Practice Question: Shear Along an Overhanging Beam

NCEES Civil PE Specification Structural Mechanics: Shear

Problem

The pictured beam overhanging a support is to be designed for uniform dead load wD and uniform live load wL based on the following strength load combination: 1.2DL + 1.6LL .

Determine the beam shear at location B based on the factored load demand.

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Solution

Answer: A) 5.5 kip

Consider the factored load demand based on the given load combination 1.2DL + 1.6LL:
$$ w_u=1.2\ast2\ klf+1.6\ast4\ klf=8.8\ klf $$
Calculate the reaction at support C by taking the moment about support A (consider counterclockwise rotation as positive):
$$ 8.8\ klf\ast5\ ft\ast\frac{5\ ft}{2}-8.8\ klf\ast20\ ft\ast\frac{20\ ft}{2}+R_C\ast20\ ft=0 $$
$$ R_C=82.5\ kip $$
Calculate the shear at 10 feet away from support C:
$$ V_B=8.8\ klf\ast10\ ft-82.5\ kip $$
$$ V_B=5.5\ kip $$
Refer to the following diagram for reactions and beam shear: