# Nonlinear finite element analysis of reinforced

# concrete deep beams

## Samir Hasan

*Abstract*:

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]

###

This page is maintained by rcb@eng.cam.ac.uk (last update 4 November
2003)