Issue 64

A. Abdo et alii, Frattura ed Integrità Strutturale, 64 (2023) 11-30; DOI: 10.3221/IGF-ESIS.64.02

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Control J1-NC J1-UHPC

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Control J1-UHPC-J

Load, kN

Load, kN

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J1-UHPFC1-J J2-UHPFC2-J

J1-UHPFC1 J1-UHPFC2

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Displacement, mm

Displacement, mm

(a) (b) Figure 10: Envelope curve for all samples. a) The same material in the whole sample; b) Different materials in the sample. Energy dissipation The dissipated energy is the work absorbed by the structure to form cracks, displacements, and plastic hinges in the element. It is a part of the external energy acting on the structure. The total dissipated energy is the area under the envelope curve [39]. The dissipated energy of one cycle is the enclosed area between the loading curve and the unloading curve for the cycle, as in Fig. (11-a) through the following equations:

net A = 1 A - 2 A (kN.mm)

Energy dissipation =

(2)

A1=h/2*(2 1 h +2 2 h +b) (kN.mm)

(3)

A2=h/2*(2 3 h +2 4 h +b) (kN.mm)

(4)

where: 1 A and 2 A ; the area under the loading and unloading curve calculated by the trapezoidal rule; h, h1, h2, h3, h4, and b are illustrated in Fig. (11-b,c). The cumulative dissipated energy at a cycle can be calculated by adding the dissipated energy during that cycle to the energy dissipated during the previous cycles, as shown in Fig. 12. The external energy on structures is dissipated by the formation of cracks, friction between surfaces of the cracks, opening and closing of the formed cracks, and expansion of cracks' lengths and widths. Using steel fibers causes bridges between the cracks, participating in dissipating energy. In the first part of the cumulative energy dissipation curve, as shown in Fig. (12-b), the curves are parallel and very close because the energy dissipation in the first cycles is close between samples, as normal concrete and UHPFC have similar elastic modulus. In the last part of the cumulative dissipated energy curve, the divergence between the curves of the samples is observed because of the difference in cumulative energy dissipation values between the samples. The energy dissipated by a cycle of the last cycles is higher than that of the first cycle because of the high dissipated energy by spreading cracks and high displacement. Total energy dissipation for a sample is the sum of energy dissipated by every cycle for that sample. UHPFC specimens dissipate more energy than normal concrete because the fibers cause bridging een cracks and inhibit the cracks from spreading or opening. UHPFC samples with 1%teel fibers (J1-UHPFC1, J1-UHPFC1-J) are higher in total energy dissipation than UHPC samples without fibers (J1-UHPC, J1-UHPC-J) with (38.6 and 38.1%) and (41.4 and 40.8%) respectively and higher than control sample (seismic dls) with (46.5 and 47.1%) and higher than (J1-NC) with (28 and 25%). UHPFC samples with 2% steel fibers (J1-UHPFC2, J2-UHPFC2-J) were higher in total energy dissipation than UHPC samples without fiber (J1-UHPC, J1-UHPC-J) with (.5 and 69.2%) and (80.1 and 72.6%) respectively. Samples poured with UHPFC in the whole sample ( J1 UHPC, J1-UHPFC1, J1-UHPFC2) were slightly more in total energy dissipation than those poured with UHPFC in the

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