887_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

887_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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SECTION 11.6 The Secant Formula 881 Problem 11.6-3 A square aluminum bar with pinned ends carries a load acting at distance from the center (see figure on the previous page). The bar has length and modulus of elasticity . If the stress in the bar is not exceed 6 ksi, what is the minimum permissible width b min of the bar? E ± 10,600 ksi L ± 54 in. e ± 2.0 in. P ± 25 k Solution 11.6-3 Square aluminum bar Pinned ends. D ATA Units: pounds and inches S ECANT FORMULA (E Q . 11-59): (1) ec r 2 ± 12 b L 2 r A P EA ± 4.5423 b 2 A ± b 2 c ± b 2 r 2 ± I A ± b 2 12 s max ± P A c 1 + ec r 2 sec a L 2 r A P EA bd s max ± 6.0 ksi ± 6,000 psi L ± 54 in. E ± 10,600 ksi ± 10,600,000 psi P ± 25 k ± 25,000 lb e ± 2.0 in. S UBSTITUTE TERMS INTO EQ . (1): or (2) S OLVE EQ . (2) NUMERICALLY : b min ± 4.10 in. ; 1 + 12 b sec a 4.5423 b 2 b ² 0.24 b 2 ± 0 6,000 ± 25,000 b 2 c 1 + 12 b sec a 4.5423 b 2 bd Units: Newtons and meters ec r 2 ± 2.0 P ± newtons L 2 r A P EA ± 0.0036515 1 P c ± b 2 ± 0.015 m r 2 ± I A ± b 2 12 ± 75 * 10 ² 6 m 2 A ± b 2 ± 900 * 10 ² 6 m 2 s max ± 150 * 10 6 N/m 2 S UBSTITUTE NUMERICAL VALUES INTO EQ
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Unformatted text preview: . (1): or (2) S OLVE E Q . (2) NUMERICALLY : P allow 37,200 N 37.2 kN ; P [1 + 2sec (0.0036515 1 P )] 135,000 150 * 10 6 P 900 * 10 6 [1 + 2sec (0.0036515 1 P )] Problem 11.6-4 A pinned-end column of length is constructed of steel pipe ( ) having inside diameter and outside diameter (see figure). A compressive load acts with eccentricity . (a) What is the maximum compressive stress in the column? (b) If the allowable stress in the steel is 50 MPa, what is the maximum permissible length L max of the column? Probs. 11.6-4 throught 11.6-6 s max e 30 mm P 10 kN d 2 68 mm d 1 60 mm E 210 GPa L 2.1 m P e d 1 d 2 11Ch11.qxd 9/27/08 3:39 PM Page 881...
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