Theory of reinforced concrete taking account off shear

Abstract

This article is an advanced summary of the original theory elaborated by Messrs. López Jamar and Tirado Cruz, on compound bending in reinforced concrete parts, taking account of shear effects. The authors assume the structure to be similar to an open web girder. The top chord is the uncracked zone, and is assumed to withstand eccentric compression and shear, in the same way as the uncracked diagonal portions of concrete, between cracks. The bottom chord consists of the longitudinal reinforcement and the complementary series of diagonal uncracked concrete portions (which may no actually exist). These are subject to almost pure tensile loads. A parabolic distribution of longitudinal stresses is supposed initially, and from this the normal and tangential forces on the non cracked zone is precisely obtained. Also assuming a parabolic stress distribution for the stirrups, the efficient stress distribution laws in the cracked zone of the concrete are obtained. These stress laws make it possible to study the partial strength of the cracked and uncracked zones: the latter, because of its intrinsic strength. Thus, the shear is mainly dependent on the relative strain of the cracked zone. There are therefore four possible ways of reaching ultimate failure: simultaneous transversal failure of concrete and stirrups; longitudinal reinforcement failure; compression failure and total failure of the structure. The complex resulting system of equations can be solved by means of computers. Graphical and tabulated results are obtained for the various cases and systems of reinforcement. A first check of the theory has been made by means of a test.