Wight Example 11-1: the canonical 16×16 column, worked and cross-checked

Example 11-1 in Wight, Reinforced Concrete: Mechanics and Design (7th ed., §11-4) constructs the P-M interaction diagram for a 16×16 in tied column with 8-#9 bars — the most cross-referenced section in published ACI 318-19 column literature. StructurePoint's public design example tabulates the same section (citing Wight 8th ed.) with spColumn-validated values. This page shows the example's control points compared four ways: Wight's text, StructurePoint's hand + spColumn values, an independent first-principles ACI 318-19 strain-compatibility baseline, and calcnote's engine. This is test case TC-1 of the calcnote verification report.

Case definition

Section	16 × 16 in (A_g = 256 in²)
Reinforcement	8-#9 (A_st = 8.00 in², ρ = 3.13%), two-face layout
Materials	f′c = 5,000 psi (β₁ = 0.80), Grade 60 (ε_ty = 0.00207)
Cover to bar centroid (δ)	2.500 in exactly — via 1.561 in clear cover + #3 tie (0.375) + half a #9 bar (0.564); matches Wight's d₁ = 13.5 in and StructurePoint's "2.5 in to center of reinforcement" verbatim
Extreme tension-steel depth	d_t = 16 − 2.500 = 13.500 in

Governing relations

Pure-compression nominal capacity and the tied-column design cap (ACI 318-19 §22.4.2):

P_o = 0.85\,f'_c\,(A_g - A_{st}) + f_y\,A_{st} = 0.85(5)(248) + 60(8) = 1{,}534\ \text{kip}

\phi P_{n,\max} = 0.80\,\phi\,P_o = 0.80(0.65)(1{,}534) = 797.7\ \text{kip}

Concrete compressive resultant via the Whitney stress block at neutral-axis depth c, and the φ transition (Table 21.2.2):

C_c = 0.85\,f'_c\,a\,b, \qquad a = \beta_1 c

\phi = 0.65 + 0.25\,\frac{\varepsilon_t - \varepsilon_{ty}}{0.003} \quad (\varepsilon_{ty} \le \varepsilon_t < \varepsilon_{ty} + 0.003)

Control-point comparison

calcnote traces the diagram through seven fixed strain-state anchors. Wight and StructurePoint tabulate four of them; the other three are checked against the independent first-principles ACI baseline (re-implemented from the code text with no dependency on calcnote source). Values are φ-reduced, in kip and kip-ft.

Anchor	Strain state	φ	Wight φP_n / φM_n	SP φP_n / φM_n	ACI baseline	calcnote
1 — cap (φP_n,max)	all compression	0.65	798 / 0	797.7 / 0.00	797.680 / 0.000	797.680 / 0.000
2 — cap intersection	c = 17.352 in	0.65	—	—	797.680 / 102.643	797.639 / 102.663
3 — compression-controlled limit	ε_t = 0.00207 (balanced)	0.65	271 / 251	270.9 / 250.77	270.891 / 250.774	270.891 / 250.774
4 — mid-transition	ε_t = 0.00357	0.775	—	—	221.095 / 272.569	221.095 / 272.569
5 — tension-controlled limit	ε_t = 0.00507	0.90	175 / 288	171.6 / 286.75	171.642 / 286.751	171.642 / 286.751
6 — deep tension-controlled	ε_t target = 0.01007 (clamped)	0.90	—	—	−3.742 / 212.221	0.032 / 213.927
7 — pure bending	P_n = 0, c = 3.249 in	0.90	—	0 / 213.96	0.000 / 213.912	0.000 / 213.927

Reading the deltas

Anchors 1, 3, 5, 7 (directly tabulated by the references): calcnote agrees with StructurePoint's hand values within ≤ 0.03% on all four. Anchors 2, 4, 6 are calcnote-specific strain states with no published reference; against the first-principles ACI baseline, calcnote agrees within ≤ 0.02% on anchors 2 and 4.

Why Wight shows 175 kip at anchor 5 while everyone else shows ~171.6: the ~2% gap is rounding propagation, not a methodology dispute. Wight's chain computes P_n = 194 kip → ×0.9 → 175; StructurePoint's computes P_n = 190.7 → ×0.9 → 171.6. Each is internally consistent with ACI 318; the upstream difference (~1.7% on P_n) reflects slightly different intermediate c and steel-stress values within code tolerance. StructurePoint's own footnote notes the reference rounded ε_t from 0.00507 to 0.0051.

Anchor 6 is a deliberate divergence, disclosed: at the ε_t = 0.01007 target, pure-ACI math gives a slightly negative axial value (P_n < 0 — axial tension with bending). calcnote constructs its diagram in the positive-(P, M) quadrant only, clamping the neutral-axis depth to the pure-bending value (c_pb = 3.249 in) — so anchor 6 collapses onto anchor 7 and the rendered diagram has six distinct points for this geometry. This matches the default rendered behavior of the major commercial RC column tools; the cap, balanced point, pure-bending capacity, and operating-point results are unaffected.

Edition notes: Wight 7th ed. (2016) computes per ACI 318-14; StructurePoint's PDF is on ACI 318-19 and cites Wight 8th ed. (2021); calcnote is on ACI 318-19. For this example's provisions — Whitney block, strain-compatibility P-M interaction, Grade-60 φ formula with ε_ty = 0.00207 — the three are numerically identical, so the comparison is apples-to-apples in both geometry (δ = 2.500 in) and code edition.

Sources

Wight, J. K., Reinforced Concrete: Mechanics and Design, 7th ed., Pearson, 2016 — Example 11-1, pp. 511–521.
StructurePoint, "Interaction Diagram — Tied Reinforced Concrete Column Design Strength (ACI 318-19)", May 2022 — Table 1; spColumn v10.00-validated.
ACI 318-19: §22.4.2 (axial cap), §22.2.2.4.1 (Whitney block), Table 21.2.2 (φ), §21.2.2 (net tensile strain classification).