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Tensile stresses are developed because of horizontal shear stresses that occur along with bending stresses where the concrete cracks.

Vertical reinforcement is required to bridge the cracks. This reinforcement is called shear stirrups (or stirrups).

The maximum shear for design, Vu is the value at a distance of d from the face of the support.

 

Nominal Shear Strength

The shear force that can be resisted is the shear stress x cross section area: V_c = u_c x b_wd

The shear stress for beams (one way):

so

where bw = the beam width or the minimum width of the stem

φ = 0.75 for shear

 

Stirrups are necessary for strength (as well as crack control):

where Av = area of all vertical legs of stirrup

s = spacing of stirrups

For shear design:

Vu ≤ φVc + φVs , φ = 0.75 for shear

 

Spacing Requirements

Stirrups are required when V_u is greater than φV_c/2

 

Table: ACI Provisions for Shear Design

Economical spacing of stirrups is considered to be greater than d/4. Common spacings of d/4, d/3 and d/2 are used to determine the values of φV_s at which

the spacings can be increased. φV_s = (φA_vf_yd)/s

 

The maximum shear permitted from the stirrups is 8√(f'_c)b_wd.

The minimum recommended spacing for the first stirrup is 2 inches from the face of the support.