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Mid-term6 - UNIVERSITY OF CALIFORNIA BERKELEY College of...

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UNIVERSITY OF CALIFORNIA, BERKELEY College of Engineering Mechanics of Materials (CE130) The Second Mid-term Examination Problem 1. Derive the differential equation for Bernoulli-Euler beam. Consider following infinitesimal beam element: (a) dV dx = q ( x ); (1) (b) dM dx = V ( x ) (2) (10 points) Figure 1: A 2D infinitesimal element Problem 2. Draw shear & moment diagrams for the following beams (see: Fig. 2 (a)(b)) and label the peak values for the corresponding maximum shear and maximum moment. (25 points) Figure 2: Beams with external loads 1
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Problem 3. A box-beam shown in Fig. 3 is subjected to a shear force V at the given cross section. Find the maximum shear stress within the cross section. τ = V Q I z t Q = A ydA = A ¯ y I z = I zc + d 2 z A parallel axis theorem I zc = bh 3 12 for rectangular cross section . (3) (20 points) Figure 3: The cross-section of a box-beam. Problem 4. A T-beam shown in Fig. 4 (a) is made of linear elastic-perfectly plastic material (shown in Fig
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