BIZOMAT MAKEOS · Fasteners
Bracket Bolts in Tension and Shear (Moment on a Bolted Flange)
What tension do the top bolts of this bracket see from the overhanging load, what shear does each bolt carry, and do they pass a combined tension–shear check?
Check of a bracket bolted to a column or wall face with the load acting at a distance from the face: the moment taken by bolt tension with the bracket pivoting about its bottom edge, tension in each bolt row in proportion to its distance from the pivot, the tension in the most loaded bolt, the shear shared equally by all the bolts (as the bolt and pin shear tool), stresses on the thread stress area and shank, and the elliptical tension–shear interaction.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Load (parallel to the face) | kN | Load on the bracket, acting parallel to the bolted face (for example a vertical load on a wall bracket). |
| Load distance from the bolted face | mm | Distance from the bolted face to the line of the load. |
| Bolt rows (height above the pivot edge) | ||
| Row 1 height | mm | Height of bolt row 1 above the edge the bracket would pivot about. |
| Row 1 bolts | Number of bolts in row 1 (0 if the row is not used). | |
| Row 2 height | mm | Height of bolt row 2 above the edge the bracket would pivot about. |
| Row 2 bolts | Number of bolts in row 2 (0 if the row is not used). | |
| Row 3 height | mm | Height of bolt row 3 above the edge the bracket would pivot about. |
| Row 3 bolts | Number of bolts in row 3 (0 if the row is not used). | |
| Row 4 height | mm | Height of bolt row 4 above the edge the bracket would pivot about. |
| Row 4 bolts | Number of bolts in row 4 (0 if the row is not used). | |
| Bolts | ||
| Bolt diameter | mm | Nominal bolt diameter. |
| Thread pitch | mm | Thread pitch. |
| Allowable tensile stress | MPa | Allowable tensile stress on the stress area (your design value). |
| Allowable shear stress | MPa | Allowable shear stress on the shank (your design value). |
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: Load (parallel to the face)
- What it is
- The total load on the bracket acting parallel to the bolted face, for example the downward load on a wall bracket. All the bolts share it in shear.
- Units and format
- Enter a number in kN: kilonewtons (1 kN = 1000 N). The form accepts 0.000001 kN to 100000 kN. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 60 kN as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Bolt tension and shear rise in proportion to the load.
- Get it right
- This is the total load on the bracket, not the load per bolt.
What this means: Load distance from the bolted face
- What it is
- The distance out from the bolted face to the line of action of the load, which makes the moment the bolts resist in tension.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 10000 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.
- Effect on the result
- Bolt tension rises in proportion; shear per bolt does not change.
- Get it right
- Measure square to the face, from the face to the load line, not from the bolts.
Bolt rows (height above the pivot edge)
What this means: Row 1 height
- What it is
- The height of bolt row 1 above the bottom edge of the bracket, the edge it would pivot about under the moment.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 10000 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
- Measure from the pivot edge, not from the centre of the bolt group.
What this means: Row 1 bolts
- What it is
- How many bolts sit in row 1 at the same height.
- Units and format
- Enter a plain number with no unit. The form accepts 0 to 20. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Enter 0 if the row is not used; its height is then ignored.
What this means: Row 2 height
- What it is
- The height of bolt row 2 above the bottom edge of the bracket, the edge it would pivot about under the moment.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 10000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 150 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Measure from the pivot edge, not from the centre of the bolt group.
What this means: Row 2 bolts
- What it is
- How many bolts sit in row 2 at the same height.
- Units and format
- Enter a plain number with no unit. The form accepts 0 to 20. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Enter 0 if the row is not used; its height is then ignored.
What this means: Row 3 height
- What it is
- The height of bolt row 3 above the bottom edge of the bracket, the edge it would pivot about under the moment.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 10000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 250 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Measure from the pivot edge, not from the centre of the bolt group.
What this means: Row 3 bolts
- What it is
- How many bolts sit in row 3 at the same height.
- Units and format
- Enter a plain number with no unit. The form accepts 0 to 20. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Enter 0 if the row is not used; its height is then ignored.
What this means: Row 4 height
- What it is
- The height of bolt row 4 above the bottom edge of the bracket, the edge it would pivot about under the moment.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 10000 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
- Measure from the pivot edge, not from the centre of the bolt group.
What this means: Row 4 bolts
- What it is
- How many bolts sit in row 4 at the same height.
- Units and format
- Enter a plain number with no unit. The form accepts 0 to 20. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Enter 0 if the row is not used; its height is then ignored.
Bolts
What this means: Bolt diameter
- What it is
- The nominal (major) diameter of the bolts, the M number for metric bolts. Shear is taken on the full shank area and tension on the thread stress area.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100 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.
- Effect on the result
- Stresses fall roughly with the square of diameter.
- Get it right
- If the threads lie in the shear plane, shear on the shank area is optimistic.
What this means: Thread pitch
- What it is
- The axial distance between thread crests of the bolts, used to work out the tensile stress area.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 10 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Coarse and fine series of the same diameter have different pitches; check the bolt designation.
What this means: Allowable tensile stress
- What it is
- The tensile stress you allow on the bolt thread stress area, from your design code and bolt grade.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 2000 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 300 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Allowable shear stress
- What it is
- The shear stress you allow on the bolt shank, from your design code and bolt grade.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 2000 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.
Method and formulas
- Moment M = P × e, resisted by bolt tension about the pivot edge: tension in a row = M y ÷ Σ n y² per bolt.
- Shear per bolt V = P ÷ Σ n (as the bolt and pin shear tool).
- σ = T_max ÷ A_s with A_s = π ÷ 4 (d − 0.9382p)²; τ = V ÷ (π d² ÷ 4).
- Interaction (σ ÷ σ_allow)² + (τ ÷ τ_allow)² ≤ 1.
- Example: 60 kN at 200 mm puts 17.143 kN on each top bolt and 10 kN shear on every bolt; interaction 0.24297.
Limitations
- Pivot at the bottom edge with a rigid bracket; prying from a flexible flange raises bolt tension.
- Preload is not credited; check the joint does not separate for fatigue loads.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check the bolts of a wall or column bracket
- Choose bolt size and row spacing for a cantilever load
- Check a hoist or pipe support bracket
Who it is for
- Structural engineers
- Design engineers
- Maintenance engineers
What you get
- Moment and tension in each row
- Shear per bolt
- Tension, shear and combined checks
Interpreting the result
- Raising the top row away from the pivot cuts the bolt tension most.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 1521–1535, 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 Bracket Bolts in Tension and Shear (Moment on a Bolted Flange) calculator