16x16 Sway-Frame Column, 8-#9
Sway-frame column with moment magnification for unbraced frames per ACI 318-19: delta_s, along-length check, f'c = 5,000 psi.
Checked about X: depth h = 16 in
Both axial and moment D/C ratios ≤ 1.00.
P-M interaction diagram
Demand (Pu, Mu) tested against the φ-reduced capacity envelope. Operating point (φPn, φMn) shown on the boundary. φ is computed per anchor from εt (§21.2.2); your operating point lies in the compression-controlled region; how the φ transition works.
Interaction Diagram Points (8 anchors, ACI 318-19 Table 22.4.2.1)
| Anchor | Description | c (in) | εt | φ | φPn (kip) | φMn (kip-ft) |
|---|---|---|---|---|---|---|
| 1 | Pure compression cap | N/A | N/A | 0.65 | 638.62 | 0.00 |
| 2 | Cap intersection | 16.56 | -0.00053 | 0.65 | 638.62 | 82.85 |
| 3 | Compression-controlled limit (εt = εty) | 8.06 | 0.00207 | 0.65 | 235.38 | 204.62 |
| 4 | Transition lower (εt = εty + 0.0015) | 6.22 | 0.00357 | 0.78 | 199.46 | 226.25 |
| 5 | Tension-controlled limit (εt = εty + 0.003) | 5.07 | 0.00507 | 0.90 | 161.93 | 239.78 |
| 6 | Tension-controlled deep (εt = εty + 0.008) | 3.13 | 0.01007 | 0.90 | 9.39 | 175.72 |
| 7 | Pure bending | 3.04 | 0.01046 | 0.90 | 0.00 | 171.43 |
| 8 | pure_tension | N/A | N/A | 0.90 | -341.28 | 0.00 |
| Quantity | Value |
|---|---|
| Pu (factored axial demand, kip) | 253.10 |
| φPn (axial capacity at operating point, kip) | 401.03 |
| Mu (Mc, sway-magnified design moment, kip-ft) | 105.34 |
No transverse load between supports. Cm from end-moment ratio per ACI 318-19 §6.6.4.5.3(a). |
|
| φMn (moment capacity, kip-ft) | 166.91 |
| c (neutral axis depth, in) | 10.94 |
| εt (extreme tension strain) | 0.00074 |
| φ (strength reduction factor) | 0.65 |
| φ regime (§21.2.2) | Compression-controlled φ = 0.65 throughout (εt ≤ εty = 0.00207) |
| D/C axial | 0.63 |
| D/C moment | 0.63 |
| Sway magnification (§6.6.4.6) | |
| Frame classification | Sway (unbraced) |
| ksway·lu/r | 28.85 |
| δs (§6.6.4.6.2(b), ΣPc method) | 1.0573 |
|
δs = 1/(1 − ΣPu/(0.75ΣPc)) = 1/(1 − 2,031.0/(0.75 × 49,976.8)) = 1.0573. |
|
| M2 = M2ns + δs·M2s (combined end moment) | 105.34 kip·ft |
= 41.90 + 1.0573 × 60.00 = 105.34 kip·ft (re-sorted: M2 = 105.34, M1 = 80.24 kip·ft, single curvature). |
|
| Mc/M1st (§6.2.5.3, ≤ 1.4) | 1.034 ≤ 1.4 OK |
After sway magnification, an along-length check per §6.6.4.6.4 follows using the magnified end moments. |
|
| Along-length magnification (§6.6.4.6.4, about X) | |
| kl/r about X | 20.75 |
Along-length check per §6.6.4.6.4 using the sway-magnified end moments. The nonsway (δns) magnifier is applied to the combined moments. |
|
| kl/r limit | 24.86 |
| Tie spacing limit (§25.7.2.1) | 16.00 in (governed by 16·d_bar) |
| Bar clear spacing (§25.2.3) | 2.75 in ≥ 1.50 in |
Force Decomposition at Operating Point (c = 10.94 in, a = 9.30 in)
| Component | Force (kip) | Moment (kip-in) |
|---|---|---|
| Cc (concrete compression) | 505.70 | 1,695.11 |
| Cs (steel in compression) | 178.86 | 1,006.07 |
| Ts (steel in tension) | -67.58 | 380.16 |
| Total = Pn, Mn | 616.98 | 3,081.34 |
| Layer | Bars | d (in) | εs | fs (ksi) | Force (kip) | Lever (in) | Moment (kip-in) |
|---|---|---|---|---|---|---|---|
| 1 | 4 | 2.38 | 0.00235 | 60.00 | 178.86 | 5.62 | 1,006.07 |
| 2 | 4 | 13.62 | -0.00074 | -21.39 | -67.58 | -5.62 | 380.16 |
| Section geometry | |
| Section | 16 × 16 in (rectangular) |
| Ag (gross area) * | 256.0 in² |
| Ast (total steel area) * | 6.32 in² |
| ρ (reinforcement ratio) * | 0.0247 (2.47%) |
| Materials | |
| f′c | 4,000 psi |
| fy (longitudinal) | 60 ksi (Grade 60) |
| Concrete | Normal weight |
| Reinforcement | |
| Longitudinal bars | 8-#8 |
| Per-face distribution | 2 per b-face, 0 per h-face (+ 4 corners) |
| Clear cover | 1.5 in |
| Transverse | #3 ties @ 12 in |
| Loads | |
| Pu | 253.1 kip |
| M2ns, M1ns (gravity moments, kip-ft) | 41.9, 16.8 |
| M2s, M1s (lateral moments, kip-ft) | 60, 60 |
| Curvature (gravity, lateral) | Single, Single |
| Bending axis | X |
| Transverse load between supports | No |
| Slenderness parameters | |
| Lu (unsupported length) | 120 in (10.00 ft) |
| k (effective length factor) | 0.83 |
| Frame type | Sway (unbraced) |
| ksway (sway effective length factor) | 1.154 |
| βds (sustained lateral shear ratio) | 0.000 |
Assumptions and limits
- Tie arrangement and crossties (§25.7.2.3) are not checked.
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Verdict method 8 · build 40c109d · generated 2026-10-23 00:15 UTC