working out the math?

[teeg123]

here is the question
You need a branch-circuit conductor for a 40 A non-continuous load in EMT with 8 current-carrying conductors. Conductors are THHN copper (90 °C). Ambient temperature is 40 °C. What is the minimum conductor size required after applying adjustment and correction factors?
I highlighted in blue what I feel is the important information to answer this question.
A-4 AWG
B-6 AWG (correct answer)
C-8AWG
D-10AWG (my answer)

I work through it like this correct me when I go wrong.
1st 40 Amps of non-continuous = 40 Amps
2nd I do temp correction 40Amps*1.15(which is in the 90 degrees for less than 50 degrees) =46Amps
3rd I do the bundle adjustment 46Amps*70%=32.2Amps which in the 90-degree column in table 310.16 shows me #10 AWG after I round up.
so, where am I going wrong and as always thanks in advance for the assistance.

 

[wwhitney]

Here is why #6 AWG is correct (how to check an answer, not how to determine the answer from scratch):

The 90C #6 Table 310.16 base ampacity is 75A, while for #8 it is 55A. Ambient temperature of 40C for tables based on 30C (such as Table 310.16) gives a correction factor of 0.91 for 90C rated conductors, per Table 310.15(B)(2)(a) (2017 NEC numbering). 8 CCCs gives you an adjustment factor of 0.7.

So the ampacity under these conditions of use for #6 would 75A * 0.91 * 0.7 = 48A, while for #8 it would be 55A * 0.91 * 0.7 = 35A. 35A is less than the 40A non-continuous load, while 48A is more than the load. So #6 is OK, while #8 is not. That makes #6 the smallest size allowed.

Now, you can determine the answer from scratch by reversing the above computation. 40A is the goal, but we are going to reduce the table value by 0.91 * 0.7. That means we need to divide 40A by (0.91 * 0.7) to get the minimum table value. 40A / (0.91 * 0.7) = 62A. So we look at Table 310.16 and find the smallest size that has entry of at least 62A in the 90C column. Which is #6.

Cheers, Wayne