02-03ChapGere.0006 - a 5 P c 5(3.5 3 10 2 6 8 F(100 8...

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SECTION 2.5 Thermal Effects 111 Solution 2.5-9 Rectangular bars held by pins C C A Pin Aluminum Copper 0.5 in. × 2.0 in. 1.0 in. × 2.0 in. 0.5 in. × 2.0 in. Area of two copper bars: A c 2.0 in. 2 Area of aluminum bar: A a 2.0 in. 2 T 100 F Copper: E c 18,000 ksi c 9.5 10 6 / F Aluminum: E a 10,000 ksi a 13 10 6 / F Use the results of Example 2-8. Find the forces P a and P c in the aluminum bar and copper bar, respectively, from Eq. (2-19). 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. Note that P a is the compressive force in the aluminum bar and P c is the combined tensile force in the two copper bars. P a P c ( a c )( ¢ T ) E c A c 1 E c A c E a A a P a P c ( a c )( ¢ T ) E a A a E c A c E a A a E c A c Area of pin: A P 4 d P 2 0.15033 in. 2 Diameter of pin: d P 7 16 in. 0.4375 in. S UBSTITUTE NUMERICAL VALUES : 4,500 lb F REE - BODY DIAGRAM OF PIN AT THE LEFT END V shear force in pin P c /2 2,250 lb average shear stress on cross section of pin t 15.0 ksi t V A P 2,250
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Unformatted text preview: a 5 P c 5 (3.5 3 10 2 6 / 8 F)(100 8 F)(18,000 ksi)(2 in. 2 ) 1 1 ¢ 18 10 ≤ ¢ 2.0 2.0 ≤ P c 2 P c 2 P a 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 d B 5 12 mm and the cable at C has nominal diameter d C 5 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 5 140 GPa and coefficient of thermal expansion a 5 12 3 10 2 6 /°C. Other properties of the cables can be found in Table 2-1, Section 2.2.) P D C B A b 2 b d B d C 2 b A-PDF Split DEMO : Purchase from www.A-PDF.com to remove the watermark...
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