Question

A vinyl [E = 2.60 GPa; ν = 0.43] block with width b = 60 mm, depth d = 120 mm, and height h = 320 mm rests on a smooth rigid base. A load P is applied to a rigid plate that rests on top of the block. Calculate the change in the depth dimension d of the block after a load of P = 160 kN is applied.

Answer 1

Explanation:

Formula to calculate lateral strain is as follows.

         Lateral strain = $\frac{P}{AE}$

                               = $\frac{160 \times 1000}{60 \times 100 \times 2.60 \times 10^{3}}$

                               = $\frac{160}{15.6 \times 10^{3}}$

                               = $10.256 \times 10^{-3}$            

It is known that,

                   v = $\frac{\text{lateral strain}}{\text{longitudnal strain}}$

 Lateral strain = $0.43 \times 10.256 \times 10^{-3}$

                        = $4.41 \times 10^{-3}$

Thus, we can conclude that the change in the depth dimension d of the block is 0.00441 mm.