Finite Element Modeling of Deep Reinforced Concrete Beams with Web Openings

Abstract

The effects of openings on the ultimate capacity of deep beams have been studied experimentally by many researchers. However, there’s still need for analytical study using numerical methods and also the development of simple stiffness reduction models that can be easily used for quick prediction of the effects of opening sizes on the stiffness of deep reinforced concrete beams. This study is focused on modeling the behavior of deep reinforced concrete beams with web openings of various configurations and the development of simple mathematical models for stiffness reduction. A total of 20 deep beam models with small and large openings are analyzed using the finite element method. A computer program written in MATLAB was used in the analysis. The computer program was tested by analyzing a plane elasticity problem with known solution to validate the program before it was used in analyzing the deep beams. Results of the analysis shows that for a small opening of size 0.1 d, where d is the depth of the beam, the effect on the stiffness is relatively low. Only 1.2% reduction in stiffness is observed. Whereas for large openings, a reduction in stiffness of 8.4% is recorded for a 210 mm (0.35 d) square opening with centre located at 675 mm from the support. Three mathematical models have been formulated for the stiffness reduction factor as a function of the depth of opening to depth of beam ratio (β/d) for openings located at 0.45 ℓ, 0.25 ℓ and 0.35 ℓ, where ℓ is the shear span of the beam.