Question

MEC 432

Mechanical Design I

The bearings at A and B exert only y and a components of force on the shaft. If Sy = 150 MPa for the selected ductile material, determine the factor of safety if the shaft diameter is 40 mm. Use the maximum distortion-energy theory of failure. Show the following procedures through the calculation steps (Free Body diagram (FBD), Reaction at A and D, Bending moment diagram, point of max. moment, Torque diagram, draw the element showing general stress (Oxxy), the equivalent von Mises stress, the factor of safety using the MDE. 200 mm SOON 150 mm 150 mm 100 mm

and draw the MDE theory please

Answer 1

o Page omm = SOON 2001. Fz=500N T 150 1 200 150 100mm shaft = 40mm dia sy=150 MPa 500 h = * @ Ć FB soooo oo og duminy forces to get moment & dueto Fifa one force Fz=500N due to E, de creates moment . and one force F3=SOON = @D W ĘY F= 500 ** Torgue Sooxloo = 50000 N-mm. Due to Fr force 1 1/2 plane? La cio * 200* 150+ RAtRg= 500 + SOON R Rei EMoment at A=0 in Z-direchon:- then 500x350 = R8X200 Rg = 875N then Ro= -375 down wardy} -375 i as taken upwardy CSscanned with.Can begin torce diagram (Shaded)

In Y-direction - Page 2) towards 500N page 150- 2004 iso RA RB - Rat Rg = 500 moment at Bizo 5 5 500 x 350 = RsX200 o RA = 875 N no Rg = – 375N Lapp to taken dirty Soon 20 375 Shear force diagram Torsion diagram for systems - Right hand thumb Tarsios moment - TM tve 650000 N-mm 1. TM-ve Bending moments :- For d t - direction : Force due to Y-directs B.Mata =0 * B.Mat AS 500x150 = 75,000 B.Mat B = 500x350 - 875x200 20 B.Mat R = 500X 500 - 875 X 350 + 375 4150.20 CSscanned with camscanner

Y X Bending moment due to z- & force] (Page-3) B.Mat C = O n B. MM 200X-3752 B Mat A co n tinental *B.Mat B = - 375 x 200 5.75,000 N-mm B.Mat o = -375 X 350 + 875x150 co Bending moment diagrams i- . Due to fz dz-plane} 75000 Nomme A 75,000 2 x ( Mresult = Macy't me x 1 M o . o at A. Due to Fy B : {y-plane} . d compressivel S ene 2: towards s fare - Fy} è *f My zo hata 9 M2= 75,000) . * Pry=75,000 ats el Mzzo J B f Mregut ARB 75,00o N-mm ut co A 75,000 Mequivalent 75,000 CSScanned with CamScanner Nomm

Ben Page-y t o Ctrcular shatt d=40mm, M= 75,000 at both A&B is critical on oma ما Namm 1b = 11.93 MPa at A & B at A & B = TTo3 = 161 < 16x 50,000 TXU Eat A&B = 3.97 Mipal & Von- misses theory :- (von-misses = 107322 von-misses 2 r. In combined Loading - g) + (50z) 02-82² + 6 seyt Tyzzzzzy CBcanned with one 7 = {yz= 3x =o pactually -my

(Pase- von = $11.934 3x3.972 induced stress I von-missex = 13.76 MPa L ut - Tmax = yield Factor of allowble Sabety (N) N= - gied Tatlowed 150 13.76 IN = lol acc to von-misses theory CScanned with CamScanner