PSI - Issue 84

Beatrice Baldan et al. / Procedia Structural Integrity 84 (2026) 569–574

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and Menichini et al. (2025). These campaigns aim to investigate the half-joint behaviour varying different geometrical features, reinforcement disposition and material properties. Experimental research on Gerber half-joints has mainly been motivated by the brittle failures observed in existing bridges. Although the available test database is not extensive and includes specimens with different geometries and reinforcement layouts, the results show consistent structural trends. Half-joints behave as discontinuity regions, where forces are transferred through diagonal concrete compression fields and steel ties rather than beam theory mechanisms. Cracking typically initiates at the re-entrant corner, followed by the formation of an inclined crack, generally observed within a 35°–50° range. This crack evolves into a failure wedge, and the structural response is characterized by limited ductility and sudden collapse. Failure is most frequently governed by concrete strut crushing, while full yielding of reinforcement is not always reached. Stirrups improve crack control, and diagonal bars can significantly enhance strength when properly anchored, but the behavior remains highly sensitive to local detailing and geometry, particularly the a’/h ratio. Overall, experiments confirm that Gerber half-joints are controlled by strut-and-tie load-transfer mechanisms and compression-dominated failure modes, providing the mechanical basis for simplified analytical models used in assessment. 3. Assessment methods methodology The elastic Strut-and-Tie (S&T) model adopted in this study represents (Palmisano et al. 2023) the Gerber half-joint as a discontinuity region (D-region) in which the internal force transfer mechanism is idealized through a truss analogy composed of concrete compression struts, steel tension ties, and nodal zones . Unlike sectional beam theory, this approach reflects the actual flow of forces in disturbed stress fields where the assumption of linear strain distribution is no longer valid. The scheme is geometrically defined by a discontinuity length equal to 1.5 times the nib depth , consistent with common D-region extensions. Within this region, the internal load path is represented through a network of inclined struts and ties connecting the load application point, the support reaction, and the reinforcement layers. Several strut inclinations are derived directly from geometry, while others are determined through calibration based on mechanical consistency and comparison with experimental evidence. In particular, the diagonal reinforcement defines one strut direction, while a 45° inclination is assumed for the principal shear strut in accordance with conventional shear design assumptions. Additional strut angles at the support and within the internal node region are treated as unknowns and determined through a preliminary parametric evaluation. The model is solved under the assumption of linear-elastic force distribution, meaning that the truss forces are proportional to the applied load and no redistribution due to yielding is allowed. All members behave elastically, and the internal forces in struts and ties are determined from static equilibrium of nodes. The compression resultant in the D-region boundary section is obtained from a bending equilibrium check, ensuring compatibility between the global flexural response and the local S&T system. Once the geometry is defined, the procedure computes the lever arms and tie lengths, allowing identification of which stirrups and reinforcement bars intersect the idealized tension ties. This step is crucial because the effective reinforcement area associated with each tie depends on the crack trajectory and nodal geometry. The tensile forces in the ties are then calculated from the equilibrium solution and compared with their yielding capacities. For each tie , a utilization ratio = / , is evaluated. Since the scheme is elastic, failure is assumed to occur when the most stressed tie reaches yielding . A load multiplier is therefore determined to scale the elastic solution up to the first yielding condition. The analytical load-bearing capacity is obtained by multiplying the initial load level by this factor. This approach ensures that the predicted ultimate load corresponds to the onset of inelastic behavior, without accounting for post-yield redistribution. The elastic S&T model thus provides a lower-bound, force-based estimate of capacity governed by tie yielding. The method emphasizes equilibrium and geometry rather than material nonlinearities, making it computationally efficient and suitable for parametric assessment of existing structures. Mechanically, this model describes the half-joint as a statically determinate truss mechanism where the load is transferred from the support region to the beam through a sequence of compressive stress fields and tensile reinforcement ties. The approach captures the essential behaviour of the D-region while avoiding the large number of