E. G. Sherwood, E. C. Bentz and M. P. Collins

Department of Civil Engineering, University of Toronto, 35 St. George St., Toronto, Ontario, Canada M5S 1A4 E-mail: sherwoo@ecf. utoronto. ca


This paper describes one phase of an extensive experimental program that has recently been completed at the University of Toronto. In this phase, eighteen lightly-reinforced shear-critical reinforced concrete beams were loaded to failure. The abilities of the ACI-318 shear design method and a simplified design method based on the Modified Compression Field Theory to predict the failure loads are compared. It is found that the ACI design method is dangerously unconservative when applied to large beams and one­way slabs constructed without stirrups, while the simplified MCFT design method is both safe and accurate. Studies of the mechanism of shear transfer indicate that approximately one quarter of the shear in a reinforced concrete beam constructed without stirrups is transferred in the compression zone, with the rest carried primarily by aggregate interlock. The development of theoretically-sound shear design methods must therefore be based on the fact that aggregate interlock plays a critical role in the shear behaviour of reinforced concrete structures.


It has long been a goal of code writers to improve the quality of reinforced concrete design procedures for shear. Unlike flexural failures, shear failures in reinforced concrete are brittle and sudden, and occur with little or no warning. Furthermore, they are less predictable than flexural failures, due to considerably more complex failure mechanisms. While flexural design provisions are based on the rational assumption that plane sections remain plane, the search for equally rational design provisions for shear continues.

The recently updated and reissued ACI-318- 05 and CSA A23.3-04 Design Codes for Concrete (Figure 1) represent the culmination of extensive research involving all aspects of the behaviour of reinforced concrete. However, the shear design provisions in the ACI code remain based on traditional empirical relationships developed over 40 years ago, and do not reflect the vast improvements in understanding of the shear behaviour of reinforced concrete that have been gained over that time. In particular, there are significant concerns that the ACI shear design provisions are unconservative when applied to large beams and one-way slabs constructed without stirrups. As such, they must be replaced with rational, theoretically-sound design provisions that can predict the shear behaviour of these brittle, complex structural elements.

A particular aspect of the shear behaviour of reinforced concrete that is deserving of additional attention is the effect of the maximum aggregate size on the shear response of reinforced concrete sections. This is particularly true for reinforced concrete beams constructed without stirrups, since aggregate interlock is the dominant mechanism of shear transfer in these element types. Increasing the size of the coarse aggregate produces rougher cracks that are better able to transfer shear stresses. Likewise, reducing the maximum aggregate size decreases the shear strength of a concrete section. Furthermore, the use of high


M. Pandey et al. (eds), Advances in Engineering Structures, Mechanics & Construction, 153-164. © 2006 Springer. Printed in the Netherlands.

strength concrete or low-density aggregate can result in fracturing of the coarse aggregate particles as cracks form, thereby producing smoother cracks with a greatly reduced aggregate interlock capacity.

The Modified Compression Field Theory (MCFT) (Vecchio and Collins, 1985) employs equilibrium, compatability and experimentally verified stress-strain relationships to model the shear behaviour of cracked concrete. A fundamental relationship in the MCFT relates the shear stress on a crack surface due to aggregate interlock to the crack’s width, the maximum aggregate size and the concrete strength. The aggregate effect was first codified when a general method of shear design was derived based on the MCFT and implemented in the AASHTO-LRFD bridge design guidelines. In 1994 the general method of shear design was implemented in the CSA concrete design code for buildings. Recently, an updated and simplified version of the general method has been developed (Bentz et al., 2005) and implemented in the 2004 CSA design code. The new general method, referred to as the Simplified Modified Compression Field Theory (SMCFT) has been found to be simpler than the original general method with, in many cases, improved predictive capabilities (Sherwood et al., 2005a).

As might be expected, there are certain areas of considerable disagreement between modern shear design methods based on the MCFT and the ACI method. The fundamental question that must be asked, therefore, is: “Are the existing ACI shear design methods sufficiently safe, such that a reworking of the provisions is not necessary”. The corollary to this question is: “Has our understanding of the fundamental behaviour of reinforced concrete in shear advanced to such a stage such that modern shear design methods represent a clear improvement over traditional design methods?” The purpose of this paper is to explore the answers to these questions by studying the behaviour of reinforced concrete beams in shear, focusing on the role played by the coarse aggregate. A significant experimental program will be presented in which eighteen shear critical concrete beams constructed with different maximum aggregate sizes were tested to failure. The SMCFT design method will be discussed, and its predictive capabilities will be compared to those of the empirical ACI shear design method.