Using Opensees for Analyzing a 9- Story Steel Building Under Post- Earthquake Fires

Tenth U.S. National Conference on Earthquake Engineering Frontiers of Earthquake Engineering July 21-25, 2014 10NCEE Anchorage, Alaska

USING OPENSEES FOR ANALYZING A 9- STORY STEEL BUILDING UNDER POST- EARTHQUAKE FIRES

N. Elhami Khorasani1 and M. E. M. Garlock2

ABSTRACT

Post-earthquake fires are major hazards with possible intense consequences. Civil engineering design is moving towards the concept of resilient cities, which requires buildings with structural systems to perform adequately after extreme hazards and ensure human safety. Current codes and standards in fire engineering are mainly based on design at the component level and deterministic approaches, where uncertainties in variables are not directly incorporated in the design process. Reliability-based approaches offer better means of evaluating resilience in the face of extreme hazards. But to measure resilience in an earthquake-fire multi-hazard scenario, uncertainties in the system must be captured, and nonlinear analyses must seamlessly transfer from seismic to fire analysis. This paper discusses the successes and challenges of this seamless analysis using the open source software OpenSees. A 9-story steel building with moment resisting frames is subject to fire following earthquake while being modeled in OpenSees. With the newly added fire module in OpenSees, the software has the capacity to perform structural analysis for both seismic and thermal loads. This way, system-level analysis is performed in one software and interaction of members with each other, under both seismic and fire events, is then considered together. The current constitutive material model for steel at elevated temperature does not properly capture behavior in fire following earthquake scenario. The constitutive model is therefore modified to capture effect of plastic strains, and strain reversals during heating or cooling. The resultant moment calculation is also modified to be consistent with other finite element programs and properly capture combined axial load and moment effects. The new model is used to analyze the 9-story building under two earthquake hazard levels and multiple fire locations. Results show that the new constitutive model works well. The sample analyses indicated that the subsequent fire can increase the drift of the column on the perimeter on the order of 0.5% in the lower floors and 1% in the upper floors. Total drifts in FFE did not exceed 2% (including the residual from earthquake) for the scenario studied.

1Graduate Student, Dept. of Civil and Environmental Engineering, Princeton University, Princeton, NJ, 08542 2Associate Professor, Dept. of Civil and Environmental Engineering, Princeton University, Princeton, NJ, 08542

DOI: 10.4231/D3PK0727C Tenth U.S. National Conference on Earthquake Engineering Frontiers of Earthquake Engineering July 21-25, 2014 10NCEE Anchorage, Alaska

Using OpenSees for analyzing a 9-story steel building under post-earthquake fires

N. Elhami Khorasani1 and M. E. M. Garlock2

ABSTRACT

Introduction

Fire following an earthquake is a major hazard in densely populated urban areas in seismic regions. There are historical examples where fire after an earthquake has caused considerable damage to structures. San Francisco 1906 and 1989, Tokyo 1923, and Kobe 1995 are a few of such examples [1]. While the occurrence of an earthquake and its consequences cannot be prevented, proper designs can minimize the damage. In a strong earthquake, buildings designed for seismic regions, may experience plastic deformations but do not collapse. However, such earthquakes may cause major destruction and damage gas and water lines, starting uncontrollable fires. When fire follows an earthquake, buildings with reduced strength or damaged fire protection materials may not have the capacity to resist the subsequent extreme event.

Previous research, performed on structural performance of post-earthquake fires, has studied the problem (1) in different programming environments for seismic and thermal analyses and (2) within a deterministic approach [2 and 3]. The first shortcoming in such approaches is that switching between programs to complete seismic and thermal analyses requires certain

Elhami Khorasani N, Garlock, MEM. Using OpenSees for analyzing a 9-story steel building under post-earthquake fires. Proceedings of the 10th National Conference in Earthquake Engineering, Earthquake Engineering Research Institute, Anchorage, AK, 2014. idealizations, such as ignoring material degradation after earthquake, which would reduce the accuracy of the results. The second concern is that although performance-based guidelines for seismic design of structures have been well established, the available design procedures for fire are fairly new and largely based on perspective codes or performance-based guidelines with deterministic input variables. Yet the available data shows that considerable uncertainty exists in defining fire load density and properties of material at elevated temperatures. Therefore, a reliability approach to evaluating structures in fires is needed.

The work presented in this paper is a step towards developing methodologies for probabilistic analysis of structures under post-earthquake fires. The program OpenSees is used to evaluate performance of a 9-story steel office building under fire and under fire following earthquake (FFE). The thermal module in OpenSees has been recently developed, and the paper illustrates the challenges to seamlessly transfer from seismic to thermal analysis in OpenSees. This paper includes the necessary modifications that the authors applied to the thermal module in OpenSees to make the analysis possible.

Design Description

The geometry and building description of the prototype Moment Resisting Frame (MRF), which will be used for the post-earthquake fire reliability analysis, is based on the SAC steel project. The SAC project included 3, 9, and 20-story prototype buildings located in Los Angeles, Seattle and Boston areas [4]. The buildings were designed as standard offices on both stiff and soft soil. The MRF in the present study is a 9-story frame that is located in downtown Los Angeles and has plan and elevations that are based on SAC buildings but considered only for stiff soil. The MRF is re-designed based on ASCE7-2010 specifications (Minimum Design Loads for Buildings and other Structures).

8 @13 8 ft

5@ 30ft.

18‘

12’ 5@ 30 ft. foundation (pinned) Figure 1: Plan and elevation of the 9-story frame

The floor plan and elevation of the 9-story structure is presented in Fig. 1. The building geometry consists of a square plan with 5 bays, each at 30 ft., in either direction. Girders are spaced at 30 ft while beams are spaced at 10 ft intervals. The 9-story building has a typical floor height of 13 ft with a basement height of 12 ft and ground floor height of 18 ft. The building consists of 4 MRFs on each side that are placed such that biaxial bending is avoided at corners. The MRFs in the two orthogonal directions are identical. The columns are pinned at the foundation, and laterally braced at the ground level. The design procedure is mainly based on the ASCE7 specifications, and the assumed gravity loads are consistent with the assumptions of the SAC models [4]. Seismic loads are according to the Equivalent Lateral Force (ELF) procedure in ASCE7 (2010). The design forces are calculated for the Site Class D (stiff soil). The design checks applied in the design of the MRF are based on the guidelines in the AISC Steel Construction Manual (2010), and AISC Seismic Provisions for Structural Steel Buildings (2010). The frame has a period of 2.0 seconds. Table 1 summarizes design of the 9-story MRF.

Table 1: Design of the 9-story frame based on ASCE 7 -10 Interior Exterior Level Beam t t Column doubler, INT Column doubler, EXT 9-roof W24X76 W14X342 0.00 W14X257 0.00 8-9 W30X108 W14X342 0.47 W14X257 0.00 7-8 W33X169 W14X455 0.92 W14X370 0.00 6-7 W33X169 W14X455 0.92 W14X370 0.00 5-6 W36X194 W14X550 0.70 W14X500 0.00 4-5 W36X194 W14X550 0.70 W14X500 0.00 3-4 W36X194 W14X605 0.38 W14X550 0.00 2-3 W36X210 W14X605 0.63 W14X550 0.00 1-2 W36X210 W14X665 0.45 W14X605 0.00 Basement-1 W36X210 W14X665 0.45 W14X605 0.00

Modeling in OpenSees

The program OpenSees is used to model and analyze the 9-story MRF under earthquake and fire. The OpenSees framework is an object-oriented software that was developed at the University of California, Berkeley, mainly for nonlinear analysis of structures under seismic loading. Recently, a fire module has been added to the program that makes thermal modeling possible [5]. This section presents the analytical model of the 9-story for both fire and FFE analysis.

Seismic Modeling

Fig. 2 shows the developed analytical model for the 9-story frame in OpenSees. The nonlinear behavior of the 9-story building under dynamic loading is modeled by the concentrated plasticity concept and using rotational springs. The frame is modeled with elastic beam-column elements that are connected with zero-length elements. The zero-length elements serve as the rotational springs that follow a bilinear hysteretic response based on Modified Ibarra Krawinkler Deterioration Model [6, 7, and 8]. Subject to seismic excitations, plastic hinges are formed in beams at an offset from the beam-column joints. The offset can be estimated as 1/3rd of the beam depth from the column edge (according to FEMA-350). Panel zones are also modeled to capture the shear distortion in beam-column joints [9]. Therefore, rotational springs are placed at a distance of 1/3rd of the beam depth from the panel zone edge.

A leaning-column that carries gravity load is linked to the frame to simulate P-Delta effects. The leaning-column is modeled with elastic beam-column elements with a large cross section area and moment of inertia to capture the effect of gravity columns on response of the frame. The beam-column elements are connected by rotational springs with very small rotational stiffness. This ensures that the leaning-column does not capture significant moment. Finally, the leaning column is connected to the frame by truss elements that are axially rigid.

Figure 2. (Left): Analytical model in OpenSees for seismic and thermal analysis, (Right): % drift at the end of earthquake.

Thermal Modeling

To meet the objective of this study, a post-earthquake fire analysis must be completed; and the most efficient means of doing this analysis is to seamlessly transition from seismic to thermal in OpenSees environment. However, thermal modeling in OpenSees is only possible with “DispBeamColumn2dThermal” type element [10]. Therefore, the seismic model discussed above uses various other element types, including zero-length deterioration spring elements to capture nonlinear behavior. The approach in this study is to model the 9-story frame using the seismic modeling with the springs, except for the beams and columns that are assumed to be heated in a fire (which will be modeled with DispBeamColumn2dThermal elements) as shown in Fig. 2. The DispBeamColumn2dThermal element is defined using fibers and considers plasticity along its length. A validation study was performed to confirm the required number of fibers in the cross section. The thermal element is modeled using 8 fibers in the web, and 4 fibers in each flange. The element requires steel inputs through the depth of the cross section. The temperature is defined using 9 temperature points (8 layers) through the depth and steel time-temperature curves.

Transition from Seismic to Thermal

Modification of the model is necessary when transferring from seismic to thermal analysis. During the seismic analysis, a constraint is placed on the nodes of every floor to ensure that they move together horizontally, representing the effect of concrete slab in the composite structure. However, a previous study by Quiel and Garlock [11] shows that, during the thermal analysis, steel in the composite girder experiences a faster increase in temperature than the slab. The steel expands at a faster rate than concrete, which eventually results in cracking of concrete, thus rendering the slab negligible for axial restraint [11]. Therefore, after the seismic analysis is completed, the constraint on the nodes of the compartment that would experience fire is removed. It should be noted that Quiel and Garlock’s study [11] shows that the slab has a considerable effect on the thermal analysis of the composite girder and the temperature of the top flange, which will be discussed later.

Proposed Modifications in OpenSees

Steel Material Model

In developing the fire module, the existing material models in OpenSees have been modified to include material degradation during fire. The modifications are based on the Eurocode3 temperature-dependent material properties. The new material class that is capable of handling both seismic and thermal loads for steel structures is the “Steel01Thermal” class. The constitutive material model in Steel01Thermal is currently programmed with two assumptions (1) a bilinear elastic perfectly plastic material model at elevated temperatures, and (2) using a stress-based formulation (as opposed to strain-based) and ignoring strain reversals.

The first assumption could be taken as a simplification; nevertheless, the elastic perfectly plastic stress strain relationship at ambient temperatures should be transformed into a non-linear relationship at elevated temperatures. Fig. 3a shows the proportional limit stress (p) that no longer equals the yield stress (y) at higher temperatures. The second assumption needs a more careful study. The implication of the current formulation is that the program is only able to start thermal analysis from a state of zero strain (which would not be the case in a FFE scenario). In addition, performance of the structure during cooling may not be correctly captured since strain reversals are not considered. The authors of this paper have modified the constitutive model in Steel01Thermal to include the nonlinearity of stress-strain at elevated temperatures (based on Eurcocode3), to account for strain reversals and the stress-strain history of the material before fire starts.

(a) (b)

Figure 3: (a) Stress-strain plot for steel at high temperature, (b) material model with plastic strain

Previous studies by Franssen [12] and El-Rimawi et al. [13] show that the plastic strain rather than the maximum stress level should be used to describe the complete stress-strain history as the steel temperature changes during heating or cooling. Quiel and Garlock [14] implemented a simplified tri-linear model (the points of proportional limit and yield are linearly connected), where the plastic strain is used to define the stress-strain relationship. In the case of Steel01Thermal material class in OpenSees, no simplification is applied and the nonlinearly between the points of proportional limit and yield are considered. The fundamental assumption of the applied formulation is that, at any point during heating or cooling, the full stress-strain curve can be constructed by knowing the plastic strain (point O’ in Fig. 3b) and the elastic modulus for the given temperature [12, 13]. In Fig. 3b, OAB is the path that the material would take starting from a zero strain. However, if the plastic strain is calculated to be at point O’, a new full stress-strain path should be constructed. Point A is the intersection of path OAB and the line extending from O’ with slope E. Point C can be found knowing that the length of linear portion is always the same (2p and 2εp). Finally point A’ is the mirror of point A. Now the material would travel on path A’CO’AB.

Resultant Moment

Axial load and moment values are calculated by stress integration along the fibers in the cross section in the FiberSection2dThermal class in OpenSees. In the seismic module of OpenSees, the reference axis for calculating the moment is taken as the geometric centroid of the cross section. However, in the thermal module, the calculated centroid takes the effect of thermal gradient in the cross section into account. Thus, the calculated centroid is equivalent to the effective centroid that is shifted from the geometric centroid. As a result, the moment in the thermal module was being calculated about the effective centroid. This has been modified by the authors so that in the thermal module, moment is always calculated with respect to the geometric centroid.

It is true that, due to the thermal gradient, the center of stiffness shifts, yet all the moment calculations should be about the geometric centroid. Reasons for this are: (1) this approach would be consistent with other finite element programs; and (2) the geometric centroid does not move, and is always in the same place, whereas the effective centroid moves with the temperature gradients, which changes with time.

Case Study

Performance of the 9-story frame is studied for one earthquake with two different hazard levels, and for one fire scenario at three possible locations in the frame. The locations are marked in Fig. 2. where B4 refers to the fourth bay, and F2, F4, and F9 refer to the second, fourth, and ninth floors. Fig. 2 shows the residual drift in the frame at the end of the earthquake (described next). Positive drift indicates permanent displacement of the columns in the positive x-direction. For the purpose of this study, all fire locations are selected in the fourth bay of the frame, where fire after the earthquake would be more critical for the perimeter columns. The drift plot in Fig. 2 shows that, for this particular earthquake, lower stories experience higher residual drift. Although columns in lower stories are stronger and have larger cross sections, they also take larger gravity loads. Therefore compartment B4-F2 is selected as one of the possible fire scenarios, and results are compared with those of compartments in the fourth and ninth floors.

Ground motion selection

Since this paper is intended as a demonstration of the procedure, only one ground motion will be used for the analysis. Future work will consider a range of possible ground motions. The ground motion used in this study will be referred to as “Gilroy” ground motion, which is the Loma Prieta earthquake, occurred in the U.S.A. in 1989 and was recorded at station 47381 Gilroy (Array #3). Only one component of the ground motion (the G03090 component) is applied since two- dimensional models are being used. The location was on stiff soil, and the earthquake had a magnitude of 6.9 with the closest distance from a fault rupture zone of 14.4 km. The two hazard levels chosen for the purpose of this study are the Design Basis Earthquake (DBE) and the Maximum Considered Earthquake (MCE). The selected ground motion is scaled to a level compatible with the 5% damped ASCE 7 -10 design spectrum, and therefore can be taken as the DBE level. The DBE scale is multiplied by 1.5 to obtain the required scale for the MCE level. The scaling procedure is based on the work of Somerville [15], where the scale factor minimizes the squared error between the ASCE 7-10 target spectrum and the response spectrum of the natural ground motion, assuming a lognormal distribution of amplitudes. The scale factors for the Gilroy ground motion are calculated to be 1.85 for the DBE level and 2.78 for the MCE level.

Fire load and heat transfer

As stated previously, the purpose of this paper is to develop a robust methodology to perform FFE analysis in OpenSees. Therefore one fire scenario is considered, and the heat transfer analysis is performed to obtain steel temperatures for the beams, perimeter columns, and interior columns of the three fire locations shown in Fig 2. The full temperature-time history is constructed based on the work of Quiel and Garlock [11] to resemble an actual fire event. This study assumes a single compartment (20 ft wide by 30 ft deep) in every floor that is subject to fire. Given that the fire occurs after an earthquake, it is assumed that the compartment has no functional active fire-fighting measures and the passive fire protection (e.g. spray) has been damaged enough to render it ineffective. Heat transfer for the two columns and a beam in the fire compartment is mainly based on the closed-form solution developed by Quiel and Garlock [14] based on a lumped-mass method. The solution is slightly modified for the beam to include the effect of concrete slab (which acts as a heat-sink) on the top flange temperature. An empirical equation developed by Ghojel et al. [16] is used to calculate the heat flux between the top flange and the slab. Fig. 4 shows the fire curve and weighted average steel temperature-time curves for beams and columns at the three locations shown in Fig. 2.

1200 1200 1200 B4-F2 Beam B4-F4 Beam B4-F9 Beam Icol Icol Icol 1000 Ecol 1000 Ecol 1000 Ecol

Fire Fire Fire

   800 800 800

600 600 600

400 400 400

Temperature ( Temperature

Temperature ( Temperature Temperature ( Temperature

200 200 200

0 0 0 0 100 200 300 400 0 100 200 300 400 0 100 200 300 400 Time (min) Time (min) Time (min) Figure 4. Temperature-time plots for fire and steel at the three fire locations (Icol refers to the left (interior) column; Ecol refers to the perimeter column)

Methodology

The procedure to evaluate post-earthquake fire performance of a frame is as follows: 1) Select an earthquake scenario; 2) Select fire location on the frame; 3) Define a fire scenario with the full temperature-time curve; 4) Perform heat transfer analysis to develop temperature-time curves of columns and the beam in the compartment; 5) Perform seismic structural analysis; and 6) perform a fire-structural analysis. Ideally, uncertainties in demand (steps 1 and 3), material properties (steps 4 and 6) and location of ignition (step 2) should be included in the analysis. The authors plan to expand this research in such directions in the near future.

Results

Results for the three fire locations are summarized in this section. For every location, the analyses are performed for (1) fire-only case, (2) fire after the DBE level earthquake, and (3) fire after the MCE level earthquake. In general, similar trends are observed for all three compartments, and for fire or post-earthquake fire cases.

Fig. 5 shows a sample of results for the compartment located at B4-F2 (Fig. 2) analyzed only under fire, with the fire curve shown in Fig. 4. Fig. 5a shows the normalized P-M (axial load-moment) path of the beam at the right and left interfaces with the columns and at mid-span. The paths are shown in relation to the normalized plastic P-M capacity envelopes (based on [17]). The P-M paths for the left and right ends of the beam reach the P-M capacity envelope at about 19 minutes. However, the beam does not fail until a third plastic hinge forms at mid-span at about 25 minutes. At this point, three plastic hinges are formed at three locations in the beam. Fig. 5b shows the pseudo-velocities of the beam and the perimeter column. It can be seen that at 25 minutes, the pseudo-velocity of the beam drops sharply, indicating loss of stability in the beam. The program stops running and the beam fails.

Figure 5. (a) Normalized P-M interaction for the beam in B4-F2 under fire, (b) pseudo-velocity for the beam and perimeter column in the B4-F2 compartment under fire.

B4-F4 and B4-F9 compartments behave similarly to the B2-F2 compartment. In the case of B2-F2 and B2-F4 compartments, floors above the compartment provide additional stiffness making it harder for the beam to expand under thermal loading. Therefore, the beam experiences higher compressive forces in comparison to B4-F9 compartment.

Table 2 summarizes results for the three locations and all the loading scenarios. The following parameters are recorded and presented in the table: (1) the residual drift after the earthquake, thus representing the initial condition before the fire; (2) the time (from the start of the fire) to form a plastic hinge at the interface of the beam and perimeter column tpR; (3) the time (from the start of the fire) to form a plastic hinge at the interface of the beam and interior column tpL; (4) the time (from the start of the fire) to form a plastic hinge at the beam mid-span tpM; (5) the residual drift at the end of fire or fire that follows earthquake. Comparison of results for the fire-only and post-earthquake fire scenarios at every location shows: (1) in lower floors, the earthquake slightly decreases the time to form a plastic hinge at the interface of beam and columns. This is mainly due to presence of locked-in moments in the beam after the earthquake. (2) Considerable column drifts, approaching 1.85%, are possible for fires that follow earthquake. During heating, the beam expands outwards, inducing positive drift in the perimeter column and negative drift in the interior column (positive indicates positive x-direction shown in Fig. 2). This implies that, especially at lower floors, the fire adds to the earthquake-drift for the perimeter column and decreases the earthquake-drift for the interior column.

Table 2: Summary of results for the three fire locations B4-F2 B4-F4 B4-F9 Parameter FireOnly DBE MCE FireOnly DBE MCE FireOnly DBE MCE Residual Drift after EQ -- 1.33% 1.38% -- 1.08% 1.19% -- 0.36% 0.95% (Fire) tpR (min) 19 17 17 18 17 16 14 14 14 (Fire) tpL (min) 19 22 22 18 20 20 14 14 14 (Fire) tpM (min) 25 25 25 23 23 23 18 18 18 -0.05% 1.35% 1.40% -0.054% 1.07 % 1.19% -0.022 0.33% 0.94% Residual Drift Left after fire Right 0.315% 1.80% 1.84% 0.36% 1.52% 1.64% -1.65 -1.36% -0.68%

If the beam fails, it no longer provides lateral support to the column. The unbraced length of the column would be two-stories high and could lead to global instability of the frame. Although connections are not explicitly modeled, research and real fire events have shown how steel connections can fail in a fire scenario. These scenarios need to be given consideration in evaluating and analyzing the results.

Conclusions

The behavior of a 9-story frame was studied for fires that follow earthquake (FFE) in OpenSees, which provides for a seamless transition from seismic to fire analysis. The authors found the software, as available in 2013, not capable of simulating a fire with an initial damaged condition. The steel constitutive model could not properly capture strain reversals. The material class Steel01Thermal was therefore modified to capture the effect of proportional limit at elevated temperatures, and to account for plastic strains and strain reversals during the fire analysis. This modification permitted the evaluation of response in a FFE scenario. Also resultant moment calculations are modified such that the reference axis to calculate the moment is the geometric centroid. This is consistent with other finite element softwares. This modification affects the cases that experience thermal gradient in the cross section, where location of effective centroid is not the same as the geometric centroid of the section.

The sample analyses run thus far indicated that the subsequent fire can increase the drift of the column on the perimeter on the order of 0.5% for fires in the lower floors and 1% in the upper floors. Total drifts in FFE did not exceed 2% (including the residual from earthquake) for the scenario studied. This presentation was intended to illustrate the challenges of modeling FFE. Future work will (1) further validate and provide necessary improvements to OpenSees for FFE; (2) examine the consequence of a column or connection failure on frame instability; and (3) include uncertainties in the fire and material models for a reliability approach to measuring earthquake resilience.

References

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