886_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

886_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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880 CHAPTER 11 Columns The Secant Formula When solving the problems for Section 11.6, assume that bending occurs in the principal plane containing the eccentric axial load. Problem 11.6-1 A steel bar has a square cross section of width (see figure). The bar has pinned supports at the ends and is 3.0 ft long. The axial forces acting at the end of the bar have a resultant located at distance from the center of the cross section. Also, the modulus of elasticity of the steel is 29,000 ksi. (a) Determine the maximum compressive stress in the bar. (b) If the allowable stress in the steel is 18,000 psi, what is the maximum permissible length of the bar? Probs. 11.6-1 through 11.6-3 L max s max e ± 0.75 in. P ± 20 k b ± 2.0 in. Solution 11.6-1 Bar with square cross section Pinned supports. D ATA (a) M AXIMUM COMPRESSIVE STRESS Secant formula (Eq. 11-59): (1) ec r 2 ± 2.25 L r ± 62.354 P EA ± 0.00017241 I ± b 4 12 ± 1.333 in. 4 r 2 ± I A ± 0.3333 in. 2 P A ± P b 2 ± 5.0 ksi c ± b 2 ± 1.0 in. s max ± P A c 1 + ec r 2 sec a L 2 r A P EA bd e ± 0.75 in. E ± 29,000 ksi b ± 2.0 in. L ± 3.0 ft ± 36 in. P ±
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Unformatted text preview: 20 k Substitute into Eq. (1): (b) M AXIMUM PERMISSIBLE LENGTH Solve Eq. (1) for the length : (2) Substitute numerical values: L max 46.2 in. ; L 2 A EI P arccos c P ( ec / r 2 ) s max A P d L s allow 18,000 psi s max 17.3 ksi ; P e Problem 11.6-2 A brass bar ( ) with a square cross section is subjected to axial force having a resultant P acting at distance e from the center (see figure). The bar is pin supported at the ends and is 0.6 m in length. The side dimension b of the bar is 30 mm and the eccentricity e of the load is 10 mm. If the allowable stress in the brass is 150 MPa, what is the allowable axial force P allow ? E 100 GPa Solution 11.6-2 Bar with square cross section Pinned supports. D ATA e 10 mm E 100 GPa b 30 mm L 0.6 m s allow 150 MPa S ECANT FORMULA (E Q . 11-59): (1) s max P A c 1 + ec r 2 sec a L 2 r A P EA bd 11Ch11.qxd 9/27/08 3:39 PM Page 880...
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