02-02ChapGere.0009 - s 1 E b A b ) d L d 5 PL E s A s 1 E b...

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Statically Indeterminate Structures Problem 2.4-1 The assembly shown in the figure consists of a brass core (diameter d 1 5 0.25 in.) surrounded by a steel shell (inner diameter d 2 5 0.28 in., outer diameter d 3 5 0.35 in.). A load P compresses the core and shell, which have length L 5 4.0 in. The moduli of elasticity of the brass and steel are E b 5 15 3 10 6 psi and E s 5 30 3 10 6 psi, respectively. (a) What load P will compress the assembly by 0.003 in.? (b) If the allowable stress in the steel is 22 ksi and the allowable stress in the brass is 16 ksi, what is the allowable compressive load P allow ? ( Suggestion: Use the equations derived in Example 2-5.) Solution 2.4-1 Cylindrical assembly in compression 88 CHAPTER 2 Axially Loaded Members P Steel shell Brass core d 3 d 1 d 2 L P Steel shell Brass core d 3 d 1 d 2 L d 1 5 0.25 in. E b 5 15 3 10 6 psi d 2 5 0.28 in. E s 5 30 3 10 6 psi (a) D ECREASE IN LENGTH ( d 5 0.003 in.) Use Eq. (2-13) of Example 2-5. P 5 ( E s A
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Unformatted text preview: s 1 E b A b ) d L d 5 PL E s A s 1 E b A b or L 5 4.0 in. A b 5 p 4 d 1 2 5 0.04909 in. 2 d 3 5 0.35 in. A s 5 p 4 ( d 3 2 2 d 2 2 ) 5 0.03464 in. 2 Substitute numerical values: (b) A LLOWABLE LOAD s s 5 22 ksi s b 5 16 ksi Use Eqs. (2-12a and b) of Example 2-5. For steel: For brass: Steel governs. P allow 5 1300 lb P s 5 (1.776 3 10 6 lb) 16 ksi 15 3 10 6 psi 5 1890 lb s b 5 PE b E s A s 1 E b A b P s 5 ( E s A s 1 E b A b ) s b E b P s 5 (1.776 3 10 6 lb) 22 ksi 30 3 10 6 psi 5 1300 lb s s 5 PE s E s A s 1 E b A b P s 5 ( E s A s 1 E b A b ) s s E s 5 1330 lb P 5 (1.776 3 10 6 lb) 0.003 in. 4.0 in. 5 1.776 3 10 6 lb 1 (15 3 10 6 psi)(0.04909 in. 2 ) E s A s 1 E b A b 5 (30 3 10 6 psi)(0.03464 in. 2 ) 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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