16x20 Biaxial Column, 10-#8
Biaxial bending for a 16x20 / 10-#8 column per ACI 318-19: demand-plane cut through the 3D P-Mx-My interaction surface and D/C.
Biaxial bending (P-Mx-My): demand-plane angle λ = 31.0 deg
Both axial and moment D/C ratios ≤ 1.00.
Demand-plane summary
- λ (demand-plane angle)
- 31.0 deg
- Mx,design
- 50.0 kip-ft
- My,design
- 30.0 kip-ft
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.
3D interaction surface
P-Mx-My capacity envelope (φ-reduced) at 10° cuts. Drag to rotate, scroll to zoom, right-drag to pan. demand point (Pu, Mux, Muy). operating point (φPn, φMnx, φMny).
Interaction Diagram Points (9 anchors, demand-plane cut at λ = 31.0 deg)
| Anchor | Description | c (in) | εt | φ | φPn (kip) | φMλ (kip-ft) |
|---|---|---|---|---|---|---|
| 1 | Pure compression cap | N/A | N/A | 0.65 | 798.27 | 0.00 |
| 2 | Cap intersection | 22.98 | -0.00009 | 0.65 | 798.20 | 107.27 |
| 3 | Arc strain (zero) (εt = 0) | 22.26 | 0.00000 | 0.65 | 773.86 | 118.46 |
| 4 | Arc strain (positive half yield) (εt = +εty/2) | 16.44 | 0.00103 | 0.65 | 502.69 | 192.90 |
| 5 | Compression-controlled limit (εt = εty) | 13.09 | 0.00207 | 0.65 | 276.24 | 211.61 |
| 6 | Transition lower (εt = εty + 0.0015) | 10.14 | 0.00357 | 0.78 | 92.28 | 228.79 |
| 7 | Tension-controlled limit (εt = εty + 0.003) | 8.94 | 0.00446 | 0.85 | 0.05 | 225.41 |
| 8 | Tension-controlled deep (εt = εty + 0.008) | 8.94 | 0.00446 | 0.85 | 0.05 | 225.41 |
| 9 | Pure bending | 8.94 | 0.00446 | 0.85 | 0.00 | 225.41 |
| Quantity | Value |
|---|---|
| Pu (factored axial demand, kip) | 200.00 |
| φPn (axial capacity at operating point, kip) | 584.56 |
| Mu (resultant in the demand plane, Mλ, design moment, kip-ft) | 58.31 |
No transverse load between supports. Cm from end-moment ratio per ACI 318-19 §6.6.4.5.3(a). |
|
| φMλ (moment capacity, kip-ft) | 170.43 |
| c (neutral axis depth, in) | N/A |
| εt (extreme tension strain) | N/A |
| φ (strength reduction factor) | N/A |
| φ regime (§21.2.2) | Compression-controlled φ = 0.65 throughout (εt ≤ εty = 0.00207) |
| D/C axial | 0.34 |
| D/C moment | 0.34 |
| Slenderness (about X) | |
| kl/r about X | 20.00 |
Nonsway frames only (ACI 318-19 §6.6.4.3). |
|
| kl/r limit | 28.00 |
| Slenderness (about Y) | |
| kl/r about Y | 25.00 |
Nonsway frames only (ACI 318-19 §6.6.4.3). |
|
| kl/r limit | 28.00 |
| Tie spacing limit (§25.7.2.1) | 16.00 in (governed by 16·d_bar) |
| Bar clear spacing (§25.2.3) | 4.08 in ≥ 1.50 in |
| Section geometry | |
| Section | 16 × 20 in (rectangular) |
| Ag (gross area) * | 320.0 in² |
| Ast (total steel area) * | 7.90 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 | 10-#8 |
| Per-face distribution | 1 per b-face, 2 per h-face (+ 4 corners) |
| Clear cover | 1.5 in |
| Transverse | #3 ties @ 16 in |
| Loads | |
| Pu | 200 kip |
| M2x (larger end moment, about X) | 50 kip-ft |
| M1x (smaller end moment, about X) | 25 kip-ft |
| Curvature about X | Single |
| M2y (larger end moment, about Y) | 30 kip-ft |
| M1y (smaller end moment, about Y) | 15 kip-ft |
| Curvature about Y | Single |
| Bending | Biaxial (P-Mx-My) |
| Transverse load between supports | No |
| Slenderness parameters | |
| Lu,x (unsupported length, about X) | 120 in (10.00 ft) |
| kx (effective length factor, about X) | 1 |
| Lu,y (unsupported length, about Y) | 120 in (10.00 ft) |
| ky (effective length factor, about Y) | 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