Lecture 39
Example Problem
Plotting Shearing Stresses
Given:
The beam with loading condition shown below
Determine:
a. the horizontal shearing stress at 2in increments from top to bottom of the beam
b. plot these stresses - use maximum vertical shear on the beam
Solution:
From the shear diagram, the maximum shear force equals 5.5k = 5500#.
I = 1/12(4in)(16in)^3 = 1365 in^4
a. At each increment, from top to bottom, use the formula fv = VA'y/Ib
at 2":
fv = (5500#)(8in^2)(7in)/(1365 in^4)(4in) = 56.4 psi
at 4":
fv = (5500#)(16in^2)(6in)/(1365 in^4)(4in) = 96.7 psi
at 6":
fv = (5500#)(24in^2)(5in)/(1365 in^4)(4in) = 120.9 psi
at 8":
fv = (5500#)(32in^2)(4in)/(1365 in^4)(4in) = 128.9 psi
The lower half of the beam will reflect the numbers on the upper half with the shearing stress decreasing at an increasing rate closer to the bottom.
b. The plot of the shearing stresses will follow a curve with the maximum shearing stress occuring at the neutral axis.
Copyright © 1995 by Chris Luebkeman and Donald Peting