PSI - Issue 84

Biruk Yenehun Lemlem et al. / Procedia Structural Integrity 84 (2026) 1255–1263

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thermal variations, and efficient load transfer (Giannetti et al., 2020). However, their discontinuous geometry and stress concentrations led to accelerated degradation, including premature corrosion, concrete spalling, and limited accessibility for visual inspection (Asso et al., 2022). The collapse of the Annone overpass in Italy (Marco et al., 2023) and the de la Concorde Overpass in Quebec, Canada (Denis et al., 2011) highlighted these vulnerabilities, prompting extensive experimental (Desnerck et al., 2016; Flores Ferreira et al., 2025; Mata-Falcón et al., 2019), numerical (De Domenico et al., 2025; Granata et al., 2022, 2023; Rossi & Spinella, 2025, Faleschini et al. 2026), and analytical investigations (Desnerck et al., 2018; Martinelli et al., 2024; Menichini et al., 2024; Palmisano et al., 2023) to diagnose failure mechanisms and develop retrofitting strategies. Despite these advances, most existing assessment methods remain deterministic, neglecting critical uncertainties in material degradation, loading conditions, and model assumptions. While strut-and-tie models (STMs) provide a rational framework for evaluating half-joint capacity, their manual application is time-consuming and limits practical implementation. Integrating STM with probabilistic methods could address both challenges—automating calculations while quantifying uncertainties inherent in aging infrastructure. To this end, this study develops a probabilistic framework that automates STM-based capacity assessment using Monte Carlo simulation in MATLAB to provide Reinforced concrete half-joints create articulated connections in multi-span bridge girders, forming statically determinate systems while transferring vertical loads (Giannetti et al., 2020). Spinella & Messina (2023) and Granata et al. (2022) investigated the internal load transfer mechanisms and stress distributions in these discontinuity regions. Load transfer is significantly influenced by reinforcement configuration: diagonal reinforcement effectively controls cracking at re-entrant corners, whereas vertical hanger bars are less effective at mitigating stress concentrations. Critical stress concentrations typically occur at geometric discontinuities, particularly at re-entrant corners where the nib meets the full-depth section, making these locations susceptible to diagonal cracking when reinforcement is insufficient or corroded. Menichini et al. (2025) identified three primary failure modes in half-joints: (1) nib failure, characterized by diagonal cracks propagating from the inner corner of the nib; (2) flexural failure of the full-depth beam section; and (3) horizontal splitting cracks resulting from reinforcement slip or bond failure. Experimental evidence demonstrates that specimens with diagonal reinforcement exhibit improved ductility and more distributed crack patterns compared to those with only vertical hanger bars, facilitating earlier visual detection of distress during inspections. 2.2. Strut-and-Tie Models (STM) Strut-and-tie models provide a rational framework for analyzing discontinuity regions (D-regions) making them well suited for half-joint assessment. Eurocode 2 presents indicative STM configurations for half-joints that can be adapted based on reinforcement layout and structural requirements (European Committee for Standardization, 2004). Desnerck et al. (2018) categorized common STM configurations for half-joints into three types based on the primary load path and reinforcement arrangement: Diagonal models utilize inclined reinforcement bars to transfer loads directly from the nib to the full-depth section; Orthogonal models rely on substantial longitudinal reinforcement in the nib, extending into the full-depth section and combined with vertical hanger bars; and Combination models integrate both diagonal and orthogonal reinforcement elements to form more complex internal load paths. The selection of an appropriate STM depends on the as-built reinforcement configuration, with tension ties positioned to coincide with reinforcing bars and compression struts oriented to ensure strain compatibility and concrete stress limits are satisfied. While diagonal models offer analytical simplicity, combination models more accurately capture the behavior of structures with complex reinforcement detailing. Despite the established utility of STM for half-joint analysis, several critical gaps remain in current practice. The existence of multiple valid STM configurations for a given geometry introduces model uncertainty that is not systematically quantified in deterministic assessments. Different STM choices can yield significantly different capacity predictions, yet design codes provide limited guidance on model selection for existing structures. Also, capacity predictions. 2. Literature Review 2.1. Half-Joints