KEVOS® 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.
Open the calculatorRuns in your browser. No account needed.
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). |
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.
WORKOS tools are screening and decision-support utilities. Verify important financial, engineering, safety, legal or operational decisions using appropriate professional standards and your organisation’s approved data.
Open the Bolted Joint at Temperature (Preload Change from Differential Expansion) calculator
