20-in Circular Spiral Column, 8-#10, f'c = 5,000 psi
Circular spiral column check per ACI 318-19: 20-in diameter, 8-#10 bars, bar-ring orientation sweep, spiral conformance, and D/C ratio.
Both axial and moment D/C ratios ≤ 1.00.
P-M interaction diagram
Demand (Pu, Mu) tested against the φ-reduced capacity envelopes of ring turned half a bar spacing and one bar on the compression axis. The D/C is checked across ring rotations, and the rotation with the largest D/C is the verdict. Solid line: ring turned half a bar spacing (governs), with the operating point (φPn, φMn) on its boundary. Dashed line: one bar on the compression axis. About ring orientation. 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 | 0.75 | 1,212.27 | 0.00 |
| 2 | Cap intersection | 21.51 | -0.00066 | 0.75 | 1,212.19 | 113.36 |
| 3 | Compression-controlled limit (εt = εty) | 9.95 | 0.00207 | 0.75 | 351.49 | 310.27 |
| 4 | Transition lower (εt = εty + 0.0015) | 7.67 | 0.00357 | 0.82 | 148.20 | 310.94 |
| 5 | Tension-controlled limit (εt = εty + 0.003) | 6.25 | 0.00507 | 0.90 | 18.21 | 290.56 |
| 6 | Tension-controlled deep (εt = εty + 0.008) | 3.86 | 0.01007 | 0.90 | -259.60 | 177.26 |
| 7 | Pure bending | 6.08 | 0.00529 | 0.90 | 0.00 | 283.66 |
| 8 | pure_tension | N/A | N/A | 0.90 | -548.64 | 0.00 |
| Quantity | Value |
|---|---|
| Pu (factored axial demand, kip) | 300.00 |
| φPn (axial capacity at operating point, kip) | 776.42 |
| Mu (= M2, design moment, kip-ft) | 100.00 |
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) | 258.81 |
| c (neutral axis depth, in) | 14.49 |
| εt (extreme tension strain) | 0.00048 |
| φ (strength reduction factor) | 0.75 |
| φ regime (§21.2.2) | Compression-controlled φ = 0.75 throughout (εt ≤ εty = 0.00207) |
| D/C axial | 0.38 |
| D/C moment | 0.38 |
| Ring position (rotation search) | Ring turned half a bar spacing D/C 0.3864 (governs) One bar on the compression axis: D/C 0.3840 |
| kl/r | 24.00 |
Nonsway frames only (ACI 318-19 §6.6.4.3). |
|
| kl/r limit | 34.00 |
| Bar clear spacing (§25.2.3) | 4.37 in ≥ 1.91 in |
| Spiral clear gap (§25.7.3.1) | 2.00 in ≥ 1.00 in |
| ρs provided / required (Eq. 25.7.3.3, fyt = 60 ksi) | 0.0188 ≥ 0.0144 |
Force Decomposition at Operating Point (c = 14.49 in, a = 11.60 in)
| Component | Force (kip) | Moment (kip-in) |
|---|---|---|
| Cc (concrete compression) | 802.60 | 2,725.88 |
| Cs (steel in compression) | 267.84 | 1,175.33 |
| Ts (steel in tension) | -35.22 | 239.68 |
| Total = Pn, Mn | 1,035.22 | 4,140.89 |
| Layer | Bars | d (in) | εs | fs (ksi) | Force (kip) | Lever (in) | Moment (kip-in) |
|---|---|---|---|---|---|---|---|
| 1 | 1 | 3.20 | 0.00234 | 60.00 | 70.80 | 6.80 | 481.77 |
| 2 | 1 | 3.20 | 0.00234 | 60.00 | 70.80 | 6.80 | 481.77 |
| 3 | 1 | 7.18 | 0.00151 | 43.89 | 50.35 | 2.82 | 141.90 |
| 4 | 1 | 7.18 | 0.00151 | 43.89 | 50.35 | 2.82 | 141.90 |
| 5 | 1 | 12.82 | 0.00035 | 10.06 | 12.77 | -2.82 | -36.00 |
| 6 | 1 | 12.82 | 0.00035 | 10.06 | 12.77 | -2.82 | -36.00 |
| 7 | 1 | 16.80 | -0.00048 | -13.87 | -17.61 | -6.80 | 119.84 |
| 8 | 1 | 16.80 | -0.00048 | -13.87 | -17.61 | -6.80 | 119.84 |
| Section geometry | |
| Section | 20 in dia. (circular) |
| Ag (gross area) * | 314.2 in² |
| Ast (total steel area) * | 10.16 in² |
| ρ (reinforcement ratio) * | 0.0323 (3.23%) |
| Materials | |
| f′c | 5,000 psi |
| fy (longitudinal) | 60 ksi (Grade 60) |
| Concrete | Normal weight |
| Reinforcement | |
| Longitudinal bars | 8-#10 |
| Clear cover | 1.5 in |
| Transverse | #4 spiral @ 2.5 in pitch (fyt = None ksi) |
| Loads | |
| Pu | 300 kip |
| M2 (larger end moment) | 100 kip-ft |
| M1 (smaller end moment) | 0 kip-ft |
| Curvature | Single |
| Transverse load between supports | No |
| Slenderness parameters | |
| Lu (unsupported length) | 120 in (10.00 ft) |
| k (effective length factor) | 1 |
Assumptions and limits
- The spiral ratio check (ACI Eq. 25.7.3.3) uses fyt, the spiral steel yield strength. Longitudinal bar calculations use fy.
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Verdict method 8 · build 40c109d · generated 2026-10-23 00:15 UTC