Final2008 - UNIVERSITY OF CALIFORNIA BERKELEY College of...

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UNIVERSITY OF CALIFORNIA, BERKELEY College of Engineering 2008 Statics (E36) Final Examination Problem 1. (20 points) Draw the shear and moment diagrams for the beam shown in Figure 1 : (a1) Find the reactions, (a2) Draw shear diagram, V ( x ), and (a3) Draw moment diagram M ( x ); Figure 1: A simply supported beam with different load distributions. Problem 2. (15 points) (1) Find the centroid of the cross-section of a T-beam as shown in Figure 2 and set up the centroidal axes. ¯ y = i ¯ y i A i A i (2) Find I x with respect to the global centroidal X-axis and I y with respect to the global centroidal Y-axis. Hints: I x = Z A y 2 dA, I y = Z A x 2 dA (1) I x = ( I x ) c + d 2 A, Parallel Axis Theorem (2) I rectangular = bh 3 12 (The genetic formula for local centroidal axis) (3) 1
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Figure 2: The cross section of a T-beam Problem 3 (15 points) A steel bar is fixed at the point B (0 , 0 , 0) in one end. At the other end A (5 , 6 , 1), a rope is attached to it, and it exerts an force
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Final2008 - UNIVERSITY OF CALIFORNIA BERKELEY College of...

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