Radius Gyration Structural Engineering

Overview

Engineering reference data for Radius Gyration Structural Engineering in statics.

Key Formulas

Equilibrium

$\sum F = 0, \quad \sum M = 0$

Sum of forces and moments equals zero for a body in equilibrium.

Stress

$\sigma = \frac{F}{A}$

Force per unit area.

Moment

$M = F \cdot d$

Force × perpendicular distance.

Variables

Radius of Gyration for Common Cross-Sections

The following provides specific formulas for calculating the radius of gyration (r) for various common structural sections, building upon the general definition.

Formulas by Section Shape

Rectangle with axis in center:

$$r_{max} = 0.289 h$$

where h is the height of the rectangle perpendicular to the axis.

Rectangle with eccentric axis:

$$r = 0.577 h$$

Rectangle with tilted axis (method I):

$$r = \frac{bh}{\sqrt{6(b^2 + h^2)}}$$

where b is the base and h is the height of the rectangle.

Rectangle with tilted axis (method II):

$$r = \sqrt{\frac{(h^2 \cos^2 \alpha) + (b^2 \sin^2 \alpha)}{12}}$$

where α is the angle of the axis tilt.

Hollow Square (or Hollow Rectangle):

$$r = \sqrt{\frac{H^2 + h^2}{12}}$$

where H is the outer dimension and h is the inner dimension.

Equilateral Triangle with eccentric axis:

$$r = \frac{h}{\sqrt{18}}$$

where h is the height of the triangle.

General Triangle:

$$r = \frac{h}{\sqrt{6}}$$

Quick Reference Table

References

• Original Source