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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 73
Edited by: B.H.V. Topping
Paper 77

Non-linear Behaviour, Failure Loads and Inelastic Buckling of Multispan Cable-Stayed Bridges

M.M. Bakhoum+, G. Helmy*, W.A. Attia+ and M. Mourad+

+Faculty of Engineering, Cairo University, Egypt
*Dar Al-Handasah Shair and Partners, Egypt

Full Bibliographic Reference for this paper
M.M. Bakhoum, G. Helmy, W.A. Attia, M. Mourad, "Non-linear Behaviour, Failure Loads and Inelastic Buckling of Multispan Cable-Stayed Bridges", in B.H.V. Topping, (Editor), "Proceedings of the Eighth International Conference on Civil and Structural Engineering Computing", Civil-Comp Press, Stirlingshire, UK, Paper 77, 2001. doi:10.4203/ccp.73.77
Keywords: linear elastic analysis, material non-linear, geometric non-linear, cable stayed bridges, multispan cable stayed bridges.


The Nonlinear behavior of Multispan Cable-Stayed Bridge (MCSB) is investigated in this paper. Both Geometric (GNL) and Material (MNL) Nonlinearities are considered. Analysis up to failure of several configurations of MCSB is carried out. The load deformation curves are drawn. Four different types of failure loads are computed in terms of (1) MNL analysis only, (2) MNL and GNL, (3) Elastic Buckling load, (4) Inelastic Buckling load. These failure loads or ultimate capacities of the different MCSB are compared.

The critical elastic buckling loads - computed using an eigen value approach and ignoring the deformations caused by combined axial forces and moments - is an overestimated approach. To overcome this inaccuracy, the GNL and MNL should be considered. The GNL arises mainly from significant changes in the structural configuration also due to axial force-bending moment interaction. The MNL arises mainly from the plastic yielding of the steel, concrete cracking, creep, cable damage and different ductile fracture of the composites. A nonlinear procedure is introduced to perform the inelastic analysis and a full nonlinear analysis will take account of any pre-buckling displacement. Obtaining the nonlinear load-deformation curve could be carried out either experimentally, or by the use of sophisticated structural analysis programs. In this paper a nonlinear finite element structural analysis program is used. The program is thoroughly checked by comparing its output results to those of structures with known analytical solution, and also to published data about well-known actual cable-stayed bridges. Results are and found to be compatible. Research work was carried out previously on nonlinear behavior and collapse of CSB. However, very few were carried out on multispan Multi span CSB. It is one of the main purposes of this paper to cover some of this lack of data.

Scope of Work

  • Nonlinear analysis of multi-span cable-stayed bridges, to study the nonlinear load - deformation behavior while considering GNL & MNL.
  • The failure loads or ultimate capacity of multi-span cable stayed bridges taking into account the MNL only, and failure loads considering both GNL & MNL.
  • The inelastic buckling capacity of multi-span cable stayed bridges can be obtained using the load - deformation relation using the suggested procedure.
This work also discusses the comparison between the elastic and ultimate load capacity of multi-span cable-stayed bridges.

Analysis Approaches

The present solution procedure includes three stages of analysis as follows: The first stage is to perform a nonlinear analysis to obtain the load deformation curve. The second stage is to obtain the critical elastic buckling loads using an eigen value approach. The third stage is to obtain the inelastic buckling load. A simplified model is suggested here to compute the inelastic buckling loads of structural systems, which is applied to MCSB.


The paper presented Nonlinear analysis of Multi-span Cable Stayed Bridges (MCSB) considering geometric and maternal nonlinearty (GNL, MNL). The failure loads considering MNL, GNL + MNL, elastic buckling, inelastic buckling are computed. A simplified model is suggested to compute inelastic buckling of MCSB. For the cases considered in this study, the following points can be concluded:

  1. The upper limit of the failure loads is the elastic buckling load, which is obtained using the eigenvalue analysis approach. In that approach any pre- buckling deformation is negligible (zero), such as the deck deflection or pylon side-sway. Therefore the failure load of MCSB load in that case is overestimated. To overcome that over estimation the geometric and material nonlinearities should be considered in estimating failure loads of multi-span cable-stayed bridges.
  2. Failure loads due to consideration of MNL and MNL + GNL are much less than the elastic buckling loads of the bridges considered. Also, the inelastic buckling loads of MCSB computed using the suggested procedure are much less than the elastic buckling loads.
  3. Deflection due to consideration of GNL could be slightly larger than linear analysis at service load level, but considerable at higher load levels.
  4. Using rigid pylon for multi-span cable stayed bridges reduces the deck deflection and magnifies the elastic and inelastic capacities.
  5. Both linear and nonlinear analyses are necessary for the analysis and design of multispan cable-stayed bridges in practical design. The nonlinear require considerable computational efforts. However, several of the currently available analysis packages after being thoroughly checked could be used.
  6. Using top cables for multi-span cable stayed bridges reduce the deck, pylon deformation and improve the ultimate capacity.

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