Better Understanding Section Modulus, Design Moment and Moment of Inertia

Both the Moment of Inertia and the section modulus are measurements of the relative stiffness of a cross section of steel piling.

The major difference is that I (Moment of Inertia) is used for more general calculations. When calculating the stress in a steel pile, for example, the formula using I is

stress = M*y / I

where M is the bending moment at a point on the steel pile (called Design Moment) and y is the vertical distance from the bending axis at the middle (centroid) of the cross section. This is a general formula, because you can determine what the stress is at any point in the cross section by plugging in a value for y.

However, for most civil engineering work using steel, the engineer is not as concerned about what the stress is at a given distance from the centroid of the steel pile as they are concerned about when it will yield. Therefore, section modulus is a more important and useful comparison and design criteria. To determine the section modulus, Z, you divide the Moment of Inertia by y.

Therefore,

Z = I/y

Why is this more useful for engineers? Because if you switch this around, it also means that

I = Z*y

Substitute this into the stress formula, and you get:

stress = M*y / Z*y

The y’s cancel out and you now have:

stress = M/Z

This is the stress at the extreme fiber of the beam, which is the worst case scenario. And obviously the worst case scenario is what civil engineers usually design for, in terms of designing a steel sheet pile for maximum strength.

Note: On most steel piling projects that are to be bid for construction, it is best to have a Design Moment specified (e.g., 100 k-in/ft.) that engineers can work from, rather than a specified steel section, as this does not tell engineers the exact stresses that they need to work from.