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USING THE SOFTWARE,

ANSYS in the calculation of cable-stayed bridge

Across the Ob River SURGUT

Prof. Kositsyn SB, Assoc. Dolotkazin DB

Moscow State University of Railway Engineering (MIIT)

At the end of September 2000 was commissioned a road bridge across the Ob

River in the city of Surgut. The structure of this transition includes odnopilonnoe

vantovo span (Fig. 1).

Fig. 1. Span cable-stayed bridge in Surgut.

Basic calculations and design of the bridge carried out "Giprotransmost", but

the design and construction of this unique artificial structures preceded research,

which involved scientists Chairs "Bridges" and "Structural Mechanics", Moscow

State University of Railway Engineering (MIIT), and several other TsAGI

organizations. MIIT scientists carried out a large range of activities and checking

calculations to evaluate the stress-strain state of the cable-stayed bridge span in the

individual stages of installation and operation. They performed static calculations of

cable-stayed span in linear and nonlinear formulations of the problem based on the

sequence of mounting the stage of construction and operation. The behavior of the

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span when wind impacts. Some fragments of the superstructure and the pylon

designed as thin-walled space of local exposure to guys. In the formulation of the

problem of volume calculation is made eye fastening guys to span. Calculations are

made using finite element method using the software package ANSYS.

1. DEFINITION OF STRESS - STRAIN STATE BRIDGE BEARING

STRUCTURES In geometrically nonlinear statement.

1.1. The computational model structures.

Numerical study was subject odnopilonnoe vantovo span (Fig. 2) with a span

of 148 m to coast and channel span 408 m Pylon - two-cross-linked between the

uprights (Fig. 3), height 146.5 m rigidly embedded in the concrete footing. Beam

stiffness - the box-like with longitudinal stiffeners and transverse diaphragms and 15

m wide Superstructure comprises two plane guys: in the coastal migration - 34, and

surfaced - 31 guy in each plane. Loads on the stages were mounting their own

weight, construction and weight load assembly crane and mounted to the

superstructure - own weight and payload.

Fig. 2. Facade span.

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Fig. 3. General view of the pylon.

Static calculations for the entire structure generally accepted pivotal spatial

model of the structure. Stiffening girder consists of 54 standard mounting blocks and

one closing. The length of a finite element corresponds to the distance between the

diaphragms. Availability eccentricities attachment points guys about the axis of the

superstructure (the guy attached to lugs) was taken into account by introducing

additional enough hard core of finite elements.

Partitioning pylon implemented by finite elements by the following scheme.

Each rack pylon broadens its part was divided into 6-dimensional beam elements

with variable cross section in order to better take into account the effect of the

variability of the cross-section of the rack. The upper part of the post where the guy

attached, was divided into finite elements between nodes attach guys. Availability

eccentricities attachment points relative to the axis of guys stand pylon taken into

account by introducing additional hard enough finite elements. Each of the cross-

linking between the uprights pylon seemed ten spatial beam elements.

Guys are divided into spatial beam elements. Attaching to the posts guys

pylon beam stiffness to the structure and abutment was considered perfectly

articulated.

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Beam stiffness in the calculation model is rigidly embedded in spatial

stability in the coastal migration and pivotally movable along the axis of the bridge is

fixed at its other end. Each rack space pylon rigidly embedded in the bottom of the

footing.

In general, finite element model of the superstructure is shown in Fig. 4.

Fig. 4. Finite model span.

1.2. Evaluation of the stress - strain state of a suspension bridge

bearing elements. BACKGROUND calculation.

Consider the features of static calculations of cable-stayed span in the

nonlinear formulation of the problem, taking into account the sequence of mounting

the stage of construction and operation. Mounting channel part of the superstructure

was carried out in the canopy without intermediate vertical supports (horizontal

supports present), leading to a large design flexibility and the need to consider in the

calculation of finite displacements of nodes of the system. Geometric nonlinearity

deformation rods sufficiently take into account full: the tangent stiffness matrix K

was obtained as the sum of the usual stiffness matrix 0K Used in calculating the

linear, matrix initial stress K and matrix initial rotations LK

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L0 KKKK . (1)

The calculations take into account the change of the superstructure design

scheme during installation, with the algorithm of "birth and death of finite elements."

Voltage and internal forces in the existing elements accumulated in the transition

from step to step. Just a computational model in postproduction 111shagov accepted.

Condition mounted superstructure defined step 112.

During installation of the span carried the so-called "charging" guys. This

process is necessary due to the fact that the initial length of the workpiece (subject to

sag under its own weight) is shorter than the distance between the points of

attachment to the beam rigidity of the shrouds and the pylon, or to help but pylon. In

practice, the guy is stretched to compensate for the initial clearance, attach, and then

remove the pretension. Guy "wound". To simulate this process in the calculation, it is

necessary to ask each guy initial deformation, calculated by the formula

0

0

00

L

LL

L

L

, (2)

where L0 - initial length of the workpiece; L absolute elongation workpiece during

"charging"; L - distance between the points of attachment guys defined in the

deformed state, the previous "zavodke" so

2ннкк2

ннкк2

ннкк wzwzvyvyuxuxL . (3)

Here xh, yn, Zload, Xk, yk, ZK - basic coordinates of the starting and ending points

of attachment of the guys; Ur, Vr, wn, Uc, Vc, Wc - move the start and end points of

attachment of the guys from the initial state at the time of "charging". When this is

taken into account that the symmetrical loading gives wn = Wc = 0 and Zload = ZK.

To calculate the span with the initial strains guys used two global stage. On

the ground in a geometrically nonlinear formulation of the problem passed the whole

assembly sequence, excluding the accumulation of internal efforts to pre-determine

the coordinates of the points of attachment of guys in the states preceding "zavodke"

and calculation of initial deformations guys. On the second - as in geometrically

nonlinear statement made the final payment on a given load with the initial strains of

guys, given the sequence of assembly and accumulation of internal forces. The

comparison of the calculation results, move attachment points guys, pre-defined in

the first stage to calculate the initial strains and the corresponding displacement,

found on the second stage of the calculation, have been very close, so the third

approximation is not required.

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The calculations analyzed the stress - strain state at all stages of the

installation (steps 1 - 111) and in the closed state (step 112). Deformed view

diagrams and longitudinal forces and bending moments Mz for step number 102

(before receiving support on a console) are shown in Figures 5 - 7. Stress - strain

state step number 112 (closed loading system load in two parts) characterize Figures

8 - 10. These design stage are the most dangerous.

Fig. 5. Deformed view of the system before closing.

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Fig. 6. Diagram of longitudinal forces in the system before closing.

Fig. 7. Bending moment in the system before closing.

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Fig. 8. Deformed view of a closed system.

Fig. 9. Diagram of longitudinal forces in a closed system.

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Fig. 10. The bending moment diagram in a closed system.

In a similar statement made payment superstructure with additional side

impact wind.

2. ANALYSIS OF STRESS - STRAIN STATE complex spatial nodes.

2.1. Statement of the problem, method of study load and impact.

Nodes pairing guys with superstructure and pylon represent spatial system

consisting of a number of structural elements that interact with each other and

provide their joint spatial work.

Statement of the Problem: It is necessary to analyze the stress - strain state of

spatial nodes span and pylon based on local influences of the guys on these sites.

Stress - strain state of such units is also space and can not be reliably

analyzed without the involvement of modern numerical methods. Since the decisive

factors determining the spatial pattern of deformation for interface are concentrated

local feedback, to solve the problem mentally cut portion corresponding structures of

limited size (according to the Saint - Venant), which includes all the interacting

elements. In places cuts are sufficiently remote from the areas local influences, put

communication, converting the selected portion in the main element of the method of

movement. Next is the calculation of this section to the local impact from the guys.

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The resulting voltage according to the principle of superposition (linear considered

fair statement of the problem) can be further added to the stresses arising in the

calculation of kinematic fragment impacts on its borders when working as part of the

whole construction of the bridge on the total load.

2.2. Calculation eyelets - attachment element to the beam

stiffness guys.

To calculate the eyes of the lot, including the eye and part of the vertical plate

(Fig. 11). Vertical plate is rigidly fixed on the plane of the horizontal and vertical

planes. Type of loading eyelets - distributed load acting in the plane at eye-thirds of

the circumference of the hole. This load simulates the impact of the guys at the

eyelet. The calculation was performed for two values of the angle of inclination to

the horizontal guy - 22 and 65 degrees.

Eyelet and adjacent sheet divided into flat rectangular and triangular finite

elements (6 degrees of freedom at the node). Such elements reliably simulate

bending and plane stress state of the structure. The maximum size of not more than

2.5 cm scheme breakdown of the computational domain into finite elements is shown

in Figure 12.

Eyelet works only on the load of the guys, so in Fig. 13, 14 shows the

distribution pattern design stresses p by IV strength theory. These stresses are

calculated according to the formula

2zx

2yz

2xy

2xz

2zy

2yxp 6

2

1 . (4)

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Figure 11. Flat computational model eye

Fig. 12. Schematic breakdown of the computational domain into finite elements.

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Fig. 13. Calculated stress distribution in kg/cm2.

Fig. 14. Distribution Calculated stress in kg/cm2 (fragment).

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Analysis of the results of calculation together with vertical lugs

whetherdentistry to the load from a guy in the eye plane showed that regardless of

the slope guys eye stress state is local, and the calculated stresses exceed 6000

kg/cm2. This required some changes to the design of eyelets.

Designers suggested strengthening eyelet holes in staging two additional

washers. Washers welded to the lug on the outer contour. Terms washers and eye

contact on the line as well as the eccentricity of the middle plane of each relative to

the median plane of the washer lugs necessitated transition to volume calculation

model construction site. This model comprising a lug, the two washers and the

vertical piece sheet shown in Fig. 15. Conditions consistent fixing flat model eye.

Given that the maximum rated voltage with two tilt angles of 22 degrees and a guy

65 degrees turned almost identical calculation on the volume model is made for only

one angle: 22 degrees - the most disadvantaged. Force in the guy distributed over the

area of the circle formed by the third hole and the sum of thicknesses of two eyelets

and washers. Three-dimensional finite element mesh is shown in Fig. 16. The largest

size of the finite element does not exceed 6 cm in the area of the opening and

washers mesh elements thickened. A flow tetrahedral finite element node 10 (at each

node - 3 degrees of freedom). In the zone of contact washers and eye (OD washers)

merged degrees of freedom of three-dimensional finite element analysis. This

operation provided washers and eye contact in finite element model of the line.

Results of calculation of three-dimensional model shown in Fig. 17 and 18.

Their analysis showed that increased eye washers played a positive role: the state of

stress in the area of attachment to the eye of the guy left the local, the maximum

equivalent stress on IV theory of strength remained in the eye, but their value has

dropped to 3000 kg/cm2.

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Fig. 15. The volume model eyelets with washers and leaf.

Fig. 16. Volumetric finite element mesh.

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Fig. 17. Calculated voltage kg/cm2 volume model.

Fig. 18. Calculated voltage kg/cm2 volume model (fragment).

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2.3. Calculation of the mount to the beam stiffness guys, including the

diaphragm.

For the calculation of the mount to the beam stiffness guy isolated fragment

span. This fragment is due to the symmetry of the problem concerning the median

longitudinal plane of the bridge includes a half box beam stiffness (the topsheet,

backsheet, and inclined side sheets eyelet, longitudinal ribs, lateral beams with

transverse connections and aperture). His model is shown in Fig. 19 (withdrawn due

to the cross beams). The isolated fragment was secured at the ends of the

longitudinal (horizontal) and transverse (vertical) displacements and rotations

relevant. On the symmetry plane of symmetry delivered due transverse to the bridge

axis (horizontal) direction and vertical linkages, as well as communication,

reinforcement units from the respective corners. All components are broken into

fragments flat shell quadrangular finite elements (considered bending, torsion and

membrane components of deformation). At each node, as taken three unknown

translational movement (along the axes X, Y, Z) and the angles of rotation relative to

the same axis. Partitioning scheme for finite element model is shown in Fig. 20.

Maximum item size does not exceed 20 cm load is the force in the guy attached to

the eyelet.

Fig. 21, 22 shows the stress distribution calculated by IV strength theory.

Analysis of the results suggests that the local load anchorage guy most intensively

working vertical and horizontal sheets adjacent to the lug. Here there is a strong

bump wall span, both in vertical and horizontal planes. In the rest of the span

tensions caused by the influence of local small guys.

Special mention should discuss the state of stress of the diaphragm. Calculate

the diaphragm span separately is impractical because it is entirely included in the

calculation fragment span, and its breakdown into finite elements is quite thick. Most

loaded part of the diaphragm was immediately adjacent to the horizontal, vertical and

inclined sheets belts span, especially in connection to the lug. The central part of the

diaphragm is almost tense.

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Fig. 19. The computational model fragment span.

Fig. 20. Scheme breakdown model into finite elements.

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Fig. 21. Calculated stress in kg/cm2.

Fig. 22. Calculated stress in kg/cm2 (fragment).

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2.4. Payment gateway node guy with pylon.

To calculate the allocated half of one branch of the pylon height of 3 meters.

On the shore-side fragment adjacent to the settlement two guys at an angle. From the

side of the bed to the calculated fragment adjacent one guy. The computational

model fragment shown in Fig. 23. Scheme breakdown fragment into finite elements

is shown in Fig. 24 (the maximum element size - 8cm). Efforts shrouds are shown in

the form of load uniformly distributed on the sides of ribs connecting the anchoring

device with special beams. At a symmetry plane of symmetry of communication set,

besides, the upper and lower ends of the fragment from the fixed vertical

displacement and displacement of the river.

The distribution of the stress calculated (by the theory of strength IV) shown

in Fig. 25 - 27. Analysis of calculation results showed that the stress state of the

pylon against efforts in the rigging is mainly local. Maximum stresses in areas

identified conjugation inclined ribs, which are attached guys, with vertical fins.

Aperture on local impacts were only strained the junction of the vertical bearing

elements, therefore, can be alleviated by making cross-cutting (similar to how it is

done between the guys in the superstructure).

In conclusion we note that, ANSYS finite element enabled a number of

scientific studies and simple enough to solve some of the important practical

problem of calculating bearing structures unique bridge across the Ob River. He can

continue to be successfully used in the calculation of building structures provided

enough highly skilled users.

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Fig. 23. The computational model fragment pylon.

Fig. 24. Settlement scheme breakdown fragment to the elements.

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Fig. 25. Calculated stress in kg/cm2.

Fig. 26. Calculated stress in kg/cm2 (part 1).

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Fig. 27. Calculated stress in kg/cm2 (fragment 2).