question_answer 20)

Two strips of metal are riveted together at their ends by four rivets, each of diameter 6 mm. What is the maximum tension that can be exerted by thick riveted strip if the shearing stress on the rivet is not to exceed\[\text{ }{{\text{ }\!\!\upsilon\!\!\text{ }}_{\text{2}}}\text{=234 km/h}\]? Assume that each rivet is to carry one quarter of the load.

Answer:

Here, r = 6/2 =3 mm = 3 x \[\text{= 65 m/s; A= 2 }\!\!\times\!\!\text{ 25 = 50 }{{\text{m}}^{\text{2}}}\text{; }\!\!\rho\!\!\text{ =1 kg/}{{\text{m}}^{\text{3}}}\] m; Max. stress \[{{\text{P}}_{\text{1}}}\text{-}{{\text{P}}_{\text{2}}}\text{=}\frac{\text{1}}{\text{2}}\text{ }\!\!\rho\!\!\text{ }\left( \text{ }\!\!\upsilon\!\!\text{ }_{\text{2}}^{\text{2}}\text{- }\!\!\upsilon\!\!\text{ }_{\text{1}}^{\text{2}} \right)\text{=}\frac{\text{1}}{\text{2}}\text{ }\!\!\times\!\!\text{ 1 }\!\!\times\!\!\text{ }\left[ \text{6}{{\text{5}}^{\text{2}}}\text{ }\!\!\times\!\!\text{ 5}{{\text{0}}^{\text{2}}} \right]\] Max. load on a rivet = Max. stress x area of cross section \[\left( {{\text{P}}_{\text{1}}}\text{-}{{\text{P}}_{\text{2}}} \right)\text{A=}\frac{\text{1}}{\text{2}}\text{ }\!\!\times\!\!\text{ }\left[ \text{6}{{\text{5}}^{\text{2}}}\text{-5}{{\text{0}}^{\text{2}}} \right]\text{ }\!\!\times\!\!\text{ 50N}\] \[\left( {{P}_{1}}-{{P}_{2}} \right)A\] Maximum tension \[\text{m=}\frac{\left( {{\text{P}}_{\text{1}}}\text{-}{{\text{P}}_{\text{2}}} \right)\text{A}}{\text{g}}=\]