4.0 NCARB QUES. No. 6 - Section Modulus Process?
Posted: Sun Dec 28, 2014 2:11 pm
Mike-SE,
Your commentary states that: "You cannot determine the S for this member directly (try to if you don't believe me.)"
Although, I can arrive at the answer given in NCARB and follow the logic you prescribed for solving for I, I don't understand why this same logic cannot be applied to solving for S directly. Once b is known, and d is known, why will it not produce the same/correct answer?
Here is the logic:
1. For solid rectangle. S = b x d (squared) /6 = 6 x 10 (squared)/ 6 = 6 x 100 / 6 = 600/6 = 100
2. For the side rectangles. S = b x d (squared) / 6 = 2.5 x 8 (squared) / 6 = 2.5 x 64 /6 = 160 / 6 = 26.667
3. Multiple by 2 to account for both sides. 2 x 26.667 = 53.333
4. Subtract solid rectangle from side rectangles. 100 - 53.333 = 46.667
If the process works for the Moment of (I)nertia , why does it not work for the (S)ection Modulus? The b's and d's are known, why can they not be applied? Why do we have to go through I to get S, if S = bd^2 /6 and/or S = I/C ?
Your commentary states that: "You cannot determine the S for this member directly (try to if you don't believe me.)"
Although, I can arrive at the answer given in NCARB and follow the logic you prescribed for solving for I, I don't understand why this same logic cannot be applied to solving for S directly. Once b is known, and d is known, why will it not produce the same/correct answer?
Here is the logic:
1. For solid rectangle. S = b x d (squared) /6 = 6 x 10 (squared)/ 6 = 6 x 100 / 6 = 600/6 = 100
2. For the side rectangles. S = b x d (squared) / 6 = 2.5 x 8 (squared) / 6 = 2.5 x 64 /6 = 160 / 6 = 26.667
3. Multiple by 2 to account for both sides. 2 x 26.667 = 53.333
4. Subtract solid rectangle from side rectangles. 100 - 53.333 = 46.667
If the process works for the Moment of (I)nertia , why does it not work for the (S)ection Modulus? The b's and d's are known, why can they not be applied? Why do we have to go through I to get S, if S = bd^2 /6 and/or S = I/C ?