Tensile stress
MPa
Mechanics · Bolts, preload and tightening
Bolt tensile stress and proof load calculator
Check a bolt using the total axial tensile force actually carried by that bolt and its tensile stress area.
Created v1.0
By Thibaut Grzelak, Mechanical Analysis Engineer
03
MetricResults
Proof-load utilization
%
Proof-load margin ratio
—
Proof load
kN
Tensile stress area
mm²
View calculation detailsFormulas, SI conversion, numerical substitution and resultsOpen ↓
Calculation note
Full calculation details
Fb is the total axial tensile force actually carried by one bolt. An external joint load requires a stiffness model to determine the bolt-load increment. Stress is nominal and excludes bending, shear, torsion, fatigue and local concentrations. Comparison with proof load is not a complete safety verdict.
01Formulas and symbols
Formulas used
At
π/4 × (d − 0.9382P)²Metric tensile stress area approximationσ
Fb / AtNominal tensile stressFproof
Sp × AtProof loadηproof
Fb / FproofProof-load utilizationMproof
Fproof / FbMargin ratio, N/A at zero load02Assumptions and limits
Scope of validity
- Fb is the total axial tensile force actually carried by one bolt.
- An external joint load requires a stiffness model to determine the bolt-load increment.
- Stress is nominal and excludes bending, shear, torsion, fatigue and local concentrations.
- Comparison with proof load is not a complete safety verdict.
03Validation example
Reference numerical case
- M12×1.75 gives At ≈ 84.27 mm².
- With Fb = 35 kN, σ ≈ 415.3 MPa.
- With Sp = 600 MPa, Fproof ≈ 50.56 kN, ηproof ≈ 69.23% and Mproof ≈ 1.444.
04Frequently asked questions
Questions about the calculation
Which force should be entered?
Enter the total axial tensile force actually carried by one bolt, including preload when it belongs to the checked state. A global external load cannot be allocated without a joint model.
Why is margin N/A at zero load?
The Fproof/Fb ratio would divide by zero. N/A is more faithful than infinity or a misleading badge.
Does utilization below 100% prove the joint is safe?
No. Other failure modes, preload scatter, fatigue, shear and applicable rules must also be checked.
05References
Technical references
- ISO 724:2023, ISO general purpose metric screw threads — Basic dimensions.
- ISO 898-1:2013, mechanical properties of steel bolts, screws and studs, confirmed in 2025.
- NASA RP-1228, Fastener Design Manual.