📏 梁挠度计算器（简支梁/悬臂梁，集中/均布荷载）Beam Deflection Calculator (Simply Supported or Cantilever, Point or Uniform Load)

使用说明与常见问题How-to & FAQ

「梁挠度计算器（简支梁/悬臂梁，集中/均布荷载）」是什么？What is the Beam Deflection Calculator (Simply Supported or Cantilever, Point or Uniform Load) tool?

选择支承和荷载形式（简支梁跨中集中力、简支梁均布荷载、悬臂梁端部集中力、悬臂梁均布荷载），输入荷载、跨度、弹性模量 E 和惯性矩 I（或矩形截面宽高），得到最大挠度、最大弯矩、支座反力和挠跨比 L/δ。本地处理。Choose supports and load (simply supported with a central point load or uniform load, cantilever with an end load or uniform load), enter the load, span, modulus E and second moment of area I (or a rectangular width and depth) and get the maximum deflection, maximum bending moment, support reaction and the span-to-deflection ratio L/δ. Processed locally.

如何使用「梁挠度计算器（简支梁/悬臂梁，集中/均布荷载）」？How do I use the Beam Deflection Calculator (Simply Supported or Cantilever, Point or Uniform Load) tool?

在「梁挠度计算器（简支梁/悬臂梁，集中/均布荷载）」中，填写「情形」、「集中力 F（kN）」、「均布荷载 w（kN/m）」、「跨度 L（m）」、「弹性模量 E（GPa）」等参数，结果会随输入实时计算并显示在下方。In the Beam Deflection Calculator (Simply Supported or Cantilever, Point or Uniform Load): Fill in "Case", "Point load F (kN)", "Uniform load w (kN/m)", "Span L (m)", "Modulus E (GPa)"; results are recalculated instantly as you type.

用的是哪些公式？Which formulas are used?

简支梁跨中集中力 δ = FL³/(48EI)；简支梁均布 δ = 5wL⁴/(384EI)；悬臂梁端部集中力 δ = FL³/(3EI)；悬臂梁均布 δ = wL⁴/(8EI)。最大弯矩分别为 FL/4、wL²/8、FL、wL²/2。Simply supported central load δ = FL³/(48EI); simply supported uniform δ = 5wL⁴/(384EI); cantilever end load δ = FL³/(3EI); cantilever uniform δ = wL⁴/(8EI). Maximum moments are FL/4, wL²/8, FL and wL²/2.

E 和 I 取多少？What values of E and I should I use?

钢约 200–210 GPa，铝约 69 GPa，木材约 8–14 GPa，混凝土约 25–40 GPa。I 可从型钢表查（cm⁴），矩形截面 I = bh³/12。Steel is about 200–210 GPa, aluminium about 69 GPa, timber about 8–14 GPa and concrete about 25–40 GPa. Take I from section tables in cm⁴, or use bh³/12 for a rectangle.

L/δ 有什么用？What is L/δ for?

挠跨比常用于判断刚度是否满足要求，例如楼面梁常见限值为 L/360（活荷载）。具体限值以适用规范为准。The span-to-deflection ratio is a common stiffness check; floor beams are often limited to L/360 under live load. Use the limits in the code that applies.

能举个计算实例吗？Can you show a worked example?

例如在「梁挠度计算器（简支梁/悬臂梁，集中/均布荷载）」中填 情形 = 简支梁，跨中集中力，集中力 F（kN） = 10，跨度 L（m） = 4，弹性模量 E（GPa） = 200，截面 = 直接输入 I，惯性矩 I（cm⁴） = 8000，结果区显示：最大挠度 δ：0.833 mm；位置：跨中；挠跨比 L/δ：L/4,800；最大弯矩：10 kN·m；支座反力：5 kN（每端）；ℹ 线弹性小挠度公式，未计自重和剪切变形；设计请按规范校核。For example, entering Case = Simply supported, central…, Point load F (kN) = 10, Span L (m) = 4, Modulus E (GPa) = 200, Section = Enter I, Second moment I (cm⁴) = 8000 in the Beam Deflection Calculator (Simply Supported or Cantilever, Point or Uniform Load) gives: Maximum deflection δ: 0.833 mm; Where: Midspan; Span/deflection L/δ: L/4,800; Maximum moment: 10 kN·m; Support reaction: 5 kN (each end); ℹ Linear elastic small-deflection formulas without self-weight or shear deformation; check designs against the relevant…

哪些输入会被检查？Which inputs are validated?

「梁挠度计算器（简支梁/悬臂梁，集中/均布荷载）」会检查这些输入——「集中力 F（kN）」、「均布荷载 w（kN/m）」、「惯性矩 I（cm⁴）」、「宽 b（mm）」、「高 h（mm）」：所选方式用到时必须填写，须大于 0；「跨度 L（m）」、「弹性模量 E（GPa）」：必须填写，须大于 0；绝对值超过 10¹⁵ 的数也会被拒绝。不符合时结果区显示具体提示，不会给出数字。The Beam Deflection Calculator (Simply Supported or Cantilever, Point or Uniform Load) checks its inputs — "Point load F (kN)", "Uniform load w (kN/m)", "Second moment I (cm⁴)", "Width b (mm)", "Depth h (mm)": required when the chosen option uses it, must be greater than 0; "Span L (m)", "Modulus E (GPa)": required, must be greater than 0; numbers above 10¹⁵ in absolute value are rejected too. When a value fails, the result area names the problem instead of showing a number.

有哪些选项可以调整？What options can I adjust?

「梁挠度计算器（简支梁/悬臂梁，集中/均布荷载）」的设置：「情形」可选 简支梁，跨中集中力、简支梁，均布荷载、悬臂梁，端部集中力、悬臂梁，均布荷载（默认 简支梁，跨中集中力）；「集中力 F（kN）」默认 10；「均布荷载 w（kN/m）」默认 5；「跨度 L（m）」默认 4；「弹性模量 E（GPa）」默认 200；「截面」可选 直接输入 I、矩形截面（默认 直接输入 I）；「惯性矩 I（cm⁴）」默认 8000；「宽 b（mm）」默认 100；「高 h（mm）」默认 200。每次生成结果都按当前设置处理。Settings in the Beam Deflection Calculator (Simply Supported or Cantilever, Point or Uniform Load) — "Case": Simply supported, central point load, Simply supported, uniform load, Cantilever, end point load, Cantilever, uniform load (default Simply supported, central point load); "Point load F (kN)" default 10; "Uniform load w (kN/m)" default 5; "Span L (m)" default 4; "Modulus E (GPa)" default 200; "Section": Enter I, Rectangle (default Enter I); "Second moment I (cm⁴)" default 8000; "Width b (mm)" default 100…

计算结果可以用于作业或工程吗？Can I use the results for homework or engineering?

「梁挠度计算器（简支梁/悬臂梁，集中/均布荷载）」使用教科书标准公式（公式写在说明和常见问题中），适合学习和估算核对；涉及安全的工程设计请以规范和实测为准。The Beam Deflection Calculator (Simply Supported or Cantilever, Point or Uniform Load) uses standard textbook formulas (given in the description and FAQ), which is good for learning and checking estimates; for safety-critical engineering follow codes and measured values.

「梁挠度计算器（简支梁/悬臂梁，集中/均布荷载）」免费吗？需要注册吗？Is the Beam Deflection Calculator (Simply Supported or Cantilever, Point or Uniform Load) free? Do I need an account?

「梁挠度计算器（简支梁/悬臂梁，集中/均布荷载）」完全免费，无需注册或安装，打开网页即可使用，手机和电脑都能用；输入的内容只在你的浏览器本地处理。The Beam Deflection Calculator (Simply Supported or Cantilever, Point or Uniform Load) is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.