Saved Bookmarks
| 1. |
A pipe has an outside diameter of 20 mm, an inside diameter of 10 mm and length 0.30 m and it supports a compressive load of 50 kN. The pipe shortens by 0.6 mm when the load is applied. Determine (a) the compressive stress, (b) the compressive strain in the pipe when supporting this load. |
|
Answer» Compressive force F = 50 kN = 50000 N, and cross-sectional area A = \(\cfrac{\pi}4\)(D2 - d2) where D = outside diameter = 20 mm and d = inside diameter = 10 mm. Hence, A = \(\cfrac{\pi}4\) (202 - 102) mm2 = \(\cfrac{\pi}4\) (202 - 102 ) x 10-6 m2 = 2.3562 x 10-4 m2 (a) Compressive stress \(\sigma\) = \(\cfrac FA\) = \(\cfrac{50000\,N}{2.3562\times10^{-4}m^2}\) = 212.2 x106 Pa = 212.2 MPa (b) Contraction of pipe when loaded, x = 0.6 mm = 0.0006 m, and original length L = 0.30 m. Hence, compressive strain \(\varepsilon\) = \(\cfrac XL\) = \(\cfrac{0.0006}{0.3}\) = 0.002 (or 0.20%) |
|