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Problem 7 Ans:(a) FSH= 1.966, FS=2.19 (b) om-H= 174.4MPa, o-K= A steel shaft with an outside diameter of 20mm is supported on flexible bearings at its ends. Two pulleys are keyed to the shaft. The pulleys carry belt tensions as shown. The steel's yield strength is oy= 350MPa. (a) Determine the factors of safety predicted at points H and K by the maximum-shear-stress theory of failure (b) Determine the Mises equivalent stresses at points H and K. (c) Determine the factors of safety at points H and K predicted by the maximum-distortion-energy theory SH=2.01. FSg= 2.25 155.7MPa, (c) F 1,400 N 160 mm 160 mm B 160 mm H 160 mm 1,100 N 135 mm 300 N

Answer 1

diamut of the solid aluminum Post d= 20mm Te aria of the Solid shaft il walar con Aecion is A A= A 314. 15qmw. nhe mommt of inuia of the sdid shaft a bout 7 amd z-axi A (2.0) -- =79 53.982 mm fola monmt of inba of the sh shaft 32 4 (20) 32 J= J15707. 963 mm Now Congidu t fosaA al dwunt AB H anpd K an at gane H omd K. diatama foron the fonaauil act at bolh H amd k apteabon loads omre of Apply equitonins of mammt about the shaft in x-diriebon) Point A ον) Σ) A O C400X160)(200 X160)+40x Dy By Nooh- Afply equibbortun, of momunt about foint A shaft in -dinsetion).

Σ), C300x490)+(0 x D2) 0 -LI100X180) C - Dzlo50N Afplyequikbiem of fanGA in amd -drton Σ Ε 0o +300 -AZ D .Az -lo50-+llo0 -+300 = O 35a N Az C Ay-400 Pry Con gtdu th equivalt foonGA at -12. OON Now H amd kdue to loads foona at dlumints dinuction at elment iA the H and k sha ft. Nosma Fx Nasmal foon at elwrernts H a k g-direcbo Fyat namal - 400 N H amd fosn at munts Nasnnal dinecbo Z- loo300-l050 - 350N

Mommt foona at elemumts dinuctior H omd k in (t00x3 00x ) Mx 2 M25000 N-mn Mommt fon at lents H and K 3-dinection iA Ma=io50 x320)-(o0 X)-30016o) l12000 N-mm Mommant fasa at elmt H ad k - dinechorn (400x320 MZ -128000 N-mm). MZ of unit Asua mommt of inuia aH) fo cinaula cnags gecbon8 712 shea stow(i at elmurt H d to 350X 666. C07 7853.982 X20 1.485 Mрa shean st at clent H due to fona M Cuabg Cz 18 moment

Mx X C Mxxdh 54000x 20/2 z E9b LOLS Bending strs at elemunt H du to moment fonG'M2 at bunding slus at ciment H i 2- dene clio i M2 xd 34.377 MPa M2Xy 12 8000 x 20/2 162.975 MPo Bendin strk at lment H cdu to momt foC My at neutra aei y-dirictors x-diructiorn at cimunt H vly bending słw acts at clmunt H 162.975MPa -dinuction, at stors actn i) z- No 6 to acs at mmt dinucion Mfa shean sto at element H. du to dinucb ors Lmant H to Fane in z- H duu faona and shaft H

34.377 1. 485 H 35.863 MPa Porincifal ste8 actng at elnunt . 1 2 65. 162.915+0 162.975- + P P2 2 81. 487 89.o30 - 170.517 MPa ; =-7.43 MPa P7-543MPa CC) mnt Zauare dmunt of canit Acal ston at ient du to namal fana load adal and FCreab na aial amint K fionatmommt of nia of he the Cno8 geci on up to elment area K. Z/2 shean stou ( at elment K faG Fcoeat kramaknse shaa du to stouss at emint K. y xQy Tyxd 7853.982X20

nanAverseshun slus (uh acks in negalave dineciov). thy odsby1- Shea st at elemnt k du to fon C Mx Ce abs tongiov shea slous Cy al mint k y M XC J 54000 x 2/2 y 15707.963 Cy 34. 377 Mfa A3 P foso elemunt of K, kangio) gheagtous Tyz acds in hon nJative dire 344.377 MPa ey Bending slouy at elment faon M Creabs K du to mommt bending stonus disrcbon My X7 Ty 12.000 х 29 7853.932 2- - 42.603 MPa Bending stnu ab elewent k Mz Lis due to mommt fanG neulorad axi8 Storu actng-diucio at diument . No axial stow ama beding stuss act at elonent p MPa.

stows aina n x-dincb o al elomunt bendin slnh and momut i oly x-dinecbo at K. 142.603 MPa shean sto at elent K du to amd -dirucbon shat subJcchd ta and y ry Tyty - . Cq8-34.377 36.075MPa forincipal strss acting at dumunt 2 03-0 j-3a 142.603-to /142 土 2 71.301 7q.908 - 151. 210 MPa ; nh maximum shua, sturs thory factos of Safe fo clmunt amd K F5k =. F5H 350 FSy 151.210-9.6) 350 FSH [no-51--7543. FSIK 2.19 - FSH 96.1

manimum diglaraion eus0g theoy fo ment Hamd K of stJ shalt |70.57)- (170.517)(-548+75412" | H 174.411 MPa 51-210-15-210X-8.60) -+-87] M)e = 155. 691 Mfa Marimum distontior erusTy thiry factos of Safely fas clunent H and k FSK 360 FSK 350 55.691 FSK=2.25 FSH T4.411 2.01 FSH

Answer 2