What Is Bearing Stress in Mechanical Joints?
Bearing stress is the compressive contact stress developed when a cylindrical pin, bolt, or rivet presses against the wall of a hole in a plate or lug. It is one of the first checks engineers perform when sizing bolted and pinned connections because it directly affects hole deformation, permanent set, joint looseness, and eventual failure risk.
In design practice, bearing stress is usually treated as an average stress over a projected contact area rather than a true Hertzian contact distribution. That simplification is practical, conservative for many cases, and easy to use in hand calculations. For a single plate with thickness t and pin diameter d, the projected area is d×t, and average bearing stress becomes load divided by that area.
Even though this is a simple equation, joint reliability depends on the full system. The hole clearance, fastener fit, edge distance, material ductility, cyclic loading, and manufacturing tolerance all influence the local stress concentration and failure mode sequence. A safe design does not rely on bearing stress alone, but bearing stress remains a core screening metric.
Bearing Stress Formula and Units
The fundamental average bearing stress formula used by this page is:
Variable Definitions
- σb: average bearing stress (Pa, MPa, or psi)
- F: applied load transferred through the pin/bolt (N, kN, or lbf)
- d: pin or bolt diameter (mm or in)
- t: connected plate thickness (mm or in)
Required Dimension Rearrangements
- Required thickness:
t_required = F / (σ_allow × d) - Required diameter:
d_required = F / (σ_allow × t)
These rearranged forms are included in the calculator when an allowable bearing stress is entered. This helps you size the geometry to meet stress limits directly.
Practical Bearing Stress Design Guide
1) Understand the Load Path
Ensure the load used in the equation is the actual force transmitted through the fastener-hole interface for the specific member you are checking. In multi-bolt groups, force distribution may be nonuniform because of eccentricity, stiffness differences, or preload behavior.
2) Choose the Correct Diameter
Use the effective diameter responsible for bearing contact. In many designs this is the nominal shank diameter, but verify code requirements and tolerance class. Oversized or slotted holes can significantly alter bearing behavior and allowable values.
3) Verify Plate Thickness and Material Condition
Thickness tolerance, corrosion allowance, and wear can reduce effective section. For critical joints, assess minimum thickness after fabrication and service exposure, not just nominal catalog values.
4) Compare Against Allowable Bearing Stress
Allowable limits should come from governing standards, test-backed material data, and your organization’s safety policy. If using yield-based criteria, include a realistic factor of safety for load uncertainty and manufacturing variation.
5) Check Complementary Failure Modes
A joint can pass bearing stress and still fail in another way. Common additional checks include:
- Fastener shear failure
- Net-section tension through the plate
- Shear-out or tear-out at small edge distance
- Block shear in connected members
- Fatigue at stress concentrations under cyclic loads
6) Consider Deformation and Serviceability
Even if ultimate strength is adequate, excessive bearing can ovalize holes and create looseness, causing alignment issues, vibration noise, and long-term damage progression. Serviceability limits may govern before strength limits in precision assemblies.
Typical Allowable Bearing Stress Ranges (Reference-Style Overview)
The following table is a broad, non-code-specific overview for conceptual estimation only. Always use official design standards and certified material values for final engineering decisions.
| Material Category | Indicative Allowable Bearing Stress | Notes |
|---|---|---|
| Mild carbon steel plates | 140–250 MPa | Depends on grade, load duration, and code basis. |
| High-strength structural steel | 200–400 MPa | Often controlled by connection detailing and edge distance. |
| Aluminum alloys | 70–220 MPa | Strongly grade and temper dependent; fatigue sensitivity may control. |
| Engineering plastics/composites | 15–120 MPa | Creep, temperature, and anisotropy can dominate behavior. |
Use this only for early-stage screening. Final design values must follow the applicable code and project specification.
Worked Bearing Stress Example
Suppose a steel plate is connected with a 12 mm pin and carries a 25 kN load. Plate thickness is 8 mm.
- Load, F = 25 kN = 25,000 N
- Diameter, d = 12 mm
- Thickness, t = 8 mm
- Projected area, A = d×t = 96 mm²
- Bearing stress, σb = 25,000 / 96 = 260.4 N/mm² = 260.4 MPa
If your allowable bearing stress is 180 MPa, the safety factor on stress basis is 180/260.4 = 0.69, which is not acceptable. You must increase thickness, increase pin diameter, reduce load, or redesign the connection layout.
Common Mistakes to Avoid
- Mixing units: Using kN with mm without proper conversion can produce errors by orders of magnitude.
- Ignoring edge distance: Bearing may look acceptable while tear-out governs the design.
- Using nominal thickness only: Real minimum thickness after tolerances or corrosion can be lower.
- Assuming equal load sharing: Multi-fastener joints rarely split load perfectly in real assemblies.
- No fatigue check: Repeated loading can fail joints far below static ultimate limits.
Frequently Asked Questions
Is bearing stress the same as contact stress?
In strict mechanics terms, true contact stress is nonuniform and can be analyzed with advanced contact models. In connection design, “bearing stress” often means an average projected stress over d×t, which is a practical engineering approximation.
What safety factor should I use for bearing stress?
It depends on code requirements, reliability targets, load uncertainty, material variability, and consequence of failure. Many organizations define minimum factors for static and fatigue applications separately.
Does bolt preload eliminate bearing stress?
No. Preload can transfer some load through friction before slip, but once slip occurs or if load exceeds frictional capacity, bearing at the hole becomes active. Many joints should be checked for both slip and bearing limit states.
Can I use this calculator for rivets and pins?
Yes, for first-pass projected bearing stress checks using d×t. For final design, apply the relevant standard and include joint-specific factors and additional failure mode checks.
Conclusion
A bearing stress calculator is one of the most efficient tools for early and intermediate mechanical joint design. By entering load, pin diameter, and plate thickness, you can immediately see whether the interface stress is within your allowable range. For robust design, combine this check with edge distance rules, net-section checks, shear checks, and fatigue considerations. Use the calculator above to iterate quickly, then finalize against your governing engineering code and project requirements.