First off, 13.75V is very close to the voltage you will get by using a 220 ohm in place of the 240 ohm resistor and 2.2K in place of the 2K resistor so there is no problem there.
Second, the use of a full-wave bridge and a capacitor will not provide you with the level of voltage regulation that you will need for your fans.
Can you provide the part number and manufacturer of the fan you are using?
The LM317 does have a thermal overload protection so the shutdown you are experiencing if probably this feature kicking in.
It sounds like your heatsink may not have sufficient surface area to dissipate the heat built up in the part due to the load. I tried to look up the specs on the heatsink you indicated you are using but I can find anything about the heatsink at www.radioshack.com.
A picture is worth a thousand words so if you could take a jpeg of the circuit and post it here that would be very helpful.
hgmjr
Second, the use of a full-wave bridge and a capacitor will not provide you with the level of voltage regulation that you will need for your fans.
Can you provide the part number and manufacturer of the fan you are using?
The LM317 does have a thermal overload protection so the shutdown you are experiencing if probably this feature kicking in.
It sounds like your heatsink may not have sufficient surface area to dissipate the heat built up in the part due to the load. I tried to look up the specs on the heatsink you indicated you are using but I can find anything about the heatsink at www.radioshack.com.
A picture is worth a thousand words so if you could take a jpeg of the circuit and post it here that would be very helpful.
hgmjr