PSI - Issue 78

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

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 Phase 2: Tension forces develop in the anchors and compression contact stresses become distributed over part of the base plate. The corresponding rotational stiffness will be indicated by S j,2 . This phase ends when a moment equal to 2/3 of the moment resistance M j,Rd is reached (EN 1993-1-8).  Phase 3: Plastic deformations develop somewhere in the connection. There is a continuous change of the rotational stiffness, which is assumed to be approximated by the empirical equation suggested by EN 1993-1-8, as reported in Fig. 1b.  Phase 4: Plastic deformations extend largely into the connection elements, or any form of relatively brittle failure occurs on the tension side (e.g., concrete cone failure); correspondingly a moment resistance, M j,Rd , is reached. In the case of a ductile failure mode, there will be a horizontal plateau with some appreciable rotation capacity (as shown in Fig. 1b); in the case of concrete failure, the response will presumably show relatively minor rotation capacity. In any case, this study did not investigate the rotation capacity.

a)

b)

Fig. 1. (a) Mechanical model; (b) Schematic moment-rotation response curve.

2.3. The elastic response

The rotational stiffness of the connection depends on the location of the neutral axis, which will be generally indicated by z n (indicating the distance of the neutral axis from the centroid of the connected member). Once the neutral axis is known, standard analysis methods of the relatively simple “bar-on-springs” model depicted in Fig. 1a can be used to calculate the rotational stiffness (such analysis is omitted here for brevity). First, the definition of “small” eccentricity is adopted consistent with EN 1993-1-8, as shown by Eq. (1), where = eccentricity of the axial force, ℎ = depth of the connected steel section, �.1 = distance of the neutral axis from the centroid of the cross section. | | ≤ℎ ⁄2 ⇒ �.1 =0 (1) When the axial force has an eccentricity larger than the limit given by Eq. (1), then tension starts developing in the anchors. Consequently, a neutral axis identifying the zone of compression contact stresses should be located. When the springs are elastic, moment equilibrium leads to Eq. (2), where .� and .� are the first and second moment of the stiffness distribution about the neutral axis. Hence, the location of the neutral axis can be obtained by solving Eq. (2) with respect to the unknown �.2 , for any given eccentricity of the axial force. | | >ℎ ⁄2 ⇒ .� ( �.2 ) .� ( �.2 ) ⁄ = | | − �.2 (2) To calculate the first and second moments of the stiffness distribution corresponding to the compressed springs, a simplification is proposed: instead of a continuous spring support, a few springs are adopted at the centroids of each stiffener. The simplification is illustrated in Fig. 2a. The parameter shown in Fig. 2a serves to consider the spread of contact stresses below each stiffener and up to the contact surface between the steel plate and the concrete; the calculation model of EN 1993-1-8 is adopted for this parameter.