Core Links Engineering CalculatorsHPに戻るCompany home

ENGINEERING CALCULATORS

Circular shaft torsion calculator

Engineering calculators (Beta)

Calculate shear stress and twist of a circular shaft or tube.

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

J = π (D⁴ − d⁴) / 32, τmax = T D / (2 J), θ = T L / (G J)

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.

この計算で求められること

丸軸・円管のねじり応力とねじれ角を求めます。

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

  • 外径 D (mm / cm / m)
  • 内径 d(丸棒は0) (mm / cm / m)
  • トルク T (N·m / N·mm / mN·m)
  • 横弾性係数 G(入力例) (GPa / MPa / Pa)
  • 長さ L (mm / cm / m)

得られる結果

  • 円断面のねじり定数 J (mm⁴)
  • 外周のせん断応力 τmax (MPa)
  • ねじれ角 θ (°)
  • ねじり剛性 GJ (N·m²)

計算式の概要

J = π (D⁴ − d⁴) / 32, τmax = T D / (2 J), θ = T L / (G J)

一定の円形断面・均質材・弾性ねじりです。非円形断面にこのJの式は使えません。キー溝・応力集中・疲労は含みません。

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

Calculate shear stress and twist of a circular shaft or tube.

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

  • Outside diameter D (mm / cm / m)
  • Inside diameter d (0 for solid) (mm / cm / m)
  • Torque T (N·m / N·mm / mN·m)
  • Shear modulus G (example) (GPa / MPa / Pa)
  • Length L (mm / cm / m)

Calculated results

  • Circular torsion constant J (mm⁴)
  • Outer-surface shear stress (MPa)
  • Twist angle (°)
  • Torsional rigidity GJ (N·m²)

Formula overview

J = π (D⁴ − d⁴) / 32, τmax = T D / (2 J), θ = T L / (G J)

Uniform homogeneous circular section under elastic torsion. The J formula does not apply to noncircular sections. Keyways, stress concentrations and fatigue are excluded.

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