152_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

152_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: Sec_2.4.qxd 146 9/25/08 11:38 AM Page 146 CHAPTER 2 Axially Loaded Members Solution 2.4-14 Bar supported by a collar FREE-BODY DIAGRAM OF BAR ABC AND COLLAR BD SOLVE SIMULTANEOUSLY EQS. (1) AND (3): PL3A1 PL1A3 RA RD L1A3 + L3A1 L1A3 + L3A1 CHANGES IN LENGTHS (Elongation is positive) RAL1 PL1L3 PL2 dBC dAB EA1 E(L1A3 + L3A1) EA2 ELONGATION OF BAR ABC AC AB AC SUBSTITUTE NUMERICAL VALUES: P 40 kN E L1 Fvert 0 RA P 0 (Eq. 1) COMPATIBILITY (distance AD does not change) AB(bar) BD(collar) 0 (Eq. 2) 125 mm A1 RD 225 mm L3 EQUILIBRIUM OF BAR ABC 250 mm L2 960 mm2 A2 300 mm2 A3 200 GPa 480 mm2 RESULTS: (Elongation is positive.) RA 0.02604 mm BC Substitute into Eq. (2): RDL3 RAL1 0 EA1 EA3 RD AB FORCE-DISPLACEMENT RELATIONS RAL1 RDL3 dBD dAB EA1 EA3 0.15000 mm AC 20 kN AB ; 0.176 mm AC (Eq. 3) Problem 2.4-15 A rigid bar AB of length L 66 in. is hinged to a support at A and supported by two vertical wires attached at points C and D (see figure). Both wires have the same cross-sectional area (A 0.0272 in.2) and are made of the same material (modulus E 30 106 psi). The wire at C has length h 18 in. and the wire at D has length twice that amount. The horizontal distances are c 20 in. and d 50 in. (a) Determine the tensile stresses C and D in the wires due to the load P 340 lb acting at end B of the bar. (b) Find the downward displacement B at end B of the bar. 2h h A C D B c d P L ...
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