engineering

Combined Loading Calculator

Calculate Von Mises stress, max shear, and principal stresses under combined axial, bending, and torsional loads

Combined Loading Calculator

Evaluate a point under simultaneous axial, bending, and torsional loading using Von Mises and max-shear criteria.

Normal stress from axial load: σ = F/A

Bending stress at outer fiber: σ = Mc/I

Shear stress from torque: τ = Tr/J

Combined Normal Stress

σ_total = σ_axial + σ_bending = 50.00 + 80.00 MPa
σ_total = 130.000 MPa

Von Mises Equivalent Stress

σ_VM = √(σ_total² + 3τ²)147.309 MPa
Factor of Safety (Von Mises)n = 1.697

Von Mises criterion: PASS (σ_VM < S_y)

Maximum Shear Stress

τ_max = √((σ_total/2)² + τ²) = √((130.00/2)² + 40.00²)
τ_max = 76.322 MPa

Principal Stresses

σ₁ (Maximum)

141.322 MPa

σ₂ (Minimum)

-11.322 MPa

σ₁,₂ = σ_total/2 ± √((σ_total/2)² + τ²)
σ₁,₂ = 65.00 ± 65000000.000 MPa

Summary of Formulas

σ_total = σ_axial + σ_bending (worst-case outer fiber)
σ_VM = √(σ_total² + 3τ_torsion²) — Von Mises distortion energy
τ_max = √((σ_total/2)² + τ_torsion²) — Max shear stress theory
σ₁,₂ = σ_total/2 ± τ_max — In-plane principal stresses
n = S_y / σ_VM — Von Mises factor of safety

How to Use This Calculator

1

Enter your input values

Fill in all required input fields for the Combined Loading Calculator. Most fields include unit selectors so you can work in your preferred unit system.

2

Review your inputs

Double-check that all values are correct and that you have selected the right units for each field. Incorrect units are the most common source of calculation errors.

3

Read the results

The Combined Loading Calculator instantly computes the output and displays results with units. All calculations happen in your browser — no loading time and no data sent to a server.

Formula Reference

Combined Loading Calculator Formula

See calculator inputs for the governing equation

Variables: All variables and their units are labeled in the calculator interface above.

When to Use This Calculator

  • •Use the Combined Loading Calculator when solving homework or exam problems that require quick numerical verification of your hand calculations.
  • •Use it during the design phase to rapidly iterate on parameters before running detailed finite element simulations.
  • •Use it when reviewing a colleague's calculation or checking a vendor's data sheet for plausibility.
  • •Use it to generate reference data for a technical report or presentation without manual computation.

Related Calculators

Stress Calculator

Calculate normal stress (σ = F/A) and shear stress (τ = V/A) with unit conversions

Strain Calculator

Calculate axial strain, percentage strain, and lateral strain with Poisson's ratio

Hooke's Law Calculator

Solve for stress, modulus, or strain using Hooke's Law for normal and shear loading

Mohr's Circle Calculator

Calculate principal stresses, maximum shear stress, and principal angle from a 2D stress state

Beam Bending Calculator

Calculate maximum deflection, bending moment, and reactions for simply supported, cantilever, and fixed-fixed beams

Beam Bending Stress Calculator

Calculate bending stress (σ = My/I) for rectangular, circular, and I-beam cross-sections