Base plates are where structural steel meets foundation concrete, and they have to satisfy three different codes at the same time: AISC 360 for the steel, ACI 318 for the concrete bearing and anchorage, and AISC Design Guide 1 (DG1) for the integration of both. DG1 is the canonical reference and we’ll follow its method here. This walkthrough sizes a concentrically loaded base plate carrying pure axial compression — the most common case.
Worked example
- Column: W10x49, A992 steel (Fy = 50 ksi)
- Concentric factored axial load Pu = 350 kips
- Concrete: f’c = 4,000 psi (normal weight)
- Base plate: A36 steel (Fy = 36 ksi)
- Pier: 24 in × 24 in (allows full A2/A1 > 1)
W10x49 dimensions: d = 10.0 in, bf = 10.0 in.
Step 1 — Required plate area
DG1 Section 3.1: the concrete bearing strength governs the required plate area.
φc·Pp = φc·(0.85·f’c·A1)·√(A2/A1) ≤ 1.7·φc·f’c·A1
φc = 0.65 per ACI. For A2/A1 = 4 (the √ limit):
A1,req = Pu / (φc·0.85·f’c·2.0) = 350 / (0.65 · 0.85 · 4 · 2.0) = 79.2 in²
That’s a 9 in × 9 in plate minimum, but we need to also clear the column flanges. Practical minimum: B ≥ bf + 2 in = 12 in. Try N = B = 14 in → A1 = 196 in².
Step 2 — Confirm bearing pressure
Actual bearing pressure:
fp,u = Pu/A1 = 350/196 = 1.79 ksi
Allowable: φc·0.85·f’c·√(A2/A1). The pier is 24×24 = 576 in²; the loaded area A1 = 196 in²; geometrically similar projection gives A2/A1 ≤ 4 anyway. So:
φfp = 0.65(0.85)(4.0)(√4) = 4.42 ksi >> 1.79 ksi ✓
Step 3 — Cantilever lengths m, n, n’
Two cantilever distances and one yield-line distance:
m = (N − 0.95d)/2 = (14 − 0.95·10)/2 = 2.25 in
n = (B − 0.8bf)/2 = (14 − 0.8·10)/2 = 3.00 in
n’ = √(d·bf)/4 = √(10·10)/4 = 2.50 in
The yield-line approach takes λn’ to capture lifting between the flanges when bearing is low. With fp = 1.79 vs φfp = 4.42, λ is small. DG1 gives:
X = [4·d·bf/(d+bf)²]·Pu/φPp
λ = 2√X / (1 + √(1−X)) ≤ 1.0
X = [4(10)(10)/400] · (350/866) = 1.0 · 0.404 = 0.404
λ = 2√0.404 / (1 + √0.596) = 1.272 / 1.772 = 0.718
λn’ = 0.718(2.50) = 1.79 in < both m and n → cantilever governs.
Step 4 — Required plate thickness
Use the larger of m, n, λn’. Here ℓ = n = 3.00 in. Plate cantilever bending under uniform pressure fp,u:
tp,req = ℓ · √[2·Pu/(φb·Fy·B·N)]
φb = 0.90.
tp,req = 3.00 · √[2(350)/(0.90 · 36 · 14 · 14)] = 3.00 · √[700/6,350] = 3.00 · √0.1102 = 3.00(0.332) = 0.996 in
Specify 1 in plate. Always round up to the next standard plate thickness (1/8 in increments up to 1.5 in, 1/4 in thereafter).
Step 5 — Anchor rods
Pure axial compression doesn’t require anchor rods for strength — gravity holds the column down. But OSHA Subpart R requires minimum 4 anchor rods per column, sized for 300 ft-lb of erection moment about either axis. Specify (4) 3/4 in ASTM F1554 Grade 36 rods, 12 in embedment with hooked or headed end, on a 10 in × 10 in pattern. Check pull-out per ACI 318-19 Chapter 17 only if you have uplift or moment load cases — not needed here.
Step 6 — Final specification
- Plate: PL 1 × 14 × 14, A36
- Anchor rods: (4) 3/4φ F1554 Gr. 36, 10×10 pattern, 12 in embedment
- Grout: 1 in non-shrink, f’c,grout ≥ 5,000 psi
- Pier: 24 × 24 with proper edge cover
When you have moment
The walkthrough above is the easy case. Add moment and you need to consider:
- Small eccentricity (e ≤ N/6): bearing across the full plate, no tension in rods
- Moderate eccentricity (N/6 < e ≤ ecrit): partial bearing, still no rod tension
- Large eccentricity: rods in tension, triangular bearing block — full DG1 Section 3.4 treatment
The break points depend on plate dimensions, axial load, and concrete strength. Run them numerically.
Iterate faster
The whole walkthrough above is automated in our free base plate calculator — concentric axial today, moment cases coming soon. Pair it with the column buckling calculator for sizing the column above and the beam calculator for the supported framing. The chain matches the way most steel building design actually flows.
Closing
Base plate design under axial load is six steps: pick a trial area, check bearing, compute m/n/λn’, size thickness from cantilever bending, add OSHA-minimum anchor rods, and specify the materials. Twenty minutes if you have the inputs. The complications — moment, uplift, seismic Ω0 overstrength — build on top of this skeleton.