Rebar Cut List Calculator

Cutting a fixed set of equal length pieces from standard stock bars is the one dimensional cutting stock problem in its simplest form. The number of pieces per bar is the stock length divided by the effective cut length, rounded down, since a partial piece is scrap. The number of bars is the total quantity divided by pieces per bar, rounded up, and whatever remains on each bar is drop. US rebar comes in 20, 40 and 60 foot stock, and bar sizes are numbered in eighths of an inch: a number 4 bar is 1/2 inch at 0.668 pounds per foot, a number 5 is 5/8 inch at 1.043, and a number 8 is 1 inch at 2.670. Effective cut length must include the lap wherever bars are spliced, because a lapped joint transfers force through bond with the surrounding concrete rather than through contact. ACI 318 derives tension lap lengths from development length, with a Class B splice at 1.3 times development, which commonly lands at 40 to 60 bar diameters, adding roughly 20 inches for a number 4 bar and 30 inches for a number 5 in normalweight concrete. Two limitations apply. The estimate solves only the uniform length case, so a schedule with many different lengths needs a real packing solution to match this efficiency, and it ignores bends, where developed length along the bar centerline exceeds the sum of outside dimensions and requires a bend deduction. Well planned jobs typically achieve 3 to 5 percent waste against 10 to 15 percent for ad hoc cutting.

Reinforced concrete became a system in the second half of the nineteenth century, with Joseph Monier patenting reinforced cement tubs and tanks in France from 1867 and Ernest L. Ransome patenting the twisted square bar in the United States in 1884 to improve mechanical bond. Deformation patterns were not standardized until much later. ASTM A305, issued in 1949, fixed the rib geometry and the numbering of bar sizes in eighths of an inch, and ASTM A615 is its modern successor for carbon steel deformed bars. The American Concrete Institute, founded in 1904 as the National Association of Cement Users, and the Concrete Reinforcing Steel Institute, formed in the 1920s, developed the detailing conventions and bar bending schedules that cut lists are written from. The optimization side has an equally specific origin. Paul Gilmore and Ralph Gomory published a linear programming approach to the cutting stock problem in the journal Operations Research in 1961, followed by a second paper in 1963, introducing delayed column generation so that the enormous number of possible cutting patterns need not be enumerated. Their method underpins the commercial bar listing and optimization software used by rebar fabricators today. Before it, fabricators worked from hand written bar bending schedules and rule of thumb allowances, typically ordering 10 percent extra to cover drop, which is why a waste percentage rather than an optimized pattern remains the common estimating shortcut on smaller projects.