Problem: The 3 kg block D is dropped from the position shown onto the end of a 16 mm square steel bar. Knowing that E = 200 GPa, determine:
a) the maximum deflection at the free end of the bar
b) the maximum bending moment in the bar
c) the maximumn normal stress in the bar
Solution: The cross section is square, with 16 mm on a side:
From Case 1, Appendix D, I write:
Using the formula for the strain energy, and assuming that the potential energy of the falling mass is completely converted to that strain energy...
a) Rearranging this and solving the resultant quadratic equation...
b) For the maximum moment the force must be computed:
c) Now I use the usual bending moment - normal stress equation:
1 This is problem 10.72 in Beer & Johnston's Mechanics of Materials, 2nd Edition.