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Solutions 5

# Solutions 5 - 5-47 The A-36 steel axle is made from tubes...

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Unformatted text preview: 5-47. The A-36 steel axle is made from tubes AB and CD and a solid section BC. It is supported on smooth bearing that allow it to rotate freely. If the gears. fixed to its ends. are subjected to 85-N - m torques. determine the angle of twist of gear A relative to gear D. The tubes have an outer diameter of 30 mm and an inner diameter of 20 mm. 'Ihe solid section has a diameter of 40 mm. 01'“ 1;. . ~85u.m H‘Pf- Tu . -854“, 85N-an :2 16 Mo mac. 4) (ssxo.25) gmms‘ 0.01‘x75xio') ;(o.02‘)(75)(to') = 0.01534M3 0.879 Ala 5-63. When drilling a well. the deep end of the drill pipe is assumed to encounter a torsional resistance TA. Furthermore. soil friction along the sides of the pipe creates a linear distribution of torque per unit length. varying from zero at the surface B to to at A. Determine the necessary torque TB that must be supplied by the drive unit to turn the pipe. Also. what is the relative angle of twist of one end of the pipe with respect to the other end at the instant the pipe is about to turn? The pipe has an outer radius to and an inner radius ri. The shear modulus is G. gamma-o n_~l.+21:. -_i_ L§L+213__r£ 1610‘ 2 ugh“ I ~L+2n ”1‘1" 3 2 6L 0 . uh am. 310 Bowen“! I go; - n.) 2L“!- + 313) . . 38(r.‘ - r.‘)G *5—80. The two 3-ft-long shafts are made of 2014-T6 aluminum. Each has a diameter of 1.5 in. and they are connected using the gears fixed to their ends. Their other ends are attached to fixed supports at A and B. They are also supported by bearings at C and D, which allow free rotation of the shafts along their axes. If a torque of 600 lb ° ft is applied to the top gear as shown, determine the maximum shear stress in each shaft. 4 r F - - 600 = o 1 A + (12) ( ) T ~ Hi) = 0 (2) ' 12 From Eqs.(l)and(2) 1"” 73 1% + 21'. - 600 a 0 (3) F 4(¢£) = 2(‘10: O; = 05¢: 151. 131. —=0.5—; T=0.5T 4 JG (JG) A a () Solving Eqs. (swam yields : 1; = 240nm; n =1201b-ft (1.0).“ = if = W = 435m A... 1 £0.15“) (1m)..‘ = E—c = w = 2.17 hi A” I {(0.75‘) 6-5. A reinforced concrete pier is used to support the stringers for a bridge deck. Draw the shear and moment diagrams for the pier when it is subjected to the stringer loads shown. Assume the columns at A and B exert only vertical reactions on the pier. 6-17. The ISO-lb man sits in the center of the boat. which has a uniform width and a weight per linear foot of 3 lb/ft. Determine the maximum bending moment exerted on the boat. Assume that the water exerts a uniform distributed load upward on the bottom of the boat. 3 "ll‘ IIIIIIIIIIIIIIII , '3 Wk to t 0 van q‘ ’ 75 '7: Mat-[u 2. 38! ' 1' ~un'2..b'h A. *6—36. Draw the shear and moment diagrams for the beam. 3 kip /ft 1500lb -ft I. "A2 . B 12 ft—+—6ft ...
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