Modelling and Simulation in Engineering

Volume 2019, Article ID 8653247, 8 pages

https://doi.org/10.1155/2019/8653247

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

^{1}Department of Civil Engineering, Engineering Faculty, Assiut University, Assiut, Egypt^{2}Department of Civil and Environmental Engineering, College of Engineering, Majmaah University, Al Majmaah 11952, Saudi Arabia

Correspondence should be addressed to Ahmed M. Sayed; moc.oohay@yoagnle_cme

Received 4 January 2019; Accepted 15 February 2019; Published 4 March 2019

Guest Editor: Qing-feng Liu

Copyright © 2019 Ahmed M. Sayed and Hesham M. Diab. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Reinforced concrete (RC) columns often require consolidation or rehabilitation to enhance their capacity to endure the loads applied. This 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. The model 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. The new model that tends to predict the axial load capacity was suggested considering the parametric analysis results.

#### 1. Introduction

Reinforced concrete (RC) columns often require strengthening to enhance their axial load capacity to endure loads. This 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.

There 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. This 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 [3–10] reproduced the findings of an experimental test chain on some RC columns fortified with the angles of steel jacketing under axial load without preloading. There was a witness confirming that the jacketing of steel enhances the failure load of the fortified RC columns.

Because the existing experimental research [3–10] 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 [13–16], 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 jacketing-reinforced 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].

#### 2. 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 of the steel jacketing-reinforced RC column is basically calculated fromwhere , , and represent the contribution of concrete, steel reinforcement, and steel jacketing, respectively.

The 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 , 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 is the plastic resistance to compression; , , and are the cross-sectional domains of steel jacketing, concrete, and steel reinforcement, correspondingly; and and together with 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. The final axial load capacity is given bywhere shows the compressive strength of confined concrete and represents a dimensionless ratio of the axial force existing in the vertical steel angles jacketing.

#### 3. 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.

The shear transfers coefficient *β*, relating to the state of the cracked face [17]. The 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]. The calculation about the modulus of elasticity of the concrete is possible to be carried out using the following equation:

The calculation of uniaxial tensile stress can be made from the following equation:

Poisson’s ratio of concrete of 0.2 was applied. The calculation of the compressive uniaxial stress-strain values for the concrete can be made using equation (9) [16]:where the modulus of elasticity is , compressive strength is , and tensile stress is , which are in MPa; is the stress at the elastic strain () in the elastic range ; is the strain at the ultimate cylinder compressive strength, ; and is the stress at any strain .

##### 3.2. 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. The definition of this element is made as 20 nodes having 3 degrees of independence at each node. This 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. The 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. The yielded stress is another thing that depends upon the use of the element.

The maximum size of the meshing elements was taken as 20 mm in length, 10 mm in height, and 10 mm in width. The 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.

##### 3.3. 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. The 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.