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DEVELOPMENTS IN COMPUTATIONAL ENGINEERING MECHANICS
Edited by: B.H.V. Topping
A Computer Program for Calculating Longitudinal and Shear Strains in Open Thin-Walled Concrete Structures
Kuwait Institute of Technology, Kuwait
S.A. El-Hammasi, "A Computer Program for Calculating Longitudinal and Shear Strains in Open Thin-Walled Concrete Structures", in B.H.V. Topping, (Editor), "Developments in Computational Engineering Mechanics", Civil-Comp Press, Edinburgh, UK, pp 143-150, 1993. doi:10.4203/ccp.19.5.3
The investigation of the behaviour of open thin-walled concrete structures in the post cracked stage of loading up to failure under the interaction of bending and torsion have not received that much concern of the researchers, as mentioned this paper was directed to predict the longitudinal and shear strains at different points along a structure and on its cross-section. A mathematical method has been developed in a computer program to compute the longitudinal and shear strains due to torsion and flexure. The results of the method were put in comparison with the experimental results of five open thin-walled concrete beams under different ratios of bending to torsion.
The longitudinal strains are made up of two components, these due flexural and warping moments, and those due to shear flow. However, the later ones are very small and do not represent more than 3% of experimental and theoretical value and may be neglected. There are two distinct regions along the beam, one tension and other compression, which are consistent in both experiment and theory, which gives further evidence that the theoretical approach is acceptable for this type of structures.
The maximum values predicted by theory and obtained experimentally are very similar.
The strains in the longitudinal steel bars are dominated by warping moment in all beams subjected to torsion. This classifies the importance of considering the effects of warping restraint in this type of structures. Even in beams with higher levels of bending moment than those predicted here, full consideration must still be given to warping moments after cracking. After yielding of the first steel bar the stiffness drops very rapidly as a result of yielding of steel and high compressive strains in concrete. These are the main factors which effect directly the stiffness of the cross-section.
The strains in stirrups which used for shear also computed by the program. The strains in stirrups are caused by shear flow due to the combined contribution of Saint-Venant's torsion, warping torsion and flexural shear.
However, after cracking, the Saint-Venant's contribution is very small in comparison with the others, particularly warping torsion.
The output of the computer program for all beams at every stage of loading is given, and compared with the corresponding of experimental ones.
At first yielding of steel the theoretical and experimental results are in fair agreement. The strains in the two legs of one stirrup are to differ from each other. This small difference is mainly due to the contribution of Saint- Venant's torsion.
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