In turbulent Rayleigh Benard Convection (RBC), we study the effect of shear by the inherent large-scale flow (LSF) on the local boundary layers (BLs) on the hot plate. We present instantaneous probability distribution functions of horizontal velocities in a horizontal plane within the local boundary layers and show that the distributions are either unimodal or bimodal. The unimodal PDFs, that peak at values slightly higher than the characteristic natural convection BL velocities (type A), predominantly occur at lower Ra. At the highest Ra, the PDFs are also predominantly unimodal, but these peak at values larger than the LSF velocities (type C). At intermediate Ra, the PDFs are predominantly bimodal (type B), with the peaks being similar to that of type A and type C. Using perturbation solutions of scaling relations obtained from integral BL equations, we obtain the scaling for Re_bs, the Reynolds number based on the BL velocities, forced externally by the shear due to LSF. We then show that the first peak of the type B PDFs and the type A PDFs scale as Re_bs, while the single peak of type C PDFs scale in the same way as the LSF velocities; these scalings then clarify the effect of shear on BL velocities in RBC. For the case of Pr and aspect ratio equal to one, this shear effect reduces to Re_bs scaling as Ra^0.375. The effect of shear on the local BLs decreases with an increase in Pr and an increase in aspect ratio and becomes negligible for Pr greater than 100 and aspect ratio greater than 20. Further, we also present the effect of shear on the heat-flux and a scaling relation for Nusselt number for a small shear in RBC.