Anchor Bolts Calculator

Steel anchor bolt design per ACI 318-19 Chapter 17. Tension, shear, and combined loading capacity including breakout and pullout limit states. Educational use only.

This page documents the scope, inputs, outputs, and computational approach of the Anchor Bolts Calculator on steelcalculator.app. The interactive calculator runs in your browser; this documentation ensures the page is useful even without JavaScript.

What this tool is for

• Checking tension, shear, and combined loading capacity for cast-in or post-installed anchors per ACI 318 Chapter 17.
• Evaluating all anchor failure modes: steel failure, concrete breakout, pullout, side-face blowout, and pryout.
• Understanding the CCD method (Concrete Capacity Design) for breakout strength with edge and spacing effects.

What this tool is not for

• It does not design the base plate or the connection between the base plate and the column.
• It does not handle adhesive (chemical) anchor design in detail or seismic qualification per ACI 355.
• It does not check the concrete pedestal or foundation for global stability.

Key concepts this page covers

• steel strength of anchor in tension and shear
• concrete breakout strength (CCD method)
• pullout strength and bearing capacity
• anchor group effects and edge distance modifications
• phi factors: 0.75 tension, 0.65 shear (AISC/ACI)

Inputs and outputs

Typical inputs: anchor diameter, embedment depth, anchor type (headed, hooked, post-installed), concrete strength f'c, edge distances (ca1, ca2), anchor spacing, number of anchors, supplementary reinforcement, and factored tension/shear demands.

Typical outputs: capacity for each failure mode (steel, breakout, pullout, pryout, blowout), controlling failure mode, modification factors applied, combined tension-shear interaction check, and demand-to-capacity ratio.

Computation approach

The calculator evaluates each limit state per ACI 318-19 Section 17.6 (tension) and 17.7 (shear). Concrete breakout uses the CCD method: the basic breakout strength of a single anchor (based on embedment depth and concrete strength) is modified by factors for edge distance, spacing, eccentricity, cracking, and lightweight concrete. Combined tension and shear is checked using the tri-linear interaction equation from ACI 318-19 Section 17.8.3.

Anchor Design Formulas — ACI 318-19 Chapter 17

Steel strength in tension

φNsa = φ × n × Ase,N × futa

Where:
  φ = 0.75 (ductile steel element)
  n = number of anchors
  Ase,N = effective cross-sectional area of anchor in tension
  futa = tensile strength of anchor steel (≤ 1.9fya or 125 ksi)

Concrete breakout strength in tension (CCD method)

φNcbg = φ × (A_Nc / A_Nco) × ψ_ed,N × ψ_ec,N × ψ_cp,N × N_b

Where:
  A_Nc = projected concrete failure area of the group
  A_Nco = 9 × hef² (single anchor, no edge effects)
  ψ_ed,N = edge distance modification factor
  ψ_ec,N = eccentricity modification factor
  ψ_cp,N = splitting modification factor (for uncracked concrete)
  N_b = k_c × √(f'c) × hef^1.5  (basic breakout strength)
  k_c = 24 (cast-in headed anchors) or 17 (post-installed)
  hef = effective embedment depth (in)

Pullout strength

φNpn = φ × ψ_c,P × N_p

Where:
  N_p = 8 × A_brg × f'c  (for headed bolts)
  A_brg = bearing area of anchor head
  ψ_c,P = 1.4 (uncracked concrete) or 1.0 (cracked)

Concrete breakout in shear

φVcbg = φ × (A_Vc / A_Vco) × ψ_ed,V × ψ_ec,V × ψ_cp,V × V_b

Where:
  A_Vc = projected concrete failure area (shear)
  A_Vco = 4.5 × ca1² (single anchor, no edge effects)
  V_b = 7 × (√(le/d_a)) × √(f'c) × ca1^1.5  (basic shear breakout)
  ca1 = edge distance in the direction of shear

Combined tension and shear interaction

If Nu / φNn ≤ 0.2: full shear capacity available (φVn)
If Vu / φVn ≤ 0.2: full tension capacity available (φNn)
Otherwise:
  (Nu / φNn) + (Vu / φVn) ≤ 1.2

Standard Anchor Bolt Properties — Quick Reference

F1554 Grade 36 anchor bolts (most common)

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).

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
• Anchor embedment reference
• Concrete footing calculator
• Bolted connections calculator
• 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

Disclaimer (educational use only)

This page is provided for general technical information and educational use only. It does not constitute professional engineering advice, a design service, or a substitute for an independent review by a qualified structural engineer. Any calculations, outputs, examples, and workflows discussed here are simplified descriptions intended to support understanding and preliminary estimation.

All real-world structural design depends on project-specific factors (loads, combinations, stability, detailing, fabrication, erection, tolerances, site conditions, and the governing standard and project specification). You are responsible for verifying inputs, validating results with an independent method, checking constructability and code compliance, and obtaining professional sign-off where required.

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