# ACI Method of Shear Design

Morsch (1909) was amongst the first to research the behaviour of reinforced concrete in shear. At the beginning of the 20th century he developed the well-known 45o truss model, whereby shear was visualized to be transferred through the web of a cracked concrete member through a field of diagonal compression in the concrete and tension in transverse reinforcement. To produce an expression for the shear strength of a concrete section, he assumed that shear cracks that formed did so at an angle, 0, of 45o:

Reflecting the design philosophy at the time, fv was taken to be the safe working stress in the stirrups. While Morsch knew from observations that failure shear cracks did not necessarily form at 45o, he saw no way to calculate the angle of what he termed secondary inclined cracks.

The 45o truss model entered use in various design methods and still forms the basis for the ACI expression for the shear resistance provided by stirrups. (The current ACI expression has simplified the equation by replacing the term jd with d.) As its use became more widespread, however, it was criticized for being overly conservative. In particular, the model assumed that only transverse reinforcement is effective at carrying shear, thereby predicting that a section without stirrups or bent-up bars would have no shear strength whatsoever. Clearly this is not the case. Extensive research efforts were undertaken in order to ascertain the so-called “concrete contribution” to shear resistance, which was eventually set at an empirically derived safe working shear stress of vc=0.03f’c. For the first time, the shear resistance of a reinforced concrete section was divided up into two components: a concrete contribution (Vc) and a web reinforcement contribution (Vs) predicted by the 45o truss model:

V = Vc + Vs

This method was used to design numerous concrete structures in the post-war construction boom of the 1950s and early 1960s. In 1955, however, a considerable portion of the roof of the Wilkins Air Force Warehouse in Selby, Ohio collapsed. The collapsed portions of the beams supporting the roof had been designed without stirrups, assuming that they could safely resist a working shear stress of 0.6MPa (90psi = 0.03 x 3000psi specified concrete strength). However, failure occurred at a shear stress of approximately 0.5MPa (70psi), corresponding to only about 80% of the safe service load on the roof. It therefore became apparent that unsafe designs could result from what had previously been considered to be a safe, conservative method.

As a result of the warehouse collapse, extensive research was undertaken to derive a better expression for Vc. In 1962, these efforts resulted in what was believed to be a simple, conservative expression for the failure shear based on a purely empirical curve-fit through 194 experimental data points (ACI Committee 326, 1962). This well-known expression (Equation 3) entered design use through incorporation into the 1963 American Concrete Institute Design Code, and has remained essentially unchanged since that time:

Vc = 0.167fbwd (MPa units) (3a)

Vc = 2fbwd (psi units) (3b)