--------------------- | ------------ | -------------------------------------------- | ----------- | ------------------------------------------ | | Steel strength (tension) | 17.6.1 | phi _ Nsa = 0.75 _ Ase * futa | 0.75 | Ductile steel, deep embedment | | Steel strength (shear) | 17.6.2 | phi * Vsa = 0.65 _ A_se * futa | 0.65 | Ductile steel, deep embedment | | Concrete breakout (tension) | 17.6.3 | phi _ Ncb = 0.70 _ kc * sqrt(f'c) _ A_Nc | 0.70 (cast) | Shallow embedment, group anchors | | Concrete breakout (shear) | 17.6.4 | phi _ Vcb = 0.75 _ kc * sqrt(f'c) _ A_Vc | 0.70-0.75 | Anchors near free edges | | Pullout (tension) | 17.6.5 | phi _ Npn = 0.70 _ psic * 8 _ A_brg * f'c | 0.70 | Headed anchors, insufficient embedment | | Side-face blowout (tension) | 17.6.6 | phi _ Nsb = 0.70 _ 160 _ ca1 * sqrt(ca2) | 0.70 | Anchors near free edge with hef > 2.5*ca1 | | Concrete pryout (shear) | 17.6.7 | phi * Vcp = 0.70 _ k_cp * Ncb | 0.70 | Short anchors in shear (hef < 2.5 in.) | | Combined tension and shear | 17.7 | (Nu/Nn)^5/3 + (Vu/Vn)^5/3 <= 1.0 | N/A | When both tension and shear are present |

Notes on the table:

• k_c = 24 for cast-in anchors, 17 for post-installed (unless manufacturer data supports higher)
• A_se = effective cross-section area of anchor (threaded area for bolts in tension)
• A_brg = bearing area of anchor head or nut
• futa = specified tensile strength of anchor steel (limited to 1.9 * fya or 125 ksi per ACI 17.6.1)
• Edge distance c_a1 is measured from the anchor center to the nearest free edge of concrete

The phi factors for concrete limit states (0.70) are lower than for steel limit states (0.75 tension, 0.65 shear) because concrete breakout is more variable and less predictable than steel yielding. When ductile anchorage is required (steel failure must control over concrete failure), the designer must ensure phi * Nsa < phi * Ncb for all concrete limit states.

Cast-in vs. post-installed anchor comparison

The choice between cast-in and post-installed anchors affects both the design procedure and the achievable capacity.

When to use cast-in anchors:

• New construction where anchor locations are known before the pour
• High-capacity base plate connections for steel columns
• Seismic force-resisting system connections (moment frames, braced frames)
• Conditions requiring the highest possible anchor capacity

When to use post-installed anchors:

• Retrofit or modification of existing structures
• Situations where anchor locations are not known during concrete placement
• Light-to-moderate loading conditions (equipment attachments, ledger angles)
• Field corrections for mislocated or omitted cast-in anchors

Anchor bolt sizing table by column size

The following table provides preliminary anchor bolt selections for common steel column sizes. These are minimum recommendations for typical gravity-loaded columns in low-to-moderate seismic regions. Final anchor design must be verified with full ACI 318 Chapter 17 calculations including all limit states.

Notes on the sizing table:

• Bolt grade assumed: ASTM F1554 Grade 55 (fy = 55 ksi, fu = 75 ksi) unless noted otherwise
• Embedment (hef) values assume headed bolts with adequate bearing area
• Edge distances assume the anchor is placed inside the base plate edge with 2x bolt diameter minimum clearance
• For high-seismic applications (SDC D-F), anchors must be designed for the maximum force that can be transmitted by the structure, including overstrength (Omega_0)
• Columns with significant uplift or moment may require larger bolts or additional anchors
• The typical axial load range assumes gravity loading with live load factor 1.6

Worked example -- (4) 1" anchor bolts for W12x65 base plate

Given: W12x65 column supporting a factored axial load Pu = 220 kips and a factored base moment Mu = 80 kip-ft (from lateral wind load). Base plate is 12 in. x 12 in. x 1 in. thick. Concrete pedestal is 20 in. x 20 in. with f'c = 4,000 psi. Four (4) cast-in 1-inch diameter anchor bolts, ASTM F1554 Grade 55 (fu = 75 ksi, fy = 55 ksi), placed symmetrically at 3.5 inches from the column centerline in each direction (9.5 in. x 9.5 in. bolt spacing).

Step 1 -- Anchor forces from eccentric loading:

Bolt group geometry: 4 bolts at 3.5 in. from center (each quadrant)
  Bolt spacing = 2 * 3.5 = 7.0 in. (each direction)

Moment eccentricity: e = Mu / Pu = (80 * 12) / 220 = 4.36 in.
Since e = 4.36 in. < bolt spacing/2 = 3.5 in... wait:
  Actually, the neutral axis must be calculated for the full base plate.

Using the simplified triangular stress block method:
  e = 4.36 in., with bolts at +/- 3.5 in. from center

For the bearing pressure approach (assuming no tension if e < L/6):
  L = 12 in., L/6 = 2.0 in.
  Since e = 4.36 > L/6 = 2.0, there is tension in the anchor bolts.

Maximum tension in one bolt:
  N_u = (Mu * 3.5 - Pu * 0) / (2 * 3.5^2) ... simplified for symmetric bolt pair
  N_u = (80 * 12 - 220 * 0) / (2 * 3.5) = 960 / 7.0 = 137 kip per pair
  Per bolt: T_u = 137 / 2 = 68.5 kip (approximately, assuming two bolts in tension)

Actually, let me use a more precise calculation. The tension in the two bolts on the tension side:

Taking moments about the compression edge (bearing point at 6 in. from center):
  T_u * 9.5 + Pu * (6 - 0) = Mu ... wait, using equilibrium:

  Sum of moments about the compression edge:
  T_total * (9.5 in.) + Pu * (6 in. - e_total) = 0

  Simpler approach: resolve the moment into a force couple.
  For 2 bolts in tension at 3.5 in. from center, and 2 bolts in compression at -3.5 in.:

  Force couple arm = 7.0 in.
  T_total = Mu / couple_arm = (80 * 12) / 7.0 = 137.1 kip
  T_per_bolt = 137.1 / 2 = 68.6 kip

Factored shear per bolt: V_u = V_base / 4 = (assume V_base = 30 kip) / 4 = 7.5 kip/bolt

Step 2 -- Steel strength check (tension):

phi * Nsa = 0.75 * A_se * fu
  A_se for 1" bolt = 0.606 in^2 (threaded area)
  phi * Nsa = 0.75 * 0.606 * 75 = 34.1 kip

Wait -- fu is limited to min(fu, 1.9*fy, 125 ksi) = min(75, 104.5, 125) = 75 ksi. OK.

T_u = 68.6 kip > phi * Nsa = 34.1 kip --> Steel strength is NOT adequate.

Need to revise: use 1-1/4" anchors or higher grade.
Let me check with ASTM F1554 Grade 105 (fu = 125 ksi):
  phi * Nsa = 0.75 * 0.606 * 125 = 56.8 kip --> Still not enough.

Or increase to 1-1/4" bolts (A_se = 0.969 in^2):
  phi * Nsa = 0.75 * 0.969 * 75 = 54.5 kip --> Still not enough.

Use 1-1/4" bolts with Grade 105:
  phi * Nsa = 0.75 * 0.969 * 125 = 90.8 kip > 68.6 kip --> Steel OK.

Let's proceed with (4) 1-1/4" Grade 105 anchors.

Step 3 -- Concrete breakout (tension):

hef = 14 in. (specified embedment)
Edge distance c_a1 = (20 - 9.5) / 2 = 5.25 in. (from anchor to pedestal edge)

Since hef = 14 > 2.5 * c_a1 = 13.125, the breakout cone is limited by the edge.
Use modified hef per ACI 17.6.3.3:
  hef_mod = 2.5 * c_a1 = 13.125 in. (controls for shallow edge)

k_c = 24 (cast-in anchors)

Single anchor breakout:
  N_co = k_c * sqrt(f'c) * hef_mod^1.5 = 24 * sqrt(4000) * (13.125)^1.5
       = 24 * 63.2 * 47.6 = 72,240 lb = 72.2 kip

Group breakout area modification:
  A_Nc = min(3*hef, s_x + 3*hef) * min(3*hef, s_y + 3*hef)
  Edge reduction: A_Nc / A_Nco < 1.0

  A_Nco = 9 * hef_mod^2 = 9 * (13.125)^2 = 1550 in^2

  Actual projected area (considering 20x20 pedestal and 9.5" spacing):
    x-direction: min(3*13.125, 20) = 20 in. (pedestal limits)
    y-direction: min(3*13.125, 20) = 20 in.
    A_Nc (group of 4) = 20 * 20 = 400 in^2 (limited by pedestal)

  Modification factor: psi_ec,N = 1.0 (eccentricity in line with bolts)

  phi * Ncbg = 0.70 * (A_Nc / A_Nco) * psi_ec,N * N_co
             = 0.70 * (400 / 1550) * 1.0 * 72.2
             = 0.70 * 0.258 * 72.2 = 13.0 kip (per anchor)

Hmm, the group effect significantly reduces capacity. With 4 bolts, total:
  phi * Ncbg_total = 4 * 13.0 = 52.0 kip ... this is less than the required 137 kip.

This indicates the pedestal is too small or the embedment is insufficient.
Options: (a) increase pedestal size, (b) increase embedment, (c) add supplementary reinforcement.

Using supplementary reinforcement (hairpin bars or surface reinforcement):
  phi = 0.75 (instead of 0.70) and the reinforcement resists the breakout.

Step 4 -- Summary and recommendations:

This example illustrates that concrete breakout is often the controlling limit state for anchor bolts, particularly when edge distances are limited by the pedestal or footing dimensions. For the W12x65 with significant overturning moment, the design requires:

• (4) 1-1/4 in. ASTM F1554 Grade 105 anchor bolts
• Minimum 14 in. embedment with headed nuts
• Supplementary reinforcement (hairpin bars or rebar) to resist concrete breakout
• Minimum pedestal size 24 in. x 24 in. to provide adequate edge distance
• f'c = 4,000 psi minimum for the concrete pedestal

For columns with predominantly axial compression and minimal moment, the anchor bolt design is much simpler, often governed by the minimum embedment and edge distance requirements rather than calculated strength.

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See Also

• Anchor Bolt Embedment Depth — ACI 318 Cast-In Reference
• Anchor Bolt Embedment Depths per ACI 318 Chapter 17
• AISC Bolt Capacity Table — A325 & A490, All Sizes
• Bolt Hole Sizes — AISC Standard, Oversize & Slotted
• Concrete Spread Footing Design — ACI 318
• Steel Fy & Fu Reference — Yield and Tensile Strength by Grade
• Plate Design
• Column Splice
• base plate design
• bolt shear capacity calculator
• bolt torque and pretension calculator
• Base Plate Checklist
• Reference Tables Directory

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