Hybrid Simulation Method for a Structure Subjected to Fire. and its Application to a Steel Frame

Transcription

1 1 2 Hybrid Simulation Method for a Structure Subjected to Fire and its Application to a Steel Frame Xuguang Wang, Graduate Research Assistant, Department of Civil Engineering, University of Toronto. xuguang.wang@mail.utoronto.ca Robin E. Kim, Ph.D., Research Specialist, Multi Disaster Countermeasure Organization, Korea Institute of Civil Engineering and Building Technology. robineunjukim@kict.re.kr Oh-Sung Kwon, Ph.D., Associate Professor, Department of Civil Engineering, University of Toronto. os.kwon@utoronto.ca. Corresponding author. Inhwan Yeo, Ph.D., Research Fellow, Multi Disaster Countermeasure Organization, Korea Institute of Civil Engineering and Building Technology. yeo@kict.re.kr ABSTRACT This paper presents a hybrid fire simulation method for civil structures in which a critical element subject to fire is experimentally tested while the remaining structural system is numerically analyzed simultaneously. The proposed method is different from previous approaches that it is fully validated with full-scale specimen subjected to high temperature and that it is automated displacement-controlled test with deformation error compensation. The two substructures (i.e. an experimental model and a numerical model) are integrated through network to enforce displacement compatibility and force equilibrium. Then, the developed simulation method is applied to a fire simulation of a steel moment resisting frame where one of the columns is assumed to be under temperature load following ISO834 fire curve. The results show that the proposed hybrid simulation method can replicate the numerical prediction, thus can be applied to 1

2 more challenging structural systems, such as the structural behaviour under fire load, which is computationally difficult using numerical models. Keywords: hybrid simulation, fire simulation, structural collapse INTRODUCTION There are largely two approaches for the design and selection of fire resistance for structural elements: prescriptive method and performance based method. In the prescriptive method, structural elements are required to have a certain level of fire resistance rating, which depends on occupancy types, height and area of the building, and construction type. In this method, possible fire scenarios or interaction between structural elements subject to elevated temperature with the remaining structural system is not considered. The prescriptive approach requires that each structural element maintain its functionality, such as insulation, integrity, and load carrying capacity (Wang 2002), when subjected to a fire curve specified in standards such as CAN/ULC- S101 (2014), ASTM E119 (2016), or ISO834 (ISO, 2014). While the prescriptive method is convenient, conservative, and applicable to majority of buildings, the method can be too restrictive limiting the creativity of architects and engineers. In addition, the standard fire testing is also carried out with idealized boundary conditions which cannot capture redistribution of loads when an element subject to fire undergoes thermal expansion or inelastic deformation. On the other hand, the performance based method considers a potential fire scenario, analyzes heat transfer from the fire to structural elements, and simulates the interaction between the structural elements subjected to high temperature with the rest of the structural system. However, numerical modelling of structural elements at an elevated temperature can be very challenging because one needs to model heat transfer through insulation barrier properly as well as the behaviour of structural material at the elevated temperature. Because the accuracy of the 2

3 element model impacts the accuracy of the evaluated performance of a structural system, the performance based method can benefit from experimental tests by validating the numerical model or by directly integrating a physical specimen with a structural system model. Numerous researchers performed element level fire testing of structural member such as tests of unprotected steel columns (Wainman and Kirby 1988), a database of 156 full-scale experimental tests on steel columns (Franssen et al. 1998), 10 full-scale fire endurance tests on high-strength concrete (Kodur et al. 2000), among many others. These element level tests cannot consider proper boundary conditions, especially when the structural element subjected to fire interact with the rest of the structural system. Idealized system level tests were also carried out and have been extensively used to verify various numerical modelling approaches (Rubert and Schaumann 1986). There were limited number of full scale testing of a structure in fire such as the Cardington Research Program in Bedfordshire, England in the mid-1990s (Wang et al. 2013). While full scale fire tests are most realistic, they are very restrictive because of required costs and testing facility to carry out a test. In the recent years, a hybrid fire simulation method has been developed in which a structural element subjected to fire is tested in a fire test laboratory while the remaining structural system is numerically simulated at each time step. These two substructures are integrated to ensure compatibility and equilibrium at the interface of the two substructures. In comparison with purely numerical fire simulation, the hybrid fire simulation method does not require large modelling assumptions for the structural element in fire. The first hybrid fire simulation was reported by Mostafaei (2013). In the study, a 6-storey reinforced concrete building with a fire compartment in the centre of the first floor was tested under thermal and mechanical loading. The column in the centre of the fire compartment was the physical specimen tested in the furnace facility, and the rest 3

4 of the building was simulated numerically using a structural analysis software. In the experiment, a CAN/ULC-S101 temperature curve was applied to the experimental specimen, which was subject to gravity load calculated using the structural analysis software. At every five minutes, the deformation of the column was measured, which was manually applied to the structural model of the system. Then, the reaction force at the boundary was applied back to the experimental specimen. This process was repeated manually. More recently, the first fully automated hybrid simulation was carried out at the Swiss Federal Institute of Technology (ETH) Zürich by Whyte et al. (2016). The hybrid simulation software, Open-source Framework for Experimental Setup and Control (OpenFresco 2015), was modified for hybrid fire testing. The experiment was carried out as a proof of concept test with a 75 mm long specimen in the elastic range subjected up to approximately 200 C of temperature. While it was the first fully automated hybrid fire simulation, the methodology needs to be further validated for large-scale specimens subjected to realistic temperature load. The other hybrid fire testing method based on finite element tearing and interconnecting method was proposed by Sauca et al. (2016). The method is fully automated and displacementcontrolled. At each load increment, the stiffness of the sub-structure is measured and used to update the stiffness matrix of the entire structure. A series of numerical simulations with different time step length and stiffness ratio was carried out to validate the method. In the numerical simulations, the integration model was defined as a stiffness matrix and the sub-structure model was modeled in the FE software, SAFIR. However, the hybrid simulation with physical specimen was failed. The deformation from the loading system was one of the major obstacles for their test. This paper presents a hybrid (experimental-numerical) fire simulation method and its application to fire performance assessment of a full-scale steel moment resisting frame (MRF) 4

5 Substructure Element UTNP Library UTNP Library NICON: Network Interface Program subject to ISO834 standard fire curve. The proposed method adopts fully-automated displacement control with displacement error compensation. In comparison with Mostafaei (2013), the proposed method is automated and displacement-controlled. In comparison with Whyte et al. (2016), the proposed method is fully validated with high temperature and a full scale specimen. In the following, a general methodology in conducting hybrid fire simulation is presented and the verification of the approach using a steel moment resisting frame is followed PROPOSED METHOD In the fire engineering, the full performance based design (PBD) approach requires three stages: Stage 1 - definition of design fire, Stage 2 - calculation of heat transfer from design fire to surrounding structural members, and Stage 3 - structural assessment subjected to the heat (CASE Fire Protection Committee 2008). Each stage is discussed in the following section including how the stage is considered in the proposed hybrid fire simulation. The overview of the architecture of the simulation is illustrated in Figure 1. B Stage 2: Heat Transfer Analysis Numerical solution of Eq. (1) Structural temperature profile, A Stage 1: Definition of Design Fire: Standard curve, parametric curve, or fire simulation Gas temperature profile, E F G C Furnace Controller D Furnace Stage 3: Nonlinear Structural Analysis Numerical solution of Eq. (2) Ethernet G H I Analog IO Actuator Controller PID Loop PID Loop J Specimen Actuator UT-SIM Framework Figure 1. Stages of hybrid fire simulation 5

6 Stage 1. Definition of Design Fire In the prescriptive design method, a standard fire curve is used in the first stage. In the PBD method, either standard fire curve or various fire scenarios, such as fully developed fire, localized fire, or external flaming can be considered (CASE Fire Protection Committee 2008). The fire scenario depends on many factors such as fuel amount, type of fuel, openings, etc. which can be considered either using parametric fire curves or fire spread simulations using a specialized software such as Fire Dynamics Simulator (McGrattan et al. 2013). The scope of the presented study aims at developing a hybrid simulation methodology for Stage 3. Thus, the fire scenario is idealized; only one column in a structure is subjected to localized fire which is represented with ISO834 fire curve (ISO, 2014), and all other structural elements are surrounded with gas at ambient temperature. The standard fire curve from Stage 1 (T g (t) from Block A in Figure 1) is used to control gas temperature of furnace (Block C) and to predict specimen temperature and the temperature of the rest of the structural system through Stage 2 heat transfer analysis (Block B) Stage 2. Heat Transfer Analysis Once a fire scenario is defined, heat transfer analysis is carried out. Unless there is extremely large deformation such as total collapse during Stage 3, the result of heat transfer analysis does not influence the definition of design fire. Thus, the outcome of Stage 1 (i.e. T g (t) from Block A) can be sequentially used in the Stage 2 (i.e. heat transfer analysis, Block B). In the same way, unless there is large deformation, heat induced vibration, or vibration induced heat, the analyses in Stages 2 and 3 can be sequentially carried out. In the study performed by Whyte et al. (2016), the transient heat transfer analysis was coupled with transient dynamic analysis of a structural system, which is useful if heat induced vibration exists. For typical civil structures 6

7 subjected to fire, however, the two analysis stages can be sequentially carried out. One- dimensional heat transfer analysis is carried out by solving the following heat equation. q = k dt dx + h c(t T ) + σt 4 Eq. (1) where q is the heat flux (W/m 2 ), k is the thermal conductivity (W/m K), dt is the temperature gradient (K/m), h c is the convective heat transfer coefficient (W/m 2 K), T is the temperature of the surrounding fluid (K), σ is the Stefan-Boltzmann constant ( W/m 2 K 4 ), and T is the temperature of the surface (K). Several parameters in Eq. (1) are a function of temperature which makes the differential equation a nonlinear function. The three terms on the right hand side of the equation considers conduction, convection, and radiation, respectively. Three-dimensional version of Eq. (1) can be solved using a general purpose finite element analysis tool. Once the heat equation is solved, temperature history at various locations in the structure, T s (t), can be obtained. dx Stage 3. Nonlinear Structural Analysis with Temperature Load This stage involves numerical simulation of structural behaviour subjected to temperature load. The temperature load for the most part of a structural system is numerically evaluated in Stage 2 while the temperature load for a tested specimen is experimentally imposed via furnace (Block D in Figure 1). Because the temperature load is applied slowly for the case of fire in building structures, the governing equation can be expressed without time-dependent terms such as inertial force or damping force: F(u, T) = f E Eq. (2) where F is a restoring force vector which is a function of displacement u and temperature T at each degree of freedom. The right hand side, f E, is an applied external force vector which is time- invariant gravity load in this study. If temperature varies rapidly which induce vibration, such as 7

8 thin foil subjected to large heat influx, Eq. (2) can be replaced with an equation of motion including temperature term. The material properties such as modulus, E, yield strength, Fy, and thermal expansion coefficient, α, are nonlinear function of temperature. Thus, Eq. (2) needs to be solved numerically using a nonlinear solution scheme. In a hybrid fire simulation, a part of the force vector is measured from an experimental specimen. Thus, Eq. (2), can be rewritten as F N (u, T) + F E (u, T) = f E Eq. (3) where F N and F E are force vectors from a numerical model and a physical specimen, respectively. At each time step, the displacement increment is calculated as below: u = k 1 (F N (u, T) + F E (u, T) f E ) Eq. (4) where k is a stiffness matrix which is a linearized relationship between the displacement and force vectors and the term in the parenthesis on the right hand side is an unbalanced force vector. The displacement increment, u, is imposed to a physical specimen and the remaining structural system. Then the restoring forces, F N and F E, are evaluated. In the Newton-Raphson method, this process is iterated until a predefined convergence criteria is met. Ideally, if k is re-evaluated at each time step considering the temperature- and path-dependent property of materials, the equilibrium can be reached quickly. In hybrid simulation, however, it is difficult to measure the stiffness of the specimen on the fly. In addition, the number of iterations need to be pre-defined to allow synchronization of temperatures of a numerical model and that of a specimen. Thus, initial stiffness of the structure at the ambient temperature is used to solve Eq. (4). Furthermore, no iterations is carried out within each time step because temperature in the furnace changes continuously, which make it challenging to achieve a converged solution through iterations in each time step. 8

9 Configuration of Hybrid Simulation The hybrid fire simulation is carried out using the UT-SIM framework ( Huang and Kwon n.d., 2015) that has been developed at the University of Toronto. The framework defines a standardized data exchange format and network communication protocol (University of Toronto Networking Protocol, UTNP) to integrate diverse numerical models and experimental equipment. As a part of the framework, a general substructure element (Block F in Figure 1) was developed for Abaqus (Hibbit et al. 2001), in which UTNP library was implemented (Block G). To allow network communication for a general purpose actuator controller, a network interface for controller (NICON, Block H) (Zhan and Kwon 2015) is used, which was written in LabView programming language. NICON receives data from a numerical model as a discrete command and generate voltage ramp with 100 Hz of update rate using a National Instrument hardware, which is fed to an actuator controller (Block I). The ramp and hold time can be specified by a user. The actuator controller runs a proportional integral derivative (PID) loop based on displacement feedback Compensation Scheme for Elastic Deformation of Reaction Frame Figure 2 illustrates the photo of the test setup, schematics of the test setup, and idealized actuation and reaction system. Because of the large stiffness of the specimen, the elastic deformation of the reaction frame is significant, which make it difficult to achieve a desired deformation of the specimen. Thus, an error compensation loop is implemented in the network interface program, NICON. 9

10 feedback displacement from LVDT in the actuator specimen deformation frame deformation feedback force from load cell Ch. 1~4 Reaction frame Ch. 5~8 Specimen Ch. 9~12 Load cell Actuator LVDT 188 (a) Column specimen in a furnace (b) Schematics of the test setup (c) Idealized actuation and reaction system Figure 2. Experimental setup to apply temperature load and target deformation In a column furnace test, it is challenging to instrument displacement transducers directly on the specimen due to the high temperature of the furnace during the test. Furthermore, because the ratio of the specimen s stiffness (k s in Figure 2c) to the reaction frame s stiffness (k f ) is relatively high, non-negligible portion of the actuator s stroke is used to deform the reaction frame. Consequently, if the displacement increment, u, in Eq. (4) is used as a command signal to the actuator controller, which uses the measured actuator s stroke (u m ) as a feedback signal, the actual deformation of the specimen (u s ) becomes less than the target displacement. Thus, in this study, to compensate the displacement control error resulting from the deformation of the reaction frame, an algorithm is developed and implemented in NICON (Block H in Figure 1). The error compensation scheme uses measured force (F E ) to indirectly estimate the deformation of the reaction frame based on the stiffness of the reaction frame (k f ) which is evaluated a priori. The measured displacement of the actuator s LVDT includes deformation of the specimen and the reaction frame: 10

11 u m = u s + u f = u s + k f 1 F E Eq. (5) Thus, assuming that the stiffness of the reaction frame does not change throughout the test, the deformation of a specimen can be estimated as below. u s = u m k f 1 F E Eq. (6) Note that experiment is carried out using a single degree of freedom. However, the above equations are expressed in vector notation to generalize the approach. Based on Eq. (6), the command displacement to the actuator controller can be modified. Because the specimen behaves within the inelastic range at the elevated temperature, the reaction force after imposing new displacement command cannot be predicted in advance. The reaction force at the end of current step remains unknown until the displacement command is imposed to the specimen. Thus, it is inevitable to run iterations within a time increment to compensate the deformation error. An algorithm for the error compensation in Figure 3 is used in this study. Block E in Figure 1. Calculate target displacement, Eq. (4) - < Yes Return to Block E to proceed to next step No Update command displacement Generate command signal Measure feedback force and displacement predicted displacement at step specimen deformation displacement command feedback force from load cell feedback displacement from LVDT allowable error duration to execute one iteration stiffness of reaction frame Evaluate specimen deformation, Eq. (6)

12 214 Figure 3. An algorithm to compensate the elastic deformation of the reaction frame Synchronization of Temperature of Numerical Model and Test Specimen The heat transfer analysis (Stage 2, Block B in Figure 1) and nonlinear structural analysis (Stage 3, Block E) are carried out sequentially using general purpose finite element analysis software, Abaqus (Hibbit et al. 2001). The temperature history of structural elements, Ts(t), from the heat transfer analysis (Block B) is used in the nonlinear structural analysis (Block E). The temperature in the furnace is controlled using the gas temperature history, Tg(t), from the design fire (Block A). The furnace controller runs PID control loop to achieve the target gas temperature, Tg(t) using the feedback temperature from furnace, T gm (t). The temperature history between the numerical model and the furnace need to be synchronized in time. In this study, the analysis time interval is controlled in NICON by returning the measured force after predefined duration, t, after NICON (Block H) receives target displacement from the analysis program (Block E). If the elastic deformation compensation loop is used, each iteration takes δt. After predefined number of iterations, NICON stays idle until t of time is reached. Figure 4 illustrates overall scheme to synchronize numerical analysis time step with the actual experiment. It is worth noting that while the target displacement is determined in the beginning of step n + 1, the temperature in the furnace continuously varies as the furnace temperature cannot be controlled in a discrete manner. Thus, the error compensation scheme does not always provide a stable solution as will be discussed later. 12

13 Displacement, u Specimen temperature, T Tolerance Iterations for elastic deformation compensation idle 232 -, analysis time increment Time step 233 Figure 4. Timing control for hybrid fire simulation NUMERICAL MODEL AND TESTED ELEMENT OF A REFERENCE STRUCTURE Reference Structure: Steel Moment Resisting Frame The reference structure is a 4-story steel frame building with a symmetrical floor plan presented in Jin and El-Tawil (2005). The perimeter frames of the building were designed as moment frames with reduced beam sections. The spans of each bay is 9.14 m. Storey height is 3.66 m except the first floor which is 4.84 m. Section dimensions and the elevation of the steel frame are presented in Figure 5a. The middle column on the 1 st floor is replaced with a physical specimen in the hybrid fire simulation m 3.66 m 3.66 m 4.84 m W14x74 W14x99 W14x193 W14x233 W14x74 W24x68 W27x94 W14x176 W27x114 W14x311 W33x130 W14x kn/m 35.6 kn/m 35.7 kn/m 35.8 kn/m Insulated End Insulated End 9.14 m 9.14 m 9.14 m 9.14 m 242 (a) Structural Layout (b) Heat Transfer Model for Single Column (HT Model 1) (c) Heat Transfer Model for the Reference Structure (HT Model 2) 13

14 243 Figure 5. Reference structure and numerical model for heat transfer analysis Applied Gravity and Temperature Loads during Hybrid Simulations The building used in this study is subjected to gravity load according to the load combination in the design prevision. Combined gravity loads of each floor are presented in Figure 5a. The gravity loads are applied in the numerical model, which is transferred to the experimental specimen during hybrid simulation. During the hybrid simulation, the gravity loads are applied in 55 load increments. Temperature load is applied after the gravity load is fully imposed to the structure. The gravity load in the numerical model remained constant during the hybrid fire simulation Numerical Models Numerical models for heat transfer analysis Two numerical models are developed for heat transfer analysis as shown in Figure 5b and c. The first model is to simulate the heat transfer between the hot air in the furnace and the tested column (Figure 5b). The column is modeled using 3D 20-node quadratic isoperimetric elements in Abaqus (DC3D20 element). The top and bottom of the column are assumed to be thermally insulated. Both thermal convection and heat radiation are considered for heat exchange between the column and the hot gas in the furnace. Heat conduction within the column is also considered. The temperature history of the hot air follows the ISO834 fire curve. The temperature history of the column is taken as the average temperature history on a cross section. The temperature history at the top of the column is applied to the numerical model (HT model 2 in Figure 5c) for heat transfer analysis. For the rest of the reference structure, it is assumed that all members are well insulated, so the temperature of the members are not affected by convection or radiation. With this 14

15 assumptions, only the heat conduction within and between the members are modeled for the entire reference structure. For the heat conduction analysis of the structure, 2D linear heat transfer link elements (DC1D2) are used. To observe the heat transfer behaviour near the tested column, nodes on the members adjacent to the tested column are defined at every 1/10 of the member length as shown in Figure 5c. Note that entire steel moment resisting frame is modelled but only the bay with fire scenario is presented in Figure 5c for clarity. The thermal properties used in the models are based on Eurocode 3 and summarized in Table 1. Table 1. Material Properties for Heat Transfer Analysis (Eurocode 3). Thermal Properties Values Temperature Range ( o C) Density, ρ (kg/m 3 ) 7580 constant T T E-10 T 3 20 < T < 600 Specific Heat, c (J/Kg/K) /(378-T) 600 < T < (T-731) 735 < T < < T < 1200 Convection Coefficient, h c (W/m 2 /K) 25 constant Emissivity, ε 0.5 constant Conductivity, k (W/m/K) E-3T 20 < T < < T < 1200 Stefan-Boltzmann Constant, σ (W/m 2 /K 4 ) 5.67E-08 Numerical models for nonlinear structural analysis with temperature load constant To evaluate force and displacement history that the specimen may experience during the hybrid fire simulation, the entire structure is first numerically analyzed before running the hybrid simulation. In addition, the numerically predicted response of the structure is used for verifying the experimental results. In the numerical model, all connections between frame elements are assumed as the fixed connection since the frame is a moment resisting frame. The thermal expansion of the steel members is modeled by applying the temperature history of the structure 15

16 Raductio Factor Thermal Strain Rate Stress (Mpa) obtained from the heat transfer models as previously mentioned. The numerical model for the hybrid simulation is the same model as the Abaqus standalone model except that the tested column is substituted with a substructure element developed in-house (Block F in Figure 1) to allow data exchange between the numerical model and the physical specimen. The initial stiffness of the substructure element is based on the material properties at 20 o C and the geometry of the column. The material properties are defined based on Eurocode 3 for steel under elevated temperature. The reduction of the elastic modulus and yielding stress of the specimen with temperature is shown in Figure 6a. The thermal strain, as suggested in Eurocode 3, is also presented in Figure 6a. The stress-strain relationship in the plastic range are presented in Figure 6b Fy E ε Temperature C 600 C 700 C Plastic Strain 291 (a) Reduction factors and thermal strain (b) Stress-plastic strain relationship 292 Figure 6. Material properties used in the numerical analysis Test Specimen A steel plate is welded at the top and bottom of the column specimen. The bottom plate of the specimen is bolted at the loading arm of the actuator. Before the top plate is bolted to the reaction frame, fast curing mortar is used to develop full contact between the top plate and the reaction frame. As shown in Figure 2, three groups of thermocouples are instrumented at each quarter along the height of the column. Each group contains 4 thermocouples to measure the average temperature of the specimen along the cross sections. 16

17 EXPERIMENTAL CASES AND RESULTS A series of experiments were carried out to validate the hybrid fire simulation method. The test cases are listed in Table 2. The Cases A to C are preliminary testes to validate heat transfer analysis (Test A), evaluate stiffness of the reaction frame (Test B), and to validate error compensation scheme (Test C). The Cases D and E are hybrid simulations. Table 2. Test Cases 306 Test case A B C D E Objective Gas Temperature Load Validation of heat transfer analysis of a single column Stiffness evaluation of reaction frame Validation of error compensation scheme Hybrid fire simulation Hybrid fire simulation ISO curve up to 910 C followed by cooling phase Ambient Ambient ISO curve up to 910 C followed by cooling phase ISO curve up to 910 C followed by cooling phase Not applied. Up to 4.8 MN Up to 4.8 MN Gravity load Gravity load Hybrid Simulation Parameters - Gravity load only on a single column k = 369 kn/mm t = 3 sec δt ramp + δt hold = 1.2 sec No. of iterations = 0 k = 2,100 kn/mm t = 6 sec δt ramp + δt hold = 0.5 sec No. of iterations = Test A: Heat transfer analysis of a single column: heating and cooling phase The objective of Test A is to validate the heat transfer analysis of a single column. The test specimen was heated using the ISO standard temperature curve. The temperature of the furnace was increased until the average temperature of the specimen reached 740 C. Then, the furnace was turned off and the gate was opened to cool the specimen. As shown in Figure 7a, the furnace temperature (labelled as Gas ) matches well with the ISO 834 fire curve (labelled as ISO Curve ). The heating phase of the column was numerically modeled in Abaqus (HT model 1 in Figure 5b) as well as with hand calculation using a spreadsheet. The numerically predicted specimen temperature (labelled as Numerical ) matches well with the sectional average temperate 17

18 1210 Temperature, C Temperature, C at three locations. It can be noted that the temperatures at three locations of the specimen (Ch. 1~4, 5~8, and 9~12) are also very similar to each other which indicates that the temperature of the column increased uniformly. The cooling phase was not numerically modeled because the heat exchange between the hot air in the furnace and the ambient air in the lab cannot be accurately modelled. Consequently, the temperature history obtained from Test A is used for the heat conduction analysis of the rest of the frame. Figure 7b compares the temperature history of various points in the structure. The specimen temperature in Figure 7b is the average temperature of the specimen obtained from Test A. The temperature of the beams and the column adjacent to the tested column does not increase much because heat dissipates quickly to the rest of the frame and because all other members are assumed to be surrounded with gas with ambient temperature Ch. 1~ Avg. ch 1~4 Avg. ch 5~8 Avg. ch 9~12 Ch. 5~ Gas Time, sec Ch. 9~ Points 2, 3, 6, Time, sec (a) Temperature profile of column: numerical prediction vs experimental results (b) Temperature history of adjacent elements 326 Figure 7. Temperature history of tested column and at various points in the structure Test B: Evaluation of stiffness of reaction frame The objective of Test B is to evaluate the stiffness of the reaction frame, k f. The specimen was loaded within the elastic range in the ambient temperature. The load was increased from 0 to -4,800 kn in ten steps and decreased back to 0 in the following ten steps. Reaction force and total displacement of the reaction frame and the specimen were measured. The test result is presented 18

19 Force, kn Expected force range Displacement, mm in Figure 8 (a) which shows nonlinear elastic behaviour at low load and linear elastic behaviour as the force is greater than -1,000 kn. The nonlinear elastic behaviour may be due to the mortar filler that is used to develop full contact between the top of the specimen and the reaction frame. To minimize the influence of the nonlinear response in the beginning of the hybrid simulation, the column was loaded with -1,000 kn of axial force initially (i.e., before the gravity load was applied). Thus, the physical specimen experienced around 1,000 kn more axial compression than reported in the hybrid simulation. Using the linear region of the test result, the stiffness of the reaction frame-specimen system (i.e. kf ks/(kf+ks)) was found to be 369 kn/mm. The stiffness of the specimen (ks = 2,100 kn/mm) was calculated based on the material property and the geometry of the specimen. Then, the stiffness of the reaction frame is calculated (kf = 450 kn/mm). This value was used for elastic deformation error compensation. It is worth noting that the stiffness of the reaction frame is small because the reaction frame was originally designed for force-controlled testing of structural components where the stiffness of the system is not important kn/m Specimen develops full contact with the loading frame Displacement, mm Analysis time step Target Command Estimated Target increment Command increment Time, sec (a) Measured force-deformation (b) Verification of error compensation relationship (Test B) scheme (Test C) 347 Figure 8. Elastic behaviour of specimen and experimental setup 19

20 Test C: Hybrid simulation of a single column subjected to gravity load only The objective of Test C is to validate the error compensation scheme by loading the specimen under ambient temperature. The test was carried out as a hybrid simulation where the load was applied to a numerical model and the column is represented as a physical specimen. The test was coordinated with NICON with the error compensation scheme summarized in Figure 3. The test result is presented in Figure 8 (b) where Target indicates target command from the numerical model (u t, n+1 in Figure 3), Command indicates the command sent from NICON to the actuator controller (u c ), and Estimated means the estimated specimen deformation (u s ) using Eq. (6). As can be observed from the figure, the estimated deformation is very close to the target deformation even though there is some noise in the response. In addition, large difference between the command to the actuator and the estimated specimen deformation are shown due to the low stiffness of the reaction frame Test D: Hybrid fire simulation without error compensation for elastic deformation The objective of Test D is to validate the overall hybrid simulation method without considering the elastic deformation of the reaction frame. Thus, in the hybrid simulation, the column is assumed to be supported on elastic spring, which is represented with the stiffness of the reaction frame (kf). In the hybrid simulation, gravity loads were applied first and then followed by temperature history both in the numerical model and the physical specimen. The time increment ( t) for the numerical model during temperature loading was 3 sec. Ramp and hold time (δt ramp + δt hold ) of 1.2 sec was used to impose the target displacement to the specimen. The elastic deformation error compensation scheme was turned off in this test because the stiffness of the reaction frame was assumed to be a part of the structural system (i.e. elastic support.) To find 20

21 displacement increment in Eq. (4), the initial stiffness of the specimen-reaction frame system (i.e. two springs in series) is defined in Abaqus. Test results are presented in Figure 9 which will be discussed in Section Test E: Hybrid fire simulation with error compensation Test E is similar to Test D except that the error compensation scheme for elastic deformation of the reaction frame was turned on. The stiffness of the specimen at ambient temperature was defined in Abaqus to find displacement increment in Eq. (4). Loading conditions and the thermal boundary conditions are identical to those of Test D. The time increment of the numerical model ( t) was 6 seconds in this test to give sufficient time for five iterations for elastic deformation compensation. The ramp time and the hold time of each iteration was 0.1 sec and 0.4 sec, respectively, to ensure all iterations could be completed within the time increment. The overall results of Test E are presented in Figure 9. 21

22 (a) Test D (b) Test E Heating Cooling Heating Cooling (c) mm mm (d) mm mm mm mm mm mm (e) (f) kn kn kn kn kn kn kn (g) 300 C 16 C Gravity load (h) 264 C 14 C 16 C Plastic deformation Heating Cooling 732 C Heating 667 C 14 C 743 C 674 C Figure 9. Hybrid simulation results of Tests D and E 22

23 OBSERVATIONS FROM TESTS D AND E Temperature Control In Test D and Test E the gas temperature of the furnace follows well with the ISO834 fire curve as shown in Figure 9a and 9b. In Test D, the temperature from the experiment increased somewhat rapidly in the first 500 sec, but soon converged to the ISO834 fire curve. Similar to Test A, the furnace was turned off when the average specimen temperature was 732 C and 743 C for Tests D and E, respectively. The cooling phase of both tests were similar Gravity Load Stage In Test D, the numerically predicted column deformation (-2.74 mm) after applying gravity load was slightly smaller than the observed deformation (-3.20 mm) from the hybrid simulation as shown in Figure 9c. It is speculated that the mortar fill between the specimen and the reaction frame contributed to the difference even though experiment was started after applying 1,000 kn of compression to minimize the effect of the inelastic behaviour of the mortar. In Test E, the numerically predicted deformation (-0.52 mm) and the result from hybrid simulation (-0.74 mm) were much closer because the elastic deformation of the mortar and the reaction frame is compensated through iterations (see Figure 9d). In Test D, the force that the column experienced after applying gravity load was -1,032 kn and -1,040 kn for hybrid simulation and numerical prediction, respectively (Figure 9e). In Test E, the difference was higher (about 8%, Figure 9f) which is due to the control error in the axial deformation of the specimen. Because of the large stiffness of the specimen, minor difference between target deformation and the actual specimen deformation can lead to large force error. 23

24 Temperature Load - Heating Phase In Test D, the numerically predicted displacement and force histories are close to the result obtained from hybrid simulation, Figure 9c and 9e. At the elevated temperature, the numerically predicted displacement tends to be slightly larger than the result from hybrid simulation. It is speculated that the slight difference is due to the minor difference in the temperature history used in the numerical model and measured temperature during the experiment as shown in Figure 9a. In Test E, the displacement history during the heating phase was very close to the result from hybrid simulation (Figure 9d). However, the force history from hybrid simulation showed quite large fluctuations (Figure 9f). The upper envelop of the force fluctuation follows well with the numerical prediction. The force fluctuation may be due to change of the temperature during the iterations for elastic deformation error compensation. Because of the temperature change, the specimen expanded, which influence measured force, and consequently estimated deformation of the specimen. Even though five iterations were carried out in each time increment, the stable force response was not accurately achieved. While the specimen was still in the heating phase, the displacement and force started decrease at approximately specimen temperature of 670 C due to plastic deformation of the specimen. As shown in Figure 6a, at approximately 670 C, the yield strength of steel reduces to 20% of Fy. In addition, the elastic modules and the relationship between the plastic strain and stress are also changed. After the specimen reached peak force, the experimental results deviate from numerical prediction. It is speculated that the difference are mainly resulted from the 1,000 kn of compression which was imposed to the experimental specimen in the beginning of the test. In addition, there may be some differences in the material behaviour at the elevated temperature, which the authors did not confirm through material testing. 24

25 Temperature Load - Cooling Phase After the furnace was turned off and gate was opened at approximately 3,000 sec from the beginning of tests, the specimen was allowed to cool down which increased the stiffness and strength of the specimen. Thus, as can be observed in Figure 9e and 9f, the rate of force decrease suddenly changed when the gate was opened. At the end of test, the temperature of the specimen was about 300 C and 264 C for Tests D and E, respectively. The specimen developed approximately -9 mm of residual deformation (shortening of the column) at the end of tests. In addition, due to the column shortening, the axial force was reduced to approximately -700 kn Hysteretic Behaviour Figure 9g and 9h present the hysteretic response of the column. The numerically predicted results show almost linear force-deformation relationship even though the column shortened due to yielding at high temperature. Similar trend can be observed from experimental results. However, the hysteretic behaviour at the elevated temperature somewhat deviate from numerical prediction. The main source of difference is the -1,000 kn of compressive force that was imposed in the beginning of the test. The other source could be the material property at the elevated temperature Load Redistribution Table 3 compares variation of member forces for the first storey columns in Figure 5a during the Test E. Column #1 through #5 represents the columns from left to right. The column tested with the physical specimen is Column #3. It can be observed from the table that the axial force in Column #3 is similar to the axial forces of Columns #2 and #4 after applying gravity load at ambient temperature. As the temperature increases, Column #3 carries much higher axial force (2,178 kn) than other members (504~584 kn) due to thermal expansion. At the end of the test, the 25

26 length of the Column #3 is shortened due to the plastic deformation which leads to decrease in the axial force in Column #3 (728 kn) while increase in the axial force in Column # 2 and #4 (1393 kn). It can be noted that summation of all axial forces are not constant. It varies about 2% with reference to the total axial force under ambient temperature. The variation of the total axial force is because of the unbalanced forces which was not fully resolved through iterations. Table 3. Load redistribution during the fire scenario 456 Column Number #1, #5 #3 (specimen) #2, #4 Reaction Force Under Gravity Load at Ambient Temperature Peak during the Heating Phase End of the Test Axial Force (kn) Shear Force (kn) Moment at Bottom (kn-m) Axial Force (kn) Shear Force (kn) Moment at Bottom (kn-m) Axial Force (kn) Shear Force (kn) Moment at Bottom (kn-m) CONCLUSIONS This study develops a hybrid fire simulation method and applied it to a four-storey steel moment resisting frame subjected to a fire scenario defined with ISO834 curve. In the experimental validation, a full-scale column was tested in a laboratory while the rest of the structural system was numerically modelled. The main findings of this study is summarized below The proposed hybrid fire simulation method could predict the behaviour of a steel moment resisting frame. There were minor differences between numerical prediction and experimental results primarily due to the limitations of the experimental setup (i.e. inelastic behaviour of mortar filler, pre-loading with 1,000 kn, elastic deformation of the reaction frame). However, the experimental results show that the developed method can be applied to performance-based fire assessment of a structural system. 26

27 Testing an axially stiff specimen poses a great challenge in the displacement-based hybrid fire simulation. In this study, an error compensation scheme was developed to minimize the impact of elastic deformation of the reaction frame. This method, however, requires further refinement to consider continuous change of furnace temperature during iterations. Numerical models for heat transfer analysis of the structural member could predict the temperature variation of the tested specimen In this study, a steel frame was used to verify the developed hybrid fire simulation method because the material behaviour of steel at elevated temperature is relatively well understood. Because the proposed hybrid fire simulation method is validated through the ideal structure, it is expected that the method can be applied to fire performance assessment of structures where the behaviour of structural elements cannot be easily numerically modelled. The observed force fluctuation issue was primarily due to the large stiffness of the specimen and the increase of thermal strain between analysis time steps. A research is in progress to refine the error compensation method and the control scheme using the continuous displacement-controlled hybrid simulation method based on polynomial extrapolationinterpolation ACKNOWLEDGEMENT The research is financially supported by the Ontario Early Researcher Award and by the National Research Council of Science & Technology (NST) grant by the Korea government (MSIP) (No. CRC KICT) REFERENCES ASTM. (2016). ASTM E119-16a: Standard Test Methods for Fire Tests of Building Construction and Materials. 27

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