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W10 column base plate on four 3/4-in headed anchor rods 6 in from a concrete edge: anchor tensions, breakout, pullout, shear breakout, interaction and plate thickness (ACI 318-19 Chapter 17, LRFD)

Tool	Anchor and Base Plate Design
Source	ACI Committee 318 (2019). Building Code Requirements for Structural Concrete (ACI 318-19) and Commentary. American Concrete Institute, Farmington Hills, MI, Chapter 17 and Section 22.8; Fisher, J. M., and Kloiber, L. A. (2006). Base Plate and Anchor Rod Design, 2nd ed. Steel Design Guide 1, American Institute of Steel Construction, Chicago, IL (the bearing-block method); single-anchor values checked against Building Seismic Safety Council (2012). 2009 NEHRP Recommended Seismic Provisions: Design Examples. FEMA P-751, Section 14.3.
Level	Professional

Problem

A W10 column (d = 10.1 in, b_f = 8.02 in, t_f = 0.62 in) stands on an 18 × 16 × 1.5 in A36 base plate held by four 3/4-10 UNC headed anchor rods (f_uta = 58 ksi, f_ya = 36 ksi) at 14 in × 10 in, embedded 12 in in cracked 4,000 psi normalweight concrete 24 in thick. One concrete edge is 6 in from the anchor line at −x; the other sides are far. The factored loads are 40 kips of compression, a moment of 45 kip-ft that compresses the +x edge and a shear of 10 kips toward the near edge, carried by the anchors through a grout pad. Find the anchor tensions, check every anchor failure mode of ACI 318-19 Chapter 17 and the tension-shear interaction, and find the required plate thickness.

Inputs to Enter

Anchors: cast-in headed rod, d_a 0.75 in, 10 threads per inch, f_uta 58 ksi, f_ya 36 ksi, h_ef 12 in, head area blank (heavy hex); pattern 2 × 2 at 14 in (x) and 10 in (y)
Concrete: f′_c 4,000 psi, λ_a 1.0, h_a 24 in, edge at −x 6 in, other edges blank, cracked, N_b by the 5/3 form, seismic factor 1.0
φ: steel 0.75 tension and 0.65 shear, breakout 0.70, pullout and pryout 0.70, bearing 0.65, plate bending 0.90
Loads: P_u 40 kips, M_ux 45 kip-ft, M_uy 0, V_ux −10 kips, V_uy 0
Plate 18 × 16 × 1.5 in, F_y 36 ksi; column d 10.1 in, b_f 8.02 in, t_f 0.62 in; A_2 blank; E_s 29,000 ksi; anchor tension by plane sections; shear by the anchors with a grout pad, front and rear lines

Open the Anchor and Base Plate Design tool (loaded with this example)

Answers

Plane-section analysis (n = 8.04): compression under the plate C = 57.17 kips at x = 7.343 in, two anchors in tension at 8.585 kips each (ΣT = 17.17 kips), peak pressure 1,438 psi
Steel: A_se = 0.334 in², φN_sa = 0.75 · 19.40 = 14.55 kips (ratio 0.590); φV_sa = 0.65 · 0.6 · 0.80 · 19.40 = 6.05 kips per anchor against 2.50 kips (0.413)
Tension breakout: A_Nc = (6 + 18)(10 + 36) = 1,104 in², A_Nco = 1,296 in², N_b = 16 √4,000 · 12^(5/3) = 63.65 kips, ψ_ed,N = 0.80, N_cbg = 43.37 kips, φN_cbg = 30.36 kips against 17.17 kips (0.565)
Pullout: N_p = 8 · 0.911 · 4,000 = 29.16 kips, φN_pn = 20.41 kips against 8.585 kips (0.421); side-face blowout does not apply (6 in is not less than h_ef / 2.5 = 4.8 in)
Shear breakout toward the edge: front line c_a1 = 6 in, A_Vc = 252 in², V_b = 8.37 kips, φV_cbg = 9.11 kips against 5.00 kips (0.549); rear line c_a1 = 20 in, φV_cbg = 37.19 kips against 10.00 kips (0.269); pryout φV_cpg = 96.15 kips (0.104)
Interaction: (0.590 + 0.549) / 1.2 = 0.949 (governs, M.S. +0.05); 5/3 power form 0.783
Base plate: f_p,max = 0.65 · 0.85 · 4,000 = 2,210 psi; e = 13.5 in above e_crit = 8.434 in, bearing length Y = 1.522 in, block tension 13.81 kips; m = 4.203 in, n = 4.792 in, M_pl = 13.557 kip-in/in, required thickness 1.294 in against 1.5 in (ratio 0.744)

Notes

The tool's default inputs are this case; press Submit. The case is illustrative (stated on the page), not a printed example: no public document was found that works an anchor group near an edge to printed digits. Checked by test_anchor_base_plate.php (1,475 checks): the projected areas, modification factors and basic strengths of 40 seeded tension groups and 40 seeded shear lines against an independent numpy implementation, the plate analysis against scipy on 24 seeded plates with equilibrium to 1e-9, the bearing block against the roots of its quadratic, and the single-anchor values of FEMA P-751 Section 14.3 (1,392 lb, 2,254 lb, 724 lb; 13,515 lb, 14,151 lb, 7,030 lb, interaction 0.99) to the printed digits. The bearing-block tension (13.81 kips) is lower than the plane-section tension used for the anchor checks (17.17 kips); choose the block in Anchor Tension by to design the anchors with it.