Second Moment of Area

The second moment of area is a measure of the stiffness of a object due to its geometric shape (see Second Moment of Area for Common Shapes). Some shapes are difficult to bend such as an I-Beam whereas others are easy to bend such as a flat sheet. The Second Moment of Area allows for the stiffness due to its shape to be calculated. (See article Moments of Area for a general explanation of first and second Moment of Area).

The second moment of Area changes depending on what direction the force is applied. The direction of force will determine the orientation of the Neutral Axis. Many non symmetrical shapes will be stronger in a particular direction. To illustrate consider the following example where the Second Moment of Area will be calculated for a timber beam for a force applied in the horizontal and vertical direction. 

The formula for the second moment of area for a rectangle around the centroid is:

Consider a cross arm that is 100mm wind and 150mm deep as shown below.

The second moment of area for a vertical and horizontal force would be calculated as:

Here the Second Moment of Area in the vertical direction Ix is larger than the Second Moment of Area in the horizontal direction Iy indicating the beam is stronger in this direction. This is why floor joists are always installed with the larger dimension in the vertical axis as it maximises the strength of the beam for a vertical force.

See Also

Cross Arm Parameter - Second Moment of Area