PSI - Issue 84

Anna Bontempi et al. / Procedia Structural Integrity 84 (2026) 1039–1046

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Finally, the experimental moment–curvature diagram was derived. At midspan, a potentiometric transducer was installed at the top of the flange to measure the compressive strain of the concrete (Figure 9a). In addition, two strain gauges were placed at the same cross-section, one on an existing steel reinforcement bar and one on a CFRP strengthening bar. By combining the strain distribution across the section at different load stages, the curvature was determined. The bending moment was then computed from the applied load. The blue curve in Figure 9b represents the experimental moment–curvature response of the midspan section.

Figure 8: crack pattern of the strengthened test.

4. Analytical Moment-Curvature diagram The experimental moment–curvature (M– ) diagram was then compared with the corresponding analytical curve. The analytical evaluation was performed by developing a MATLAB script that computes, for successive increments of curvature , the corresponding resisting bending moment by enforcing strain compatibility and internal force equilibrium. For each curvature value, an iterative procedure was adopted to determine R , in which the neutral axis depth was progressively varied until equilibrium of horizontal forces within the cross-section was satisfied. Consequently, each iterative procedure corresponds to a single point of the moment–curvature curve. The analytical M– diagram is presented in Figure 9 b with the grey line.

(a)

(b)

Figure 9: potentiometric transducers for the measurement of the compression strain of the concrete (a); Comparison between experimental and analytical curves of moment-curvature (b).

The input data consist of the geometric characteristics of the cross-section, which in this case is T-shaped (flange thickness and width, overall section depth, effective depths of the existing and strengthening reinforcements, and web width), as well as the main material properties of both the existing section and the strengthening materials (yield stress, ultimate stress, yield and ultimate strains, and elastic modulus).