The Shared-Volume Anchorage Method: A Volume-Based Treatment of Anchor Groups at Concrete Corners and in Three-Sided Channel Connections

Abstract

Revision 2 (29 August 2026) — what changed. The degeneracy claimed in Revision 1 — that the construction reduces identically to a plain EN 1992-4 verification when the corner interaction vanishes — was verified numerically for the first time, on the one configuration where the code gives an exact answer: two anchor plates on a plain face. It did not hold, and two corrections follow. (1) The secondary anchorage now carries its own EN 1992-4 group resistance (Ac,N/A⁰c,N and the ψ factors) instead of n × a single anchor, which had over-estimated it by ×2.56 on average. (2) The sharing between the competing bodies is now measured on their projected area — the quantity the concrete capacity design method is calibrated on — rather than on their volume; closed-form coefficients quantifying the volume bias, χ = 2/(2 − β − β²) for the tension cone and a two-variable form for the edge wedge, are derived in §10 and reported there as the analytical account of the bias rather than as applied factors. With both corrections the degeneracy holds exactly. §10 documents the verification in full, including a correction attempt that was tried and rejected. This version adds a full Hebrew edition of the paper alongside the English one. EN 1992-4:2018 verifies a fastening on one concrete face. It contains no provision for the case in which two anchor plates sit on perpendicular faces of the same corner, nor for a channel section that wraps a member on three sides. Both configurations are ordinary in façade and precast practice, and both leave the designer with two poor options: superpose the two anchorages, which counts the same concrete twice, or verify each in isolation and discard the interaction, which is uneconomic and still not a proof. This paper sets out the Shared-Volume Anchorage Method, developed by the author and implemented in AAS (Adit Anchor Software), for these two configurations. Its central idea is that competition between anchorages is a question of volume, not of area. Each potential failure body — the tension cone of EN 1992-4 §7.2.1.4 and the concrete edge wedge of §7.2.2.5 — is integrated numerically over the concrete of the member by voxel quadrature. The fraction of a body that is neither shared with a stronger neighbour nor outside the member becomes a scalar reduction factor r. The stronger anchorage — the leading face — is then verified at its full, unmodified EN 1992-4 resistance; the weaker one contributes a secondary term reduced by r and by a non-simultaneity factor of 0.85. For shear toward a shared free edge the same construction yields a doubly reduced corner-anchor term, max(0, 2·rz − 1), and no non-simultaneity reduction, because both legs act in the same direction. The construction is deliberately degenerate: as the corner interaction vanishes, r → 1 and the result reduces identically to a plain EN 1992-4 verification, so the method adds nothing where nothing is shared. The paper presents the geometric model, the numerical integration, the decomposition into leading and secondary contributions, the equivalent edge distance and equivalent embedment depth, the treatment of the three-sided (U / channel) case, a fully worked calculation in Annex A, and an explicit statement of the method's open assumptions and its boundaries. Scope and status. The method is offered as an engineering design aid, not as a code-verified resistance. It lies outside EN 1992-4:2018 and is presented as such. Full responsibility for the design remains with the qualified engineer. Contents: 12 sections, 6 figures (including three-dimensional renderings produced directly by AAS), 6 tables, Annex A (worked calculation) and references. Implementation: AAS — Adit Anchor Software, a free EN 1992-4 anchor design application requiring no registration. Author's engineering commentary: eng.adit.org.il/articles.