The FEM was developed using Abaqus software with inputs from experimental results (Zheng et al., 2021). The column had a height of 500 mm with variable cross-sections (2a × 2 b) of 194 × 194, 230 × 154, and 252 × 126 mm, representing an aspect ratio of 1.0, 1.5, and 2.0, respectively. Aspect ratios 1, 1.5, and 2.0 were designated by letters A, B, and C, followed by numbers 1, 2, and 3, referring to the number of CFRP layers used. The layers of CFRP were attached to the steel tube using tie constraints. The steel tube confined inside the concrete is the modelled in ABAQUS tool as a tie constraint Figure 1. For all of these constraints, the steel tube was set as the master surface due to its high strength compared to the strength of the concrete and CFRP.

An extra repeated model was run in each set of CFRP layers and labeled with Romanic numbers, I and II. Since steel tubes are ductile, their plastic failure was established based on their yield strength. Concrete was modeled with compressive strength, Young’s modulus, and peak strain of 32 MPa, 24.8 GPa, and .0022, respectively. These parameters were used to establish the post-behavior of concrete using stress-inelastic crushing and cracking strains curves, as shown in Eq. 2.1 and Eq. 2.2. The behavior of the steel tube exhibited a bilinear stress-strain curve; an example from existing models is provided in Figure 2A. The incremental compressive stress can be calculated using the expression provided in Figure 2C, in which the stress at the elastic stage is considered to be 50% of the standard cylinder compressive strength. Figure 2B provides a mathematical equation to generate the tensile stress train response of unconfined concrete; however, the failure of concrete was controlled as CFRP failed. ε i n = ε − σ c E 0 (2.1) ε c r = ε − σ t E 0 (2.2) Where ε i n is the inelastic crushing strain, ε is the total strain in tension or compression, σ c is the compressive stress at the yield, E 0 is the initial modulus of elasticity for the undamaged material, i.e., at the linear elastic zone of stress-strain curves, and σ t is the tensile strength of concrete. After defining the yield stress-inelastic strain pair of variables, the damage variables of concrete, both in tension and compression, need to be defined as well in Eq. 2.3. d c , t = 1 − σ σ p e a k (2.3)

In these equations, σ p e a k is a peak tensile or compressive stress of the concrete test specimen, d c , t is a damage parameter in compression or tension. It ranges from zero for undamaged material, i.e., just before peak stress, to one for completely damaged material in the descending part of the stress-strain curve. Using damage parameters, elastic strain, and inelastic strain, the plastic strains are established as in Eq. 2.4 and Eq. 2.5. ε p l = ε i n − d c 1 − d c σ E O (2.4) ε p l = ε c r − d c 1 − d c σ E O (2.5)

In the concrete model, the dilation angles were varied, and the effect of confining pressure was assessed as shown in Figure 3, in which eccentricity, viscosity, a ratio of biaxial and uniaxial compressive stress, and K were maintained as default values (3DS, 2011; Tao and Chen, 2015). The CFRP had thicknesses of .167, .334, and .501 mm, with engineering constants shown in Table 1. The details of the column specimens and parameters used in modeling are shown in Tables 2, 3.

The column was loaded axially, necessitating the boundary condition. To maintain homogeneity of the composite specimens during loading, steel tube, CFRP, and concrete were coupled using kinematic coupling at the top and bottom to the created reference points in ABAQUS. All displacements and rotation degrees of freedom for the composite specimens were displaced by this coupling. At reference points, the axial displacement and axial load were prescribed and extracted in ABAQUS as shown in Figure 4. Since the column becomes more fragile as its aspect increases, the E-C, E-B, and E-A columns were assigned displacements of 0.04 H, 0.03 H, and 0.02 H, respectively.

Abaqus/Explicit was used in the analysis step. This was because of some advantages of this solver: it has a stable time increment and saves the storage capacity of computers as it does not permit iterations. It uses the stable known result or parameter from the previous step and generates the next output through a central difference integration scheme (3DS, 2011). This integration scheme utilizes very small time increments, resulting in a long computation time. To limit this, mass scaling was introduced at the beginning of the analysis step at a factor of 10. The Abaqus/Explicit is normally used to model the dynamic problem; however, step smoothing was used to minimize the velocity in the model, hence low kinetic energy. The kinetic energy of the whole model (ALLKE) was 5% of the total internal energy of the whole model (ALLIE), as recommended for static analysis (3DS, 2011). During discretization of modeling in ABAQUS, steel tubes and CFRP were assigned four nodes-shell elements (SC4R) with homogeneous and composite characteristics. Concrete was modeled using a solid, homogenous element called the hexagon (C3D8R). All elements had the same mesh size of 25 mm, with any variations being avoided since the small mesh sizes control the time increment in ABAQUS. Figure 5 shows the mesh of concrete, steel tube, and CFRP with their respective finite elements.

The ANN technique is widely used for many purposes, such as classification, pattern recognition, and modeling. In particular, the use of ANN for predicting the compressive strength and strain of FRP-confined concrete has been studied (i.e., Cascardi et al., 2017). However, the use of ANN for CFRP-confined concrete columns with elliptical cross-sections has not yet been explored. Therefore, the aim of this is to use the ANN toolbox provided in MATLAB (MATLAB, 2012) to estimate the axial compressive stress and strain capacities of confined concrete that exhibit hardening behavior as the number of CFRP increases. The number of experimental and FEM data used to train and test the ANN model was 24 in total. In the development processes of the ANN model, an appropriate selection of the input variables is a very important process. The axial load capacity of CFRP-confined structures depends on the geometric dimensions (i.e., elliptical dimension of column, thickness of steel tube, layers of CFRP) and the properties of the confining material (i.e., CFRP and steel tube). As a result, the input variables, which appear to have significant effects on the axial load capacity and strain, were taken into account with the following factors: 1) x 1 represented by Eq. 3.1 is the aspect ratio of an elliptical column, 2) x 2 represented by Eq. 3.2 is a non-dimensional factor to account for the effect of the confinement by a steel tube, and 3) x 3 represented by Eq. 3.3 is a non-dimensional factor to account for the effect of the confinement by the CFRP layer, and 5) f _co is the compressive strength of concrete. x 1 = 2 a / 2 b (3.1) x 2 = f l s / f c o (3.2) x 3 = f l f / f c o (3.3)

The output variables were: 1) y₁ is the ultimate stress of the ratio of composite-to-compressive strength of concrete as in Eq. 3.4, and 2) y₂ is the ratio of ultimate strain-to-strain of concrete for the confined concrete column loaded with axial compression loads, as shown in Eq. 3.5: y 1 = f c u / f c o (3.4) y 2 = ε c u / ε c o (3.5)

The database was randomly divided into training (60%), validation (20%), and testing (20%). Choosing the appropriate number of hidden neurons and the number of hidden layers is a major parameter in obtaining an accurate ANN model. The number of hidden layers and the number of nodes in hidden layers are usually determined via trial-and-error procedures or using suggested rules (Amani and Moeini, 2012). Therefore, one layer of hidden nodes was based on previous suggestions (Isleem et al., 2022b), and the optimum model parameters (i.e., the number of hidden nodes and the rate of learning) were found by a proposed training approach. This can be accomplished using one of several available approaches, in which the network was trained with a set of random values for the initial weight, hidden node number, and learning rate. The Levenberg–Marquardt denoted by Trainlm (Demuth and Beale, 1998) was selected as the training function. The performance function is MSE, and the transfer functions in both hidden and output layers are Purelin transfer functions. It is to be noted that the default transfer functions in the ANN toolbox are Tansig (Demuth and Beale, 1998). By transforming the data in the first and last ANN layers using the function (Eqs 3.6 and Eq. 3.7) and choosing Purelin transfer functions, the ANN model reveals an acceptable performance: x = x 1 , x 2 , x 3 T (3.6) y = y 1 , y 2 T (3.7)

Once the ANN model is built and the first and last data layers are chosen and normalized, the network can now be trained. The performance of the system on the test data is used to measure the success of the learning process. These test data are usually not involved in the training process; rather, they are used in determining the generalization capability of the trained network, which ensures that the trained data are not memorized during the learning process (Awolusi et al., 2019). On the other hand, the validation data set is used to evaluate the performance of trained data in each epoch sequentially. Based on the overall model performance and the least mean square error achieved across a wide range of training parameters, the optimal number of hidden nodes was found to be three, and the optimal number of iterations (epochs) in performing the training was found to be four. Using these resulting parameters in a training approach, the most accurate results can then be obtained. Figure 14 clearly shows the result of R ² for the train, validate, and test data, which have the best correlation of test data, indicating the best training has been achieved. The performance and accuracy of trained data were assessed using the mean square error. Figure 15 shows that the data in training, validation, and testing had a close mean square error. In Eqs 3.8–3.15, the predictions from the ANN model in practical form were generated, in which the inputs (x) and outputs (y) were scaled using the minimum and maximum values provided in Table 4, w is the order of weight for hidden and output neurons, w 1 and w 2 , respectively; a is the linear function that combines the intercept/bias in the hidden and output layers, w 2 σ is the weight of the output layer resulting from the stress ratio, w 2 ε is the weight of the output layer resulting from the strain ratio, The b ₁ and b ₂ are the matrices containing the bias of the hidden and output layers. y − y min y max − y min − 0.5 × 2 = w x − x min x max − x min − 0.5 × 2 + a (3.8) w = w 2 × w 1 (3.9) a = w 2 × b 1 + b 2 (3.10) w 2 = w 2 σ w 2 ε (3.11) w 1 = − 0.871 3.402 − 0.699 1.803 0.427 0.2 − 2.868 − 0.471 1.957 (3.12) w 2 = 0.535 0.031 0.639 0.922 − 0.912 0.4254 (3.13) b 1 = 1.128 − 1.213 1.429 (3.14) b 2 = − 0.942 − 1.330 (3.15)