PSI - Issue 81

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

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Frame R1-PR was subjected to short-term repeated low-cycle loading. Prior to testing, similarly to frame R1-KR, a force of 3 kN was introduced into the frame tie of R1-PR. During the first loading cycle, the first cracks appeared at F cyc = 7.5 kN in the frame joints. At F cyc = 22.5 kN, the widths of normal cracks in the beam span reached 0.10 mm, while in the joints they were 0.16 mm and 0.14 mm. 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 (Fig. 3). 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 = 61.25 × 10 ⁻ ⁵ and ε s,sp,cyc = 194.38 × 10 ⁻ ⁵ , respectively (Fig. 3 ). After unloading, the residual strains in concrete and reinforcement were ε c,sp,res = 14.12 × 10 ⁻ ⁵ and ε s,sp,res = 33.47 × 10 ⁻ ⁵ , respectively. At the same time, the corresponding strains in the joint sections were ε c,sup,cyc = 116.51 × 10 ⁻ ⁵ and ε s,sup,cyc = 172.01 × × 10 ⁻ ⁵ , while the residual strains amounted to ε c,sup,res = 26.70 × 10 ⁻ ⁵ and ε s,sup,res = 78.21 × 10 ⁻ ⁵ . The higher residual strains in the reinforcement are explained by the formation of residual crack openings.

Fig. 3. Variation of tensile reinforcement and compressed concrete strains in the beam span of frame R1-PR under repeated loading: 1 – during the first cycle; 2 – during the eleventh cycle with loading to failure After the second loading cycle, the increment of residual strains in the beam span decreased significantly and did not exceed Δε s,sp,res = 1.17 × 10 ⁻ ⁵ and Δε c,sp,res = 1.09 × 10 ⁻ ⁵ . After the fifth cycle, this increment practically ceased (Δε s,sp,res = 0.52 × 10 ⁻ ⁵ and Δε c,sp,res = 0.50 × 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. The maximum strain increments up to the fifth cycle were Δε s,sup,res = 9.38 × 10 ⁻ ⁵ and Δε c,sup,res = 5.68 × 10 ⁻ ⁵ , while after stabilization they amounted to Δε s,sup,res = 1.00 × 10 ⁻ ⁵ and Δε c,sup,res = 0.60 × 10 ⁻ ⁵ , respectively. Residual strains increased with the number of loading cycles and, after the sixth cycle, practically reached their maximum values, indicating stabilization. Over ten loading cycles, residual strains in the beam reached ε c,cyc,res = 19.8 × 10 ⁻ ⁵ ; however, the majority of residual strains developed during the first five cycles. After the first cycle, residual strains accounted for 71.3% of the maximum values recorded after the tenth cycle, and after the fifth cycle this value reached 88.9%. A similar trend was observed in the frame joint, where residual strains rea ched ε c,cyc,res = 40.57 × 10 ⁻ ⁵ ; after the first cycle, they accounted for 65.8% of the maximum values recorded after the tenth cycle, and after the fifth cycle they reached 94.6%. During the eleventh cycle, frame R1-PR was further loaded until failure. 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 became nonlinear. At a load of F = 25.0 kN, plastic hinges formed in the frame joint and beam (ε s,sup = 269.29 × 10 ⁻ ⁵ ; ε s,sup = 258.19 × 10 ⁻ ⁵ ; ε c,sup = 169.36 × 10 ⁻ ⁵ ). With further increase in load, a third plastic hinge formed, resulting in frame failure at F u = 29.8 kN. Immediately before failure, the deflection of the beam in the frame with artificial force regulation was 15.28 mm, while the crack widths were 0.48 mm at the joint and 0.24 mm in the beam span.

Fig. 4. Failure pattern of the frame