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705_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

705_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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SECTION 8.5 Combined Loadings 699 Solution 8.5-20 P 1.0 kN b 1 80 mm b 2 120 mm b 3 40 mm P ROPERTIES OF THE CROSS SECTION d 20 mm A 314.159 mm 2 I 7.854 10 3 mm 4 I p 2 I I p 1.571 10 4 mm 4 Q 666.667 mm 3 S TRESS RESULTANTS AT THE SUPPORT V x P (Axial force in X-dir.) V y 0 (Shear force in Y-dir.) V z P (Shear force in Z-dir.) M x Pb 2 (Torsional Moment) M x 120 kN mm M y P ( b 1 b 3 ) (Bending Moment) M y 120 kN mm M z Pb 2 (Bending Moment) M z 120 kN mm (a) S TRESSES AT POINT A # # # Q 2 3 r 3 I p 64 d 4 A p 4 d 2 r d 2 s x 155.972 MPa (compressive) s y 0 t xy 76.394 MPa M AX . TENSILE STRESS M AX . COMPRESSIVE STRESS M AX . SHEAR STRESS (b) S TRESSES AT POINT B s x V x A + M z I r t max 109.2 MPa ; s 2
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