Modeling of the Axial Load Capacity of RC Columns Strengthened with Steel Jacketing under Preloading Based on FE Simulation

Reinforced concrete (RC) columns often require consolidation or rehabilitation to enhance their capacity to endure the loads applied. /is paper aims at studying the conduct and capacity of RC square columns, those reinforced with steel jacketing under static preloads. For this purpose, a three-dimensional model of finite element (FE) is devised mainly to investigate and analyze the effect of this case./emodel was tested and adjusted to ensure its accuracy using the previous experimental results obtained by the author. Results of testing, experimentally, the new developed FE model revealed the ability to use the model for calculating RC columns’ axial load capacity and for predicting accurate failure modes./e newmodel that tends to predict the axial load capacity was suggested considering the parametric analysis results.


Introduction
Reinforced concrete (RC) columns often require strengthening to enhance their axial load capacity to endure loads. is reinforcement may be needed because of the alteration in the use which ended in addition to loads that are live; errors of design, problems in the construction while making erection, elevating for confirming to existing code necessities or aging of RC columns itself were studied.
ere are three commonly used methods for reinforcing RC columns including concrete and/or steel jacketing and fiber-strengthened polymer (FRP) jacketing.All these methods have led to an effective rise in the load capacity of RC columns. is study refers to RC columns loaded by axial compressive load strengthened under load by steel jacketing.Strengthened existing steel columns under preloading through welding steel plates is frequently rendered [1,2], but there is hardly any study of RC columns under preloading exists.Some researchers [3][4][5][6][7][8][9][10] reproduced the findings of an experimental test chain on some RC columns fortified with the angles of steel jacketing under axial load without preloading.ere was a witness confirming that the jacketing of steel enhances the failure load of the fortified RC columns.
Because the existing experimental research [3][4][5][6][7][8][9][10] ignores the effect of the preloading that found when the strengthening is done on the axial load capacity, reliance on the research that already exists is problematic for an accurate prediction of the axial load capacity relating to RC columns reinforced with steel jacketing under preloading.Moreover, the existing codes ACI Committee 318 [11] and Eurocode 4 [12] only predict the axial load capacity, based on the composite concrete-steel structure without preloading effect.
Other studies [13][14][15][16], using FE modeling, revealed that the conduct of RC members can be simulated precisely, especially the RC members that was strengthened by steel jacketing.At the same time, conducting experimental researches taking into account all the parameters which affect the ultimate capacity of the load is not sensible, especially if the strengthening is under preloading.Accordingly, there is a need to develop a special FE model that could be used for simulating RC columns reinforced by steel jacketing and investigate the behaviors of each parameter under preloading.
While predicting RC columns' axial load capacity, fortified with steel jacketing, it is necessary to take into consideration the factors mentioned above and under preloading.In this research, the FE simulation model was built in 3D aiming at predicting the axial load capacity of steel jacketingreinforced RC columns with and without preloading.On the basis of the findings derived from the parametric study, it is proposed to resort to prediction model to consider the effect of the preloading on the load capacity pertaining to steel jacketing-fortified RC columns.Moreover, experimental outcomes of tests conducted on RC columns as reflected in the literature review [3,4] were gathered to use the same for verification of the precision of the analytical results obtained through the FE program (ANSYS-15) [17].

Existing Models
Many authors introduced design models for a similar problem.However, Campione [5], ACI Committee 318 [11], and Eurocode 4 [12] reported that the designed axial load capacity P u of the steel jacketing-reinforced RC column is basically calculated from where P c , P s , and P sj represent the contribution of concrete, steel reinforcement, and steel jacketing, respectively.e models offered by ACI Committee 318 [11] and the majority of the models that already exist implement the equation given below for calculating the design axial load capacity of the RC column without strengthening: For designing, the ACI code allows using the factors, such as ϕ, 0.85f c ′ and 0.80 to equivalent rectangular compressive stress distribution to replace the more exact concrete stress distribution and to make safety design.So if there is a need to predict failure axial load capacity, then the equation is formulated to As stated by Eurocode 4 [12], the ultimate load capacity of RC columns fortified with steel jacketing as a combined cross section is expressed by the following equation: where N pl,Rd is the plastic resistance to compression; A a , A c , and A st are the cross-sectional domains of steel jacketing, concrete, and steel reinforcement, correspondingly; and f sd and f cd together with f yd are their design values characteristic strengths.For concrete-filled sections, the coefficient 0.85 may be replaced by 1.0, so equation (4) will be reduced to However, several authors proposed models to acquire a precise equation for the axial load capacity of RC column reinforced by steel angles jacketing and horizontal steel plat strips.
Campione [5] stated an analytical expression for predicting the axial load capacity of reinforced RC columns with steel angles and strips jacketing.e final axial load capacity is given by where f cc ′ shows the compressive strength of confined concrete and n a represents a dimensionless ratio of the axial force existing in the vertical steel angles jacketing.

ANSYS Finite Element Model Study
3.1.Concrete Modeling and Properties.While making an analysis, the commercial program of FE (ANSYS) was employed.For modeling the concrete, 65 solid elements were used ANSYS-15 [17].Such an element consists of 8 nodes together with freedom of 3 degrees between every translations and node in the nodal x, y, and z directions.Also, such an element can result in deforming of the plastic, breaking in 3 orthogonal directions with a simultaneous crushing.For modeling the concrete, to have a simulation of real concrete behavior, ANSYS needs linear and multilinear isotropic substance characteristics for centering, together with a few supplementary properties of the concrete substance.e shear transfers coefficient β, relating to the state of the cracked face [17].e range of the coefficient value is from 0.0 to 1.0, with 0.0, and 0.0 represents a smooth crack, and 1.0 suggests a rough crack [13,14].An open crack coefficient, β t � 0.2, and the closed crack coefficient, β c � 0.8, were taken in the study in hand [15].e calculation about the modulus of elasticity of the concrete is possible to be carried out using the following equation: e calculation of uniaxial tensile stress can be made from the following equation: Poisson's ratio of concrete of 0.2 was applied.e calculation of the compressive uniaxial stress-strain values for the concrete can be made using equation ( 9) [16]: 2 Modelling and Simulation in Engineering where the modulus of elasticity is E c , compressive strength is f c ′ , and tensile stress is f r , which are in MPa; f el is the stress at the elastic strain (ε el ) in the elastic range f el � 0.30f c ′ ; ε 0 is the strain at the ultimate cylinder compressive strength, f c ′ ; and f is the stress at any strain ε.

Strengthening of Steel, Steel Angles, and Steel Plates
Modeling and Characteristics.SOLID186 elements ANSYS-15 [17] were employed for modeling the steel strengthening, steel angles, and steel plates.SOLID186 is a 3D 20-node solid element of higher order, which displays how quadratic displacement behaves.e definition of this element is made as 20 nodes having 3 degrees of independence at each node. is element also assists plasticity, creep, hyperelasticity, large deflection, stiffening of stress, and larger capabilities of strain.Also, it carries a blend of the capability of the formulation to simulate the deformations of elastic-plastic materials almost incompressible and the hyperelastic materials that are completely compressible.SOLID186 is an identical structural solid that is very suitable for modeling asymmetrical meshes.e steel reinforcement, steel angles, and the plates of steel integrated into the FE models were expected to be materials of linear elasticity together with a modulus of elasticity concerning 210 GPa and Poisson's ratio of 0.3.e yielded stress is another thing that depends upon the use of the element.
e maximum size of the meshing elements was taken as 20 mm in length, 10 mm in height, and 10 mm in width.e contact between steel and concrete was modeled using a set of TARGE170 and CONTA174 contact elements [17], which function on the basis of Coulomb's friction model.

Model Studies
Pertaining to the Structure.Seventeen RC columns (with variable cross sections and heights) exposed to axial loading were considered in the present study.e columns were divided into two groups: First group: consists of four columns according to previously published work [3,4], as shown in Figure 1, which were examined to testify the accurateness of the FE model.Second group: consists of thirteen columns under preloading with different percentages of preloading on the strengthened column, which were analyzed to propose a new model for predicting RC column's axial load capacity, reinforced with steel jacketing.Tables 1 and 2 demonstrate the key material and geometric characteristics of the test data.

Comparison of FE Modeling with the Experimental Results
To scrutinize the FE model for its validity and reliability, a comprehensive verification was done utilizing a chain of experimental data that exist in the background literature.e database taken into account comprises the outcomes of four experimental tests, together with the outcomes of tests on 2 columns without reinforced and 2 columns strengthened with steel angles jacketing.e key material, as well as geometrical characteristics about the experimental data, has been summarized in Tables 1 and 2.
Table 3 illustrates loads of failure including the findings of both experiments and analysis also showing the ratios between them.Figure 2 graphically compares the values derived through experiment and analysis.e table and the figure show the mean values of P Exp /P FE as 1.003, the conforming coefficient of variation as 3.16%, and the coefficient of correlation as 0.987.e given values illustrate that the FE model turns out to be an excellent match from a Modelling and Simulation in Engineering statistical perspective, and it can be observed for all RC columns with or without strengthening the configurations dealt with while making an analysis.Figures 3 and 4 bear the curves showing how the load is displaced for specimens used on the experiments and the resultant FE modeling.One comparing the curves of load displacement attained from findings of experiments with the ones attained from the FE models for RC columns with or without strengthening can note an excellent match between them.
e way how FE models deal with all the specimens together with deformed shapes, failure loads, and failure modes was recorded.Figures 5 and 6 illustrate the deformations, failure modes, and locations for experimental specimens and the corresponding FE modeling.When comparing the deformations, failure modes, and locations acquired from the experimental outcomes with the ones acquired from the FE models for RC columns with or without strengthening, it can also be observed as an excellent match.

Predicting the Axial Load Capacity under Preloading of RC Columns Founded on Simulation of FE
For assessment of the influence of the parameters on a load of axial capacity, a parametric study was carried out.ese parameters incorporated the column dimensions, the concrete strength, the cross section of the zone and yield stress of the steel fortification, the cross section of the zone and the stress yielded by the steel jacketing, and the percentage of preloading.Meanwhile, the typical model from Eurocode 4 [12] was utilized for comparison.illustrate how the axial load and column axial displacement are related to each other.Generally, the final load increases when steel jacketing strengthening was used.When the RC column is strengthened under preloading, the ultimate load decreases when the preloading increases.

Predicting the RC Columns' Axial Load Capacity Based on FE Simulation
. By means of the parameters considered in the present research, it is possible to calculate the axial load capacity of RC columns through the addition of the normal force from concrete and the normal force from steel reinforcement, independently for RC column without strengthening.Furthermore, by making an addition of steel jacketing contributions right to the normal force of the RC column, the procedures ACI Committee 318 [11] and Eurocode 4 [12] come to an excellent match.As a result, the axial load capacity of a reinforced RC column is articulated as the total of the 3 normal constituents in consonance with the internationally accepted procedures as incorporated in equation ( 2).Table 4 demonstrates the RC column parameters appraised in the current study and the eventual axial loads, derived from simulating and analyzing the FE. e prediction regarding the axial load capacity by the Eurocode 4 [12] design model proposed can be seen in Table 4.
For the evaluation of the FE results' reliability, the findings attained from the design model suggested by Eurocode 4 [12] is compared with the results obtained from the FE simulation, as illustrated in Figure 9.An identical prediction between the Eurocode models and the FE simulations for RC columns can be seen without preloading.In this figure, the mean value of P u.Eurocode /P u.FE is 0.998, the corresponding coefficient of variation is 2.01%, and the coefficient of correlation is 0.99.e aforementioned values reveal that the FE model is an excellent match, and it can be observed for all RC columns without preloading with the prediction values from the Eurocode 4 [12] model.Otherwise, for RC columns with preloading, the mean value of P u.Eurocode /P u.FE is 1.199, the  Modelling and Simulation in Engineering    conforming coefficient representing variation is 13.58%, and the coefficient of correlation is 0.33; these values show that the prediction values from the Eurocode 4 [12] model are too far from the values obtained from FE simulation.So the Eurocode model needs to be modified to take the preloading when strengthening into consideration.
On the basis of FE simulating 17 RC columns, a clarification was made earlier regarding the rise in the axial load capacity that registered variation with the fluctuation of percentage in preloading; hence, the relationship between the rise in the axial load capacity and percentage of preloading is framed in equation (10), where the equation is a polynomial of the relationship between the ratios of the percentage of preloading with ultimate failure load of the control RC column (P P.L /P u.f ) and percentage of steel jacketing stress obtained from the FE simulation with yield stress (f sj /f yj ), as shown in Figure 10: Equation ( 5), which is employed in the majority of the prevailing models for predicting the axial load capacity for RC column without strengthening, and the proposed new model in equation (10) predict the steel jacketing stress under preloading.
e new model that has been recently proposed for predicting the axial load capacity and can be applied to RC columns extrinsically reinforced with steel jacketing strengthening is formulated in the following equation: (11)

Conclusions
e introduction of the FE simulation model has been made for predicting the contribution of steel jacketing to the RC columns' axial load capacity.ere are parametric studies conducted for assessing the influences of several parameters on the capacity of axial load and failure modes relating to RC columns.
e investigative findings derived from the FE model were subjected to a comparison with outcomes attained from previously published work cited in the literature, involving a different structure, concerning test geometries.ere is a proposal for a new model which takes into account the investigated parameters.On the basis of this research, the conclusions drawn are given below: (1) In comparison with the findings of the experiments, the FE model is considered to be more accurate in making a prediction about the mode of failure and determining the axial load capacity.e mean value  Modelling and Simulation in Engineering

Figure 4 :
Figure 4: Curves showing displacement of load gained from both experimental Tarabia and Albakry [4] and FE outcomes.

Figure 5 :
Figure 5: Deformations, failure modes, and locations obtained from both experimental Belal et al. [3] and FE results.

Figure 6 :
Figure 6: Deformations, failure modes, and locations obtained from both experimental Tarabia and Albakry [4] and FE results.

Figure 7 :
Figure 7: e curves relating to load displacement obtained from FE simulation for columns strengthened by 4L•50 × 50 × 10 with different percentages of preloading.

Figure 8 :
Figure 8: e curves relating to load displacement obtained from FE simulation for columns strengthened by 4L•100 × 100 × 10 with different percentages of preloading.

Table 1 :
A brief account of RC columns assessed in the current study using FE modeling.

Table 2 :
Summary of RC columns reinforced with steel jacketing in the present study.

Table 3 :
Comparison of failure load and ratios of P Exp /P FE for experimental and FE results.

Table 4 :
(10)ary of RC columns strengthened with steel jacketing in the present study.Figure9: Comparison between the Eurocode model[12]and FE simulation for axial load capacity.ofPExp /P FE is 1.003 for columns that strengthened by steel jacketing or without strengthening.ecorrespondingcoefficient of variation is 3.16%, and the coefficient of correlation is 0.987.(2)Evaluationwith the results obtained from the design model in Eurocode 4[12]is compared with the results obtained from the FE simulation; there is an excellent match prediction between the Eurocode models and the FE simulations for RC columns without preloading.(3)enew model equation(10)can predict steel jacketing stress and the RC columns' axial load capacity strengthened by means of steel jacketing under preloading.Figure 10: e relation between percentage of preloading columns the corresponding percentage of steel jacketing stress obtained from the FE simulation.