Roymech engineering encyclopedia

Bolt Group Eccentric Load Calculator




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Use this bolt group eccentric load calculator to estimate the force distribution in a rectangular bolt group subject to direct shear and eccentric loading. The calculator determines the direct shear per bolt, eccentric moment, torsional load components and maximum resultant bolt force.

What does this calculator do?

This calculator estimates the load on each bolt in a rectangular bolt group where the applied force does not pass through the bolt group centroid. The eccentric force creates both direct shear and a torsional moment about the centroid.

The calculator provides:

  • bolt coordinates relative to centroid
  • direct shear force per bolt
  • eccentric moment from offset loading
  • torsional force components
  • resultant force on each bolt
  • maximum bolt force
  • worked calculations

The maximum resultant bolt force can then be used in a bolt shear stress, bearing stress or combined stress calculation.

Engineering note: This calculator is intended for preliminary engineering calculations and educational use. It assumes a rectangular bolt group with equally sized bolts and simplified elastic load distribution. Final bolted joint design should also consider bolt grade, preload, friction, bearing stress, plate shear, fatigue, prying action, hole clearance and the relevant design standard.

How to Use the Calculator

  1. Enter the number of bolt columns and rows. This defines the rectangular bolt group layout.
  2. Enter the horizontal and vertical bolt pitch. These are the centre-to-centre spacings between bolts.
  3. Enter the applied shear force, F. This is the external load applied to the joint.
  4. Enter the eccentricity, e. This is the distance from the bolt group centroid to the line of action of the applied load.
  5. Enter the load direction. Select whether the applied force acts vertically or horizontally.
  6. Click calculate. The calculator determines the direct shear, torsional components and resultant force at each bolt.

Bolt Group Eccentric Load Diagram

Bolt group eccentric load calculator diagram showing rectangular bolt group, applied force F, eccentricity e, centroid and bolt coordinates
Rectangular bolt group subject to an eccentric load causing direct shear and torsional loading.

Formulae Used

Direct shear force per bolt:

Fd = Fn

Eccentric moment:

M = Fe

Radius of bolt from centroid:

ri = √(xi2 + yi2)

Polar bolt group term:

J = ∑(xi2 + yi2)

Torsional force components at bolt i:

Ftx,i = -M yiJ
Fty,i = M xiJ

Resultant bolt force:

Fr,i = √(Fx,i2 + Fy,i2)

Variables

Symbol Description Units
F Applied shear force N
n Number of bolts -
e Eccentricity from bolt group centroid mm
M Eccentric moment Nmm
xi, yi Bolt coordinates relative to centroid mm
J Polar bolt group term mm²
Fd Direct shear force per bolt N
Fr Resultant force on bolt N

Calculator Inputs

Results

Enter the bolt group details, then click calculate.

Understanding the Results

Result Meaning
Direct shear per bolt The applied force divided equally between all bolts before eccentric effects are added.
Eccentric moment The moment produced because the applied force does not pass through the bolt group centroid.
Torsional force components The additional bolt forces caused by rotation of the bolt group about its centroid.
Resultant bolt force The vector combination of direct shear and torsional components for each bolt.
Maximum bolt force The largest resultant force in the bolt group. This bolt usually governs the design check.

Calculator Limitations

This calculator uses a simplified elastic bolt group method for rectangular bolt groups with equal bolt sizes.

This Calculator Includes This Calculator Does Not Include
Rectangular bolt group layouts Irregular bolt groups
Direct shear force per bolt Bolt preload or friction-grip behaviour
Eccentric moment from offset load Prying action
Torsional load distribution Plate bending or local deformation
Resultant bolt force at each bolt Bolt shear stress, bearing stress or combined stress check

For converting the maximum bolt force into bolt shear stress, use the Bolt Shear Stress Calculator.

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

Bolt Group Eccentric Load Calculation Notes

When an applied force does not pass through the centroid of a bolt group, the bolts are subject to direct shear and additional torsional loading. The direct shear is usually shared equally between bolts, while the torsional component depends on the bolt position relative to the centroid.

Bolts further from the centroid generally attract higher torsional force. The critical bolt is usually the one with the largest resultant force after direct and torsional components are combined.

This calculator gives the resultant force on each bolt. A separate stress check is required using the bolt diameter, bolt grade, plate thickness and allowable stresses.

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 Group Eccentric Load Calculator FAQ

What is an eccentric bolt group?

An eccentric bolt group is a group of bolts where the applied force does not pass through the bolt group centroid. This creates direct shear and a torsional moment.

How is direct shear shared in a bolt group?

For a simplified elastic calculation with equal bolts, the direct shear force is divided equally between all bolts.

Why do some bolts carry more load than others?

When the load is eccentric, the moment creates additional torsional force. Bolts further from the centroid usually experience larger torsional components.

Does this calculator check bolt stress?

No. This calculator gives the resultant force on each bolt. The maximum bolt force should then be checked using a bolt shear stress, bearing stress or combined stress calculator.

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, plate stiffness, preload, fatigue requirements and safety factors.

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