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prel2__soln

# prel2__soln - ENGRD 202 Prelim 11 November 4 2003 ”...

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Unformatted text preview: ENGRD 202 . Prelim 11 November 4, 2003 ” Problem #2 (35 pts) SOONm lOOONm 750N111 250Nm [(‘lm A solid shaft with shear modulus G = 78 GPa, diameter d = 10 cm, and total length L = 6 'm is subject to the torques as above. a) (5 pts) Calculate the maximum torque in the shaft and the section in which it occurs. b) (10 pts) Calculate the maximum torsional shear 7 and the corresponding maximum normal stress a},1 . c) (5 pts) Calculate the maximum rate of twist 0 in the shaft and where it occurs. d) (5 pts) If the shaft is hollow and the maximum allowable shear stress in the shaft is 70 1 MPa, What is the maximum inside diameter? 1 e) (10 pts) If the shaft is rotating at 50 rpm, what is the horse power transmitted to disk A, l at the right-hand end of the shaﬂ? ' i Page 3 of 4 I ‘ 4-3“; Turmﬁf—nxﬁgmﬁ’m—w l i I I i ¢ § 1 ‘ i ‘ , ‘ 1 f < «4.4;.W‘;n.;NR“w-~gw_u_m;&‘..M;.m;;;‘£__s , a u -A ‘ ,. a a: ‘<.:=,T;=,,-+:..=s,m.gﬁ;wymmf—mfﬂL .. . * «1;: My 2 T9 ,_ 5m;— 1W0+9Lm \$17515 1222 X . v.:-,2:,,§;m&m-mmmm. 22103220 .. m2w22:22 “\$0 34420 ’5 fa :ﬁ ‘— f223222 2 32 .. 2 - 2 2 2.22. J @2252; 252(232331: "6.25) .22 3 31 x 3233:232221. #22 L [M 23.. 52m“- .5 .—. mm ”3525.254 (”ﬁe wry/3M3?) (93055) 22222é83~323 m3 3 [3 35le - 222__22_. 2 21133- =2 6;:(2-;2222Xu>“‘9 w _ -2222 22.2 22-223.723-332 2390* 33535 P 2 , PM ~—— T 353 5» 2m [30 5.553 17333 333.....3325303 5 1333 :2335313. - 222MA§2\$¢©23222222339MK 1 M: m ,. 52c .2 ‘ .2 he 3- :- 7:231 W/ .1/355 ‘7 ,, E .. .52.” pm. 3.3... .2. ,me6 am .i. M 22222QJ2LQ_('£21~2 *WWC“" ______ 2 __ 355 43 33-3 5X3 3332.... 333 ‘ _ : _ _ __ 2 W" i W" 3535“ :3 1.3 002 NW“ 2. 2:303 A1530 _ 3 3 3 ‘ see We 93% 33/55 ENGRD 202 Prelim II Problem #3 (25 pts) A cantilever beam of length L is subject to the loads shown to the right. a) (5 pts) Draw and label a complete free body diagram for the beam. b) (5 pts) Identify all the locations Where the shear force Vis zero. c) (5 pts) Identify the location where the shear force is maximum, and determine its value. d) (2 pts) ldentify all the locations where the bending moment M is zero. e) (8 pts) Determine the bending moment at the ﬁxed end: B Page 4 of4 Novembet 4, 2003 r A. M w W W M ENGRD 202 Prelim II November 4, 2003 . Problem #3 (25 pts) A cantilever beam of length L is subject to the loads shown to the Solutions right. a) (5 pts) Draw and label a complete free body diagram for the beam. L ‘10 an 4L/27 P = 2 By b) d) e) The resultant force of distributed load: R = %qu +§qu0 = (—g + 9qu = iqu And, measuring from B at right-hand edge, letting x = 1/3L, and using it = (3590 )(ix)+ @qu )(ix) : ixZQO +‘é‘x290 : %+% (xqo)+(%xqo) xqo +%xqo %+% actsat x: x: - NIUJ |ox|4> who oxI-A k H \oh: H II I-h h (5 pts) Identify all the locations Where the shear force Vis zero. ZFy=0:—;—LqO—V=O:>%LqO=V l V holds until distributed load applied, and the I P _ L 410 entire distributed load equals %Lq0, so the shear 2 force V only goes to zero at I: , the right—hand ed ;- of the beam. (5 pts) Identify the location Where the shear force is maximum, and determine its value. The shear force Vis at its maximum, all the wa from the left-hand edge to the start of the distributed loa. (2 pts) Identify all the locations Where the bending moment M is zero. he left-hand ed e (8 pts) Determine the bending moment at the fixed end: B 21% =0:> —%quL—5+%LqO%L+MB = 0 MB ziLZQO +6—i'2i7LZQO :(i—TZ7MZQO +C = (”3%)11240 + C Page 4 of 4 ...
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