High-performance Nb3Sn conductors are intended to be used in large-scale magnets like the International Thermonuclear Experimental Reactor (ITER) and in the upgrade of the Large Hadron Collider (LHC). Due to the occurrence of high electromagnetic forces, a detailed knowledge of the response of the critical current to the three-dimensional mechanical loads acting on the wires inside the cables is required. A detailed analysis of transverse stress effects on the critical current for powder-in-tube and bronze route Nb3Sn wires is presented. In an earlier publication, we have described the effect of transverse stress exerted on a Nb3Sn wire by means of two parallel plates. In the present paper, we analyse the effect of transverse stress exerted simultaneously by four walls on a wire being confined in a U-shaped groove. In order to get a more realistic picture of the situation of wires embedded in a Rutherford cable, the compression by four walls was also performed after impregnating the wire with epoxy in the same U-shaped groove. The result is very different from the case of pressing by means of two walls: the effect of pressure on Ic is now strongly reduced, which is attributed to the almost hydrostatic pressure in the U-shaped groove. This is further confirmed by the comparison between the effects of axial and transverse loads on the upper critical field and the pinning force. The present data are also compared against the effects of mechanical load on the critical current of cables in large-scale magnets