We find families of integrable n-leg spin-1/2 ladders and tubes with genera
l isotropic exchange interactions between spins. These models are equivalen
t to su(N) spin chains with N = 2(n). Arbitrary rung interactions in the sp
in tubes and ladders induce chemical potentials in the equivalent spin chai
ns. The potentials are n-dependent and differ for the tube and ladder model
s. The models are solvable by means of nested Bethe ansatze.