Please show stey by step works Answer is sigma p1 9818 psi

Please show stey by step works ( Answer is sigma p1 = 981.8 psi )

Consider a cylindrical vessel that is subjected to both an internal pressure p and an applied torque T at the ends (as shown). Using Mohr\'s circle, find the principal stresses and maximum shear stress in the wall of the tank. Assume an inner cylinder radius r_i = 25 inches, wall thickness t = 1 inch, applied torque T = 1500 kips-in and internal pressure p = 30 psi.

Solution

Use stress formula for thin cylinder. get the stresses as 2pr/t, pr/t , comes to 750 psi and 375 psi

The torque is major source of stress being so high at 1500 Kips.

Formula for principal stress : sigma 1,2 = (750+375)/2 +- sqrt(( 375/2)² + tau² )

PS 1 1500562.5

PS2 1499437.5

Max shear stress: (PS1-PS2)/2 = sqrt (( 187.5 ^{^2} + 15^{^2} * 10^{^10})

approx 1500 Kips.

( cannot reconcile with given answer)