COE 3001: Week 4
COE 3001: Week 4 coe 3001 I
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This 6 page Class Notes was uploaded by Eleanor Notetaker on Sunday September 13, 2015. The Class Notes belongs to coe 3001 I at Georgia Institute of Technology taught by Dr. Kennedy in Summer 2015. Since its upload, it has received 32 views. For similar materials see Deformable Bodies in Engineering and Tech at Georgia Institute of Technology.
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Date Created: 09/13/15
COE 3001 Mechanics of Deformable Bodies Week 4 El TxfTrdAdArdrd0 A a T T TxGd pf rszIGIP Tx IPTmax x rm dx A dx rmax I p a I r2 dA I p A 34 Nonuniform torsion 0 Crosssection varies along the length 0 Applied torques vary along the length Case 1 Prismatic segmentslyith constant torque Determine the internal torque in each segment 0 Cut the shaft and use freebodydiagram Cut BC COE 3001 Mechanics of Deformable Bodies Week 4 Cut AB 0 Once we have the internal torques we can determine the max shear stress T The angle of twist in each segment cpAB LAB T L TxGIPdpTECOI lStantGIPEconstantIdpf idxcp AB AB dx 0 0 G11 GIP 0 only applies to prismatic bars with cnan orque T1 01g i Case 2 0 Bar with constant torque but continuously varying crosssection r r IP dT 5 m 16d3 16d3 smaller diameter larger shear stress COE 3001 Mechanics of Deformable Bodies Week4 Calculate the twist TxGI xd pTxEconstantT Tedsz To dx P dx 0 0 0 GIPx tX E torquelength 0 d1 25 in i 2m 1 I f L1 25 in T1 9000 ib in 4 139 E C L218in T24000 ib in quotquot LI 39 f 39 quoti G 11 x 106 psi 0 Find max shear stress T2T1TAOTAZTl TZZ SOOOZbEZ COE 3001 Mechanics of Deformable Bodies Week 4 M TABzTAz SOOOZbEZ BC T24OOOleL Txr 16Tx max I max 3 P Hd different for hollow bar 16T 16T A33 1630 psi TM if 2546 psi Hd1 11 13 AB Example 0 Solid steel bar 0 d 15 in 0 L 54 in 0 G 11 x 106 psi 0 T1 250 lb ft 3000 lb in 0 max shear stress 0 max twist 4 Hd TrW16T3x163004530psi 32 Ed H15 COE 3001 Mechanics of Deformable Bodies Week 4 P TL 323200544 02834radl62 GIp 1110n15 Part 2 If allowable shear stress is 6000 psi and allowable twist is 25 what is the max allowable torque I 6 4 Tch P143241110 n15 214502107lbe L 3254 torque maxi Tmax d3 6000n153 T 16 16 397611beo Example 0 Steelbar 0 Solid circular section Tallowable 60 MP3 Panow 30 05236 L 800 mm G 75 GPa Question 0 Find min bar diameter as function of applied torque l 1 l E E T3 d T s 2275 16 H Tm 16T 33 l6T d3 3 Hds HTW max 32TL d432TL dd 32L ITid T4 GI 1482 GHda4 quot 611 p Determine a max shear stress b angle of twist COE 3001 Mechanics of Deformable Bodies Week 4 16T16T aLT max Ed3 1161 max shear stress occurs at dA d d H d d bQIPX 3 2dx4dxdA BL A XIPX3 2abx4adAb B A p Z T deL 32T x 32TL ii AB 0 01PM oGHabx4 3HGdB dA dA3 dB3 1 dx L o abx4 3dB dA dA3 6133
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