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ENGINEERING CALCULATORS

Tall-object tipping and sliding calculator

Engineering calculators (Beta)

Separate tipping and sliding boundaries using the centre of gravity, footprint, floor slope and lateral force.

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

N=mg cosθ; M=mg cosθ·x−mg sinθ·hc+Fh; xR=M/N; RL=N/2−M/B; RR=N/2+M/B; friction demand=|F−mg sinθ|.

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.

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この計算で求められること

重心・接地幅・床の傾き・横荷重から、左右の浮上りと滑りの境界を分けて確認します。

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

  • 対象全体の質量 m (kg / g / mg)
  • 検討方向の接地幅 B (mm / cm / m)
  • 接地中央から重心まで x（右が正） (mm / cm / m)
  • 床から重心までの高さ hc (mm / cm / m)
  • 床に平行な横荷重 F（右が正） (N / kN / mN)
  • 横荷重の作用高さ h (mm / cm / m)
  • 床の角度 θ（右上がりが正） (° / rad / % grade)
  • 静摩擦係数 μ（入力例） (—)

得られる結果

  • 転倒モーメントの余裕（負は浮上り） (N·m)
  • 静摩擦力の余裕（負は滑り境界超え） (N)
  • 左端の鉛直反力（床に垂直） (N)
  • 右端の鉛直反力（床に垂直） (N)
  • 右へ転倒する横荷重の境界値 (N)
  • 左へ転倒する横荷重の境界値（符号付き） (N)
  • 垂直反力の位置 xR (mm)

計算式の概要

N=mg cosθ; M=mg cosθ·x−mg sinθ·hc+Fh; xR=M/N; RL=N/2−M/B; RR=N/2+M/B; friction demand=|F−mg sinθ|.

検討する鉛直断面内の剛体・準静的なつり合いです。Bは外形幅ではなく実際の接地端間です。重心位置xと高さhcは床の座標系で指定します。負の反力は接地を保てない計算結果です。転倒と滑りを別々に表示し、転倒後・滑走後の挙動、衝突、地震応答、アンカー、キャスター、床のたわみは計算しません。奥行き方向も別に確認します。

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

Separate tipping and sliding boundaries using the centre of gravity, footprint, floor slope and lateral force.

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

  • Total mass m (kg / g / mg)
  • Footprint width in the checked direction B (mm / cm / m)
  • CG offset x from footprint centre (right positive) (mm / cm / m)
  • CG height above floor hc (mm / cm / m)
  • Force parallel to floor F (right positive) (N / kN / mN)
  • Lateral-force height h (mm / cm / m)
  • Floor slope θ (rising right positive) (° / rad / % grade)
  • Static friction coefficient μ (example) (—)

Calculated results

  • Tipping moment reserve (negative: uplift) (N·m)
  • Static friction reserve (negative: exceeded) (N)
  • Left normal reaction (N)
  • Right normal reaction (N)
  • Force at right-tipping boundary (N)
  • Signed force at left-tipping boundary (N)
  • Normal reaction position xR (mm)

Formula overview

N=mg cosθ; M=mg cosθ·x−mg sinθ·hc+Fh; xR=M/N; RL=N/2−M/B; RR=N/2+M/B; friction demand=|F−mg sinθ|.

Rigid-body quasi-static equilibrium in one vertical section. B is the actual contact-edge spacing, not overall width. CG x and hc use floor coordinates. A negative reaction means contact cannot be maintained. Tipping and sliding are separate; post-tip/post-slip motion, impacts, earthquake response, anchors, casters and floor flexibility are excluded. Check the other horizontal direction separately.

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.

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目的から順に確認する設計ガイド

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。

Purpose-based design guides

Understand conditions with diagrams, calculate, then verify actual specifications.