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ENGINEERING CALCULATORS

Combined beam loads & required I / Z calculator

Engineering calculators (Beta)

Superpose point, uniform and self-weight loads to obtain required section properties.

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

qtotal=q+λg; δ=δpoint+δudl; Ireq=Iδ/δlimit; Zreq=Mmax/σallow

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

集中荷重と等分布荷重・自重を重ね、必要な断面特性を求めます。

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

  • 支持条件 (—)
  • 梁の長さ L (mm / cm / m)
  • ヤング率 E (GPa / MPa / Pa)
  • 検討する断面二次モーメント I (mm⁴ / cm⁴ / m⁴)
  • 検討する最小弾性断面係数 Z (mm³ / cm³ / m³)
  • 集中荷重 F (N / kN / mN)
  • 外部の等分布荷重 q (N/m / N/mm / kN/m)
  • 梁自重の単位長さ質量 (kg/m / g/mm / lb/ft)
  • 目標最大たわみ (mm / cm / m)
  • 比較する許容曲げ応力 (MPa / GPa / Pa)

得られる結果

  • 最大たわみ (mm)
  • 最大曲げ応力 (MPa)
  • 目標たわみに必要なI (mm⁴)
  • 比較応力に必要なZ (mm³)
  • 左・固定端の反力 (N)
  • 右端の反力 (N)
  • 最大曲げモーメント絶対値 (N·m)

計算式の概要

qtotal=q+λg; δ=δpoint+δudl; Ireq=Iδ/δlimit; Zreq=Mmax/σallow

一定断面・線形弾性・小変形。荷重は全て下向きで、単純支持は中央、片持ちは先端の集中荷重です。任意位置の複数荷重・固定梁・せん断変形はこの画面では未対応。

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

Superpose point, uniform and self-weight loads to obtain required section properties.

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 condition (—)
  • Span L (mm / cm / m)
  • Young modulus E (GPa / MPa / Pa)
  • Current second moment I (mm⁴ / cm⁴ / m⁴)
  • Current minimum elastic modulus Z (mm³ / cm³ / m³)
  • Point load F (N / kN / mN)
  • External uniform load q (N/m / N/mm / kN/m)
  • Beam mass per length (kg/m / g/mm / lb/ft)
  • Target maximum deflection (mm / cm / m)
  • Allowable bending stress for comparison (MPa / GPa / Pa)

Calculated results

  • Maximum deflection (mm)
  • Maximum bending stress (MPa)
  • I required for target deflection (mm⁴)
  • Z required for comparison stress (mm³)
  • Left / fixed-end reaction (N)
  • Right reaction (N)
  • Maximum absolute bending moment (N·m)

Formula overview

qtotal=q+λg; δ=δpoint+δudl; Ireq=Iδ/δlimit; Zreq=Mmax/σallow

Prismatic linear-elastic small-deflection beam. All loads act downward; point load is at centre for simple supports or at tip for a cantilever. Arbitrary point-load sets, fixed-fixed beams and shear deformation 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.

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