PSI - Issue 78

Gaetano Della Corte et al. / Procedia Structural Integrity 78 (2026) 199–206

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range of response. On the contrary, in the case of stiffened plates, it is proposed that the location of the plastic neutral axis be explicitly computed, by means of equilibrium equations and considering limit values of the reacting spring forces. In fact, the plate stiffeners extending beyond the compressed flange of the connected member, usually up to the compressed edge of the plate, generally provide a significant increase of the lever arm. Assuming that a full plastic state can be reached, with the force resistance reached in both the tension anchors and in the compressed springs, the plastic neutral axis can be readily located by means of Eq. (6): �� ⋅ = �,�� + �� (6) where �� is the design value of the compressive joint strength (eventually reduced to consider the grout layer and taking into account the local bending of the plate according to EN 1993-1-8), is the compressed area below the plate, �,�d is the force resistance on the tension side, and �d is the design value of the axial force acting on the connection. The compressed area, , can be written as a function of the distance of the plastic neutral axis from a reference line, e.g. from the centroid of the connected member or from the compressed edge of the plate. Therefore, in Eq. (6) there is only one unknown variable, that is the location of the plastic neutral axis. Once the plastic neutral axis has been located, a simple moment equilibrium about the centroid of the connected member allows calculating the plastic resistance moment of the connection M j,pl,Rd . Any concrete failure due to tension forces in the anchors, if occurring prior to steel yielding, will produce a premature failure of the connection and a moment resistance smaller the full plastic resistance will result. This aspect is discussed in the following section. Concrete failure modes on the tension side should be checked and avoided for the applicability of the limit analysis method described at section 2.4. In cases where a sufficient anchorage length (or anchorage system) is not possible, the tension force is limited by one of the concrete failure modes, as specified by EN 1992-4 (2018) which also provides methods to evaluate the corresponding resistance. In such cases, failure of the anchorage on the tension side might occur either when the concrete on the compression side is still elastic (second phase of the connection response as outlined in Fig. 2) or with the compressed concrete entering the plastic range prior to the anchorage failure. To check for the occurrence of any anchorage failure in the elastic range of the connection response, the tension anchor forces can be obtained starting from the elastic moment-rotation response curve. The calculation procedure is readily outlined as follows: (i) for the applied moment M Ed and the known moment-rotation axial force elastic response curve (section 2.3), the required connection rotation can be calculated; (ii) from the connection rotation, then, the elongations on the tension side can be obtained multiplying the rotation by the distance of the anchors from the neutral axis (Eq. (2)); (iii) the tension force can be obtained multiplying each spring elongation by the corresponding stiffness. If concrete failure occurs for the calculated tension force in a fastener, then the calculation must be stopped and the corresponding moment must be taken as the connection moment resistance, M j,Rd < M j,pl,Rd . In the case of failure of the anchorage system not occurring in the elastic range, then we should still check whether it occurs for a moment that is less than the plastic moment resistance M j,pl,Rd . The procedure already outlined for failure in the elastic range can be applied also in the elasto-plastic range, if the empirical elasto-plastic moment rotation curve shown in Fig. 1b is assumed to retain its validity. It is apparent that this procedure leads to larger tension forces in the anchors, compared with the elastic response phase, because the plasticity leads to a larger connection rotation. The empirical elasto-plastic transition curve proposed by EN 1993-1 8 does not distinguish whether plasticity starts because of concrete in compression followed by yielding of the anchors in tension and/or the plate in bending, or viceversa. Therefore, the applicability of this procedure to the elasto-plastic range as described by the approximate equation shown in Fig. 1b, should be verified by further research. It is worth noting that the assumption of an indefinitely elastic response with a linear distribution of spring forces to check for the failure of concrete on the tension side does not necessarily lead to safe-side calculations because of the increased rotation due to (partial) plasticity. 2.5. Premature connection failure due to the anchorage system