Shear Strength Calculation of Reinforced Concrete Beam with Inclined Stirrups (ACI 318-19)

Shear reinforcement in a concrete beam is required when the shear strength of concrete alone is inadequate to carry the vertical shear from external loads. ACI 318 stipulates the general equation for computing the vertical shear strength of a concrete beam with inclined stirrups as follows.

Vs = As*fy*d/s*(sin(a) + cos(a))

where a = horizontal angle of the inclined stirrup

It's first astonishing to see the term cos(a) for the shear strength of the stirrup, which should only be in the vertical component. In this article, we shall demythify this by considering the freebody of the beam as shown below.

The vertical component due to the inclined stirrup consists of 2 parts: the vertical component of the shear stirrup itself and the part due to friction at the shear interface. The shear friction occurs even when the stirrup is not inclined. This is not the component of shear strength due to the concrete compression strut (Vc).

In conclusion, the friction term shall be included when the shear stirrup is inclined. For the vertically aligned stirrup, this term is obscured by the zero component of horizontal concrete compression.