Calculating the section modulus

To calculate the section modulus, the following formula applies:

An equation: Z = I divided by y. where I = moment of inertia, y = distance from centroid to top or bottom edge of the rectangle An equation: d divided by 2.

For symmetrical sections the value of Z is the same above or below the centroid.

For asymmetrical sections, two values are found: Z max and Z min.

To calculate the value of Z for a simple symmetrical shape such as a rectangle:

An equation: Zxx = I xx divided by y. where An equation: Ixx = bd3 divided by 12 which equals mm4.

and y = An equation: ½ depth or d divided by 2 mm.

This gives the formula for Z as: An equation: Z = bd2 divided 6 mm3.

Note: The standard form of writing the value of Z is to write it as a number x 103 mm3, eg a value of 2,086 is written as 2.086 x 103.

Calculating Z

Two diagrams of oblong beams with x and y axes marked. For beam A the breath (b) is 50 mm and the depth (d) is 200 mm. For beam B the b is 200 mm and d is 50 mm.