Research review: Post-earthquake fire assessment of steel buildings in the United States

Abstract

Researchers and practitioners have traditionally analyzed building hazards independently; however, with the recent focus on resilience, a multi-hazard analysis approach has emerged which considers the implications of cascading hazards. This article reviews the state of the art for analysis and design of steel moment frame buildings subjected to fires following earthquakes, also known as post-earthquake fires. The current design and analysis approaches for fire and seismic hazards in the United States, which follow prescriptive approaches, are each explained. Performance-based methodologies for each hazard are described. A literature review pertaining to the system behavior of buildings exposed to post-earthquake fires is provided. This includes consideration of nonstructural damage caused from earthquakes that could in turn affect building fire performance. Finally, recommendations are made for future post-earthquake fire analyses and design using incremental dynamic analyses and incremental fire analyses to capture building performance when subjected to various levels of these cascading hazards. The procedure for this methodology is explained, providing a direction for future research.

Keywords

fire moment frame post-earthquake fire seismic state of the art steel

Introduction

Buildings are designed to resist earthquake loads by dissipating energy through inelastic behavior. This can cause structural and nonstructural damage and residual drifts within the building. Ground motions can also lead to fire ignitions through short-circuiting, abrasions, chemical reactions, and other causes (Scawthorn, 2008). These fires result in strength and stiffness reductions in structural members due to elevated temperatures, which can further exacerbate the seismic damage. The interdependencies between earthquake and fire damage have motivated this study on system behavior, analysis, and design of steel buildings. This article will review the current state of the art in analysis and design for post-earthquake fire (PEF) hazards subjected to steel moment frame buildings. While some important work on component and assembly behavior will be reviewed, this article will focus primarily on system-level behavior.

An understanding of building response to earthquake and fire as separate hazards is necessary to further evaluate buildings subjected to PEFs. Fire and seismic hazards require different analysis and design approaches and result in different potential failure mechanisms within the structure.

Each of these aspects will be discussed in the article: (1) fire hazards will be reviewed, covering the current fire design approach and the state of the art in determining the fire scenario, conducting heat transfer analyses, and development of incremental fire analyses; (2) seismic hazards are discussed pertaining to the current design approach, typical analysis procedures, determining the seismic hazard, and development of incremental dynamic analyses; (3) the state of the art of PEF analyses will be reviewed, including implications of nonstructural damage; and (4) recommended future steps and research needs will be explained. This includes a methodology for assessment of steel buildings exposed to PEFs.

Fire hazards

Current fire design approach

Structural engineers in the United States do not usually conduct fire analyses or design; instead, architects are typically responsible to specify the fire-resistance rating requirements and determine the fire protection necessary to achieve that rating. The International Building Code (IBC) specifies fire-resistance ratings for structural components and assemblies based on the building use, size, and combustibility of building materials. This rating is the time (in hours) that an element or system can be exposed to a standard fire before failure would likely occur. Table 601 in IBC provides these hourly resistance ratings, which vary for primary members, floor and floor secondary beams, roof and roof secondary beams, bearing walls, and nonbearing walls (IBC, 2011). Primary members are defined as columns and members with direct connections to columns, as well as bracing members necessary for stability. There is no distinction between gravity and lateral frames.

The strength and stiffness of steel is greatly reduced at elevated temperatures, which may require passive fire protection measures to increase the fire-resistance rating. Spray-applied fire-resistive materials (SFRM) are commonly applied to steel structures. Fire tests can be conducted using ASTM E119 to determine the required thickness of SFRM (ASTM, 2015). However, a more common, alternative approach is to reference a database of tests that have been conducted on a limited variety of steel shapes and assemblies. Underwriters Laboratory’s database is commonly used for this approach (UL, 2016). Each wide flange beam has a W/D value, where W is the weight per linear foot and D is the perimeter of the member exposed to the fire. The W/D for the tested beam is divided by the W/D for the beam being designed and the thickness of the fireproofing used in the test is scaled by that amount. The AISC Design Guide 19 also contains fire test results and example problems for determining fireproofing thicknesses (Ruddy et al., 2003).

State of the art of fire analysis procedures

The prescriptive approach of fire-resistance ratings per IBC, which is based on standard furnace tests of short span members, does not necessarily translate well into real building behavior. Following the World Trade Center collapse in 2001, this approach has been further scrutinized with many professionals calling for a change to performance-based fire-resistance design and for the structural engineer to take over the responsibility of fire-resistance design of the structure through conducting fire analyses (Kodur et al., 2011). This transition within the design industry has been slow to develop; nevertheless, within the realm of research, various fire analyses have been conducted. The following sections will highlight the typical procedure for conducting these analyses using the following models: fire, heat transfer, and structural.

Determining the fire hazard

In the performance-based approach, the fire hazard is considered a thermal load applied to the structure and is referred to as a design-basis fire (Kodur et al., 2011). Design-basis fires are typically classified as either localized or compartment fires. Localized fires do not cause flashover because of the low rate of released heat. Because this study focuses on global response, only compartment fires, which are large, post-flashover fires, will be considered. Determination of this load can be approached in a number of ways: computational fluid dynamics (CFD) or two-zone models can be developed, time-temperature curves from a standard can be used, or actual fire tests can be conducted.

CFD models involve modeling the growth and behavior of the fire by dividing the compartment into many different zones to reflect the different temperatures throughout the space. These models are highly complex and require a number of detailed assumptions of materials and properties within the compartment. The National Institute of Standards and Technology provides software called FDS (Fire Dynamics Simulator), which can be used to conduct CFD analyses. Other programs also exist that specifically focus on CFD for fires.

As an alternative, time–temperature curves from ASTM E119 (ASTM, 2015), ISO 834 (ISO 834-1:1999, 2015), and Eurocode 1 (EN 1991-1-2:2002, 2002) are used. As shown in Figure 1, the ASTM and ISO curves only have a heating phase. These curves are commonly used for fire furnace testing and are not influenced by ventilation or other factors that would affect an actual fire. In contrast, Eurocode parametric curves include a cooling phase and vary depending on the thermal inertia of the enclosure (b), opening factor (O), and fire load density (q_t,d). Varying these parameters affects the peak fire temperature, fire duration, and rate of heating and cooling. This cooling phase is important as it results in thermal contraction, which can produce large tensile forces that fail connections. The Eurocode parametric time–temperature curves are restricted to room fires in the post-flashover phase intended for use in spaces with rectangular enclosures, floor area less than 500 m², ceiling heights less than 4 m, and no ceiling openings. In this post-flashover phase, it is assumed that the room contains a fully developed fire with uniform temperature throughout the compartment. This is called a one-zone approach.

Figure 1.

Design fires using ISO834, ASTM E119, and Eurocode.

While Eurocode assumes a one-zone approach, designers recognize that there are actually at least two zones: an upper, hot zone and a lower, cooler zone. Structural members in the lower zone (such as the floor slab below the fire) are not usually analyzed, as the change in internal temperatures in those members is expected to be insignificant (Franssen and Vila Real, 2012).

Pope and Bailey (2006) conducted comparisons among CFD models, Eurocode, and fire tests and determined that Eurocode provides reasonable predictions for average compartment temperatures, though it over predicts the growth phase of the fire and should include a nonlinear decay rate. Additionally, CFD analysis results can be too complex to apply to the heat transfer structural models. For these reasons and due to its simplicity, standard fire curves are often used in favor of CFD analyses (Wang et al., 2013).

Determination of active fire protection, such as sprinklers, detectors, and smoke exhaust systems, must be considered as well. Eurocode (EN 1991-1-2:2002, 2002), for example, allows a reduction in the fire severity if sprinklers are installed; however, many designers choose to not account for this reduction and conservatively assume that the sprinklers are defective. Once the fire severity is determined, the location of the fire also needs to be decided on: the story or stories affected, full-story or compartment fires, interior or exterior compartments, moving or stationary fires, and so on. All these factors affect the fire hazard and the building response.

Heat transfer analyses

Once the fire time–temperature curve has been selected, finite element method (FEM) models can be used to conduct heat transfer analyses to determine the temperature of each structural component throughout its cross-section. Two-dimensional (2D) heat transfer analyses are commonly used because the fire time–temperature curves assume that the room contains a fully developed fire with uniform temperature throughout the compartment; thus, there is no need to use more computationally expensive three-dimensional (3D) modeling. When using a CFD fire hazard, this assumption no longer applies and 3D FEM models are used to conduct heat transfer analyses.

In FEM heat transfer models, the structural member and its corresponding fireproofing is modeled and exposed to the predetermined fire hazard. Thermal expansion, specific heat, thermal conductivity, and density are defined for each material in order to model the thermal transfer of heat from the air to the structural component. These models perform conduction, convection, and radiation calculations to determine the internal temperatures of the structural member along its cross-section. These internal temperatures are determined at specific nodes, which are then applied to the structural building model.

More simplified analytical methods, such as the “lumped mass method,” can also be employed, which assumes that the entire member cross-section has the same temperature. This can be a valid assumption for steel thicknesses less than 100 mm and when exposed to a sudden rise in temperature (Wang et al., 2013). The AISC Specification for Structural Steel Buildings (ANSI/AISC 360-10, 2010) allows designers to use this simplified assumption.

Case studies of structural analyses

Many researchers have focused on studying individual structural components to observe behavior when subjected to a fire. In particular, beam-to-column connections have been studied at length (Al-Jabri et al., 2006; Fischer and Varma, 2017; Garlock and Selamet, 2010; Hu and Engelhardt, 2011; Mahmoud et al., 2016; Memari and Mahmoud, 2014; Pakala et al., 2012; Qian et al., 2008; Sarraj, 2007; Tan and Huang, 2005; Wang et al., 2011; Yang et al., 2009; Yu et al., 2009). Beams, columns, and floors have also been studied in isolation (Agarwal et al., 2014; Agarwal and Varma, 2011, 2014; Choe et al., 2011; Dwaikat et al., 2011; Kodur et al., 2013; Naser and Kodur, 2016; Selamet and Garlock, 2012; Selden et al., 2016; Selden and Varma, 2016; Takagi and Deierlein, 2007; Zhao and Kruppa, 1997). While the above-mentioned research informs modeling decisions, system-level behavior will be focused on.

Very few full-scale fire tests have been conducted due to the associated costs. One of the most familiar series of experiments is the Cardington fire tests, which consisted of six full-scale fire tests on an 8-story structure in Bedfordshire, United Kingdom (STC, 1999). The observations of these large-scale tests helped to inform and benchmark computational modeling of fires. Beams experienced significant deflection, which led to catenary action but no instability or collapse. The bottom flange of beams were often distorted due to thermal expansion and deflection when pushed against the column. Fracture in the end-plate beam to column connection occurred during cooling, due to thermal contraction causing high tensile forces in the connection. The top of columns, near connections where fireproofing was not present, resulted in localized buckling failure.

Agarwal and Varma (2014) studied the system-level performance of a steel moment frame building using 3D FEM models. They found that if all structural components were designed for the same level of fire safety, gravity columns would likely fail first. Upon failure of the columns, catenary and flexural action redistribute load to the adjacent columns. Fang et al. (2011) found that, depending on the loading, it is even possible for loads to be redistributed to upper, ambient temperature floors.

Fischer (2015) expanded upon Agarwal’s work by studying full-story fires and varying the fire-resistance ratings on the structural members. Again, gravity columns were the first component to fail. When these members were protected with excess fire protection, significant deflections occurred in the beams and slab but failure did not occur. Moving fires were also considered, but it was found that full-story fires were an appropriate conservative approach in place of modeling moving fires.

Memari and Mahmoud (2014) explored moment frames with reduced beam section connections for 3-, 9-, and 20-story frames using 2D modeling. Gravity frames were idealized as a leaning column. They found that the global stability of the structure was not compromised by only a one compartment fire. At a local level, beams experienced residual axial tensile forces and deflections.

Jiang et al. (2014) conducted 2D frame analyses to observe various collapse mechanisms: heated bay collapse, column buckling, local lateral drift of heated floor, and global lateral collapse. This study also compared the influence of beam sizes on the structural response. Additionally, the magnitude of gravity loading was varied. They determined that local lateral drift occurred at low loading levels; with increased loading, column buckling occurred. As the beam sections increased, column failure mechanisms occurred instead of beam mechanisms. Additionally, edge bays were more susceptible to progressive collapse because these bays were not able to develop adequate catenary action. Similar analyses and findings were determined by Sun et al. (2012).

Some studies have shown that thermal expansion (bowing) usually controls the behavior over that of material degradation due to the elevated temperatures. Flint et al. (2007) and Usmani et al. (2003) studied the World Trade Center collapse using 2D FEM models. They found that, as the floor deflected due to thermal expansion, tensile membrane action occurred. The exterior columns were pulled inward, forming plastic hinges in these columns at the floor levels. Similar responses were found when using 3D models. However, redistribution of loads throughout the structure was observed with the 3D models, making it a more robust model and slower to fail than the 2D models (Flint, 2005). It is important to note that the truss system of the World Trade Center is different than that of traditional floor framing with conventional hot rolled steel shapes.

In another study, vertically traveling fires were simulated to account for the time that it takes for actual fires to move between floors (between 6 and 30 min based on observations of actual buildings; Röben et al., 2010). This is different than the approach of modeling multiple floor fires at once because it accounts for the heating and cooling response of the floors relative to each other. The rate of the moving fires greatly affected the global response of the structure.

Incremental fire analysis

There is a trend in fire research that favors a performance-based approach that is probabilistic as opposed to deterministic (Khorasani et al., 2015a; Kodur et al., 2011; Rush et al., 2014). Due to this initiative, the incremental dynamic analysis (IDA) approach that is typically used in earthquake engineering, which will be explained in a later section, is being adapted for fire scenarios.

This type of analysis involves exposing a structure to a hazard and incrementally increasing the intensity measure (IM) of the hazard with each analysis. Once the demand is determined through scaling of the IM, the capacity is evaluated through a damage measure (DM). This is the output from the analysis which is used to determine the suitability of the structure. The IM and DM are incorporated to generate response curves that show how the level of damage changes as intensity varies.

This concept is articulated by Moss et al. (2014), which named the approach incremental fire analysis (IFA) and performed preliminary studies to validate the process. Unlike IDA, which commonly uses peak ground acceleration (PGA) or the spectral acceleration as the IM, there does not seem to be a consensus among researchers on the most indicative IM to use for fire.

Moss et al. studied a two-span concrete beam using both peak room temperature and the total radiant heat energy (RHE) as the IMs. The total RHE is the calculated area under the radiant heat flux versus time curve. In this study, 16 fires were chosen using 4 different ventilation factors and 4 different fuel load densities. These time–temperature curves were then scaled by the IMs. The maximum displacement in the beam was recorded as the DM. RHE was found to be a more efficient IM than the peak temperature because it had less dispersion of values; however, RHE is not a simple value to calculate, as it involves radiant heat transferring back and forth between the enclosure and the members inside.

Devaney (2014) considered different IMs for a performance-based fire study. He considered Ingberg’s equal area concept from 1928, which was a rough method for measuring fire severity. It calculated the area under a temperature–time curve, which constitutes no numerical significance in terms of units. This concept also does not consider heat transfer or the difference between a fast, hot fire and a slow, cool one.

Other suggested IMs included maximum steel temperature (but this does not account for varying fire protection levels), rate of temperature increase (but this does not consider fire peak or duration), and peak compartment gas temperature, which was the chosen IM. Devaney used Monte Carlo simulation to determine the range of realistic results. The engineering demand parameter for the beam was midspan deflection. In another study, Lange et al. (2014) also used peak compartment temperature as the IM.

A concrete column study was conducted using the maximum temperature within the column cross-section as the IM. A total of 27 fire scenarios were studied by varying the compartment size, fuel load, and ventilation. A clear correlation between opening factor and the residual strength index of the column was found, as the column capacity was affected by both the peak temperature and the duration of the fire (Rush et al., 2014).

In another study, fire load in a compartment (MJ/m²) was used as the IM (Gernay et al., 2016). At least one compartment was studied per story. The damage states used were flexural resistance of beams (local failure) and maximum resistance of columns (could lead to collapse).

Seismic hazards

Current seismic design approach

Moment-resisting frames (often referred to as moment frames) are the focus of this study. These frames consist of beams and column members connected with rigid beam-to-column connections that are designed to resist the lateral loads on the structure. The lateral stiffness of the frame is provided through the fixed connections and bending rigidity of the framing members. This system is appealing to architects as it allows for a more open floor plan that is not inhibited by braces or walls. However, because the stiffness is dependent on bending rigidity, it tends to result in larger building drifts than braced frame or shear wall systems.

The seismic-force-resisting system dissipates energy generated by the ground motion through inelastic behavior. Steel moment frames are designed to form plastic hinges at beam ends, acting as fuses to minimize additional damage to the remainder of the structure. Depending upon the post-yield capacity of the members, these fuses may need to be replaced after an earthquake. Locating the hinges in the beams and preventing hinging in the columns is called the strong column-weak beam philosophy, which is required for special moment frame systems in the seismic provisions of AISC (ANSI/AISC 341-16, 2010). This philosophy not only provides a more efficient way to dissipate energy but also minimizes the potential of collapse due to a soft-story mechanism (Bruneau et al., 2011).

Reduced beam sections are sometimes employed to ensure the strong column-weak beam concept. The flanges of the beam section near the ends are reduced to a dog-bone shape, which enables the fuse (hinge) to form in this location. Haunched connections and flange rib connections are other approaches to move the hinge away from the column and connection. Lately, there has been a push to further limit damage and increase resilience using self-centering, rocking frames; with this design, post-tensioning strands are anchored at the beam-to-column connections to pull the frame back to plumb without causing inelastic damage (Lin et al., 2013).

The Northridge Earthquake of 1994 brought to light some potential issues with moment frame connections. Fractures were found at or near the beam flange groove welds, proving that moment frames were not as ductile as researchers and practitioners originally believed. Although these failures did not result in collapse, extensive retrofitting of the connections was required. There were a number of contributing factors to these failures which include low fracture toughness of the weld metal in the beam flange to column connection, poor quality of welding due to limited access, and stress concentrations from the backing bar/weld tab. Following Northridge, minimum toughness requirements for weld metal were improved and quality control was more closely monitored, among other improvements. The Kobe Earthquake, which occurred in Japan 1 year after Northridge, also resulted in severely damaged buildings due to brittle fractures of beam to column connections (Bruneau et al., 2011). These earthquakes represented a milestone for the improvement of steel seismic-resistant structures.

As the damage from these two earthquakes illustrated, the beam to column connections of the moment frames are critical to the performance of the structure. The panel zone, which is the area of the column web where the beam frames in, can experience very high shear forces and must be designed to prevent column web yielding or crippling and flange distortion. Recognizing the importance of connection design, AISC developed a list of prequalified moment connections that have been tested (ANSI/AISC 358-10, 2010). These include standard connections, such as welded unreinforced flange-welded web connections, but also some proprietary connections using untraditional methods, such as SidePlate, that have been extensively tested and certified. Newly proposed connection types must undergo rigorous testing.

Typical seismic analysis procedures

As outlined in ASCE 41 (ASCE, 2013), there are four primary procedures to analyze buildings subjected to seismic loads: linear static, nonlinear static, linear dynamic, and nonlinear dynamic. Static procedures do not consider dynamic effects so they should only be used with regular structures and when higher mode effects are considered insignificant. Linear static procedure (LSP) applies pseudo seismic forces to each story through the equivalent lateral force procedure developed in ASCE 7 (ASCE, 2010). Nonlinear response is then accounted for through the use of the response modification coefficient (R) and the deflection amplification factor (C_d), also provided in the code and varying based on the type of lateral system. Nonlinear static procedure (NSP) incorporates nonlinearity in the analysis itself. An example of this is static pushover, which involves incrementally applying a static force to the building and plotting the force versus displacement. Linear dynamic procedure (LDP) assumes elastic properties of the material and applies the loads dynamically, accounting for higher modes. An example of this is response spectrum analysis, which uses the equations of motion to develop mode shapes and spectral accelerations. Nonlinear dynamic procedure (NDP) incorporates both the nonlinearity of the material and the dynamic effects of the building response through a time history record. This procedure is more computationally expensive, but it can be used for all building types and most closely represents true building behavior.

Determining the seismic hazard

In order to perform advanced analyses using the NDP, it is critical to model the seismic hazard through adequate selection and scaling of ground motion records. Chapter 16 of ASCE 7-10 requires three or more appropriate ground motion records. When using 3D analyses, each individual record should have orthogonal pairs of horizontal ground motion accelerations. These records must be selected from events with similar “magnitudes, fault distance, and source mechanisms” as the maximum considered earthquake (MCE) (ASCE, 2010). Online databases, such as PEER (2016) and COSMOS (2016), provide earthquake records based on station readings from actual events. Synthetic ground motions can also be created but are discouraged in favor of actual records.

Each component of the ground motion record has a resulting 5% damped response spectrum. The orthogonal components must result in a square root of the sum of the squares (SRSS) with a mean value of the records that must be greater than the design response spectrum in the range of 0.2–1.5T, as shown in Figure 2, where T is the period of the fundamental mode of the structure. If at least seven records are used, design forces and drifts can be averaged. With less than seven records, the worst case controls.

Figure 2.

Structural response spectrum (in bold) with ground motion records overlaid.

National Institute of Standards and Technology (NIST) provides its own guidelines through work with the ATC-82 project (NIST, 2011). This initiative aims to provide improved and clearer guidance on ground motion selection and scaling, as there seems to be a lack of general consensus in the earthquake engineering community. It supports ground motion selection based on the conditional spectrum, which is a computational method for selecting a ground motion spectrum that has properties of a naturally occurring ground motion at the site. Other approaches are uniform hazard spectra and conditional mean spectra. FEMA P-58 (Federal Emergency Management Agency (FEMA), 2012) also provides ground motion scaling guidance.

Case studies of structural analyses

Chi et al. (1997) explored different modeling techniques for steel moment frame buildings subjected to ground motions through pushover analyses and a time history analysis. A 17-story building was analyzed using 2D frames (with and without second-order effects) and 3D buildings. 3D-B is a basic model which includes all lateral frames and gravity columns which are connected rigidly through kinematic restraints. The 3D-F model is the full model which includes the gravity beams and shear connections. Results showed that the 3D models produced more improved building response. It was found that the stiffness contribution due to the gravity frames could be attributed primarily to the gravity columns, which provided additional lateral strength to critical stories in the lower region of the building. When a time history analysis was performed, the maximum story drift ratio was about 0.025 for the 2D model, 0.023 for the 3D-B model, and 0.016 for the 3D-F model.

Foutch and Yun (2002) compared modeling techniques for steel moment frames subjected to seismic loads. The report considered elastic (linear centerline models) as well as nonlinear centerline models, with and without panel zones modeled. Panel zones were idealized as a scissor model using the approach developed by Krawinkler (2000). Results showed that the modeling decisions listed above can significantly affect building response. Refer to the original work for detailed results of the pushover analyses.

Earthquake engineering has been transitioning from the traditional prescriptive approach to a performance-based approach of analysis and design that compares designated DMs to the anticipated level of damage for a given hazard level as a method for evaluating seismic risk. These analyses require nonlinear models that are reliable and calibrated based on experimental data that appropriately represent the deterioration of strength and stiffness in the structural components. Work by Lignos and Krawinkler (2013) explains the approach and calibration of such models. A number of agencies provide guidelines for the performance-based seismic design approach: Pacific Earthquake Engineering Research Center Tall Building Initiative (PEER, 2010), FEMA 445 (ATC, 2006), and the Los Angeles Tall Buildings Structural Design Council (LATBSDC, 2014).

Incremental dynamic analyses, used for assessment of building performance under seismic loads, will be explained later, as it pertains to recommendations for PEF design and assessment procedures.

Gravity frame contribution to lateral stiffness of building

Traditionally, the gravity system is neglected in lateral-force-resisting system design; however, studies have shown that gravity frames can offer additional stiffness and energy dissipation to the building system that is not negligible (Flores et al., 2012; Foutch and Yun, 2002). Because gravity frames experience essentially the same drift as the lateral frames, gravity shear connections can experience large rotations. Also, gravity frames typically constitute a significant portion of a building, as moment frames are more costly and usually limited to the exterior. Tests of simple shear connections were conducted with and without the floor slabs (Liu and Astaneh-Asl, 2000). Findings showed that large rotations of 0.14 rad could be achieved and that approximately 15%–20% of the beam plastic moment capacity could be transferred in the connection. With the floor slab contribution, the maximum lateral load resistance increased by nearly two.

Flores et al. (2012) studied 2-, 4-, and 8-story buildings with and without the gravity framing. The gravity connections were modeled as partially restrained assuming 0%, 35%, 50%, or 70% of the plastic moment capacity of the beam. When subjected to design basis earthquake (DBE) and MCE loading, residual deformations reduced as the percentage of gravity connection resistance increased. In fact, for the 8-story building, soft-story collapse of the building was prevented by including the gravity framing contribution. This influence is also reflected in the reduced interstory drift ratios.

In seismic analyses, even if the stiffness contributions of the gravity system are ignored, the engineer cannot ignore the inherent P-delta effects. This P-delta effect is often modeled with a leaning column rigidly attached to the lateral-force-resisting system that has gravity loading applied so as to simulate the destabilizing load of gravity frame imperfections (Chi et al., 1997; Foutch and Yun, 2002). When the lateral contribution of gravity framing is not included in the design, the leaning column is assigned zero flexural stiffness. When its contribution is to be included, the equivalent lateral stiffness of the columns can be modeled through an equivalent bay that is rigidly attached to the lateral frame. Similarly, gravity beam stiffnesses are modeled as the equivalent stiffness of all the gravity frame beams in that direction. Rotational springs can be used to model equivalent strength and stiffness of the gravity connections (Flores et al., 2012), using assumptions for elastic rotation based on connection tests by Liu and Astaneh-Asl (2000). A similar procedure is outlined by Foutch and Yun (2002). The equivalent gravity frame reduced maximum interstory drifts, though the contribution could sometimes be considered negligible. In the 20-story building, these effects were more pronounced due to the greater P-delta effects.

Gupta and Krawinkler (1999) accounted for gravity contributions in their work using an equivalent bay rigidly attached to the lateral load resisting frame. Each of the two equivalent gravity columns had a moment of inertia equal to half of the gravity columns at that level. The out-of-plane resistance of the orthogonal moment-resisting frame columns was also considered. It was determined that the lateral stiffness contribution of the gravity frame was most influenced by the gravity columns and a smaller influence was with the gravity connection.

Judd et al. (2016) suggested implementation of the dual system design concept for integrating the response of lateral and gravity frames. This approach would be similar to the dual systems already specified in ASCE 7-10 (ASCE, 2010), but would require that 10% of the seismic forces would need to be resisted by the gravity framing system. Work funded through the National Science Foundation is currently ongoing to further explore the role of gravity framing on the seismic performance (NSF, 2013).

Incremental dynamic analyses

As mentioned previously, IDA follows the same principle as IFA. IDA is commonly used in conjunction with the NDP to create a parametric study of building behavior to seismic loads. Each ground motion record can be scaled using an IM to generate response curves. According to Vamvatsikos and Cornell (2002), some possible IM variables are PGA, peak ground velocity (PGV), 5% damped spectral acceleration, and the R-factor. Once the demand is determined through scaling of the IM, the capacity must be evaluated through a DM. Examples of the DM can be maximum base shear, node rotations, peak roof drift, interstory drift ratios, and so on. Results of the analysis can show a progression of behavior with varying results including softening, hardening, and weaving, as shown in Figure 3 (Vamvatsikos and Cornell, 2002). Results of IDA can then be used to generate fragility curves.

Figure 3.

IDA curves of a T = 1.8 s, 5-story steel braced frame subjected to four different records (Vamvatsikos and Cornell, 2002).

PEF hazards

The 1906 San Francisco earthquake and the 1923 Tokyo earthquake are classic examples that brought to light the potential damage of fire following earthquakes. The San Francisco earthquake resulted in 80% of the total damage occurring due to PEFs (Scawthorn, 2011). The Tokyo earthquake resulted in 77% of the total losses due to the fire, causing 140,000 lives lost and 447,000 homes destroyed (Mousavi et al., 2008). This has continued to be a problem in more recent years, as the Kobe earthquake in 1995 resulted in 108 fires. Because of its dense urban setting and due to thousands of breaks in the underground water distribution system caused by the earthquake, fires spread following the Kobe earthquake (Scawthorn, 1996).

Scawthorn et al. (2005) and Botting (1998) summarized the historical cases of fires following earthquakes and the community level impacts to utilities, communications, roadways, and buildings. Most conflagrations occur in low- or mid-rise timber buildings. Although the threat to high-rise steel buildings is unlikely, the risk would be very great, as adequate time would be needed to allow for safe evacuation of inhabitants (Taylor, 2003).

Earthquakes can cause structural damage and residual drifts, potentially preventing people from safely exiting the building during a fire. In addition, nonstructural components, such as sprinklers and pipelines, may be damaged, which could increase the duration and intensity of the fire. Additionally, first responders may be slow to react to fires because they are already preoccupied responding to earthquake-related issues. Ground motion from earthquakes has been known to ignite fires through short-circuiting, abrasions, chemical reactions, among other causes (Scawthorn et al., 2005). These issues together inflame the potential for damage due to PEFs.

Potential nonstructural damage

Nonstructural damage can occur as a result of large drifts and accelerations due to seismic loads. This damage can be detrimental to the fire resistance of the structure. While nonstructural damage will not be explored in depth, some potential implications of this damage on subsequent fire hazards will be considered.

For instance, when steel yields during an earthquake, the adherence of the SFRM can be affected. This was studied by Braxtan and Pessiki (2011). Steel plates were tension yielded and the adhesive and cohesive strengths of the SFRM were tested. Debonding, cracking, and spalling were all possible failure mechanisms of SFRM in cyclically loaded beam-to-column moment connections (Keller and Pessiki, 2012). At an interstory drift ratio of 3%, debonding and cracking of the insulation occurred. Detachment was more frequent for dry-mix (DM) than wet-mix (WM) fireproofing, while cracking was more likely in WM than DM. Using computer modeling, they found a 20%–30% reduction in flexural capacity of these connections when fireproofing had spalled and the steel was exposed to elevated temperatures.

Sprinkler systems may also be damaged in an earthquake event, which would increase the duration of a subsequent fire. Fragility curves were developed based on physical tests conducted at the University of Buffalo. These curves show the likelihood of leaking for different components of the sprinkler system when subjected to peak floor accelerations (Soroushian et al., 2015). Interstory drift can also affect piping performance. In another study (Zaghi et al., 2012), hospital piping was tested for seismic loading, and it was found that restrained welded assemblies could withstand interstory drift ratios of 4.34% without any damage or leaking; however, threaded assemblies could only withstand drifts of 2.2% before leaking occurred. Unrestrained piping fared worse with only 1.08% of drift causing leakage.

Cladding failures could also occur. Excessive drifts could lead to breakage of windows. Both of these scenarios would in turn affect the opening factor of exterior compartment fires. However, studies have shown that if the cladding and its connections are properly detailed, façade damage is unlikely, even with drifts up to 0.04 rad (Carpenter, 2004; Okazaki et al., 2007).

State of the art of PEF analyses

Case studies of structural analyses

Researchers have shown that, in the event of a gravity member failure from fire, the lateral system can prevent the collapse of a building through load redistribution (Agarwal and Varma, 2014; Fischer, 2015). However, if many lateral members have already yielded in the earthquake, the post-yield behavior may not be adequate to accept load redistribution from failing gravity members during a fire. The implications of this hazard are explored in the following case studies.

Della Corte et al. (2003) classified earthquake damage as “geometrical” and “mechanical.” Geometrical damage is defined as residual deformations caused by plasticity in the structure. Mechanical damage is “degradation of mechanical properties” due to plastic deformation. A simple single-bay, single-story portal frame was studied to show that the buckling critical load of the column frames was significantly lower than the Euler buckling load when considering the effects of seismic damage. Multi-bay, multi-story 2D frames were then analyzed. The study found a 10% reduction in fire resistance for a design-level seismic event but, for very rare earthquakes, the contribution of earthquake damage to fire resistance was much more significant.

Pantousa and Mistakidis (2014) conducted analyses of PEFs by considering the nonstructural damage caused by the earthquake, namely, the functionality of the sprinkler system and the breakage of windows. As the seismic loads increased, so did the assumed nonstructural damage. CFD was used to study scenarios where broken windows affect the ventilation. The structural system was found to fail at the heated beams where restrained thermal expansion and catenary action occurred. They found a 14% reduction in fire-resistance time for the design earthquake when nonstructural damage was assumed.

Behnam and Ronagh (2014b) analyzed a 10-story moment frame building using 2D frame analyses and accounted for earthquake effects through stiffness degradation and residual deformations. Three different fire scenarios were used: fire at the first, fourth, and seventh floors, respectively, with both 5- and 25-min delays before spreading the fires between floors. The application of the fire (time delay and story level) changed both the fire-resistance time and failure shape of the building. In some cases, one level was in the cooling phase while the upper level was heating. For fast-moving vertical fires, collapse occurred during heating, but for slower spreading fires, collapse occurred during the cooling phase. Sway mechanisms were observed for fast-moving fires but beam mechanisms were observed for slower moving fires.

Khorasani et al. (2015b) compared a fire-only and PEF scenario using OpenSees, an open-source analysis software from UC Berkeley. They found that the earthquake decreases the time to form a plastic hinge due to fire at the beam to perimeter column interface. Column drifts of 1.7% were achieved in fire following earthquake, due to thermal expansion and the residual drift of the earthquake.

Memari et al. (2014) studied moment-resisting frames with reduced beam section connections in low-, medium-, and high-rise structures, using 2D frame analyses. The leaning column approach was used to represent P-delta effects and stiffness of the gravity columns. Panel zones in the beam to column connections were modeled using the scissor model, with rigid links and a rotational spring to capture the moment–rotation of the connection. Life safety performance was determined in 80% of the analyses, while collapse prevention consisted of the remaining 20%. PEFs tended to produce lower interstory drift ratios than the earthquake scenarios and system-level collapse was not imminent. Large tensile forces were developed in the beams during the cooling phase, while axial compressive force-bending (caused during heating because of thermal expansion and restraint) tended to control the beam design.

Zaharia and Pintea (2009) used pushover frame analysis and both ISO 834 and natural fire curves to compare three different frames. The frames that were designed for higher seismicity levels appeared to have reserve fire resistance. Also, the fire-resistance time of the structure was affected by its level of damage, with undamaged structures resisting fire loads for longer prior to collapse; however, in some cases, this difference is very minimal (roughly 1 min). Two primary methods of collapse were observed: a global (structural) sway mechanism and a beam mechanism. Typically, the same mode of collapse was observed in the frames, whether or not the structure was damaged in the earthquake.

Behnam and Ronagh (2014a) proposed a post-earthquake factor to be applied to the equivalent static equation for calculating base shear due to seismic loads. In this, V_PEF = C_PEF(t)C_s × W. This C_PEF(t) value would be evaluated iteratively through redesign of the frame until it achieves a satisfactory performance level when subjected to the PEF.

Quiel and Marjanishvili (2012) studied the effect of damage on the fire resistance of steel buildings, focusing on fire following blast or impact scenarios. They found that the structure was very susceptible to global instabilities and that further studies would be needed to compare the effects of fire intensity and fireproofing with the acceptance criteria and collapse time. A performance-based design approach was suggested.

Research needs and future directions

Further research is needed to advance the understanding of steel building performance when subjected to PEF hazards. In particular, very few experimental tests have been conducted on steel components and assemblies subjected to PEF (Braxtan, 2010; Huang et al., 2012). Instead, most work on PEF has been done computationally. Advancements in understanding of PEF behavior can be achieved through experimental testing of beam-to-column assemblies for both gravity and moment frames. Researchers can determine through computational modeling which other components or assemblies should be experimentally tested. These tests can in turn be used to verify and benchmark the computational models.

As mentioned previously, IDA has been widely used by researchers and practitioners and it follows an established procedure that has been well documented. IFA, however, is a relatively new procedure, which has not yet garnered consensus among researchers regarding the most indicative IMs and engineering damage parameters to use to understand building behavior to fire hazards. IFA conducted thus far has focused on individual components, such as beams and columns. Additional research is needed to study IFA at a building system level.

Additionally, a methodology needs to be established for analyzing and evaluating the performance of structures subjected to PEF. Faggiano and Mazzolani (2011) made notable strides toward assessing robustness. In their study, 2D frame analyses were conducted using pushover analysis. Fire loads were applied to two bays in each of the two stories. Seismic performance levels were benchmarked by interstory drift ratios and plastic hinge rotations according to FEMA 356 (FEMA, 2000). Similar criteria were established for fire: Operational Fire, Life Safety fire, Local Collapse fire, Section Collapse Fire, and Global Collapse fire, based on yielding, plastic hinging, beam mechanisms, failure of the cross-section, and a global mechanism, respectively. A performance chart was generated which compared seismic performance levels, fire performance levels, and fire resistance in a 3D bar chart. This approach can be further advanced by developing 3D fragility curves to determine the probability of collapse for various hazard severities. These 3D surface plots can be used to show the interrelationship between the level of each hazard and the corresponding probability of collapse. The methodology for this approach is explained in the following sub-section.

Outline of PEF methodology

Based on the current state of the art, the following methodology is proposed for evaluating steel buildings exposed to PEFs. The methodology is outlined in Figures 4 and 5. Figure 4 includes steps (1) through (6) described below, including the design of the structure, selection of the seismic hazard, and implementation of incremental dynamic analyses. Figure 5 illustrates steps (7) through (13) described below, which include the process of determining fire hazards, conducting incremental fire analyses, and developing fragility curves. Each of these steps is explained in more detail below:

Design of the structure using applicable building codes. Standard design procedures should be used to determine the structural framing members, connection details, and fireproofing requirements. Structures that are regular and symmetric in shape are usually designed using 2D LSPs outlined in ASCE 7 for seismic and wind analyses.

Development of a 3D FEM model. A detailed nonlinear, inelastic 3D finite element model of the complete building structure should be developed. This includes consideration of the gravity framing contribution, such as the composite slab and gravity connections. The model should account for inelastic deformations, instability failures, and connection damage at elevated temperatures. It should also incorporate the effect of temperature on material properties. Separate seismic and fire models may need to be developed, with the ability to import the results of the seismic analyses into the fire model.

Selection of ground motions. Ground motions may be selected using the ASCE 7 procedure explained previously, or by other means. This includes selection of at least seven ground motions which are scaled to fit the design response spectrum of the building. Ground motion records scaled from actual seismic events should be used.

Apply ground motion to base of building. The selected time histories should be applied to the building base using either acceleration or displacement records. Ground motions should be applied in both orthogonal directions.

Incrementally scale ground motion. Ground motions must be scaled by a selected IM, which can include PGA, PGV, or S_a, among others. The procedure outlined in Figure 4 suggests scaling PGA after each analysis.

Generate IDA response curve. After each analysis is run, the maximum story drift ratio for each IM (PGA) should be recorded and used to develop a plot of PGA versus story drift ratio. This will show a progression of the building response as the intensity of the seismic event increases.

Select fire locations. Fires should be considered at strategic locations throughout the building. At a minimum, fire analyses should be conducted at a mid and upper level. Corner, exterior, and interior compartments should be studied as well. Each bay of the structure could be considered one compartment. Full-story fires may also be considered.

Select fire time–temperature curves. Eurocode parametric time–temperature curves should be used to represent compartment fires. Multiple (three or more) fire curves are recommended to accompany the seven seismic time histories required by ASCE 7. Opening factor, thermal inertia of the enclosure, and fire load density should be varied to produce distinct curves, which vary in peak fire temperature and rate of heating and cooling.

Conduct 2D heat transfer. 2D heat transfer is necessary to determine the internal temperatures of all of the structural members exposed to the fire. This should be performed using FEM or other numerical analysis software. The fireproofing should be modeled at the design thickness, or the thickness determined using the prescriptive approach. Thermal properties for each material should be taken as per Eurocode where applicable.

Apply temperatures to building model. The internal temperatures, which are determined through heat transfer analyses, should be assigned to the members in the building model that are exposed to the compartment fire. Five-minute increments are recommended.

Incrementally scale fire time–temperature curves. The fire time–temperature curves should be scaled in a manner similar to the scaling of PGA used in IDA. The curves may be scaled by peak fire temperature, as shown in Figure 5.

Generate IFA response curve. The recommended damage parameter for IFA of building systems is the story deflection ratio, which measures the maximum vertical deflection divided by the story height. This damage parameter or another representative value should be recorded for each fire time-temperature curve using the results of the incremental analyses conducted in the previous step.

Develop fragility curves. The IDA and IFA results should be used to generate fragility curves, which identify the probability of failure to occur. Fragility curves have been used extensively in seismic analyses to calculate the probability of collapse or failure of a structure at different IMs. Fragility curves are determined using the following equation

P (C | x) = φ (\frac{\ln (\frac{x}{θ})}{β})

(1)

where $P (C | x)$ is the probability of collapse or failure at an IM of x. $φ (\cdot)$ indicates a normal cumulative distribution function. θ is the mean of the fragility function and β is the standard deviation. The results from IDA and IFA should be plotted relative to one another to create a 3D surface plot, which is illustrated in Figure 5. This plot will indicate the probability of collapse of the structure with varying severities of earthquake and cascading fire hazards. This will evaluate the vulnerability of steel moment frame buildings subjected to fire following earthquake hazards.

Figure 4.

Part 1 of proposed PEF methodology.

Figure 5.

Part 2 of proposed PEF methodology.

This methodology has been implemented recently by the authors to evaluate the design of a 10-story steel office building located in Chicago, IL. The results from this evaluation are beyond the scope of this article and the subject of a future publication.

Footnotes

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

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