BIZOMAT MAKEOS · Fasteners
Bolted Joint at Temperature (Preload Change from Differential Expansion)
How much does this bolt’s preload rise or fall when the joint heats up or cools down, and does it stay between the clamp needed and the proof load?
Preload change in a bolted joint when bolt and clamped parts expand differently: bolt stiffness from shank and thread lengths, member stiffness by the frustum method (as the bolted joint design check), assembly preload from the share of proof load, the preload change (α_m − α_b) ΔT × grip × k_b k_m ÷ (k_b + k_m), the preload at temperature, and checks against the least clamp force needed and the bolt proof load.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Bolt diameter | mm | Nominal bolt diameter. |
| Thread pitch | mm | Thread pitch. |
| Proof strength | MPa | Proof strength of the bolt grade. |
| Bolt modulus | GPa | Elastic modulus of the bolt. |
| Grip length | mm | Total thickness clamped. |
| Threaded length in the grip | mm | Length of thread inside the grip. |
| Clamped part modulus | GPa | Elastic modulus of the clamped parts (70 aluminium, 207 steel). |
| Assembly preload as share of proof load | % | Preload at assembly as a share of the proof load. |
| Bolt expansion coefficient | µm/m·K | Expansion coefficient of the bolt. |
| Clamped part expansion coefficient | µm/m·K | Expansion coefficient of the clamped parts. |
| Temperature change from assembly | K | Change from the assembly temperature to the operating temperature (negative for cooling). |
| Least clamp force needed | kN | Least clamp force the joint needs in service (sealing, slip, separation). |
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: Bolt diameter
- What it is
- The nominal (major) diameter of the bolt, the M number for metric bolts.
- 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 12 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Bolt and member stiffness and the proof load all rise with it.
What this means: Thread pitch
- What it is
- The axial distance between thread crests of the bolt, 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 1.75 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 designation.
What this means: Proof strength
- What it is
- The proof strength of the bolt grade, the stress it must carry without permanent set, from the bolt standard or supplier.
- 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 600 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The assembly preload and the proof load limit are proportional to it.
- Get it right
- Proof strength is lower than yield and tensile strength; do not mix them.
What this means: Bolt modulus
- What it is
- The elastic modulus of the bolt material, from the material data sheet or a materials reference.
- Units and format
- Enter a number in GPa: gigapascals (1 GPa = 1000 MPa). The form accepts 0.000001 GPa to 300 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 GPa, not MPa: the tool multiplies by 1000.
What this means: Grip length
- What it is
- The total thickness of the parts clamped between the bolt head and the nut, washers included.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 2000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 30 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The preload change is proportional to the grip for given stiffnesses.
What this means: Threaded length in the grip
- What it is
- The length of threaded shank that lies inside the grip, between the clamped faces.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 2000 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.
- Get it right
- It cannot exceed the grip; enter 0 if only plain shank is within the grip.
What this means: Clamped part modulus
- What it is
- The elastic modulus of the clamped parts, from the material data sheet or a materials reference.
- Units and format
- Enter a number in GPa: gigapascals (1 GPa = 1000 MPa). The form accepts 0.000001 GPa to 400 GPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 70 GPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Enter GPa; if the parts are different materials, the tool takes one value only.
What this means: Assembly preload as share of proof load
- What it is
- The preload put into the bolt at assembly, as a percentage of its proof load. It comes from your tightening specification.
- Units and format
- Enter a number in %: percent: the number is read as a percentage, so type 8 for 8 %. The form accepts 10% to 100%. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 70% as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The assembly preload is proportional to it; the preload change is not.
- Get it right
- Type the percentage itself, for example 70, not 0.7.
What this means: Bolt expansion coefficient
- What it is
- The coefficient of thermal expansion of the bolt material, from the material data sheet.
- Units and format
- Enter a number in µm/m·K: micrometres per metre per kelvin. The form accepts 0 µm/m·K to 40 µm/m·K. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 11.5 µm/m·K as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- µm/m·K is the same number as 10⁻⁶ per K.
What this means: Clamped part expansion coefficient
- What it is
- The coefficient of thermal expansion of the clamped parts, from the material data sheet.
- Units and format
- Enter a number in µm/m·K: micrometres per metre per kelvin. The form accepts 0 µm/m·K to 40 µm/m·K. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 23 µm/m·K as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- If it is higher than the bolt’s, heating raises preload; if lower, heating reduces it.
What this means: Temperature change from assembly
- What it is
- The change in temperature from when the joint was tightened to the operating condition, with bolt and parts at the same temperature.
- Units and format
- Enter a number in K: kelvin (a difference of 1 K equals 1 °C). The form accepts -300 K to 600 K. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 60 K as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The preload change is proportional to it.
- Get it right
- Enter a negative value for cooling. Run both the hot and cold cases.
What this means: Least clamp force needed
- What it is
- The least clamp force the joint must keep in service, for sealing, to prevent slip or to prevent separation, from your joint design.
- Units and format
- Enter a number in kN: kilonewtons (1 kN = 1000 N). The form accepts 0 kN to 10000 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 force per bolt, matching the preload the tool calculates for one bolt.
Method and formulas
- k_b = 1 ÷ [(grip − L_t) ÷ (E A_d) + L_t ÷ (E A_t)]; k_m = 0.5774π E_m d ÷ {2 ln[5(0.5774 grip + 0.5d) ÷ (0.5774 grip + 2.5d)]} (as the bolted joint design check).
- Assembly preload F_i = share × S_p A_t.
- Preload change ΔF = (α_m − α_b) ΔT × grip × k_b k_m ÷ (k_b + k_m).
- Preload at temperature = F_i + ΔF, checked against the clamp needed and S_p A_t.
- Example: a 60 K change shifts the preload by 7.927 kN, from 35.392 to 43.319 kN.
Limitations
- Moduli taken at assembly temperature; they fall at high temperature, and creep or relaxation are not included.
- Uniform temperature through bolt and parts; transients can be worse.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check steel bolts in an aluminium housing at temperature
- Find whether a joint loosens when cold
- Choose assembly preload for a hot joint
Who it is for
- Design engineers
- Mechanical engineers
- Maintenance engineers
What you get
- Bolt and member stiffness
- Preload change and preload at temperature
- Clamp and proof checks
Interpreting the result
- Aluminium parts with steel bolts gain preload when hot and lose it when cold: check both extremes.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 1521–1536, 371–378. 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
Temperature, hole patterns and the joint register
In Bolted Joints by the Numbers
What it covers: How differential expansion changes preload in a warm joint, how to plan a bolt circle's holes and position tolerances for clearance and tapped holes, and what a joint register holds.
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