Anchor Bolt Embedment Length Calculator

Embedment depth, written hef, is the distance from the concrete surface to the effective bearing point of an anchor, and it controls the most common non-steel failure mode: a cone of concrete tearing out around the bolt. The Concrete Capacity Design equation Nb = kc lambda sqrt(fc) hef to the 1.5 power comes from fracture mechanics rather than a simple area calculation. A pure cone model would scale with hef squared; real tests show the exponent is closer to 1.5 because larger fracture surfaces mobilise lower average tensile stress, a size effect. The coefficient kc is 24 for cast-in headed bolts and 17 for post-installed anchors unless product testing justifies a higher value, and lambda drops to about 0.75 for lightweight concrete. The idealised breakout surface projects outward at roughly 35 degrees, which is why the full projected area is taken as 9 hef squared and why an edge distance of at least 1.5 hef is needed before the cone can develop without truncation. Common cast-in-place anchors run 3/4 inch to 1-1/2 inches in diameter with embedments of 8 to 20 diameters into concrete of 3000 to 5000 psi. Five failure modes must all be checked: steel rupture, concrete breakout, pullout, side-face blowout near edges, and pryout in shear. This tool evaluates a single anchor in uncracked concrete without supplementary reinforcement; anchor groups, cracked-section factors, ductility requirements and seismic design categories change the answer materially.

For most of the twentieth century, anchorage into concrete was governed by manufacturer test data and rule-of-thumb embedment multiples rather than a unified theory. The first widely used analytical model was the 45-degree cone method that appeared in ACI 349, the code for nuclear safety-related concrete structures developed in the 1970s. It assumed a uniform tensile stress across a cone projecting at 45 degrees, which made capacity proportional to hef squared and systematically overpredicted the strength of deep anchors. The modern approach came from research at the University of Stuttgart led by Rolf Eligehausen, with Werner Fuchs and collaborators including John Breen at the University of Texas at Austin and Richard Cannon. Their paper introducing the Concrete Capacity Design approach for fastening to concrete was published in the ACI Structural Journal in 1995, and it replaced the 45-degree cone with a shallower 35-degree projection and the hef to the 1.5 power size-effect term calibrated against a large international test database. ACI adopted the CCD method as Appendix D of ACI 318-02, and the 2014 edition moved those provisions into Chapter 17 as fully integrated code text. On the materials side, ASTM F1554, introduced in the 1990s, consolidated scattered anchor rod specifications into Grades 36, 55 and 105.