---------- | ----------- | ---------------------------- | -------------------------- | | 1/2 | 0.142 | 4.3 | 2.6 | | 5/8 | 0.226 | 6.8 | 4.1 | | 3/4 | 0.334 | 10.0 | 6.0 | | 7/8 | 0.462 | 13.9 | 8.3 | | 1 | 0.606 | 18.2 | 10.9 | | 1-1/4 | 0.969 | 29.1 | 17.4 |

φ = 0.75, futa = 58 ksi (F1554 Gr 36). Single anchor, single shear plane.

Minimum embedment depth for concrete breakout

Min hef based on concrete breakout ≥ steel capacity for f'c = 4,000 psi, single anchor, no edge effects.

Worked Example — Column Base Plate Anchor Group

Problem: A W12x65 column base plate has four 3/4-inch F1554 Gr 36 headed anchor bolts with 8-inch embedment in 4,000 psi concrete. The base plate is 14" × 14" with anchors at 10" × 10" spacing centered. Edge distances: ca1 = 2" (minimum). Determine the tension capacity.

Step 1 — Steel strength

4 anchors: n = 4
Ase,N = 0.334 in² (3/4" bolt)
futa = 58 ksi (F1554 Gr 36)

φNsa = 0.75 × 4 × 0.334 × 58 = 58.1 kips

Step 2 — Concrete breakout (group)

hef = 8 in, k_c = 24 (cast-in headed)
Nb = 24 × √4000 × 8^1.5 = 24 × 63.25 × 22.63 = 34,344 lb = 34.3 kips

Group area A_Nc (4 anchors, 10" spacing, 2" edge distance):
ca1 = 2 in (edge), hef = 8 in → 1.5hef = 12 in

The breakout area is limited by the 2" edge distance.
A_Nco = 9 × 8² = 576 in²
A_Nc ≈ (10 + 2×12) × (10 + 2×min(12,2)) = 34 × 14 = 476 in²
  (Edge distance limits one side to 2" + hef direction)

Actually: A_Nc = (ca2 + 1.5hef + s/2) × (s + 2×min(1.5hef, ca1,edge))
  This requires careful geometry. For the simplified case:
  A_Nc/A_Nco ≈ 0.70 (reduced by edge proximity)

ψ_ed,N = 0.7 + 0.3 × (ca1/1.5hef) = 0.7 + 0.3 × (2/12) = 0.75

φNcbg = 0.65 × 0.70 × 0.75 × 1.0 × 1.0 × 34.3 = 0.65 × 18.0 = 11.7 kips

CONCRETE BREAKOUT GOVERNS: φNcbg = 11.7 kips << φNsa = 58.1 kips

The edge distance of 2 inches severely limits breakout capacity. Increasing ca1 to 4 inches:

ψ_ed,N = 0.7 + 0.3 × (4/12) = 0.80
A_Nc/A_Nco ≈ 0.85 (improved)
φNcbg = 0.65 × 0.85 × 0.80 × 34.3 = 15.2 kips

Still low. For adequate capacity, either increase edge distance to 6 inches or provide supplementary reinforcement (tie reinforcement around the breakout cone).

Edge Distance and Spacing Requirements

Minimum edge distances per ACI 318

For 3/4" anchors: 6 × 0.75 = 4.5 in minimum (without reinforcement). Edge distance is the single most important parameter for concrete breakout capacity.

Minimum anchor spacing

ACI 318-19 Section 17.7: minimum spacing = 6da

For 3/4" anchors: 6 × 0.75 = 4.5 in minimum
For 1" anchors: 6 × 1.0 = 6.0 in minimum

Preferred spacing: 3× embedment depth (3hef) for full breakout cone development.

Post-Installed Anchor Types and Applications

Post-installed anchors are installed in hardened concrete after construction, making them essential for retrofit, tenant improvements, equipment mounting, and conditions where cast-in anchors were omitted or mislocated. The following table summarizes the major categories and their design considerations.

Post-installed anchor classification

*Capacity range for single anchor in 4,000 psi concrete, no edge effects. Actual capacity depends on specific product, embedment, spacing, and concrete strength.

Key considerations for post-installed anchor selection

• Cracked vs. uncracked concrete: Anchors in regions of concrete that may crack under service loads (tension zones of beams, slabs, or near construction joints) must be qualified for use in cracked concrete per ACI 355.2 (mechanical) or ACI 355.4 (adhesive). Not all expansion anchors are rated for cracked concrete.
• Seismic qualification: For structures assigned to Seismic Design Category C through F, anchors resisting seismic forces must be prequalified per ACI 355.2 or ACI 355.4 with seismic testing protocols. This includes simulated seismic cycling tests where the anchor is loaded in cracked concrete under alternating tension and shear.
• Fire resistance: Adhesive anchors lose bond strength at elevated temperatures. For fire-rated connections, cast-in anchors or mechanical post-installed anchors are preferred. Adhesive anchors in fire-rated assemblies require special evaluation.
• Installation sensitivity: Adhesive anchors are particularly sensitive to hole cleanliness (dust must be brushed and blown out), concrete temperature during installation (epoxy may not cure below 40 deg F), and pot life (mixed adhesive must be placed before gel time expires). Torque-controlled expansion anchors are sensitive to proper torque application and hole diameter tolerance.
• Inspection requirements: ACI 318 Section 17.8 requires special inspection for post-installed anchors. Adhesive anchors require continuous special inspection during installation (watching hole cleaning, adhesive mixing, and placement). Mechanical expansion anchors require periodic special inspection (verifying hole depth, diameter, and torque).

Worked Example

Problem: Determine the tensile capacity of a 3/4-inch diameter ASTM F1554 Grade 36 anchor bolt with 6 inches embedment in 3,000 psi concrete. Edge distance = 4 in. (sufficient to preclude edge breakout).

Given:

• Anchor: 3/4 in. dia. F1554 Gr. 36 (Fy = 36 ksi, Fu = 58 ksi)
• Embedment depth: hef = 6.0 in.
• Concrete: fc' = 3,000 psi, normal weight (lambda = 1.0)
• Edge distance: c1 = 12 in. (not governing)
• No supplementary reinforcement

Solution:

Step 1 -- Steel strength in tension (ACI 318-19 Section 17.4.1):

Nsa = Ase * Futa = 0.334 * 58 = 19.4 kips (nominal)
phi*Nsa = 0.75 * 19.4 = 14.5 kips (design)

where Ase = 0.334 in^2 (tensile stress area for 3/4 in. UNC).

Step 2 -- Concrete breakout strength (ACI 318-19 Section 17.4.2):

Ncb = (Anc / Anco) * psi_ed,N * psi_c,N * psi_cp,N * Nb

Anco = 9 * hef^2 = 9 * 36 = 324 in^2
Anc = Anco (no edge distance reduction)

psi_ed,N = 1.0 (c_min > 1.5*hef = 9 in. -- assume yes)
psi_c,N = 1.0 (cracked concrete assumption at service, no supplementary reinf.)

Nb = kc * lambda * sqrt(fc') * hef^1.5
   = 24 * 1.0 * sqrt(3000) * (6.0)^1.5
   = 24 * 54.8 * 14.7 / 1000
   = 19.3 kips

Ncb = 1.0 * 1.0 * 1.0 * 1.0 * 19.3 = 19.3 kips
phi*Ncb = 0.70 * 19.3 = 13.5 kips

Step 3 -- Pullout strength (ACI 318-19 Section 17.4.3):

Npn = psi_c,P * Np

For headed bolt, bearing area Abrg = pi/4 * (1.25^2 - 0.75^2) = 0.785 in^2
Np = 8 * Abrg * fc' = 8 * 0.785 * 3.0 = 18.8 kips

phi*Npn = 0.70 * 18.8 = 13.2 kips

Result: Governing limit state is concrete pullout at phi*Nn = 13.2 kips (design). The steel strength of 14.5 kips is not governing. For increased capacity, consider deeper embedment or Grade 55 anchor bolts. Per ACI 318-19, ductile anchor design requires steel to govern -- supplementary reinforcement may be needed.

Frequently Asked Questions

What is the CCD method for concrete breakout? The Concrete Capacity Design (CCD) method assumes a 35-degree breakout cone projected from the anchor head to the concrete surface. The basic breakout strength of a single anchor in tension is Nb = kc sqrt(f'c) hef^1.5 (in US customary units). This basic strength is then modified for edge distance (the breakout cone is truncated), anchor spacing (overlapping cones reduce per-anchor capacity), eccentricity of the resultant tension force, and whether the concrete is cracked. The CCD method is the basis of ACI 318 Chapter 17.

Why are the phi factors different for anchor tension and shear? ACI 318 uses phi = 0.75 for anchor steel strength in tension and phi = 0.65 for anchor steel strength in shear (when the anchor is governed by a brittle failure mode in concrete). The lower shear phi reflects the greater uncertainty in concrete breakout and pryout failure modes, which can be sudden and brittle compared to ductile steel yielding. If supplementary reinforcement is provided to restrain the breakout cone, the phi factor may be increased.

What is the difference between cast-in and post-installed anchors? Cast-in anchors (headed bolts, J-bolts, headed studs) are placed before the concrete is poured and develop capacity through bearing on the anchor head. Post-installed anchors (expansion, undercut, adhesive) are installed in hardened concrete by drilling a hole and engaging the concrete through expansion, mechanical interlock, or adhesion. Post-installed anchors generally require product-specific qualification testing and may have different capacity equations than the generic ACI 318 provisions for cast-in anchors.

How do adhesive anchors compare to mechanical expansion anchors? Adhesive (chemical) anchors use a two-component resin (typically epoxy, polyester, or vinylester) that bonds a threaded rod or reinforcing bar to the concrete wall of a drilled hole. Mechanical expansion anchors use a wedge or sleeve that physically expands against the concrete when torque or impact is applied. Each type has distinct advantages. Adhesive anchors can achieve higher capacities at closer edge distances because the bond stress distributes along the entire embedment length rather than concentrating at the expansion point. Adhesive anchors also allow deeper embedments (20+ inches is common) and smaller hole diameters relative to the anchor diameter. However, adhesive anchors are sensitive to installation conditions: hole cleanliness, concrete temperature (many epoxies will not cure below 40 deg F or above 110 deg F), moisture in the hole, and shelf life of the adhesive cartridges. Mechanical expansion anchors are faster to install, less sensitive to environmental conditions, and immediately loadable after installation (adhesive anchors require curing time, typically 24 hours at 70 deg F). For overhead applications, adhesive anchors are generally prohibited by code unless specifically evaluated, because uncured adhesive can drip from the hole. For seismic applications, both types require product-specific qualification per ACI 355.4 (adhesive) or ACI 355.2 (mechanical).

What are the ACI 318 seismic provisions for anchors? ACI 318-19 Section 17.2.3 imposes additional requirements for anchors in structures assigned to Seismic Design Category (SDC) C through F. The core philosophy is to ensure that anchors are governed by a ductile steel failure mode rather than a brittle concrete failure mode. The three primary seismic requirements are: (1) the design must satisfy one of four options — Option A requires the anchor steel to be the controlling failure mode (phi Nsa < phi Ncbg and phi Nsa < phi Npn), Option B allows concrete breakout to govern but requires supplementary reinforcement to redirect the breakout force into the structural member, Option C applies to tension-only anchors in structures assigned to SDC C or D with low seismic demand, and Option D applies when the anchor tension demand is very low relative to capacity. (2) Anchors must be prequalified for seismic applications per ACI 355.2 (mechanical) or ACI 355.4 (adhesive), which involves passing simulated seismic cycling tests. (3) The phi factor for concrete breakout under seismic loading is further reduced to account for the additional uncertainty in concrete behavior under reversed cyclic loading. For base plate connections in steel moment frames, the anchor design must also satisfy the overstrength provisions of ASCE 7, which amplify the design forces by the system overstrength factor (Omega-0) to ensure that the anchors remain elastic while the lateral system yields and dissipates energy.

How should anchor bolts be specified on structural drawings? Anchor bolt specifications on structural drawings should include enough information for the contractor to procure and install the anchors correctly without ambiguity. A complete anchor bolt specification includes the following: (1) anchor standard and grade (e.g., ASTM F1554 Grade 36 or Grade 55), (2) anchor diameter and length (e.g., 3/4 in diameter x 12 in long), (3) anchor type (headed, L-bolt, or J-bolt), (4) minimum embedment depth, (5) projection above the top of concrete (typically 1 to 3 inches above the top of the base plate, including grout, plus the nut and washer height), (6) exact plan location with dimensions from column grid lines (including tolerances, typically +/- 1/4 inch for cast-in anchors), (7) edge distance requirements from the concrete pedestal or footing edge, (8) number of anchors per base plate, (9) thread requirement (e.g., UNC, full thread, or partial thread with minimum engaged length), (10) material requirements (e.g., weldable Grade 55 with Supplement S1 if the anchor will be field-welded), and (11) any special requirements such as hot-dip galvanizing for corrosive environments. For post-installed anchors, the drawing must also specify the product manufacturer and model (e.g., "Hilti HIT-Z epoxy adhesive anchor, or equivalent per ACI 355.4 evaluation report"), the hole diameter and depth, the installation torque, and whether special inspection is required. Anchor bolt templates are recommended for cast-in anchors to maintain position accuracy during concrete placement.

What are the different grades of ASTM F1554 anchor bolts? ASTM F1554 is the primary specification for anchor bolts and covers three grades: Grade 36 (Fy = 36 ksi, Fu = 58 ksi) is the most commonly specified grade for standard column base plate connections where the anchor does not resist significant tension. Grade 55 (Fy = 55 ksi, Fu = 75 ksi) is used for moderate tension demands and is available with Supplement S1 for weldability. Grade 105 (Fy = 105 ksi, Fu = 125 ksi) is a high-strength bolt used for heavy column bases, moment-resisting bases, and anchorages with high uplift forces. Grade 36 is ductile (elongation >= 23%), which is advantageous for seismic applications where the anchor must undergo inelastic deformation. Grade 105 has lower ductility (elongation >= 12%) and is more susceptible to hydrogen embrittlement in certain environments. All grades are available in carbon steel or with a galvanized coating; however, hot-dip galvanizing of Grade 105 requires careful temperature control to avoid hydrogen embrittlement. The engineer should specify the grade based on the required capacity, ductility demand, and fabrication requirements, and should always confirm that the specified grade is compatible with the base plate design and the overall connection behavior.

Related pages

• Baseplate anchors calculator
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• Tools directory
• How to verify calculator results
• Disclaimer (educational use only)
• Anchor bolt embedment reference
• Anchor bolts reference
• Concrete footing design
• Base plate design reference

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