I have a machine that requires 56A 3-phase, according to the nameplate. It will be cord-and-plug connected with 100A pin&sleeve connectors, fed from a 100A breaker. This machine will be considered a continuous load, so I multiplied the 56A nameplate by 1.2 to get 67A (thus, the 100A connectors and breaker). Do I size the SO cable for 56A, or 67A? I'd select 2/5 SO and just be done with it, but I have concern about the #2 conductors fitting in the supplied lugs. #4 wire should fit, no problem.
Thanks,
SceneryDriver
This is approaching a DIY type project given the lack of understanding that your question itself shows.
I don't know where you came up with the idea to multiply the FLA by 1.2. This is not something supported by any electrical code that i have seen. Normally if it is a continuous load the multiplier to get the ampacity of the cord would be 1.25. 56 X 1.25 = 70 Amps.
I think that by 2/5 cord you mean five #2 conductors. I don't know why you would need 5 conductors. Normally the 3 phase conductors and a ground would be adequate, although sometimes you might need a neutral which could account for the 5th wire.
The use of cords is covered in article 400.
T400.5(A)(1) will tell you what the allowable ampacity of SO cord is. For #2 conductors it is 80 Amps. For #3 it is 70 Amps. At least in the 2017 code.
You can make the cord larger than the minimum required.
Regardless of the wire size, you have to protect the wire at its ampacity. Article 240 will tell you what the maximum size circuit breaker or fuse is allowed for the ampacity of the conductors. 240.4 allows you to select the next standard higher rated CB above the conductor ampacity under 800 Amps. T240.6(A) tells you what the standard breaker and fuse ratings are. Since 70 and 80 are standard ratings, you would need to protect #2 SO cord with an 80 A rated device, and #3 SO cord with a 70 A rated device.
Incidentally, the instructions that come with the connector will tell you what the maximum size of the conductors can be. It is not whether they will fit or not. It is whatever the instructions say.
Personally, I might be looking at using a cord other than SO that has higher ampacity ratings at smaller conductor sizes, keeping in mind that many devices are rated for a maximum of 75 deg C terminations so even if the conductor insulation can go higher than that, as a practical matter you may well be limited to the 75 deg C column. The connector instructions should tell you what the temperature limits are. if they don't say, it is 75 deg C.
Please be careful to read the notes at the bottom of the tables. The ampacity ratings are different depending on how many of the conductors in the cord are considered current carrying.