Flexural Reinforcement ratio

Most of the code of practises CSA S806 (Canadian Standards 2012), ACI 440 (ACI Committee 440 2015), and JSCE (JSCE et al. 1997) recommends that FRP reinforced concrete flat slab to be over reinforced in most situation. Also, due to

0 100 200 300 400 500 600 700 2 7 12 17 Lo ad (k N )

column perimeter to effective depth ratio

H=250mm H=150mm 𝑉 = 95.327 𝑏0 𝑑 0.3636 𝑉 = 293.62 [𝑏0 𝑑] 0.3303

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the fact that the type of GFRP reinforcement and its bond characteristics in addition to GFRP is an elastic material with smaller stiffness compared to that of steel, a larger deflection and cracks widths are expected to be available in the GFRP reinforced concrete flat slab compared to that of SR concrete flat slab. Therefore, the effective compressive area in case of punching shear will be reduced as well as the contribution of aggregate interlock resisting will also be reduced accordingly. A wide range of flexural reinforcement ratio was selected between 0.8, 1, 1.2, 1.5, and 2% (2.2, 2.8, 3.4, 4.2 and 5.6 𝜌_𝑏, where 𝜌_𝑏 is the balanced reinforcement ratio) in order to evaluate the effect the flexural reinforcement ratios on the punching shear behaviour GFRP reinforced concrete flat slab under concentric load.

Results of the FE models are similar in the behaviour of that experiments in case of a bi-linear relation with differences in the smoothness of the transition according to the slab's depth (Figure 4-17). In all cases, the deflection increased linearly in the uncracked zone up to the initial first crack. In addition, nonlinearity was observed in the load-deflection curve when the tensile stress is exceeding the tensile strength of the concrete. Generally, the post-cracking stiffness is increased when axial stiffness is increased from about two times the balanced reinforcement ratio to about five times the balanced reinforcement ratio, whereas the deflection is decreased at the same load level.

GFRP bars are unidirectional materials with little strength in the transverse direction which leads to a smaller failure load and almost discounted contribution in case of shear resistance. Figure 4-17 shows the effect of flexural reinforcement ratio on punching shear strength. It can be observed that concrete flat slabs having the same depth exhibited similar behaviour. For a slab having H = 150mm, increasing reinforcement ratio from 1.0% to 2.0% results in a growth in

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load capacity by approximately 23%. In case of slabs having a depth of 250mm, increasing reinforcement from 0.8% to 1.0% improved load capacity by roughly 8.0%, whereas a rise of reinforcement ratio from 1.0% to 1.2% led to a tiny increment in load capacity by about 3.0%. However, the load capacity was improved by approximately 7.0% when reinforcement ratio increased from 1.2% to1.5%.

Figure 4-17. Effects of flexural reinforcement ratio on punching shear strength

The relationship between ultimate load strength and reinforcement ratio is presented in Figure 4-18 Though, this relationship can vary according to any change in geometry of the model or material properties.

0 100 200 300 400 500 600 0 5 10 15 20 25 Loa d (kN ) Deflection (mm) P=1,H=150mm P=2,H=150mm P=0.8,H=250mm P=1,H=250mm P=1.2, H=250mm

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Figure 4-18. Relationships between ultimate load strength and reinforcement ratio

4.6 Conclusions

The finite element analysis was implemented with the concrete damaged plasticity model for predicting punching shear strength of GFRP reinforced concrete flat slab. The proposed FE model can predict the behaviour of GFRP reinforced concrete flat slab under concentric load in terms of ultimate capacity and load deflection curve with reasonable precision. The mean, SD, and COV of experimental to finite element modelling shear strength ratio were approximately 0.98, 8.5% and 8.67%, respectively.

Concrete material modelling is the most challenging part of finite element modelling. The parametric examination was performed in ABAQUS Explicit to calibrate the material model specified in ABAQUS. Many material parameters were included in the study and found to be critical for the accurate definition in the concrete modelling. It was practical that the load-displacement response should be taken into account for implementation of appropriate mesh size. Given the parametric investigation for the material modelling, the analysis of the results gave a precise punching shear prediction. The main conclusions which can be

400 420 440 460 480 500 520 540 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 Lo ad (k N ) Reinforcement ratio

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drawn from the parametric study described previously in this chapter are summarised as follows:

• The mesh size was selected according to the sensitivity of different mesh sizing and on the computational time.

• The shear failure loads predicted from the current computational analysis were very close to those obtained experimentally.

• Overall the load-deflection curves behaviour predicted by ABAQUS showed reasonable agreement with that of experimental results.

• Regardless slabs thickness values, the prediction of the proposed ABAQUS model showed a steady increase in the load carrying capacity by increasing the concrete strength.

• The effect of increasing the concrete compressive strength on punching shear strength is more pronounced in normal concrete strength rather than high concrete compressive strength in both GFRP concrete flat slab depths.

• The effect of the shear perimeter to effective depth ratio is less pronounced on deflection rather than punching shear capacity.

• The effect of tensile reinforcement ratio on deflection is more pronounced in GFRP reinforced flat slab with greater depth.

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5

CHAPTER FIVE

ARTIFICIAL NEURAL NETWORKS (ANN)

5.1 Introduction

The main restriction of previous studies was the uncertainty emphasised by the difference between the predictions and the experimental results of the punching shear strength, as mentioned in section 2.8. The difficult relationship between the parameters considered in the punching shear phenomena, in addition, the lack of knowledge regarding FRP reinforcement and the concrete bond all add up together to complicate the relationship. In addition, the brittle failure of concrete structures, cannot be adequately described by plastic limit analysis. However, using computational techniques delivers an effective and uncomplicated approach for modelling complex and nonlinear functions. Artificial Neural Networks are the biological neuron counterpart in the engineering applications, which are inspired from the ability of the human brain in learning. ANN is used in this research to predict punching shear strength, and the results were shown to match more closely with the experimental results.

Sixty-nine tests results were examined, including all punching shear results of different types of scale specimens. Moreover, from the current parametric study, five parameters were identified which were most effective in the punching shear results. These were used to evaluate the ANN modelling results against the experimental test data and code of practice CSA S806 (2012). It is also evaluated against best modified equation in the prediction of punching shear capacity proposed by Ospina et al (2003).

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