ACI 318-19 Column Design Glossary
Definitions of the terms used across calcnote's methodology, verification report, and calculation output, in the sense ACI 318-19 uses them for rectangular tied columns.
Strength-reduction factor (φ)
The factor that reduces a member's nominal capacity to its usable design capacity: design strength = φ·(nominal strength). For tied columns, ACI 318-19 Table 21.2.2 sets φ = 0.65 for compression-controlled sections, φ = 0.90 for tension-controlled sections, and interpolates linearly through the transition zone between them. See how calcnote applies the φ transition · Grade 60 vs Grade 80 comparison.
φPn,max (design axial cap)
The ceiling on usable axial capacity for a tied column: φPn,max = 0.80·φ·Po per ACI 318-19 §22.4.2.1, where Po is the pure-compression nominal capacity. The 0.80 factor accounts for accidental eccentricity — no real column is loaded perfectly concentrically. On the interaction diagram this appears as the horizontal cap truncating the top of the curve.
Nominal capacity (Pn, Mn)
The axial force (Pn) and bending moment (Mn) a section can resist based on material strengths and strain compatibility, before any safety reduction. Design capacity is the nominal value times φ; demand from factored loads (Pu, Mu) must not exceed it.
P-M interaction diagram
The curve of all (axial force, bending moment) pairs a column section can simultaneously resist. Points inside the φ-reduced curve are acceptable designs; points outside fail. Columns need this curve — rather than separate axial and moment checks — because axial load and moment interact: compression initially increases moment capacity, then reduces it past the balanced point. See a live example.
Balanced point
The point on the interaction diagram where the concrete reaches its crushing strain (0.003) at the same moment the extreme tension steel reaches its yield strain — the boundary of compression-controlled behavior. Above it, failure initiates by concrete crushing; below it, the tension steel yields first, giving more ductile behavior.
Compression-controlled section
A section whose net tensile strain at nominal strength is at or below the yield strain εty (0.00207 for Grade 60) — the concrete crushes before the tension steel yields. Failure is sudden, so ACI 318-19 Table 21.2.2 assigns the lowest φ (0.65 for tied columns). Heavily-loaded columns typically operate here.
Tension-controlled section
A section whose net tensile strain at nominal strength is at least εty + 0.003 (0.00507 for Grade 60) — the tension steel yields well before the concrete crushes, giving visible, ductile warning of failure. ACI 318-19 Table 21.2.2 rewards this with the highest φ (0.90). Columns under low axial load and high moment can reach this regime.
Transition zone
The band of net tensile strain between the compression-controlled limit (εty) and the tension-controlled limit (εty + 0.003), where φ interpolates linearly between 0.65 and 0.90 per ACI 318-19 Table 21.2.2. Many practical column designs at moderate axial load land in this band, which is why the φ value on a calc-note is often neither 0.65 nor 0.90.
Net tensile strain (εt)
The tensile strain in the extreme-tension layer of longitudinal reinforcement at nominal strength, excluding strains from prestress, creep, shrinkage, and temperature (defined in ACI 318-19 Ch. 2; applied in §21.2.2). It is the single variable that classifies a section as compression-controlled, transition, or tension-controlled — and therefore sets φ.
Whitney stress block
The equivalent rectangular stress distribution ACI 318-19 §22.2.2.4.1 permits in place of the true curved concrete stress-strain profile: uniform stress 0.85·f′c over a depth a = β1·c, where c is the neutral-axis depth and β1 steps down from 0.85 as f′c rises above 4,000 psi. It gives essentially the same force resultant with far simpler algebra, and is the basis of nearly all hand and software column calculations.
Tied vs spiral columns
Tied columns confine their longitudinal bars with discrete rectangular ties; spiral columns wrap them in a continuous helix. The spiral's better confinement earns a higher φ (0.75 vs 0.65 compression-controlled) and a higher axial cap factor (0.85 vs 0.80) under ACI 318-19. calcnote's scope is rectangular tied columns only — spiral columns are out of scope (see scope).
Slenderness ratio (klu/r)
The measure of a column's tendency to buckle: effective length factor k times unsupported length lu, divided by the section's radius of gyration r (0.30·h for rectangular sections). For nonsway frames, ACI 318-19 §6.2.5 permits neglecting slenderness effects when klu/r ≤ min(34 − 12·M1/M2, 40) — a limit between 22 and 40 depending on the end-moment ratio (M1/M2 positive for single curvature, as calcnote's inputs define it), not a flat 34.
Short vs slender columns
A short column fails by cross-section strength; a slender one is additionally weakened by second-order (buckling) effects, which ACI 318-19 §6.6.4 addresses through moment magnification. The dividing line is the §6.2.5 slenderness limit. calcnote covers short columns only: inputs exceeding the limit are rejected with an explanatory message rather than magnified — slender-column design requires analysis outside calcnote's scope.
Minimum moment (M2,min)
A floor on design moment: M2,min = Pu·(0.6 + 0.03·h) with h in inches (result in kip-in), representing construction-tolerance eccentricity. ACI 318-19 §6.6.4.5.4 formally applies it within slender-column moment magnification — it is not a required check for short columns. When user-entered M2 falls below this threshold, calcnote emits an advisory and proceeds with the user's value; the engineer of record retains the decision to substitute. Full rationale · full treatment.
Demand-capacity (D/C) ratio
Factored demand divided by design capacity at the operating point: D/C ≤ 1.00 passes, D/C > 1.00 is overstressed. calcnote reports axial (Pu/φPn) and moment (Mu/φMn) ratios along the demand ray — see how the ratio is computed.
Grade 60 / Grade 80 reinforcement
Deformed-bar grades by specified yield strength: Grade 60 (fy = 60 ksi, εty = 0.00207) is the long-standing default; Grade 80 (fy = 80 ksi, εty = 0.00276) reduces congestion in heavily reinforced members. The grade changes the strain limits that define the φ transition, so the same section can classify differently under different grades.
Reinforcement ratio (ρ)
Total longitudinal steel area over gross section area: ρ = Ast/Ag. ACI 318-19 §10.6.1.1 bounds it between 1% (so creep and shrinkage don't shed sustained-compression stress onto too little steel) and 8% (congestion; practical designs rarely exceed ~4%). calcnote validates every input section against these bounds before running the check.
Eccentricity (e = M/P)
The equivalent offset of the axial load that would produce the applied moment: e = Mu/Pu. Small eccentricity means nearly concentric compression (top of the interaction diagram); large eccentricity means bending-dominated behavior (bottom). Reference texts often locate capacity points by eccentricity — calcnote's verification compares against Wight's tabulated eccentricities.
Tie spacing
The vertical distance between transverse ties. ACI 318-19 §25.7.2.1 caps it at the least of 16 longitudinal-bar diameters, 48 tie-bar diameters, and the smallest section dimension; §25.7.2.2 sets the minimum tie size (#3 for longitudinal bars up to #10, #4 for #11 and larger). calcnote enforces both as input validation. See the full tie spacing requirements.