I am nearing the end of my studying and I think my brain is mush. i need help in understanding why ncarb's answer is 57.3. and why I'm getting two separate answers, for that matter.

Let me show you my process.

We know that I = bd(cubed)/12 and S=I/C and (in this case) C=d/2

If we substitute bd(cubed)/12 in and the C/2 the section modulus formula, you get bd(cubed)/12/d/2

or bd(squared)/6

When i calculate using the revised formula (bd(squared/6), i get 46.7.

for illustration purposes:

(6)(10)(10)/6 - (2)(2.5)(8)(8)/6 = 100 - 53.3 = 47.7

If i go the long way, i.e. calculating for I of larger rectangle and subtracting 2 times the I of the void rectangles and then substituting that for I in the S=I/C formula, I get what ncarb gets.

I = (6)(10)(10)(10)/12 - (2)(2.5)(8)(8)(8)/12 = 500 - 213.4 = 286.7

S = I/c/2 = 286.7/5 = 57.3

Mathematically this should not happen and for the life of me, I can't figure out why it is happening that way. Maybe it is is something really simple but my brain is fried and I'm at a loss to see it.

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any insight would be appreciated.

Thanks!