A hallmark of low-temperature plasticity in body-centered cubic (BCC) metals is its departure from Schmid's law. One aspect is that non-glide stresses, which do not produce any driving force on the dislocations, may affect the yield stress. We show here that this effect is due to a variation of the relaxation volume of the 1=2h111i screw dislocations during glide. We predict quantitatively nonglide effects by modeling the dislocation core as an Eshelby inclusion, which couples elastically to the applied stress. This model explains the physical origin of the generalized yield criterion classically used to include non-Schmid effects in constitutive models of BCC plasticity. We use first-principles calculations to properly account for dislocation cores and use tungsten as a reference BCC metal. However, the methodology developed here applies to other BCC metals, other energy models and other solids showing nonglide effects.