165_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

165_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: Sec_2.5.qxd 9/25/08 3:00 PM Page 159 159 SECTION 2.5 Thermal Effects DISPLACEMENT DIAGRAM SUBSTITUTE NUMERICAL VALUES INTO EQ. (5): 1,338,000 TB(346) TC(76.7) in which TB and TC have units of newtons. SOLVE SIMULTANEOUSLY EQS. (1) AND (6): TB 0.2494 P 3,480 TC 1.1253 P 1,740 in which P has units of newtons. COMPATIBILITY: C 2 (Eq. 2) B FORCE-DISPLACEMENT AND TEMPERATURE-DISPLACEMENT RELATIONS dB dC TBL + a( ¢ T)L EAB TCL + a( ¢ T)L EAC (Eq. 3) (Eq. 4) (Eq. 6) (Eq. 7) (Eq. 8) SOLVE EQS. (7) AND (8) FOR THE LOAD P: PB 4.0096 TB 13,953 PC 0.8887 TC 1,546 ALLOWABLE LOADS From Table 2-1: (TB)ULT 102,000 N Factor of safety (TB)allow From Eq. (9): PB TCL + a( ¢ T)L EAC From Eq. (10): PC 2TBL + 2a( ¢ T)L EAB or 2TBAC (TC)ULT 231,000 N (TC)allow 46,200 N 5 20,400 N SUBSTITUTE EQS. (3) AND (4) INTO EQ. (2): (4.0096)(20,400 N) 95,700 N (0.8887)(46,200 N) 39,500 N Cable C governs. TCAB E ( T)AB AC (Eq. 5) Pallow 39.5 kN Problem 2.5-11 A rigid triangular frame is pivoted at C and held by two identical horizontal wires at points A and B (see figure). Each wire has axial rigidity EA 12.5 10 6/°F. and coefficient of thermal expansion 120 k (a) If a vertical load P 500 lb acts at point D, what are the tensile forces TA and TB in the wires at A and B, respectively? (b) If, while the load P is acting, both wires have their temperatures raised by 180°F, what are the forces TA and TB? (c) What further increase in temperature will cause the wire at B to become slack? (Eq. 9) (Eq. 10) ; 13,953 N 1546 N ...
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