708_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

708_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: 08Ch08.qxd 9/18/08 702 11:08 AM Page 702 CHAPTER 8 Applications of Plane Stress Problem 8.5-22 A mountain bike rider going uphill applies force P 65 N to each end of the handlebars ABCD, made of aluminum alloy 7075-T6, by pulling on the handlebar extenders (DF on right handlebar segment). Consider the right half of the handlebar assembly only (assume the bars are fixed at the fork at A). Segments AB and CD are prismatic with lengths L1 and L3 and with outer diameters and thicknesses d01, t01 and d03, t03, respectively, as shown. Segment BC of length L2, however, is tapered and, outer diameter and thickness vary linearly between dimensions at B and C. Consider shear, torsion, and bending effects only for segment AD; assume DF is rigid. Find maximum tensile, compressive, and shear stresses adjacent to support A. Show where each maximum stress value occurs. Handlebar extension d01 = 32 mm F t01 = 3.15 mm d03 = 22 mm t03 = 2.95 mm B y x C A F Handlebar extension d = 100 mm z D d03 L3 = 220 mm P 45° D L1 = 50 mm L2 = 30 mm y Handlebar (a) (b) Section D–F Solution 8.5-22 P z 65 N 50 mm 30 mm L3 220 mm d01 32 mm d03 22 mm A2 A1 ax y Vm T 100 mm A3 M d 45° ° L2 45 L1 PROPERTIES OF THE CROSS SECTION AT POINT A r d01 2 A p2 [d 4 01 1d01 t 0122] I p4 [d 64 01 1d01 t 012 ] Ip 2I Q 1 [ d3 12 01 t01 3.15 mm STRESS RESULTANTS AT POINT A1 Nx 150.543 mm2 A 0 (Axial force in X-dir.) Vmax. 4 I 1.747 Ip 1 d01 x Section at point A t 012 ] 3 3.493 Q 4 4 10 mm 104 mm4 729.625 mm 3 P Vmax. 0.065 kN (Max. Shear force) T Pd (Torsional Moment) M P (L1 M 19.5 kN # mm L2 L3) T 6.5 kN # mm (Bending Moment) ...
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