681_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

681_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: 9/18/08 11:04 AM Page 675 675 SECTION 8.5 Combined Loadings Solution 8.4-12 sx( y) My I sy Q( y) Prin. stresses (MPa) 08Ch08.qxd ba 1 h yb a b a + yb 2 2 txy( y) V Q( y) Ib sx( y) sx( y) 2 a + b + txy( y)2 2 A 2 PRINCIPAL STRESSES s1( y) dist.y(mm) M b 65 kN # m 20 mm L h 0.75 m c 0.18 m 120 mm RA bh 12 I RB 4 2.88 * 10 mm RA RA 86.667 kN RB (upward) 86.667 kN (downward) RA c V RA s2(0) 54.2 MPa 54.2 MPa s1( 60 mm) s2( 60 mm) 325 MPa 0 MPa 162.5 MPa 15.6 kN # m M V 325 MPa 162.5 MPa 54.2 MPa tmax( 60 mm) At section m-n M tmax(0) s2(60 mm) 0 MPa tmax(60 mm) s1(0) M L sx( y) 2 b + txy( y)2 A 2 a tmax( y) s1(60 mm) 6 sx( y) 2 b + txy( y)2 A 2 a sx( y) 2 s2( y) 3 I h 2 0 86.667 kN Combined Loadings y0 The problems for Section 8.5 are to be solved assuming that the structures behave linearly elastically and that the stresses caused by two or more loads may be superimposed to obtain the resultant stresses acting at a point. Consider both in-plane and out-of-plane shear stresses unless otherwise specified. b2 b1 D B C P Problem 8.5-1 A bracket ABCD having a hollow circular cross section consists of a vertical arm AB, a horizontal arm BC parallel to the x0 axis, and a horizontal arm CD parallel to the z0 axis (see figure). The arms BC and CD have lengths b1 3.6 ft and b2 2.2 ft, respectively. The outer and inner diameters of the bracket are d2 7.5 in. and d1 6.8 in. A vertical load P 1400 lb acts at point D. Determine the maximum tensile, compressive, and shear stresses in the vertical arm. A z0 x0 ...
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