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Restrained-bar thermal stress calculator

Engineering calculators (Beta)

Find elastic thermal stress and axial force for a fully restrained bar.

Inputs

Choose units and enter numbers. Full-width digits and fractions such as 1/8 or 1 3/8 are accepted. Changing a unit converts the entered value.

Results

Reference calculation only. Results do not certify suitability for an actual design or its safety.

Diagram

Inputs: select a blue symbol to edit Results: red-orange values and lines

Formula and applicability

σ=−EαΔT; F=σA; ΔLfree=αLΔT.

Displayed values are rounded. Diagrams illustrate the calculation conditions. Initial material and fluid properties are examples; replace them with values for the actual material, temperature and conditions.

Reference
Using this information as a reference

Equations assume particular loads, supports and deformation ranges. Check inputs, units and the applicability of each equation. Diagrams explain conditions; they are not manufacturing drawings or proof of safety.

Material values are typical values or reference ranges, not certified product properties or ready-to-use design allowables. They vary with standards, product form, dimensions, temper and temperature. Check the specifications and inspection certificates for the actual product.

Displayed safety factors and checks apply only to the supplied inputs and calculation model. They do not automatically establish the safety of a complete design, including code compliance, service life, fatigue or joints. For actual design, manufacture and use, separately verify applicable regulations and standards, product specifications, and the necessary tests and engineering review.

Calculations do not submit input values to a server. Results are not an automatic code-compliance or safety determination.

この計算で求められること

両端が完全に拘束された棒の温度変化から、弾性熱応力と軸力を求めます。

入力・結果・適用条件を確認する

選択した形状・計算方法により、使う項目は変わります。実際の計算は上の図と入力欄で行えます。

主な入力

  • ヤング率 E (GPa / MPa / Pa)
  • 線膨張係数 α（入力例） (µm/(m·K) / 1/K)
  • 温度変化 ΔT（冷却は負） (K / °C difference / °F difference)
  • 断面積 A (mm² / cm² / m²)
  • 拘束前の長さ L (mm / cm / m)

得られる結果

  • 熱応力（引張が正・圧縮が負） (MPa)
  • 拘束に生じる軸力（符号付き） (N)
  • 自由なら生じる伸び・縮み (mm)

計算式の概要

σ=−EαΔT; F=σA; ΔLfree=αLΔT.

均質な棒、温度は全体で一様、係数一定、両端の変位が完全に0の線形弾性モデルです。実際の支持の柔らかさ、塑性化、圧縮座屈、温度勾配、接合部の強度は計算しません。圧縮時は座屈も別に検討します。

現在選択中の方法には、操作欄の「計算式・適用条件」を使ってください。参考計算であり、設計全体の安全性を保証するものではありません。

関連する計算

What this calculator does

Find elastic thermal stress and axial force for a fully restrained bar.

Inputs, outputs and applicability

The selected model determines which of these inputs and outputs apply. Use the working diagram and input panel above to calculate.

Inputs

  • Young modulus E (GPa / MPa / Pa)
  • Expansion coefficient α (example) (µm/(m·K) / 1/K)
  • Temperature change ΔT (negative for cooling) (K / °C difference / °F difference)
  • Section area A (mm² / cm² / m²)
  • Original bar length L (mm / cm / m)

Calculated results

  • Thermal stress (tension positive) (MPa)
  • Signed restraint axial force (N)
  • Unrestrained length change (mm)

Formula overview

σ=−EαΔT; F=σA; ΔLfree=αLΔT.

Uniform temperature and constant properties in a homogeneous linear-elastic bar with zero end displacement. Support compliance, yielding, compressive buckling, temperature gradients and joint strength are excluded. Check buckling separately for compression.

The displayed formula and conditions in the working panel apply to the currently selected model. Reference calculation only; it does not certify a complete design.

Related tools

入力する単位を確認・換算する

Check and convert input units

数値の感覚を、図と動きで確かめる

説明用の別モデルです。適用条件を確認してください。数値は自動転記しません。

See the idea in diagrams and motion

A separate explanatory model. Check its assumptions; values are not transferred.