Plate with circular opening

Calculate signed-area, polygon, density-weighted, and line centroids with explicit invalid-geometry checks.

Advanced engineering statics simulation

Centroids and Centers of Gravity Suite

Validated signed area, density weighting, polygon geometry, and length-weighted wire centroids.

Simulation

Treat a fully contained opening as negative area; invalid openings are rejected instead of silently subtracting a full circle.

Primary width160 mm

60–300

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

Primary height120 mm

40–260

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

Opening diameter40 mm

10–180

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

Opening offset from plate center25 mm

-140–140

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

valid geometry

Signed area

17943.36

mm²

x centroid

78.249 mm

y centroid

60.000 mm

Component	measure	xi	yi	measure·xi	measure·yi
Plate	19200.00	80.00	60.00	1536000.00	1152000.00
Circular opening	-1256.64	105.00	60.00	-131946.89	-75398.22

\bar{x}=\frac{\sum m_i x_i}{\sum m_i},\qquad \bar{y}=\frac{\sum m_i y_i}{\sum m_i}

For uniform areas use mᵢ=Aᵢ; use negative area for a fully contained hole, density-weighted area for nonuniform materials, and length for wires.

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.

Composite-area centroid builder Parameter-edited polygon centroid Density-weighted center of gravity Straight and curved wire centroid

Related simulations