A Two Degree of Freedom Kinematic Model for Predicting the Deformations of Deep Beams

In modern construction, it is not unusual to require a short span member to carry a very large load such as with a transfer girder. These members generally have high shear strengths with strut-and-tie models being able to predict these strengths generally in a conservative manner. For serviceability checks, cracked stiffness estimates, and seismic design, however, it is also important to be able to predict the deformations of the member accurately. In this paper a set of eight large and heavily instrumented reinforced concrete deep beams subjected to monotonic or cyclic loading are summarized. The displacements of these tests are explained in detail with particular attention paid to the development of deformations over the full load history. From these deformations, the paper notes that a simple 2 degree of freedom (DOF) kinematic model can be developed to predict the entire displacement field for a beam after diagonal cracking has occurred. These two degrees of freedom are the average longitudinal strain in the flexural reinforcement, and the vertical distortion of the critical loading zone near the applied load. When the results of the measured displacements of the beam tests are compared to the pattern of deformations from the 2 DOF model, excellent agreement is obtained. In addition, it is shown that the width of the main diagonal crack can also be explained well using the same 2 DOF model once these parameters are known. A forthcoming paper will explain how these parameters themselves can be predicted.