Principal axes and Mohr's circle

Calculate basic, transferred, composite, principal, and radius-of-gyration section properties.

Open the complete lesson

Advanced engineering statics simulation

Area Moments of Inertia and Section Properties Suite

Exact shape formulas, validated composite geometry, physical inertia tensors, principal axes, and radii of gyration.

Simulation

Transform Ix, Iy, and a physically admissible Ixy into principal values and orientation.

Section width120 mm

40–300

Drag for exploration or enter an exact value. Press Enter to apply and Escape to restore.

Section height200 mm

50–400

Drag for exploration or enter an exact value. Press Enter to apply and Escape to restore.

Product of inertia Ixy1500000 mm⁴

mm⁴

-100000000–100000000

Drag for exploration or enter an exact value. Press Enter to apply and Escape to restore.

physical model

Maximum principal

8.004e+7 mm⁴

Minimum principal

2.876e+7 mm⁴

Principal angle

-1.677°

Tensor determinant

2.302e+15 mm⁸

I_{1,2}=\frac{I_x+I_y}{2}\pm\sqrt{\left(\frac{I_x-I_y}{2}\right)^2+I_{xy}^2}

A physical area-inertia tensor must satisfy Ix≥0, Iy≥0, and Ixy²≤IxIy.

Model scope and verification

Scope: Educational rigid-body statics model using the selected geometry, stated idealizations, and displayed SI units.

Acceptance check: Check the governing equilibrium, compatibility, geometry, or limiting-condition statement before accepting the numerical result.

Rectangle and circle properties Parallel-axis theorem T-section with circular opening Radius-of-gyration comparison

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