About Anchor Bolt Design Calculator (ACI 318-19 Ch.17)
The anchor bolt design calculator evaluates the tension and shear strengths of a SINGLE cast-in anchor in concrete following ACI 318-19 Chapter 17, using SI units (MPa, mm, N). In tension it computes the steel strength, the concrete breakout strength, and the pullout strength; in shear it computes the steel strength and the concrete breakout strength.
Concrete breakout uses the basic strength Nb = kc*lambda*sqrt(fc)*hef^1.5 with kc = 10 for cast-in anchors (SI), the projected area ratio ANc/ANco with ANco = 9*hef^2, and the edge and cracking modification factors. The tool applies the ACI strength-reduction (phi) factors and reports the governing design strengths phi*Nn and phi*Vn. SCOPE: a single cast-in anchor optionally near one edge; it does not cover anchor groups, post-installed anchors, side-face blowout, supplementary reinforcement, or seismic design.
How It Works
- Enter the anchor properties: effective area Ase (mm^2), steel tensile strength futa (MPa), embedment hef (mm), and outside diameter da (mm).
- Enter the concrete strength fc (MPa), the edge distance ca1 (mm), and the head bearing area Abrg (mm^2). Set lambda for lightweight concrete and toggle cracked/uncracked concrete.
- For tension the calculator computes Nsa = Ase*futa, the breakout Ncb = (ANc/ANco)*psi_ed,N*psi_c,N*Nb (reducing ANc and psi_ed,N when ca1 < 1.5 hef), and the pullout Npn = psi_c,P*8*Abrg*fc.
- For shear it computes Vsa = 0.6*Ase*futa and the breakout Vcb from Vb. It applies the phi factors (tension 0.75 steel / 0.70 breakout & pullout; shear 0.65 steel / 0.70 breakout) and reports the governing phi*Nn and phi*Vn.
Worked Example
A single cast-in anchor has Ase = 157 mm^2, futa = 400 MPa, hef = 125 mm, in fc = 28 MPa cracked concrete with edge distance ca1 = 300 mm (>= 1.5*hef = 187.5 mm, so away from the edge), head bearing area Abrg = 200 mm^2, da = 16 mm, lambda = 1.0. Tension: Nsa = 157*400 = 62.8 kN (phi*Nsa = 47.1 kN); Nb = 10*1.0*sqrt(28)*125^1.5 = 73.95 kN with ANco = 9*125^2 = 140625 mm^2 and ANc = ANco, so Ncb = 73.95 kN (phi*Ncb = 51.8 kN); pullout Npn = 8*200*28 = 44.8 kN (phi*Npn = 31.4 kN). Pullout governs, phi*Nn = 31.4 kN. Shear: Vsa = 0.6*157*400 = 37.68 kN (phi*Vsa = 24.5 kN); breakout uses the capped coefficient 3.7, giving Vb = Vcb = 3.7*sqrt(28)*300^1.5 = 101.7 kN (phi*Vcb = 71.2 kN). Steel governs shear, phi*Vn = 24.5 kN.
Formulas
- Tension steel and pullout
Nsa = Ase*futa ; Npn = psi_c,P * 8 * Abrg * fc (psi_c,P = 1.0 cracked / 1.4 uncracked)- Concrete breakout in tension (17.6.2)
Ncb = (ANc/ANco)*psi_ed,N*psi_c,N*Nb ; Nb = kc*lambda*sqrt(fc)*hef^1.5 ; ANco = 9*hef^2 ; kc = 10 (cast-in, SI)- Edge-distance projected area (single anchor, one edge)
ca1 >= 1.5 hef: ANc = ANco | ca1 < 1.5 hef: ANc = (ca1 + 1.5 hef)*(2*1.5 hef)- Shear strengths and phi factors
Vsa = 0.6*Ase*futa ; Vb = min(0.66*(le/da)^0.2*sqrt(da), 3.7)*lambda*sqrt(fc)*ca1^1.5 ; phi: N 0.75/0.70/0.70, V 0.65/0.70
Standards & References
- ACI 318-19 Building Code Requirements for Structural Concrete
- ACI 318-19 Chapter 17 (anchoring to concrete)
Frequently Asked Questions
Does this calculator handle anchor groups?
No. It is scoped to a single cast-in anchor, optionally near one edge. Anchor groups require the group projected area ANc with overlapping breakout cones, eccentricity factors psi_ec, and load distribution among anchors, which are not modelled here.
What is the difference between cracked and uncracked concrete?
Cast-in anchors in cracked concrete use psi_c,N = 1.0 for breakout and psi_c,P = 1.0 for pullout, while uncracked concrete (verified by analysis at service loads) uses psi_c,N = 1.25 and psi_c,P = 1.4. Most designs conservatively assume cracked concrete unless the uncracked condition can be demonstrated.
Why does pullout sometimes govern the tension strength?
Pullout depends on the head bearing area Abrg and fc only (Npn = 8*Abrg*fc cracked), independent of embedment. A small head with a deep embedment can make pullout the smallest of the steel, breakout, and pullout strengths, so it governs phi*Nn. Increasing the head bearing area raises the pullout strength.
What strength reduction (phi) factors are used?
For ductile-steel anchors without supplementary reinforcement (Condition B): tension steel phi = 0.75, tension concrete breakout and pullout phi = 0.70, shear steel phi = 0.65, and shear concrete breakout phi = 0.70, per ACI 318-19 §17.5.3.