Designing an embedded column base

The Embedded column base type (Wizard group Column bases, mark prefix EB) checks a W-shape column set into a concrete footing, pier or grade beam, so that the foundation itself holds the column's moment. It follows AISC Design Guide 1, Base Connection Design for Steel Structures, 3rd Edition (2024), Chapter 5, and for Type II connections Hassan and Kanvinde (2023), AISC Engineering Journal, 4th quarter. Bending is about the column's strong axis.

Choose the connection type:

• Type I (the default). The concrete below the column end is there to set the column, not to carry vertical load. The moment and shear are resisted by the column flanges bearing sideways on the concrete, plus any horizontal bars attached to the flanges (DG1 §5.2.1).
• Type II. The concrete below the embedded base plate is designed for vertical stress. The base plate adds a second mechanism, vertical bearing, to the flange bearing: M = MHB + MVB (Hassan and Kanvinde 2023). Type II needs the embedded base plate.

Embedded base inputs #

• Loads: axial force P (compression positive, tension negative), shear V and strong-axis moment M at the top of the foundation. Enter service dead and live loads, required strengths, ASCE 7 combinations or load cases. Both LRFD and ASD are available.
• Column: the connection type (I or II), the W-shape and its material. Seismic design: strong base replaces the moment with 1.1 Ry Fy Z of the column (DG1 §6.4.1, AISC 341-22 D2.6c(b)(1); ÷ 1.5 in ASD); enter P and V from the overstrength combinations. You enter Ry; the line under the input shows the AISC 341-22 Table A3.2 value for the column grade, for reference. With the strong base you can also choose:
  • Strong-base moment: 1.1 Ry Fy Z / αs (default) or the lesser of that and the overstrength moment you enter (AISC 341-22 D2.6c(b)(2), only when a ductile limit state of the base or the foundation controls; the column flexure in the embedment is then checked);
  • Story height H: ILX generates the D2.6b shear, the lesser of 2 Ry Fy Z / (αs H) and your shear, at least 0.7 Fy Z / (αs H) (turn the minimum off for Exceptions (a) and (b); limit it by analysis for Exception (c));
  • Special cantilever column system (E6): the column axial force at most 0.15 Fy Ag, the protected zone 2 d above the foundation (hatched on the elevation) and demand-critical welds.
• Foundation and embedment:
  • the concrete strength f'c;
  • the foundation width bw, perpendicular to the plane of bending;
  • the foundation length in the plane of bending and its depth. They are optional, but the depth is needed for the checks of the concrete below the column (punching), and the length for one-way shear;
  • the embedment depth (0 gives the required depth, rounded up to 1 in.).

  Confined concrete takes the bearing limit under the plates as 1.7 f'c, as DG1 does. Limit damage uses Mn = 0.8 MHB (0.8 (MHB + MVB) for Type II), the load at which the concrete starts to crack and crush in tests.

• Face bearing plates: plates between the flanges at the top of the foundation that carry axial compression. Enter their thickness and material.
• Embedded base plate: a plate on the column end, with width B, length N and thickness. It widens the concrete panel that bears on the flanges, bj = (bf + B)/2, carries axial tension by bearing up on the concrete above it, and in a Type II connection bears down on the concrete below.
• Anchor rods below the plate: none, 2 (on the axis along N) or 4 (a rectangle), with:
  • the rod diameter and material;
  • the embedment of the heavy hex nut below the underside of the plate;
  • the spacing along N and along B;
  • cracked or uncracked concrete.
• Attached horizontal bars:
  • welded to the flanges (they work in tension and compression) or U-bar hairpins around the flanges (tension only);
  • the bar size and yield strength;
  • the number of bars per flange in a top row and a bottom row, and the depth of each row below the top of the foundation;
  • the clear cover at the foundation ends.

Embedded base checks #

• Moment strength of the embedment. ILX checks Mu ≤ φMn with φ = 0.75 (DG1 §5.3; ASD Ω = 2.00 = 1.5/0.75):
  • the bearing stress is fb = 1.54 √f'c (bw/bf)^0.66, at most 1.7 f'c (Eq. 5-1);
  • fb acts over a top block on one flange and a bottom block on the other (Eqs. 5-2 to 5-4);
  • MHB is the closed form of Eq. 5-6 at the actual shear, with the bar forces Asr Fysr. A row of bars welded to both flanges counts twice, 2 n Asr Fysr: tension on one flange and compression on the other. The report says so.

  The required embedment depth is reported as a note. With bars, ILX also checks that the neutral axis lies between the two rows, which Eq. 5-6 assumes.

• Type II: vertical bearing. ILX adds MVB to MHB (Hassan and Kanvinde Eq. 20):
  • The stress under the plate is idealized as three steps. The two outer steps are Y = 0.3 N wide (Eqs. 8, 9).
  • Without attached bars (Scenario 1), the uplifting end is held by a concrete breakout, Ft = (40/9) √f'c A35 / √dembed with A35 = (B + 3 dembed)(0.3 N + 1.5 dembed) − 0.3 N B (Eqs. 12, 13).
  • Then MVB = (Ft + P Y/N)(N − Y) (Eq. 11). Compression P adds to MVB and tension reduces it.
  • With attached bars (Scenario 2), the tension field behind the column removes this restraint, so MVB = 0.
  • Scenario 3, bars with vertical stirrups, is not modeled. ILX uses MVB = 0, which is conservative.

  The paper gives no resistance factor. ILX uses the DG1 φ = 0.75 on MHB + MVB. The demand is shared between the two mechanisms in proportion to their strengths. The share on the plate gives the outer-step stress on the concrete below. The concrete below is then checked for bearing, plate bending and punching, as for compression below. A warning shows when the embedment depth to column depth ratio or f'c is outside the tested range.

• Attached bars. Development length by ACI 318-19 Table 25.4.2.3 ("other cases"), with ψt = 1.3 for a row with more than 12 in. of concrete below it. ILX compares it with the length available beyond the flange when you give the foundation length. Welding of the bars (ASTM A706, AWS D1.4) is noted, not designed.
• Axial compression with face bearing plates. The face bearing plates are checked for:
  • concrete bearing, φ fp(max) A1 with A1 = (bf − tw)(d − 2tf) and φ = 0.65;
  • thickness, tmin = l √(2Pu / (0.9 Fy A1)) with l = √(d bf)/4 (Eqs. 5-7, 5-8);
  • the AISC 341 F3.5b.4 minimum, 0.75 tw and 3/8 in. This is a recommendation, and a requirement for strong-base seismic design.

  DG1 calls for CJP groove welds.

• Axial compression through the bottom. This applies to Type I without face bearing plates, and always to Type II. ILX calculates the load path below the column:
  • bearing of the embedded base plate (or of the bare column end) on the concrete below. This uses ACI 318-19 22.8 and AISC J8: 0.85 f'c √(A2/A1) ≤ 1.7 f'c, with A2 within the depth below the plate and the foundation plan, and φ = 0.65;
  • bending of the base plate on that bearing (DG1 §4.3.1 cantilevers m, n and λn');
  • two-way (punching) shear of the concrete below, ACI 318-19 22.6.5.2, with the size factor λs. The effective depth is the depth below the plate less the cover and half a bar;
  • one-way shear of the foundation at d from the plate, when its length is given.

  A check fails only when the calculated strength is too small.

• Axial tension. Tension needs an embedded base plate, which bears up on the concrete above it. ILX checks:
  • the plate bending between and outside the flanges (§4.3.1 cantilevers);
  • concrete bearing on top of the plate;
  • the breakout of the concrete above the plate. This applies DG1 Eq. 5-9, a 35° cone, to the plate's uplift. It is an ILX extension.

  With anchor rods below the plate, ILX also computes the rod group by ACI 318-19 Chapter 17, using the same engine as the base plate:

  • steel strength in tension (17.6.1);
  • concrete breakout of the group (17.6.2). The embedment hef runs from the top of the foundation to the nuts, and the foundation edges limit the projected area;
  • pullout of the heavy hex nut (17.6.3);
  • side-face blowout where hef > 2.5 ca1 (17.6.4).

  The uplift resistance is the larger of the plate path and the anchor path. Each path's parts are listed in the report. Without an embedded base plate, the calculated uplift resistance is zero.

• Column within the embedment. ILX checks the column's own strength:
  • flexure for the moment Mu + Vu²/(2 fb bj) where the column shear is zero (F2 or F3);
  • axial force and flexure together (H1-1, no buckling in the concrete).

  The shear in the column web between the two bearing blocks is not checked. The bearing load spreads through the flanges and plates into the concrete over a large area, and DG1 has no such check. The report shows a line explaining this.

• Design basis. The report states the factors used:
  • LRFD: φ = 0.75 on the embedment moment, 0.65 on concrete bearing and 0.90 on the steel;
  • ASD: Ω = 2.00, 2.31 and 1.67;
  • ACI 318 shear and anchor items: φRn, or φRn/1.6 with ASD loads.

Embedded base limits #

• Type II follows a paper validated on ten tests (W14X370 and W18X311 columns, 20 and 30 in. embedments, about 4 ksi concrete). Use judgement outside that range; ILX warns.
• Scenario 3 of Type II (vertical stirrups with attached bars) is not modeled; MVB = 0 is used.
• Headed studs on the flanges are not designed.
• The foundation's flexure and reinforcement are outside ILX. Punching and one-way shear below the column are checked when compression goes through the bottom.
• Weak-axis bending is not covered.
• The rotational stiffness of the base is not computed; see DG1 Appendix C.2.3.
• Erection (DG1 §5.4): the setting nuts, shims or setting plate must resist the forces of placing the concrete around the column.

Embedded base drawings #

• The elevation shows the column embedded in the foundation, with:
  • the face bearing plates;
  • the embedded base plate and the anchor rods below it, with their nuts;
  • the two DG1 bearing zones, on opposite flanges;
  • for Type II, the outer vertical bearing steps above and below the base plate;
  • the attached bars on both sides;
  • the embedment and bar depths.
• The plan at the top of the foundation shows the column section with the face bearing plates, the embedded plate and anchor rods (hidden), the bars, and the foundation width.

Embedded base verification #

• DG1 Example 5.3-1 is reproduced row by row: W14X176, 22 in. embedment, bw = 60 in., f'c = 4 ksi, Pu = 250 kips, Vu = 96 kips, Mu = 700 kip-ft. The rows include fb, the three terms of Eq. 5-6, MHB = 958 kip-ft, φMHB = 719 kip-ft, A1, φPp = 827 kips, l and tmin = 0.941 in. DG1 prints the resistance factor as "(0.7)". The product, 719 kip-ft, is 0.75 × 958, the φ = 0.75 of §5.3.
• Hassan and Kanvinde (2023), Table 1. ILX reproduces the model strength of the ten tests within 3 %:
  • five Type II tests by Grilli et al. without bars, 1G to 5G (Scenario 1, including tension and zero axial load);
  • three tests with attached bars, Tests 1 to 3 (Scenario 2).

  Tests 4 and 5 (Scenario 3, stirrups) are listed as a documented deviation: ILX takes MVB = 0 and is conservative.

See the Verification page.