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 5 2.0 in. 2 Area of aluminum bar: A a 5 2.0 in. 2 D T 5 100 8 F Copper: E c 5 18,000 ksi a c 5 9.5 3 10 2 6 / 8 F Aluminum: E a 5 10,000 ksi a a 5 13 3 10 2 6 / 8 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 a for aluminum is larger than a 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 5 P c 5 ( a a 2 a c )( ¢ T ) E c A c 1 1 E c A c E a A a P a 5 P c 5 ( a a 2 a c )( ¢ T ) E a A a E c A c E a A a 1 E c A c Area of pin: A P 5 p 4 d P 2 5 0.15033 in. 2 Diameter of pin: d P 5 7 16 in. 5 0.4375 in. S UBSTITUTE NUMERICAL VALUES : 5 4,500 lb F REE - BODY DIAGRAM OF PIN AT THE LEFT END V 5 shear force in pin 5 P c /2 5 2,250 lb t 5 average shear stress on cross section of pin t 5 15.0 ksi Ê t 5 V A P 5 2,250 lb 0.15033 in. 2 P
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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 60C 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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This note was uploaded on 09/20/2009 for the course COE 3001 taught by Professor Armanios during the Spring '08 term at Georgia Institute of Technology.

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