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Cable stayed Bridge Static Analysis 4
- Thread starter Emma123
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You can request demonstration versions from CSI Berkeley. They are full versions with a time limit of 30 days I believe. You will have to check to be sure.
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The best software for cable stayed bridge analysis is LARSA from REI ( I am not sure if they are owned by STAAD or are just a partner. STAAD and SAP are good for cables, but don't take into consideration true large deformations, variance in axial loads, post-tensioning and segmental construction.
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I would use just a plane frame program to find out the forces in the system as the first stab and look for refinement if needed. The large deflection theory isn't as complicated as it looks because in order to be serviceable the bridge has to be pretty stiff and its variation with linear/elastic solution would not be too great. Even a footbridge wouldn't be allowed to bounce as it will cause discomfort/alarm to the users. I once compare the two solutions for a suspension bridge and the difference was only 4%.
The normal liner/elastic analysis assumes the equilibrium condition at the "unloaded" geometry whereas the true equilibrium should be in the deflected shape of the structure.
The normal liner/elastic analysis assumes the equilibrium condition at the "unloaded" geometry whereas the true equilibrium should be in the deflected shape of the structure.
i think Bbird has a simple way to solve the problem, ie linearize the problem. I would represent the cables as axial rods and apply the preload tension to them as a load. then check the results to ensure that the cables are always in tension.
this wway any simple FE program will do the problem, and being linear, any program should give reasonable results, depending on your model !
good luck
this wway any simple FE program will do the problem, and being linear, any program should give reasonable results, depending on your model !
good luck
All structural elements are springs with axial, shear and torsional stiffness. If the cables are properly modelled they should have very little shear and torsional stiffness and should take up the bulk of the axial loads as expected. For its small cross section a cable can take very little bending and torsion in practice and this will automatically reflect in the analysis, even the cable is not hinged but accidentally connected to the deck rigidly. All FEA and frame analysis programs are based on stiffness method whereby the bending at any node is resisted by the members attached to it in proportional to their bending stiffness.
To refine a linear-elastic solution there are at least two ways to model the cable. My earlier remark of solving the equilrium at the "loaded" shape is a common iterative method. One can actually sum the deflections (linear portions of dx, dy & dz) with the original geometry to obtain a new shape for the next analysis which yields the a new set of revised deflection. By doing it iteratively, always with the new deflection added to the original "unloaded" geometry a solution will converge, indicating an equilirium position has been reached.
There is nothing wrong with the traditional linear-elastic theory. The extra accuracy to go deeper is just seldom required for the normal engineering applications
The other method is to use the stability functions to modify the stiffness. If a member is subjected to an increasing axial load it can eventually buckle or have zero bending siffness. The stability function automatically reduce the member's bending stiffness to zero when the Euler buckling load is approached.
The same stability functions are equally applicable to member subjected to tension, as in the case of a cable where the tension increases the bending stiffness. The stability functions are introduced to the stiffness terms of a structural member as indiviual multipliers.
(There is a third method which takes the deflection into account by "adding" a correction term to the element's stiffness matrix. It produces comparable results)
Either method will yield the similar result. With the stability function one performs the analysis at least twice. The first one is to obtain the tension/compression for modifying the stiffness in the members for the next analysis. In general 3 to 4 iterations should yield a good convergence.
I admit that there is some over-simplification but the methods are based on the fundamental laws of physics - equilibrium and the elastic theory.
I have investigated large deflection theory (nonlinear geometry in elastic material range) in my undergraduate project back in 1976. I computerised three different methods (as described above) and conducted tests on both tension and compression members in the laboratory to verify my results. For tension member I hung the load on a "V" shape structure comprised of just spring elements. On loading the "V" could drop several times more than a practical structure would be able to tolerate. The theoretical predictions and laboratory results were in excellent agreement with each other.
As far as I am aware the equilibrium that can be significantly influenced by its deflected shape is a rubber tyre (ot tire). Most civil and building structures cannot be made too flexible and that is equally true for a cable stayed bridge.
To refine a linear-elastic solution there are at least two ways to model the cable. My earlier remark of solving the equilrium at the "loaded" shape is a common iterative method. One can actually sum the deflections (linear portions of dx, dy & dz) with the original geometry to obtain a new shape for the next analysis which yields the a new set of revised deflection. By doing it iteratively, always with the new deflection added to the original "unloaded" geometry a solution will converge, indicating an equilirium position has been reached.
There is nothing wrong with the traditional linear-elastic theory. The extra accuracy to go deeper is just seldom required for the normal engineering applications
The other method is to use the stability functions to modify the stiffness. If a member is subjected to an increasing axial load it can eventually buckle or have zero bending siffness. The stability function automatically reduce the member's bending stiffness to zero when the Euler buckling load is approached.
The same stability functions are equally applicable to member subjected to tension, as in the case of a cable where the tension increases the bending stiffness. The stability functions are introduced to the stiffness terms of a structural member as indiviual multipliers.
(There is a third method which takes the deflection into account by "adding" a correction term to the element's stiffness matrix. It produces comparable results)
Either method will yield the similar result. With the stability function one performs the analysis at least twice. The first one is to obtain the tension/compression for modifying the stiffness in the members for the next analysis. In general 3 to 4 iterations should yield a good convergence.
I admit that there is some over-simplification but the methods are based on the fundamental laws of physics - equilibrium and the elastic theory.
I have investigated large deflection theory (nonlinear geometry in elastic material range) in my undergraduate project back in 1976. I computerised three different methods (as described above) and conducted tests on both tension and compression members in the laboratory to verify my results. For tension member I hung the load on a "V" shape structure comprised of just spring elements. On loading the "V" could drop several times more than a practical structure would be able to tolerate. The theoretical predictions and laboratory results were in excellent agreement with each other.
As far as I am aware the equilibrium that can be significantly influenced by its deflected shape is a rubber tyre (ot tire). Most civil and building structures cannot be made too flexible and that is equally true for a cable stayed bridge.
Bbird,
thank you for your informative post. I am currently working for a contractor on a medium (some may say short!) span cable stay bridge, main span 185m. We are responsible for the construction engineering which entails carrying out the construction stage analysis of the bridge. Currently we are having an alignment problem on the bridge which we are resolving by the use of shims (the bridge is segmental) and additional stay forces(an increase in the number of strands in the stays is required). The structure is sensitive during construction of the cantilevers to both weight of permanent & temporary works and to temperature. It is my opinion that the designer should study the construction stages as well as the in service design analysis. For this I would still recommend a specialist software package, several of which have been mentioned earlier in the thread.
Zambo
Zambo
thank you for your informative post. I am currently working for a contractor on a medium (some may say short!) span cable stay bridge, main span 185m. We are responsible for the construction engineering which entails carrying out the construction stage analysis of the bridge. Currently we are having an alignment problem on the bridge which we are resolving by the use of shims (the bridge is segmental) and additional stay forces(an increase in the number of strands in the stays is required). The structure is sensitive during construction of the cantilevers to both weight of permanent & temporary works and to temperature. It is my opinion that the designer should study the construction stages as well as the in service design analysis. For this I would still recommend a specialist software package, several of which have been mentioned earlier in the thread.
Zambo
Zambo
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