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Beam Deflection

  1. Sep 5, 2006 #1
    Ok I was given this problem:

    Problem: The deflection d of a cantilever beam of length L is given by the mechanics of materials equation [tex]d=PL^3/3EI[/tex]

    Where P is the force on the end of the beam and E is the modulus of elasticity, which has the same dimensions as pressure.Determine the dimensions of I which is the moment of Inertia.

    Are they simply asking you to manipulate the equation for I? If so would the following be correct? A little help would be appreciated, thanks.

    [tex] I= 1/d(PL^3/3E)[/tex]:confused:
    Last edited: Sep 5, 2006
  2. jcsd
  3. Sep 5, 2006 #2
    Any help appreciated.
  4. Sep 5, 2006 #3


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    is this a dimensional problem?, like stress is F/L^2, in a gravitational system (FLT)
  5. Sep 6, 2006 #4


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    Generally, we define the moment of inertia for a rigid body as [tex]\int_{V} r^2 \rho dV = \int_{V} r^2 dm[/tex], so the dimension is [kg*m^2]. But, in mechanics of materials, we define the axial moment of inertia of a cross section with the area A, as [tex]\int_{A} r^2 dA[/tex], where r is the perpendicular distance of the elementary area dA to the axis for which the moment of inertia is defined, so, for example, we have [tex]I_{z}=\int_{A} y^2 dA[/tex]. So, the dimension is [m^4], which fits into your problem of expressing I out of d = PL^3 / 3EI.

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