عنصر محدود ورقه های بتونی
Abstract
Nomenclature
1. Introduction
2. Finite element limit analysis of slabs
3. Layer model for shear-bending limitations
4. Implementation of the optimized layer model in finite element limit analysis
5. Numerical examples
6. Conclusion
Acknowledgement
References
Abstract
In the last decades, finite element limit analysis has shown to be an efficient method to determine the loadcarrying capacity of slab bridges in bending. However, the load-carrying capacity of concrete slabs can be limited by the shear capacity and the redistribution of shear forces when subjected to high-intensity loads such as tire pressure from heavy vehicles. In this paper, an optimised layer model is presented which include limitations on both shear and bending. The layer model is based on a sandwich model, which provides a simple way to determine a safe stress distribution for reinforced concrete slabs with shear reinforcement subjected to shear and bending. The yield criteria in the layer model are formulated as second-order cones which enables an efficient implementation in finite element limit analysis where general convex optimisation algorithms are used. The interaction of section forces is investigated for different combinations of shear forces, moments and torsion. The optimised layer model is used, in combination with finite element limit analysis, to evaluate concrete slabs subjected to different load configurations. The results show that the layer model performs very well with finite element limit analysis and it is possible to determine a safe distribution of shear forces, moments and torsion very efficiently. However, the model cannot handle local effects such as punching shear and concentrated loads near the support.
Introduction
The load-carrying capacity of reinforced concrete slab bridges can be limited by the shear capacity and the capability of the structure to redistribute the internal forces. The shear problem arises when heavy vehicles with axle loads are crossing the slab bridges. This is especially critical for wide slab bridges where the redistribution of internal forces is essential for the load-carrying capacity. In practice, the shear problem is often solved by increasing the thickness of the slab to avoid shear reinforcement. However, there can be geometrical constraints fora slab bridge, which limits the thickness. In that case, shear reinforcement, together with redistribution of shear, can be used to increase the load-carrying capacity. Limit analysis based on the assumption of perfect plastic materials has shown to be an efficient method to determine the load-carrying capacity of reinforced concrete slabs in bending. The most well-known methods are the Yield Line Method [1] and the Strip Method [2]. The yield line method is based on the upper bound theorem and assumes infinite shear capacity. The strip method is based on the lower bound theorem and assumes zero torsional moment which makes it ineffective with respect to redistribution of internal forces.