Parallel-axis theorem

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

Separate the centroidal term from the transfer term Ad² for a rectangle.

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.

Reference-axis offset80 mm

0–220

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

physical model

Centroidal Ix

8.000e+7 mm⁴

Transfer Ad²

1.536e+8 mm⁴

Reference-axis Ix

2.336e+8 mm⁴

Offset

80.0 mm

I=I_c+Ad^2,\qquad J_O=I_x+I_y,\qquad k=\sqrt{\frac{I}{A}}

Negative components are permitted only for openings that are fully contained within the parent section.

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 T-section with circular opening Principal axes and Mohr's circle Radius-of-gyration comparison

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