Numerical method for predicting first crack load on hollow-cored beams subjected to point load at Midspan

Abstract

Predicting the initial crack load in concrete is important to detect early warning of a problem. In this study, a model for predicting the first  crack load on a hollow-cored rectangular beam point loaded at mid-span was developed by combining a numerical method and an  experimental approach. The modulus of rupture was introduced into the governing moment-curvature relationship. Experimentally,  flexural testing with point loads at mid-span was performed on fifteen (15) beams made up of three (3) beam types at 1 kN intervals for a  span of 750mm using the Universal Testing machine. The beams were simply supported by roller points. The dimensions of the beams  were kept constant and later varied while investigating the following hollow diameters: 0, 30, 60, 75, and 105mm. Numerically, the beams  were designed as a beam element point loaded at mid-span with a span of 700mm centers, and the support conditions were defined as  pinned support. Governing equations relating failure load with the modulus of rupture, stiffness matrix, shape functions, and moment of  inertia were developed. The equation for predicting the first crack load, incorporating the modulus of rupture, was derived. The moment  of inertia was calculated by discretizing the hollow-cored beam section using an isoparametric geometric transformation. The  experimental results were used to validate the numerical model. 90.55% agreement between experimental and numerical results was observed. The overall average percentage difference between the two methods recorded is 9.45%. This shows that at about 91%  confidence level, both approaches are the same and can be applied with confidence in the prediction of the first crack load on hollow- cored reinforced concrete beams.