Point of Contra Flexure:- point where BM is zero (BM=0)
Point of Inflection:- point where SF is zero (SF=0)
Principle of Super Position: - If two or more force act on object we can calculate their combination effect by adding them together as long as the system behaves linearly.
😀 \( \frac{dM}{dx} = SF \)
Center of Gravity :- point in the object where its weight is evenly distributed in all direction .
😀 symmetrical – lies at center
😀 Uneven object – lies at closer to the heavier end
Centroid It is the center of a shape where it can balance perfectly.
😀 For a triangle:- lies from corners to the middle of the opposite sides meet.
😀 For a rectangle or circle :- Lies the middle of the shape.
| Shape | Moment of Inertia (Formula) | Description |
|---|---|---|
| Rectangle | \( I_x = \frac{b \cdot h^3}{12}, \ I_y = \frac{h \cdot b^3}{12} \) | Base width (b), height (h). |
| Circle | \( I = \frac{\pi \cdot r^4}{4} \) \( I = \frac{\pi \cdot D^4}{64} \) |
Radius (r). |
| Triangle | \( I_x = \frac{b \cdot h^3}{36}, \ I_y = \frac{h \cdot b^3}{36} \) | Base width (b), height (h). |
| Ellipse | \( I = \frac{\pi \cdot a \cdot b^3}{4} \) | Semi-major axis (a), semi-minor axis (b). |
| Hollow Circle (Ring) | \( I = \frac{\pi}{4} \cdot (R^4 - r^4) \) | Outer radius (R), inner radius (r). |
| Thin Rod | \( I = \frac{m \cdot L^2}{3} \) | Mass (m), length (L). |