Luke Wright and debutant Craig Cachopa combined to put Sussex in a strong position at tea on the first day of their Championship match with Warwickshire at Horsham.
The pair have so far put on 110 for the fourth wicket to guide Sussex to 230-3 after they had lost two quick wickets after lunch.
Wright continued his excellent form with the bat as he brought up his second 50 of the season from 72 balls.
Cachopa showed why Sussex gave him a two-year deal last week by making his maiden Championship half century from 89 deliveries.
Joyce was first to go when Keith Barker swung a ball past his drive to knock over middle stump after the Sussex skipper had made 16.
Nash had reached his third half century of the season when he was trapped lbw trying to work a ball from Rankin off his legs.
Cachopa has offered one chance when he was put down behind the stumps by Tim Ambrose off the bowling of Jeetan Patel.
Warwickshire also thought they had Wright caught at gulley on 45 but a bouncer from Boyd Rankin hit him on the body rather than the bat.
Wright will resume on 54 after tea chasing a third Championship century of the season with Cachopa on 52.
Sussex – who won the toss and elected to bat - had lost Luke Wells in the morning session when he was superbly caught behind by Ambrose off the bowling of Rikki Clarke for 35.