FINITE ELEMENT STUDY ON HOLLOW CORRUGATED STEEL BEAMS UNDER IMPACT LOADING

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1 International Journal of Civil Engineering and Technology (IJCIET) Volume 9, Issue 10, October 2018, pp , Article ID: IJCIET_09_10_015 Available online at ISSN Print: and ISSN Online: IAEME Publication Scopus Indexed FINITE ELEMENT STUDY ON HOLLOW CORRUGATED STEEL BEAMS UNDER IMPACT LOADING Mohammad R.K.M. Al-Badkubi Building and Construction Technical Engineering Department, College of Technical Engineering, the Islamic University, Najaf, Iraq ABSTRACT This paper presents a nonlinear finite element analysis on the behavior of corrugated steel beams subjected to impact load using ABAQUS (6.14-4) computer program. Six corrugated steel beams with length 1.8 m and three unit profile of corrugated steel for each side of the square cross section rested on fixed steel blocks at the ends were modeled. The parametric study was made on the corrugated steel plate thickness and the magnitude of the total impact force. The adopted model was validated by using data from experimental test. In these models a nonlinear materials behavior for steel plate was simulated using appropriate constitutive model. The results showed that the general behavior of the finite element models represented by the mid span deflection - time history curves, maximum mid span deflection, vibration time of the beams, and residual impact deformation show good agreement with the experimentally tested specimen. After analyzing the models it was found that by increasing the thickness of the corrugated steel plate the mid span deflection along with vibration time will decreases up to (29.3 %) and (45.9 %), respectively. Also, reduction in total impact force causes the decrease in mid span deflection and vibration time up to (32.6 %) and (46.12 %), respectively. Key words: Finite Element Modeling, Corrugated Steel Beams, Impact Load, and Residual Impact Deformation. Cite this Article: Mohammad R.K.M. Al-Badkubi, Finite Element Study on Hollow Corrugated Steel Beams under Impact Loading, International Journal of Civil Engineering and Technology (IJCIET) 9(10), 2018, pp INTRODUCTION Nowadays almost all industries are redirecting their strategic plans on developing environmentally friendly products that building and construction industry is not an exempt. Although numerous research is being conducted to commercialize incorporation of novel materials in infrastructures applications, structural elements made from steel alloys are yet the most common ones. This popularity can be due to the high strength to weight ratio attributes and remarkable fabrication versatility of steel material [1] editor@iaeme.com

2 Mohammad R.K.M. Al-Badkubi Corrugated sheets and plates have been used in lots of engineering fields. They have a several advantages like lightweight, economical, self-strengthen, and easy shipping and storage process. Hitherto have attracted researcher's interests to broaden their applications, since they were introduced for the first time. The corrugated shape provides continuous stiffening for the sheets similar to stiffened panels, but allows using thinner plates. They can be bent in one direction easily while it retains its rigidity in the other direction. Furthermore, the fabrication cost of elements with corrugated panels are normally lower than those with stiffened plates [2-4]. The use of fabricated hollow sections built up from corrugated plates was introduced by Nassirnia et al. [5] for the first time. The idea was further developed by implementing in concrete-filled double skin columns [6] and combining with ultra-high strength steel tubes [7]. Also, the performance of new sections under uniaxial loading was investigated. During the lifetime of a structure, in addition to bearing quasi-static loads induced by live and dead loads, it may inevitably suffer from various natural hazards such as impact loads, earthquakes, and fire [8]. Thus, in this study, A theoretical analysis was performed to predict the behavior (deflection and impact deformation) of corrugated beams subjected to impact load by using a nonlinear finite element program (Abaqus ). The validity of analytical test results are compared with experimental test results [1]. 2. SPECIMENS DESCRIPTION This paper represents an analytical study on the behavior of the corrugated steel beams under impact load. The total number of six corrugated steel beams were tested. The parameters which are studied are the thickness of the corrugated steel beam and the magnitude of the total impact force applied on the beams. The detail of the test specimens is shown in Table (1): Beam No. Table 1 Specimens Identification. Beam Symbol Thickness t (mm) 1 CB CB CB CB CB CB Impact force Factor It is worth noting that the analytical tests are verifying due to comparison of experimental results and analytical results for beam (CB31), after which the remaining specimens were tested using the same calibrated model. 3. FINITE ELEMENT MODELING OF THE SPECIMENS 3.1. Modeling of Corrugated Steel Beam The first step involved in the finite element analysis method consists of building the model. In this step, the structure is created and then divided intofinite elements connected together at their nodes. In building a finite element model, it is necessary to define the geometry of the model, element type and material properties editor@iaeme.com

3 Finite Element Study on Hollow Corrugated Steel Beams under Impact Loading Selecting Geometry Generally, a corrugated plates are formed by repeating identical unit profile. The number of units depends on the application and the target size. In this study, three units (n = 3) are considered [1]. Also, there are several type of unit corrugation profiles for various applications. In this study, trapezoidal corrugated unit as shown in Figure (1) is chosen to be studied [1]. Figure 1 A Trapezoidal Corrugated Unit Profile. Since unit geometrical dimensions could affect the overall performance of corrugated beams, the unit profile dimensions are shown in Table (2). Table 2 Corrugated Unit Profile Dimensions [3]. α ( o ) a (mm) b (mm) h (mm) d (mm) L (mm) Drawing All of the beam specimens in this study are 1.8 m long and Figure (2) illustrates the generated finite element model for the corrugated steel beam. Figure 2 Modeling of Corrugated Steel Beam Selecting Element Type A 4-node shell element S4R (4-node doubly curved general-purpose shell, reduced integration) is adapted in this study to represent the corrugated steel beam. The shell element which has displacement and rotation degrees of freedom (6 D.O.F) at each node is shown in Figure (3). Also, Figure (4) shows the meshed shape of the corrugated steel member editor@iaeme.com

4 Mohammad R.K.M. Al-Badkubi Figure 3 Two Dimensional 4-Node Conventional Shell Element [9]. Figure 4 Meshed Shape of Corrugated Steel Beam Model Constitutive Model of Steel The adapted stress-strain relation for structural steel in this study is shown in Figure (5), where fp, fy and fu are proportional limit, yield stress and ultimate stress of steel respectively. The plastic deformation of steel in this work is described using the Von Mises yielding criterion. Figure 5 Stress-Strain Curve for Steel [10]. During the elastic-plastic stage (a-b), by increase in applied stress, the tangent modulus of elasticity for steel (Est) decreases from Young s modulus (Es) to zero (during the yielding editor@iaeme.com

5 Finite Element Study on Hollow Corrugated Steel Beams under Impact Loading stage b-c).hence, the calculation of (Est) is done by using the formula which proposed by Bleich in (1952): where (σs) is the stress in the steel. Furthermore, the change in steel response to the applied stresses the Poisson's ratio (µs) also changes by increase of stress at the elasticplasticstage. Hence, the Poisson's ratio in this stage is calculated using the following formula which was proposed by Han in (2004): It should be noted that the steel was assumed to have identical properties in tension and compression. The steel parameters which used in this study are shown in Table (3): Table 3:Steel Material Properties. f y (MPa) E s (MPa) ,000 (1) (2) 4. BOUNDARY CONDITIONS In order to obtain a unique solution in analyzing the deformation displacement for the corrugated steel beams the boundary conditions at beam edges are needed. To make sure that the FEM model acts similar to the experimental specimen's condition, the boundary conditions were applied at two edges of the beam[11]. In the experimental system all of the specimens were placed on a supporting steel section frame as shown in Figure (6). Then the specimens were fastened with bolts inside the frame to obtain fixed support as much as possible. Also, this configuration of the boundary conditions restrained any outward deformation. However, any inward deformation could happen since the specimens have hollow section. Figure 6 Experimentally applied Boundary Condition [1]. In the analytical system, the experimental boundary conditions was simulated by resting and bounding the specimens inside a blocked steel section frame. In finite element model a 20-node standard 3D stress reduced integration quadratic hexahedral (brick) element (C3D20R) was used to represent the steel frame elements. The geometry and node locations editor@iaeme.com

6 Mohammad R.K.M. Al-Badkubi for the element type are shown in Figure (7). The original shape of blocked steel section frame and the meshed shape of the frame is shown in Figure (8). Figure 7 20-Node Quadratic Brick Element (C3D20R) [9]. Figure 8 Original and Meshed Shape of Blocked Steel Frame. The blocked steel frame considered to has fixed supports at its outer surfaces, as shown in Figure (9). Also, the contact between the specimens and the steel frame was simulated by using surface to surface contact interaction which defined the inner faces of the frame as master surface and the outer most surface of the corrugated beam as slave surface with finite sliding formulation and the contact property was considered to have rough friction formulation in tangential behavior which do not allow any slip to occur once points are in contact along with hard contact property that will allow separation of the beams from the frame when the deformation occurs. Figure 9 Modeling of the Boundary Condition of the Specimens editor@iaeme.com

7 Finite Element Study on Hollow Corrugated Steel Beams under Impact Loading 5. LOADING SYSTEM In the finite element modeling, the impact force was modeled by using a steel plate to simulate the dropped steel hammer. A 20-node quadratic, reduced integration, hexahedral (brick) element with linear elastic properties for steel material was used to represent the steel plate. The used element is shown in Figure (7), and the steel plate model is shown in Figure (10). Figure 10 Steel Plate Modeling. To simulate the impact force resulting from modeled steel plate there are two different approaches which are as following: 1) Subjecting the steel plate to gravitational acceleration during the solution in order to leave the weight to fall freely. This method recommended to save analysis time by starting at small distance from the top of steel beam and apply initial velocity according to the shifted distance [9]. 2) Simulating the impact force by a pulse such a rectangular or triangular load function, the magnitude of maximum impact force and its duration time has to be taken from the experimental results [9]. In the present study the second method is adopted to simulate the impact force. The magnitude of impact force and its duration has taken from experimentally tested specimen [1] and illustrated as a rectangular pulse shown in Figure (11): Figure 11 Impact Force and Its Magnitude Simulation. So, for both hammer weight the impact force duration has taken to be (0.03 s) and its magnitude taken as (1486 KN) and (1243 KN) for normal weight and half weight hammer, respectively. The kinetic impact energy was calculated by using the following equation: editor@iaeme.com

8 Mohammad R.K.M. Al-Badkubi Where (m) is the steel plate (steel hammer) mass (Kg) and (v) is the velocity of drop steel hammer which is calculated based on the governing velocity formula of a falling object which is defined as: (4) Where (g) is the gravitational acceleration which is about (9.81 m/sce 2 ) and (t) is the travelling time for dropped steel hammer from the starting height of the fall to impact with the steel beam. Also, this time of travel can be calculated if the height of the drop (h) is known using the following formula: ( ) (5) Table (4) shows the kinetic energy calculation results for specimens (1-6): Table 4 Impact Test Level Definition v KE Test No. h (m) m (kg) t (s) (m/s) (kj) TIME-DEFORMATIONCURVES Deformations are measured at mid-span from the upper face of the beam to the lowest location of the deformed beam. By comparing the analytical result curve and experimental result curve as shown in Figure (12), it can be seen that the adapted finite element model is in good agreement with the experimental results. This good agreement shows that the model can be utilized for some other cases other than this experimental case. So, the analytical cases mentioned previously were considered to be investigated. (3) Figure 12 Comparison of Mid Span Deformation History for FEM CB31 Model and Experimental Test editor@iaeme.com

9 Finite Element Study on Hollow Corrugated Steel Beams under Impact Loading From the Figure (12) it can be seen that the finite element deflection curve have about four pulses of vibration which is more than that obtained from the experimental curve which leave the beam at rest after about two pulses of vibration. This response of the beam in FEM shows that in the FEM the computer program can observe the deformation of the model more adequately from the experimental specimens in this very small time interval. Also, it is may be due to the other factors which affect the experimental work more than that in the FEM, such as human error, equipment efficiency, corrugated steel beam making process, etc. Figure (13) shows the comparison between mid-span deformation history curves for FEM models with different corrugated steel thicknesses. Figure 13 Comparison between Mid-Span Deformation History Curves for FEM CB31, CB41 and CB61 Models. As it can be seen from Figure (13) by increasing the corrugated steel beam thickness the mid-span deflection decreases as well as the time period between each pulse ofvibration decreases that will lead to make the beam at rest much sooner than the beam with smaller thickness. Furthermore, it shows that the thinner plates response to vibration more than those of thicker plates which tend to be more resistance to vibration effects. As it was mentioned previously another factor which investigated in this study is the mass of the impact force. By reducing the falling steel hammer weight to half the respond of the corrugated steel beam to this new impact force is shown in following figures. Figure (14): Comparison between Mid-Span Deformation History Curves for FEM CB31 and CB30.5 Models

10 Mohammad R.K.M. Al-Badkubi Figure 15 Comparison between Mid-Span Deformation History Curves for FEM CB41 and CB40.5 Models. Figure 16 Comparison between Mid-Span Deformation History Curves for FEM CB61 and CB60.5 Models. From Figures (14, 15 and 16) it can be seen that by decreasing the steel hammer weight to its half original weight, the corrugated steel beams show smaller deflection as mid span as well as smaller time of vibration which leads the beam to be at rest in shorter time compare to beams respond to original hammer weight. As it can be seen from Figure (17) the behavior of steel beams subjected to half weight of original hammer weight is similar to behavior of the beams subjected to original hammer weight which is by increasing the corrugated steel beam thickness the mid-span deflection decreases as well as the time period between each pulse of vibration decreases that will lead to make the beam at rest in shorter timecompared tothinner steel beams

11 Finite Element Study on Hollow Corrugated Steel Beams under Impact Loading Figure 17 Comparison between Mid-Span Deformation History Curves for FEM CB30.5, CB40.5 and CB60.5 Models. The Finite Element Method (FEM) analysis results for maximum mid-span deflection and the impact vibration time are shown in Table (5): Beam No. Table 5 FEM Test Results. Beam Symbol Δ max (mm) 1 CB CB CB CB CB CB Vibration Time (s) 7. FAILURE DEFORMATION Figures (18-24)illustrate the corrugated steel beam deformation shape due to the application of the impact load for tested beams in finite element analysis model as well as experimentally tested beam. Figure 18 Residual Failure Deformation for Experimentally Tested CB31 [1] editor@iaeme.com

12 Mohammad R.K.M. Al-Badkubi Figure 19 Residual Failure Deformation for FEM Tested CB31. Figure 20 Residual Failure Deformation for FEM Tested CB41. Figure 21 Residual Failure Deformation for FEM Tested CB61. Figure 22 Residual Failure Deformation for FEM Tested CB

13 Finite Element Study on Hollow Corrugated Steel Beams under Impact Loading Figure 23 Residual Failure Deformation for FEM Tested CB40.5. Figure 24 Residual Failure Deformation for FEM Tested CB60.5. By comparing the experimental failure shape with finite element failure shape Figures (18) and (19), it can be seen that the local deformation of the beam due to the applied load as well as global bent in the beam are very similar. Also, by comparing failure shape of Figures (19) to (24), it can be seen that when the corrugated steel beam thickness increases the overall behavior of the beam enhanced due to the increase in steel section strength. This enhancement make it possible for the beam to utilizes the strength of the whole beam in resisting the applied impact load and make the load distributed in the whole section rather than just little area around and under the impact load steel hammer. 8. CONCLUSIONS In this paper, an analytical study on hollow corrugated steel beams under impact loading is performed by using a nonlinear finite element computer program (Abaqus). Based on the results obtained by testing simulated steel beam models, the following conclusions can be obtained: 1. The general behavior of the finite element models represented by the mid span deflection - time history curves show good agreement with the experimentally tested result curve. However, the finite element models tend to be slightly stiffer than the experimental beam in the linear stage of respond. 2.for normal weight steel hammer by increasing the corrugated steel beam thicknesses from (3 mm) to (4 mm) and (6 mm), the maximum mid-span deflection decreases about (13.4 %) and (29.3 %), respectively.also, the vibration time decreases about (20.4 %) and (36.12 %) for (4mm) and (6mm) respectively compared to (3 mm) beam thickness. 3. for half weight steel hammer by increasing the corrugated steel beam thicknesses from (3 mm) to (4 mm) and (6 mm), the maximum mid-span deflection decreases about (9.4 %) and editor@iaeme.com

14 Mohammad R.K.M. Al-Badkubi (19.72 %), respectively. Also, the vibration time decreases about (30.7 %) and (45.9 %) for (4mm) and (6mm) respectively compared to (3 mm) beam thickness. 4. By using half weight steel hammer there is reduction in maximum mid span deflection and vibration time about (32.6 %) and (36.34 %) for beam thickness (3 mm) and about (29.5 %) and (44.6 %) for beam thickness (4 mm) and about (23.4 %) and (46.12 %) for beam thickness (6 mm), respectively. CONFLICT OF INTEREST SATEMENT On behalf of all authors, the corresponding author states that there is no conflict of interest. REFERENCES [1] Mohammad Nassirnia, Amin Heidarpour, Xiao-Ling Zhao, "Experimental Behavior of Innovative Hollow Corrugated Columns under Lateral Impact Loading", International Symposium on Plasticity and Impact Mechanics, Procedia Engineering 173 (2017) [2] H. Qu, G. Li, S. Chen, J. Sun, M.A. Sozen, "Analysis of Circular Concrete-Filled Steel Tube Specimen under Lateral Impact", Adv. Struct. Eng., 14 (2011) [3] Mohammad Nassirnia, Amin Heidarpour, X.-L. Zhao, J. Minkkinen, "Innovative Hollow Columns Comprising Corrugated Plates and Ultra-High-Strength Steel Tubes", Thin- Walled Structures, 101 (2016) [4] G. Ren, Z. Li, "Impact Force Response of Short Concrete Filled Steel Tubular Columns under Axial Load", International Journal of Modem Physics B, 22 (2008) [5] Mohammad Nassirnia, Amin Heidarpour, X.-L. Zhao, J. Minkkinen, "Stability Behavior of Innovative Fabricated Columns Cosisting of Mild-Steel Corrugated Plates", in: 7 th European Conference on Steel and Composite Structures, Naples, (2014). [6] M. Farahi, Amin Heidarpour, X.-L. Zhao, R. Al0Mahaidi, "Compressive Behavior of Concrete-Filled Double-Skin Sections Consisting of Corrugated Plates", Engineering Structures, 111 (2016) [7] Mohammad Nassirnia, Amin Heidarpour, X.L. Zhao, J. Minkkinen, "Innovative Corrugated Hollow Columns Utilizing Ultra High Strength Steel Tubes", in: 15 th International Symposium on Tubular Structures, Rio de Janeiro, (2015). [8] W. Li, D. Wang, C.-M. Hu, L.-H Han, X.-L. Zhao, "Behavior of Grout-Filled Double Skin Steel Tubular T-Joints under Impact Loads", in: 8 th International Conference on Advances in Steel Structures, Lisbon, Portugal, (2015). [9] Abaqus (6.14-4), "Analysis User's Manual", U.S.A. (2014). [10] F. W. Lu, S. P. Li and Guojun Sun, "Nonlinear Equivalent Simulation of Mechanical Properties of Expansive Concrete-Filled Steel Tube Columns", Shanghai Jiao Tong University, Advances in Structural Engineering Vol. 10, No. 3, (2007) [11] K.N.Kadhim & Hassan I." Development An Equations For Flow Over Weirs Using Mnlr And Cfd Simulation Approaches" International Journal of Civil Engineering and Technology.Volume 9, Issue 3, March 2018, pp editor@iaeme.com