15 AmP is just 1800 watts I hope you aren't consuming more than that through the socket? It's more then that can be the issue, 13x RX580 is bad news if that's the RX card you are referring to, that's almost 1500+ watts from the gpu only minus other things that are using power too
I will say this was good answer.
If you are a 120 volt home you are simply not able to pull more than 15 x 120 x 80% = 1440 watts for any length of time.
So op pull three cards off the rig.
10 cards are going to do about 1200 -1300 watts at the wall.
13 are going to do 1600-1700 watts at the wall. This is a liable act of deliberate mis use of your power circuit. If you are 120 volt.
So
A) Burn the place down you get zero for insurance.
B) Burn the place down you get charged with a crime if some one is hurt.
C) Burn the place down you get charged for arson.
This is USA law in every state.
You are not allowed to intentionally overload a circuit.
And you are now aware that is what you are doing.
Now if you pull three cards off the rig and you feel cool by the switch good.
If the switch/circuit breaker is still too hot there are more possible issues.
Get back to us and see if running 10 cards works.
I will further explain.
There are many sapphire cards.
You did not tell us which one.
I used common ones to get my numbers
the rx470 8gb
the rx 480 8gb
the rx 570 8gb
the rx 580 8gb
if set correctly they do 120-130 watts and about 25mh
they can do 200 watts
they sometimes go runaway and even when set to 120-130 watts they say fuck you I am burning 200 watts. which means 200 x 13 or 2600 watts really over loading your circuit.
So next issue did you do this under linux or with windows. windows has runway power issues way more often than linux.
So may this is happening which is worse since you are already using too much power on the circuit and if you go run away it is worse.