Five-spring model for complete shear behaviour of deep beams

This paper presents a five-spring model capable of predicting the complete pre- and post-peak shear behaviour of deep beams. The model stems from a two-parameter kinematic theory (2PKT) for the shear strength and displacement capacity of deep beams under single curvature. Four of the springs of the model represent the shear resistance mechanisms of the beam, while the fifth spring models the flexural behaviour. The model predicts not only the load-displacement response, but also the deformation patterns of the beam and how these patterns change with increasing load. Validation studies are performed by using 28 tests from the literature, showing excellent results. The model is used to interpret the tests and to draw conclusions about the behaviour of deep beams. It is shown that shear strength variations of up to 60 % between nominally identical specimens can be caused by variations in the path of the critical shear cracks. It is also demonstrated that loss of bond of large reinforcing bars increases the shear capacity of deep beams. Finally, the five-spring model is shown to predict the post-peak shear behaviour effectively, which is important for the analysis of structures under extreme loading.