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.
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:
The maximum resultant bolt force can then be used in a bolt shear stress, bearing stress or combined stress calculation.
Direct shear force per bolt:
Eccentric moment:
Radius of bolt from centroid:
Polar bolt group term:
Torsional force components at bolt i:
Resultant bolt force:
| 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 |
Enter the bolt group details, then click calculate.
| 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. |
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.
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.
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.
For a simplified elastic calculation with equal bolts, the direct shear force is divided equally between all bolts.
When the load is eccentric, the moment creates additional torsional force. Bolts further from the centroid usually experience larger torsional components.
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.
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.