Question

Question 1 Time Allowed: 2 hours The figure shows a transmission shaft. The steel solid shaft is 200 mm long between self-aligning bearings at A and B. Belt forces (in the same horizontal direction) are applied to a 120-mm diameter sheave at C. The left end of the shaft is connected to an electric motor attached to a clutch by means of a flexible coupling. Nothing is attach to the right end (it is free). Assuming the shaft has a constant diameter, d, (a) Perform the necessary stress analysis and draw the critical stress element (b) Using stress element and Mohr circle approach, find the principal stresses and the maximum shear stress. (c) For a factor of safety of 2, and material made of plain carbon steel (AISI 10XX), specify a safe diameter d and a material for the part B 100 Free end of shaft I J-mm- 1. shaft 100 2000 N A sheave is a pulley with a grooved wheel for holding a belt, wire rope, or rope. The grooved wheel spins inside the frame of the sheave. This allows the wire or rope to move freely minimizing wear and abrasion on cable. Sheaves can be used to redirect a cable or rope, lift loads, and transmit power. Source: Wikipedia. 120-mm-dia. sheave 400 N Connected to flexible coupling and clutch

Answer 1

Giver power transmitting shalt is shown below: loomm > loomm #B yz > 2000N lrommedia) ox id > A Motor Connection YOON Griven loadings on the shatt Can converted into force - Torque loadings below in the X-2 plane: as shown px I 2 A B F = (20004 400)N we have fore, F= 2000+400 - 200N Torque, T = (2000 - 400) x 0.12 2. T= 96 N.m (a) Given that is connected to the motor side All through fluible coupling to a clutch and end s' is free.

Produces Torsional shearstrey Torque T' in the section Ac only. shaft can be seen belows the loadings on the A 960 m AB M 1 2 loomm LOO.mm RA R 24OON see that RATRB = 2400N and due to symmetry about point & RA= RB from Eg. Cand @ RA=R8 = 1200N. we see that Marimum bending monment will occur in the shaft at Point'c', which is given by M = RAX Ad. 120 Nom 1200 X 0 1 Mc = {20N.m. Marinum Bending strees caused by Mr at . point d' is adh 64

32MC ad3 Also, Torque, T = 96 N.m. will induce Marimum Torsional shear strees at Point Es given by 7.(2) ad IGT nd 32 T= 16T ad This critical strees element at Point 'c' in 2- is shown below: Trx-T T-Tx2 4 "- "ь To= Tx Tx2=T Tx=T b) and By ming. The above strees element Mohl's circle approach, Principal streeses induced at this The Critical point can be given in the following way.

Tutt T-T2 + + TZ 2 2 we have 32MC nd 16T T=0 = 7 X2 nd 16 Me + 2 16 Me nd ad? su, 16 hd [Mart2 ] have we Me= 120N.m and T= 96 N.m. 16 ad [120 + /120796 16 (120 + 153-675] ad 16 [rro + 153-675] ad? 16 nd? [120-153-675). 1393-815 N - 171.505 d? d? These are Monimus and Minimum Principal stresses:

느 (Syt Fs (1393.815 ) A-171-505 + d3 1393.815 + Moxio 171.505 d? с 2 1487.004 < (225x106). d 2 0.018766 m Y d I 18.766 mm, in The minimum sate diameter of the shatt made of AISI 1045 plain carbon sted for this application is 18.766 mm AJ 19 mm