About this calculator
This tool sizes a steel column base plate and its anchor bolts for concentric and eccentric (moment) loading. It computes the concrete bearing pressure, required plate thickness, anchor tension and shear demand, and compares those demands against anchor steel and concrete anchorage capacities. It is intended for structural and civil engineers doing preliminary base-connection sizing under axial load, moment, and shear.
Method & formulas
Eccentricity and kern check: e = Mu/Pu. If e ≤ N/6 (the kern of a plate of length N), the whole footprint stays in bearing and the anchors see no net uplift.
e = Mu / Pu kern = N/6
Anchor tension beyond the kern: once e > N/6, the plate rotates about a bearing (compression) zone of length Y at one edge, with the anchors on the far side carrying tension T. Equilibrium of the plate as a free body — sum of vertical forces and sum of moments about the anchor — gives two equations solved together for Y and T:
ΣF: C − T = Pu, C = fp·B·Y
ΣM (about the anchor): C·(d′ − Y/2) = Pu·(e + d′ − N/2)
d′ is the distance from the tension anchor to the compression edge, and fp is the design bearing pressure, taken as the classic concrete bearing allowable fp ≈ 0.85·φc·f′c (φc = 0.65).
Plate thickness (cantilever/yield-line method): tp = l·√(2fp / (0.9Fy)), where l = max(m, n, λn′) is the governing cantilever distance from the column flange/web line to the plate edge.
Anchor steel capacity: φNsa = φ·n·Ase·Futa (φ = 0.75); φVsa = φ·n·0.6·Ase·Futa (φ = 0.65), with Ase ≈ 0.78 times the gross bolt area.
Concrete breakout in tension: the basic single-anchor strength Nb = kc·λ·√f′c·hef1.5 (kc ≈ 10 for cast-in anchors, SI units) is scaled by a group multiplier approximating the ratio of projected concrete failure area to that of one isolated anchor.
Worked example
Inputs: Pu=400 kN, Mu=90 kN·m, N=B=500 mm, Fy=250 MPa, dcol=bf,col=300 mm, f′c=25 MPa, nA=2, db=20 mm, hef=300 mm, Futa=825 MPa, ca=100 mm (d′=400 mm), Vu=80 kN.
e = 90/400 = 225 mm > kern (500/6 ≈ 83 mm) → anchors see tension.
fp = 0.85×0.65×25 ≈ 13.8 MPa. Solving the equilibrium equations: Y ≈ 59 mm, C ≈ 405 kN, T ≈ 4.6 kN.
Plate: l = max(107.5, 130, 75) = 130 mm; tp = 130√(2×13.8/(0.9×250)) ≈ 45.6 mm.
Anchors (Ase≈245 mm²): φNsa≈303 kN; φVsa≈158 kN; breakout φNcb≈253 kN.
Checks: T=4.6 kN ≤ 253 kN OK; Vu=80 kN ≤ 158 kN OK.
Assumptions & limitations
- A rigid plate with a linear/triangular bearing stress distribution is assumed; real plates and grout beds can behave somewhat differently.
- The breakout check uses a simplified area-ratio group multiplier, not the full projected-area (CCD) geometry — edge distances, overlapping cones, and eccentricity factors are not all modeled.
- Anchor stress area is approximated as ~0.78 of the gross bolt area; confirm the exact value from the manufacturer for final design.
- Combined tension-shear interaction and pryout/side-face-blowout modes on the anchors are not checked.
- Verify results against the governing code and a licensed engineer's judgment before construction.
FAQ
- What loading condition puts the anchor bolts into tension?
- Whenever e = Mu/Pu exceeds N/6 (the plate's kern), part of the plate lifts off the concrete and the far-side anchors must carry tension to keep the base in equilibrium.
- Why is the required plate thickness often thicker than expected?
- The plate acts as a cantilever from the column flange/web line to the plate edge under the full assumed bearing pressure fp; a larger footprint or stiffeners shorten that cantilever and reduce tp.
- Does the breakout check capture edge-distance and spacing effects precisely?
- No — it applies a simplified group multiplier for preliminary screening. For anchors near an edge or closely spaced, run the full concrete capacity design (CCD) procedure or dedicated anchor software.