Shear Reinforcement in Reinforced Concrete Beams

1. Introduction

In members where the shear strength provided by the concrete is not sufficient to resist the (factored) design loads shear reinforcement is often detailed. Shear reinforcement is typically perpendicular to the longitudinal reinforcement and thus oriented vertically in a typical (horizontal) beam. The idea behind shear reinforcement is to arrest the development of the diagonal tension cracking, and, generally, shear reinforcement is detailed such that any potential diagonal tension crack will have to cross two such reinforcements. Since the design shear force may vary along any particular structural member, it may be necessary to reinforce some sections, and not others, and where reinforcement is necessary, the spacing of such reinforcement may vary.

(See Figures 13.11, 18, 19 and 20 in the Ambrose text.)

2. Design Equations

Our design check is as follows:

... Is Vu ≤ φ (Vc + Vs)?

Where Vu is the factored shear load,

... φ is our strength reduction factor for shear in reinforced concrete ... 0.75,

Vc is the strength provided by the shear, covered in the lesson for shear (here),

and,

Vs is the strength provided by the shear reinforcement ...

V_s = A_v f_y (d / s),

where,

A_v = the cross sectional area of the shear reinforcement,

f_y = the specified yield strength of the shear reinforcement,

d = the effective depth,

and

s = the spacing of the shear reinforcement.

Typical shear reinforcement consists of double-leg stirrups perpendicular and tied around the longitudinal reinforcement (see Figures 13.4, 13.11 and 13.14, for starters).

In some cases of more lightly loaded members (but still requiring shear reinforcement) I specify single-leg stirrups, and instead of deformed bars, I specify deformed wire.

Note that in the case of double-leg stirrups, the areas of both legs are considered.

Also note that shear reinforcement is to be provided until ...

... Vu ≤ ½ φ (Vc) ... for reinforced concrete members except those noted below, or

... Vu ≤ φ (Vc) ... for reinforced slabs and footings, concrete joist construction (as defined by the Code), and beams with depths total depths not greater than 10 in., blah, blah (see the lesson on beam shear).

Also, from that lesson, recall that if the section is subject to axial tension it may be advisable to carry all of Vu with the shear reinforcement, or at least take into consideration the effect of the axial tension on Vc.

3. Stirrup Spacing, Amount of, etc.

As mentioned (though worded perhaps a bit differently) stirrups shall be spaced so that any potential diagonal tension crack will pass through at least two stirrups. In equation form this is,

... s ≤ d/2 ... (note the use of the effective depth, not the total depth),

the first stirrup must be located not farther than s/2 from the face of the support,

the minimum amount of shear reinforcement, A_{v min}, is,

A _{v min} = 0.75 √ f '_c b s / f_y, ... but not less than ≤ 50 b s / f_y.

If Vs exceeds ... 4 b d √f'_c ( ... 2 Vc) then the required spacing computed above shall be cut in half ... (yikes),

and (ACI 318 11.5.6.9) ... Vs may in no case be taken to be greater than ... 8 b d √f'_c ( ... 4 Vc).

These latter requirements make sure that we don't have so much steel that we end up obliterating the concrete. Plus, at some point things start getting pretty congested.

And, in lightly loaded beams the above conditions are sometimes quite nicely satisfied using single leg bars or deformed wire.

NOTE: you can see from the referenced figures that stirrups generally go around/outside of the longitudinal reinforcement. In this regard the use of stirrups must be considered in the detailing of the longitudinal reinforcement so that minimum cover and spacing requirements are (still) satisfied. (The reason I say this is that often in design we pick a member size,, determine the longitudinal reinforcement, and then check shear ... shear calcs going last. So, as a matter of practice, commence the calculations with the longitudinal reinforcement located such that shear reinforcement can be accommodated if (later) it is determined it is necessary.

4. Example(s)

An example is ... here.

5. References

Simplified Engineering for Architects and Builders, Ambrose, J. and P. Tripeny, 10^th edition, John Wiley & Sons, Hoboken, New Jersey, Pages 410 - 425.

Beam Shear in Reinforced Concrete, Jeff Filler, Associated Content.

Example of Shear Reinforcement in a Reinforced Concrete Lintel, Jeff Filler, Associated Content.

Building Code Requirements for Structural Concrete, ACI 318, American Concrete Institute, P.O. Box 9094, Farmington hills, Michigan, 48333, Chapter 11.