Question

P6.042 The composite shaft shown in the figure consists of two steel pipes that are connected at flange B and securely attached to rigid walls at A and C. Steel pipe (1) has an outside diameter of 173 mm and a wall thickness of 6 mm. Steel pipe (2) has an outside diameter of 101 mm and a wall thickness of 7 mm. Both pipes are 3.4 m long and have a shear modulus of 80 GPa. If a concentrated torque of 22 kN-m is applied to flange B, determine (a) the maximum shear stress magnitudes in pipes (1) and (2). (b) the rotation angle of flange B relative to support A. LL L2 TB (1) (2) x B Answers: (a) Ti = MPa T2 = MPa (b) PBIA = rad

Answer 1

Pipe I Pipe 2 D = 143mm do to D2 ²101 mm ti 6 mm t2²7 mm L = 3.4m L2-3.4m p Ti=80 Gpa Calon G2= sogla 6 TB = 22 kN.m - for flange B EM.co tja 29 CUTI- Tit TB + T2 = 0 IF Ti - Tz a TB = 22x100 N.m - o oto2=0 TIL t G o TEL2 G2J2 32 JJ = T 4-die) 1926 1734 - 10142 = 2.1976 x 107 107 mm4 13 32

TT Jo = 172 Co" - de) (101" - 874) 32 = 4.59169 x106 mm + TI (3.4) Tal 3.0) SÓ (2.1976X107) S0(2.591696100) + TI = - 2:1976X107 T2 4.59169x106 ti = -4.7861 Tz 2 - solving eq.c) & C2), we get 4.7861 T2 - Tz = 22/106 Tz = -3.8022x106 Nomm T = 18. 1977x106 N.mm

Shear stress in Pipe I! Z= TRI Jr3 173 18.1977x 2.1976x, 07 G= 71.63 MPa - Answer - Shear stress in pipe 2 Z2 = T2 R2=PLG JZLE 3-8022x10x11012 4.591698106 41.82 MPa pin V x Answer b Rotation angle of flange B relative to A