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164_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

164_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: Sec_2.5.qxd 9/25/08 158 3:00 PM Page 158 CHAPTER 2 Axially Loaded Members Copper: Ec 18,000 ksi Aluminum: Ea a 13 9.5 c 10 6/°F 10,000 ksi SUBSTITUTE NUMERICAL VALUES: Pa Pc (3.5 * 10 6 1+a 10 6/°F Use the results of Example 2-8. Find the forces Pa and Pc in the aluminum bar and copper bar, respectively, from Eq. (2-19). /° F)(100°F)(18,000 ksi)(2 in.2) 18 2.0 ba b 10 2.0 4,500 lb FREE-BODY DIAGRAM OF PIN AT THE LEFT END Replace the subscript “S” in that equation by “a” (for aluminum) and replace the subscript “B” by “c” (for copper), because for aluminum is larger than for copper. Pa Pc ac)( ¢ T)Ea Aa Ec Ac Ea Aa + Ec Ac (aa Note that Pa is the compressive force in the aluminum bar and Pc is the combined tensile force in the two copper bars. Pa Pc (aa ac)( ¢ T)Ec Ac Ec Ac 1+ Ea Aa V shear force in pin Pc/2 2,250 lb t average shear stress on cross section of pin t V AP t 15.0 ksi 2,250 lb 0.15033 in.2 ; Problem 2.5-10 A rigid bar ABCD is pinned at end A and supported by two cables at points B and C (see figure). The cable at B has nominal diameter dB 12 mm and the cable at C has nominal diameter dC 20 mm. A load P acts at end D of the bar. What is the allowable load P if the temperature rises by 60°C and each cable is required to have a factor of safety of at least 5 against its ultimate load? (Note: The cables have effective modulus of elasticity E 140 GPa and 12 10 6/°C. Other properties of coefficient of thermal expansion the cables can be found in Table 2-1, Section 2.2.) Solution 2.5-10 Rigid bar supported by two cables FREE-BODY DIAGRAM OF BAR ABCD From Table 2-1: AB 76.7 mm2 E 140 GPa T 60°C AC 173 mm2 12 10 6/°C EQUATION OF EQUILIBRIUM MA 0 TB(2b) or 2TB 4TC 5P TB force in cable B TC dB 12 mm dC 20 mm force in cable C TC(4b) P(5b) 0 (Eq. 1) ...
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