[Univ of Cambridge] [Dept of Engineering]

 Nonlinear finite element analysis of reinforced 

concrete deep beams

Samir Hasan


Reinforced concrete deep beams have many useful structural applications, particularly in tall buildings, foundations, bridges and offshore structures. However, comprehensive theories that tackle the detailed analysis and design of deep beams are not well established yet.

One possible solution is to use the Finite Element Method (FEM) to analyse, and hence design, deep beams. The FEM is advantageous since it can model to an acceptable degree the various combinations of geometry, loading, properties of concrete and steel, and the non-homogeneous and nonlinear behaviour of the composite material.
This thesis describes a series of analyses carried out using the commercial finite element package, DIANA, to analyse three types of reinforced concrete continuous two spans deep beams, S1, S2 and S3. The beams were identical in geometry and the only difference between them was in the reinforcement patterns. The beams are tested annually in Cambridge University Engineering Department as part of Module 4D7: “Concrete and Masonry Structures”.
A three-dimensional finite element model that is capable of predicting the ultimate load and mode of failure of the three series is presented. The model is kept as simple as possible in terms of element selection and integration schemes without detaching from the accuracy of the results. Two constitutive models for concrete were used, namely plasticity model in compression incorporated with a smeared cracking model in tension, and total strain-based crack model. Reinforcement, loading plates, and supports were modelled as elastic-perfectly plastic materials.

The project has shown that the finite element method, if properly used, can be a powerful technique that is capable of providing a detailed analysis for complex structural elements such as deep beams.


[Cambridge University | CUED | Structures Group | Geotechnical Group]

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