BIZOMAT MAKEOS · Fasteners
Eccentrically Loaded Bolt Group
Which bolt in this group carries the most shear when the load is offset?
Shear force on each bolt of a group of up to six under an in-plane load applied away from the group centroid, by the elastic (vector) method, against the bolt shear capacity.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Number of bolts | bolts | How many of the listed bolts are used (the first n). |
| Bolt 1 | ||
| X | mm | X position of bolt 1. |
| Y | mm | Y position of bolt 1. |
| Bolt 2 | ||
| X | mm | X of bolt 2. |
| Y | mm | Y of bolt 2. |
| Bolt 3 | ||
| X | mm | X of bolt 3. |
| Y | mm | Y of bolt 3. |
| Bolt 4 | ||
| X | mm | X of bolt 4. |
| Y | mm | Y of bolt 4. |
| Bolt 5 | ||
| X | mm | X of bolt 5 (used when n ≥ 5). |
| Y | mm | Y of bolt 5. |
| Bolt 6 | ||
| X | mm | X of bolt 6 (used when n = 6). |
| Y | mm | Y 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 coordinate of a point on the load’s line of action. |
| Load Y position | mm | Y coordinate of that point. |
| Shear capacity per bolt | kN | Design shear capacity of one bolt from your code (see the bolt shear and bearing tool). |
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
- How many bolts the group has; the tool uses the first that many bolt positions listed 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
- Positions for bolts beyond this number are ignored, even if they have values.
Bolt 1
What this means: X
- What it is
- The horizontal coordinate of the centre of bolt 1, measured from any origin you choose on the plate or bracket.
- 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 and axis directions for all bolts and for the load position.
What this means: Y
- What it is
- The vertical coordinate of the centre of bolt 1, from the same origin as the X coordinates.
- 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
- Positive Y is upward; keep the same sign convention for the load.
Bolt 2
What this means: X
- What it is
- The horizontal coordinate of the centre of bolt 2, from the same origin used for bolt 1.
- 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.
What this means: Y
- What it is
- The vertical coordinate of the centre of bolt 2, from the same origin used for bolt 1.
- 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.
Bolt 3
What this means: X
- What it is
- The horizontal coordinate of the centre of bolt 3, from the same origin used for bolt 1.
- 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.
What this means: Y
- What it is
- The vertical coordinate of the centre of bolt 3, from the same origin used for bolt 1.
- 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.
Bolt 4
What this means: X
- What it is
- The horizontal coordinate of the centre of bolt 4, from the same origin used for bolt 1; used when the group has four or more bolts.
- 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.
What this means: Y
- What it is
- The vertical coordinate of the centre of bolt 4, from the same origin used for bolt 1; used when the group has four or more bolts.
- 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.
Bolt 5
What this means: X
- What it is
- The horizontal coordinate of the centre of bolt 5, from the same origin; used only when the group has five or six bolts.
- 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.
What this means: Y
- What it is
- The vertical coordinate of the centre of bolt 5, from the same origin; used only when the group has five or six bolts.
- 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.
Bolt 6
What this means: X
- What it is
- The horizontal coordinate of the centre of bolt 6, from the same origin; used only when the group has six bolts.
- 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.
What this means: Y
- What it is
- The vertical coordinate of the centre of bolt 6, from the same origin; used only when the group has six bolts.
- 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.
Load
What this means: Load X component
- What it is
- The horizontal part of the in-plane load on the bracket, acting in the plane of the bolted plate.
- 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
- Enter kilonewtons with a sign: positive in the +X direction, negative in the −X direction.
What this means: Load Y component
- What it is
- The vertical part of the in-plane load on the bracket; a load hanging downward is negative.
- 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 kilonewtons with a sign: a downward load needs a minus sign.
What this means: Load X position
- What it is
- The X coordinate of any 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.
- Effect on the result
- Moving the load further from the centroid increases the moment and the force on the outer bolts.
- Get it right
- Its distance from the bolt group centroid is the lever arm that creates the twisting moment.
What this means: Load Y position
- What it is
- The Y coordinate of the same point on the load’s line of action, 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.
- Get it right
- For a purely vertical load, this coordinate does not change the moment.
What this means: Shear capacity per bolt
- What it is
- The design shear capacity of one bolt from your code, taking account of bolt grade, shear planes and whether threads are in the shear plane.
- Units and format
- Enter a number in kN: kilonewtons (1 kN = 1000 N). The form accepts 0.000001 kN to 10000000 kN. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 30 kN as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Enter the capacity per bolt in kilonewtons, not for the whole group.
Method and formulas
- Centroid = mean of bolt positions; M = (lx − xc)Py − (ly − yc)Px.
- Direct shear: Px ÷ n, Py ÷ n per bolt.
- Torsional shear: Fx = −M (y − yc) ÷ Σr², Fy = M (x − xc) ÷ Σr², with r² = (x − xc)² + (y − yc)².
- Resultant per bolt = vector sum; the largest governs.
- Example: 20 kN at 300 mm on the default 4-bolt pattern puts 21.506 kN on the critical bolt.
Limitations
- Elastic method with equal bolt stiffness and rigid plate; the instantaneous-centre method gives higher capacity for ductile bolts.
- Out-of-plane loads (prying, tension) are not included.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check bracket and gusset bolt patterns
- Find the critical bolt in a group
- Compare bolt layouts
Who it is for
- Design engineers
- Maintenance fitters
- Quality inspectors
What you get
- Group centroid and moment
- Force on each bolt
- Critical bolt and utilisation
Interpreting the result
- Spreading bolts further from the centroid reduces the torsional share.
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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