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Cantilever leaf spring load and deflection calculator

Engineering calculators (Beta)

Calculate tip load and root bending stress from the deflection of one uniform rectangular cantilever leaf.

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

I=bt³/12; k=3EI/L³=Ebt³/(4L³); F=kδ; σ=6FL/(bt²); U=kδ²/2; θ=FL²/(2EI).

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

一定幅・厚みの1枚板ばねについて、先端の変位から必要荷重と固定端の曲げ応力を求めます。

入力・結果・適用条件を確認する

主な入力

  • 固定端から荷重点までの有効長 L
  • 板幅 b
  • 板厚 t
  • ヤング率 E（例）
  • 先端の変位 δ（大きさ）
  • 比較用許容曲げ応力 σa（例）

得られる結果

  • 指定変位に必要な先端荷重 F (N)
  • 先端のばね定数 k (N/mm)
  • 固定端の公称曲げ応力 σ (MPa)
  • 弾性エネルギー U (J)
  • 先端のたわみ角 θ (°)
  • 変位／有効長 δ/L (%)
  • 入力許容応力／公称曲げ応力 (—)

I=bt³/12; k=3EI/L³=Ebt³/(4L³); F=kδ; σ=6FL/(bt²); U=kδ²/2; θ=FL²/(2EI).

根元を完全固定した一定矩形断面・等方材の1枚板に、先端で板面に直角な集中荷重を加えるEuler–Bernoulli小変形モデルです。板厚方向に曲げます。せん断たわみ、幅広板の2方向効果、固定端の局所応力・滑り、初期曲がり、積層ばね、接触、塑性、疲労は含みません。δ/L>0.1は小変形の仮定を見直すための注意表示で、規格上の合否境界ではありません。厚い短い板や大変位は別のモデルで確認します。許容応力は実材料・温度・加工・繰返し条件に合わせて指定し、入力例を製品保証値として使わないでください。

関連する計算

What this calculator does

Calculate tip load and root bending stress from the deflection of one uniform rectangular cantilever leaf.

Inputs, outputs and applicability

Inputs

  • Effective length L from clamp to load point
  • Leaf width b
  • Leaf thickness t
  • Young modulus E (example)
  • Tip deflection δ (magnitude)
  • Entered bending allowable σa (example)

Results

  • Tip load F for the entered deflection (N)
  • Tip spring rate k (N/mm)
  • Nominal root bending stress σ (MPa)
  • Elastic strain energy U (J)
  • Tip slope θ (°)
  • Deflection / effective length δ/L (%)
  • Entered allowable / nominal bending stress (—)

I=bt³/12; k=3EI/L³=Ebt³/(4L³); F=kδ; σ=6FL/(bt²); U=kδ²/2; θ=FL²/(2EI).

Euler–Bernoulli small-deflection model for one uniform rectangular isotropic leaf, ideally clamped at one end and loaded normal to its face at the free end. Bending is through thickness. Shear deflection, wide-plate effects, local clamp stress/slip, pre-curvature, stacked leaves, contact, plasticity and fatigue are excluded. δ/L>0.1 triggers a modelling alert, not a code acceptance threshold. Use an appropriate model for short thick leaves or large motion. Establish the allowable for actual material, temperature, manufacturing and cyclic duty; examples are not product guarantees.

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