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Wight Example 11-4: a 16×22 column at two load cases

Example 11-4 in Wight, Reinforced Concrete: Mechanics and Design (7th ed.) designs a 16×22 in tied column and checks it under several load cases using the printed design chart R-5-60.75. This page cross-checks calcnote's engine against the two load cases covered by the calcnote verification report: LC1 (compression-controlled, deliberately loaded at the capacity boundary — test case TC-2) and LC3 (transition zone, mid-curve — test case TC-3). Wight's LC2 is not verified here. Unlike the Example 11-1 page, which checks interaction-curve anchors, this page checks the operating point — the capacity calcnote reports for a specific factored demand.

Case definition

Section16 × 22 in (Ag = 352 in²), strong-axis bending
Reinforcement8-#8 perimeter all-face (Ast = 6.32 in², ρ = 1.80%)
Materialsf′c = 5,000 psi, Grade 60
Cover to bar centroid (δ)2.500 in exactly — via 1.625 in clear cover + #3 tie + half a #8 bar; matches Wight's convention
Loading — LC1Pu = 680 kip, M2 = 264 kip-ft → e = 4.66 in (e/h = 0.21, compression-controlled)
Loading — LC3Pu = 170 kip, M2 = 214 kip-ft → e = 15.10 in (e/h = 0.69, transition zone)

Operating-point relations

The demand's eccentricity fixes a direction through the origin of the P-M plane; calcnote reports capacity at the intersection of that ray with the φ-reduced interaction polygon (ray-scaling):

$$e = \frac{M_2}{P_u}, \qquad (\phi P_{n,op},\ \phi M_{n,op}) = t \cdot (P_u,\ M_2)\ \text{at the polygon boundary}$$
$$\text{D/C} = \frac{P_u}{\phi P_{n,op}} = \frac{M_2}{\phi M_{n,op}} = \frac{1}{t}$$

Curve-level agreement (the rigorous check)

At Wight's published nominal capacities, calcnote's strain-compatibility curve passes within printed design-chart reading precision on eccentricity:

Load case Wight Pn (kip) Wight e (in) calcnote e (in) Δe
LC1 (boundary) 1,110 4.66 4.605 −1.17%
LC3 (mid-curve) 383 15.10 15.030 −0.47%

Operating-point comparison

At Wight's factored demands, ray-scaled capacity and the resulting verdicts:

Quantity LC1 calcnote LC1 Wight LC3 calcnote LC3 Wight
φPn,op (kip) 670.3 722 313.6 328
Δ φPn,op −7.2% −4.4%
D/C 1.014 0.942 0.542 0.518
Verdict FAIL (marginal) PASS PASS PASS

Why does calcnote show FAIL where Wight shows PASS?

Because LC1 sits essentially on the capacity line, and the two methods locate that line by different means: a graphical chart read versus computed strain compatibility. Both agree the interaction curve itself to within 1.2%, while their operating-point capacities differ by about 7% — landing on opposite sides of D/C = 1.0. The disagreement is a property of checking a boundary-loaded design against a printed chart's read precision, not of either method's code compliance. Away from the boundary the effect vanishes: at LC3 both methods agree on PASS with comfortable margin.

What LC3 adds

LC3 sits in the transition zone, so it exercises the φ-interpolation logic: calcnote computes φ from the actual net tensile strain at the operating neutral-axis depth per ACI 318-19 Table 21.2.2, rather than from a pre-tabulated target strain. LC3 also shows the divergence pattern shrinking away from the boundary — Δe drops from 1.17% to 0.47% and ΔφPn,op from 7.2% to 4.4% — consistent with chart-read precision as the mechanism, and with no effect on the verdict.

Edition note: Wight 7th ed. (2016) computes per ACI 318-14; calcnote is on ACI 318-19. The strain-compatibility provisions are identical between editions, but 318-19 changed the Grade-60 compression-controlled strain limit from a fixed εty = 0.002 to εty = fy/Es = 0.00207, which shifts transition-zone φ by roughly 0.7% — a small, code-edition-driven contributor to the LC3 operating-point delta on top of chart-read precision.

Sources