Question

Several forces are applied to the pipe assembly shown. the inner and outer diameters of the pipe are equal to 1.50 and 1.75 inches, respectively. (a) determine the principal planes and principal stresses at pt. h located at the top of the outside surface of the pipe (b) determine the maximum shear stress at pt. h (c) provide a sketch (to-scale) of mohr's circle for the state of stress at pt. h

Answer 1

To replace all forces on a pipe by the equivalent force
T= 8× 50 = 400lb.in
M = 16.30 = 480lb.in
F₂ = 50lb
To calculate the polar moment of inertia of shaft is 
J = π/π²×(R⁴-r⁴)
= π²/2×(0.875⁴ - 0.750⁴)
= 0.423in.³
To calculate the moment of inertia
J= 1/2(J)
=1/2 (0.423)
=0.21188in.³
To calculate shear flow
Qy= 2/3(R³-r³) 
= 2/3(0.875³- 0.750³) 
= 0.16536in.³
To calculate the thickness of the shaft
t= R-r = 0.875 - 0.750 = 0.125 in.
The stress due to torsions is.
Tx = TR/J = 400 × 0.875/0.42376 
=825. 9psi.
The stress due to bending 
Qx =My/T = 480 × 0.875/0.2118
=1982.3psi
The stress due to transverse shear
Qx = VQ/I(2t)
=50 × 0.16536/0.2118× 0.250
=156.1psi