02-02ChapGere.0010 - L 5 0.350 mm Use Eq(2-13 of Example 2-5 5 490.9 mm 2 E a 5 72 GPa Ê E b 5 100 GPa Ê A b 5 p 4 d b 2 A a 5 p 4 d a 2 2 d b 2

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Problem 2.4-2 A cylindrical assembly consisting of a brass core and an aluminum collar is compressed by a load P (see figure). The length of the aluminum collar and brass core is 350 mm, the diameter of the core is 25 mm, and the outside diameter of the collar is 40 mm. Also, the moduli of elasticity of the aluminum and brass are 72 GPa and 100 GPa, respectively. (a) If the length of the assembly decreases by 0.1% when the load P is applied, what is the magnitude of the load? (b) What is the maximum permissible load P max if the allowable stresses in the aluminum and brass are 80 MPa and 120 MPa, respectively? ( Suggestion: Use the equations derived in Example 2-5.) Solution 2.4-2 Cylindrical assembly in compression SECTION 2.4 Statically Indeterminate Structures 89 Aluminum collar Brass core 25 mm 40 mm P 350 mm A B d b d a P 350 mm A 5 aluminum B 5 brass L 5 350 mm d a 5 40 mm d b 5 25 mm 5 765.8 mm 2 (a) D ECREASE IN LENGTH ( d 5 0.1% of
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Unformatted text preview: L 5 0.350 mm) Use Eq. (2-13) of Example 2-5. 5 490.9 mm 2 E a 5 72 GPa Ê E b 5 100 GPa Ê A b 5 p 4 d b 2 A a 5 p 4 ( d a 2 2 d b 2 ) Substitute numerical values: E a A a 1 E b A b 5 (72 GPa)(765.8 mm 2 ) 1 (100 GPa)(490.9 mm 2 ) 5 55.135 MN 1 49.090 MN 5 104.23 MN (b) A LLOWABLE LOAD s a 5 80 MPa s b 5 120 MPa Use Eqs. (2-12a and b) of Example 2-5. For aluminum: For brass: Aluminum governs. Ê P max 5 116 kN P b 5 (104.23 MN) ¢ 120 MPa 100 GPa ≤ 5 125.1 kN s b 5 PE b E a A a 1 E b A b Ê P b 5 ( E a A a 1 E b A b ) ¢ s b E b ≤ P a 5 (104.23 MN) ¢ 80 MPa 72 GPa ≤ 5 115.8 kN s a 5 PE a E a A a 1 E b A b Ê P a 5 ( E a A a 1 E b A b ) ¢ s a E a ≤ 5 104.2 kN P 5 (104.23 MN) ¢ 0.350 mm 350 mm ≤ P 5 ( E a A a 1 E b A b ) ¢ d L ≤ d 5 PL E a A a 1 E b A b Ê or 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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