Roymech engineering encyclopedia

Bolt Combined Stress Calculator




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Use this bolt combined stress calculator to estimate the equivalent stress in a bolt subject to both tensile load and shear load. The calculator uses the Von Mises stress method to combine tensile stress and shear stress, then compares the result against a selected allowable or yield stress.

What does this calculator do?

This calculator checks a bolt subject to combined axial tension and transverse shear. It calculates bolt area, tensile stress, shear stress, Von Mises equivalent stress, design allowable stress, utilisation and factor of safety.

The calculator provides:

  • bolt cross-sectional area
  • tensile stress from axial load
  • shear stress from transverse load
  • Von Mises equivalent stress
  • design allowable stress
  • factor of safety
  • utilisation percentage
  • pass/fail result
  • worked calculations

This calculator is useful for bolts where direct shear and axial tension act together, such as bracket connections, bolted supports, lifting plates and mechanically loaded joints.

Engineering note: This calculator is intended for preliminary engineering calculations and educational use. It assumes a simplified combined tensile and shear stress state in the bolt. Final bolted joint design should also consider preload, fatigue, thread engagement, bearing stress, plate shear, prying action, joint slip, bolt grade and the relevant design standard.

How to Use the Calculator

  1. Enter the tensile load, Ft. This is the axial tensile force acting along the bolt.
  2. Enter the shear load, Fs. This is the transverse shear force acting across the bolt.
  3. Select the force unit. Loads may be entered in newtons or kilonewtons.
  4. Enter the bolt diameter, d. Use the effective diameter at the critical section. If the thread is critical, use an appropriate stress area or reduced diameter.
  5. Enter the allowable or yield stress. This value is used as the stress limit for the simplified Von Mises check.
  6. Enter the safety factor. The calculator divides the allowable or yield stress by the safety factor to obtain the design allowable stress.
  7. Click calculate. The calculator gives the equivalent stress, utilisation and pass/fail result.

Bolt Combined Stress Diagram

Bolt combined stress calculator diagram showing tensile force, shear force, bolt diameter and Von Mises equivalent stress calculation
Bolt subject to combined tensile and shear loading, checked using the Von Mises equivalent stress method.

Formulae Used

Bolt cross-sectional area:

A = πd24

Tensile stress:

σ = FtA

Shear stress:

τ = FsA

Von Mises equivalent stress:

σvm = √(σ2 + 3τ2)

Design allowable stress:

σdesign = σallowSF

Factor of safety:

FoS = σallowσvm

Utilisation:

Utilisation = σvmσdesign × 100%

Variables

Symbol Description Units
Ft Axial tensile load N
Fs Transverse shear load N
d Bolt diameter or effective diameter mm
A Bolt cross-sectional area mm²
σ Tensile stress N/mm²
τ Shear stress N/mm²
σvm Von Mises equivalent stress N/mm²
σallow Allowable or yield stress N/mm²
SF Safety factor -

Calculator Inputs

Results

Enter the bolt loading and dimensions, then click calculate.

Understanding the Results

Result Meaning
Tensile stress The axial tensile stress in the bolt caused by the tensile load.
Shear stress The average shear stress in the bolt caused by the transverse shear load.
Von Mises equivalent stress A combined stress value used to compare tensile and shear loading against a single stress limit.
Design allowable stress The selected allowable or yield stress divided by the safety factor.
Factor of safety The ratio of allowable or yield stress to the calculated Von Mises stress.
Utilisation The Von Mises equivalent stress divided by the design allowable stress. A value below 100% passes this simplified check.

Calculator Limitations

This calculator checks a simplified combined tensile and shear stress condition in a bolt. It does not check every possible bolted joint failure mode.

This Calculator Includes This Calculator Does Not Include
Tensile stress from axial load Bolt preload effects
Shear stress from transverse load Joint slip or friction-grip behaviour
Von Mises equivalent stress Bearing stress between bolt and plate
Factor of safety and utilisation Plate shear, tear-out or net section failure
Simple circular bolt area Fatigue, prying action or thread stripping

For bolt shear stress only, use the Bolt Shear Stress Calculator.

For bolt bearing stress, use the Bolt Bearing Stress Calculator.

For eccentric bolt group forces, use the Bolt Group Eccentric Load Calculator.

Bolt Combined Stress Calculation Notes

For ductile metallic bolts, the Von Mises stress method is commonly used to combine tensile stress and shear stress into a single equivalent stress. This equivalent stress can then be compared with an allowable or yield stress.

This calculator uses the circular bolt area based on the entered diameter. If the threaded portion of the bolt is critical, the tensile stress area or thread root area may be more appropriate than the nominal shank diameter.

A complete bolted joint design may also need to consider preload, joint stiffness, fatigue, bolt grade, thread engagement, nut strength, bearing stress, plate shear, edge distance and design standard requirements.

For further bolted joint theory, see the RoyMech reference page: Bolted Joint Design and Calculations.

For the full calculator section, see: Bolted Joint Calculators.

Bolt Combined Stress Calculator FAQ

How do you calculate combined stress in a bolt?

Combined stress in a bolt can be estimated using the Von Mises equivalent stress formula:

σvm = √(σ2 + 3τ2)

where σ is tensile stress and τ is shear stress.

What is Von Mises stress?

Von Mises stress is an equivalent stress used to assess ductile materials under combined loading. It allows tensile and shear stresses to be compared against a single allowable or yield stress.

When should combined bolt stress be checked?

Combined bolt stress should be checked when a bolt is subject to both axial tensile load and transverse shear load.

Should I use bolt shank area or thread stress area?

Use the area at the critical section. If the plain shank is critical, the shank diameter may be used. If the threaded portion is critical, the tensile stress area or thread root area may be more appropriate.

Does this calculator include preload?

No. This calculator does not include preload effects. Preload can significantly change the stress state in a bolted joint and should be considered separately where relevant.

Can this calculator be used for final design?

This calculator is intended for preliminary engineering calculations and educational use. Final bolted joint design should be checked against the relevant design standard, bolt grade, preload method, fatigue requirements and safety factors.