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Unformatted text preview: UNIVERSITY OF CALIFORNIA, BERKELEY FALL SEMESTER 2001 FINAL EXAMINATION (CE130-2 Mechanics of Materials) Problem 1: (15 points) A pinned 2-bar structure is shown in Figure 1. There is an external force, W = 5000 N , acting on the point C. (1) ﬁnd internal axial forces for bar AC, BC; (2) ﬁnd the normal stresses in bar AC and BC ( A 1 = A 2 = 0 . 01 m 2 , and E = 200 MPa); (3) ﬁnd the vertical displacement at nodal point C. o 1 θ = θ 2 30 o = 60 C L = 1 m W = 5000 N A B Figure 1: Schematic illustration of problem 1 (Hint: (1) Statics and equilibrium equations; (2) σ = P A ; (3) use Castigliano’s second theorem, ∆ v = ∂U ∂W , or the energy method to ﬁnd the vertical displace-ment at point C. The elastic potential energy in a single bar is: U = P 2 L 2 EA , where P is the internal axial force, L is the length of the bar, E is the Young’s modulus, and A is the cross section of the bar, and W e = 1 2 W ∆ v . ) 1 Problem 2 (15 points) A three-bar system as shown in Figure 2. The external force F is acting at the point C, i.e. the interface between the 2nd bar and the third bar. The system is statically indeterminate of rank one. (1) Find the reaction force at point A and B, i.e. R A and R B ; (2) Find the displacement at point C. (2) Find the displacement at point C....
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This note was uploaded on 09/17/2011 for the course CE 130 taught by Professor S.li during the Spring '06 term at Berkeley.
- Spring '06