Case study of building failure due to buckling of an RC column

Transcription

1 Southern Cross University 23rd Australasian Conference on the Mechanics of Structures and Materials 2014 Case study of building failure due to buckling of an RC column S C. Fan Nanyang Technological University Q J. Yu Nanyang Technological University Publication details Fan, SC, Yu, QJ 2014, 'Case study of building failure due to buckling of an RC column', in ST Smith (ed.), 23rd Australasian Conference on the Mechanics of Structures and Materials (ACMSM23), vol. II, Byron Bay, NSW, 9-12 December, Southern Cross University, Lismore, NSW, pp ISBN: epublications@scu is an electronic repository administered by Southern Cross University Library. Its goal is to capture and preserve the intellectual output of Southern Cross University authors and researchers, and to increase visibility and impact through open access to researchers around the world. For further information please contact epubs@scu.edu.au.

2 23rd Australasian Conference on the Mechanics of Structures and Materials (ACMSM23) Byron Bay, Australia, 9-12 December 2014, S.T. Smith (Ed.) CASE STUDY OF BUILDING FAILURE DUE TO BUCKLING OF AN RC COLUMN S.C. Fan* Protective Technology Research Centre, Nanyang Technological University 50 Nanyang Avenue, , Singapore. (Corresponding Author) Q.J. Yu Protective Technology Research Centre, Nanyang Technological University 50 Nanyang Avenue, , Singapore. ABSTRACT The objective of this case study is to investigate the structural failure of a 20-year old building due to local buckling of a reinforced concrete (RC) column at lower floor. Firstly, the stress history of the concrete and steel rebar in the column is reproduced through analysing the core samples. Secondly, the buckling event is simulated using the computer code, LS-DYNA. The failure mode was successfully reproduced. The simulation would show the process of concrete spalling and buckling of steel re-bars. It agreed well with the failure scene. KEYWORDS RC column, buckling, spalling, cohesive element, numerical simulation. INTRODUCTION Buckling failure of an RC column may lead to collapse of a building. In this study, one RC column is selected to investigate the buckling failure. According to the post investigation, the strength of concrete is much weaker at the central part than the upper/lower parts. At failure, concrete crushing and spalling were observed. Numerical simulation by LS-DYNA is carried out to reproduce the failure scene. It demonstrates the brittle failure of concrete and subsequent buckling failure of rebars at the weaker sections, which was probably derived from poor construction. Techniques to simulate the spalling phenomenon of concrete are to be discussed. Logical reasons to adopt cohesive element will be given. Numerical simulation results will demonstrate its capability. NUMERICAL MODELING Geometry and Finite-element Mesh The RC column is 2.4m high and the section is 1.5m by 0.4m. Considering the symmetry, a model for a quarter geometrical is setup for finite-element analysis. Reinforcement bar is modelled by solid element. In order to reproduce the spalling phenomenon, cohesive element is introduced in the modelling. There are 7 kinds of cohesive elements according to the interface strength, namely, weaker concrete vs. weaker concrete, normal concrete vs. normal concrete, weaker concrete vs. normal concrete, weaker concrete vs. steel, normal concrete vs. steel, steel vs. steel and steel vs. steel cross (this is to simulate the tie-up of crossing steel bars). The finite element model is shown in Figure 1. This work is licensed under the Creative Commons Attribution 4.0 International License. To view a copy of this license, visit

3 ¼ symmetric model (a) Concrete elements (b) Steel elements (c) Cohesive elements for concrete (d) Other cohesive elements Figure 1. Finite-element model for the RC column Simulation of Concrete Spalling In the finite element (FE) method, the fracture simulation is often achieved through element erosion. However, the proper erosion criteria are not easy to determine, and the element erosion process will lead to some losses of material information. An alternative approach is to adopt the nodal-splitting technique to simulate practical fracture problem [Fan et al (2008, 2009)]. In it, the FE mesh is shattered into separate element-size pieces. Then the nodes at the same location are bundled together by a nodal constraint. The bundled nodes will be disintegrated upon a strain-based criterion is met. Prior to the nodal split, the whole FE assembly behaves as a continuum and the nodal displacements are continuous. When nodal split occurs, a cluster of free surfaces are formed immediately along the fracture planes which run along the FE mesh interface. Figure 2 illustrates the situations before and after the nodal split. Figure 2. Illustration of Nodal Split The merit of this approach is simplicity, but the major shortcoming is its inability to simulate nonhomogeneous formation of fractured planes. When a bundled node disintegrates, fractured free surfaces will be formed in all three directions indiscriminately. ACMSM

4 In the following, another alternative approach is adopted. Cohesive elements are put in place at all FE interfaces. It aims at overcoming the inadequacies of erosion and nodal-splitting method, Cohesive Element In this method, the conventional continuous finite elements are first shattered into disjoined elements and then re-connected to each other by cohesive elements. These cohesive elements are inserted along the element interfaces between all the 3D elements in the initial finite-element mesh. Figure 3 defines a typical cohesive element referred as Element type 19 in LS-DYNA. It is an 8-nodes solid element. The mid-surface is defined by the mid-points between the nodal pairs 1-5, 2-6, 3-7, and 4-8. Differing from the normal solid element, the tractions on the mid-surface are defined as functions of the differences of nodal displacements between nodal pairs. Initial volume of the cohesive element may be zero, in which case, the density may be defined in terms of the area embraced by nodes Figure 3. Cohesive element defined in LS-DYNA (LSTC 2007) A fracture surface is formed along the interface between two elements once the corresponding cohesive element fails (i.e., when the maximum fracture energy is exceeded or consumed). Obviously, such cohesive element has a sound physical meaning but it needs a material model to reflect its response. This material model is normally called a cohesive law (or traction-separation law). The fundamental idea for the cohesive law was formulated by Barenblatt (1962) originally for defining the de-cohesion in atomic lattices. More information about the cohesive element implement can be found in Fan et al (2014). Material Model Material models and the accurate parameters are critical for a successful numerical simulation. Apart from the correctness of material model itself, the involved parameters should be easily obtained and reliable. Concrete model The LS-DYNA code supplies quite a few concrete models. Here, the Karagozian & Case (K&C) Concrete Model - Release III is adopted. K&C 3 Rd is a three-invariant model, uses three shear failure surfaces, includes damage and strain-rate effects, and has origins based on the Pseudo-TENSOR Model (Material Type 16). The most significant improvement provided by Release III is a model parameter generation capability, based solely on the unconfined compression strength of the concrete (LSTC 2007). The default parameter in K&C Concrete Model has been calibrated using a well characterized concrete for which uniaxial, biaxial, and triaxial test data in tension and compression were available, including isotropic and uniaxial strain data. Said that, it refers to the well-characterized 45.6 MPa unconfined compression strength concrete derived from Geotechnical & Structures Laboratory of the US Army Engineering Research & Development Center (ERDC). In addition, that original calibration was modified or completed via generally accepted relationships, such as those giving the tensile strength (or modulus of elasticity) as a function of compressive strength. The ACMSM

5 Loading pressure (MPa) constitutive model inputs are trivial, yet the complex responses for many different types of material characterization tests, are adequately reproduced. In the present study, the concrete strength in the middle part is weaker and thus stochastically distributed into 9 bins having a mean value of 8 MPa and variance of 4 MPa. The concrete strength in other normal parts is 30 MPa. Reinforcement steel model The reinforcement steel material is assumed isotropic with kinematic hardening plasticity and strain rate. Strain rate effect is calculated using the Cowper and Symonds model which scales the yield stress 1 C with the factor 1 (2004)). The strength of steel is 348 MPa. Cohesive model P, where C = 800 and P = 3.6 (Abramovicz, et al (1986); Maraism, et al The cohesive law or traction law is traction-displacement relation, not the normal stress-strain relation. The cohesive model yields three force resultants (tractions) rather than the usual six stress components. The in-plane shear resultant along the local 1-2 edge replaces the x-stress, the orthogonal in-plane shear resultant replaces the y-stress, and the normal stress resultant replaces the z-stress. In this study, the model MAT_COHESIVE_TH (available in LSTC 2007) is used and a stochastically fracture energy model is implement in the cohesive model of concrete vs concrete. Loading The RC column is first evenly loaded with a constant gravity load acted at the top of column. Then, a small disturbing transient load is added. As such, the value of disturbing load necessary to cause column buckling can be estimated. Figure 4 shows the loading curve adopted in the present study Loading pressure Time (ms) Figure 4. Loading pressure curve ACMSM

6 RESULTS AND DISCUSSIONS Figure 5 shows the simulation results. In it, Figures 5a and 5b show the overall response of RC column and the steel bars at t=0.030 second, respectively. Blow-ups in Figures 5c and 5d highlight the concrete spalling and steel-bar buckling. (a) The overall response (b) Response of reinforced bar (c) Spalling (d) Bar buckling Figure 5. Simulation results of RC column buckling CONCLUSIONS In this paper, buckling of an RC column having a weak central portion is investigated numerically. Cohesive elements are employed to simulate the concrete spalling. Imperfection of concrete is considered through stochastically fracture energy for cohesive elements. Detailed rebar configuration is incorporated. Results clearly demonstrate the capability of the present model in simulating the concrete spalling and rebar buckling. REFERENCES Abramowicz W. and Jones N.(1986) Dynamic Progressive Buckling of Circular and Square Tubes, International Journal of Impact Engineering, Vol. 4, No. 4, pp Barenblatt, G. I. (1962) The mathematical theory of equilibrium cracks in brittle fracture, Adv Appl Mech. 7, pp Fan S.C., Yu Q.J. and Lee C.K. (2014) Simulation of fracture/breakup of Concrete Magazine using Cohesive Element, Materialwissenschaft und Werkstofftechnik (Materials Science and Engineering Technology, Vol. 45, No.5, pp Fan S.C., Yang Y.W. and Yu Q.J., et al.(2008) Parametric Studies and Development of Numerical Solver for Earth-Covered/Uncovered Concrete Magazine. Technical report No.5 for Debris Modeling Study, Singapore, Oct ACMSM

7 Fan S.C., Yu Q.J and Xiong C.,et al. (2009) Case Studies and Design Guidelines for IBD for Earth- Covered/Uncovered Concrete Magazine. Technical report No.7 for Debris Modeling Study, Singapore, Oct LSTC (2007) LSDYNA Keyword User's Manual, Version 971. Marais S.T., Tait R.B., Cloete T.J. and Nurick G.N. (2004) Material testing at high strain rate using split Hopkinson pressure bar, Latin American Journal of Solids and Structures, pp , ACMSM