Area Moment of Inertia for Solid Shafts

[teng125]

for a solid shaft,the area moment of inertia is (pi*d^4) / 64 or (pi*d^4) / 32 ?? i mean in bending and buckling case.

ihave two formulas but don't know which one is correct??


does anybody has those formulas for other cross sections ??
pls help

 

[Meson]

For a shaft with cross section d,

Area moment of inertia is $$I=\frac{\pi*d^4}{64}$$ with unit $$mm^4$$

Widerstandsmoment, $$W=\frac{\pi*di^3}{32}$$ with unit $$mm^3$$

Relation between W and I, for the case of bending and bulking, is given by:
$$W_{by}=\frac{I_{y}}{C}$$ where C is the (maximum) distance from the neutral axis to the outermost fiber or layer of atoms.

Hence, do not be confused as they are different and yet related. If one is known, let's say I, the other can be found, W in this case.

 

[piercas]

I can confirm that both formulas are correct for calculating the area moment of inertia for solid shafts in bending and buckling cases. The difference lies in the assumption of boundary conditions and loading conditions. The (pi*d^4) / 64 formula assumes fixed-fixed boundary conditions and uniform loading, while the (pi*d^4) / 32 formula assumes simply supported boundary conditions and central loading.

For other cross sections, there are different formulas for calculating the area moment of inertia depending on the shape and boundary conditions. Some common cross sections and their corresponding area moment of inertia formulas are:

- Rectangular cross section: (b*h^3)/12, where b is the base and h is the height
- Circular cross section: (pi*d^4)/64, where d is the diameter
- Triangular cross section: (b*h^3)/36, where b is the base and h is the height
- I-beam cross section: (b*h^3)/12 - 2*(b-2*t)*(h-t)^3/12, where b is the total width, h is the total height, and t is the thickness of the flanges

It is important to use the correct formula for the specific cross section and boundary conditions in order to accurately calculate the area moment of inertia. I recommend consulting a reference book or online resource for a comprehensive list of area moment of inertia formulas for different cross sections.