ARCH 461/561 Lecture 38 Bending Stress in a Beam Example Problem

Lecture 38
Example Problem

Bending Stress in a Beam

Given:
the rough wood beam spanning 16ft and loaded with a concentrated load of 2000# as shown below. The beam is 12 in deep and 8 in wide.
Determine:
the maximum bending stress in this beam.

Lecture 38

Solution:
First find the reactions and draw the shear and moment diagrams. From the moment diagram it is obvious that the maximum internal moment occurs 8 ft from the left support and is equal to 8000#ft.

To find the maximum bending stress, use the formula
f = Mc / I.
M = 8000#ft
c = 6 in
I = 1/12 bh^3 = 1152 in^4.

Therefore:
f = (8000#ft)(12 in/ft)(6 in) / 1152 in^4 = 500 psi

Lecture 38 Example Problem

Lecture 38
Example Problem