ENGINEERING CALCULATORS
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Engineering calculators (Beta)
Choose supports and load to calculate deflection, reactions and bending stress.
Click the grid to add ordered vertices. Edit coordinates in mm; separate holes with a blank line. The last vertex closes to the first automatically.
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.
Reference calculation only. Results do not certify suitability for an actual design or its safety.
Inputs: select a blue symbol to edit Results: red-orange values and lines
3D shows an illustrative extrusion. Its display length does not enter the section calculations. Edit dimensions in 2D.
σmax = |M|max / Zmin
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.
ReferenceEquations 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.
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支点と荷重を選び、たわみ・反力・曲げ応力を確認します。
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。
σmax = |M|max / Zmin
一定断面・均質・線形弾性・小変形のEuler–Bernoulli梁です。荷重は下向き。上向き反力、正曲げモーメント、下向きたわみを正とします。せん断変形・自重・応力集中・座屈・疲労は含みません。IとZは同じ主軸まわりの値を使用します。図の変形は拡大表示です。
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。
Choose supports and load to calculate deflection, reactions and bending stress.
The selected model determines which of these inputs and outputs apply. Use the working diagram and input panel above to calculate.
σmax = |M|max / Zmin
Uniform homogeneous linear-elastic Euler–Bernoulli beam with small deflection. Loads act downward. Upward reactions, sagging moments and downward deflection are positive. Shear deformation, self-weight, stress concentrations, buckling and fatigue are excluded. I and Z must refer to the same principal bending axis. Deflection is exaggerated in the diagram.
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.
図で条件を整理してから計算し、最後に実際の部品仕様を確認します。
Understand conditions with diagrams, calculate, then verify actual specifications.
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。
A separate explanatory model. Check its assumptions; values are not transferred.
この計算の「単純梁」は、両端をピンとローラーで支え、端の回転を拘束しないモデルです。「両端支持梁」と呼ばれることもあります。両端の回転も止める「両端固定梁」とは別の条件なので、実際の取付け方と図を合わせてください。
長さL = 500 mm、荷重F = 100 N、ヤング率E = 200,000 MPa、幅b = 40 mm・高さh = 20 mmの長方形断面を例にします。曲げる向きのI = bh³/12 = 26,666.666… mm⁴です。荷重点は、各代表モデルに合わせて自由端または中央に変わります。
| 支持・荷重点 | 最大たわみの式 | この例の最大たわみ |
|---|---|---|
| 片持ち梁・自由端にF | FL³ / (3EI) | 0.78125 mm |
| 単純梁／両端支持梁・中央にF | FL³ / (48EI) | 0.048828125 mm |
一様な線形弾性梁・小たわみ・1点荷重の例です。自重は含みません。この2条件での比較であり、どんな荷重点や支持条件でも同じ倍率になるわけではありません。
たわみは変形量、曲げ応力は材料内部の負担です。必要な機能に対するたわみの上限と、材料・製品状態に対応する許容応力を分けて確認します。ヤング率だけで許容応力は決まりません。
The simple-beam model uses a pin and a roller at the ends and allows end rotation. A fixed-fixed beam also restrains end rotation and is a different model. Match the support diagram to the actual connection.
Use L = 500 mm, F = 100 N, E = 200,000 MPa and a rectangular section of width b = 40 mm and height h = 20 mm. About the chosen bending axis, I = bh³/12 = 26,666.666… mm⁴. The point load is at the free end or the centre, as specified in each standard arrangement.
| Support and load position | Maximum deflection formula | Deflection in this example |
|---|---|---|
| Cantilever, tip load F | FL³ / (3EI) | 0.78125 mm |
| Simply supported, central point load F | FL³ / (48EI) | 0.048828125 mm |
These examples assume a uniform linear-elastic beam, small deflection and one point load, without self-weight. Their ratio does not apply to arbitrary support or load positions.
Deflection measures displacement; bending stress measures internal material loading. Check the functional deflection limit separately from the allowable stress for the actual material and product condition. Young’s modulus alone does not determine allowable stress.
See beam deflection and stress with diagrams → · Calculate second moment of area I →
