2025-08-21 12 min
Bearing Stress Calculator
Calculate bearing stress (σ_b = F/(d {"×"} t)) for bolted, riveted, and pinned connections in mechanical engineering.
Calculator
Unit System
Preset Values
Applied Force(N) Help
N
Axial force transmitted through the connection
Fastener Diameter(mm) Help
mm
Diameter of bolt, rivet, or pin
Plate Thickness(mm) Help
mm
Thickness of the connected member
Decimal Precision
Results update live as you type
Results
Normal
Bearing Stress
156.25MPa
Bearing Area
96mm²
Visualizations
Results Overview
156.3MPaBearing Stress
96MPaBearing Area
Formula
Bearing stress equals the applied force divided by the projected bearing area (fastener diameter times plate thickness).
σ_b = F / (d {"×"} t)
Variables
| Symbol | Name | Unit | Description |
|---|---|---|---|
| σ_b | Bearing Stress | MPa | Compressive contact stress on the projected area |
| F | Applied Force | N | Axial force transmitted through the connection |
| d | Fastener Diameter | mm | Diameter of the bolt, rivet, or pin |
| t | Plate Thickness | mm | Thickness of the connected member |
Explanation
Bearing stress is the compressive contact stress between a fastener and the connected plate. The projected area approach (d {"×"} t) provides the average bearing stress. Peak local stress can be 2-3 times higher at the hole edge.
Derivation
Starting from stress = force/area: The projected contact area between a cylindrical fastener of diameter d and a plate of thickness t is A_bearing = d {"×"} t. Therefore σ_b = F / (d {"×"} t). This is a simplification that gives the average bearing stress over the projected area.
Step-by-Step Calculation
Follow each step to understand how the result is calculated from your inputs.
Step 1
Identify the applied force F, fastener diameter d, and plate thickness t.
Result: Parameters identified
Step 2
Calculate the projected bearing area: A_b = d {"×"} t.
Result: Area computed
Step 3
Apply the formula: σ_b = F / A_b.
Result: Bearing stress calculated
Step 4
Compare against allowable bearing stress from the relevant design code.
Result: Safety assessment complete
Final Answer
156.25
Worked Examples
See how the calculator works with different scenarios.
Scenario
An M12 bolt connects two 8 mm thick A36 steel plates with a 15 kN load. Calculate the bearing stress.
Inputs
Force (F):15,000 N
Diameter (d):12 mm
Thickness (t):8 mm
Calculation
A_b = 12 {"×"} 8 = 96 mm²; σ_b = 15,000 / 96
Result
σ_b = 156.25 MPa
Interpretation
A36 steel has an allowable bearing stress of approximately 396 MPa (1.5 {"×"} F_u = 1.5 {"×"} 400). Safety factor = 396/156 = 2.54, which is adequate.
Understanding Your Result
Your Result: Bearing Stress: 156.25 MPa
Typical range: Mild steel bearing: 200-600 MPa. High-strength steel: 400-1000 MPa. Aluminum alloys: 200-500 MPa. Stainless steel: 300-800 MPa.
What This Means
Bearing stress (σ_b = F/(d {"×"} t)) measures the compressive contact pressure between a fastener (bolt, rivet, pin) and the hole wall in the connected plate. It tells you how intensely the plate material resists being crushed by the fastener.
Why It Matters
If bearing stress exceeds the plate material's bearing strength, the hole will elongate, the joint will loosen, and the connection will fail. Bearing failure is one of the three primary failure modes in bolted/riveted connections (along with shear and tensile failure).
Professional Interpretation
Compare calculated bearing stress against the allowable bearing stress from the applicable design code (AISC, Eurocode, etc.). Ensure edge distance and spacing requirements are met to develop full bearing capacity.
Recommendations
- •Always check both bearing on the plate and shear on the bolt
- •Verify minimum edge distance per design code requirements
- •Use the thinner plate thickness when plates differ
- •Consider bearing-bypass interaction in multi-fastener joints
Educational Content
Introduction
Bearing stress is a critical concept in the design of bolted, riveted, and pinned connections. It measures the contact pressure between a fastener and the connected material.
Concept Explanation
When a bolt or rivet transfers load between two plates, the fastener presses against the wall of the hole. The projected contact area is d {"×"} t, and the average bearing stress is σ_b = F/(d {"×"} t). This simplified approach is used in most engineering design codes.
Applications
▸Structural steel connections
▸Bridge design
▸Machine frame assembly
▸Aerospace airframe joints
▸Boiler and pressure vessel construction
▸Automotive chassis connections
Benefits
- •Simple calculation using basic parameters
- •Direct comparison with material bearing strength
- •Applicable to all fastener types (bolts, rivets, pins)
- •Foundation for connection design codes
Limitations
- •Assumes uniform stress distribution (peak stress is higher)
- •Does not account for stress concentrations
- •Edge distance and spacing effects require separate checks
- •Not applicable to press-fit or interference fit connections
Best Practices
- •Check bearing on the thinnest plate in the connection
- •Verify minimum edge distance per design code
- •Consider bolt grade and shear capacity alongside bearing
- •Use fatigue analysis for cyclic bearing loads
Common Misconceptions
Myth: Bearing stress acts on the bolt
Truth: Bearing stress is the compressive stress on the plate (or connected member) from the bolt. The bolt itself experiences shear stress, not bearing stress.
Myth: Larger bolts always reduce bearing stress
Truth: Larger bolts increase the bearing area (d {"×"} t), but they also create larger holes that reduce the net section area of the plate, potentially causing tensile failure.
Practical Tips
- •Memorize: 1 MPa = 1 N/mm², so bearing stress in N/(mm {"×"} mm) is directly in MPa
- •Use the thinner plate thickness when two plates differ in thickness
- •Check bearing before shear — bearing failure is often the governing mode
- •For edge bolts, use reduced bearing allowable per AISC (1.2 {"×"} F_u vs 1.5 {"×"} F_u for inner bolts)
- •Bearing stiffness matters for connection slip behavior in slip-critical joints
Common Mistakes
Using bolt area (πd²/4) instead of projected area (d {"×"} t)
Bearing stress uses the projected rectangular area d {"×"} t, not the circular cross-sectional area of the bolt.
Ignoring the thinner plate
Always check bearing on the thinnest connected member, as it will have the highest bearing stress.
Confusing bearing stress with shear stress
Bearing stress acts on the plate hole wall; shear stress acts through the bolt cross-section. Both must be checked independently.
Assumptions
This calculator makes the following assumptions to provide estimates:
Uniform Bearing Stress: The formula assumes uniform stress distribution over the projected area. In reality, peak stress at the hole edge is 2-3 times the average value.
Rigid Fastener: The bolt or rivet is assumed to be rigid relative to the plate. In practice, fastener deformation can redistribute bearing stresses.
Single Shear Plane: The basic formula applies to a single bearing interface. Double shear connections have two bearing planes that must be checked separately.
Limitations
Be aware of these limitations when using this calculator:
Edge Distance Effects: Insufficient edge distance can cause tear-out failure before full bearing capacity is reached. Minimum edge distances must be verified separately.
Fatigue Loading: Under cyclic loading, fatigue crack initiation at the hole edge may occur well below the static bearing strength.
Thin Plates: Very thin plates (t < d) may fail by bearing deformation or punching shear before reaching the calculated bearing capacity.
Frequently Asked Questions
Answers to common questions about this calculator.
What is bearing stress?
Bearing stress (σ_b) is the contact pressure between a fastener (bolt, rivet, pin) and the material it passes through. It is calculated as σ_b = F / (d {"×"} t), where F is the applied force, d is the fastener diameter, and t is the plate thickness. It represents the compressive stress on the projected contact area.
What is the formula for bearing stress?
The formula is σ_b = F / (d {"×"} t), where σ_b is bearing stress in MPa, F is the applied shear or tensile force in Newtons, d is the bolt or rivet diameter in mm, and t is the connected plate thickness in mm. The result is directly in N/mm² which equals MPa.
How does bearing stress differ from shear stress?
Bearing stress acts on the projected contact surface between a fastener and the connected member. Shear stress acts parallel to a cross-section (e.g., through the bolt shank). A bolt connection must be checked for both bearing failure on the plate and shear failure on the bolt.
What is bearing stress in a bolted connection?
In a bolted connection, bearing stress is the compressive stress between the bolt shank and the wall of the hole in the connected plate. It arises when a tensile load pulls the plates together, pressing the bolt against the hole edge. The projected area for calculation is d {"×"} t.
What is bearing stress in a riveted joint?
In riveted joints, bearing stress is the contact pressure between the rivet shank and the plate hole. It is calculated identically to bolted joints: σ_b = F / (d {"×"} t). Riveted joints are common in structural steel, bridges, and boiler construction.
What are typical allowable bearing stresses?
Allowable bearing stress depends on the material and design code. For structural steel (AISC), the allowable bearing stress is typically 1.2 {"×"} F_u (ultimate tensile strength) for edge bolts and 1.5 {"×"} F_u for inner bolts. For aluminum, values are typically 1.5 {"×"} F_u.
What is the bearing stress concentration factor?
The bearing stress distribution is not uniform around the fastener hole. Peak bearing stress can be 2-3 times the average value near the hole edge. Some design codes account for this with stress concentration factors, though most standard designs use the average bearing stress approach.
What is the relationship between bearing stress and bolt preload?
Bolt preload creates compressive clamping force between joined plates. When external shear load is applied, friction between the plates resists the load. Bearing stress only develops when the friction capacity is exceeded and the bolt contacts the hole wall.
How does edge distance affect bearing strength?
Edge distance is the distance from the center of the bolt hole to the nearest plate edge. Insufficient edge distance can cause plate tear-out before full bearing capacity is reached. Most codes specify minimum edge distances of 1.5 {"×"} to 2.0 {"×"} the bolt diameter.
What is the bearing yield strength of steel?
The bearing yield strength is typically 1.5 to 2.0 times the tensile yield strength of the plate material. For ASTM A36 steel (σ_y = 250 MPa), the bearing yield strength is approximately 375-500 MPa. The bearing ultimate strength is typically 1.5 to 2.0 times F_u.
What is the difference between bearing stress and contact stress?
Bearing stress refers to the compressive stress on the projected area of a fastener in a hole (a simplified 2D calculation). Contact stress (Hertzian stress) is the 3D stress state at the surface of two curved bodies in contact (e.g., gear teeth, rolling bearings).
How do I calculate bearing stress in a pin joint?
For a pin joint: σ_b = F / (d {"×"} t), where d is the pin diameter and t is the thickness of the loaded member. If the pin passes through a clevis with two lugs, the bearing area doubles: σ_b = F / (2 {"×"} d {"×"} t).
What is the effect of hole size on bearing stress?
Larger holes reduce the bearing area (d increases, but if oversized, the contact geometry changes). Standard holes are nominally d + 0.8 mm for bolts. Oversized or slotted holes reduce the effective bearing length and should be checked carefully.
Can bearing stress cause fatigue failure?
Yes. Cyclic bearing loading can initiate fatigue cracks at the hole edge where peak bearing stress occurs. This is particularly critical in connections subjected to repeated load reversals, such as bridge connections and machine frames.
What is bearing stress in a press-fit connection?
In press-fit (interference fit) connections, bearing stress arises from the radial pressure between the shaft and the hub. It is calculated differently using the interference amount, shaft diameter, and elastic properties of both materials (Lame equations).
How do I design for bearing in aluminum?
Aluminum has lower bearing strength than steel. Use alloy-specific bearing allowable values (e.g., 6061-T6: bearing yield ~380 MPa). Apply appropriate safety factors (typically 2.0-3.0 for aerospace). Consider bearing-bypass interaction in multi-fastener joints.
What is bearing-bypass stress?
In multi-fastener joints, the total tensile load is shared among fasteners. The critical fastener experiences the full bearing load, while the plate cross-section at that fastener also carries the remaining load (bypass load). The combined effect must be checked.
What standards reference bearing stress?
Key standards include: AISC 360 (structural steel), Eurocode 3 Part 1-8, ASME BPVC Section VIII, ASTM A325/A490 bolt standards, and NAS (aerospace) standards for fastener design.
How is bearing strength affected by plate thickness?
Bearing strength is directly proportional to plate thickness (bearing area = d {"×"} t). Thicker plates distribute the load over a larger area, reducing bearing stress. However, very thin plates may fail by bearing deformation before reaching full capacity.
What is the minimum bearing length for a bolt?
The minimum bearing length (plate thickness) is typically 1.0 to 1.5 {"×"} the bolt diameter for steel connections. Below this, bearing deformation becomes excessive. Some codes specify a minimum of 1.2 {"×"} d for structural applications.
What is the relationship between bearing stress and friction?
In slip-critical connections, friction between the faying surfaces resists the applied load. Bearing stress only develops when the friction capacity ( {"μ} {"×"} n {"×"} F_bolt) is exceeded. Slip-critical connections are used in fatigue-sensitive and high-seismic applications.
How does temperature affect bearing strength?
Elevated temperatures reduce bearing strength similar to tensile strength. At 300°C, steel bearing strength drops approximately 20-30%. At cryogenic temperatures, bearing strength typically increases but ductility decreases. Temperature-dependent values should be used for extreme conditions.
What is the bearing capacity of a single bolt?
Bolt bearing capacity = min(σ_b_allowable {"×"} d {"×"} t, shear capacity of bolt). The bearing capacity depends on both the plate material and the bolt grade. For an M16 grade 8.8 bolt in A36 steel (t=10 mm): bearing capacity ≈ 192 kN.
What is the difference between bearing stress and punching shear?
Bearing stress acts on the projected contact area (d {"×"} t). Punching shear is the through-thickness shear failure around the bolt hole perimeter (τ = F / ({π} {"×"} d {"×"} t)). Both must be checked in thin plate connections.
How do slotted holes affect bearing stress?
Slotted holes reduce the effective bearing length and create eccentric loading. The bearing area is based on the slot width (typically equal to bolt diameter), but the effective contact length may be reduced. Design codes specify reduction factors for slotted hole connections.
What is bearing in composite materials?
Bearing in composites is complex due to anisotropic properties. Bearing strength depends on fiber orientation, layup sequence, and edge distance. Composite bearing design uses empirical knockdown factors and requires testing for certification.
How do I check bearing in a gusset plate?
Check bearing at each bolt hole: σ_b = F_i / (d {"×"} t), where F_i is the force at bolt i. Also check block shear, net section fracture, and gross section yielding. The critical failure mode depends on geometry and loading.
What is the bearing strength of high-strength bolts?
High-strength bolts (ASTM A325, A490) have higher shear and tensile capacity, but bearing strength is governed by the plate material, not the bolt. The bolt must be strong enough to transfer load without failing in shear before the plate reaches bearing capacity.
How does bolt preload affect bearing behavior?
Higher bolt preload increases the friction capacity of the joint, reducing the likelihood of bolt-to-hole contact. In properly designed slip-critical connections, bearing stress never develops under service loads. Bearing is only checked for ultimate limit state.
What is the bearing stiffness of a bolted connection?
Bearing stiffness describes the load-displacement relationship when the bolt contacts the hole wall. It depends on the plate material, thickness, hole size, and bolt diameter. Typical bearing stiffness is 10-50 kN/mm for steel connections.
How is bearing stress distributed around a hole?
Bearing stress is not uniform around the hole. It peaks at approximately 90° from the load direction and is lowest at the load axis. The distribution depends on the ratio of hole diameter to plate width and edge distance.
What is the bearing strength reduction for bolt holes?
Standard holes (d + 1/16 in) have full bearing strength. Oversized holes (d + 1/8 in) may have reduced bearing capacity per AISC. Slotted holes have significant reductions, particularly in the direction of loading.
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Glossary
Technical terms used in mortgage calculations explained in plain language.
- Bearing Stress (σ_b)
- Compressive contact stress on the projected area between a fastener and the connected plate.
- Projected Area
- The rectangular contact area d {"×"} t used to calculate average bearing stress.
- Edge Distance
- Distance from the center of a bolt hole to the nearest plate edge, affecting tear-out capacity.
- Bearing Yield Strength
- The stress level at which permanent bearing deformation begins; typically 1.5-2.0 times tensile yield strength.
- Bearing-Bypass
- The combined effect of bearing stress at one fastener and bypass tensile stress at the same cross-section.
- Slip-Critical Connection
- A connection where friction between plates resists the load, preventing bearing until slip occurs.
Authoritative References
Trusted sources and standards referenced by this calculator.
AISC 360 - Structural Steel Design Eurocode 3 Part 1-8 - Steel Connections Hibbeler, Mechanics of Materials Engineering Toolbox - Bolt Strength
Applicable Standards
ASTM A325 - High-Strength BoltsASTM A490 - Alloy Steel BoltsAISC 360 Section J - ConnectionsEurocode 3 Part 1-8ASME BPVC Section VIII
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Last Updated:
2025-08-21
Version:
2.0.0
References:
License:
Free to use for educational and professional purposes.