264 Mechanics of Materials s11.9 of,for example,machine parts to exclude the possibility of sudden applications of load since associated stress levels are likely to be doubled. 11.9.Impact loads-axial load application Consider now the bar shown vertically in Fig.11.7 with a rigid collar firmly attached at the end.The load W is free to slide vertically and is suspended by some means at a distance h above the collar.When the load is dropped it will produce a maximum instantaneous extension 6 of the bar,and will therefore have done work(neglecting the mass of the bar and collar) =force x distance W(h+6) Load W Rigid collar Fig.11.7.Impact load-axial application. This work will be stored as strain energy and is given by eqn.(11.2): g2AL U=2E where o is the instantaneous stress set up. o2AL =W(h+δ) 2E (11.9) If the extension 6 is small compared with h it may be ignored and then,approximately, 2 =2WEh/AL 2WEh i.e. (11.10) AL If,however,6 is not small compared with h it must be expressed in terms of o,thus stress oL E= and 6=L E Therefore substituting in eqn.(11.9) o2AL WaL 2E-Wh+E264 Mechanics of Materials $1 1.9 of, for example, machine parts to exclude the possibility of sudden applications of load since associated stress levels are likely to be doubled. 11.9. Impact loads - axial load application Consider now the bar shown vertically in Fig. 11.7 with a rigid collar firmly attached at the end. The load W is free to slide vertically and is suspended by some means at a distance h above the collar. When the load is dropped it will produce a maximum instantaneous extension 6 of the bar, and will therefore have done work (neglecting the mass of the bar and collar) = force x distance = W (h + 6) Load W Bar-- Fig. 11.7. Impact load-axial application. This work will be stored as strain energy and is given by eqn. (1 1.2): where o is the instantaneous stress set up. (11.9) If the extension 6 is small compared with h it may be ignored and then, approximately, o2 = 2 WEhJAL i.e. u = J(F) (11.10) If, however, b is not small compared with h it must be expressed in terms of 6, thus stress OL OL E=- =- and 6 =- strain 6 E Therefore substituting in eqn. (1 1.9) O~AL WOL -- - Wh+- 2E E