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Finding spring constant and inertia

  1. May 28, 2014 #1
    1. The problem statement, all variables and given/known data

    "the question is included in the attachment"

    2. Relevant equations

    F=ks, E=stress/strain=(force/area)/(change in L/L)

    Second moment of inertia=I=(1/2)*base*height^3

    3. The attempt at a solution

    Sice F=ks

    k=F/s where F=p and s= d(L) (change in L)

    E=(P/A)/(strain)=> EA(Strain)=P E=Young Modulus A = Area
    area of the beam is equal to base*height, let height be equal to L

    Second moment of inertia=I=(1/2)*base*height^3 => base=b= (12*I)/(L^3)

    Thus P=E*(strain)*L*b=(E*dL*12*I)/(L^3)

    Thereby K=P/s=P/dL=(12*I*E)/(L^3)


    However the suppose answer is (48*I*E)/(L^3), can anyone tell me what I did wrong?
     

    Attached Files:

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  2. jcsd
  3. May 28, 2014 #2

    SteamKing

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    Staff Emeritus
    Science Advisor
    Homework Helper

    I think for this problem, use the following:

    F = k δ

    where F is the applied load (P in this case),
    k is the spring constant, and
    δ is the central, transverse deflection of the beam due to the load P.
     
  4. May 28, 2014 #3
    Ahh, I see. Thank you so much,
     
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