HW12 - s. t g . PROBLEM 3.31 3.31 (a) For the solid steel...

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Unformatted text preview: s. t g . PROBLEM 3.31 3.31 (a) For the solid steel shaft shown (G = 77 GPa), determine the angle of twist ‘ at A. (b) Solve part a, assuming that the steel shafi is hollow with a 30-mm outer diameter and a 20-mm inner diameter. SOLUTION (a) c=sz= 0-0/5") =%C"=%(0-0’5V , = Law 9 G: 77x/o“ Pct * J = 77.522xzo“mj L ) D T '-‘ 250 N‘VH @ = 6:5: 250x211. 9 :fi% = 13.49xlO-3 Md (P = (73'4q;°_37‘§°: 4.21" a-q (bl c2: 00:5 w) c.2150“: 0,010.01) J=§(Cz”_ Cl“) I J= lif<0.0l5q— 0.010%} = 53.8Hxlo'qm” g) = 61% L @=%: angsxld‘wad = 1%(crl.58rto’3)=é’.25° ‘4 3.32 For the aluminum shafl shown (G = 3.9 X 10 6 psi), determine (a) the torque T j which causes an angle of twist of 5 °, (b) the angle of twist caused by the same torque , T in a solid cylindrical shafi of the same length and cross-sectional area. PROBLEM 3.32 SOLUTION ,- -r' (CL) g>= 7‘: ML <3) = S” = 37-2eexlo‘5mr, L: 4H = 43 .‘n J=¥(Cz”-C.") = -’E(o.7§"- 0.5“) = 0.37384 in” £3.9xm‘“ " 0.??3’?‘ F 7.2 x 0'“ :23”? x103 94,-.” 2 2-23 warm 4 Hoipou) Shapi' A '-‘ 7T(C2‘- Cf) Solidi SL‘F'" A = 77C; 7. 7. Maud"? areas c = c2 —c,‘= any-0.5" = 0.3125 :n‘ J= ETC" = EMJWD)" = '53-378 “10—3 M4 62- C = 0-5570 in) 99 : TL ___ (2.32741le3 )(43) __ GJ (3.47 xlo‘)(153.3fiewo'3 ' r I3-oo° ' ‘ 226.8?Ho‘3 V'Aof 3.33 The ship at A has just started to drill for oil on the ocean floor at a depth of PROBLEM 3-33 5000 ft. Knowing that the top of the 8-in.-diameter steel drill pipe (G = 11.2 x 106 psi) rotates through two COmplete revolutions before the drill bit at B starts to operate, determine the max1mum shearing stress caused in the pipe by torsion. T SOLUTION ,, —_- _ £419 ‘ 50°” (5) 61 T ‘ L :IthJC_ nge r J '3’?“ ‘ L g) = 2m; =(Ql(2n)= muses Wadi} c. = é'el .— 4-0.», 1/: 'll.:zx10‘){la.554;(q.o 60000 : 9-3326x103 pst‘ = 7.38 ksl' «I l. = 5000‘H = 60000 .‘n 3.34 Determine the largest allowable diameter of a 3—m—long steel rod (G = 77 GPa) if the rod is to be twisted through 30° without exceeding a shearing stress of 80 MPa. PROBLEM 3.34 SOLUTION = 3m) 30: fig?“ = 523.5XIO'3MA) 1’: 80>!!!)er <9 2%?) “if—2» "LN-Lie = ‘j—{QC £5- 0. ‘(go “'D‘KEEL—H— = 5%?»40'3 m = 5353 Mm -(_77xlo’)(523.éx10‘3) d=2c= H-CHMM '4 PROBLEM 3 35 3.35 The torques shown are exerted on pulleys A and B. Knowing that the shafts are ' solid and made-of aluminum (G = 77 GPa), determine the angle of twist between (a) A and B, (b)A and C. T‘ = SOON-m ‘ 1' CT SOLUTION mm 0.9m . 3°- B (0.1 “a = 300 N'mJ LAG =03 M, Cm: id = 00‘5"” "V “""M‘F Dis J” : 1(0.0ls)" = 77.522 “0‘7 in * 46mm .1 m .3 c tillage _ We .0 o «A —-L 9‘3 GJ ’ (77x/o")(7‘1.522no' 1” as x, r C?“ ': 253° 4 OD) Tue = 3004-400 = 700 NW"; LN ‘ 0-75“ ) can?“ = o'm‘s W“ — Its-£59.- (7003(o.75 ‘ 4 Qac GJ‘Q - — x10 rad (Pk. 2 (PAS + (pee = 57-406’4’0’3 Map = 3.42° .4 PROBLEM 3 36 3.36 The torques shown are exerted on pulleys B, C and D. Knowing that the entire ‘ shalt is made of steel (G = 27 GPa), determine the angle of twist between (a) C and 30 mm B, (b) D and 3- .1 m5: _ m 36 mm SOLUTION ' 900N411 36mm : = My” Jag, = 36" = 7?.522xlo“ m” j 9 __ = (Qoo)(o.8) 3° 66' {37 x!o")(7°7.522wo-') = .149904 N = 8.59°-¢ (& Sha‘F‘i’ CD: 4: = id = 0.013 M Jan = Ea” = 159.3q5xlo'” m“ ' LCD: LO M Tm ‘4 400-?00 = ~5'OO N‘m : TL (-500)(l.o3 vi = ~— = -» = - . I . (RD 63' (27VI09X14‘L8‘76HO‘7 O l 230 “4 ~V (Pep = 4236+ 90” = o.tt+ao¢-o.:mao = 0.03424”?! 2.!1" - 3.37 The solid brass rod AB (G= 39 691.. ’)isbonded to the solid aluminumrod PROBLEM 3'37 BC(G= 27 61%.). Determine the angle oftwist (a) at B, (b) atA, J; SOLUTION ShaH AB: owls! = 0.0/5m L: 0.50 G = 39>‘IO‘7 Pa. T= I80 N-m J = lira" -: 79.6-22w0‘1 m“ _ TL _ (180')(o.25'o) = .3 @AB- 2}?“ NJ L = 0.320 m - 141a - qutsqcxno“ m .. , (180)(O-310) _ -3 (Par. ‘ W - I2337Ho V‘ad A Answers: (Q) g; = ct)“ = H.937)! 10’3 Md :2 0.741‘ OD) (PA ‘- (pgc'l‘ (PM; : 2.7.497xlo'3v‘ncl : l.573° .— . ...
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This note was uploaded on 12/09/2009 for the course CE 3400 taught by Professor Moorthy during the Fall '09 term at LSU.

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HW12 - s. t g . PROBLEM 3.31 3.31 (a) For the solid steel...

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