## Z/H/I beam moment of inertia calculator

## How to use calculator

This I beam moment of inertia calculator is programmed to calculate the moment of inertia about specified axis, centroid about specified axis, section modulus, radius of gyration and cross sectional area.

Step 1: Select the units from the dropdown menu.

Step 2: Specify the axis about which the moment of inertia is to be found about, note that equation for X-X axis is y=__ and equation for Y-Y axis is x=__.

Step 3: The user can enter different dimensions for bottom and top flange left and right side, thus making this I beam moment of inertia calculator a versatile one which can also be used to calculate moment of inertia of Z section and H section.

## Z section moment of inertia

For a Z section input one side of top and bottom flange as 0 in both width and thickness.

Here in this case the top left flange and bottom left flange has been kept as 0.

The units of each quantity can be individually changed according to users preference.

Centroid is calculated from the specified axis, by default the axis start from (0,0). The bottom left point of bottom flange is considered as origin by default.

## Section modulus

Section modulus is the property of the cross section which is directly related to the flexural strength of a section. More the section modulus of a given section more bending moment it can resist.

The section modulus is calculated for centroidal axis by taking ratio of centroidal moment of inertia to the distance of extreme fiber from the centroid. Therefore section modulus formula is given as

- Sxx = Igx/ymax
- Syy = Igy/xmax

## Radius of gyration

Radius of gyration is the hypothetical distance where if the entire area or mass is assumed to be concentrated, then it will produce same moment of inertia about the axis as the actual area or mass does.

Radius of gyration is given by following formula:

- r_{x x}=\sqrt{\frac{I_{x x}}{A}}
- r_{y y}=\sqrt{\frac{I_{y y}}{A}}