4.0 NCARB QUES. No. 6 - Section Modulus Process?

[BAA]

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 ?

[Mike-SE]

you math is correct. BUT the correct answer is 57.33 in^3 Your method came up with a wrong answer

[BAA]

you math is correct. BUT the correct answer is 57.33 in^3 Your method came up with a wrong answer

Is there any rule to know which and when to apply a certain method? I feel like I'm missing something very fundamental.

[Mike-SE]

ALWAYS calculate the moment of inertia

[BAA]

Found a great explanation for this. See:

http://www.dustingoffron.com/ARE/NCARB3.pdf


Parallel Axis Theorem

[cam]

Thank you BAA, that explanation was extremely helpful!! I was stumped!

[14Finish]

When calculating the moment of inertia I am double guessing which dimension should be d and thus be cubed. In ballast I think I read that d is always perpendicular to the axis. No primary axis is given in this example. How would you know to pick the X-X axis? I get a completely different answer when I try to calculate it through the Y-Y axis.

How would your process change if an axis is shown in the diagram vs. not shown?

I test Monday. Any help is much appreciated! Thanks!!

[SoonArch]

14Finish,

I was confused too. Finally I realized the diagram is given in section, and you can assume the B for BASE is the bottom plane, the one that is "grounded". Does this make sense?

If there is no diagram, they would have to tell you in text. There is no other way.

[14Finish]

Thanks SoonArch! That is very helpful.

All the guides emphasized the direction of the axis so I thought I must be missing something.