# Beam Deflection

1. Sep 5, 2006

### 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 $$d=PL^3/3EI$$

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.

$$I= 1/d(PL^3/3E)$$

Last edited: Sep 5, 2006
2. Sep 5, 2006

### EE_Student

Any help appreciated.

3. Sep 5, 2006

### Pyrrhus

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

4. Sep 6, 2006

Generally, we define the moment of inertia for a rigid body as $$\int_{V} r^2 \rho dV = \int_{V} r^2 dm$$, 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 $$\int_{A} r^2 dA$$, 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 $$I_{z}=\int_{A} y^2 dA$$. So, the dimension is [m^4], which fits into your problem of expressing I out of d = PL^3 / 3EI.