KEVOS® MAKEOS · Strength
Restrained Bar Heating (Thermal Stress, Yield and Buckling)
When this bar or pipe is held between fixed supports and heats up, does the thermal stress stay below yield, and will it buckle before then?
Check of a round bar or member held at both ends while its temperature changes: free thermal strain, restrained thermal stress and the force on the supports (as the thermal stress tool), the yield safety factor, the buckling load of the member by Euler or Johnson for its effective length (as the column buckling tool), the buckling safety factor against the thermal force, and the temperature rise at which yielding and buckling would begin.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Bar diameter | mm | Diameter of the round bar (solid). |
| Length between restraints | mm | Length between the supports that stop it growing. |
| Effective length factor | Effective length factor for the end fixity (0.5 fixed at both ends, 1 pinned). | |
| Elastic modulus | GPa | Elastic modulus. |
| Expansion coefficient | µm/m·K | Linear expansion coefficient. |
| Temperature rise | K | Rise in temperature from the fitting temperature. |
| Degree of restraint | % | Share of the free growth the supports prevent (100% for rigid anchors). |
| Yield strength | MPa | Yield strength at temperature. |
| Safety factor required (yield and buckling) | Safety factor you require on both yield and buckling. |
Method and formulas
- Thermal stress σ = E α ΔT × restraint; force = σ A (as the thermal stress tool).
- Buckling stress by Euler for slender bars or Johnson for intermediate ones, with slenderness K L ÷ r (as the column buckling tool); buckling factor = P_cr ÷ force.
- Temperature rise at yield = S_y ÷ (E α × restraint); at buckling = σ_cr ÷ (E α × restraint).
- Example: 40 K gives 96 MPa and 120.64 kN; the bar buckles at 71.185 K and yields at 104.17 K.
Limitations
- Uniform temperature along the bar; local hot spots and bowing from uneven heating are not covered.
- Real supports are not fully rigid: the actual restraint is often less.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check a pipe or rod anchored at both ends
- Find the temperature rise a tie rod can take
- Decide whether an expansion joint is needed
Who it is for
- Design engineers
- Piping engineers
- Maintenance engineers
What you get
- Thermal stress, force and yield factor
- Buckling load and factor
- Temperature rise at yield and at buckling
Interpreting the result
- Long slender members buckle long before they yield: a guide or an expansion loop is then the answer.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 375–376, 281–287. Topic reference; no source tables or recommended settings are reproduced.
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Open the Restrained Bar Heating (Thermal Stress, Yield and Buckling) calculator
