AISC 360-22 Column Base Plate Design — Verification Benchmark

Complete hand calculation of a W10x49 column base plate against the Steel Calculator WASM engine, covering concrete bearing, plate bending, and minimum thickness determination per AISC Design Guide 1 methodology.

PRELIMINARY — NOT FOR CONSTRUCTION. All results are for educational and reference use only. Must be independently verified by a licensed Professional Engineer (PE) or Structural Engineer (SE) before use in any project.

Problem Statement

Column: W10x49, ASTM A992 (Fy = 50 ksi) Base plate: ASTM A36 (Fy = 36 ksi, Fu = 58 ksi), dimensions B x N to be determined Concrete pedestal: f'c = 4,000 psi, 26 in x 26 in (unreinforced) Loading: Factored axial compression Pu = 250 kips (no moment, no uplift) Anchor rods: 4 x 3/4 in diameter, ASTM F1554 Grade 36 Objective: Determine the minimum required base plate dimensions and thickness per AISC 360-22 / AISC Design Guide 1

Section Properties — W10x49

Hand Calculation — AISC Design Guide 1, 3rd Edition

Step 1: Select Trial Plate Dimensions

Assume plate dimensions B = 16 in, N = 16 in (square plate). Area of plate: A1 = B _ N = 16 _ 16 = 256 in^2

Step 2: Concrete Bearing Capacity — AISC 360-22 J8

The design bearing strength of concrete beneath the base plate is:

Pp = 0.85 * f'c * A1 * sqrt(A2 / A1)

where A2 = maximum area of the supporting concrete surface that is
geometrically similar to and concentric with A1.

Pedestal = 26 in x 26 in, so A2 = 26 * 26 = 676 in^2

sqrt(A2 / A1) = sqrt(676 / 256) = sqrt(2.641) = 1.625

Per J8: sqrt(A2/A1) shall not exceed 2.0.  Value of 1.625 is acceptable.

Pp_nominal = 0.85 * 4,000 * 256 * 1.625
           = 0.85 * 4,000 * 416.0
           = 0.85 * 1,664,000
           = 1,414,400 lb
           = 1,414.4 kips

Capacity reduction factor for concrete bearing: phi_c = 0.65 (AISC 360-22 Section J8).

phi * Pp = 0.65 * 1,414.4 = 919.4 kips

Check: phi*Pp = 919.4 kips >= Pu = 250 kips ✓ (utilization = 0.272)

Step 3: Bearing Pressure

The uniform bearing pressure acting upward on the base plate:

fp = Pu / (B * N) = 250 / 256 = 0.9766 ksi

Step 4: Base Plate Thickness — AISC DG1, Equation 3.3.14a

The plate must resist cantilever bending from the column face to the plate edge. The controlling cantilever dimension is the larger of m and n:

m = (N - 0.95 * d) / 2 = (16 - 0.95 * 10.0) / 2
  = (16 - 9.50) / 2 = 3.25 in

n = (B - 0.80 * bf) / 2 = (16 - 0.80 * 10.0) / 2
  = (16 - 8.00) / 2 = 4.00 in  ←  CONTROLS

l = max(m, n) = 4.00 in

Step 5: Required Plate Thickness

Per AISC DG1 Equation 3.3.14a (LRFD):

t_min = l * sqrt(2 * fp / (phi * Fy))

where:
  l = max(m, n) = 4.00 in
  fp = bearing pressure = 0.9766 ksi
  phi = 0.90 (flexure, AISC 360-22 Section F1)
  Fy = 36 ksi (A36 plate)

t_min = 4.00 * sqrt(2 * 0.9766 / (0.90 * 36))
      = 4.00 * sqrt(1.9531 / 32.40)
      = 4.00 * sqrt(0.06028)
      = 4.00 * 0.2455
      = 0.982 in

Use 1-inch plate (t = 1.00 in). For a 1-inch plate:

phi * Mn (per inch width) = phi * Fy * t^2 / 4
                          = 0.90 * 36 * 1.00^2 / 4
                          = 32.40 / 4
                          = 8.10 in-k per inch width

M_u = fp * l^2 / 2 = 0.9766 * (4.00)^2 / 2 = 0.9766 * 8.00 = 7.81 in-k/in

phi*Mn = 8.10 > Mu = 7.81 ✓  (utilization = 0.964)

Step 6: Anchor Rod Check — No Uplift

No moment = no uplift. Anchor rods are nominal: 4 x 3/4 in dia. ASTM F1554 Gr 36 (Fy = 36 ksi, Fu = 58 ksi). Edge distance and minimum embedment per ACI 318 Chapter 17 verified separately.

Step 7: Summary

All checks pass. The 16x16x1 base plate is adequate.

WASM Output Comparison

The Steel Calculator WASM engine (AISC 360 region), run with identical inputs:

All 12 quantities match within 0.00%. The AISC base plate calculation is algebraically exact for axial-load-only base plates (no moment, no eccentricity).

Sensitivity — What If Plate Is Too Thin?

For a 3/4 in plate (t = 0.75 in) instead of 1 in:

phi*Mn = 0.90 * 36 * 0.75^2 / 4 = 0.90 * 36 * 0.5625 / 4 = 4.56 in-k/in
Mu = 7.81 in-k/in > phi*Mn = 4.56 → FAIL

| Quantity | Hand Calc (t=0.75) | WASM (t=0.75) |
|----------|---------------------|-----------------|
| phi*Mn (in-k/in) | 4.56 | 4.56 |
| DCR | 1.714 | 1.714 |
| Verdict | FAIL | FAIL |

The WASM engine correctly detects under-thick plates and provides a "FAIL" flag with the required thickness uplift.

Code References — AISC 360-22 / AISC DG1

How to Reproduce

1. Navigate to the Steel Calculator Base Plate Design tool
2. Select AISC 360-22 as the design code
3. Enter: W10x49 column, 16x16 plate, f'c=4ksi, pedestal 26x26, Pu=250k
4. Click Calculate — the WASM engine designs and checks the base plate

The WASM engine handles both axial compression and combined axial-plus-moment base plates, including anchor rod tension from uplift moment and shear key design.

Why Verification Matters

Base plate design is one of the most frequently used calculations in structural steel practice. Steel Calculator's base plate engine is verified against AISC Design Guide 1 worked examples, AISC Design Example Base Plate Problems (v16.0), and independent FEA benchmarks for large-moment base plates. These public verification pages provide reproducible evidence of accuracy.

See also: AISC Beam Verification, EN 1993 Column Verification, AS 4100 Bolt Verification, CSA Weld Verification.

Last verified: 2026-05-08. WASM version: core-wasm-v2 stage-5-connection-design. Tolerance standard: all quantities within 1.0% of hand calculation or published value. AISC Design Guide 1, 3rd Edition methodology used.

Disclaimer: This content is for educational purposes only. Results must be verified by a licensed professional engineer. Steel Calculator provides preliminary design tools — NOT a substitute for professional engineering judgment.