Concrete column

A tied or spiral reinforced concrete column, rectangular or circular, designed to ACI 318-19 (Chapters 6, 10, 21, 22 and 25) for axial force and bending about one or both axes, with the slenderness of braced columns by the moment magnifier method and the ASCE 7-22 load combinations.

Inputs of the concrete column #

• Materials: f'c, Grade 60 or 80 bars, normalweight or lightweight concrete, the modulus Ec (19.2.2.1) and the tie or spiral grade (spirals may use fyt up to 100 ksi for confinement, Table 20.2.2.4(a)).
• Section: rectangular (width b along x, depth h along y) or circular (diameter D), ties or a spiral (spirals in circular sections), clear cover to the ties (1.5 in. prefilled, Table 20.5.1.3.1) and the maximum aggregate size. Ties or a spiral set φ (Table 21.2.2) and Pn,max (Table 22.4.2.1).
• Reinforcement: bars around the perimeter (bars per face along b and along h, corners included, or a number of bars on a circle) or bars at entered coordinates from the centroid (any layout), the tie or spiral bar and the tie spacing or spiral pitch (center to center).
• Loads: per load type, the axial force P (compression positive) and the end moments about x and about y at the top and bottom, combined by ASCE 7-22 2.3.1; or factored load cases entered directly with βdns. Enter the end moments with the same sign at both ends for single curvature and opposite signs for double curvature. Mx bends the column about the x axis (the depth h resists it). For combinations from load types, βdns is the factored dead axial force over Pu (the live load is taken as not sustained).
• Slenderness: braced against sidesway or not, the unsupported length ℓu (0 = slenderness not considered), the effective length factors kx and ky (k = 1.0 is permitted for nonsway members, 6.6.4.4.3), whether a transverse load acts between the supports (Cm = 1.0) and the (EI)eff expression (Eq. 6.6.4.4.4a, b or c).
• Biaxial bending: the code leaves the method to the engineer. The Bresler reciprocal load method or the load contour method with the exponent α (1.0 is conservative; 1.15 to 1.55 is typical for square columns).

Auto-design (editor toolbar) varies the bar size and bars per face (or number of bars of a circular column), with the tie size and the largest tie spacing allowed; the section when unlocked. Objectives: least reinforcement; lowest cost index (concrete, formwork, reinforcement). Kept unless you select them: width b (along x), depth h (along y), diameter D. Every other input is kept; see Auto-design.

Checks performed #

The drawings (on screen, in the report and on the DXF / PDF drawing sheet) show the column section with its bars, ties or spiral, clear cover and the x and y axes; the design interaction diagram φPn-φMn about x (and about y, dashed, when it differs) with the factored load points and the governing one called out (not to scale); and the column elevation over ℓu with the vertical bars and the ties at the designed spacing (or the spiral pitch). Crossties, splices, dowels, the first tie location and the floor members are not part of the calculation and are not drawn; the sheet notes say so.

Limitations #

• Columns not braced against sidesway are covered only when k ℓu/r ≤ 22 (6.2.5.1(a)); above that the sway magnifier of 6.6.4.6 needs the story data and the input is reported as not feasible. Use a second-order analysis (6.7, 6.8) and enter its factored moments with ℓu = 0 instead.
• Biaxial bending uses Bresler's or the load contour approximation, not a full biaxial strain-compatibility surface; neither is code text (Bresler 1960; PCA load contour) [verify against the source papers].
• Shear in the column, the reduced effective area of 10.3.1.2, splices, special moment frame requirements (Chapter
  18. and composite columns are not covered. The lateral support of the bars by crossties is an advisory: the crosstie layout is the engineer's detail.
• The live load is taken as not sustained in βdns for combinations from load types; enter factored cases with βdns to use another value.

Verification examples #

The column is verified against the free StructurePoint ACI 318-19 design examples and against hand calculations derived step by step in the test file. For each control point of a published interaction diagram the published (φPn, φMn) is entered as a load and the program's capacity on the ray through that point is compared.

The sway-frame example (moment magnification by 6.6.4.6) is outside the module's scope.

Hand calculations: