Question

P2. Two solid steel shafts, each of 30-mm diameter, are connected by the gears shown. Knowing that G- 77.2 GPa, determine the angle through which end A rotates when a torque of magnitude T= 200 N.m is applied at A. 0.2 m 30 mm 0.4 m 0.2m 60 mm 0.1m 90 mm 30 mm 0.5 m

Answer 1

Givendata Two solid steel 30-mm diameter G1 77.2 G Pa T200 NW Ans:- The shaft A Bis free to rotate and is not fixed at our of ibsends hus, torsion in the shel AB is equal to the tong applied at Point A- TAB=TA where: TAB = the torsion in the shaft AB TA: The tooque applied at Point A substitute 200N-mforta TAB = 200N.m calculate the moment momont about cenler of the four B EMB=0

F{60 mmx 103 m 2 ) a=0 F (60 x 10 m) - TATO FC 0.06m} - TA: 0 F 60-06m] : TA Fi Tam --> 0 0.06m - Calc Calculate the moment about center of the geaud EMO=0 *[tomm x personal F[ 90 x 103m) - Toc=0 F[0.09 m] - TDG=0 F(0.09m] = TOE F = TDE - 0.09m

wherein DE ; the torsion in the shaft DG equate the cauation 0 and 2 TA : 200 Nm TA - DE - 200Nm - TDE 0-06 0-09 006 009 TOE = 2009 X0-09 Ta - 2, 333 - 33 - TP xo -o9 ITDE = 300 Nm -> calculate the polar moment of inertia of the shaft AB JAB = 7 ha Where, DAB = the diameter of the shaft AB

substitutc 30 mm for dab hos #Comments * 1 ( 09)" [001834 C0 000 0000 506) = 1.57(0.0000002500) -7.948810-8 my 2 - calculate the polaru moment of inertia of the shaft DE FAB T A C" DE * [ date]" where diameter of the shaft DE

doe = 30mm zomm x 10ml 0 f 30x10 3 27 1 [uomoja (0.01534 - I [ 5.0625x108 31.570[5.0625x108] = 7.948X10-8 mu - calculate the angular twist made by the rear D The end of Point & the shaft DG isfired, and thus Actual angulare twist for the ppoint o is equal to the angular tw- s of a with respect to the pointe - Po=Pole TOE GOE IDEG

where :- LDE = Length of the shaft De toePaar moment of inertia of the shaft DE Shear modulus of the Material where: Toe 300 Nm LDE = 0.5m G= 77.2 GPA IDE = 7.952x168 1. TDE LOG IDEG 300 nm X0.5 m (7.952X10-2 (177.2 GPG x 109 N/m2 Gra J 3oon.mxo.5m (7.95.2 x 15 m ) (77.2x 10° Nim?] - 0.02uu voud - calculate the anguar twist made by the seat B both the gears Bound D must be equal. hence the prode of angular twist und radius for both & caus is constount

YB P13 = ropo Poc where PB is the angular twist Made by the gap PD is the aungdaotwist Made by the Ye.B %D8% = roudius of glars Daundi Yo = 90mm YB = Gomm Po= 0.0au4 tauld PB = 90 mm xo.0248ood Gorm PB = 90 10-024 tood = 1.5xo.o2urood PO = 0.0366 Xud 2-) calculate the length of the shaft AB LAR=0.2 to 4to.ato. I :0.9m

- - Calculate the angular twist of the end A with zespot to the point B Malg - TABLAB JARG Where TAB = 200 Nm LAB=o.am G = 77 aG pa JAB= 7952x10-8 my 2000 m xo.am (7.952410-8 mH] [ 77.2 GPax 109 Nm2 Gra_ 200 N-mxo am (7452X10% vu][77 2x 10°Where O 0243 pod -) calculate the total angular twist at the end A PAPA/B * PB PA - (0.0293 Vod) 760.0366 dod]

= 0. o66о од - осью в 4 180° sivad | з 9)