Example 5⁵

Stresses Under Bending - Elastic Range

Problem: A 900 mm strip of steel is bent into a full circle by applying two couples as shown. Determine:

a) the maximum thickness t of the strip

b) the corresponding moment M of the couples.

Solution: Assuming that the gap where the couples are applied is negligible, the radius is

Using the allowable stress in the standard equation for the stress produced by a bending moment...

Now I use the equation for the radius of curvature of the neutral surface:

Solving equations (1) and (2) simultaneously, I get t = 0.602 mm and M = 0.203 Nm.

⁵ This is Problem 4.24 in Beer & Johnston's Mechanics of Materials, 2^nd Edition, McGraw-Hill.