16x22 Column, 8-#8, Pu = 170 kip (Transition Zone)
Transition-zone demand for a 16x22 / 8-#8 column per ACI 318-19: phi interpolation between compression-controlled and tension-controlled limits.
Checked about X: depth h = 22 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 transition 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 | 961.14 | 0.00 |
| 2 | Cap intersection | 22.98 | -0.00045 | 0.65 | 961.16 | 168.77 |
| 3 | Compression-controlled limit (εt = εty) | 11.54 | 0.00207 | 0.65 | 405.72 | 343.39 |
| 4 | Transition lower (εt = εty + 0.0015) | 8.91 | 0.00357 | 0.78 | 342.60 | 383.31 |
| 5 | Tension-controlled limit (εt = εty + 0.003) | 7.25 | 0.00507 | 0.90 | 275.51 | 409.95 |
| 6 | Tension-controlled deep (εt = εty + 0.008) | 4.48 | 0.01007 | 0.90 | 78.72 | 310.46 |
| 7 | Pure bending | 3.48 | 0.01383 | 0.90 | 0.00 | 257.38 |
| 8 | pure_tension | N/A | N/A | 0.90 | -341.28 | 0.00 |
| Quantity | Value |
|---|---|
| Pu (factored axial demand, kip) | 170.00 |
| φPn (axial capacity at operating point, kip) | 315.94 |
| Mu (= M2, design moment, kip-ft) | 214.00 |
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) | 397.71 |
| c (neutral axis depth, in) | 8.09 |
| εt (extreme tension strain) | 0.00423 |
| φ (strength reduction factor) | 0.83 |
| φ regime (§21.2.2) | Transition φ transitions between 0.65 and 0.90 (εty = 0.00207 < εt < 0.00507) |
| D/C axial | 0.53 |
| D/C moment | 0.53 |
| kl/r about X | 18.18 |
Nonsway frames only (ACI 318-19 §6.6.4.3). The other axis (about Y) was not checked. kl/r about Y = 25.00, which exceeds the worst-case short-column limit of 22 (actual limit depends on the other-axis moments). Run the check about Y separately. Run about Y |
|
| kl/r limit | 34.00 |
| Tie spacing limit (§25.7.2.1) | 16.00 in (governed by 16·d_bar) |
| Bar clear spacing (§25.2.3) | 4.50 in ≥ 1.50 in |
Force Decomposition at Operating Point (c = 8.09 in, a = 6.47 in)
| Component | Force (kip) | Moment (kip-in) |
|---|---|---|
| Cc (concrete compression) | 440.08 | 3,416.83 |
| Cs (steel in compression) | 132.13 | 1,123.08 |
| Ts (steel in tension) | -191.65 | 1,208.70 |
| Total = Pn, Mn | 380.55 | 5,748.61 |
| Layer | Bars | d (in) | εs | fs (ksi) | Force (kip) | Lever (in) | Moment (kip-in) |
|---|---|---|---|---|---|---|---|
| 1 | 3 | 2.50 | 0.00207 | 60.00 | 132.13 | 8.50 | 1,123.08 |
| 2 | 2 | 11.00 | -0.00108 | -31.30 | -49.45 | 0.00 | -0.00 |
| 3 | 3 | 19.50 | -0.00423 | -60.00 | -142.20 | -8.50 | 1,208.70 |
| Section geometry | |
| Section | 16 × 22 in (rectangular) |
| Ag (gross area) * | 352.0 in² |
| Ast (total steel area) * | 6.32 in² |
| ρ (reinforcement ratio) * | 0.0180 (1.80%) |
| Materials | |
| f′c | 5,000 psi |
| fy (longitudinal) | 60 ksi (Grade 60) |
| Concrete | Normal weight |
| Reinforcement | |
| Longitudinal bars | 8-#8 |
| Per-face distribution | 1 per b-face, 1 per h-face (+ 4 corners) |
| Clear cover | 1.625 in |
| Transverse | #3 ties @ 12 in |
| Loads | |
| Pu | 170 kip |
| M2 (larger end moment) | 214 kip-ft |
| M1 (smaller end moment) | 0 kip-ft |
| Curvature | Single |
| Bending axis | X |
| Transverse load between supports | No |
| Slenderness parameters | |
| Lu (unsupported length) | 120 in (10.00 ft) |
| k (effective length factor) | 1 |
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