Question

1. Figure (1) shows a 20 mm diameter shaft mounted in bearings at A and D and having pulleys at B and C. The forces shown acting on the pulley surfaces represent the belt pulls. Find the magnitude and exact location of the following stresses: (1) Principal stresses (2) Maximum shear stress Given dimensions are in millimeters and forces are in Newtons. 150 D 1335 N 225 N 1600 N 120 N 200 D C150 B 200 Figure (1) 200

Answer 1

Pue to hovce 225N torue OCcuYs 335N C C.w 225N Tニ225× I00 N.mm T 22500 N m CC W Due to bo rC e b0rCe torgue occurs 13 35 200D デ= 1335 ×100 N.MK デこ133500 150 D N mm C W bovce 120 N Due to tov2ue O CCUYS 1600N Cow n ブニ120 ×T5 Nmm 120N T E 9000 N.mm Cw bo vc e Due to to1gue C.C4 1600N OC GUYS n 1600x75 Nmm TE 120oo0 N,mm TT Cicw C.w is tve FEnal . . to tal to 1ue C.C.w is -ve - 2250O 1335 oO +900o-12000 o TE O balance (eeuilibiam the bvom toveue values 4 133500 Nm CW 1560N C172 N 150 う about z-anS due 1560N P1oment at A iS My15 60 X200 Nmm in c.ra 200 312000 N mm A CiCiW Mu Z 200 Moment due to 1720N abo ut z-atis at A iS C M 1720 x 400. Nemm M 688 000 N.nmm C. w

Moment due to about at D is 1720 N Z-oxis MZ 17 20 x 150 N.mm in c.cu M, 2580 00 Nimm Z-adis at Dis Moment due to 15 60 N about Cw MZ 1560x350 N.mm M, 5460oO N.mm Theveove at A due to 1720 N C.W Mmax 6 88000 N. mm at A. Cfitical section is : The Bending stven due to moment Mmax 9iven MmaXy N.A O x is peripheny top most pointbs (point) at outer yEDistance hom .A to the the Point Heve ate tension Since M iS in Clock wise 9d 20-10mm NhmM I,= dMom tnt of inertia about Z-aruis IT (20) 6 4 64 875.988 MPa sheav stvers stis given 64 tovzuee (tu) Zry due C= distance am Centve to Point Z is manimum at the periphevy c=d Tmon XC J 133500 X1o 1 N/mm2 10mm 32 TPolar moment of inertia 84.989 M Pa J= 32 Stvemes Ptinciple that OT,2 2- know we 875.988 S75.988 12 +84 9892 2 L437.994 t 446.1635 1,2

a 4.158 MPo 3.17 MPa 7 ) Marimurm sheav stvem 2 Zmax 2 2 Cmax 875.989 1 2 + 94.9892 2 *Dw2 446.164 MPo which acts 'A' at the top mast point at ave