Answer to Question #120206 in Mechanical Engineering for Kale

Question

For the solid steel shaft shown (G = '77 GPa}, determine the “v angle of twist at A. (b) Solve part (a), assuming that the steel shaft is hollow with a 30-mm enter diameter and a 20-mm inner diameter.

Answer 1

Given G = 77 GPa

Outer diameter of shaft = 30 mm

Inner diameter of shaft = 20 mm

Length of shaft = 1.8 m

a)

Solution

d = 30 mm

Therefore radius c = 15 mm

From Torsional equation

T/J = G0/I

For solid steel shaft angle of twist at 0 = TI/GJ

= (250*1.8)/(77*10⁹*3.14/2*15⁴*10^-12)

= 0.073491*(180/3.14)

= 4.21⁰

Hence angle of twist = 4.21⁰

b)

Solution

d = 30 mm

c = 15 mm

Hence inner radius c_i = 10 mm

Polar moment of inertia of hollow cylinder J = 3.14/2(c⁴-c⁴_i)

Hence; from torsional equation, angle of twist 0_H = (TI/GJ)

= - (TI)/(G*3.14/2(c²-c⁴_i)

= (250*1.8*2)/(77*10⁹*3.14*(15⁴-10⁴)*10^-12

= 5.247⁰

Therefore the angle of twist is 5.247⁰