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梁弯曲计算器
计算简支梁和悬臂梁在各种载荷类型下的最大弯矩、挠度和应力。
成果
简支梁——中心点受力
简易支撑 — UDL
悬臂梁——端部受力点
弯曲应力
其中： σ 是弯曲应力， M 是弯矩， c 是到极端纤维的距离，而且 I 是转动惯量。
| 载荷工况 | M_max | δ_max |
|---|---|---|
| SS — 中心点 | PL/4 | PL³/(48EI) |
| SS——指向 | Pa(L-a)/L | 复杂公式 |
| SS - UDL w | wL²/8 | 5wL⁴/(384EI) |
| 悬臂梁——临界点 | PL | PL³/(3EI) |
| 悬臂梁 — UDL w | wL²/2 | wL⁴/(8EI) |
⚠️ 注意： 这些公式假设梁为线弹性梁，挠度较小，且梁为棱柱形（截面恒定）。对于复杂载荷，请使用叠加法。
Beam bending occurs when a transverse load is applied to a structural member, causing it to deflect. The beam develops internal bending moments and shear forces. Bending stress varies linearly across the section — zero at the neutral axis and maximum at the extreme fibers.
A simply supported beam rests on two supports at its ends and is free to rotate at those points. A cantilever beam is rigidly fixed at one end and free at the other.
Cantilevers have larger deflections and moments at the fixed support than equivalently loaded simply supported beams.
Deflection depends on load type, span length (L), elastic modulus (E), and moment of inertia (I):
- SS center point load: δ = PL³/(48EI)
- SS UDL: δ = 5wL⁴/(384EI)
- Cantilever tip load: δ = PL³/(3EI)
The second moment of area (I) is a geometric property that measures the cross-section's resistance to bending. Larger I means less deflection and stress for the same load. For a rectangle: I = bh³/12. For a circle: I = πd⁴/64.
Common limits per building codes:
- L/360 — Floor beams (live load)
- L/240 — Total load
- L/180 — Roof beams
- L/500 — Precision machinery supports
Always check applicable design standards.
本页所述的操作流程由 Vibromera 团队使用 Balanset-1A（一款用于现场转子平衡的便携式双通道动平衡仪及振动分析仪）开发并经过实地测试。
专业现场平衡仪器和软件。已在50多个国家使用。
