Influence of transverse reinforcement on elastic shear stiffness of cracked concrete elements

Various truss models for calculating the cracked elastic shear stiffness due to transverse reinforcement are investigated to determine the threshold of the geometrical configuration of concrete beams and columns, in which the more convenient continuum truss model can substitute for the discrete truss model without losing accuracy. For this purpose, a comparison is made between continuum and discrete truss models, between constant and variable angle truss models, and between rectangular hoops and circular hoops and spirals. For the continuum truss model to substitute for the discrete truss model, the center-to-center space between transverse reinforcements should be limited to s≤dc/5s≤dc/5 for rectangular hoops and s≤dc/3s≤dc/3 for circular hoops and spirals.The minimization of energy due to combined flexure and shear mechanisms leads to the construction of formulae for the inclination of diagonal cracks. This angle, θθ, is a key parameter for a shear strength and stiffness analysis. The validity of the crack angle formulae is verified through a comparison of the theoretical crack angles with those measured from experimental results reported in a number of earlier studies.