Question 1

How do I calculate the moment of inertia of an arbitrary polygon?

Accepted Answer

Enter the (x, y) coordinates of each vertex of the polygon in order (clockwise or counter-clockwise). The calculator applies the shoelace formula for area and the standard surveyor integration formulas to compute Ix, Iy and Ixy about the centroidal axes.

Question 2

What is the difference between Ix, Iy and the principal moments of inertia I1, I2?

Accepted Answer

Ix and Iy are the second moments of area about the centroidal x and y axes, which depend on the orientation you chose for your coordinate system. I1 and I2 are the principal moments of inertia — the maximum and minimum possible values — about the principal axes, which are oriented at angle θp relative to the centroidal axes. I1 and I2 are independent of the initial orientation.

Question 3

What is Mohr's circle of inertia?

Accepted Answer

Mohr's circle of inertia is a graphical representation in the plane (I, Ixy) that shows how the moment of inertia and product of inertia change as the reference axes are rotated. The circle's centre is at (Iavg, 0) and its radius equals (I1−I2)/2. Points A(Ix, −Ixy) and B(Iy, +Ixy) are diametrically opposite on the circle.

Question 4

Can I calculate section properties for an I-beam or T-section?

Accepted Answer

Yes. The calculator includes parametric presets for I-beam (HEB/IPE style), T-section, L-section, rectangle, triangle, pentagon and hexagon. Enter the flange width, total height, flange thickness and web thickness and click Apply to generate the polygon automatically.

Steel Cross-Section & Inertia Calculator (Eurocode 3 / AISC)