# How to calculate the moment of inertia for 4 welded c beams?

I'm trying to figure out if an existing bus shelter can support additional weight on its roof. To do that, I need to figure out the bending moment of it's supporting beams, but I'm stuck on the unusual beam structure it uses. Basically it's 4 welded C beams. I have the engineering drawings for the structure, so I've attached the relevant detail I think. Any help would be appreciated.

• The quickest way would be to design this in autocad and use the MASSPROP Command, or similar functionality in other drafting software (e.g. Solidworks inventor etc).
– NMech
Mar 23, 2022 at 17:26

For the 4 channels assembly, due to symmetry, the neutral axes fall on the centroidal axes x & y.

$$I_x = \sum (I_i + Ai*d_i^2)$$

$$I_i$$ = moment of inertia of the individual channel with respect to its centroid. You can get it from a steel table.

$$A_i$$ = crossectional area of the individual channel.

$$d_i$$ = distance measured from the centroid of the individual channel to the "x-axis"

If needed, do the same for $$I_y$$.

Note: In calculating $$I_x$$, the $$A*d^2$$ term for C10 is zero, because the center of the channel is coincident with the neutral (x) axis (d = 0).

Suggestion: For a quick feel, you may start with the assumption that only the two C10s contribute to the strength of the beam. Then add C6s only if necessary.

For information:

• The welds are offset on top through unknown members! And 1/4" weld is not enough to develop full tension or compression in channels. Mar 23, 2022 at 3:54
• @kamran OP is checking on the strength of an "existing" structure that was already been "designed and built". He is only asking how to calculate the member property, not the design.
– r13
Mar 23, 2022 at 13:23