Bars drive gas inflow. As the gas flows inward, shocks and shear occur along the bar dust lanes. Such shocks and shear can affect the star formation (SF) and change the gas properties. For four barred galaxies, we present Hα velocity gradient maps that highlight bar-driven shocks and shear using data from the PHANGS-MUSE and PHANGS-ALMA surveys, which allow us to study bar kinematics in unprecedented detail. Velocity gradients are enhanced along the bar dust lanes, where shocks and shear are shown to occur in numerical simulations. Velocity gradient maps also efficiently pick up H II regions that are expanding or moving relative to the surroundings. We put pseudo-slits on the regions where velocity gradients are enhanced and find that Hα and CO velocities jump up to ∼170 km s‑1, even after removing the effects of circular motions due to the galaxy rotation. Enhanced velocity gradients either coincide with the peak of CO intensity along the bar dust lanes or are slightly offset from CO intensity peaks, depending on the objects. Using the Baldwin–Philips–Terlevich BPT diagnostic, we identify the source of ionization on each spaxel and find that SF is inhibited in the high-velocity gradient regions of the bar, and the majority of those regions are classified as a low-ionization nuclear emission-line region (LINER) or composite. This implies that SF is inhibited where bar-driven shear and shocks are strong. Our results are consistent with the results from the numerical simulations that show SF is inhibited in the bar where the shear force is strong.