You don't really need the parallel axis theorem because the cross section is symmetric, so you can just take the moment of inertia about the centroid, which is [(b*h^3)/12] + [(h*b^3)/12] (actually, a bit less, because you have to take out that small square where the rectangles cross). But to get the section modulus, your calculation is not correct, you have to take the total I and divide it by b/2. Note that if b is much greater than h, that first term is insignificant, and essentially the moment of inertia approximates hb^3/12, and the section modulus approximates hb^2/6.GodBlessTexas said:Jay,
Wouldn't this require parallel axis theorem?
Or without getting into that could you just say [(b*h^2)/6] + [(h*b^2)/6] <-- (wait, isn't this the same as perpendicular axis theorem?)
where b is the length from end to end of the cruciform, and h is the width of the segment?
(for section modulus)
Moment of inertia is a measure of an object's resistance to changes in its rotational motion. It is important because it helps engineers and scientists understand how an object will behave when subjected to forces or torques.
Moment of inertia for a cruciform can be calculated by adding the moments of inertia for each individual component of the cross, using the parallel axis theorem. This involves calculating the moment of inertia for each individual rectangular section and then adding them together.
Section modulus is a measure of a cross section's resistance to bending. It is related to moment of inertia because it takes into account the distribution of material around the axis of rotation, which directly affects the moment of inertia. Section modulus is calculated by dividing the moment of inertia by the distance from the neutral axis to the outermost fibers of the cross section.
The shape of a cruciform greatly affects its moment of inertia and section modulus. The farther the material is from the axis of rotation, the higher the moment of inertia and section modulus will be. This means that a cruciform with a larger cross section will have a higher moment of inertia and section modulus compared to a cruciform with a smaller cross section.
Some factors that can affect the moment of inertia and section modulus of a cruciform include the dimensions of the cross section, the material the cruciform is made of, and the distribution of material around the axis of rotation. Additionally, any holes or cutouts in the cross section can also greatly affect the moment of inertia and section modulus.