PSI - Issue 81

Serhii Filipchuk et al. / Procedia Structural Integrity 81 (2026) 401–405

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Already during the first cycle, a redistribution of internal forces practically occurred, and in subsequent cycles the frame exhibited more elastic behavior. Under repeated loading, an increase in concrete and reinforcement strains was observed up to the fifth cycle, after which this increase ceased. At F = 22.5 kN during the first cycle, the strains of compressed concrete and tensile reinforcement in the mid- span section of the beam reached ε c,sp,cyc = 81.06 × 10 ⁻ ⁵ and ε s,sp,cyc = 227.44 × 10 ⁻ ⁵ , respectively. After unloading, the residual strains in concrete and reinforcement amounted to ε c,sp,res = 22.58 × 10 ⁻ ⁵ and ε s,sp,res = 73.06 × 10 ⁻ ⁵ , respectively. At the same time, the corresponding strains in the joint sections were ε c,sup,cyc = 36.13 × 10 ⁻ ⁵ and ε s,sup,cyc = 84.42 × × 10 ⁻ ⁵ . The higher residual strains in the reinforcement are explained by the formation of residual crack openings. After the second loading cycle, the increment of residual strains significantly decreased and did not exceed Δε s,sp,res = 2.61 × × 10 ⁻ ⁵ and Δε c,sp,res = 2.35 × 10 ⁻ ⁵ . After the fifth cycle, this increment practically ceased (Δε s,sp,res = 1.3 × 10 ⁻ ⁵ and Δε c,sp,res = 0.81 × × 10 ⁻ ⁵ ), indicating stabilization of the stress – strain state of the beam cross-section in the span. Similar changes in concrete and reinforcement strains were observed in the joint normal sections of the beam along the inner faces of the columns. In particular, the maximum strain increments up to the fifth cycle were Δε s,sup,res = 2.94 × 10 ⁻ ⁵ and Δε c,sup,res = 1.02 × 10 ⁻ ⁵ , while after stabilizatio n they amounted to Δε s,sup,res = 1.43 × 10 ⁻ ⁵ and Δε c,sup,res = 0.95 × 10 ⁻ ⁵ , respectively. Residual strains increased with the number of loading cycles and, after the sixth cycle, practically reached their maximum values, indicating their stabilization. Ove r ten loading cycles, residual strains in concrete reached ε c,cyc,res = 30.31 × 10 ⁻ ⁵ ; however, the main portion of residual strains developed during the first five cycles. After the first loading cycle, residual strains accounted for 74.5% of the maximum values recorded after the tenth cycle, and after the fifth cycle this value reached 90%. It should be noted that the deformation pattern of the extreme compressed concrete fiber in the beam span is similar to that observed in concrete prisms under central compression (Filipchuk et al. (2024); Korniychuck et al (2024); Filipchuk et al. (2025)). In the tensile reinforcement of the beam span, residual strains also predominantly developed during the first five cycles. After the first cycle, they reached 80.1% of the maximum values recorded after the tenth cycle (εs,cyc,res = 91.15 × 10 ⁻ ⁵ ), and after the fifth cycle they reached 97.4%. It should also be noted that during loading cycles, along with the increase in residual strains in compressed concrete, an increase in short-term strains occurring during direct loading was observed. For example, at Fcyc = 22.5 kN, such strains in the beam span were εc,el = 84.63 × 10 ⁻ ⁵ during the second cycle and εc,el = 93.70 × 10 ⁻ ⁵ during the tenth cycle, indicating a certain reduction in the elastic – plastic modulus of concrete. During the sixth to tenth loading cycles, changes in tensile reinforcement strains were almost linearly dependent on the applied load, which can also be explained by stabilization of the cracking process. From the graph in Fig. 2 (the inflection point of curve 1), it can be concluded that the first cracks in the tensile zone of the beam occurred at F = 10 kN, followed by only minor crack development. In this stage, residual strains in the reinforcement incre ased by 15.97 × 10 ⁻ ⁵ from the second to the tenth cycle, corresponding to 17.5% of the maximum total strains recorded during the tenth cycle. A somewhat different behavior was observed in the deformation curves of concrete in the compressed zone. After stabilization of concrete strains during the fifth to sixth loading cycles, the loading and unloading branches of the strain curves were reversed with respect to the strain axis (Fig. 2). This behavior is explained by the development of cracking processes and the accumulation of plastic deformations in concrete.

Fig. 2. Variation of tensile reinforcement and compressed concrete strains in the beam span of frame R1-P under repeated loading: 1 – during the first cycle; 2 – during the eleventh cycle with loading to failure

During the eleventh cycle, frame R1-P was further loaded until failure (curves 2 in Fig. 2). Exceeding the load level of F = 22.5 kN led to the development of new plastic deformations in concrete and to further crack propagation. The relationship between concrete and reinforcement strains and the applied load began to exhibit a nonlinear character. At a load of F = 22.5 kN, plastic hinges formed at the frame joints (ε s,sup = 262.5 × 10 ⁻ ⁵ ; ε s,sup = 288.8 × 10 ⁻ ⁵ ; ε c,sup = 158.0 × 10 ⁻ ⁵ ). At F = 25 kN, the reinforcement strains in the beam span reached their limiting values (ε s,sp = 268.53 × 10 ⁻ ⁵ ), indicating the formation of a plastic hinge in the span. As a result, the frame failed at F u = 25.75 kN. Immediately before failure, the beam deflection was 17.21 mm, while the crack widths were 0.6 mm at the joint and 0.28 mm in the beam span.