We run N-body smoothed particle hydrodynamics (SPH) simulations of a Milky Way-sized galaxy. The code takes into account hydrodynamics, self-gravity, star formation, supernova and stellar wind feedback, radiative cooling and metal enrichment. The simulated galaxy is a barred spiral galaxy consisting of a stellar and gas disc, enveloped in a static dark matter halo. Similar to what is found in our pure N-body simulation of a non-barred galaxy in Grand et al., we find that the spiral arms are transient features whose pattern speeds decrease with radius, in such a way that the pattern speed is similar to the rotation of star particles. Compared to the non-barred case, we find that the spiral arm pattern speed is slightly faster than the rotation speed of star particles: the bar appears to boost the pattern speed ahead of the rotational velocity. We trace particle motion around the spiral arms at different radii, and demonstrate that there are star particles that are drawn towards and join the arm from behind (in front of) the arm and migrate towards the outer (inner) regions of the disc until the arm disappears as a result of their transient nature. We see this migration over the entire radial range analysed, which is a consequence of the spiral arm rotating at similar speeds to star particles at all radii, which is inconsistent with the prediction of classical density wave theory. The bar does not prevent this systematic radial migration, which is shown to largely preserve circular orbits. We also demonstrate that there is no significant offset of different star-forming tracers across the spiral arm, which is also inconsistent with the prediction of classical density wave theory.