Stiffness

Overview

Engineering reference data for Stiffness in miscellaneous.

Key Formulas

Unit Conversion

$y = x \cdot k$

Multiply by conversion factor.

Linear Interpolation

$y = y_1 + \frac{(x - x_1)(y_2 - y_1)}{x_2 - x_1}$

Estimate between two known points.

Percentage

$p = \frac{\text{part}}{\text{whole}} \times 100\%$

Part as fraction of whole.

Variables

Types of Stiffness

Stiffness manifests differently depending on the type of loading and deformation:

Axial Stiffness relates to elongation or compression along the member's axis: $k_{axial} = \frac{EA}{L}$ where $E$ is Young's modulus, $A$ is cross-sectional area, and $L$ is member length.

Torsional Stiffness resists angular twist: $k_{torsion} = \frac{GJ}{L}$ where $G$ is shear modulus and $J$ is polar moment of inertia.

Bending Stiffness resists lateral deflection of beams: $k_{bending} = \frac{48EI}{L^3}$ (simply supported beam with central point load)

Stiffness in Series and Parallel

When combining multiple springs or elastic elements:

Series Configuration: $\frac{1}{k_{total}} = \frac{1}{k_1} + \frac{1}{k_2} + \cdots + \frac{1}{k_n}$

The total stiffness is always less than the softest individual element.

Parallel Configuration: $k_{total} = k_1 + k_2 + \cdots + k_n$

The total stiffness is the sum of all individual stiffness values.

Key Properties

• Stiffness is not an intrinsic material property — it depends on geometry and boundary conditions
• Higher stiffness means less deformation under a given load
• Stiffness relates directly to natural frequency: $\omega_n = \sqrt{k/m}$ for a simple mass-spring system

References

• Original Source