Issue 73

V. Bomfim et alii, Fracture and Structural Integrity, 73 (2025) 12-22; DOI: 10.3221/IGF-ESIS.73.02

cross-section of 20cm × 25cm and were submitted to a four-point bending test, where the effective span is 2.7m (Fig. 5). The distance between two consecutive load points is the same, i.e. 90cm. The displacements of all beams were measured at mid-span by an LVDT. By taking advantage of the problem’s symmetry, only two finite elements were needed (Fig. 5). For the tested beams [8], the first cracking moment ( M r ) and the ultimate bending moment ( M u ), as well as the model parameters R 0 and k , are given in Tab. 1. Note that the finite element between the support and the applied load is defined as ‘element #1’ and the finite element between the applied load and the symmetry support is named ‘element #2’. Both elements presented the same ultimate damage value for each beam’s set: 0.8899 for BRCB-1, 0.8900 for BRCB-2, and 0.8901 for BRCB-3. The comparison between the numerical and experimental results is depicted in Fig. 5. For the three sets, the numerical results present good agreement with the experimental envelope, especially considering the BRC beams’ load bearing capacity. The numerical failure, i.e. when the damage reaches its ultimate value, was quite close to the experiments.

Figure 5: Test set-up [8], mathematical model and numerical results compared to the experimental ones.

Element #1

Element #2

M r (kN.mm)

M u (kN.mm)

Beams

R 0 (kN.mm)

k (kN.mm)

R 0 (kN.mm)

k (kN.mm)

BRCB-1 BRCB-2 BRCB-3

13,500.0 15,007.5 15,606.0

34,200.0 46,107.0 51,115.5

5.826 7.199 7.785

-1.795 -3.264 -4.013

2.913 3.600 3.892

-0.897 -1.632 -2.006

Table 1: Model parameters for the finite element analysis.

BRC beams from Mali and Datta [32] Mali and Datta [32] tested several BRC beams under different reinforcement ratios. Only three of those beams showed flexure failure. Such beams have a cross-section of 14cm × 15cm and were submitted to a four-point bending test, where the effective span is L = 1.10m (Fig. 6). By taking advantage of the problem’s symmetry, only two finite elements were used (Fig. 6). The longitudinal reinforcement ratio is 3.8%. For the tested beams [32], the first cracking moment ( M r ) and the ultimate bending moment ( M u ) are 3,300.00kN.mm and 8,121.67kN.mm, respectively. Therefore, the model parameters are R 0 = 0.939kN.mm and k = -0.273kN.mm for the finite element between the support and the applied load, and R 0 = 0.469kN.mm and k = -0.137kN.mm for the finite element between the applied load and the symmetry support. Both

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