PSI - Issue 64

Francesco Bencardino et al. / Procedia Structural Integrity 64 (2024) 932–943 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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Following a site inspection, all beams of the seven internal portal frames exhibited almost vertical cracks, more than 200 mm deep and 5 mm wide, localized at a distance of 2200 mm (section K-K) measured from both beam column joints (Figure 2 and Figure 3). In this context, it was necessary to carry out a structural assessment to evaluate the feasibility of a potential repair/strengthening intervention for the damaged structural elements.

(a)

(b)

Figure 3. View of structural damage: (a) deep cracks left and right of beam and (b) enlargement of crack on right of beam.

2.2. Existing capacity of the beams

The overall assessment of the structure was based on a thorough site inspection together with a capacity analysis carried out in accordance with the principles of Eurocode 2 (Part 1-1, 2004), considering both ultimate limit states and serviceability limit states. This procedure ensures that a member will not become unfit for its intended use and that its design strength is not less than the design action. By comparing the results of the capacity analysis with the results of the structural analysis, it is possible to identify any deficiencies or sections where the structure may not meet the required design strength criteria, thus indicating potential weaknesses or areas for improvement in the structural design. It is worth mentioning that the analysis to establish the distribution of either internal forces and moments, over the whole structure shall be carried out using idealizations of both geometry and behavior of the structure. In this case, the structural analysis of the RC portal frame was based on a linear elastic behavior considering only the vertical loads. With regard to the material properties used in the section capacity analysis, the average yield strength of the steel was 215 MPa, while the average compressive strength of the concrete was assumed to be 20 MPa. The calculations were carried out with reference to the average strength properties for the materials, taking into account a knowledge level (KL) equivalent to 3, and thus applying a confidence factor (CF) of 1.00, in accordance with Eurocode 8 (Part 3, 2005). In this study, two main sections were considered as reported in Figure 2: (i) section K-K, where concentrated cracks occurred (distance of ~2.60 m from the centerline of the column) and (ii) section M-M, where maximum sagging bending moment is expected (distance of ~5.60 m from the centerline of the column). Using the stress-strain relationships for concrete and steel according to Eurocode 2 (Part 1-1, 2004), the analysis of the cracked section K-K gave a bending moment of ~77.3 kNm, at first yielding of the tension steel (two 18 mm diameter bars), while the flexural strength of the section was ~87.3 kNm. The capacity analysis of the M-M section gave a first yielding moment of ~277.5 kNm and a flexural strength of ~301 kNm. With reference to a simple static scheme such as a portal frame, which represents the structural behavior well, and assuming a loading strip width of 3,10 m and performing a linear static analysis, it is then possible to determine the load F d which induces the yield moment in section K-K, where the cracks occurred ( F d = ~25.35 kN/m). After conducting a thorough analysis of the applied loads, it was then possible to accurately determine the value of the permanent loads acting on the structure, ~24.0 kN/m. From the obtained results and the previously determined load F d , it can be seen that the maximum allowable live load to avoid exceeding the yield moment in section K-K is practically negligible (~0.435 kN/m 2 ). Notably, this value is even lower than the minimum live load suggested by the