Shear resistance of beams based on the effective shear depth

Despite extensive experimental and theoretical studies the shear resistance of beams with longitudinal reinforcement is described by empirical expressions. A reliable empirical formula is derived by Rafla [10]. This formula is based on 442 experimental results. In this report no experiments are described. It is endeavoured to make a new contribution to the theoretical study of shear strength. The model presented in this report is based on the idea that apart from the effective depth of the compressive zone there is an effective shear depth. The model developed is compared with empirical expressions defined by Rafla and other investigators. The results are promising. With the model the time-dependent behaviour of the shear resistance, the strength criterion and the durability are discussed. For beams with web reinforcement it is explained which mechanism causes the almost constant contribution of the 'compressive zone' to the shear resistance in spite of the increasing deformations. According to the model derived, a formula is presented for lightweight concrete by substitution of the proper material properties into the general expressions for the shear resistance. This formula is in good agreement with the experinents reported by other investigators. Due to the complex internal equilibrium in the case of (partially) prestressed concrete the influence of a normal force on the shear strength is not discussed in detail. The general principle is presented and an example is given. The observed experimental behaviour can be explained with the model derived