Shear Stress in Beams

Example: * The simply supported beam AB of length L = 6 ft, is acted on by a uniformly

distributed load, w, (including the weight of the beam) of 1800 lb/ft. The X-section of the beam

is b = 8 inches wide and h =10 inches deep as shown below. Find the values and locations

of the maximum shear stress and maximum bending stress.

Strategy: From equilibrium of the beam (or use symmetry), find the support reactions at A

and at B. Then plot the shear and bending moment diagrams. Find the locations and values of

the maximum shear force and maximum bending moment. Use these values to calculate the

value and location of the maximum shear stress and maximum bending stress.

The total downward vertical load is wL = (1800 lb/ft)(6 ft) = 10800 lb. Apply the equations

of equilibrium to determine the reactions at each support. See the FBD below.

→∑ F_x = 0, Ax = 0, ↑ ∑ F_y = 0, Ay + By ˗ wL = 0, Ay + By = 10800

CCW ∑ M_A = 0, By L ˗ wL(L/2) = 0, By = w(L/2) = 1800(6/2) = 5400 lb

So Ay = 10800 ˗ 5400 = 5400 lb (which follows from symmetry)

Click here to recall the sign convention for shear force and bending moment.

Click here to continue with this example.

Return to Notes on Solid Mechanics

Copyright © 2019 Richard C. Coddington
All rights reserved.