# Mechanics torsion analysis help

1. Nov 21, 2012

### bigbang42

1. The problem statement, all variables and given/known data
the statement:
You are taked to design a 2m long shaft which is to be manufactured either as a solid circular bar or a circular tube. the shaft is required to transmit a torque of 100Nm without exceeding the alloqable strength of material.

Find the required outer diameter of the tube if the thickness of the tube is specified as one-eigth of the outer diameter?

shear stress = 320Mpa

2. Relevant equations
T/J = $\tau$ /r

J= [pi(D^4 - d^4)] / 32

3. The attempt at a solution

thickness is 1/8
1/8 + 1/8 = 1/4

J= pi( D^4 - 0.75^4 D^4) / 32

work it out in sections
0.75^4 = 81/256 >>> 1 - 81/256 = 175/256 >>> 175/256 x pi = 2.14 >> 2.14 / 32 = 0.067D^4

then using the formula T/J = t/r

1000/0.067D^4 = 320x10^6 / D/2

get D on one side i get

1000 / 2 x 320 x 10^6 = 0.067D^4 / D

worked all that out then cube root it to get 0.028 which i then x1000 to get 28mm

I feel i'm on the right path ( i hope) but the whole 1/8 of the diameter has confused me and i'm wondering whether ive done that right. finding the "J" has to be my main concern i feel ive got the method right for finding D later on. If anyone can help my go through it and check everything is correct or if its wrong, advice on how to correct it would be fantastic.
thanks.

2. Nov 23, 2012

### PhanthomJay

Looks like you got it all correct, good step by step work. I assume the torque is 1000 Nm and not 100 Nm as originally stated.