Issue 53

M. C. Oliveira et alii, Frattura ed Integrità Strutturale, 53 (2020) 13-25; DOI: 10.3221/IGF-ESIS.53.02

Figure 3: Force-time graph for impact loads.

R ESULTS AND DISCUSSION

E

xperiments performed by Zhao et al. [22] and Bhatti et al. [37] were used in order to analyse the proposed shear impact model.

Zhao et al. [22] The beams present 3m span (2 L ), longitudinal reinforcement composed of four bars with 20mm in the tension side and two bars with 16mm in the compression side, with yield stress of 495.5MPa and ultimate tension of 620.2MPa. The stirrups consisted of 6mm bars spaced by 30cm, with yield stress 344.7MPa and ultimate tension of 550.4MPa [22]. Other properties of the beams are presented in Tab. 1, as well as some dynamic response values.

Beam – impact weight (kg) – drop height (m) Beam C-1700-4.60 Beam C-1300-5.56

Compressive strength of concrete (MPa)

Mean impact force (kN)

Cross section (cm)

32.14 30.25 26.26

205.22 296.88 286.71

20×50

Beam C-868-7.14

Table 1: Properties of the analysed beams.

Therefore, for each beam, the damage variable ( d s ) and the plastic distortion are obtained from Eqn. (9) and (22). This calculation process was performed to evaluate the applicability of the proposed formulation. The damage and the plastic distortion calculated on each beam is shown in Tab. 2. Fig. 3 shows a scheme with the crack pattern after impact. The obtained damage values are high, meaning that a severe cracking level in the three beams, which is consistent with the experimentally observed cracking patterns (Fig. 4). Furthermore, by knowing the value of the plastic distortion (  p ), it is possible to determine the plastic displacement of the beam (Fig. 2):

L w p

 

(24)

p

In order to illustrate the proposed approach, the solution of Beam C-1700-4.60 [22] is described as follows. Firstly, Eqn. (9) must be rewritten to agree with the mathematical model of the beam (Fig. 2). Therewith, it is assumed that the inelastic effects due to bending moment are negligible. Then, the constitutive relation for a simply supported beam is given as:         M F F γΦ s s f p d    (25)

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