Beam Deflection

EE_Student

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]

EE_Student

Any help appreciated.

Pyrrhus

is this a dimensional problem?, like stress is F/L^2, in a gravitational system (FLT)

radou

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.