Question

A round steel shaft is subjected to a concentrated moment M=1000 lbf.in at point B, which is located at distances a=8,b=9 in from either end. Modulus E=30 Mpsi. The shaft is mounted on bearings that cannot tolerate a slope in excess of θ=0.002 rad. The bearings can be assumed to behave as simple supports. Calculate: ∙ The minimum diameter d required so that the slope at the supports does not exceed the limit.

Answer 1

dmin = 1.4374in

Step-by-step explanation:

In the question, it says slope at the support should not exceed the limit. When such a sentence is given always use the maximum value of the property. So here the maximum moment of inertia is used.

θ₁ = Pb(l² – b²)/6lEI

0.002 = 1000 x 8 x (142 - 82)/6 x 14 x 30 x 10⁶ x I₁

I₁ = 0.209523 in⁴

θ₂ = Pab(2l - b)/6lEI

0.002 = 1000 x 6 x 8 x (28 - 8)/6 x 14 x 30 x 10⁶ I2

I₂ = 0.190476 in⁴

For design point of considerations, taking higher value of M.I, which is I₁

I₁ = 0.209523 = (π/64) x d⁴

d⁴ = 4.2683

dmin = 1.4374in