Microsoft Word - ETASR_V13_N2_pp10419-10424 Engineering, Technology & Applied Science Research Vol. 13, No. 2, 2023, 10419-10424 10419 www.etasr.com Le: Numerical Investigation of the Axially Compressive Behavior of Circular Concrete Encased Steel … Numerical Investigation of the Axially Compressive Behavior of Circular Concrete Encased Steel Composite (CESC) Columns Hoang An Le Ho Chi Minh City University of Transport, Vietnam hoangan.le@ut.edu.vn (corresponding author) Received: 29 December 2022 | Revised: 5 February 2023 | Accepted: 8 February 2023 ABSTRACT This research presents a numerical investigation of circular Concrete Encased Steel Composite (CESC) columns. To simulate the circular CESC columns under axial compression in the previous tests, a Finite Element Model (FEM) with some modifications of material models for the steel and concrete was established in ABAQUS software. The curves of load versus longitudinal displacement and the ultimate loads obtained from the FEM were compared with those measured in previous tests. The numerical results agreed well with the test results. Furthermore, the distribution of the stresses on the cross-section at different heights and the effect of initial imperfections were observed by the FEM results. A highly confined concrete zone enclosed by steel web and steel flanges was observed. Finally, the established FEM was used in the parametric study that investigated the influence of concrete strength, steel yield strength, and spacing of the spiral hoops. Keywords-composite columns; FEM; CES; ABAQUS; concrete; steel I. INTRODUCTION Concrete Encased Steel Composite (CESC) columns are being widely applied in heavy-loading structures such as in top-down construction methods, high-rise buildings, or support structures [1, 3-4, 24-28]. The utilization of circular CESC columns in construction was found to be necessary due to their ability to support higher loads than the rectangular or square CESC columns and their aesthetical appearance. A steel section is constructed inside the reinforced concrete to form a CESC column, thereby fully exploiting the advantages of steel and concrete materials [1, 24-26]. Ductility and seismic resistance can be greatly enhanced by the use of a steel section, while the concrete works as a protective layer for the steel section against buckling, fire, and aggressive environments [1-2, 8, 19, 28-30]. For these reasons, several attempts have been made to test the structural behavior of CESC columns [1-5, 8, 13-14, 24, 27, 29-30]. The testing equipment for CESC columns requires very high capacity and complexity, thus restricting the range of parameters. Therefore, many efforts have been undertaken to simulate the behavior of CESC columns through Finite Element Models (FEMs). Authors in [4] presented a FEM to analyze the pin-ended axially loaded square CESC short and long columns using various concrete strengths (20-110MPa) and various steel yield strengths (275-690MPa). Authors in [11] introduced a new simplified technique of FEM incorporating the confinement effect of square CESC columns to construct strength interaction diagrams. Authors in [7] constructed FEMs to compare the difference between square CESC columns and reinforced concrete columns with different concrete strengths. Authors in [15] constructed a FEM to study the buckling resistance of CESC columns using concrete strength up to 100MPa. Authors in [9] conducted simulations to address the impact of concrete strength, steel strength, and column slenderness on the performance of square CESC columns. Authors in [10] simulated a square CESC long column with 3.6m length and a steel column made of welded H-profile with the same length under axial compression and uniaxial bending to compare the difference between CESC and pure steel columns. Authors in [12] constructed a FEM of square CESC columns using Fiber-Reinforced Concrete (FRC) to verify the test results and the effect of tensile strength of FRC. The literature review revealed that the majority of existing numerical investigations of the behavior of CESC columns were concerned with square sections, while the studies on CESC columns with circular sections are extremely limited. As compared to square or rectangular sections with the same dimensions, the use of circular sections results in some beneficial characteristics for CESC columns such as higher confining stress induced by steel profile and transverse reinforcements, higher strength and ductility, and better Engineering, Technology & Applied Science Research Vol. 13, No. 2, 2023, 10419-10424 10420 www.etasr.com Le: Numerical Investigation of the Axially Compressive Behavior of Circular Concrete Encased Steel … architectural performance [5, 7, 18, 20]. Only two test results of circular CESC columns were reported in [7]. For this reason, there is a need for the study of circular CESC columns, in general, and FEM studies for circular CESC columns, in particular. To fulfill this gap, this paper presents a FEM to simulate the circular CESC short columns. Firstly, the FEM was established in ABAQUS software with some modifications to material models. After this, the accuracy of the FEM was checked by comparing it with the test results of [7]. The distribution of stresses on the cross-section at different heights was also plotted. Finally, the effect of the concrete strength, steel yield strength, and spacing of spiral hoops on the load versus displacement response of circular CESC short columns was determined by conducting a parametric study. II. DESCRIPTION OF FEM A. Configuration of Test Specimens Test specimens reported in [7] were used for the simulation. Two circular CESC short columns using an I cross-shaped steel section were constructed for testing under concentric loading. Table I shows the geometry and the dimensions of the columns and Table II demonstrates the properties of the materials used for the test specimens. TABLE I. DIMENSIONS OF TEST SPECIMENS Specimens Diameter (mm) Height (mm) Steel section HSRC-SP1 411 1233 2H206×120×12×12 HSRC-SP2 411 1233 2H206×120×12×12 Specimens Longitudinal reinforcement Spiral hoop Spacing of spiral hoop (mm) Ultimate load (kN) HSRC-SP1 20d10 d10 50 11363 HSRC-SP2 20d10 d10 50 10890 TABLE II. MATERIAL PROPERTIES OF TEST SPECIMENS Specimens Concrete strength fc (MPa) Yield strength of steel section fy (MPa) Yield strength of longitudinal reinforcement fy,r (MPa) Yield strength of spiral hoop fh,h (MPa) HSRC-SP1 37 517 426 426 HSRC-SP2 37 517 426 426 B. Mesh and Finite Elements The circular CESC columns consisted of concrete, steel section, longitudinal reinforcements, and spiral hoops. The solid element C3D8R (8-node brick element) was selected for simulating the concrete and the embedded steel profile. The truss element T3D2 (2-node) was selected to simulate the embedded longitudinal reinforcements, while the B31 beam element was adopted for modeling the spiral hoops. After the performance of different mesh sizes, a reasonable aspect ratio of solid element size of 1:3 was assumed. A coefficient of friction of 0.25 [4] was chosen in the "surface-to-surface contact" to simulate the interface of the concrete and the steel profile. It should be noted that this friction coefficient is adopted by numerous studies. Master and slave surfaces were assigned to the concrete and the encased steel section, respectively. Figure 1 shows the finite element mesh and type. Fig. 1. Finite element mesh and type C. Boundary Conditions and Loading Application Two loading plates were simulated at both ends of the column and tied to the end surface of the concrete and steel section to ensure a uniform load transfer to the whole section of the column. Two reference points (RP1 and RP2) were located in the middle of the upper and lower loading plates, respectively. A rigid body constraint was assigned between the reference point and the surface of the loading plate for easier loading application. All degrees of freedom of loading plates were fixed, while the axial displacement of the upper loading plate was set free to permit the axial movement. The numerical analysis in ABAQUS [21] was carried out using displacement control. An implicit procedure with the Newton-Raphson method [21] was adopted for the analysis. Figure 2 demonstrates the modeling of boundary conditions, the interaction between structural steels and concrete, and the loading application. Fig. 2. Boundary condition and loading application. Engineering, Technology & Applied Science Research Vol. 13, No. 2, 2023, 10419-10424 10421 www.etasr.com Le: Numerical Investigation of the Axially Compressive Behavior of Circular Concrete Encased Steel … The buckling mode was determined by eigenvalue buckling analysis of the simulated columns. The eigenmode 1 as the first buckling mode was adopted to incorporate the geometric initial imperfection for nonlinear inelastic analysis of the composite column. The value of the initial imperfection for each column was selected as L/500 and L/1000, in which L is defined as the column length. D. Material Models The behavior of structural steels (steel section, longitudinal reinforcement, and spiral hoop) was simulated using the stress- strain model [22] as seen in Figure 3. The value of Poisson’s ratio was set as 0.3 for steel. In Figure 3, fy represents the yield stress and εy denotes the strain at fy. The modulus E1 was taken as 0.01Ey, while the modulus of elasticity Ey of the first elastic stage was set as 200GPa. Fig. 3. Stress-strain model for structural steels. The nonlinearity of the concrete was simulated using the Concrete Damage Plasticity Model (CDPM). Some parameters of CDPM employed to model the triaxial stress state of the concrete are:  Angle of dilation φ=30 o .  Eccentricity ε=0.1.  Ratio of fbo/fc=1.16, where fbo is the biaxial compressive yield stress.  Ratio of the second stress invariant on the tensile meridian for the yield function K=0.667. Furthermore, the viscosity parameter µ =0.0001 was used to ensure the convergence. The CEB model [23] was adopted to estimate the curve of stress versus strain (σc-ε) of the concrete. The CEB model [23] is applicable to various concrete strengths (10-100MPa). The (σc-ε) curves can be drawn using the equations of the CEB model [23]: �� � �� ���� � � � �� � � �� � � 1 � ��� � 2� � �� �� For ε ≤ ε0 (1) �� � 0.7�����.�� � 10�� (2) �� � 22000���/10��.� (3) �� � ��1 � " ## ��$�� %� for ε > ε0 (4) & � ��� � 0.001�/�� (5) where ε0 is the longitudinal strain at fc, E0 is defined as the secant modulus at fc, and Eit is the tangent modulus. The curve of stress versus plastic strain of concrete (fc = 37MPa) for the test specimens in [7] used as input in ABAQUS is shown in Figure 4. Fig. 4. Stress – plastic strain relation of concrete. III. FEM VALIDATION The load versus displacement (L-D) curve and the ultimate load obtained from FEM were compared with those measured in the tests conducted in [7] to evaluate the suitability of the FEM. Figure 5 shows the L-D curves of the FEM and the test results of [7]. It can be seen that the L-D curves from the FEM matched well with the test results. Furthermore, the FEM L-D curves of FEM with and without imperfections were plotted. Figure 5 shows that there is no significant change in the L-D curves with and without initial imperfections in FEM. The ultimate loads measured in the tests (NTest) and FEM (NFEM1 and NFEM2) are compared in Table III. It is evident that the ultimate loads of FEM are close to those obtained from the tests in [7] with FEM underestimating the ultimate loads with a difference ranging from 5% to 9%. Fig. 5. Comparison of the L-D curves between FEM and the experimental results from [7]. Engineering, Technology & Applied Science Research Vol. 13, No. 2, 2023, 10419-10424 10422 www.etasr.com Le: Numerical Investigation of the Axially Compressive Behavior of Circular Concrete Encased Steel … TABLE III. COMPARISON OF THE ULTIMATE LOADS BETWEEN FEM AND THE EXPERIMENTAL RESULTS Specimens NTest (kN) NFEM1 (kN) (with imperfection) NFEM2 (kN) (without imperfections) NFEM1/ NTest NFEM2/ NTest HSRC-SP1 11363 10406 10393 0.92 0.91 HSRC-SP2 10890 10406 10393 0.96 0.95 Based on the FEM results, the stress state of the concrete of circular CESC columns in [7] is demonstrated in Figure 6. It can be observed from the stress in the 3-3 direction of the concrete that the I cross-shaped steel section provides a good confinement effect to the concrete. The stress concentration of the concrete inside the steel section is maximal at both ends and decreases to the middle of the column. A highly confined concrete zone is observed as seen in Figure 6. This zone is enclosed by steel web and flanges. This result is in line with the FEM result reported in [8]. Fig. 6. Stresses in the concrete and the confined concrete zone. IV. PARAMETRIC STUDY The verified FEM was adopted for the parametric study to determine the effect of fc, fy, and s on the L-D curves of circular CESC short columns. All columns for the parametric study have the same diameter of 270mm and the same height of 800mm (L/D = 2.96). A steel section of 70×140×10×12 was chosen for the I-cross shape. The grade of the steel section is S355. The diameter of longitudinal reinforcement is d13 with a S500 grade. The diameter of spiral hoops is d10 with a S500 grade. Various concrete strengths (30, 100, 150MPa) and steel yield strengths (350, 550, and 650MPa) were modeled. The spacing of spiral hoops was taken as 30, 60, and 90mm. Eight longitudinal reinforcements were constructed for the columns. Figure 7 describes the circular CESC columns for the parametric study. Fig. 7. The circular CESC columns for the parametric study. Fig. 8. Results of the parametric study using the verified FEM. The results of the parametric study are illustrated in Figure 8. As expected, higher values of fc and fy result in higher composite column strength. When increasing fc from 30 to 100MPa and from 30 to 150MPa, the loading capacity of the column was improved by about 76% and 123%, respectively. Engineering, Technology & Applied Science Research Vol. 13, No. 2, 2023, 10419-10424 10423 www.etasr.com Le: Numerical Investigation of the Axially Compressive Behavior of Circular Concrete Encased Steel … The descending stage of the L-D curves of the columns using higher values of fc was steeper than that when using lower values of fc. When increasing fy from 350 to 550MPa and from 350 to 650MPa, the strength enhancement of the CESC columns was about 13% and 19.7%, respectively. Unlike the effect of fc, there was no significant improvement in the ductility of the columns with increasing yield strength fy. Similar to the effect of fy, smaller spacing of spiral hoops leads to higher column strength. Increasing the spacing of spiral hoops from 30 to 60mm and from 30 to 90mm decreased the column strength by about 4.7% and 7.8%, respectively. The quantitative value of strength improvement with increasing concrete strength fc was higher than that with increasing fy or decreasing s. 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