I am building a deck and will have 2x10 joists. I want to put a BBQ that unfortunately will run parallel with the joists, so the last two joists will support the full weight of the BBQ distributed across 10'? The span of the joists are 13' 6" between the header and supporting beam. The outer rim will be doubled 2x10s. My overestimate of the BBQ is that it will weight 2000-2200lbs. Will the current joists support the weight? If I double the 2nd joist, will that help? Does that effectively support twice the weight or is that not how that works? Should an additional post be added mid-span?
Yes, two 2x10's spanning 13'-6" will support 2,200 lbs. Grade of lumber can be No. 2 & better of typical framing lumber, like Hem.-Fir...it need not be Doug. Fir-Larch. In fact, each 2x10 will support 1,200 lbs.
To be clear, spans are measured as "clear spans". That is to say, from face of support to face of support. Also, if your BBQ is located in the middle of the span so that people can stand around the BBQ, then there will be an additional "Live Load" acting on the joists. This assumes the BBQ extends from support to support.
By the way, the code doesn't require blocking until you use 2x12's. However, for this "concentrated" load, I'd use blocking. (Yes, I know, technically, it's not a concentrated load, because it extends from support to support. However, it could be considered "concentrated" because it's resting on only 2 joist, not over multi-joists, like in a large space (room).)
If the joists rest on a beam, then secure the joists to the beam with a clip. If they "hang" on a beam, make sure the hangers are rated for the load, because you're approaching the joists maximum load. The joists need a minimum of 1 1/2" bearing at each end.
You didn't ask, but don't forget to install seismic deck straps (or rods) at about 20' oc. This is new to the 2014 code for all decks.
Re: your question about doubling joists...will that double the allowable supporting load...yes, that is how it works.
By the way, you reference a 10' space. Shouldn't that be 13'-6" space (span), or are you referring to the distance in the other direction. However, to me, that doesn't seem relevant because it doesn't contribute load to the 2x10 joists supporting the BBQ, right?