Shear strength theories for beams of variable depth

Flexibly formed reinforced concrete beams usually have varying cross sections along their longitudinal axis, capitalising on the fluidity of concrete to create optimised geometries. According to Orr et al. [1], these new shapes have led to challenges for shear design, especially when the depth of the beams is relatively small. It is crucial to be able to accurately determine the shear strength of such beams to maintain structural safety whilst achieving material optimisation.
The effective shear force method is adopted for tapering beams in many design codes. Recent work by Paglietti et al. [2] has highlighted concerns over the use of such an approach. In this paper, the theoretical basis for stress distributions in tapered beams built by Timoshenko [3] and Oden [4] in their elastic range is reviewed and then extended to included cracked behaviour.
It is found that the effective shear force method used in design codes does not accurately account for the stress distribution in a section both in elastic and cracked stage of concrete, underestimating the peak shear stress for beams with inclined soffits. This is important for flexibly formed beams, and has implications for designers
As a result of this work, a new calculation and design method for shear reinforcement is proposed.
Keywords: variable depth beam, shear strength, shear stress distribution, flexible formwork.