BIZOMAT MAKEOS · Fasteners
Eccentric Bracket Bolt Check (Bolt Group Forces, Shear and Bearing Stress)
For a bracket bolted with a group of bolts and loaded off-centre, which bolt carries most, and are its shear stress and the plate bearing stress within limits?
Check of a bolted bracket with an eccentric load in the plane of the bolts: the centroid of the bolt group, the moment of the load about it, the direct and torsional force on each bolt and the most heavily loaded bolt (as the eccentric bolt group tool), then the shear stress in that bolt and the bearing stress it puts on the plate (as the bolt shear and bearing tool), against your allowable stresses.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Number of bolts | bolts | Number of bolts in the group (the first n positions are used). |
| Bolt 1 | ||
| X | mm | X position of bolt 1. |
| Y | mm | Y position of bolt 1. |
| Bolt 2 | ||
| X | mm | X position of bolt 2. |
| Y | mm | Y position of bolt 2. |
| Bolt 3 | ||
| X | mm | X position of bolt 3. |
| Y | mm | Y position of bolt 3. |
| Bolt 4 | ||
| X | mm | X position of bolt 4. |
| Y | mm | Y position of bolt 4. |
| Bolt 5 | ||
| X | mm | X position of bolt 5. |
| Y | mm | Y position of bolt 5. |
| Bolt 6 | ||
| X | mm | X position of bolt 6. |
| Y | mm | Y position of bolt 6. |
| Load | ||
| Load X component | kN | Horizontal component of the load. |
| Load Y component | kN | Vertical component of the load (negative downwards). |
| Load X position | mm | X position of the load’s line of action. |
| Load Y position | mm | Y position of the load’s line of action. |
| Bolts and plate | ||
| Bolt diameter at the shear plane | mm | Bolt diameter where it is sheared (shank or thread). |
| Shear planes per bolt | choice | Whether each bolt is sheared once or twice. |
| Thinnest plate thickness in bearing | mm | Thickness of the thinnest plate the bolts bear on. |
| Allowable bolt shear stress | MPa | Allowable shear stress of the bolts. |
| Allowable bearing stress | MPa | Allowable bearing stress of the plate. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Number of bolts
- What it is
- The number of bolts in the group; the tool uses the first n bolt positions below and ignores the rest.
- Units and format
- Enter a number in bolts: bolts. The form accepts 2 bolts to 6 bolts. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 4 bolts as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Fill in the bolt positions from bolt 1 upwards; positions after the nth bolt are not used.
Bolt 1
What this means: X
- What it is
- The horizontal position of this bolt in the plane of the bracket, measured from one origin chosen for all the bolts and the load.
- Units and format
- Enter a number in mm: millimetres. The form accepts -100000 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use the same origin for every bolt and for the load position; the tool finds the group centroid itself.
What this means: Y
- What it is
- The vertical position of this bolt in the plane of the bracket, measured from the same origin as the X positions.
- Units and format
- Enter a number in mm: millimetres. The form accepts -100000 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Keep one sign convention: positive Y upwards for every bolt and for the load position.
Bolt 2
What this means: X
- What it is
- The horizontal position of this bolt in the plane of the bracket, measured from one origin chosen for all the bolts and the load.
- Units and format
- Enter a number in mm: millimetres. The form accepts -100000 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 100 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use the same origin for every bolt and for the load position; the tool finds the group centroid itself.
What this means: Y
- What it is
- The vertical position of this bolt in the plane of the bracket, measured from the same origin as the X positions.
- Units and format
- Enter a number in mm: millimetres. The form accepts -100000 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Keep one sign convention: positive Y upwards for every bolt and for the load position.
Bolt 3
What this means: X
- What it is
- The horizontal position of this bolt in the plane of the bracket, measured from one origin chosen for all the bolts and the load.
- Units and format
- Enter a number in mm: millimetres. The form accepts -100000 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use the same origin for every bolt and for the load position; the tool finds the group centroid itself.
What this means: Y
- What it is
- The vertical position of this bolt in the plane of the bracket, measured from the same origin as the X positions.
- Units and format
- Enter a number in mm: millimetres. The form accepts -100000 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 100 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Keep one sign convention: positive Y upwards for every bolt and for the load position.
Bolt 4
What this means: X
- What it is
- The horizontal position of this bolt in the plane of the bracket, measured from one origin chosen for all the bolts and the load.
- Units and format
- Enter a number in mm: millimetres. The form accepts -100000 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 100 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Ignored when the number of bolts is less than 4.
What this means: Y
- What it is
- The vertical position of this bolt in the plane of the bracket, measured from the same origin as the X positions.
- Units and format
- Enter a number in mm: millimetres. The form accepts -100000 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 100 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Ignored when the number of bolts is less than 4.
Bolt 5
What this means: X
- What it is
- The horizontal position of this bolt in the plane of the bracket, measured from one origin chosen for all the bolts and the load.
- Units and format
- Enter a number in mm: millimetres. The form accepts -100000 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Ignored when the number of bolts is less than 5.
What this means: Y
- What it is
- The vertical position of this bolt in the plane of the bracket, measured from the same origin as the X positions.
- Units and format
- Enter a number in mm: millimetres. The form accepts -100000 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 200 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Ignored when the number of bolts is less than 5.
Bolt 6
What this means: X
- What it is
- The horizontal position of this bolt in the plane of the bracket, measured from one origin chosen for all the bolts and the load.
- Units and format
- Enter a number in mm: millimetres. The form accepts -100000 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 100 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Ignored when the number of bolts is less than 6.
What this means: Y
- What it is
- The vertical position of this bolt in the plane of the bracket, measured from the same origin as the X positions.
- Units and format
- Enter a number in mm: millimetres. The form accepts -100000 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 200 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Ignored when the number of bolts is less than 6.
Load
What this means: Load X component
- What it is
- The horizontal component of the load on the bracket, acting in the plane of the bolts.
- Units and format
- Enter a number in kN: kilonewtons (1 kN = 1000 N). The form accepts -10000000 kN to 10000000 kN. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 kN as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Sign matters: positive acts along +X, negative the other way.
What this means: Load Y component
- What it is
- The vertical component of the load on the bracket, acting in the plane of the bolts, negative when it acts downwards.
- Units and format
- Enter a number in kN: kilonewtons (1 kN = 1000 N). The form accepts -10000000 kN to 10000000 kN. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with -20 kN as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Enter the total load on the bracket, not the load per bolt; the tool shares it between the bolts.
What this means: Load X position
- What it is
- The X coordinate of a point on the load’s line of action, measured from the same origin as the bolt positions.
- Units and format
- Enter a number in mm: millimetres. The form accepts -1000000 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 300 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- The farther the line of action is from the bolt group centroid, the larger the moment and the bolt forces.
What this means: Load Y position
- What it is
- The Y coordinate of a point on the load’s line of action, measured from the same origin as the bolt positions.
- Units and format
- Enter a number in mm: millimetres. The form accepts -1000000 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 50 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Bolts and plate
What this means: Bolt diameter at the shear plane
- What it is
- The bolt diameter at the plane where it is sheared: the shank diameter, or a reduced thread diameter if the thread crosses the shear plane.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 1000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 16 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Shear planes per bolt
- What it is
- Whether each bolt is cut by one shear plane (two plates joined) or by two (three plates, as in a clevis).
- Units and format
- Choose one of 2 options from the list: Single shear; Double shear.
- Example
- The form opens with “Single shear” selected as a worked example. Choose the option that matches your case.
What this means: Thinnest plate thickness in bearing
- What it is
- The thickness of the thinnest plate the bolts bear against, which carries the highest bearing stress.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 1000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Bearing stress is inversely proportional to the plate thickness.
- Get it right
- In double shear, compare the middle plate with the two outer plates added together and use the smaller.
What this means: Allowable bolt shear stress
- What it is
- The allowable shear stress of the bolt material, from your design code or the bolt standard.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 100000 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 150 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Allowable bearing stress
- What it is
- The allowable bearing stress of the plate material on the bolt hole, from your design code.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 100000 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 250 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Method and formulas
- Centroid of the bolts; polar moment J = Σ r²; moment of the load about the centroid (as the eccentric bolt group tool).
- Each bolt: direct share P ÷ n plus M r ÷ J perpendicular to its radius; the largest resultant governs.
- Shear stress = F ÷ (planes × π d² ÷ 4); bearing stress = F ÷ (d t) (as the bolt shear and bearing tool).
- Example: bolt 2 carries 21.506 kN, giving 106.96 MPa shear and 134.41 MPa bearing.
Limitations
- Elastic method with rigid plates; the instantaneous-centre method gives more capacity.
- Bolts in bearing (no slip-critical friction).
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check a bracket carrying an offset load
- Find the critical bolt in a connection
- Choose bolt size and plate thickness for a bracket
Who it is for
- Design engineers
- Structural detailers
- Fabrication engineers
What you get
- Group centroid and moment
- Force on each bolt and the critical bolt
- Shear and bearing stress of the critical bolt
Interpreting the result
- Spreading the bolts further from the centroid cuts the moment share faster than adding bolts near it.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 1535, 1720–1735. Topic reference; no source tables or recommended settings are reproduced.
Learn the Concepts Behind This Tool
These BIZOMAT Library readings explain the method this tool uses, with worked examples.
Method explained here · BIZOMAT original book
Eccentric loads on bolt groups and brackets
In Bolted Joints by the Numbers
What it covers: How a load applied away from a bolt group's centre loads its bolts unequally: the elastic method for in-plane loads, bracket bolts in tension and shear, and the most loaded bolt.
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Open the Eccentric Bracket Bolt Check (Bolt Group Forces, Shear and Bearing Stress) calculator