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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.
Формула
For common shapes: rectangles I = bh³/12, circles I = πd⁴/64
- I
- bh³/12 — bh³/12
Пошаговое руководство
- 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
Решённые примеры
Ввод
Rectangular beam 200 mm wide × 400 mm tall
Результат
I = 200×400³/12 ≈ 1.07×10⁹ mm⁴
Significant bending resistance
Распространённые ошибки
- ✕Using wrong axis (major vs. minor axis moment)
- ✕Confusing moment of inertia with mass moment of inertia
Часто задаваемые вопросы
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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