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# hw12-10sol - r T t M2'— SoLu'neNS 5—50 The hydrofoil...

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Unformatted text preview: r ' T t M2 '— SoLu'neNS 5—50. The hydrofoil boat has an A-36 steel propeller shaft that is 100 ft long. It is connected to an in-line diesel engine that delivers a maximum power of 2500 hp and causes the shaft to rotate at 1700 rpm. If the Outer diameter of the shaft is 8 in. and the wall thickness is g in., determine the maximum shear stress developed in the shaft. Also, what is the “wind up,” or angle of twist in the shaft at full power? Internal Torque: rev (217 rad) 1 mm = 56.677de/S = 17 '—.— a) 00 mm rev 60 s 550 ft - lb/s P=2500hp( lhp ) = 1' 375 000 ft-lb/s ng 1375000 to = 7723.7 Ib'ft Maximum Shear Stress: Applying torsion Formula. Tc Tmax=7 7723.7(12)(4) = ————— = 2.83 k - . Ans. g (44 — 3.6254) . 5‘ , Angle of Twist: ¢ = IE = W JG ’r'(4“ — 3.6254)11.0(106) = 0.07725 rad = 4.43° Ans. ~5—53. The 20-mm-diameter A-36 steel shaft is subjected to the torques shown. Determine the angle of twist of the end B. Internal Torque: As shown on FBD. Angle of Mist: TL 4’3 = 75 = [-80-0(0.8) + (—60.0)(o.6) + (—90.0)(0.2)] 80N-m = —0.1002 rad = |5.74°| Am I -: ‘BON-W 7§c 12D? ‘0» in T54: -90N' m gourd aaﬂ'm ‘ , 39".»? ' V « 80M *5—72. The 80-min diameter shaft is made of.6osi-T6 aluminum alloy and subjected to the torsional loading shown. Determine the angle of twist at end A. Equilibrium: Referring to the free - body diagram of segment AB shown in Fig. a, 2M, = 0; —TAB — 2003) = 0 TAB = -2(103)N-m And the free - body diagram of segment BC, Fig. b, EMx = 0; —TBC — 10(103)x — 2(103) = 0 » THC = —[10(103)x + 2(103)]N-m Angle of Twist: The polar moment of inertia of the shaft, is = 125(0042) = 1.28(10‘6)1r m4.We have TiLi TABLAB [an TBC dx 4“ 1.0.- JG. 0 16.1 = -2(103)(0.6) + /°~6m—[10(103)x +2(103)]dx 1.28(10'5)7r(26)(109) o 1.28(10‘6)1r(26)(109) 0.6m 0 _ 1 3 3 1-28(10"")w(26)(1o9) {1200 + [500 >19 + 2(10 )x] 40.04017 rad = 230° Torsional Members Angle of Twist I The ﬁgure below shows four members all constructed of the same. material. The modulus of rigidity { (G) is the same for all members. A torque of the same magnitude and direction is applied to each member. Locations shown are at the midway point of the member. Rank these situations, from greatest to least, on the basis of the angle of twist ((p) at each point relative to the left end of the member. \ r=1" r=1" Greatest 1 C/ 2 A _3 E 4 Least , Or, the angle of twist ((p) is the same for every beam. Please carefully explain your reasoning. A} ¢:':’\:—- , ﬂ? w 4 TC» y a(\)(, VG! W ¢ : r, — ‘3 ‘6 3G E(1Y‘Q— '35 1G 2. TL T U} C, ¢o : :' I L —. E N 36 UYG 0'1 «(A [a 9 '56 v \T 4G 1 E, :6 i (ll How Sure are you of your ranking? (Circle one) Basically Guessed Sure Very Sure ). 1 2 3 4 5 6 7 , 8 9 10 ...
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hw12-10sol - r T t M2'— SoLu'neNS 5—50 The hydrofoil...

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