Conference WCCM 2008

Modelling of gradual construction of road bridge and its creep

Modelling of gradual construction of roadbridge and its creep

Jaroslav Brož, Jaroslav Kruis

Department of MechanicsFaculty of Civil Engineering, Czech Technical University in Prague

WCCM8 and ECCOMAS 200830 June - 4 July 2008

Lido Island in Venice, Italy


Outline

Outline

MotivationModelling of Gradual ConstructionRoad Bridge

Aims of WorkDescription of ConstructionNumerical ModelsResults of Computations

ConclusionAcknowledgement


Motivation

Motivation

Gradual construction


Motivation

Motivation

Possible solution?

NO! Because:

J(t , t ′) =

1E0

+ C(t , t ′)


Motivation

Motivation

Solution of the previous problem with E = 0?

Perhaps But:Direct solvers→ problem with rounding error (nearlysingular matrix)Iterative solvers→ problem with the large number ofiterations (large condition number)


Modelling of Gradual Construction

Concept of Gradual Construction

Better solution - Gradual ConstructionNodes and elements are switched on or off with respect to timefunctions

Switched on - value of the time function is equal oneSwitched off - value of the time function is equal zero



Algorithm of Gradual Construction

New time step

?

Start time

?Search new nodes and elements of problem

? ?Found new nodes or elements

?No new nodes and elements

Change of the number of unknowns?

Assembling of new matrix

?Solving of problem

?End time? - Yes - End�No

-



Illustration of the Previous Algorithm 1/2



Illustration of the Previous Algorithm 2/2



Gradual Construction - Problem

computed solution exact solutionstep one

u(1)2 =

12

fl21 u(1)

2 =12

fl21

step two

u(2)2 =

12

fl21 + fl1l2 u(2)

2 =12

fl21 + fl1l2

u(2)3 =

12

fl22 + fl1l2 u(2)

3 =12

fl22 + fl1l2+

12

fl21



Gradual Construction - Solution of the PreviousProblem

computed solution exact solutionstep one

u(1)2 =

12

fl21 u(1)

2 =12

fl21

step two

u(2)2 =

12

fl21 + fl1l2 u(2)

2 =12

fl21 + fl1l2

u(2)3 =

12

fl22 + fl1l2+

12

fl21 u(2)

3 =12

fl22 + fl1l2 +

12

fl21



Aims of Work

More accurately way of computation for simulation ofgradual construction of bridgeFE model of road bridge construction and false-workComputation of the creep of road bridge construction


Description of construction

Map



False-work

False-work

Figure: Lattice Girder of the False-work



Bridge Construction

Bridge Construction

Figure: Cross-section of the Bridge


Numerical Models

Concept of Supporting of False-work

Concept of Supporting of False-work

Figure: Concept of Supporting of the False-work for Version One

Figure: Concept of Supporting of the False-work for Version Two


Numerical Models

Used Material Characteristics

Used Material Characteristics

Material parameters for bridge:Young modulus of elasticity E = 30 GPa,Age of concrete in loading 3 days.

Material parameter for steal false-work:Young modulus of elasticity E = 210 GPa.


Numerical Models

Used Model of Concrete Creep


Accelerated version of the Bazant’s model B3

J(t , t ′) = q1 +

M∑µ

L (τµ)

[1− exp

(−ξτµ

)]ln 10∆ (log τµ) ,

where L (τµ) is equal to time interval two neighbouringmembers of Kelvin chain in log scale


Numerical Models



More details about this creep model can be find in thisreference:Continuous Retardation Spectrum for Solidification Theory ofConcrete Creep, Zdenek P. Bažant and Yunping Xi, Journal ofEngineering Mechanics, Vol. 121, 1995,pp. 281 - 288


Numerical Models

FE Models

FE Models

FE model The Number of The Number of Type ofNodes Elements Element

False-work 6 900 14 040 bending beamBridge 28512 20 904 hexahedralFinal model 35412 34 944 combination


Numerical Models

FE Models

FE Models

Figure: Discretized Cross-Section

Figure: Part of Discretized Side View


Numerical Models

Loads of Construction

Loads of Construction

Dead load of the bridgeDead load of the false-workLongitudinal presstresing forces of the bridgeTransversal presstresing forces of the bridge


Results of Computations

Table of Selected Nodes for Comparison betweenVersion One and Version Two and Their Coordinates

The Number x y z Description ofof Node [m] [m] [m] Position

7393 13,5 3,375 -1,6875 in the middle of the 1 span7409 31,5 3,375 -1,6875 on the first cantilever

10359 40,5 3,375 -1,6875 in the middle of the 2 span



Graph of the Creep - Node Number 7393




Graph of the Creep - Node Number 7409.




Graph of the Creep - Node Number 10359.

Graph of the creep - node number 10359


Conclusion

Conclusion

The algorithm for gradual construction solves manyproblems in finite element technology.The proposed modification of the algorithm leads to betterresponse of the structure.The analysis of bridge and false-work based on thealgorithm for gradual construction reveals:

1 significant differences between two variants of attachmentof false-work to the bridge

2 significant differences in comparison with the analysis ofthe whole bridge (without gradual construction).


Conclusion

Acknowledgement

Thank you for your attentionFinancial support for this work was provided by project103/07/1455 of Czech Science Foundation. The financialsupport is gratefully acknowledged.

Conference WCCM 2008

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