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Engineering formulas

A compact index of engineering mechanics and strength of materials formulas grouped by topic.

Membrane Theory

Tension and Compression

Hooke's Law in Uniaxial Tension or Compression
\(σ = Eε\)

Mechanical Properties of Materials

Hooke's Law in Uniaxial Tension or Compression
\(σ = Eε\)

Stresses in Bending

Eccentric Compression

Section Kern under Eccentric Compression
\(rk = d / 8\)

Tensile Test Diagram and Characteristic Points

Hooke's Law in Uniaxial Tension or Compression
\(σ = Eε\)

Three-Dimensional Force Systems

Force Magnitude from Three Components
\(F = √(Fₓ² + Fᵧ² + F_z²)\)

Sliding Friction. Coulomb's Laws

Limiting Dry Friction Force
\(Ffr,max = μN\)

Shear and Torsion

Deflections in Bending

Beam Curvature, Bending Moment, and Flexural Rigidity
\(M = EI / ρ\)

Combined Bending and Torsion

Force Projections

Projection of a Force onto an Axis
\(Fₓ = F cos α\)

Elastic Properties of Materials

Hooke's Law in Uniaxial Tension or Compression
\(σ = Eε\)

Parallel-Axis Theorem and Composite Sections

Parallel-Axis Theorem for Second Moments of Area
\(I = Ic + Aa²\)

Moment of a Force About a Point and an Axis

Moment of a Force About a Point
\(M = Fd\)

Rolling Resistance

Rolling-Resistance Moment
\(Mrr = Nδ\)

Geometric Properties of Plane Areas

Parallel-Axis Theorem for Second Moments of Area
\(I = Ic + Aa²\)

Force Couples and Couple Moment

Moment of a Force Couple
\(M = Fd\)

Bending

Addition of Forces. Resultant of a Force System

Magnitude of a Resultant from Two Components
\(R = √(Rₓ² + Rᵧ²)\)

Distributed Loads and Their Resultants

Resultant of a Uniformly Distributed Load
\(R = qL\)

Combined Loading

Equivalent Stress under Combined Bending and Torsion
\(σeq = √(σb² + 3τt²)\)

Stability of Compressed Members

Dynamic and Cyclic Loading

Dynamic Factor for Vertical Impact
\(δmax = δst + √(δst² + 2hδst)\)

Shell Analysis

Contact of Two Bodies: Types and Geometry

Reduced Radius of Curvature in Hertz Contact
\(1/R* = 1/R1 + 1/R2\)

Pure Shear and Design of Joints (Riveted and Welded)

Hooke's Law in Shear
\(τ = Gγ\)

Contact Stresses

Torsion of Solid and Hollow Circular Shafts

Design of Helical Springs

Polar Properties of Solid and Hollow Circular Sections
\(Jp = πd⁴ / 32\)

Power Transmission by Shafts

Stress and Angle of Twist of a Circular Shaft
\(φ = TL / (GJp)\)

Differential Equation of the Elastic Curve

Beam Curvature, Bending Moment, and Flexural Rigidity
\(M = EI / ρ\)

Initial Parameter Method (Macaulay's Method)

Beam Curvature, Bending Moment, and Flexural Rigidity
\(M = EI / ρ\)

Hertz Theory: Main Assumptions and Formulas

Euler's Formula for Critical Load

Limits of Applicability of Euler's Formula (Yasinsky Formula)

Applicability Limit of Euler's Buckling Formula
\(λlim = π√(E / σp)\)

Contact of Spheres and Spherical Surfaces

Impact Loading Calculations

Dynamic Factor for Vertical Impact
\(δmax = δst + √(δst² + 2hδst)\)

Contact of Cylinders and Rollers

Reduced Radius of Curvature in Hertz Contact
\(1/R* = 1/R1 + 1/R2\)