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How to rearrange to find the height of a hollow beam

  1. Apr 16, 2012 #1
    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. jcsd
  3. Apr 18, 2012 #2
    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.
     
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