# Neural Networks--Deflection Prediction of Continuous Beams with GFRP Reinforcement
## 2 Materials and Methods
A monotonically increasing static load was gradually applied at the beams in increments from zero to failure. The load was applied in increments from 2 to 5 kN at the very beginning, and then, after cracks started appearing, in increments of 5-10 kN. Results were measured on each 5 kN. The loading rate was about 5 kN/min. Figure 3: Scheme of continuous beams measuring equipment [3; 4]. Figure 2: Samples of glass fiber-reinforced polymer (GFRP) longitudinal and transverse reinforcement [3; 4]. The measurement was performed after each load increment. The effective moment of inertia changes for each step as the load is applied. The highest value is the gross concrete cross-section. The effective moment of inertia decreases with increasing load and is calculated by formula (3) [3]:  
\[I_{e}=\left(\frac{M_{cr}}{M_{a}}\right)^{3}\cdot\beta_{d}\cdot I_{g}+\left(1- \left(\frac{M_{cr}}{M_{a}}\right)^{3}-K\right)\cdot I_{cr}\cdot 0.7\leq I_{g} \tag{3}\]  
where \(K\) is calculated by formula (4) [3]:  
\[K=\left(\frac{1}{11}\cdot\left(\frac{M_{cr}}{M_{a}}\right)\right)^{4} \tag{4}\]  
This is a proposed formula for the effective moment of inertia based on experimental results for six beams [3]. \(M_{cr}\) is a moment at the appearance of the first crack (cracking moment). The force at the appearance of the first crack is defined, as well as the moment \(M_{cr}\), on the basis of the measured reactions at the ends of the beam and the force itself. \(M_{a}\) is a moment corresponding to each load increment. It changes with the change in force both in the midspan and above the support. For the purposes of forming the prediction model, data were selected and collected, and the values of the force applied in the midpoints of the beam span, the value of the effective moments of inertia of the cross-section in the middle of the span and above the support and the deflection values were measured. After the data were collected, determining the input model data was performed. The criterion for their choice was their direct impact on deflections. Based on the previous, the input variables were selected, namely: force, effective moment of inertia of the cross-section in the middle of the span and effective moment of inertia of the cross-section above the support. In addition to the above values, the deflection is affected by the span and cross-section. In the conducted experiment, these quantities were identical so that they were not chosen for the input variables of the model. The percentage of reinforcement was considered through the effective moments of cross-section inertia. Data were collected from the conducted experimental research. The input data, with their limit and mean values, are shown in Table 3.  
The next step was to define the output from the model. Based on the considered parts of the research, it was determined that the model has one output which is a deflection in the midpoint of the continuous GFRP-reinforced beam (see Table 4). \begin{table}
\begin{tabular}{c c c c c c} \hline
**Input Data** & **Input Data** & **Data Type** & **Units of Measure** & **Min** & **Max** & **Mean Value** \\ \hline Input 1 & Force & numerical & kN & 5 & 137.75 & 55.571 \\ \hline \multirow{4}{*}{Input 2} & Effective moment of & & & & \\  & inertia of the & & & & \\  & cross-section in the & & & & \\  & middle of the span & & & & \\ \hline \multirow{4}{*}{Input 3} & Effective moment of & & & & \\  & inertia of the & & & & \\  & cross-section above & & & & \\  & the support & & & & \\ \hline \end{tabular}
\end{table} 
Table 3: Input data. There are various recommendations in the literature for dividing available data into training and test sets. The authors generally selected data at 90% to 10%, 80% to 20% or 70% to 30% [27]. In addition to the established practice in choosing the percentage of each of the sets, the specificity of each of the problems to be solved determines the appropriate relationship between these two sets. In this research, a division of 80-20% of the training set in relation to the test set was adopted.