A circular plate with its edges clamped carries distributed lateral load, whose intensity varies linearly with radius r, from zero at r = 0 to q at r = a. a. Derive the expressions for w = w(r). Also determine the center deflection.

b. Combine the answer of part (a) with one other case to obtain the center deflection due to distributed load that varies linearly with r, from q at r = 0

to zero at r = a

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.