Anchor Bolt Pattern Calculator

An anchor bolt pattern arranged on a circle is analyzed as an elastic bolt group: the base plate is assumed rigid, so bolt force varies linearly with distance from the neutral axis. Direct shear is divided equally, P/n, because every bolt sits the same distance from the load centroid. The overturning moment is resisted by a couple, and the force in any bolt is M times r divided by the sum of r-squared over all bolts. When all n bolts lie on one bolt circle of radius R, that sum collapses to n times R-squared, so the peak moment force reduces to M divided by (n times R). This is why doubling the bolt circle diameter halves the tension demand far more cheaply than adding bolts of the same size. Practical detailing limits usually govern before the bolt steel does. ACI 318 requires anchor spacing of at least 4 times the anchor diameter, and edge distance for cast-in anchors is commonly taken at 6 diameters so that overlapping concrete breakout cones do not strip capacity. A 3/4 inch rod therefore wants roughly 3 inches of spacing and 4.5 inches of edge distance as a floor. The main caveat is that this calculation checks steel demand only: concrete breakout, pryout, side-face blowout, and pullout under ACI 318 Chapter 17 frequently control. Adding direct shear to moment-induced tension arithmetically, as done here, is conservative but is not a substitute for the code interaction check, and shear lugs, grout beds, and plate washers all change how load actually reaches the rods.

Anchor bolts predate any code that describes them: nineteenth century millwrights and bridge builders grouted forged rods into masonry and sized them by experience. Formal design rules for anchorage to concrete emerged from the nuclear power industry, where ACI Committee 349 published appendix provisions in the late 1970s that treated concrete failure as a 45 degree cone radiating from the anchor head. That cone model was simple, but it overpredicted the strength of large anchors and of anchors placed close together. The modern approach came from fracture mechanics research in Germany. Rolf Eligehausen at the University of Stuttgart, working with Werner Fuchs and John Breen of the University of Texas at Austin, developed the Concrete Capacity Design method, published in the ACI Structural Journal in 1995. It replaced the 45 degree cone with a flatter idealized prism and added a size effect term, and it matched the available test databases far better. ACI adopted it as Appendix D of ACI 318-02, and the 2014 edition moved the provisions into Chapter 17, where they remain. On the steel side, AISC Design Guide 1, covering base plate and anchor rod design, was first issued in 1990 and substantially revised in 2006; it standardized the elastic bolt group and bearing checks that this calculation follows.