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Abstract The paper presents the application of computer

codes in the advanced analysis of structures with tension

elements, cables. Static and dynamic analyses are performed

for a suspension pipeline crossing by considering a real wind

intensity recorded by a weather station. The effect of pre-

tension is discussed from the structure Eigen-modes aspect.

The static and dynamic analysis reveals different values for

element forces. A construction stage analysis is performed

using a particular module of finite element computer code

Keywords cable, construction stage, dynamic analysis,

suspension crossing.

I. INTRODUCTION

TRUCTURAL systems supporting fluid materials

transportation pipelines may be regarded as a continuous

structure avoiding encountered obstacles between the two

points of interest. The linear impediments such as rivers or

valleys met in their path may be overcome with

superstructures (above) or infrastructures (below). For both

solutions advantages and disadvantages are present and for a

good design the important factor is the area environment

either from geometry, sustainability or protection point of

view. The waterway crossing is an example that the choice of

solution is influenced by several considerations. One of themrefers to the environment impact. The disturbance of

environment for both aquatic and terrestrial plant and animal

life has to be minimized since a waterway crossing affects

these factors. Both crossings, under and above water, have to

take care at the hazardous and contaminated materials during

construction [1]. The underwater crossing might have a

greater effect over the environment because of the instability

of the river bed and from here a catastrophic event is possible

to occur. Waterways constructed above obstacles have the

advantage that it allows better site inspections and most of the

loading can be easily determined. Having a decision for a

structural system over the obstacle it only remains to decidewhich solution of the structure is better to use: suspension

This publication was supported by the European social fund within the

framework of realizing the project Support of inter-sectoral mobility and

quality enhancement of research teams at Czech Technical University in

Prague, CZ.1.07/2.3.00/30.0034.

I. Both is with the Czech Technical University in Prague, Prague, 16629

Czech Republic (corresponding author, phone: 0040-727882621; e-mail:

[email protected]).

A. Ivan is with the Politehnnica University of Timisoara, Timisoara,

Timisoara, 300006 Romania (e-mail: [email protected]).

crossing, cable-stayed crossing, self-supporting or trussstructure as a bearing structural system for the pipeline. The

span that needs to be covered by the crossing is the main

factor that influences this decision. Two reasonable solutions

are suspension crossing and cable-stayed crossing. The last

one has the advantage of smaller anchors and possibility of

building on soft soil, but if the span increases the towers will

have to increase too much [2]. To overcome this disadvantage

the appropriate solution are suspension crossings.

Towers, main cables (suspension cable), hangers, anchors,

lateral cables, cantilever (not necessary) and the pipeline are

components of the structural system of a suspension crossing.

The load path for these structures is created as follows: thegravitational loadings from the self-weight and the loading

given by the gas in the pipe is transmitted by the hangers to

the main cable. The hangers have various lengths

corresponding to the sag of the main cable. The main cables

transmit a part of the vertical component of the force in the

cable to the towers and the horizontal component is

transmitted to the anchors. The horizontal actions,

perpendicular to the crossing, are taken by the lateral cables

(wind guy cable), connected to the pipeline by the wind ties

[3].

The cable elements in these structures have an important

role and it is characterized by high resistance, high flexibility,

and a very small damping. Due to large displacements,

suspension crossings design should consider both static and

dynamic analysis.

Numerous methods of crossing erection are available in

practice and the decision for the solution is taken upon the

security and economic aspects. The forces in the cable

elements and bending moment in the pipeline are dependent

on the steps of structure assembling and a construction stage

analysis may reveal critical stages of force development.

Results of numerical simulations for a suspension crossing

with the span of 160m considering static and dynamic actions

are presented within the contents of this paper. The numerical

model was defined by means of members: cables weremodeled as cable elements taking into account initial stress,

2nd order geometrical nonlinearity and beam local

nonlinearity, towers elements and the pipe was modeled

using linear bar elements.

The paper will give the results of the analysis of the same

structure taking into consideration different masses for modal

analysis. A real wind velocity-time variation as recorded on

site is used for establishing the dynamic response of the

structure to wind action. Also a simulation on the staged

construction for the suspension crossing is performed.

Numerical simulations of a pipeline crossing

Ioan Both, Adrian Ivan

S

New Developments in Computational Intelligence and Computer Science

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II. CASE STUDY

The structure analyzed in this paper represents a crossing

with a span of 160m and two adjacent spans of 35m, an initial

deflection of suspension cable of 12.5m leading to a value of

12.8 for the span to cable sag ratio. The vertical hangers are

positioned at each 5m and the pipeline has a circular hollow

section with a diameter of 700mm and a thickness of 8mm.

There are two main cables in the vertical planes situated at 2m

and two inclined cables for lateral load and vertical

stabilization. Two towers are placed at the end of the pipeline

consisting of hot-rolled profiles HEB400 as vertical elements

and square hollow sections 150/4 as bracings. The hangers

and the wind ties have a diameter of 40mm whereas the main

cables and the lateral cables have a diameter of 60mm (Fig. 1).

Such structures are highly complex since flexible support

system may be attributed to the structure and for each element

the boundary conditions are determined and influenced by the

characteristics of the linked element [4]. Due to length

variation each node of the main cable will have different

interactions for the boundary conditions.

The cross section and material properties of the crossing are

presented in Table I, where: M-main, L-lateral, T-torsional

moment of inertia, E-modulus of elasticity, A-area of the

cross-section, Ix-moment of inertia with respect to x axis, Iy-

moment of inertia with respect to y axis. The properties of the

tower are given for the entire truss structure.

Table I

Element E

[N/mm2]

A

[mm2]

T

[mm4]

Ix

[mm4]

Iy

[mm4]

M cable 1.5-2e5 2827 0 0 0L cable 1.5-2e5 2827 0 0 0

Hangers 1.5-2e5 1194 0 0 0

Windguy 1.5-2e5 1194 0 0 0

Tower 2.1e5 46.6e3 3.17e5 4.7e10 1.2e9

Pipe 2.1e5 17.4e3 2.8e9 1.04e9 1.04e9

In the analysis of the structure the following values of

loading were considered:

self-weight program computed,

permanent load - 0.7kN/m,

imposed load from fluid - 3.675kN/m,

wind - 0.46kN/m,

pretension - variable.

All supports were considered to follow the restrictions only

for translational degrees of freedom and the elements of the

tower were also considered to be hinges.

For a dynamic analysis a load case defined function of the

recordings of the wind action was considered. The values of

the wind velocities were provided by the local weather station

for the west region of Romania monitored by an automatic

station with ultrasonic transducer VS425 (Fig. 2) on the

Mures river in Arad county, Varadia area. The maximum

values recorded since the weather station was installed, 2009,

are depicted in Fig.3.

III. LIMIT STATE ANALYSIS OF STRUCTURE

The forces and moments in the structural elements were

determined using the FEM computer code SAP2000 for both

static and dynamic analysis.

Damping ratios of such tension bar systems are particulardue to their range interval as shown in [5]. It is common to use

for a dynamic analysis proportional damping values from 0.04

to 0.1.

A certain level of pretension force is introduced in the

cables of the structure in order to obtain the desired geometry

in the final stage of construction. The Eigen modes of the

Due to the difference of 1.6s between the two cases of

considered structural mass the resulting forces may vary

Fig. 2 Wind recording station VS425

Fig. 3 Wind velocity

Fig. 1 Model of the case study


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significantly. The behavior of structure taking into

consideration the equivalent mass of self-weight is shown in

Fig. 4 and Fig. 5

Fig. 4 shows the displacement of pipeline nodes in the

horizontal plane for the dynamic analysis of wind action,

applying the modal matrix for the pretensioned state of

structure.



applying the modal matrix for the pretensioned and filled pipe,

state of structure.

The curve following the maximum values in the chart of

Fig. 4 Fig. 7 represent the midspan of the crossing whereas

the intermediate curves represent nodes between midspan and

towers.

Table II

Mode

mperm mperm+cvp

T [s]

(Kpretens)

T [s]

(Kfill)

T [s]

(Kpretens)

T [s]

(Kfill)1 3.2568 3.0821 4.8562 4.6177

2 2.1806 2.2154 3.2711 3.3525

3 2.0228 1.8336 2.9839 2.7400

4 1.8965 1.7298 2.8045 2.5675

5 1.4258 1.3731 2.0976 2.0711

6 1.3193 1.3669 1.9664 2.0195

The behaviour of structure taking into consideration the

equivalent mass of self-weight and imposed load is shown in

Fig. 6 and Fig. 7.



applying the modal matrix for the pretension state of structure.



applying the modal matrix for the pretension and filled pipe,

state of structure.

It can be seen that the maximum deflection of central node,

when the mass is taken only the self-weight, is larger than the

deflection in the case of equivalent mass from loaded pipeline,

200mm (Fig. 4) and 145mm (Fig. 6).

Not every node of the pipeline is following the sinusoidal

path but their period (frequency) is the same for each node,

therefore the first Eigen mode is relevant for analysis.

Table III Forces in the elements of the structure

Comb. AnalysisMain cable Wind cable Hanger Anchor Pipeline

N [kN] N [kN] N [kN] N [kN] Mz[kNm]

P+VStatic 810.1 551.7 12.4 898.4 60.5

Dynamic 805.8 444.2 12.6 893.8 21.6

P+

VP+V

Static 1596.8 376.6 30.5 1759.3 63.2

Dynamic 1593.0 390.9 30.6 1750.7 19.4

After 30s the deformed shape of the structure is stabilized

and by comparing the figures where the mass is taken from the

self-weight and the figures where the mass includes the

loading (filling) of the pipeline, we can observe that the final

displacement of the central node has the same value.

The remaining displacement is the result of the wind action

that does not cause a dynamic effect on the structure.

All the above show how much the state of stress, used for

dynamic analysis, influence the analysis results. Forces in

cables have insignificant variation whereas the dynamic

analysis leads to smaller bending moments in the pipeline

Fig. 5 Deflection - loaded state of structure (mperm)

Fig. 6 Deflection - pretensioned state of structure (mperm+cvp)

Fig. 7 Deflection - loaded state of structure (mperm+cvp)

Fig. 4 Deflection - pretensioned state of structure (mperm)


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cross-section.

IV. CONSTRUCTION STAGE ANALYSIS

The erection of suspension structures is performed in stages

where force values have a wide range of variation due to high

deformations permitted by cables. As an effect of structural

instability the structural system can change significantly and

may lead to critical situations. Therefore a construction stage

analysis is recommended to check the stability and stresses

that may develop during intermediate stages.

For tension bar systems the effects of pre-tensioning forces

are very important for the geometry during and after erection.

According to design codes there has to be no compression

forces in the cable elements of the structure. This would be the

case when the finite elements used for modeling the cables are

beam type elements.

In practice the errors caused by cable forces or mechanical

properties are necessary to be monitored and corrected during

construction stages. The main objectives of construction stage

analysis may be summarized as follows:

stress evaluation in cables for several stages,

geometric shape plotting related to final stage,

leveling of pipeline,

plastic deformations monitoring of elements during

erection,

stress and stability control in structural elements

Computer code SAP2000 allows the analysis of a structure

in different stages of erection with the help of Construction

Scheduler module. Function of the chronological order two

possibilities of construction stage analysis may be defined:

progressive or regressive. Resulting forces are very similar for

each type of analysis but due to the already defined structure a

regressive analysis is more convenient.

After defining the structure and the construction stage load

case element groups of hangers and pipe elements must be

defined according to the solution of assembling of structure.

For the regressive analysis the entire structure has to be

defined in a group and added in a construction stage. The

following steps represent removal of groups of elements. Load

action is allowed to be defined also with safety factors.

Construction stage analysis may be defined with consideration

of geometric non-linearity effects

A simple construction stage analysis may be defined with 5

phases [6] by defining groups of main parts of structural

elements although it may be omitted critical situations as

presented in the following.

There are multiple solutions for erecting the crossing to its

final structural configuration and the forces are distributed

accordingly. Fig. 8 presents the case of starting assembling the

pipeline from the midspan of the crossing. Another possibility

is to start the pipeline assembling from both ends as presentedin Fig. 9 or just from one end, Fig. 10.

By performing a staged construction analysis for each of

these cases it may be observed that for an intermediate phase

the pipe is subjected to higher values of bending moments

than as considered for the final stage. This situation is caused

by the large deflections allowed by the main cable between

the end connection points.

The maximum value for assembling the structure from the

midspan is 182kNm and for the following two situations the

circular section is subjected to 192kNm. These valuesrepresent almost double of the bearing capacity of the pipe

cross-section.

As mentioned before the flexibility of the intermediate

supports of the pipe allows high displacements leading to

large equivalent spans. The high bending moments will result

only if the pipeline is considered to be continuous. If the

connections between adjacent pipe elements are not fully

fixed the hinges resulted will reduce the bending moments. In

a construction stage analysis the connection between elements

cannot be modified therefore the results of an analysis that

Fig. 8 Construction stages: midspan-towers

Fig. 9 Construction stages: towers midspan

Fig. 10 Construction stages: tower - tower


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includes simple connections between elements may only be

simulated if groups of elements are not considered until the

final stage of contruction.

V. CONCLUSION

Analysis of structural systems with cables as tension

elements exhibit a particular complexity owned by the large

deformations resulted from the high flexibility of cables. The

pretension of cables influences the Eigen-modes of the

structure but a higher importance over the response to

dynamic action is the consideration of the structure rigidity.

The unloaded structure and the case of filled pipeline define

two situations that lead to rigidities of structure that are

considered as an initial condition in dynamic analysis and lead

to different values of deformations.

For a dynamic and static analysis the resulted forces in

cable elements are similar whereas distinct values result for

the pipe bending moment.

The construction stage analysis reveals that plastic

deformation of pipeline may occur during intermediate phase

of an erection method.

ACKNOWLEDGMENT

This publication was supported by the European social fund

within the framework of realizing the project Support of

inter-sectoral mobility and quality enhancement of

research teams at Czech Technical University in Prague,

CZ.1.07/2.3.00/30.0034.

REFERENCES

[1] ASCE Manuals and Reports on Engineering Practice, Pipeline

Crossings, No.89, 1996

[2] Zhang Xin-jun, Sun Bing-nan, Aerodynamic stability of cable-stayed-

suspension hybrid bridges, in Journal of Zhejiang University Science,

No. 6A(8), 2005, p. 869-874

[3] I.Both, Dynamic response analysis of a pipeline crossing,Bulletin ofthe Transilvania University of Braov,pp.33-38, 2012

[4] P. Cosmulescu, Spatial Steel Structures, Junimea, 1991.

[5] Dragulinescu. M., Ghenoiu C., Suspension crossings for pipelines,

Revista Constructiilor si a materialelor de Constructii, no.9, vol. 14,

1962, p.447-456.

[6] I. Both, A.Ivan, Analiza pe faze de construcie a unei traversri

suspendate, a 12-a Conferina Naionala de Construcii Metalice, 26-27

noiembrie 2010, Timisoara, Romania, pg. 129-134, ISBN 978-973-638-

464-6, 2010


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