Anchors in concrete
Cast-in headed anchors (headed bolts or studs) and hooked bolts, single or in a rectangular group of up to 4 × 4, in tension and shear, to ACI 318-19 Chapter 17 with ASCE 7-22 strength combinations. Chapter 17 is strength design, so the calculation always uses the LRFD combinations.
Inputs of the anchor group #
- Anchors: headed or hooked, diameter da, ASTM steel (F1554 Gr. 36, 55, 105, A449, A36; futa ≤ 1.9 fya and 125 ksi), whether the steel element is ductile (ACI 2.3; F1554 and A449 rods are), the effective embedment hef, the bearing area Abrg (0 = heavy hex nut) or the hook length eh.
- Pattern and edges: anchors along x and y with their spacings, the distance from the outermost anchors to the edge on each of the four sides (0 = no edge on that side) and the member thickness ha.
- Concrete: f'c (2,500 to 10,000 psi), λa, cracked or uncracked, supplementary reinforcement for tension and for shear (Table 17.5.3(b): φ = 0.75 with, 0.70 without; the former Conditions A and B), and the edge reinforcement of 17.7.2.5.1 for ψc,V.
- Loads: service forces per load type at the group centroid: tension N, moments Mx (tension on the +y anchors) and My (tension on the +x anchors), shears Vx and Vy, and where the shear acts (ex, ey from the centroid).
- Seismic: Seismic Design Category C to F; the tension option of 17.10.5.3 (d) Eh × Ω0 or (a) a ductile steel element (with its stretch length), and Ω0 (ASCE 7-22 Table 12.2-1, the engineer's input).
- Code options: built-up grout pad (0.80 Vsa), torqued anchors (Table 17.9.2(a) spacing and edge 6 da), the specified cover (20.5.1.3) for the minimum edge distance, and anchors welded to the attachment (shear breakout Case 2 of Fig. R17.7.2.1b).
Auto-design (editor toolbar) varies the anchor diameter and effective embedment hef (the layout is kept); anchor steel when unlocked. Objectives: least anchor steel; lowest cost index (diameter × length). Kept unless you select them: anchor steel. Every other input is kept; see Auto-design.
Checks performed #
| Check | Basis |
|---|---|
| Anchor forces | Rigid attachment: tension by the elastic distribution about the centroid with compressed anchors at zero (the compression bears at them); shear in equal shares plus the polar share of the torsion of an eccentric shear |
| Steel in tension | 17.6.1: Nsa = Ase,N futa, most highly stressed anchor, φ = 0.75 (ductile) or 0.65 |
| Concrete breakout in tension | 17.6.2: ANc/ANco, ψec,N, ψed,N, ψc,N (1.25 uncracked); hef' near three or more edges (17.6.2.1.2); Nb by Eq. 17.6.2.2.1, or 16 λa √f'c hef^5/3 for 11 ≤ hef ≤ 25 in. |
| Pullout | 17.6.3: 8 Abrg f'c (headed) or 0.9 f'c eh da (hooked, 3 da ≤ eh ≤ 4.5 da), ψc,P = 1.4 uncracked, φ = 0.70 |
| Side-face blowout | 17.6.4: headed anchors with hef > 2.5 ca1, the anchors along each edge (Nsbg), corner factor |
| Steel in shear | 17.7.1: 0.6 Ase,V futa, × 0.80 through a grout pad; the row that takes the whole shear in Cases 2 and 3 |
| Concrete breakout in shear | 17.7.2 toward and parallel to every edge: Cases 1 and 2 (row spacing s ≥ ca1,1), Case 3 (s < ca1,1) or Case 2 only (welded) of Fig. R17.7.2.1b; ca1' in narrow, thin members (17.7.2.1.2); ψec,V, ψed,V, ψc,V, ψh,V; parallel shear twice the perpendicular value with ψed,V = 1.0 |
| Pryout | 17.7.3: kcp Ncpg, kcp = 1.0 (hef < 2.5 in.) or 2.0, φ = 0.70 |
| Interaction | 17.8: either ratio ≤ 0.2 ignores it; otherwise the sum ≤ 1.2 |
| Seismic (SDC C to F) | 17.10.5 and 17.10.6 when the earthquake share of the tension or the shear exceeds 20 %: 0.75 on the concrete tension strengths (17.10.5.4); option (d) Eh × Ω0 or option (a) steel governs (1.2 Nsa), stretch length ≥ 8 da and futa/fya ≥ 1.3; shear by Eh × Ω0 (17.10.6.3(c)) |
| Detailing | Table 17.9.2(a): spacing 4 da (6 da torqued); edge distance cover + da/2 (6 da torqued); hook length |
Drawings #
The drawing sheet (screen, PDF and DXF) has the anchor plan (the member with the edges you entered, the sides without an edge cut off with break lines, the anchors, their spacing and edge distances, the section cut) and section A through an anchor row (the member hatched, the anchors with their headed or hooked end at hef, the embedment and the member thickness). The attachment, anchor length and projection, nuts and washers at the attachment and any anchor reinforcement are not part of the calculation and are not drawn; the sheet notes say so.
Limitations #
- Cast-in anchors only: post-installed (expansion, screw, undercut) and adhesive anchors are not covered.
- Anchor reinforcement (17.5.2.1) is not designed; with supplementary reinforcement only φ changes.
- Shear with components perpendicular and parallel to the same edge is combined linearly (the code gives no rule; conservative). Intermediate rows of a 3- or 4-row group are not checked separately for shear breakout.
- The anchor tension ignores a bearing zone beyond the anchors (the lever arm is at most the anchor spacing), which is conservative for an attachment larger than the pattern.
- Seismic options 17.10.5.3(b) and (c) and 17.10.6.3(a) and (b) (attachment-limited forces) are not modelled: enter the attachment-limited force as the earthquake load if you use them. The seismic provisions were written from the code text; no worked seismic example was available to verify them.
Verification examples #
AISC Design Guide 1, 3rd Ed. (2024) checks anchor rods to ACI 318-19 Chapter 17:
| Example | What it checks | Published | ILX Calcs |
|---|---|---|---|
| DG1 4.7-3 | Four ⅞ in. rods, hef = 15 in., uplift 70 kips | φNsa = 20.1, φNpn = 26.7, Nb = 92.3, φNcbg = 76.3 kips | 20.1, 26.6, 92.3, 76.6 |
| DG1 4.7-3 | Same rods with a 3½ in. hook | φNpn = 5.80 kips | 5.79 |
| DG1 4.7-4 | Shear toward an edge, ca1 = 12 in. | AVc = 720 in.², Vb = 23.7, φVcbg = 18.4 kips | 720, 23.7, 18.4 |
| DG1 4.7-9 | Two 1 in. rods | ANc = 1,510 in.², φNcbg = 51.7, φNpn = 33.6 kips | 1,512, 52.0, 33.6 |
| DG1 4.7-15 | Four rods in a 20 in. column | hef' = 5.33 in., ANc = 400 in.², Ncbg = 29.2, φNcbg = 20.4 kips | 5.33, 400, 29.2, 20.4 |
| DG1 4.7-7 | Eight 1½ in. rods, hef = 24 in., grout pad, brace tension and shear | φNsa = 61.4, ANc = 7,850 in.², φNcbg = 239, φNpn = 87.5, φVsa = 25.5, φVcpg = 479 kips, interaction 1.15 | 61.1, 7,850, 239.5, 87.3, 25.4, 478.9, 1.146 |
For DG1 4.7-7 the rods sit on a 28 × 6.5 in. outline with unequal x spacings; ILX takes a uniform 4 × 2 grid with the same outline, which gives the same ANc and forces per rod. The engine tests (tests/test_aci_anchors.py) add the narrow, thin member of ACI 318-19 Fig. R17.7.2.1.2 (ca1' = 5.33 in., AVc = 168 in.², AVco = 128 in.²). For ψed,V that figure prints 0.98 (0.3 × 5/5.33); ILX applies Eq. 17.7.2.4.1b, 0.7 + 0.3 × 5/(1.5 × 5.33) = 0.89. The load distribution and the seismic rules are covered by hand-calculation tests.