The discussion revolves around finding a formula for the Moment of Inertia and Section Modulus of a cruciform (rectangular cross) section. Participants explore theoretical approaches and mathematical formulations relevant to structural engineering concepts.
Participants express differing views on the necessity of the parallel axis theorem and the correctness of the proposed formulas, indicating that multiple competing approaches and interpretations remain unresolved.
Participants have not reached consensus on the formulas or the assumptions underlying their calculations, and there are unresolved details regarding the geometry of the cruciform shape.
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)