# How to rearrange to find the height of a hollow beam

1. Apr 16, 2012

### bobmarly12345

1. The problem statement, all variables and given/known data
i had a solid rectangular beam of max stress equalling 1.65x10^6N/m²
a new beam, a hollow rectangular beam is made to reduce weight, it has the same maximum bending stress 1.65x10^6N/m² but this time has a horizontal dimension of 0.2m and a constant wall thickness of 0.02.
i need to find the vertical dimension but am really having trouble rearranging the formula

M=550

2. Relevant equations

I=B.D^3/12 - b.d^3/12

max stress = MY/I
3. The attempt at a solution

1.65x10^6 N/m²= 12X550/(BD^3-bd^3)
then
(BD^3-bd^3)=12x550/1.65x10^6

having trouble getting the D value to equal a calculation

2. Apr 18, 2012

### LawrenceC

You know M and you know the stress for each beam.

Sigma = Mc/I

Solve the above for the ratio of c/I, a number. Then set that number equal to c/I for the hollow beam taking the wall thickness into consideration. Solve equation for the height of the hollow beam.