Core Links Engineering CalculatorsHPに戻るCompany home

ENGINEERING CALCULATORS

Roller tube / round shaft bending stress and deflection calculator

Engineering calculators (Beta)

Check nominal stress and centre deflection of a uniform simply supported roller tube/round shaft under a centre point or centred patch load plus self-weight.

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=π(D⁴−d⁴)/64; Z=2I/D; W=ρπ(D²−d²)Lg/4; M=F(2L−b)/8+WL/8; δ=F(8L³−4Lb²+b³)/(384EI)+5WL³/(384EI); b=0 for a centre point; R=(F+W)/2; σ=M/Z.

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

一定断面のローラー胴・丸軸を両端支持として、中央荷重または中央の分布荷重と自重による公称応力・中央たわみを確認します。

入力・結果・適用条件を確認する

主な入力

  • 荷物から1本に加わる荷重の形
  • 両支持点の中心間距離 L
  • 計算する一定断面の外径 D
  • 同断面の内径 d（中実は0）
  • 中央の荷重が広がる幅 b
  • 荷物からこの1本に加わる合計荷重 F
  • 実材料のヤング率 E（例）
  • 実材料の密度 ρ（自重用、例）
  • 比較用許容曲げ応力 σa（例）
  • 比較する中央たわみ上限 δlim（例）

得られる結果

  • 最大公称曲げ応力 σ (MPa)
  • 中央のたわみ δ (mm)
  • 中央の最大曲げモーメント M (N·m)
  • 支持点1か所の反力 R (N)
  • 支持間の部材自重 W (N)
  • 断面二次モーメント I (mm⁴)
  • 弾性断面係数 Z (mm³)
  • 入力許容応力／公称曲げ応力 (—)
  • 入力たわみ上限／中央たわみ (—)

I=π(D⁴−d⁴)/64; Z=2I/D; W=ρπ(D²−d²)Lg/4; M=F(2L−b)/8+WL/8; δ=F(8L³−4Lb²+b³)/(384EI)+5WL³/(384EI); b=0 for a centre point; R=(F+W)/2; σ=M/Z.

一定円形・中空円形断面、理想的な両端単純支持、中央対称の静荷重のEuler–Bernoulli小変形モデルです。0≤d<D、0<b≤L（分布時）。Fは1本へ実際に伝わる荷重で、搬送物総重量そのものとは限りません。密度から求める自重は支持点間の同断面の部分だけです。段付き軸、別部品の軸と外筒の組合せ、はめあい、端栓、ベアリング部、溶接部、局所接触・つぶれ、ねじり、疲労、回転による繰返し応力、接着やコーティングは含みません。実物が中央の細い軸で支える構造なら、その軸の荷重経路を別に評価してください。L/D<10やδ/L>0.05では基本梁モデルの適用を見直す注意を出します（規格の合否基準ではありません）。許容応力は同じ公称応力基準・材料・加工・温度・寿命条件に合わせ、入力例を製品定格にしないでください。

関連する計算

What this calculator does

Check nominal stress and centre deflection of a uniform simply supported roller tube/round shaft under a centre point or centred patch load plus self-weight.

Inputs, outputs and applicability

Inputs

  • Load shape on one roller
  • Centre-to-centre support span L
  • Outside diameter D of the uniform section
  • Inside diameter d of that section (solid: zero)
  • Centred loaded width b
  • Total external load F on this one roller
  • Actual material Young modulus E (example)
  • Material density ρ for self-weight (example)
  • Entered nominal bending allowable σa (example)
  • Entered centre-deflection limit δlim (example)

Results

  • Maximum nominal bending stress σ (MPa)
  • Centre deflection δ (mm)
  • Maximum centre bending moment M (N·m)
  • Reaction R at each support (N)
  • Self-weight W between supports (N)
  • Second moment of area I (mm⁴)
  • Elastic section modulus Z (mm³)
  • Entered allowable / nominal bending stress (—)
  • Entered deflection limit / centre deflection (—)

I=π(D⁴−d⁴)/64; Z=2I/D; W=ρπ(D²−d²)Lg/4; M=F(2L−b)/8+WL/8; δ=F(8L³−4Lb²+b³)/(384EI)+5WL³/(384EI); b=0 for a centre point; R=(F+W)/2; σ=M/Z.

Euler–Bernoulli small-deflection model for a uniform solid/hollow circular section, ideal simple supports and centred symmetric static loading. Require 0≤d<D and 0<b≤L for the patch. F is the load actually carried by one roller, not necessarily the total product weight. Density adds only self-weight of the uniform section between supports. Excludes stepped shafts, separate axle/tube assemblies, fits, end caps, bearing seats, welds, local contact/crushing, torsion, fatigue/rotating stress, bonding and coatings. If an internal smaller axle carries the real load, assess that load path separately. L/D<10 or δ/L>0.05 triggers a basic-beam-model warning, not a code threshold. Establish the allowable for the same nominal-stress basis, material, process, temperature and life; examples are not product ratings.

Related tools