02-02ChapGere.0021 - ¢ p d 1 2 4 ≤ 1 s 2 ¢ p d 2 2 4...

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Problem 2.4-13 A horizontal rigid bar of weight W 7200 lb is supported by three slender circular rods that are equally spaced (see figure). The two outer rods are made of aluminum ( E 1 10 10 6 psi) with diameter d 1 0.4 in. and length L 1 40 in. The inner rod is magnesium ( E 2 6.5 10 6 psi) with diameter d 2 and length L 2 . The allowable stresses in the aluminum and magnesium are 24,000 psi and 13,000 psi, respectively. If it is desired to have all three rods loaded to their maximum allowable values, what should be the diameter d 2 and length L 2 of the middle rod? Solution 2.4-13 Bar supported by three rods 100 CHAPTER 2 Axially Loaded Members W = weight of rigid bar d 1 d 1 d 2 L 2 L 1 BAR 1 A LUMINUM E 1 10 10 6 psi d 1 0.4 in. L 1 40 in. 1 24,000 psi BAR 2 M AGNESIUM E 2 6.5 10 6 psi d 2 ? L 2 ? 2 13,000 psi F REE - BODY DIAGRAM OF RIGID BAR E QUATION OF EQUILIBRIUM © F vert 0 2 F 1 F 2 W 0 (Eq. 1) F ULLY STRESSED RODS F 1 1 A 1 F 2 2 A 2 Substitute into Eq. (1): Diameter d 1 is known; solve for
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Unformatted text preview: ¢ p d 1 2 4 ≤ 1 s 2 ¢ p d 2 2 4 ≤ 5 W A 1 5 p d 1 2 4 Ê A 2 5 p d 2 2 4 S UBSTITUTE NUMERICAL VALUES : E QUATION OF COMPATIBILITY d 1 5 d 2 (Eq. 3) F ORCE-DISPLACEMENT RELATIONS (Eq. 4) (Eq. 5) Substitute (4) and (5) into Eq. (3): Length L 1 is known; solve for L 2 : (Eq. 6) S UBSTITUTE NUMERICAL VALUES : 5 48.0 in. L 2 5 (40 in.) ¢ 24,000 psi 13,000 psi ≤ ¢ 6.5 3 10 6 psi 10 3 10 6 psi ≤ L 2 5 L 1 ¢ s 1 E 2 s 2 E 1 ≤ s 1 ¢ L 1 E 1 ≤ 5 s 2 ¢ L 2 E 2 ≤ d 2 5 F 2 L 2 E 2 A 2 5 s 2 ¢ L 2 E 2 ≤ d 1 5 F 1 L 1 E 1 A 1 5 s 1 ¢ L 1 E 1 ≤ d 2 5 0.338 in. 5 0.70518 in. 2 2 0.59077 in. 2 5 0.11441 in. 2 d 2 2 5 4(7200 lb) p (13,000 psi) 2 2(24,000 psi) (0.4 in.) 2 13,000 psi W = 7200 lb 1 2 1 W F 1 F 2 F 1 A-PDF Split DEMO : Purchase from www.A-PDF.com to remove the watermark...
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