Home Work 4 - Me 202

ME 202 – Solid Mechanics – Winter 2019 Homework-4

Deflection of Beams

Due Date: 18th March

1. A uniform cantilever beam carries a total load of W, which is distributed in the linearly varying fashion shown in figure 1. Find the deflection at the right end. 2. Using the singularity function method, find the deflection at the center of the beam for shown in figure 2. Solve this problem using the direct integration method as well as the superposition of point load method. 3. For the figure 3, find the beam deflection using superposition method. Calculate the maximum deflection, maximum bending stress and their location. 4. A uniform beam is built in at both ends as shown in figure 4. Find the maximum bending moment and the maximum deflection due to uniformly distributed load of intensity w per unit length. Also find the reaction force at the both ends of the beam. Solve this problem using the direct integration method as well as the superposition of point load method. 5. The two systems shown in figure 5 are identical in every respect expect in (a) there are two beams of length L while in (b) there is a single beam of length 2L. The uniformly distributed load of intensity w is the same in both cases. Compare a. The reactions at the central support b. The maximum bending moments c. The maximum deflections in the two cases.

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5