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ENGINEERING CALCULATORS

Tabletop / shelf load and deflection calculator

Engineering calculators (Beta)

Estimate payload limits from bending stress and deflection for a stated span, width and thickness.

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; Z=Bt²/6; σ=M/Z; simple UDL δ=5WL³/(384EI); centre line δ=PL³/(48EI); self-weight is added separately.

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

支持間隔・幅・厚みから、曲げ応力とたわみの制限に対応する積載荷重を概算します。

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

  • 支持・荷重のモデル (—)
  • 支持間隔・張出し長さ L (mm / cm / m)
  • 荷重を受ける有効幅 B (mm / cm / m)
  • 天板の厚さ t (mm / cm / m)
  • 追加する積載質量 m (kg / g / mg)
  • 天板材の密度 ρ（入力例） (kg/m³ / g/cm³ / g/L)
  • ヤング率 E（入力例） (GPa / MPa / Pa)
  • 比較する曲げ許容応力 (MPa / GPa / Pa)
  • たわみの上限 δlim (mm / cm / m)

得られる結果

  • 応力・たわみ制限からの追加積載の目安 (kg)
  • 応力制限からの追加積載 (kg)
  • たわみ制限からの追加積載 (kg)
  • 今回の曲げ応力 (MPa)
  • 今回の最大たわみ (mm)
  • 天板の自重に対応する質量 (kg)
  • 各支持辺の鉛直反力（片持ちは固定端） (N)
  • 最大曲げモーメント (N·m)

計算式の概要

I=Bt³/12; Z=Bt²/6; σ=M/Z; simple UDL δ=5WL³/(384EI); centre line δ=PL³/(48EI); self-weight is added separately.

均質・一定厚みの天板を幅Bの1方向の梁として扱います。2辺支持は支持辺が幅全体に連続する条件です。中央荷重も幅全体に分布する線荷重で、狭い面積への点荷重ではありません。四隅の脚だけで支える板、四辺支持の2方向板、合板・木材の異方性、補強、せん断・局部変形は対象外です。脚・架台・締結部・床や転倒の耐荷重は別に確認します。許容応力とたわみ上限は使用条件から指定します。

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

Estimate payload limits from bending stress and deflection for a stated span, width and thickness.

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

  • Support and loading model (—)
  • Span / overhang L (mm / cm / m)
  • Effective load-carrying width B (mm / cm / m)
  • Top thickness t (mm / cm / m)
  • Additional payload mass m (kg / g / mg)
  • Top density ρ (example) (kg/m³ / g/cm³ / g/L)
  • Young modulus E (example) (GPa / MPa / Pa)
  • Bending stress limit for comparison (MPa / GPa / Pa)
  • Deflection limit δlim (mm / cm / m)

Calculated results

  • Additional payload within stated limits (kg)
  • Payload from stress limit (kg)
  • Payload from deflection limit (kg)
  • Bending stress at entered payload (MPa)
  • Maximum deflection at entered payload (mm)
  • Top self mass (kg)
  • Vertical reaction per edge (clamp for cantilever) (N)
  • Maximum bending moment (N·m)

Formula overview

I=Bt³/12; Z=Bt²/6; σ=M/Z; simple UDL δ=5WL³/(384EI); centre line δ=PL³/(48EI); self-weight is added separately.

A homogeneous constant-thickness top is modelled as a one-way beam of width B. Supported edges must be continuous across the width. The centre load is a line load spread across the full width, not a small-area point load. Four isolated corner legs, two-way four-edge plate action, plywood/wood anisotropy, reinforcement, shear and local deformation are excluded. Legs, frame, joints, floor and tipping require separate checks. Specify applicable stress and deflection limits.

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.