7.1 INTRODUCTION

The complexities involved in obtaining a progressive-failure solution to a reinforced concrete problem can be illustrated by considering the simple beams shown in Fig. 7.1a and b, subjected to a simple centerpoint load. The crack patterns shown are those obtained experimentally in two identical beams which failed in shear, one without and one with stirrups (Scordelis, 1972). The load-displacement response of the beams under increasing load can be roughly divided into three stages:

1. The uncracked elastic stage. At low loads the beam behaves essentially like an uncracked elastic member.

2. The crack-propagation stage. Vertical flexural cracks then occur at midspan, resulting in a redistribution of stress and causing some bond slip.

3. The plastic stage. If shear and diagonal tension are not critical, the beam eventually fails by yielding of the longitudinal tensile steel reinforcement or by crushing of the concrete in the compression zone. If shear and diagonal tension are critical, the formation of a significant diagonal-tension crack activates resistance to vertical shear by dowel action in the main longitudinal reinforcement, subsequent aggregate interlock along the diagonal crack, and resistance in vertical stirrups, if any exist. This leads to the final shear-compression failure of concrete under a combined state of stress.

Figure 7.1: Experimental crack patterns of beams failing in shear: ( a) beam without stirrups and ( b) beam with stirrups. ( Scordelis. 1972.)

A rational analytical solution to this problem, which includes the effects of cracking, bond slip, dowel action, and...