# 3.6 Shear capacity

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#### Introduction to shear capacity

The fifth limit state for beams is Shear Capacity. The shear capacity of a beam is the maximum amount of shear thebeam can withstand before failure. Usually the shear capacity is the controlling limit state on short spans withlarge loads.

#### Equations for shear capacity

The shear strength relationship is:

${V}_{u}\le {\phi }_{v}{V}_{n}$
where
• ${V}_{u}$ = maximum shear based on the controlling combination of factored loads
• ${\phi }_{v}=0.9$ = resistance factor for shear
• ${V}_{n}$ = nominal shear strength

The design shear strength then can be found depending, first, on whether or not the web is stiffened. If the webof a singly or doubly symmetric beam is unstiffened and $\frac{h}{{t}_{w}}\le 260$ , then Chapter F2 in the Specification Section of the Manual (page 16.1-35) can be used to define ${V}_{n}$ , otherwise, Appendix F2 in the Manual (page 16.1-102) can be used.

As long as the shear strength, ${V}_{u}$ , of a beam satisfies the maximum shear strength, ${\phi }_{v}{V}_{n}$ , value, shear is not a limiting factor of the beam design. If the shear strength, does exceed the maximum allowableshear, a different load or a different cross-section must be chosen.

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