A solid copper bar of circular cross section has length L 5 1.25 m and shear modulus of elasticity G 5 45 GPa. The bar is designed to carry a 250 N m? torque acting at the ends. If the allowable shear stress is 30 MPa and the allowable angle of twist between the ends is 2.58, what is the minimum required diameter?

Afoot bridge is made as a simple deck, 4 m long, with a cross section 2 m (wide) and 20 cm thick, and made of wood. the deck is supported at the two ends. the maximum load allowable on the bridge is 10 tons, provided it is uniformly distributed on the deck. to sense this load, a strain gauge is placed at the center of the bridge and its resistance is monitored. if the sensor has a nominal resistance of 350 s2 and a gauge factor of 3.6, what is the reading of the strain gauge at maximum load? the modulus of elasticity for the wood used in the construction is 10 gpa.