Question

A structural steel shaft with an outer diameter of 1.9 inches and an applied torque of 82.7 ft*lbs. Find: The maximum torsional shear stress in the shaft. Select one: a)- 736.88 ksi b)- 61.41 psi c)- 1473.76 ksi d)- 736.88 psi e)- 368.44 psi

Answer 1

Answer is part d -736.88 psi

Step-by-step explanation:

We know that for a bar subjected to pure torsion the shear stresses that are generated can be calculated using the following equation

`(T)/(I_(P) ) =(t)/(r)`....................(i)

Where

T is applied Torque

`I_(P)` is the polar moment of inertia of the shaft

t is the shear stress at a distance 'r' from the center

r is the radial distance

Now in our case it is given in the question T =82.7 ft*lbs

converting T into inch*lbs we have T = 82.7 x 12 inch*lbs =992.4 inch*lbs

We also know that for a circular shaft polar moment of inertia is given by

`I_(P)=(\pi D^(4) )/(32)`

`I_(P)= (\pi\ 1.9^(4) )/(32) =1.2794 inch^(4)`

Since we are asked the maximum value of shearing stresses they occur at the surface thus r = D/2

Applying all these values in equation i we get

`(992.4 inch*lbs)/(1.2794 inch^(4) ) (1.9 inches)/(2)` = t

Thus t = 736.88 psi