如何计算Moment Of Inertia
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Moment of inertia measures a shape's resistance to bending. Higher I values indicate better deflection resistance and are key in beam selection.
公式
For common shapes: rectangles I = bh³/12, circles I = πd⁴/64
- I
- bh³/12 — bh³/12
分步指南
- 1Calculate I by integrating area times distance squared from neutral axis
- 2For common shapes: rectangles I = bh³/12, circles I = πd⁴/64
- 3Results show bending stiffness contribution
例题解析
输入
Rectangular beam 200 mm wide × 400 mm tall
结果
I = 200×400³/12 ≈ 1.07×10⁹ mm⁴
Significant bending resistance
常见错误注意事项
- ✕Using wrong axis (major vs. minor axis moment)
- ✕Confusing moment of inertia with mass moment of inertia
常见问题
Why does I depend on axis location?
Material farther from neutral axis contributes more to bending resistance; parallel axis theorem accounts for location.
How does I affect beam weight?
I-beams maximize I while minimizing weight by placing material far from neutral axis.
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