The full-matrix set of combined temperature (4.2–14 K) and applied axial strain (εa) data for the bulk pinning force of a technological Nb3Sn wire (OST type-I) has been studied at fields up to 19 T by combining transport (variable εa) and magnetic (variable T) measurements. Some length of the wire was also jacketed with AISI 316L stainless steel, in order to apply a radial strain and to simulate the thermally induced axial compressive strain that the Nb3Sn wires experience in a cable-in-conduit-conductor (CICC). Within the framework of the unified scaling law, raw scaling data for the effective upper critical field B*c2(T, ɛ), have been used in order to experimentally determine the strain function, s(ε), of both the bare and the jacketed wires. A direct testing of the various proposed models for s(ε) has been carried out, including the power law, the deviatoric description and the polynomial form. All models adequately fit to the s(ε) of the bare wire, but in the jacketed wire none of them is able to describe the tensile strain region above the Ic maximum, where the enhanced radial compression cannot be neglected. The origin of the onset of a reduced Bc2 is also discussed.