Statics

Overview

Engineering reference data for Statics 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

Material Properties and Elastic Constants

Understanding the interrelationship between material properties is crucial for statics analysis. These constants define how materials deform under load.

• Young's Modulus (E) measures tensile/compressive stiffness (resistance to elastic strain).
• Shear Modulus (G or Modulus of Rigidity) measures resistance to shear deformation.
• Poisson's Ratio (ν) describes the ratio of transverse strain to axial strain. For most metals, it typically ranges between 0.25 and 0.35.
• These constants are related for isotropic, linear-elastic materials: G = E / [2(1 + ν)]

Equilibrium and Support Reactions

A body is in static equilibrium when the net force and net moment acting on it are zero. This is the foundational condition for solving most statics problems.

• *Σ F = 0 (Sum of all forces equals zero)
• *Σ M = 0 (Sum of all moments equals zero)

Support reactions are the forces and moments exerted by supports (like pins, rollers, or fixed connections) to maintain equilibrium. Calculating these reactions is typically the first step in analyzing structures like beams and trusses.

Stress and Deformation

• Stress (σ) is the internal resistance force per unit cross-sectional area (σ = F/A). It is measured in Pascals (Pa) or psi.
• Strain (ε) is the measure of deformation, defined as the change in length per original length (ε = ΔL/L₀). It is dimensionless.
• For linear elastic materials, stress and strain are proportional up to the yield point, a relationship governed by Hooke's Law.
• Deformation (Deflection) in structural members like beams depends on the applied loads, material stiffness (E), member geometry (I, A), and span length.

References

• Original Source