Question

A pedestrian bridge is constructed from 100 mm thick planks using the cross section shown in Fig. Q 2(a). The bridge is 10 m long and is supported as shown below in Fig. Q 2(b). After a heavy snowfall, there is a thick layer of snow that weighs 500 N for every metre of the bridge. A 500 kg snowplough has partially clcared the snow by pushing it off the side of the bridge. Another crane is hoisting a 200 kg mass Mas depicted in Fig. Q 2(b). What is the deflection of the bridge directly under the plough at the instant shown? The planks have a modulus of elasticity of 50 GPa. You may ignore the mass of the crane and assume that it is rigidly fixed to the bridge. You may also assume that the mass of the plough acts through their respective centres of mass. 400mm 600mm 100mm -- 600mm 1.5m Fig. Q 2(a) im 2m 1m' 2m 1m 10m Fig. Q 2(b)

Answer 1

The cross-section of the bridge will have a rotation along the dashed line as depicted in Fig. Q 2(a).

The moment of Inertial can be calculated along this axis of rotation.

Furthermore, if the snow has been partially cleared by pushing it to the side, the pushed snow will have the weight of (10 * 500) / 3 N/m.

taking these factors into consideration and, using the FBD of the bridge, we will proceed to calculate the deflection at the snowplough Center of Mass.