PSI - Issue 84

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

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material property degradation and loading variability are typically treated through nominal values and global safety factors rather than explicit probabilistic treatment. This study addresses these limitations by developing an automated probabilistic framework that evaluates multiple STM configurations while systematically incorporating uncertainties in material properties, applied loads, and resistance model assumptions. 3. Methodology 3.1. The Case Study The half-joint beam originally designed and tested by Desnerck et al. (2016) and later replicated by Luyten et al. (2024), is adopted as the case study. The beam has an overall depth of 700 mm, a width of 400 mm, and a concrete cover of 40 mm. The beam was designed to support a 300 kN point load applied at the nib. Two reinforcement configurations are investigated, consistent with the study by Luyten et al. (2024): the reference case and an increased- reinforcement case. The reference case includes 5φ25 mm bars as bottom reinforcement, 5φ20 mm bars as top reinforcement, 3φ12 mm U - bars, 4φ10 mm double - legged stirrups near the nib, and 4φ12 mm diagonal bars. The overall geometry of the beam and the reinforcement arrangement for the reference case are shown in Figure 1. The increased-reinforcement case simulates a strengthening intervention for a beam with degraded concrete. The concrete compressive strength is reduced to 20 MPa to represent deteriorated conditions, while the reinforcement is enhanced by increasing the U- bars to 3φ16 mm, the diagonal bars to 6φ12 mm, and replacing the double -legged stirrups with four- legged φ10 mm stirrups.

Figure 1 Geometry and reinforcement layout of reference case

3.2. Analytical Framework The analytical framework for evaluating each STM comprises four principal stages: calculation of member acting forces, determination of nodal dimensions, evaluation of acting stresses, and verification against resistant stresses. The acting forces in the ties and struts are determined by applying static equilibrium conditions at each node of the STM. For STM A, shown in Figure 2, the truss member forces are expressed as functions of the applied action (E d ) and the geometric angles (α, β, γ, and δ). The member forces are determined by applying static equilibrium at each node, expressing forces as functions of the applied load and geometric parameters. This equilibrium-based procedure is applied systematically to all four STM configurations. The nodal dimensions are determined following the procedure used by Luyten et al. (2024). For support nodes, the nodal area is defined as shown in Eq. (Errore. Nel documento non esiste testo dello stile specificato. .1) where b 0 is the support length and d 1 is the concrete cover, measured from the rebar’s center line. For nodes formed by tension ties, the nodal length u is calculated as shown in Eq. (Errore. Nel documento non esiste testo dello stile specificato. .2) where n is the number of rebar layers, s is the distance between their axes, and ϕ is the bar diameter. If two nodal sides are known, the third is determined using the Pythagorean theorem. Otherwise, a hydrostatic stress state is assumed, in which stresses are uniformly distributed, and intersecting struts and ties are perpendicular to the nodal areas. This condition yields Eq. (Errore. Nel documento non esiste testo dello stile specificato. .3). Nodes with more than three