1. Rectangular Section:
* Formula: I = (b * h^3) / 12
* where:
* I = Moment of inertia
* b = width of the rectangle
* h = height of the rectangle
2. Circular Section:
* Formula: I = (π * d^4) / 64
* where:
* I = Moment of inertia
* d = diameter of the circle
3. Hollow Circular Section:
* Formula: I = (π/64) * (D^4 - d^4)
* where:
* I = Moment of inertia
* D = outer diameter of the hollow circle
* d = inner diameter of the hollow circle
4. I-Section:
* Formula: I = (b * h^3) / 12 - 2 * [(b/2 - t) * (h/2 - t)^3 / 12]
* where:
* I = Moment of inertia
* b = width of the I-section flange
* h = total height of the I-section
* t = thickness of the flange and web
5. T-Section:
* Formula: I = (b * h^3) / 12 + (b * h/2)^2 * (h/2 - t)^2 / 12
* where:
* I = Moment of inertia
* b = width of the T-section flange
* h = total height of the T-section
* t = thickness of the flange and web
Parallel Axis Theorem:
If you need to calculate the moment of inertia about an axis that is not the centroidal axis, you can use the parallel axis theorem:
* Formula: I = I_c + A * d^2
* where:
* I = Moment of inertia about the desired axis
* I_c = Moment of inertia about the centroidal axis
* A = Area of the cross-section
* d = Distance between the centroidal axis and the desired axis
Important Notes:
* These formulas assume the cross-section is homogeneous and has a uniform material throughout.
* The moment of inertia is always calculated with respect to a specific axis.
* The units for the moment of inertia are usually expressed in mm^4 or inches^4.
Remember to choose the appropriate formula based on the shape of your beam section and use the correct units for your calculations.
