Question

The propeller shaft of the submarine experiences both torsional and axial loads. Draw Mohr's Circle for a stress element on the outside surface of the solid shaft. Determine the principal stresses, the maximum in-plane shear stress and average normal stress using Mohr's Circle.

Answer 1

Answer: Attached below is the missing detail and Mohr's circle.

i) б1 = 9.6 Ksi

б2 = -10.7 ksi

ii) 10.2 Ksi

iii) -0.51Ksi

Step-by-step explanation:

First step :

direct compressive stress on shaft

бd = P / π/4 * d^2

= -20 / 0.785 * 5^2 = -1.09 Ksi

shear stress at the outer surface due to torsion

ζ = 16*T / πd^3

= (16 * 250 ) / π * 5^3 = 010.19 Ksi

Calculate the Principal stress, maximum in-plane shear stress and average normal stress

Using Mohr's circle ( attached below )

i) principal stresses:

б1 = 4.8 cm * 2 = 9.6 Ksi

б2 = -5.35 cm * 2 = -10.7 ksi

ii) maximum in-plane shear stress

ζ = radius of Mohr's circle

= 5.1 cm = 10.2 Ksi ( Given that ; 1 cm = 2Ksi )

iii) average normal stress

= 9.6 + ( - 10.7 ) / 2

= -0.51Ksi