Understanding the Calculation of Force in Bolted Connections
Calculating force in bolted connections is essential for structural integrity and safety. This process determines the load a bolt can withstand without failure.
This article explores detailed formulas, common values, and real-world applications for precise force calculations in bolted joints.
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- Calculate tensile force on an M16 bolt under a 10 kN axial load.
- Determine shear force capacity of an M20 bolt in a double shear connection.
- Evaluate preload force required for an M12 bolt in a steel flange joint.
- Analyze combined shear and tensile forces on an M24 bolt in a structural beam.
Comprehensive Tables of Common Values in Bolted Connection Force Calculations
| Bolt Size (Metric) | Nominal Diameter (mm) | Thread Pitch (mm) | Proof Load (kN) | Ultimate Tensile Strength (MPa) | Yield Strength (MPa) | Typical Preload (kN) | Shear Strength (kN) |
|---|---|---|---|---|---|---|---|
| M8 | 8 | 1.25 | 12.5 | 800 | 640 | 10 | 20 |
| M10 | 10 | 1.5 | 20 | 830 | 664 | 16 | 32 |
| M12 | 12 | 1.75 | 30 | 830 | 664 | 25 | 48 |
| M16 | 16 | 2.0 | 50 | 830 | 664 | 45 | 80 |
| M20 | 20 | 2.5 | 75 | 830 | 664 | 70 | 125 |
| M24 | 24 | 3.0 | 110 | 830 | 664 | 100 | 180 |
| M30 | 30 | 3.5 | 160 | 830 | 664 | 150 | 260 |
These values are based on ISO 898-1 standards for property class 8.8 bolts, commonly used in structural applications. Proof load represents the maximum tensile load the bolt can sustain without permanent deformation.
Fundamental Formulas for Calculating Force in Bolted Connections
Tensile Force Calculation
The tensile force a bolt experiences can be calculated using the formula:
Ft = σt Ć As
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Where:
- Ft = Tensile force on the bolt (N or kN)
- σt = Tensile stress in the bolt (MPa)
- As = Tensile stress area of the bolt (mm2)
The tensile stress area As depends on the bolt diameter and thread pitch, typically found in standards such as ISO 898-1. For example, an M16 bolt has a tensile stress area of approximately 157 mm2.
Shear Force Calculation
Shear force capacity is critical when bolts are subjected to lateral loads. The shear force can be calculated as:
Fv = τ Ć As
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Where:
- Fv = Shear force on the bolt (N or kN)
- τ = Shear stress in the bolt (MPa)
- As = Shear area of the bolt (mm2)
Shear stress is often taken as 0.6 to 0.7 times the ultimate tensile strength for steel bolts, depending on the design code.
Preload Force Calculation
Preload is the initial tension applied to a bolt during tightening to ensure joint integrity. It can be estimated by:
Fp = k Ć D Ć T
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Where:
- Fp = Preload force (N or kN)
- k = Nut factor or torque coefficient (dimensionless, typically 0.15 – 0.25)
- D = Nominal bolt diameter (mm)
- T = Applied torque (NĀ·m)
The nut factor k accounts for friction in threads and under the bolt head or nut. Accurate preload calculation is essential to avoid bolt loosening or joint failure.
Combined Shear and Tensile Force
Bolted connections often experience combined loading. The interaction can be evaluated using the von Mises criterion or simplified interaction equations such as:
&frac;Ft⁄Ft,allow + &frac;Fv⁄Fv,allow ≤ 1
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Where:
- Ft = Applied tensile force
- Fv = Applied shear force
- Ft,allow = Allowable tensile force
- Fv,allow = Allowable shear force
This ensures the combined stresses do not exceed the boltās capacity.
Detailed Explanation of Variables and Their Typical Values
- Nominal Diameter (D): The outer diameter of the bolt shank, critical for stress area calculation.
- Tensile Stress Area (As): The effective cross-sectional area resisting tensile loads, smaller than the nominal area due to threads.
- Tensile Stress (σt): Stress experienced by the bolt under axial load, limited by yield or proof strength.
- Shear Stress (τ): Stress due to forces acting perpendicular to the bolt axis, typically 60-70% of tensile strength.
- Preload Force (Fp): Initial tension applied to the bolt to maintain joint integrity and prevent loosening.
- Torque (T): The tightening moment applied to the bolt, directly related to preload.
- Nut Factor (k): Empirical coefficient accounting for friction, lubrication, and thread conditions.
Understanding these variables and their typical ranges is crucial for accurate force calculations and safe bolted joint design.
Real-World Application Examples of Force Calculation in Bolted Connections
Example 1: Tensile Load on an M16 Bolt in a Steel Frame
A steel frame uses an M16 bolt (property class 8.8) to resist an axial tensile load of 40 kN. Determine if the bolt can safely carry this load.
- Nominal diameter, D = 16 mm
- Tensile stress area, As ā 157 mm2
- Proof strength, σproof = 640 MPa (from property class 8.8)
Calculate the allowable tensile force:
Fallow = σproof Ć As = 640 Ć 157 = 100,480 N = 100.48 kN
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The applied load is 40 kN, which is less than the allowable 100.48 kN, so the bolt is safe under tensile loading.
Example 2: Shear Force on an M20 Bolt in a Double Shear Connection
An M20 bolt is used in a double shear connection subjected to a shear load of 90 kN. Verify the boltās adequacy.
- Nominal diameter, D = 20 mm
- Tensile strength, σu = 830 MPa
- Shear strength, τ = 0.6 Ć σu = 0.6 Ć 830 = 498 MPa
- Stress area, As ā 245 mm2
- Double shear means the shear area is doubled: Ashear = 2 Ć As = 490 mm2
Calculate the allowable shear force:
Fv,allow = τ Ć Ashear = 498 Ć 490 = 244,020 N = 244.02 kN
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The applied shear load of 90 kN is well below the allowable 244.02 kN, confirming the boltās safety in shear.
Additional Considerations for Accurate Force Calculations
- Effect of Bolt Preload: Proper preload reduces the risk of fatigue and loosening by maintaining clamping force.
- Fatigue Loading: Repeated loads require consideration of fatigue strength, often lower than static strength.
- Environmental Factors: Corrosion and temperature can affect bolt material properties and force capacity.
- Standards and Codes: Refer to ISO 898-1, ASME B18.2.1, and Eurocode 3 for detailed design requirements.
- Thread Engagement: Adequate thread length ensures full load transfer and prevents stripping.
Incorporating these factors ensures robust and reliable bolted connections in engineering designs.