Tube Bend Wall Thinning and Bend Ratio

Bending stretches the outside of a bend and compresses the inside. Taking the neutral axis at the centerline, the outer fiber is stretched in proportion to how far it sits outside that centerline and the wall thins by the same proportion -- so the thinning depends ONLY on the ratio of the bend radius to the tube radius, not on the material and not on the bend angle. Two ratios do the work. R/D is how tight the bend is: at 3D the thinning is modest, at 1.5D it is severe, and below about 2D on thin wall a mandrel and a wiper die are needed to keep the tube from collapsing or wrinkling on the inside. D/t is how thin the tube is relative to its diameter, and a high D/t tube is a thin shell that buckles rather than bends. Together they are the two axes of every tube-bending capability chart. A 2.0 in OD tube with a 0.120 in wall bent 90 degrees on a 3.0 in centerline radius is a 1.5D bend at D/t 16.7, and the wall goes to 0.090 in -- a quarter of it gone -- over a 4.71 in arc. Open the bend to 6.0 in and the same tube thins only to 0.1029 in, 14.3%, for a bend that takes twice the space, which is the trade on every job and why 3D is the default when the package allows it. The consequence downstream is pressure rating: a pressure calculation done on the nominal wall is wrong for a bent tube, because the thinned outer wall is the governing section. A geometric estimate; the bender's own capability chart, a measured first article, and the applicable piping code govern.

bend_ratio = clr_in / od_in; d_over_t = od_in / wall_in; wall_after_in = wall_in x clr_in / (clr_in + od_in / 2); thinning_pct = (1 - clr_in / (clr_in + od_in / 2)) x 100; arc_length_in = clr_in x bend_angle_deg x pi / 180.

Tube bend wall thinning from the neutral-axis-at-centerline geometry, so the thinning depends only on the radius ratio, by name; public bending geometry. The R/D and D/t ratios are the two axes of every bender's published capability chart, cited and not reproduced. The bender's capability chart, a measured first article, and the applicable piping code govern.

The thinning relation is geometry on the tube's own dimensions; nothing is reproduced from a tooling chart.

Estimate. AHJ and licensed professional govern.

Field names used by the API: od_in, wall_in, clr_in, bend_angle_deg, bend_ratio, d_over_t, wall_after_in, thinning_pct, arc_length_in

• Neutral axis at the centerline a simplifying assumption; real neutral-axis shift makes actual thinning somewhat less than this predicts, so the figure is conservativetube bending geometry
• Independent of material and angle thinning depends only on the radius ratiotube bending geometry
• Governing section the thinned outer wall governs a pressure calculation on a bent tube, not the nominal wallpiping practice