536_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

536_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: 06Ch06.qxd 9/24/08 530 5:54 AM Page 530 CHAPTER 6 Stresses in Beams (Advanced Topics) Solution 6.5-1 Channel section NEUTRAL AXIS nn (EQ. 6-40) Iz tan b Iy b 32.6 (1/3) 1.32 tan u 8.2323 ; 83.07° MAXIMUM TENSILE STRESS (POINT A) (EQ. 6-38) zA c 0.571 in. st sA yA (M sin u)zA Iy tan u 20 k-in. C8 u 1/3 ; MAXIMUM COMPRESSIVE STRESS (POINT B) (EQ. 6-38) 18.435° zB 11.5 c 0.571 in. d 8.00 in. b (b c) (2.260 Iz 32.6 in.4 2.260 in. yz d/2 sB (M sin u)zB Iy 0.571) 1.689 in. 4.00 in. sc 1.32 in.4 Iy 4.00 in. (M cos u)yA Iz 5060 psi M d/2 (M cos u)yB Iz ; 10,420 psi Problem 6.5-2 A beam of channel section is subjected to a bending moment M having its vector at an angle u to the z axis (see figure). Determine the orientation of the neutral axis and calculate the maximum tensile stress st and maximum compressive stress sc in the beam. Use a C 200 20.5 channel section with M 0.75 kN # m and u 20°. Solution 6.5-2 M 0.75 kN # m C 200 20.5 u Iy 106 mm4 Iz 15.0 c MAXIMUM TENSILE STRESS (AT POINT A) 20° 0.633 # 106 mm4 d 203 mm b 14.1 mm 59.4 mm smax smax BENDING MOMENTS My Msin(u) My Mcos(u) Mz 705 N # m smax NEUTRAL AXIS b nn Iz atan a tan(u) b Iy smax b 83.4° Mz a Iy d b 2 Iz 10.5 MPa ; MAXIMUM TENSILE STRESS (AT POINT B) 257 N # m Mz My(c) ; My( b + c) d Mz a b 2 Iy Iz 23.1 MPa ; ...
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