A closed-Form Upper Bound on the Concrete Breakout Resistance of Anchor Groups in Rectangular Pedestals Under the EN 1992-4 Narrow-Member Rule

Abstract Column bases, tower stanchions and equipment supports often anchor tension through cast-in headed bolts into concrete pedestals of limited plan size. In such members the EN 1992-4 narrow-member rule fixes the effective embedment by the edge distances and bolt spacing, so the calculated concrete breakout resistance stops increasing with embedment. This paper derives the maximum of that resistance over all symmetric bolt layouts in a rectangular pedestal of sides a ≤ b. The optimum places the outer anchors at a spacing of b/2 along the long side, and the resulting ceiling is (√6/9)k₁√f ck a√b ψ(r)/γ Mc , where r = a/b and ψ(r) = 1 for r ≥ 0.5 and 0.7 + 0.6r otherwise. For a single anchor the ceiling is k₁√f ck b 1.5 r(0.7 + 0.3r)/(3 1.5 γ Mc ). The bound is independent of bolt diameter, grade and number of anchors, and for a given plan area it is largest for a square pedestal, falling as r 0.25 . Numerical optimisation over the gauges of 1 by 1 to 4 by 4 groups reproduced the closed forms to within 0.03%, and symbolic algebra confirmed the derivation. The ACI 318 − 19 counterpart has the same form and is 1.18 times higher up to a pedestal side of about 1.7 m. Because the ceiling grows only with the 1.5 power of pedestal size, a four-bolt M24 grade 4.6 group requires a 1.6 m square C30/37 pedestal before its steel strength can be reached; in practical pedestals concrete breakout governs and ductility requires anchor reinforcement. A design chart for the pedestal size needed to carry a given tension is provided.