A series of barium substituted La0.5Sr0.5-xBaxMnO3 materials has been synthesized and investigated using neutron powder diffraction. We show that Ba substitution suppresses the low-temperature orbital ordering that has been previously observed in La0.5Sr0.5MnO3, and demonstrate the evolution of the magnetic and nuclear structures as a function of increasing Ba content. All our samples exhibit paramagnetic and ferromagnetic properties near room temperature with the ferromagnetic structures described as I4/mc(')m(') and P4/mm(')m(') for x=0, 0.1, and 0.2 and x=0.3, 0.4, and 0.5, respectively. The Mn magnetic moments align ferromagnetically in the direction of the c axis with no evidence for any spin canting. The effects of A-site ionic size, size variance, and strains in the lattice on the ferromagnetic ordering temperature, T-C, are discussed and compared with other members of the general La-0.5(Ca,Sr,Ba)(0.5)MnO3 series. Depending on the substitution path, the relationship between T-C and < r(A)> is either near constant or looks like an inverted parabola. Finally, details of the magnetic, resistive, structural, and interatomic properties are presented.