## Shear Stirrup Spacing (for concrete beams)

Shear stirrups are used to resist shear cracking in concrete beams along the 45° angle failure plane.

The following sections will be addressed in this section:

• Design for Shear Stirrups
• smax, smin, and Av-min
• Situations where no stirrups will be necessary
• An example of shear stirrup design
• Common design practices for stirrups

### Design for Shear Stirrups:

1) Calculate Vu:
This is the ultimate factored shear that the concrete beam is experiencing.

2) Calculate Vc:
The equations for this have been provided in the Concrete Beam Design section.

3) Find when {řV_c\over2} \ge V_u :
This region of the concrete beam will not require any stirrups, [ACI 11.5.6.1].

Where:

4) Find Vs-reqd:

V_{s-reqd} = {V_u\over ř}-V_c
Where:

Vs-reqd = The required shear strength that the steel must provide.

5) Find the spacing (s):

s = {A_vf_{yt}d\over V_{s-reqd}}
Where:

Av = Assumed based on what type of rebar? you are using. Note that Av is not the area of one bar but 2* the area of one bar since you would have to shear through both sides of the stirrup for failure to occur.
fyt = the strength of the rebar (e.g. 40 ksi, 60 ksi)
d = the depth of the concrete beam (note: that this is not the same as the height of the beam)

### smax, smin, and Av-min

• smax
• smax = min [24" or d/2] for  V_s \le 4\sqrt{f'_c}b_wd
• smax = min [12" or d/4] for  V_s \ge 4\sqrt{f'_c}b_wd

This is to ensure that for high shear zones the stirrup spacing is tighter than in low shear zones.

• smin = 3"
• Av-min

A_{v-min} = {0.75\sqrt {f'_c}{b_ws \over f_{yt}} \ge {50b_ws\over f_{yt}}}

Where:

Av-min = the minimum shear steel required if {řV_c\over2} \le V_u
f'c = The compression strength of the concrete (e.g. 4 ksi, 6 ksi)
bw = the width of the concrete beams web
fyt = the strength of the rebar (e.g. 40 ksi, 60 ksi)

### Situations where no stirrups will be necessary:

If {řV_c\over2} \ge V_u then it is not necessary to consider Vs. [ACI 11.5.6.1]

This assumes that:
• h < 10"
• d ≤ 2.5 tf
• d ≤ tw / 2

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