# Homework Help: Cart Wheel Problem

1. Feb 7, 2010

### hellboydvd

1. The problem statement, all variables and given/known data
This is from Strength of Materials. A cart wheel of diameter 1.2m is to be provided with a thin steel tyre. Assuming the wheel to be rigid and if the stress in steel is not to exceed 140 MPa, find the minimum diameter of the tyre and the minimum temperature to which it should be heated before slipping it onto the wheel. Take Young's Modulus of steel=200 GPa and coeffficient of thermal expansion (alpha)= 12* 10^-6 per degree celsius

2. Relevant equations

alpha*(delta t)*original length=dl
Young's modulus=Stress/Strain

3. The attempt at a solution

Thought- The required diameter of the steel tyre would be less than 1.2m. This is because after heating it to a certain minimum temperature, it has to be slightly bigger than 1.2 then put on the cart wheel and cooled so that it provides a firm grip. Therefore:-

Permissible stress= 140 N/mm^2 = Strain*Young's modulus
calculate strain from this equation
strain= dl/l
dl=change in length in this case= 1.2-d ( where d is the assumed initial diameter of the steel tyre)
and l is d ( original length of the steel tyre)

Getting d from this, equate alpha*d*(delta t)= 1.2-d to get the change in temperature (Rise)

Is this approach correct or i made some error?