factor α y 0.34

φ y 0.5 1 α y λ y 0.2. λ y2.

χ y1

φ y φ y2 λ y

2χ y 0.873=

buckling resistance [N] N b.Rd.y χ y A c.eff.

f y

γ M1

. N b.Rd.y 2.176106.=

4.5.1.3 Out-of-plane buckling

- Examination of the O1 column part (upper part of the column)

equivalent structural length [mm] L z.1 3650

buckling length factor ν z.1 1.0

buckling length [mm] L cr.z.1 ν z.1L z.1. L cr.z.1 3.65 103.=

critical force [N] N cr.z.1π 2

E. I c.z.

L cr.z.12

N cr.z.1 5.738106.=

reduced slenderness λ z.1A c.eff f y

.

N cr.z.1λ z.1 0.659=

reduction factor α z 0.49

φ z.1 0.5 1 α z λ z.1 0.2. λ z.12.

χ z.11

φ z.1 φ z.12 λ z.1

2χ z.1 0.75=

buckling resistance [ N] N b.Rd.z.1 χ z.1A c.eff.

f y

γ M1

.N b.Rd.z.1 1.869106.=

- Examination of the O2 column part (buttom part of the column)

equivalent structural length [mm] L z.2 3650

buckling length factor ν z.2 0.7

buckling length [mm] L cr.z.2 ν z.2L z.2. L cr.z.2 2.555103.=

critical force [N] N cr.z.2π 2

E. I c.z.

L cr.z.22

N cr.z.2 1.171107.=

reduced slenderness λ z.2A c.eff f y

.

N cr.z.2λ z.2 0.461=

reduction factor α z 0.49

φ z.2 0.5 1 α z λ z.2 0.2. λ z.22.

χ z.21

φ z.2 φ z.22 λ z.2

2χ z.2 0.864=

reduction factor [N] N b.Rd.z.2 χ z.2A c.eff.

f y

γ M1

.N b.Rd.z.2 2.155106.=


125

4.5.1.4 Lateral torsional buckling (LTB)

Examination of the O1 column part equivalent structual length [mm] L LT 3650

LTB length factor ν LT 1.0

LTB length[mm] L cr.LT ν LT L LT. L cr.LT 3.65 103.=

ctritical moment [Nmm]relevant load combination: LC 4design bending moments [kNm] M max.1 492

M min.1 72---ábra---

gradient of moment ψ 1M min.1

M max.1ψ 1 0.146=

moment coefficient C1 1.88 1.4ψ 1. 0.52ψ 1

2. C1 1.686=

M cr C1π 2

E. I c.z.

L cr.LT2

.I c.w

I c.z

L cr.LT2 G. I c.t

.

π 2E. I c.z

.. M cr 2.537109.=

A csökkentõ tényezõ számításánál feltételezzük, hogy az oszlopszelvény a "hengrelt szelvényekkel egyenértékû" kategóriába sorolható:

λ LT.0 0.4

β 0.75

reduced slenderness for LTB λ LTW c.y.pl f y

.

M crλ LT 0.461=

reduction factor α LT 0.76

φ LT 0.5 1 α LT λ LT λ LT.0. β λ LT

2..

χ LT.11

φ LT φ LT2 β λ LT

2.

χ LT.1 0.948=

χ LT.21

λ LT2 χ LT.2 4.701=

χ LT χ LT.1

k c1

1.33 0.33ψ 1.

k c 0.78=

f 1 0.5 1 kc. 1 2 λ LT 0.8

2..

χ LT.modχ LT

f χ LT.mod 1.036=

χ LT.mod 1

LTB resistance [Nmm] M b.Rd.1 χ LT.modW c.y.pl.

f y

γ M1

. M b.Rd.1 5.397108.=


126

Examination of O2 column part structural length [mm] L LT 3650

LTB length factor ν LT 0.7

LTB length [mm] L cr.LT ν LT L LT. L cr.LT 2.555103.=

critical bending moment [Nmm]relevant load combination: LC 4design bending moment [kNm] M max.2 354

M min.2 72

moment gradient

ψ 2M min.2

M max.2ψ 2 0.203=

moment coefficient C2 1.88 1.4ψ 2. 0.52 ψ 2

2. C2 2.186=

M cr C1π 2

E. I c.z.

L cr.LT2

.I c.w

I c.z

L cr.LT2 G. I c.t

.

π 2E. I c.z

.. M cr 4.977109.=

reduced LTB slenderness λ LTW c.y.pl f y

.

M crλ LT 0.329=

reduction factor α LT 0.76

φ LT 0.5 1 α LT λ LT λ LT.0. β λ LT

2..

χ LT1

φ LT φ LT2 β λ LT

2.

χ LT 1.062=

χ LT 1.0

LTB resistance [Nmm] M b.Rd.2 χ LT W c.y.pl.

f y

γ M1

. M b.Rd.2 5.397108.=

4.5.1.5 Interaction of Flexural Bucklings and LTB moment factor Cmy 0.9

design normal force [kN] N Ed 175

interaction factors (cross-section Class 1 and 2)

k yy.1 Cmy 1 λ y 0.2β N N Ed

.

χ y A c.eff. f y

... k yy.1 0.924=

k yy.2 Cmy 1 0.8β N N Ed

.

χ y A c.eff. f y

... k yy.2 0.958=

k yy k yy.1- Examination of the O1 column part CmLT 0.6 0.4ψ 1

. CmLT 0.659=

interaction factors

k zy.1 10.1λ z.1

.

CmLT 0.25

β N N Ed.

χ z.1A c.eff. f y

.. k zy.1 0.985=

k zy.2 10.1

CmLT 0.25

β N N Ed.

χ z.1A c.eff. f y

.. k zy.2 0.977=

k zy k zy.1


127

used capacity

η O1.1β N N Ed

.

N b.Rd.yk yy

β M M max.1.

M b.Rd.1

. η O1.1 0.922=

η O1.2β N N Ed

.

N b.Rd.z.1k zy

β M M max.1.

M b.Rd.1

. η O1.2 0.991= Megfelel!Adequate!

- Examination for the O2 column part CmLT 0.6 0.4ψ 2. CmLT 0.519=

interaction factors

k zy.1 10.1λ z.1

.

CmLT 0.25

β N N Ed.

χ z.2A c.eff. f y

.. k zy.1 0.98=

k zy.2 10.1

CmLT 0.25

β N N Ed.

χ z.2A c.eff. f y

.. k zy.2 0.97=

k zy k zy.1used capacity

η O2.1β N N Ed

.

N b.Rd.yk yy

β M M max.2.

M b.Rd.2

. η O2.1 0.686=

η O2.2β N N Ed

.

N b.Rd.z.2k zy

β M M max.2.

M b.Rd.2

. η O2.2 0.724= Megfelel!Adequate!

The examination of the columns was preformed by the Member Designer Module of the ConSteel 6.0 design software too:


128

7.3 General method 7.3.1 Introduction The general method may be used where the simple method (method of equivalent members) is not applicable. It allows the verification of the resistance to lateral and lateral torsional buckling for structural components such as – single members which are built-up or not, uniform or not, with complex support conditions or not; – plane frames or subframes composed of such members. The frame structure of this design project satisfies these conditions. The milestone of the method is the global elastic stability analysis of the structure. If the model response contains flexural torsional or lateral torsional buckling modes, the method requires finite element analysis using general beam-column element with warping effect (14 DOF element) or shell finite element. 7.3.2 Application of the method Step 1: Load amplifier Firstly the cross-sectional resistances of the structure should be calculated applying the conservative interaction design formulae. The load amplifier should be calculated in the ‘critical’ cross-section due to the adequate load combination, where the utilization of the resistance is the greatest:

yy

Ed.y

y

Edk,ult

fW

M

fA

N1

⋅+

⋅

=α

It is noted that the load amplifier as a design parameter which is relevant for the whole structure. Step 2: Critical load amplifier Global elastic stability analysis should be performed on the adequate load combination (see Step 1). The structural model should have realistic lateral support system. The critical load amplifier (αcr,op) is equal to the lowest linear eigenvalue where the appropriate buckling mode is out-of-plane mode (such as out-of-plane flexural buckling or lateral torsional buckling). Step 3: Reduced slenderness The reduced slenderness is relevant for the whole structure and related to out-of-plane buckling mode:

op,cr

k,ultop

αα

λ =

Step 4: Reduction factors On the base of the reduced slenderness (see Step 3) the χz out-of-plane buckling reduction factor and the χLT lateral torsional buckling reduction factor should be calculated for the ‘critical’ cross-section (see Step 1).


129

Step 5: Checking The global stability resistance of the structure should be checked at the ‘critical’ cross-section for the design forces of adequate load combination (see Step 1). The design formulae is derived form the conservative design interaction formulae:

1MyyLT

Ed.y

1Myz

Edstab.glob /fW

M

/fA

N

γχγχη

⋅⋅+

⋅⋅=

The resistance of the structure is adequate if 0.1stab.glob ≤η .

7.3.3 Application The follow example shows the application of the general method. The examination was performed by the ConSteel software too. The application guide can be found in the Annex 17.

4.5.2 Global stability resistance by general method

4.5.2.1 Load amplifier

According to the examination of the cross-sectional resistances (see Section 4.4) it can be seen that the critical cross-section is the K2 section, which is situated at the top of the column. The adeauate load combination for the examination is the Load Combination 4.

- utilization of cross-sectional resistance in K2 section

η K2β N N K2.Ed

.

A c.eff f y.

β M M K2.y.Ed.red.

W c.y.pl f y.

η K2 0.866=

- load amplifier

α ult.k1

η K2α ult.k 1.155=

4.5.2.2 Critical load amplifier

The global stability analysis was performed on the reastically supported design model using ConSteel software (see Section 4.5.2.1).

- ctirical load amplifier (first eigenvalue)

α cr 5.37

- buckling mode (relevant eigenvector)


130

4.5.2.3 Reduced slenderness

The reduced slenderness is relevant for the whole structure:

λ opα ult.k

α cr.opλ op 0.464=

4.5.2.4 Reductions factors

Reduction factors for both of the pure lateral buckling and LTB are calculated with the general slenderness computed in Section 4.5.2.3.

- buckling about weak axis

α 0.49

φ 0.5 1 α λ op 0.2. λ op2. φ 0.672=

χ z1

φ φ 2 λ op2 χ z 0.863=

- lateral torsional bucklingα LT 0.76

φ LT 0.5 1 α LT λ op λ LT.0. β λ op

2..φ LT 0.605=

χ LT1

φ LT φ LT2 β λ op

2.χ LT 0.946=

4.5.2.5 Global stability resistance of the frame

The global stability resistance of the frame is calculated in the cross-section determioned in Section 4.5.2.1 using the reduction factor method and the conservative interaction formulae:

η Nβ N N K2.Ed

.

χ z A c.eff. f y

. η N 0.079=

η Mβ M M K2.y.Ed.red

.

χ LT W c.y.pl. f y

.η M 0.843=

η glob.stab η N η M η glob.stab 0.922= Megfelel!Adequate!

The examination was performed by the ConSteel software too.


131

The utilization of global buckling resistance at the bottom flange of the beam haunch may be calculated by linear interpolation. The result is approximately: 0,89.


132

Annex 12 Method of reduction factor

The method of reduction factor is based on the linear elastic analysis of the geometrically perfect design model. The buckling phenomenon is taken into consideration by the appropriate buckling reduction factor. The main properties of the method are summarized in the table:

model & analysis details imperfections no type of analysis 1st order design formula reduction factor

Example: Column buckling resistance The column has rigid column base. The top of the column is free in direction y and fix in direction z. The column is loaded by 160kN concentrated load at top. The cross-section of the column is HEA200, the grade of material is S235 and the height is 6 meters.

structural length [mm] L 0 6000

elastic moduli [N/mm2] E 210000

cross-sectional aera [mm2] A 5383

moment of inertia [mm4] I z 13360000

buckling length factor υ z 2.0

design force [kN] N Ed 160

critical force [kN] N cr.zπ 2

E. I z.

υ z L 0. 2

1

1000. N cr.z 192.293=

cross-sectional resistance [kN] N pl.Rk A f y. 1

1000. N pl.Rk 1.265103.=

reduced slenderness λ zN pl.Rk

N cr.z

imperfection factor α z 0.49

coefficient φ 0.5 1 α z λ z 0.2. λ z2.

buckling reduction factor χ z1

φ φ 2 λ z2

χ z 0.127=

partial factor γ M1 1.0

buckling resistance [kN] N b.Rd.zχ z N pl.Rk

.

γ M1N b.Rd.z 160.023=

utilization of resistance ηN Ed

N b.Rd.zη 1=

Fig. M12 Column buckling resistance by the method of reduction factor


133

Annex 13 Method of equivalent imperfection

The method of equivalent imperfection is based on the non-linear elastic (second order) analysis of the geometrically imperfect design model. The buckling phenomenon is taken into consideration by the appropriate local (initial out-of-curvature) and global (initial inclination) imperfections. The examination of the cross-section resistance involves the effect of the global buckling phenomenon. The main properties of the method are summarized in the table:

model & analysis details imperfections local & global type of analysis 2nd order design formula conservative interaction formulae

Example: Column buckling

The structure can be seen in Annex 12.

The design model with initial out-of-curvature (local imperfection) and inclination (global imperfection) is shown by the Figure M13. The method leads the result which was given by the method of reduction factor: • Initial equivalent imperfections - global imperfection

0041,0

0,1

816,06

2

L

2200

1

mh0

m

h

0

===

===

=

ααφφα

α

φ

- local imperfection

200

Le

curve'c'

0 =

• Design forces in the appropriate cross-section due to the design force and the

equivalent imperfections, see Figure M13:

kNm33,41M

0M

kN160N

Ed.z

Ed.y

Ed

=

==


134

Fig. M13 Column buckling resistance by the method of equivalent imperfections

Fig. M13 Column buckling resistance by the method of equivalent imperfections

cross-sectional resistance [kN]

N pl.Rd

A f y.

γ M1

1

1000. N pl.Rd 1.265103.=

sectional moduli [mm3]

W pl.z 200000

partial factorγ M0 1.0

nyomatéki ellenállás [kNm]

M pl.Rd.zW pl.z f y

.

γ M0

1

1000000. M pl.Rd.z 47=

design force [kN]

N Ed 160

design moment [kNm]

M z.Ed 41.33

utilization of resistance

ηN Ed

N pl.Rd

M z.Ed

M pl.Rd.zη 1.006=


135

Annex 14 Method of partial equivalent imperfection

The method of partial equivalent imperfection is based on the non-linear elastic (second order) analysis of the geometrically partial imperfect design model. The buckling phenomenon is taken into consideration partially by the appropriate reduction factor and partially by the equivalent global imperfection. The main properties of the method are summarized in the table:

model & analysis details imperfections global type of analysis 2nd order design formula buckling interaction formulae (the

structural length is the buckling length)

Example: Column buckling

The structure can be seen in Annex 12.

The design model with the initial inclination (global imperfection) and the calculation are shown by the Figure M14. It can be seen that the method overestimates the buckling resistance of the column with 7%. This method may be used for preliminary design.

• Global equivalent imperfection

0041,0

0,1

816,06

2

L

2200

1

mh0

m

h

0

===

===

=

ααφφα

α

φ

• Design forces calculated on imperfect model with non-linear elastic analysis

kNm71,19M

0M

kN160N

Ed.z

Ed.y

Ed

=

==


136

structural length [mm] L 0 6000

elastic moduli [N/mm2] E 210000

design strength [N/mm2] f y 235

cross-sectional area [mm2] A 5383

moment of inertia [mm4] I z 13360000

sectional moduli [mm3] W pl.z 200000

design force [kN] N Ed 160

design moment [kNm] M z.Ed 19.71

elastic ctritical force [kN] N cr.zπ 2

E. I z.

L 02

1

1000. N cr.z 769.171=

cross-sectional resistance [kN] N pl.Rk A f y. 1

1000. N pl.Rk 1.265 103.=

reduced slenderness λ zN pl.Rk

N cr.zλ z 1.282=

imperfection factor α z 0.49

coefficient φ 0.5 1 α z λ z 0.2. λ z2.

buckling reduction factor χ z1

φ φ 2 λ z2

χ z 0.396=

partial factors γ M0 1.0 γ M1 1.0

buckling resistance [kN] N b.Rd.zχ z N pl.Rk

.

γ M1N b.Rd.z 501.344=

bending resistance [kNm] M pl.Rd.zW pl.z f y

.

γ M0

1

1000000. M pl.Rd.z 47=

coefficient CMz 0.9

interaction factor k zz CMz 1 2 λ z. 0.6

N Ed

χ z N pl.Rk.

.. k zz 1.464=

utilization of resistance ηN Ed

N b.Rd.zk zz

M z.Ed

M pl.Rd.z

. η 0.933=

Fig. M14 Column buckling resistance by the method of partial equivalent imperfection


137

Annex 15 Interaction factors for Method 2

The following expressions are from EN 1993-1-1:2005 Eurocode 3: Design of steel structures, Part 1.1: General rules and rules for buildings, Annex B. The expressions and parameters are valid for compressed and bended members with hot-rolled or welded I sections susceptible to torsional deformations. Class 1 & 2 cross-sections

( )

⋅⋅⋅⋅+⋅

⋅⋅⋅⋅−+⋅=

yy

EdMmy

yy

EdMymyyy fA

N.C;

fA

N.Cmink

χγ

χγλ 11 801201

If 40.z ≥λ then

( ) ( )

⋅⋅⋅−⋅⋅−

⋅⋅⋅−⋅⋅⋅−=

yzmLT

EdM

yzmLT

EdMzzy fA.C

N.;

fA.C

N.maxk

χγ

χγλ

25010

1250

101 11

If 40.z <λ then

( )

⋅⋅⋅−⋅⋅⋅−+=

yzmLT

EdMzzzy fA.C

N.;.mink

χγλλ

25010

160 1

Class 3 & 4 cross-sections

⋅⋅⋅⋅+⋅

⋅⋅⋅⋅⋅+⋅=

yy

EdMmy

yy

EdMymyyy fA

N.C;

fA

N.Cmink

χγ

χγλ 11 601601

( ) ( )

⋅⋅⋅−⋅⋅−

⋅⋅⋅−⋅⋅⋅−=

yzmLT

EdM

yzmLT

EdMzzy fA.C

N.;

fA.C

N.maxk

χγ

χγλ

250050

1250

0501 11

The Cmy and CmLT equivalent moment factors depend on the shape of the bending moment diagram: • Linear moment diagram (-1≤ψ≤1) 404060 ...Cm ≥⋅+= ψ

• Non-linear moment diagram (0≤ψ≤1) 0≤ψ≤1 és 0≤α≤-1 - distributed design force 408010 ...C sm ≥⋅−= α

- concentrated design forces 4080 ..C sm ≥⋅−= α

M ψM

M ψM

αM


138

-1≤ψ≤1 and 0≤α≤1 - distributed design force hm ..C α⋅+= 050950

- concentrated design forces hm ..C α⋅+= 100900

Important rules for the equivalent moment factors: • For sway frame 90.Cmy = should be applied!

• For CmLT the moment diagram between two neighbouring lateral and fork supports should be considered!

• For Cmy the moment diagram on the column or on the whole beam should be considered

(between two neighbouring supports in the plane of the structure)!

M ψM

M/α


139

Annex 16 Simple method using ConSteel software

(application guide) The simple method for global stability resistance of structural members (columns, beams) may be preformed by the ConSteel program. Before the stability examination the First order and the Second order analysis as well as the Cross-section resistance options should be executed on the structure, see Figure M16.1. The options of the stability examination can be found under Member checks (1) label. Selecting the Start designer module option (2) the structural model appears on the graphical window where the member to be examined should be selected (3). The selected member should be added to the Member table (4) where more members can be collected. Selecting the actual member in the table (5) the Select option (6) can activate the Design table, see Figure M16.2. The load combination related to the critical cross-section resistance is selected automatically as actual load combination (7). In the next step the appropriate examination should be selected. The examination can be one of the Pure cases (8) or one of the Interaction cases (9). In the case of the actual design project the Interaction cases, the Method 2 (10) and the Interaction of buckling and lateral torsional buckling (11) options should be selected.

Fig.M16.1 Select member to examine by the interaction design formulae

After setting the initial parameters of the examination, the design procedure can be started by the Next option (11). First the design parameters of the flexural buckling about the y-y major axis should be determined, see Figure M16.3. The graphical window shows the member (12) with the appropriate supports in the plane of the structure (in-plane buckling). The in-plane buckling length is assumed automatically equal to the structural length (13).

2 1

3

5

4

6


140

Fig. M16.2 Set design properties for global stability examination The default buckling length can be modified by the engineer (14). Figure M16.4 shows the table of modification. In the table the buckling length factor (15) or the critical load amplifier (16) can be defined. (The critical load amplifier may be determined by partial stability analysis too. The method is over the objectives of this teaching material, therefore the details are neglected.) Using the Next option on the design table (Figure M16.3), the procedure steps to the out-of-plane flexural buckling problem, see Figure M16.5. The content of the table is similar to the table of the in-plane buckling problem. The graphics shows the lateral supports (17) which divide the member into equivalent members (18). Accepting or modifying the design parameters, the next stability problem is the lateral torsional buckling, see Figure M16.6. The content of the table is similar to the table of the in-plane buckling problem, but it is a bit complicated.

Fig.M16.3 Design parameters for in-plane flexural buckling

7 8

10

11

12

13

9

11

14


141

Fig.M16.4 Modification of the initial design parameters

Fig.M16.5 Design parameters for out-of-plane flexural buckling

Fig.M16.6 Design parameters for lateral torsional buckling

15

16

17

18

19


142

It is noted that the program assumes fork support (restricted rotation) at the lateral supports. Accepting or modifying the design parameters, the Check option (19) executes the evaluation of the interaction design formulae. The table of results contains the following information, see Figure M16.6: - the adequate case (member, load combination and buckling case) (20); - the adequate equivalent members (21); - the summary of the result (22); - the design parameters for the pure buckling modes, respectively (23).

Fig.M16.7 Result of the interaction design formulae for global stability resistance Notes: The actual version of the design module does not allow the examination of haunched beams and tapered members. The new version which allows the design of these members will be launched at the end of 2011.

20

21

22

23

23


143

Annex 17 General method using ConSteel software

(application guide) The application of the general method requires a design model which has realistic lateral support system. First the Analysis label (1) should be selected, and then the Analysis parameters option (2), see Figure M17.1. On the table the Buckling analysis option (3) should be switched on, and then the analysis can be executed.

Fig.M17.1 Set design parameters for global stability analysis

After the execution of the stability analysis it should be checked whether the buckling mode and the critical load amplifier related to the adequate load combination satisfy the conditions required by the general method (see Paragraph 5.2.2), or not. For visualisation the Buckling option (4) and then the adequate load combination (5) should be selected. The graphics will show the buckling mode with the selected graphical style (6), see Figure M17.2.

Fig.M17.2 Check the buckling mode and the critical load amplifier

3

1 2

5 6 4


144

The number of the critical load amplifiers was specified at the setting of the analysis. In the eigenvalue box (7) the lowest value is selected by program. The program uses this lowest critical load amplifier in the formulae of the general method, unless the engineer changes it. The default critical load amplifier can be changed selecting a new one from the list (8). Clicking on the graphics (9) the Select eigenvalue for design option (10) should be selected in the opened menu, see Figure M17.3.

Fig.M17.3 Select critical load amplifier for the general method

Accepting the default lowest critical load amplifier or selecting a higher one, the Global checks label (11) should be selected, and then the Global resistance option (12). In the appeared Design… table (13) only the appropriate load combination (which is related to the critical cross section resistance) should be switched on (14), see Figure M17.4.

Fig.M17.4 Select the adequate load combination for the examination

7

8

10

12

11

14

9

13


145

In the Design settings table the Buckling check option (15) should be switched on, and then the appropriate design options should be selected (16,17,18), see Figure M17.5. Check of the global stability resistance of the structure by general method can be executed by the Calculation option (19).

Fig.M17.5 Set the parameters for the general method

The result of the general method appears in the graphics, see Figure M17.6. The utilization of the global stability resistance of the cross-sections can be visualized by the cursor (20). The actual value can be fixed to the cross-section using the right button and the Marker option (21). The parameters of the general design formula can be available by the Calculate section option (22). The table contains all the parameters of the general formulae, including the utilization (23) and the appropriate standard paragraph (24), see Figure M17.7.

Fig.M17.6 Visualise utilization of resistance and design parameters

15

16

17

18

19

20

21

22


146

Fig.M17.7 Design parameters

23 24


147

Practice 8

DESIGN OF THE JOINTS


2010-2011 Budapest


148

8.1 General The frame structure should be divided into structural members in order to reasonable transmission conditions and erection. Both points of view may be satisfied if the frame is divided into straight members such as columns and beams. In this case the following joints should be designed (see the Figure 54):

� Column bases � Beam-to-column joints � Beam-to-beam joint

Fig.54 Joints of the frame to be designed

The column bases can be rigid or pinned. Rigid column bases are favorable from steel structural point of view, but the cost of the basement may be higher. The beam-to-column joints are located at the maximum of the in-plane bending moment. The beam-to-beam joint is located at the ridge point. The suggested constructions of the joints are shown in the following paragraphs. Design of the joints is performed by the ConSteel/Joint software which follows the specifications of the EC3-1-8 standard. The application of the software is illustrated in the Annex 18.

8.2 Design of the column bases Theoretically there are three types of column bases:

• Simple (pinned) • Semi-rigid • Rigid

The specific problems of the construction and the design of the column bases are discussed in the following paragraphs.


149

8.2.1 Simple (pinned) column base Figure 55 shows the construction of the simple column base. The base plate is connected to the concrete basement by two anchor bolts. This construction may be used for hot-rolled or welded I or H sections as well as for tapered columns. The following sizes may lead to the ‘optimal’ solution:

• 12-16 mm thick base plate • 4.6, 4.8 or 5.6 grade of anchor bolt • 20, 24 or 30 mm diameter of anchor bolt.

This column base has been assumed as pinned connection in the static calculation for many years. According to EC3-1-8 this column bases construction belongs to the class of semi-rigid joints. However, the previous assumption (such as the simple column base is pinned) has not been led to any degradation or structural failure. For favorable practice we can declare that the simple column base can be considered as pinned joint. The resistance of the frame with simple column bases is higher than the resistance of the same frame with real pinned column bases. In case of relatively high depth sections (more than 400-500 mm) and thick base plate (thicker than 16 mm) the construction is not suggested applying. The moment resistance of the column base may be relatively large due to the considerable distance between the rotational point (compressed flange) and the anchor bolts. This constructional response may lead to considerable tension force in the anchor bolts. The tension force may destroy the anchor bolts or/and the base plate.

Fig.55 Simple column base construction with anchor bolts

8.2.2 Semi-rigid column base Figure 56 shows the typical construction of the semi-rigid column base. This column base may be applied for hot-rolled or welded columns. Basically, this construction leads to semi-rigid class. The rigid class may not be reached due to the following reasons:

• the cross-sectional area of the tensioned anchor bolts is relatively small • the 8.8 or 10.9 grade of anchor bolts may lead large elongation • too large base plate would be required.

The moment resistance of this column base depends on the diameter and the grade of the anchor bolts, and the thickness and the extension of the base plate. Relatively large extension of base plate may disturb the architectural construction of the wall system. However, any construction with reasonable design parameters may lead to semi-rigid behavior, and the initial elastic stiffness of the joint should be taken in the analysis of the frame into consideration. Because of these problems this column base construction is not suggested using within the present design project.


150

Fig.56 Semi-rigid column base construction

8.2.3 Rigid column base Figure 57 shows a special construction for rigid column bases. In the lack of design specifications the design of this construction requires special consideration. The algorithm of the calculation of the moment resistance is shown in the Annex 19. The ConSteel/Joint software follows this procedure. The stiffness classification of this construction is not performed, but it can be assumed that this column bases is rigid . Following design guidelines may lead to adequate and economical construction:

• First the design forces and moments should be defining (the quadratic equation for the length of the compressed concrete area can not be solved for excessive or extremely low design moment).

• The optimal height of the stiffener plates is about 200-300 mm, depending on the depth of the column section.

• The thickness of the stiffeners should be equal to, or grater than, the thickness of the flanges of the column section.

• The optimal size of the base plate has at least 100-100 mm extensions. The width of the base plate should be the minimum which is possible.

• The optimal thickness of the base plate is 20-30 mm, depending on the size of the column section.

• The grade of the anchor bolts should be 4.6, 4.8 or 5.6. The optimal diameter of the bolts depends on the thickness of the base plate. Extremely the diameter can be 48 or 56 mm.

• The type of the welds connecting the base plate to the stiffener is basically double fillet welds. In case of sections with narrow flanges (ex. IPE 300-400) a single fillet weld is used outside of the stiffener. For the safe the program takes the welds which located at the extended part of the base plate into consideration.

Fig.57 Rigid column base construction


151

8.2.4 Application The details of the design of the rigid column bases of the actual example are shown in this following paragraph. The design was performed by the ConSteel/Joint software. The application guide of the software can be found in the Annex 18.

4.6 Design of the joints

The frame consists of straight fabrication units (columns and beams) which are connected by moment resistance joints. Following joints are designed:- column bases- beam-to-column joints- beam-to-beam jointDesign is performed by the ConSteel/Joint software.

4.6.1 Design of the column bases

Fix column bases were assumed in the analysis. Therefore rigid column bases sholud be designed.

4.6.1.1 Initial parameters

Design forces- relevant load combination: LC 5- design forces [kN;m]

N Ed 179.7 M y.Ed 354.4 V z.Ed 116.7

Geometrical parameters [mm]- base plate: 460-780 (t=20)- stiffener plates: 240-780 (t=20)- anchor bolts: grade 5.6 M30

Welds [mm]- fillit welds which connect the column section to the base beam

double welds at the flanges: 5double welds at the web : 4

- fillit welds which connect the stiffener plates to base plateflange-to-stiffener weld: 5stiffener-to-base plate weld: 6

4.6.1.2 Computer based design

Results of the computer based design are shown in the picture below. The full design documentation can be found in the Annex.


152

8.3 Design of the beam-to-column joints 8.3.1 Types of joint construction From constructional point of view there are two solutions for the beam-to-column joint:

• end-plated • end-plated with haunch.

The aim of the design is a rigid and full strength joint excepting the situation where the construction does not allow full strength behavior. For example the beam-to-column joint with tapered structural members is normally partial strength joint. Figure 58 shows the joint construction with end-plate. The end-plate has 10-15 mm extension to ensure room for the double fillet welds. The extension may be neglected using deep penetration fillet or but welds, but the solution may be expensive.

Fig.58 Construction for beam-to-column joint with end-plate

Figure 59 shows the beam-to-column solution with haunch. From the joint design point of view it does not matter that the haunch is short or long. The haunch is made from a piece of beam section which is cut across as it is illustrated in the figure.

Fig.59 Construction for beam-to-column joint with haunch

piece of beam section

cross cut


153

8.3.2 Stiffeners Stiffeners are the important parts of the joint. The types of the stiffener can be the following:

• Web stiffener • Flange stiffener • Shear stiffener.

The web stiffener is welded to the web of the column in the line of the beam flanges, see Figure 60. Stiffeners mean higher cost but basically they are needed to get rigid and full strength joint.

Fig.60 Web stiffeners in the beam-to-column joints (a) end-plated joint; (b) haunched joint

The flange of the hot-rolled column may be reinforced by flange stiffener (backing plate), see Figure 61. The backing plate can be considered in the calculation if the plate is connected to the web of the column with appropriate size of weld.

Fig.61 Reinforced column flange using backing plate The resistance of the sheared column panel may be reinforced by shear stiffener, see Figure 62. The shear stiffeners may lead to much labor work.

(a) (b)


154

Fig.62 Column web panel with shear stiffener (a) end-plated joint; (b) haunched joint

8.3.3 Design parameters The construction of the joint may lead to rigid and full strength joint if the next guidelines are followed:

• The L b beam length may be taken as the distance between the two columns. • The thickness of the end-plate should be equal to (or greater than) the thickness of the

column flange. Thicker end-plate may be inefficient. • The grade of bolts should be 10.9 rather than 8.8. The diameter of the bolts should

exceed the thickness of the end-plate. • The thickness of the web stiffeners should be equal to (or greater than) the thickness

of the beam flange. Thicker stiffener may be inefficient. • Shear stiffener is normally not applied. If it is applied, its thickness should be equal to

the thickness of the web stiffeners. • In many cases the resistance of the joint is determined by the resistance of the column

flange for bending. The thickness of the flange of the welded sections may be increased using thicker plate at the joint, see the Paragraph 8.3.4. The flange of hot-rolled sections may be reinforced by backing plate.

• The arrangement of the bolts may be based on two methods. The conservative method uses uniformly distributed bolts, while the progressive method applies the required number of tensioned bolts and one row of bolts at the compressed flange, see the Figure 60.

• In case of haunched beam the size of the room between the beam flange and the haunch flange should be checked: the bolt should be placed and turned freely.

8.3.4 Special construction for welded sections with high depth Extended end-plate or haunch are normally not used in the joints of tapered members, see the Figure 63a. Tapered members can be constructed with relatively thin web (6-8 mm) and flanges (12-16 mm). These thicknesses often lead to semi-rigid and partial strength joint. It is not suggested applying web and shear stiffeners to reinforce the thin web and flange plates. Instead of stiffeners special end construction is used where the web panel and the flange plate are replaced by thicker plates, see the Figure 63b. The replacing plates are 1,5÷2,0 times thicker than the original ones.

(a) (b)


155

Fig.63 Beam-to-column joint of welded members with slender plates (a) original construction;

(b) construction with replacing plates.

8.3.5 Application The details of the design of the rigid beam-to-column joint are shown in this paragraph. The design is performed by the ConSteel/Joint software. The application guide of the software can be found in the Annex 18.

4.6.2 Design of the beam-to-column joint

In the analysis rigid beam-to-column connections were assumed. Therefore moment resistant connections sholud be desined. The web panels should be reinforced by shear stiffener.

4.6.2.1 Initial design parameters

Design forces- relevant load combination: LC 4.- design forces [kN;m]

in the beam

N Ed 142.2 M y.Ed.1 368.0 V z.Ed 148.6

M y.Ed.2 469.6

reduced moment is used at the connection (interpolation between two points)L k 3500

M y.Ed.red M y.Ed.2 h cM y.Ed.2 M y.Ed.1

L k

4

. M y.Ed.red 411.543=

in the column N Ed 171.0 M y.Ed 491.8 V z.Ed 114.3

Geometrical parameters [mm]- end-plate: 240-750 (t=20) - flange of the haunch: 240-3500 (t=20)- web of the haunch : 300-3500 (t=6) - web stiffeners: 112-468 (t=16)- grade of the bolts: M27 10.9 - shear stiffener: 460-700 (t=8)- backing plate: 112-700 (t=8)

(a) (b)

Replacing web plate

Replacing flange plate


156

Welds [mm]- welds

double fillet welds for the upper flange: 6double fillet welds for the web: 3double fillet welds for the bottom flange: 6

- welds for the haunchdouble fillet welds for the flange: 7double fillet welds for the web: 3

4.6.2.2 Checking

The results of the computer based design are shown in the picture (see below). The full computer documentation of the design can be found in the Annex.

8.4 Design of the beam-to-beam joint 8.4.1 Joint constructions Design of the beam-to-beam joint is based on the design rules and constructional details which were used for to the design of the beam-to-column joints (see the Paragraph 8.3). Figure 64 shows the possible constructions.

Fig.64 Constructions for the beam-to-beam joint

(a) (b) (c)


157

Construction (a) leads to the lowest cost. If the utilization of the cross-sectional resistance of the beam is relatively low as well as the depth of the section is high (ex. IPE section), the construction may have adequate moment resistance. The moment resistance can be increased by two rows of tension bolts. Construction (b) with extended end-plate and tensioned bolts may give higher resistance. The size of the extension of the end-plate should be the minimum which is allowed by the bolts. Conservatively, extended web plate may be used too. Construction (c) gives the strongest joint, but the placing of the bolts in the room between the flanges of the beam and the haunch may lead to problems. Following the next guidelines the construction may lead to optimal joint:

• the L b beam length may be taken as the distance between the two columns; • the thickness of the end-plates are 16-25 mm, respectively, depending on the size of

the beam section; • it is suggested using the same grade and size which were used at the beam-to-column

joints; • construction (c) might be avoided; • uniformly distributed and high density bolt arrangement might be avoided.

8.4.2 Application Details of the design of the rigid beam-to-beam joint are shown in this paragraph. The design is performed by the ConSteel/Joint software. Guidelines for the software application can be found in the Annex 18.

4.6.3 Design of the beam-to-beam joint

In the analysis rigid beam-to-beam connection was assumed. Therefore moment resistant end-plated connection should be designed.

4.6.3.1Initial parameters

Design forces

- relevant load combination: LC 4- design forces [kN;m]

N Ed 109.2 M y.Ed 172.6 V z.Ed 19.3

Geometrical parameters [mm]

- end-plate: 240-426 (t=20)

- grade of bolts: 10.9 M27

Welds [mm]

- double fillet welds at upper flange: 6- double fillet welds at web: 3- double fillet welds at bottom flange: 6

4.6.3.2 Checking

Results of the computer based design procedure are shown by the picture (see below). The full computer documentation can be found in Annex.


158


159

Annex 18 Design of the end-plated moment resistant joints using

the ConSteel software (application guide)

M.18.1 Execute the csJoint program (starting) The csJoint program can be executed in two modes:

• within the ConSteel program • directly (csJoint.exe)

There two modes to execute the program within the ConSteel program: • model independent • based on structural model

Both of the two modes are shown below, but details are given for the structural model based design method. M.18.1.1 Model independent mode The csJoint program can be executed within the ConSteel program. Actual structural model is not needed for this application. First a new structural model folder should be created, and then the Structural members label (1), and then the Edit joints option (2) should be selected, see Figure M18.1. If there are joint models in the folder, the actual model can be selected from the list (3). If there is no model in the folder or a new model is wanted creating, the Create… option (4) should be selected.

Fig.M18.1 Execute csJoint program within the ConSteel and create new joint model

In the appeared table the Name (5) of the joint model should be given firstly, and then the sections of the joint can be selected by the Load sections option (6). By the Next ⟩⟩⟩⟩ option (7) the design of the joint can be started, see Figure M18.2.

M.19.1.2 Structural model based mode The structural model based mode requires a structural model which has the joints to be designed. First the Structural members label (8) and then the Create joint by model option (9) should be selected, see Figure M18.3. The joint can be created by clicking on the

1 2

3 4


160

Fig.M18.2 Give the name of the joint model and select sections

Fig.M18.3 Create joint model by model based mode

actual node of the structural model. The program realizes the type of the joint and the sections which compose the joint. Figure M18.4 shows the procedure where the column base is created by the model based mode (10-12).

Fig.M18.4 Create column base by model based mode If the joint consists of more than two members, the joint model can be simplified by neglecting members (13).

5

6 7

8 9

11

12

10

13


161

M.18.1.3 Model independent mode The ConSteel/Joint software can be executed directly by the csJoint. This mode is useful when there is no ConSteel structural model or the model was built up in other software. Figure M18.5 shows the starting panel where the actual existing joint folder (14) can be opened, or a new joint folder can be created (15). In case of new folder the name of it should be given, and then the design procedure can be started by the Create… option. From this point the program follows the steps described in the Paragraph M18.1.1.

Fig.M18.5 Starting panel of the csJoint software

M.18.2 Design of simple column base First the type of the joint (16) and then the type of the column base (17) should be selected, see Figure M18.6. Using the Create… option (18) the design panel appears with the initial construction of the simple column base, see Figure M18.7.

Fig.M18.6 Select the type of the joint and the type of the column base First the End-Plate option (19) of the menu may be selected, and then the design parameters of the base plate and the initial bolt arrangement can be defined, see Figure M18.8. The relevant values of the design parameters may be the follows: • Number of bolt rows (20): 1 • Position of end-plate (21): -15 • Height (22): „actual value” • Thickness (23): 12 or 16 • Bolt distances (24): „actual value”

14 15

17

16

18


162

Fig.M18.7 The design panel with the initial column base construction

Fig.M18.8 Initial and final settings of the design parameters In the next step the Joint loading option (25) may be selected and then the Input of joint loading (26) and the User defined joint loading (27) options, see Figure M18.9.

19

20

21

22 23

24


163

Fig.M18.9 Design joint loading and results of design

The design force table can be opened by the New option (28). According to the rules of directions (see the figure below the force table) the normal force (29) and the shear force (30) can be defined. The results of the checking (31) can be found in the table at the right hand side part of the design panel. M.18.3 Design of rigid column base First the type of the joint and then the type of the column base (32) should be selected, see the Figure M18.10. The design panel and the initial construction of the rigid column base appear by the Create… option (33), see the Figure M18.11. In the next step the Joint loading option (25) can be selected, and then the Input of joint loading (26) and the User defined joint loading (27) options can be switched on, see the Figure M18.9. The design force table can be opened by the New option (28). According to the rules of directions the design forces can be given, see the Figure M18.12. The results of the actual checking (34) can be found in the table at the right hand side part of the design panel, where the actual „error message” (red color message) means that the size of the base beam is too low. Selecting the Base plate option (35) the height of the plate (36) can be increased as far as the „error message” disappears, see the Figure M18.13.

Fig.M18.10 Select the type of column base

25

26 27

28

29

30

31

32

33


164

Fig.M18.11 Initial construction for the rigid column base

Fig.M18.12 Set design loading and discuss the result of the checking

Fig.M18.13 Set the adequate height of the base beam

34

35

36


165

In the next step the size of the stiffeners (37-39) and the welds (40-41) can be set, see the Figure M18.14.

Fig.M18.14 Set the adequate size of the stiffeners and the welds The “optimal” construction may be reached by the change of the design parameters, see Figure M18.15. The construction of the column base may be “optimal” if the following guidelines are met:

• the maximum utilization is close to 100%; • the other utilizations are high as possible; • the height of the stiffeners is low as possible; • the thickness of the base plate is low as possible; • the width and the height of the base plate is low as possible; • the diameter of the anchor bolts is low as possible.

Fig.M18.15 The “optimal” construction

37

38

39

40

41


166

M.18.4 Design of beam-to-column joint with haunched beam First the type of the joint (42) and then the type of the connection (43) should be selected, see Figure M18.16. The design panel and the initial construction of the beam-to-column joint appears by the OK… option (44), see the Figure M18.17.

Fig.M18.16 Type of joint and connection

Fig.M18.17 Initial construction for the beam-to-column joint The required joint construction can be reached by the following steps:

• Height of the column The Column option of the menu should be selected and then the Lc – Average height of column (45) should be given. The Lsr – Position of reference plane (46) may be taken as 10-15 mm, see the Figure M18.18.

42 43

44


167

Fig.M18.18 Height of the column

• Slope of the beam The slope of the beam can be set in the Position of beam sub-panel (47), see the Figure M18.19.

Fig.M18.19 Slope of the beam

• Size of the haunch Selecting the Beam option (48) and the Haunch on bottom flange label (49) and then selecting the Haunch with flange option (50) the size of the haunch can be set. Initial size can be generated by the Default option (51). The optional bottom web stiffener can be positioned to the flange of the haunch (it is suggested) if the Assign the stiffener to haunch flange option (52) is switched on, see the Figure M18.20.

Fig.M18.20 Set the haunch for the beam

47

48

49

50

51 52

45

46


168

• Size and position of the end-plate Selecting the End-plate option (53) the position (54) and the height (55) of the end-plate can be set, see Figure M.18.21.

Fig.M18.21 Size of the end-plate

• Grade and size of the bolts The grade and the size of the bolts can be defined using the Modify… option (56). In the appeared table first of all the size of the bolt (57) and the grade of the material (58) can be set, see the Figure M18.22.

Fig.M18.22 Size and grade of the bolts

• Arrangement of the bolts Selecting the End-plate option (53) the arrangement of the bolts can be set in the Vertical positions of bolts sub-table (59), Figure M.18.23. First the number of the bolts (60) should be set and then the positions of the rows (61). The setting is controlled by graphics (62).

• Web stiffeners Web stiffeners are applied optionally. Selecting the Stiffeners option (63) the upper

(64) and the lower (65) web stiffeners can be switched on, respectively, see Figure M.18.24. The initial thicknesses of the stiffeners are the minimum (they are equal to the thickness of the flanges).

54

55

53

57

58

56


169

Fig.M18.23 Set arrangement of the bolts

Fig.M18.24 Web stiffeners

• Design joint loading Selecting the Joint Loading option (66) the Input of joint loading (67) and the User defined joint loading (68) options can be switched on. In the next step the design forces should be wrote into the force table (69), see Figure M18.25.

Fig.M18.25 Design joint loading

59 60

61

62

63

64

65

66

67 68

69


170

The construction of the joint and the result of the checking are shown on the design panel, see Figure M18.26. The no adequate utilizations of the components are written by red color (70).

Fig.M18.26 Evaluation of the design The next step is to refine the design parameters. Keeping the following guidelines the “optimal” construction can be reached:

• The thickness of the end-plate is optimal if the moment resistance is not increased applying thicker plate.

• The size of the bolts is optimal if the moment resistance is not increased applying greater diameter.

• The number of the bolt rows is optimal if the moment resistance is not increased or slightly increased applying more rows.

• It is checked that the L b beam length is equal to the distance between the columns. If the design is not adequate, the sizes of the joint components determined by the program should be changed. Figure M18.27 shows a program message as an example.

Fig.M18.27 The weakest components determined by the program

70


171

Higher shear resistance for the web component of hot rolled section may be reached by shear stiffeners (71) such as diagonal plates (72) or additional web plate (73), see Figure M18.28. Thicker column web plate rather than web stiffener may be used in case of welded section.

Fig.M18.28 Web stiffeners Sometimes the weakest component of the joint is the column flange. In case of hot rolled sections the flange may be reinforced by backing plate (74-76), see Figure M18.29. In case of welded sections thicker flange plate rather than backing plate may be used.

Fig.M18.29 Backing plate to reinforce the column flange of the hot rolled section

M.18.5 Design of beam-to-column joint with tapered members The creation of the beam-to-column joint can be seen in the Figure M18.16. The beam and the column are welded sections with 240-16 flanges and 868-8 web, respectively. The initial construction which is generated by the program is shown in Figure M18.30. Because of the relatively high web haunch or extended end-plate are not used. If the following guidelines are met in the design, an ‘optimal’ construction can be reached:

71

72 73

76

75

74


172

Fig.M18.30 Initial construction for the beam-to-column joint of tapered members

• Selecting the Column menu option the L sr (length of the column up to the reference

plane) may be defined as 15-20 mm, and the L c (actual length of the column) should be defined, see the Figure M18.31.

Fig.M18.31 The actual length of the column • Selecting the Beam menu option the L b (length of the beam) may be defined as the

distance between the two columns, and the αααα (slope of beam) can be given, see the Figure M18.32.

Fig.M18.32 The length and the slope of the beam


173

• Selecting the Stiffeners menu option the Use upper stiffener and the Use lower stiffener options should be switched on, see the Figure M18.33.

Fig.M18.33 The web stiffeners

• Selecting the Joint loading menu option the design forces should be defined according to the rules of directions which are shown by the figure, see the Figure M18.34.

Fig.M18.34 Design joint loading

• Selecting the End-plate menu option the Position of end-plate should be defined as 15-20 mm, according to the actual value of L sr parameter. Later the Height end-plate parameter should be defined which is adequate if there is room for the outer fillet weld at the bottom flange of the beam, see the Figure M18.35. Selecting the Modify… option the grade of the bolts can be defined as 10.9 (optionally 8.8) and the diameter of the bolts can be defined as 24 or 27 mm. The number of bolt rows can be selected as 3 or 4. The adequate bolt arrangement is defined in the Pitch of holes table.

After the first setting of the parameters the result of the checking should be examined. Figure M18.36 shows the actual design situation of the example. The problems emerged by the program should be solved by the next steps:

• The column web thickness does not satisfy the requirements. This problem may be solved if 1,5-2,0 times thicker web plate is used, see the Figure 63. In the example 14 mm thick column web is used. New reinforced column section can be defined according to the Figure M18.37.


174

Fig.M18.35 Size of the end-plate and the bolt arrangement

Fig.M18.36 Result of the checking (not adequate!)


175

Fig.M18.37 New cross-section

• The utilization of the moment resistance of the joint is more than 100%. The resistance can be increased using 1,5-2,0 times thicker column flange at the connection, see the Figure 63. In the example 20 mm thick column flange is used.

• The shear stiffness of the web is too low, therefore the joint is semi-rigid. The shear

stiffness can be increased if shear stiffener is applied, see the Figure M18.38.

Fig.M18.38 Shear stiffeners After refining the joint parameters the checking of the joint may show an adequate beam-to-column construction, see Figure M18.39.

Fig.M18.39 The adequate beam-to-column joint (reinforced column end and shear stiffener are used in the example)