A non-pneumatic tire comprising an annular band, a hub, and a plurality of resilient, composite structures; the tire defining axial, radial, and circumferential directions; each of the composite structures comprising: a radially-outer joint for connecting with the annular band of the tire; a radially-inner joint for connecting with the hub of the tire; a support membrane extending continuously from the radially-outer joint and the radially-inner joint, the support membrane having a radially-outer end that is located radially inward of the radially-outer joint, the support membrane having a radially-inner end that is located radially outward of the radially-inner joint, the support membrane defining a pair of opposing sides, the support membrane having an arcuate shape as viewed along the axial direction of the tire, the support membrane extending continuously from the radially-outer joint to the radially-inner joint; and wherein the radially inner joint and the radially-outer joint are movable relative to each other so as to allow bending of the support membrane, and wherein the radially-inner joint and the radially-outer joint are both located on one of the opposing sides of the support membrane, characterized in that in a cross section of each of the composite structures perpendicular to the axial direction of the tire, the support membrane includes a first reinforced layer and a second reinforced layer, which are separated by a non-reinforced, elastomeric shear layer. an annular band, a hub, and a plurality of resilient, composite structures; the tire defining axial, radial, and circumferential directions; each of the composite structures comprising: a radially-outer joint for connecting with the annular band of the tire; a radially-inner joint for connecting with the hub of the tire; a support membrane extending continuously from the radially-outer joint and the radially-inner joint, the support membrane having a radially-outer end that is located radially inward of the radially-outer joint, the support membrane having a radially-inner end that is located radially outward of the radially-inner joint, the support membrane defining a pair of opposing sides, the support membrane having an arcuate shape as viewed along the axial direction of the tire, the support membrane extending continuously from the radially-outer joint to the radially-inner joint; and wherein the radially inner joint and the radially-outer joint are movable relative to each other so as to allow bending of the support membrane, and wherein the radially-inner joint and the radially-outer joint are both located on one of the opposing sides of the support membrane, characterized in that a radially-outer joint for connecting with the annular band of the tire; a radially-inner joint for connecting with the hub of the tire; a support membrane extending continuously from the radially-outer joint and the radially-inner joint, the support membrane having a radially-outer end that is located radially inward of the radially-outer joint, the support membrane having a radially-inner end that is located radially outward of the radially-inner joint, the support membrane defining a pair of opposing sides, the support membrane having an arcuate shape as viewed along the axial direction of the tire, the support membrane extending continuously from the radially-outer joint to the radially-inner joint; and wherein the radially inner joint and the radially-outer joint are movable relative to each other so as to allow bending of the support membrane, and wherein the radially-inner joint and the radially-outer joint are both located on one of the opposing sides of the support membrane, characterized in that