14x14 Slender Column, k = 0.86, Lu = 22 ft
Slender 14x14 column per ACI 318-19: non-sway moment magnification (delta_ns), effective stiffness (EI)eff, and critical buckling load Pc.
Checked about X: depth h = 14 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 tension-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 | 417.16 | 0.00 |
| 2 | Cap intersection | 13.85 | -0.00051 | 0.65 | 417.20 | 47.06 |
| 3 | Compression-controlled limit (εt = εty) | 6.81 | 0.00207 | 0.65 | 172.48 | 93.92 |
| 4 | Transition lower (εt = εty + 0.0015) | 5.25 | 0.00357 | 0.77 | 148.12 | 101.07 |
| 5 | Tension-controlled limit (εt = εty + 0.003) | 4.28 | 0.00507 | 0.90 | 126.24 | 104.80 |
| 6 | Tension-controlled deep (εt = εty + 0.008) | 2.64 | 0.01007 | 0.90 | 36.30 | 73.25 |
| 7 | Pure bending | 2.17 | 0.01290 | 0.90 | 0.00 | 58.98 |
| 8 | pure_tension | N/A | N/A | 0.90 | -129.60 | 0.00 |
| Quantity | Value |
|---|---|
| Pu (factored axial demand, kip) | 82.40 |
| φPn (axial capacity at operating point, kip) | 91.87 |
| Mu (Mc = δns·M2, magnified design moment, kip-ft) | 83.98 |
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) | 93.63 |
| c (neutral axis depth, in) | 3.61 |
| εt (extreme tension strain) | 0.00656 |
| φ (strength reduction factor) | 0.90 |
| φ regime (§21.2.2) | Tension-controlled φ = 0.90 (εt ≥ εty + 0.003 = 0.00507) |
| D/C axial | 0.89 |
| D/C moment | 0.89 |
| kl/r about X | 54.06 |
Nonsway frames only (ACI 318-19 §6.6.4.3). The other axis (about Y) was not checked. kl/r about Y = 54.06, 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 | 25.03 |
| Cm (§6.6.4.5.3) | 0.899 |
Cm from end-moment ratio per §6.6.4.5.3(a). |
|
| (EI)eff (§6.6.4.4.4(b), βdns = 0.728) | 2,151,365 kip·in² |
Normal-weight concrete (Ec = 57,000√f′c psi, §19.2.2.1(b)). |
|
| Ec (§19.2.2.1) | 3,605 ksi |
| Pc (critical buckling) | 411.9 kip |
| δns (§6.6.4.5.2) | 1.226 |
| Mc = δns·M2 (design moment) | 84.0 kip·ft |
| Tie spacing limit (§25.7.2.1) | 14.00 in (governed by 16·d_bar) |
| Bar clear spacing (§25.2.3) | 8.12 in ≥ 1.50 in |
Force Decomposition at Operating Point (c = 3.61 in, a = 3.07 in)
| Component | Force (kip) | Moment (kip-in) |
|---|---|---|
| Cc (concrete compression) | 146.06 | 798.32 |
| Cs (steel in compression) | 28.02 | 126.09 |
| Ts (steel in tension) | -72.00 | 324.00 |
| Total = Pn, Mn | 102.08 | 1,248.41 |
| Layer | Bars | d (in) | εs | fs (ksi) | Force (kip) | Lever (in) | Moment (kip-in) |
|---|---|---|---|---|---|---|---|
| 1 | 2 | 2.50 | 0.00092 | 26.75 | 28.02 | 4.50 | 126.09 |
| 2 | 2 | 11.50 | -0.00656 | -60.00 | -72.00 | -4.50 | 324.00 |
| Section geometry | |
| Section | 14 × 14 in (rectangular) |
| Ag (gross area) * | 196.0 in² |
| Ast (total steel area) * | 2.40 in² |
| ρ (reinforcement ratio) * | 0.0122 (1.22%) |
| Materials | |
| f′c | 4,000 psi |
| fy (longitudinal) | 60 ksi (Grade 60) |
| Concrete | Normal weight |
| Reinforcement | |
| Longitudinal bars | 4-#7 |
| Per-face distribution | 0 per b-face, 0 per h-face (+ 4 corners) |
| Clear cover | 1.6875 in |
| Transverse | #3 ties @ 12 in |
| Loads | |
| Pu | 82.4 kip |
| M2 (larger end moment) | 68.5 kip-ft |
| M1 (smaller end moment) | 51.2 kip-ft |
| Curvature | Single |
| Bending axis | X |
| Transverse load between supports | No |
| Slenderness parameters | |
| Lu (unsupported length) | 264 in (22.00 ft) |
| k (effective length factor) | 0.86 |
| βdns (sustained-load ratio) | 0.728 |
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 00:14 UTC