Question

1. A shaft subjected to bending moment varying from -200 N m to +500 N m and a varying torque from 50 N m to 175 N m. If material of the shaft is 30C8, stress concentration factor is 1.85, notch sensitivity is 0.95 reliability 99.9% and factor of safety is 1.5, find the diameter of the shaft. The load on a bolt consists of an axial pull of 10 kN together with a transverse shear force of 5 kN. Find the diameter of bolt required according to 

1. Maximum principal stress theory;

2. Maximum shear stress theory; 

3. Maximum principal strain theory;

4. Maximum strain energy theory; and

5. Maximum distortion energy theory. 

Take permissible tensile stress at elastic limit = 100 MPa and poisson’s ratio = 0.3

Answer 1

obtain the property of 300g material from appendix of о aney text book. Tensile strength is (Sut) = 500 N/mm? Yield strength is (Syt) = 400 N/mm2 Calculate Mean bending moment using the relation Mmax + Mmin Mm 2. 500 Nm 200Nm २ 2. Mm Ibo Năm Calculate alternate bending moment using the relation. Ma- Mmax Mmin 2 500 + 200 2 350 Nm Calculate Mean tosque using the relation

Tm Tmax + Tmin 2 50 +175 2 11205 Nm Calculate alternate topque using the relation Ta Tmax -Tmin २ 175-50 2 = 6205 nom ben Calculate mean stress inding interm de diameter m m 32 mm Td3 = 32 4150 N-m x 1000 mm im Td3 1527887.45 d3 Calculate alternate bending stress ra 32 Ma T 03

327 350 X1000 N-mm IT d 3 3, 565, 070-725 d3 Calculate Mean and alternate shear stresses Pm 16 Tom Td3 164 112-581000 N-mm Td3 572,957.8 3 و Ya — 16 Та Td3 3 16x 62.5 X1000 N-mm Td3 318,30१.१ N/mm² d3 and alternate stress Calculate equivalent mean according distortion enelay theory. (a), - Vatt3 Ta?

(a), -/ (3,565,070 070.125) + 3 (318, 30909 •g) d? d3 3, 607, 449.63 N/mm² d3 (3) m² + 3 Tont e ro 1527887.45 92.06) * + 3 ( 572, 95708 708)2 d3 03 = 4821,890 Nm (me d3 Determine Correct endurance strength of material using the relation. Ka.ky keokdosel sel 0.5 ut (for steel =005x 550 N/mm² = 250 Nimmt ka surface finish factor

a (gut) b For Machined a = 4.51 b=-0.265 ka = 4:51 (50050-265 8688 kca reliability factor at aqoq.4. Reliability ke=0.753 Kb size factor Assume 7.5L d < 50mm kb=0.85 kd Temperature factor 2. Se 0.8688 X 0.8570.753 X250 Se = 139 N/mm²

Determine actual stress con centration factor (kg) using the relation q 인 kf-1 KL-1 Here, q is notch sensitivity, if actual stress Concentration factor and k4 is theoritical stoess concentration factor is 0.95 - kful 1.85-1 kg 1.8075. Determine diameter of shaft using Good - Man relation kg (tm) e kt (ale + Sut st se 1.8075X1821890 1.8075 x 3607 449.63 d3 d3 I 105 500 139

6586:13235 4-6909.82 ㅜ t d3 L ㅗ 1.5 d3 da = 43.1324 mm. Therefore, diameter of shaft is 43.13 mm

Given Data! Axial load bolt (P) TO KN Tranverse load 5kN on bot (vo Permisible tensile stress at Elastic limit (pes) - 100MPa poisson's ratio (e) =0.3 Normal Calculate the teama stress in the bolt using the Р А A is Here, is normal stress in bolt and Cross section area of bolt substitute 10 kN for P and Id² for A. 10kN X03 N IIN 242 = 12732-4 N/mm² the bolt using in stress Calculate shear relation

러 = A Here, ? is Shear stress in bolt and Vis Shear force. substitute 5KN for v and Id2 for A. 퓨어 a 구 5 kN XON/IKN 포 6366,2 러 Ni mm² d2 Determine principal stress in bolt using the relation 에

1,2 (5) I ſE² + 92 12732.4 (2732.4 :) +(636602 dz 2d2 d2 2 6366.2 d2 2 9003.16 d2 ハ - 15369.4 N/mm² 02 a 2636.96 N/mm² Determine diameter of bolt According to Maximum Normal stress using the relation. max = oper substitute 15369.4 for max and 100 N for da mm Opex 1536904 =100 N/mm² dz d = 12.397 mm bolt according maximem Therefore, diameter of principal stress theory is 12 •4 mm

Determine diameter of bolt according to Maximum shear stress theory using the relation a02 о per 15369.4 2636.96 + 100 N/mm d2 2 و d. 13.418 mm Therefore, diameter of bolt according to maximery Shear stress 13.42mm Determine diameter of bolt according to principal Strain theory using the relation 9 до, Ta per 15369.4 0.3% (-2636-96) 100 N/mm² da d2 d = 12.712 mm of bolt according to There fore, diameter max principal strain theory is 112.7mm

Determine diameter of bolt according theory using strain energy the Gelation. 22+ 22 zu oara oper > 5369.4 +) + (-263696 + 240.3x15369.4 -263694) d2 100 N/mm2 16355.09 100 N/mm² d2 d=12.788 mm diameter of bolt There fore, according to strain energy is 112.79 mm ) Determine diameter of bolt according to distorsion energy theory using the relation. VaR + on -— of Ta pes V (5z&q:+1) + (-2424 ) (1536.4) (-242444 = 100 N/mm2

16843:41 - 100 d2 d 12.978 mm to Therefore, diameter of bolt according distortion energy theory is 112.978 mm