Methodology
How calcnote computes ACI 318-19 column capacity.
calcnote is a strain-compatibility implementation of ACI 318-19 for short, rectangular, tied, uniaxially-loaded reinforced concrete columns. This page documents the code provisions it implements, the design choices it makes, and the independent verification we have run against it.
Independent verification
Verification Report v1.0
Eight test cases spanning the V0 input envelope, cross-validated against three independent authority types: Wight's Reinforced Concrete: Mechanics and Design (7th ed.), StructurePoint's published interaction-diagram example for the canonical 16×16 column, and an independent first-principles ACI 318-19 strain-compatibility re-implementation.
Directly-tabulated control points for the canonical 16×16 column.
Eccentricity at reference Pn; within published design-chart reading precision.
Independent Python strain-compatibility re-implementation, no calcnote source dependency.
calcnote-verification-report-v1.0.pdf
20 pages · 555 KB · full per-case derivations, three-authority cross-checks, ACI clause map.
Range of applicability
V0 product scope
Inputs outside this envelope are rejected before any calculation runs.
| Parameter | V0 range |
|---|---|
| Section shape | Rectangular tied (b × h) |
| Section dimensions | 8 in ≤ b, h ≤ 60 in |
| Concrete strength | 3,000 psi ≤ f'c ≤ 10,000 psi (normal-weight) |
| Steel grade | Gr60, Gr80 |
| Number of longitudinal bars | n ∈ {4, 8, 12, 16, 20} |
| Bar size | #6, #7, #8, #9, #10, #11 |
| Tie size | #3, #4 |
| Bar layout | Perimeter two-face, perimeter all-face |
| Bending axis | Uniaxial (strong or weak) |
| Column length | Short (klu/r ≤ 34 per §6.6.4.1) |
Not in V0: biaxial bending · slender columns (klu/r > 34) · circular spiral or unsymmetric sections · composite (steel + concrete) sections · torsion or shear-friction · fire-rating · seismic special-frame detailing · post-tensioned reinforcement. Each will be re-verified in its own future report revision.
Code compliance
ACI 318-19 clauses implemented
Each provision is exercised by at least one of the eight verification test cases.
| ACI clause | Provision |
|---|---|
| §22.2.2.1 | Extreme-fiber concrete crushing strain εcu = 0.003 |
| §22.2.2.4.3 | β1 formula (Whitney stress-block factor) |
| §22.4.2.1 / §22.4.2.2 | Pure-compression nominal capacity Po; tied-column design cap φPn,max = 0.80·φ·Po |
| §21.2.2 | φ formula: 0.65 to 0.90 with linear transition; Grade-dependent εty |
| §10.6.1.1 | Longitudinal-steel ratio limit 0.01 ≤ ρ ≤ 0.08 |
| §6.6.4.5.4 | M2,min = Pu·(0.6 + 0.03·h) minimum primary moment |
| §6.6.4.1 | Slenderness limit klu/r ≤ 34 (for short-column treatment) |
| §20.5.1.3 | Minimum clear cover for columns (1.5 in standard) |
| §25.2.3 | Minimum clear bar spacing |
| §25.7.2.2 | Minimum tie size for given longitudinal bar size |
Design decisions
Design choices documented
calcnote makes three intentional design choices that an engineer reviewing its output should be aware of. All three are aligned with the default behaviors of every commercial RC column-design tool in the same market segment (StructurePoint spColumn, RISA, ENERCALC, SkyCiv).
Positive-(P, M) quadrant polygon truncation
The interaction-diagram polygon is constructed in the positive-(P, M) quadrant only. At high reinforcement ratios where a fixed-εt anchor would otherwise show a small negative-P excursion (axial tension with bending), the affected neutral-axis depth is clamped to cpb (the pure-bending value) and the anchor collapses onto the pure-bending point. This matches the default rendered behavior of all major commercial RC column-design tools. The cap, balanced point, pure-bending capacity, and operating-point ray-scaling result are all unchanged.
Ray-scaling for operating-point capacity
For a user demand (Pu, M2), calcnote reports capacity at the intersection of the interaction polygon with the ray from the origin through the demand point. This is the ACI 318-19 standard interpretation of “capacity at a demand point,” used by every commercial RC column-design tool. Both demand-side D/C ratios collapse to a single scalar 1/t by construction.
M2,min governance — engine raises rather than silently substitutes
When the user-applied moment M2 is less than the ACI 318-19 §6.6.4.5.4 minimum eccentricity M2,min, calcnote's engine raises an explicit error instructing the user to re-enter M2 ≥ M2,min. It does not silently substitute M2,min into the calculation. This treats minimum-eccentricity governance as an input decision the engineer must explicitly acknowledge.
For the engineer of record
Verification establishes that calcnote's calculations agree with the cited authorities within their respective precision tolerances. It does not constitute a license to use calcnote's outputs without independent engineering review.
calcnote outputs are draft calculation notes intended to assist a licensed structural Professional Engineer. Final designs require independent engineering review and signature/seal by a licensed Engineer of Record. The .docx output is not a licensed deliverable; this is stated as a footer on every generated page.