Question

the material is structural steel with σf = 220 MPa, E = 200 GPa, ν = 0.3, and α = 12x10-6/oC.

The steel shaft AD is subjected to the torques shown in Figure 2. Calculate: 1. The internal reaction in AB 2. The internal reaction in BC 3. The internal reaction in CD 4. The maximum shaft diameter consistent with a safety margin of 50% (Tresca's criteria) 5. If points A, B, C and D are all 1 m apart, calculate the angle of twist of section 'A' relative to the fixed base at 'D' T(N·m) = +150 = -280 = -40 Α Σ D B С Figure 2: Shaft with multiple torques

please have correct answers

Answer 1

50 per cent margin mean factor of safety is 2
criven & 66= 220 MPa E 2oolipa V = 0.3 d = 12x106 le From hemd thumb rule it is outward Stepl! tve Torque, when it is mward. ove Torque 2 150 Nom 150 MM cel B (1) - 130 Mim c 150-280 =-130N.m G 12) -170 M 170 Nm (3) >44€ Step 2! let radius of circlar shaft ar J = Polar moment of inerta J = IT ry 2

CD applies in the section Maximum Torque Т. 17р ут Эс ) ту 170 Хіроох х2- Ter T = IT x 34 Max Shear stress, Т. 34 хуру Т 3 ( max Tmax Forom Tresca's criteria 34хіру 27 6) 2-6 Tmay a ГX3 Е, - Tmay FOS = 2 220 MP4 available yield &tress (34 хоч applied stress ТҮЗ с. 226 341 0° х ру3 34х2хоч т? 2.2017) Теп. Ичтт rñ 10mm

Hence Diameter of Shaft- 2x10 =20mm D = 20 mm Step 3 - op TL 150X LAB 130X LBC PAID 170* LCD JU son JU LAB = LBC = LCD = im I= I x 10" 15707.963 mmy G = = 76.923 Gpa 200 2x1.3 2(lt)) 3 cr = 76.923 X10 MPa 130 XI DO X1000 1700106 150X1000X1000 & PAID 150x106 15707.963 % 76.923x10? AI PAID -0. 124 rad