Abstract: A tubular structure particularly but not exclusively useful as a window shade support roller comprises a convolutely-wound tube structure having a number of closely-wound wraps or layers of paper stock, preferably Stress Kraft paper coated with adhesive over all or most of its surface and wound into close layer-upon-layer surface adhesion, approximately six such layers providing high beam strength with low wall section or thickness. In addition, the tubular structure has readily-removable segmental lengths provided by use of "tear strips", i.e., tear strings, tear tapes, etc., which are placed upon the paper prior to winding thereof so as to be wound into spiral form during the convolute winding of the layers of paper, whereby pulling of such a tear strip around and around the tube progressively severs the tube at that point.