I agree with howie ll that you didn't need the relay for a 3amp draw.
Typically DC ratings are lower than AC due to the fact that AC is figuratively speaking only half on. AC voltage is reversing polarity from + to - and - to + at 60Hz (60 times a second). DC is always + or - on any given circuit when on. If it was rated for DC they would have probably given it a 10amps DC rating. 9amps would likely be the Max that I would use it for, and 6amps for continual use. I figure about half the rated AC for DC use to play it safe.
Here is a better definition of SSR Relays:
3. Solid State Relays (SSR)
SSRs are constructed using a photo-sensitive MOSFET device with an LED to actuate the device. See Figure 3.
Solid State Relay (SSR): Light from the encapsulated LED actuates the photo-sensitive MOSFET and allows current to flow through it.
SSRs are a faster alternative to electromechanical relays because their switching time is dependent on the time required to power the LED on and off - approximately 1 ms and 0.5 ms respectively. Because there are no mechanical parts, their life expectancy is higher than an electromechanical or reed relay.
SSRs are useful for high-voltage applications because the LED actuation does provide a galvanic isolation barrier between the control circuitry and the MOSFET. Because the MOSFET is doing the switching, however, there is no galvanic barrier between its contacts. When there is no gate drive on the MOSFET, the drain-source channel on the MOSFET has a very high resistance providing the disconnection between the contacts.
Because the connection is made via a transistor instead of physical metal like in electromechanical and reed relays, the contact resistance for an SSR is greater. Although technology improvements are continually improving the contact resistance of SSRs, it is still not uncommon to find them in production today with resistances of 100 Ohms or more.
SSRs are not as robust as electromechanical relays. Much like reed relays, they are highly susceptible to surge currents and damage when used at signal levels above their rating. Although there are no metal contacts to weld, damage to the MOSFET can render the relay unusable.SSRs are common on matrices and multiplexers.
Info about relay types found here:
http://www.ni.com/white-paper/2774/en/