Question

(30 pts) Shaft Yielding. A solid circular shaft with 125 mm diameter rotates in bearings at 30 rad/s. Transverse loadings produce a maximum bending moment of 10 kNm. (For 3. e meaning of transverse loading see the image below.) Given the tensile yield strength th of the shaft material as 300 MPa, find the power this shaft can transmit according to the Tresca and von Mises yield criteria. Hint: You may need to use Engineer's Theory of Bending (ETB) to find the bending stress from the bending moment. Trasverse Traaserse load Axial Lead Twist dur brsional lead Tersional load Tarsional ead ending mment Aial Lead Trannerse ead Typical shaft loading and delection

Answer 1

Solukio;n The given loading system are complex loading condi tion (1) Due to transverse loading ( Bending) (ii) Due to torsionel moment that is transmi tted Paoer nsmitted Power to anoe system (i) Axial loadin (Dato are mot given in questior) iven in ques tion 2. Here we determine the stresses due fa followinj oadin components (1 ) Bending moment- U') Torque ú) eendlin stess ( Beom Theory 32 M 3 3 πχ(0-125)

(ii) Torsional sheav stress lue to tov Tovsion quation used _-l0 T OY 2- case T)Tresca theoy C rj) Maximum Sheav stress fheo here S1 →Yield she nght. S300 MPa max 3o o 2 M P 2 C1) てmax 50x10 , N calculating principal stresses (σ'/02) + (2607-GT) 12. 2 679. 96xlo12+6799 ST.8 T2 12 2. てmax

usig equations (G) and (2) 2. 2. 67 9957.8 T- 21. 82 xlo 2 T - 56 6 48.3 N- Nnswer Hence the power that can tvansmitted by Shaft > 30 rad p - 169 9449 N-m 1699.449 kW pnswer case (U) ,-Von-Mises Theory : 2 2 we know hat 12. -e' o76x10が+ (67,.96x1j') t6793577.RT2. σ' 2 112t 6-1 g9577. g. T 2. 」C79-96x1ot 6795577.872.

same IS Now usina etion (3) 1S 2 2 36.016 xlo -<79.9<x lo + 6799577.2 T 2 ις 12 2 12 S) usina equation (3), (4) md S) ,we in onte 12 6 2 IS 12 IS 20 ‘ 3 ggx1o .ナ 2 4.31x10 1969.518 kW AnSweY