BIZOMAT MAKEOS · Fasteners
Bolted Joint Load Sharing and Separation
How much of the external load reaches the bolt, and when will the joint separate?
Bolt and member stiffness, joint constant, bolt load, remaining clamp force and separation load of a preloaded tension joint, with an optional frustum estimate of member stiffness.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Nominal diameter | mm | Nominal bolt diameter. |
| Pitch | mm | Thread pitch. |
| Grip length (clamped thickness) | mm | Total thickness of the parts clamped between the bolt head and nut faces. |
| Threaded length within the grip | mm | Length of thread inside the grip (the rest is plain shank). |
| Bolt elastic modulus | GPa | Bolt modulus. |
| Member stiffness | choice | Estimate for plain steel-on-steel plates with washer-face bearing, or enter a value from FEA or tests. |
| Member elastic modulus | GPa | Modulus of the clamped material (for the estimate). |
| Member stiffness (if entered) | kN/mm | Member stiffness from analysis or tests, used when "Enter a value" is chosen. |
| Bolt preload | kN | Installed preload (see the torque and preload tool). |
| External tensile load per bolt | kN | External load trying to separate the joint, per bolt. |
| Proof strength of the bolt | MPa | Proof strength of the bolt property class. |
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: Nominal diameter
- What it is
- The nominal (major) diameter of the bolt. It sets the shank area for bolt stiffness and the bearing size used in the member stiffness estimate.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 500 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 12 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use the thread size, not the hole diameter.
What this means: Pitch
- What it is
- The axial distance between thread crests of the bolt, used to work out the tensile stress area of the threaded part.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 20 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1.75 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Check whether the bolt is coarse or fine thread; the pitch differs.
What this means: Grip length (clamped thickness)
- What it is
- The total thickness of all parts clamped between the underside of the bolt head and the nut face, including washers.
- 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 40 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Add washer thickness; leaving it out understates the grip and overstates the stiffness.
What this means: Threaded length within the grip
- What it is
- The length of threaded bolt inside the grip; the remainder of the grip is plain shank. The threaded part is more flexible because of its smaller area.
- 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 10 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- More thread in the grip lowers bolt stiffness, so the bolt takes a smaller share of the external load.
- Get it right
- It cannot exceed the grip length. For a fully threaded bolt it equals the grip.
What this means: Bolt elastic modulus
- What it is
- The elastic (Young’s) modulus of the bolt material, from the material data sheet or a materials handbook.
- Units and format
- Enter a number in GPa: gigapascals (1 GPa = 1000 MPa). The form accepts 0.000001 GPa to 1000 GPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 207 GPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Enter it in GPa, not MPa.
What this means: Member stiffness
- What it is
- How the stiffness of the clamped parts is found: estimated from a 30° pressure cone in one material, or entered from analysis or tests.
- Units and format
- Choose one of 2 options from the list: Estimate (30° frustum, one material); Enter a value.
- Example
- The form opens with “Estimate (30° frustum, one material)” selected as a worked example. Choose the option that matches your case.
- Get it right
- The estimate suits plain plates of one material; for gaskets, castings or mixed materials enter a value.
What this means: Member elastic modulus
- What it is
- The elastic modulus of the clamped parts, used only by the frustum estimate of member stiffness.
- Units and format
- Enter a number in GPa: gigapascals (1 GPa = 1000 MPa). The form accepts 0.000001 GPa to 1000 GPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 207 GPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A stiffer member material raises member stiffness, so the bolt sees less of the external load.
- Get it right
- Enter it in GPa. Ignored when you enter the member stiffness directly.
What this means: Member stiffness (if entered)
- What it is
- The axial stiffness of the clamped parts together, from finite element analysis or a test. Used only when the member stiffness is set to be entered.
- Units and format
- Enter a number in kN/mm: kN/mm. The form accepts 0.000001 kN/mm to 10000000 kN/mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 3000 kN/mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Higher member stiffness lowers the joint constant, so the bolt load rises less with external load.
- Get it right
- Enter kN/mm for the whole clamped stack around one bolt; it is ignored in estimate mode.
What this means: Bolt preload
- What it is
- The clamping force in the bolt after tightening, before the external load is applied, from the torque and preload calculation or a measurement.
- 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 35 kN as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- More preload raises both the remaining clamp force and the bolt load one for one.
- Get it right
- Enter kilonewtons per bolt; torque-controlled preload scatters widely, so check the lowest likely value.
What this means: External tensile load per bolt
- What it is
- The external tensile force that tries to pull this joint apart, as carried by one bolt.
- Units and format
- Enter a number in kN: kilonewtons (1 kN = 1000 N). The form accepts 0 kN to 10000000 kN. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10 kN as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Raises bolt load by C × P and reduces clamp force by (1 − C) × P.
- Get it right
- Divide the total separating load by the number of bolts sharing it; do not enter the total load.
What this means: Proof strength of the bolt
- What it is
- The proof strength of the bolt for its property class, used to check the bolt stress under the combined preload and external load.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 3000 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 600 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Take it from ISO 898-1 or the supplier for the property class; it is not the tensile strength.
Method and formulas
- kb = 1 ÷ (Ls ÷ (E Ad) + Lt ÷ (E At)); Ad = πd²/4, At = π/4 (d − 0.938194P)².
- Estimate: km = 0.5774 π E d ÷ (2 ln(5(0.5774 l + 0.5d) ÷ (0.5774 l + 2.5d))).
- C = kb ÷ (kb + km); bolt load Fb = Fi + C P; clamp Fm = Fi − (1 − C) P.
- Separation load P₀ = Fi ÷ (1 − C).
- Example: 35 kN preload with 10 kN external load gives C = 0.19434, a bolt load of 36.943 kN and 26.943 kN left clamping.
Limitations
- Concentric tension joint; prying, bending and thermal loads are not modelled.
- The frustum estimate suits plates of one material with washer-face bearing; gaskets and different materials need a measured or calculated stiffness.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check flange, cap and bracket bolts under external tension
- Find the preload needed to prevent separation
- Compare short and long grip bolts
Who it is for
- Design engineers
- Maintenance fitters
- Quality inspectors
What you get
- Bolt and member stiffness
- Joint constant C
- Bolt load and stress
- Remaining clamp force
- Separation load and load factor
Interpreting the result
- Keep a clear margin against separation; a separated joint transfers the full alternating load to the bolt and loosens.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 1521–1535. Topic reference; no source tables or recommended settings are reproduced.
- VDI 2230 Part 1: Systematic calculation of highly stressed bolted joints
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
Preload and joint stiffness: how a bolted joint carries load
In Bolted Joints by the Numbers
What it covers: Why a bolt and the parts it clamps act as two springs, how preload and their stiffnesses share an external load, when a joint separates, and what the joint constant means.
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