Lecture 38
Example Problem
Bending Stresses
Given:
the T-beam of the indicated section spans 10 ft and is loaded with a distributed load of 120#/ft as shown below.
Determine:
a. the maximum bending stress in tension and compression in this beam;
b. the maximum bending stresses 3 ft from the left end;
c. the bending stress in the beam 3 ft from the left end and 2 in below the neutral axis.
Solution:
First draw the shear and moment diagrams. The moment diagram shows that the maximum internal bending moment will occur 5ft from the left end and will equal 1500#ft.
In each case use the formula f = Mc/I
a. Max tension:
M = 1500#ft
c = 5 in
I = 136 in^4
f = (1500 #ft)(12 in/ft)(5 in) / 136 in^4 = 660 psi
Max compression:
M = 1500#ft
c = 3 in
I = 136 in^4
f = (1500 #ft)(12 in/ft)(3 in) / 136 in^4 = 396 psi
b. bending stresses at 3 ft
M at 3' = 600#(3ft) - 120#/ft(3 ft)(3/2 ft) = 1260 #ft
Tension:
f = (1260 #ft)(12 in/ft)(5 in) / 136 in^4 = 552 psi
Compression:
f = (1260 #ft)(12 in/ft)(3 in) / 136 in^4 = 336 psi
c. bending stress 2 in below the neutral axis
f = My/I = (1260 #ft)(12 in/ft)(2in) / 136 in^4 = 222 psi tension
Copyright © 1995 by Chris Luebkeman and Donald Peting