post-earthquake fire performance-based behavior of unprotected moment resisting 2d steel frames

Post-Earthquake Fire Performance-based Behavior of

Unprotected Moment Resisting 2D Steel Frames

Behrouz Behnam* and Hamid Reza Ronagh**

Received October 26, 2012/Revised December 16, 2013/Accepted February 16, 2014/Published Online August 20, 2014

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Abstract

Post-Earthquake Fire (PEF) can lead to the collapse of buildings that are partially damaged in a prior earthquake that occurredimmediately before the fire. The majority of standards and codes for the design of structures against earthquake ignore the possibilityof PEF and thus buildings designed with those codes fail prematurely when subjected to PEF. A sequential analysis based onFEMA356 is performed here on the Immediate Occupancy (IO), corresponding to a structure designed as school occupancy, and LifeSafety (LS) performance levels, corresponding to a structure designed as reside ntial occupancy, of two steel moment resistingframes. These frames are first subjected to an earthquake load with the PGA of 0.35g. This is followed by a fire analysis, using boththe ISO834 model and the Natural fire model. The time it takes for the structure weakened by the earthquake to collapse under fire isthen calculated. As a point of reference, fire only analyses are also performed for the undamaged structures. The results show thatearthquake weakened structures are more vulnerable to fire than undamaged structures. The results also show that both fire resistanceand PEF resistance of the frame designed as school are more than the frame designed as residential. Whilst the investigation is for acertain class of structures (steel moment resisting frames, 5 stories), the results confirm the need for the incorporation of PEF in theprocess of analysis and design and provides some quantitative measures on the level of associated effects.

Keywords: post earthquake fire, sequential analysis, fire resistance, steel moment resisting structures, performance based design,

immediate occupancy, life safety

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1. Introduction

The “life safety” criterion is the criterion by which most (if not

all) building structures are designed. Life safety guarantees that

even under extreme loading situation, structures will remain

gravity load bearing allowing occupants to safely evacuate the

building even though minor to major damage depending on the

level of importance of structure is allowed during an extreme

load level (Borden, 1996). While the codes guarantee the safety

under a number of load combinations representing the extreme

loading possibilities, the Post-Earthquake Fire (PEF) loading has

not been considered in the available codes. Recorded experiences

have proved that PEF can potentially bring about even more

damage in comparison with the earthquake itself. For instance, in

the PEF in Kanto, Japan in 1923, more than 447000 houses were

destructed (Scawthorn et al., 2005).

From a different perspective, as earthquake causes serious

damage to lifelines structures, arterial roads and bridges, the fire

brigades will have difficulty in suppressing burning buildings

(Collier, 2005). Accordingly, more time will be spent to control

the fire than the usual situations. This time may even be more as

helping people trapped under the rubble take priority. Thus, the

requirements of the code for the fire resistance which is often

expressed in time will be considerably more in a PEF situation in

comparison to fire alone situation. Mitigation the effect of PEF

on buildings in such a way that provides adequate time for

evacuating people trapped under the rubble shall therefore be a

key aspect of any PEF safety strategy.

Using the philosophy of earthquake design based on performance

(ATC, 2001), structural elements are normally designed to satisfy

various levels of performance some of which are Operational

(O), Immediate Occupancy (IO), Life Safety (LS) and Collapse

Prevention (CP). In buildings designed for IO performance level,

it is expected that after an earthquake, only minor damage is

sustained by structural elements. These structures are expected to

remain below 0.7% drift. Hospitals and educational centers are

normally designed to meet the IO level of performance as these

buildings are expected to remain serviceable after earthquake. By

contrast, buildings designed to meet the LS level of performance,

will sustain notable damage with the values of total drift around

2.5%, if hit by the design level earthquake. However, the

structures at this level of performance can still carry all gravity

loads and no failure will occur. Most buildings in urban areas,

such as residential and light commercial buildings are designed

Post-Earthquake Fire Performance-based Behavior of Unprotected Moment Resisting 2D Steel Frames

Vol. 19, No. 1 / January 2015 − 275 −

to meet the LS level of performance. The main objective at this

performance level is to limit the level of damage in the buildings

and as a result ensure life safety of the inhabitants. Obviously,

buildings designed for CP performance level, will sustain more

damage compared to the other mentioned levels of performance.

At this level, it is expected that the imposed drift would be more

than 5%, which can lead to extensive damage to structural

components (FEMA356, 2000). Often, temporary structures are

designed to meet the CP level of performance. These types of

structures are not considered in this study.

Understanding the structural behavior is more important when

a fire occurs after earthquake as it adds to the level of complexity.

In general, fire resistance rating is defined as a period of time in

which the integrity of a member subjected to fire is maintained to

resist applied loads (Kodur and Dwaikat, 2007). This definition

is correlated with various factors, one of which is the type of the

building being designed. Indeed, the purpose is not only to

provide sufficient time to evacuate people entrapped due to the

fire, but also to reduce the possibility of any conflagration (Taylor,

2003). Although, typically fire-resistance rating are presented in

national building codes such as NRCC (2005) and IBC (International

Building Code, 2006); much of them are provided for fire alone

and not for PEF (Mousavi et al., 2008).

Investigating PEF resistance, Della Corte et al. (2003) studied

unprotected steel moment-resistant frames and their response to fire

following earthquake. Assuming elastic Perfectly Plastic (EPP)

behavior for steel and considering P-∆ effect with P from gravity

loads and ∆ from the earthquake, the fire resistance rating was

then studied. Della Corte et al., ignoring of the degradation of

stiffness is an issue subject to discussion. Another study which

contained both numerical and experimental elements on single-

story, multi-bays steel frames when are exposed to large

uncontrolled PEF was carried out by Hosam et al. (2004). They

considered unprotected elements in their analyses, however,

every bay was assumed to be protected by firewalls to reduce

losses in uncontrolled fire. Using ABAQUS software (ABAQUS,

2008), a method was then proposed to simulate the effect of

thermal activity on laterally deformed frames. It was also shown

that the type of failure, whether inward or outward collapse, and

the PEF resistance of the models are greatly dependent on both

fire scenarios and the values of gravity loads. Compared with the

previous studies, this study was more comprehensive as it allowed

for geometrical effects as well as degradation in stiffness of

models exposed to fire. However, extrapolation to multi-storey

frames with various bays and different fire scenarios cannot be

made without further research. Further study on steel frames was

carried out by Zaharia and Pintea (Zaharia and Pintea, 2009).

They investigated two different steel frames, designed for two

various return periods of ground-motion: 2475 years return

period and 475 years. The seismic response of the structures was

then evaluated by a pushover analysis developed by Fajfar. While

the frame designed for the 2475 years return period remained

elastic in the pushover analysis, the weaker frame designed for

475 years return-period sustained notable inter storey drift. They

then performed a fire analyses on both frames, which confirmed

that the fire resistance of the structures considering their

deformed state under earthquake is lower than the structures that

do not have any history of deformation prior to the application of

the fire.

Another study was performed by Faggiano et al. (2010) on

steel structures exposed to post earthquake fire. They performed

a couple analyses consisting of both earthquake and fire. Based

on FEMA356 procedure, Faggiano et al. developed a method for

evaluating the various fire performance levels for different

conditions of fire. Recently et al. (2011) investigated the performance

of steel-concrete composite joints when seismic actions were

followed by fire loads. Using numerical analysis and experimental

tests, they showed that the composite joints designed for fire or

earthquake separately, could not provide the required minimum

fire resistance if subjected to same level fire following a same

level earthquake. They then suggested that at least 15 minutes

fire resistance should be provided in case of fire following

earthquake and accordingly, proposed a design method. A similar

studies on the performance of steel frames Sprayed by Fire-

Resistive Materials (SFRM) was performed by Ryder et al. (2002)

and Braxtan and Pessiki (2011). Two SFRM beam-columns joints

were analyzed in different situations; fire alone as a benchmark,

and quasi-static cyclic loading that was followed by fire. Their

study showed that PEF has a negative effect on the bond of

SFRM to steel when joints sustain significant deformation as a

result of earthquake load. Imperfection of insulation, i.e., SFRM,

accordingly, causes increases of heat inside the elements, which

in turn accelerates the rate of decrease in both strength and

stiffness.

Aligned with the abovementioned studies and FEMA356

performance levels definition, in this study, a series of numerical

investigations are carried out on the PEF resistance of two types

of buildings designed as a school building (corresponding to the

IO level of performance) and a residential building (corresponding

to the LS level of performance). The study includes a sequential

analysis of steel frames designed based on the AISC (2005) together

with FEMA356 definition of performance levels, subjected to

earthquake and the aftermath fire.

Fig. 1. PEF in Natori City, Japan, 2011 (Thomson, 2011)

Behrouz Behnam and Hamid Reza Ronagh

− 276 − KSCE Journal of Civil Engineering

2. Methodology

2.1 Sequential Analysis

A sequential analysis is a proper method for considering the

effect of both earthquake and fire on a structure. Fig. 2 schematically

shows the stages of the nonlinear sequential analysis.

The first stage of loading is the application of gravity loads,

which are assumed to be static and uniform. A pseudo earthquake

load then follows in a pushover form reaching its maximum and

returning back to zero in a short time. Clearly, during this time,

gravity loads are also applied. The pattern that is chosen for the

application of earthquake load is similar to pushover analysis

with the difference that the structure is unloaded after reaching

certain level of load. Here, it is assumed that the maximum level

of earthquake load corresponds to IO or LS level of FEMA356

(2000). This assumption is in-line with the seismic design

philosophy in which the performance level of structures shall not

exceed the intended level when subjected to the “Design

earthquake”. Therefore, the structures are pushed to these levels

and then are unloaded. Load duration is not important for both

gravity and earthquake loads, as long-term effects such as creep

are not incorporated in the analysis. Thus, any arbitrary load

duration could be chosen for the loads patterns. It should also be

noted that no dynamic effects are considered in this study, which

can be an issue subject to discussion. Finally, as can be seen in

Fig. 2, the fire load is applied to the structure. Prior to fire

loading, properties of structures are set to the reference

temperature, but during fire, mechanical properties change with

time.

2.2 Pushover Analysis

The static pushover analysis is one of the nonlinear static

methods that are used for analyzing structures subjected to

seismic loads. This method is becoming a popular tool for

seismic performance evaluation of existing and new structures

(Fardis, 2007; Isakovi et al., 2008). In this method, using a

specific load pattern, the structure is pushed to arrive at a

displacement called the target displacement. The target displacement

serves as an estimate of the global displacement that the

structures is expected to experience in a design earthquake often

represented by the roof displacement at the center of mass of the

structure. In this study, a vertical distribution of loads proportional

to the shape of the fundamental mode in the direction under

consideration is used. As mentioned, in FEMA356, the structural

performance level is divided into four main categories, i.e., O,

IO, LS and CP, which represent states of minor damage to

notable damage. Using the definition of lumped plasticity, the

potential locations of high plasticity are introduced by plastic

hinges in SAP2000 (2002). The moment-rotation behavior of each

plastic hinge follows FEMA definitions as shown in Fig. 3.

2.3 Steel Behavior under the Effect of Fire

Materials’ thermal and mechanical characteristics considerably

change when they are exposed to fire which in many cases result

in producing high level of thermal stresses in structures. In

addition, when a heterogeneous composite material with different

thermal characteristics is subjected to elevated temperature;

differential thermal stresses can bring about crushing and rapid

decaying. Steel, is considered as a sensitive material toward

elevated temperature with high thermal conductivity (Kathryn

and Buchanan, 2000). This characteristic leads to a rapid reduction

in the strength and the modulus of elasticity faced with elevated

temperature (Preston and Kirby, 1988). As the temperature goes

beyond 500oC, the steel ultimate strength decreases of 50%

(Purkiss, 1996).

2.4 Fire Patterns

Several parametric models have been developed to calculate

the thermal actions produced by a fire on a compartment (Lundin,

2005; Remesh and Tan, 2007). These models are established

either using “time-temperature curve” methods - sometimes called

“standard fire” - such as those mentioned in ISO 834 (ISO 834

cé

Fig. 2. Stages of the Sequential Analysis

Fig. 3. Conceptual Plastic Hinge States


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International Standard, 1999), and ASTM E119 (ASTM, 2006)

(based on experimental observations) or using “natural fire”

methods (British Standard, 2002) which rely mainly on the

volume of the produced gas by the combustible materials in a

covered space such as those stated in SEI and ASCE (ASCE,

2006). Fig. 4 shows the fire patterns according to ISO 834 and

ASTM E119.

While “time-temperature curve” methods are good enough for

estimating the temperature at a point of time in conventional

buildings such as residential and commercial buildings (Zehfuss

and Hosser, 2007), they present certain limitations such as being

applicable only to certain sizes of compartments and a limited

range of thermal properties (Lennon and Moore, 2003). By

contrast, “natural fire” methods are more accurate, because along

with directly applying the thermal properties of boundaries such

as openings and walls, other factors such as the situation of fire

detection/protection systems are also involved. However, both

models, i.e., the “time-temperature curve” and the “natural fire”,

only schematically represent fire from early ignition to the time

its fully developed as shown in Fig. 5. While these methods

differently arrive at the final temperature at a certain point in

time, they all share the common feature of representing the fire

through one single parameter, i.e., a time dependent single room

temperature (Buchanan, 2001).

The cooling phase in Fig. 5 (the dotted line) is based on the

assumption that after a while, either the air or the combustible

materials become less and less available and thus, temperature or

fire load decreases. This assumption is more realistic in the case

of fire before earthquake assuming closed openings. However, in

buildings previously damaged by an earthquake, there is a high

probability of windows breakage. As a result, the pattern of fire

progression is different comparing to normal fire (Tanaka, 1998).

For the purpose of this study, the above-mentioned methods

are used. In addition, calculating the fire resistance of the selected

models, a computer program written based on Finite Element

Method (FEM) called SAFIR (Franssen, 2011) is employed. The

program performs non-linear analyses on one, two or three

dimensional structures in which both geometrical and material

non-linearity are taken into account. The analyses can also be

performed under ambient or elevated temperature. The stress-

Fig. 4. Fire Pattern according to ISO834 and ASTM E119 (ISO

834 International Standard, 1999; ASTM, 2006)

Fig. 5. Temperature-Time Curve for Fully Developed Fire (Bucha-

nan, 2001)

Fig. 6. Case Study (Dimensions are in mm): (a) Plan View, (b) Geometric Properties



strain relationships for various materials as well as their thermal

characteristics are embedded in the software, according to

Eurocodes. Structures that are exposed to fire are analyzed in

two stages, thermal analysis and structural analysis. In the

thermal analysis, the temperature inside the cross-sections at

every thermal step is stored to be used for the subsequent

structural step.

3. Case Study

A Steel resisting frame is selected from a building as shown in

Fig. 6, designed for two levels of performances, IO and LS; with

the former loaded as if it were a school and the later as if it were

a residential building. These assumptions are then needed for

calculating fire load density. The floor and the ceiling are made

of normal weight concrete and the compartment partitions are

done with standard bricks.

The selected frame is loaded and then is designed using steel

plates (welded compact sections) with the yield stress of 240

MPa and for PGA of 0.35 g. The frame is dimensioned for the

load combinations of 8.0 kPa for dead load and 2.5 kPa for live

load. Combination of 100% dead load and 20% of live load for

the designed frame in LS level of performance, i.e., residential

building, and 40% of live load for designed frame in IO level of

performance, i.e., school building, are used to find the required

mass for calculating the earthquake load (ASCE, 2006). The

resulting sections for the designed frames are shown in Table 1.

In order to consider thermal actions, the two methods previously

mentioned in Section 2.4 are used. In order to improve our

understanding of the behavior, fire alone analyses are also

performed on the un-deformed frames. It is worth mentioning

that while exterior side of external columns is not exposed to fire,

all sides of internal columns are subjected to fire. Meanwhile,

only three sides of beams are exposed to fire, because it is

assumed that the top side is well protected by the concrete slab.

Table 2 and Fig. 7 show the thermal characteristics of the materials

in the building and the assumed fire scenarios, respectively.

3.1 Using ISO 834 Curve

Ignoring the possibility of having fire retardant materials on

the frames, both analyses, with and without earthquake are

performed assuming unprotected frames. As we are dealing with

a comparative issue, the results would be indicative of the

worsening effects of earthquake. The frames are exposed to 60

minutes ISO834 fire.

3.2 Using the Natural Fire Method

As described in Annex E of Eurocode 1, using the Natural Fire

method is valid for a covered area smaller than 500 m2 when

there is no opening in the roof (Franssen and Real, 2010). In

addition, the maximum height of the compartment is limited to

4m. The fire load density is then calculated according to Eq. (1),

which allows for the type of occupancy and the influence of

active measures.

qt,d = qf,d × (Aroof /At) (1)

in which, qt,d (MJ/m2) is the fire load of the compartment, qf,d is

the occupancy of the fire compartment, and Aroof (m2) and At (m

2)

are the areas of the roof and the total area consisting of the area

of walls, roof and floor, respectively.

qf,d = δq1 δq2 δn m qf,k (2)

where, δq1 is the risk of fire activation, which increases while the

floor area increases. For this study, δq1 is 1.54. δq2 is the type of

occupancy, which for the purpose of this study is 1.0. Combustion

Table 1. Sections Dimensions for Two Case Studies: School and Residential

Dimensions are in mm

Section typeCase study

Col 1 Col 2 Beam 1 Beam 2

School (designed for IO level)

H=450B=350tf =20tw=15

H=400B=300tf =15tw=10

H=350B=300tf =20tw=15

H=300B=300tf =15tw=10

Residential (designed for LS level)

H=400B=300tf =20tw=15

H=350B=300tf =15tw=10

H=300B=300tf=20tw=15

H=250B=250tf =15tw=10

Table 2. Thermal Characteristics of the Considered Materials

Specific heat(J/kgK)

Material’s density(kg/m3)

Thermal conductivity(W/mK)

Floor and Roof 1000 2400 1.6

Walls 840 1600 0.7

Fig. 7. Fire Scenarios: (a) Scenario 1, (b) Scenario 2


Vol. 19, No. 1 / January 2015 − 279 −

factor, shown by m in Eq. (2), is between 0 and 1, and is derived

from experimental results. It is assumed to be 0.8 for most

cellulosic materials. qf,k, or the so-called characteristic fire load

density can be calculated using the mentioned values in Annex E

of Eurocode 1, which for residential buildings and schools is 948

MJ/m2 and 347 MJ/m2, respectively. In order to take into account

the effect of active fire-fighting, the factors δn are applied in Eq.

(2). The factors are based on either available fire-extinguishing

systems established in the building such as detection systems,

and sprinklers or those used by fire brigades and rescue teams in

a professional manner. The proposed values are based on a

normal condition and as such cannot be utilized in a PEF

scenario where the whole response teams are under stress.

Consequently, the mentioned factors shall be modified. Here

based on the high possibility of disturbance of both internal

facilities such as sprinkler and detection systems and urban

facilitates as a result of earthquake, such modifications are done

as shown in Table 3. It is worth noting that the time-temperature

curve based on the natural fire method relies on several factors

some of which are thermal characteristics of materials, type of

occupancy, total area of compartment and size and shape of

openings. The fire then may behave as ventilation controlled or

fuel controlled. In most small- and medium-size compartments,

fire is governed by a ventilation mode, which means that the

growth of fire is limited by the availability of air. By contrast, in

large compartments, fires are mostly fuel-controlled, which

means that the growth of fire is limited by the availability of

combustible materials (Zehfuss and Hosser, 2007). Fig. 8 shows

time-temperature curves for the case studies and at two different

situations, before and after earthquake.

4. Results

Sectional dimensions of the beams and columns for the considered

structures were given previously in Fig. 6. All material properties

were also introduced in previous sections. The sequential analysis

comprises three main stages that are the gravity loading, followed

by the seismic pushover analysis, and finally the PEF. In seismic

analysis, the structure is subjected to a monotonically increasing

lateral load. Indeed, the structure is pushed to a certain level of

displacement. According to the philosophy of performance-based

design, it is expected that structures designed for a specific level

of performance remain at the assumed level when subjected to

the “design earthquake”. Accordingly, for the two different

levels of performance, i.e., IO and LS, two different pushover

analyses are needed. Using the FEMA356 procedure, a target

displacement shall be calculated for controlling the situation of

the structure for the assumed performance level. To do this, the

well-accepted Eq. (3) is used, in which T stands for the target

displacement and Ci are the coefficients used to convert the

elastic structural response into the inelastic response. In addition,

Sa and Te are the spectral response acceleration and the effective

fundamental period, respectively, which are determined using

the mentioned procedure in Section 1.6.1.5 of FEMA356. Using

Eq. (3), the target displacements of 340 mm and 395 mm are

calculated for the IO and the LS levels, respectively.

(3)

In this respect, SAP2000 program is used for the pushover

analysis. Moreover, FEMA procedure is used to define hinge

positions and properties. Fig. 9 shows the state of hinges resulting

from the pushover analyses at the two mentioned performance

levels. The results show that none of the hinges go beyond the

defined levels of performance. Nevertheless, it is evident that

∆T CiSa T 2π⁄( )2

gi 0=

i 3=

∑=

Table 3. Fire-fighting Measures

Types of occupancy

Fire situation

Automatic water

extinguishing systems

Water supply

Automatic fire

detection

Automatic fire alarm

Automatic transmission

A work fire brigades

An off site fire brigades

Safe access routes

Normal fire fight devices

Smoke exhaust systems

Sum

δ1 δ2 δ3 δ4 δ5 δ6 δ7 δ8 δ9 δ10 Π δn

SchoolNormal Condition 0.61 0.7 1.0 1.0 0.87 0.61 0.71 1.0 1.0 1.5 0.37

After EQ 1.0 1.0 1.0 1.0 0.87 1.0 1.0 1.5 1.5 1.5 4.52

ResidentialNormal Condition 1.0 1.0 1.0 1.0 1.0 1.0 0.71 1.0 1.0 1.5 1.64

After EQ 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.5 1.5 1.5 5.20

Note: Residential designed for LS level of performance and School designed for IO level of performance

Fig. 8. Fire Pattern according to the Natural Fire Method



after the pushover analysis some degree of damage would exist

in the structure. The damaged structure is then loaded with fire as

a sequential load, which arrives at the structure in its residually

deformed state. To do this, the SAFIR program allows a function

to be written inside its computing environment that allows

importing of the pushover loads, which are extracted from

SAP2000 at such step where the target displacement is attained.

With the structural model at the target displacement step

imported into the SAFIR environment, unloading is performed

followed by re-loading with fire.

Figure 10. shows the pushover curves for the mentioned

performance levels resulted from SAP2000 and used for the

sequential analysis in SAFIR.

The final stage of sequential analysis is to apply a PEF on the

structure. Two different scenarios are used for the fire analysis,

for both damaged and undamaged frames and using both ISO834

model and Natural Fire model. In case one, the undamaged

structure is exposed to the fire load, while in case two, the

deformed structure is exposed to the fire load. In other words, in

the first case, the fire follows the applied gravity loads, but in the

second case, the fire follows the gravity and the earthquake

loads. Fig. 11 shows the temperature distribution of fire exposure

Fig. 9. Hinge States resulted from Pushover Analyses: (a) IO Level, (b) LS Level

Fig. 10. Pushover Analysis and the Response Spectrum: (a) Pushover Curve, (b) Response Spectrum

Fig. 11. Distribution of Temperature inside the Sections using ISO834

Model: (a) Beam exposed on 3 Sides of fire, (b) Column

exposed on 4 Sides of Fire


Vol. 19, No. 1 / January 2015 − 281 −

on two types of applied sections using ISO curve and after 60

minutes.

Figures 12(a) and 12(b) show the fire resistance based on the

scenario 1 and using the ISO model in both situations, i.e., fire

alone and PEF and for the defined performance levels. The sharp

increase and then decrease in PEF analysis is due to, the

structures are firstly pushed to a certain level of displacement

and the unloaded. The deformed structures are then exposed to

fire as mentioned earlier. The fire resistance is defined as a time

at which the displacements either globally (i.e., is the drift of a

certain point) or locally (i.e., the deformations at the middle of a

beam) go beyond chosen thresholds. The thresholds have been

identified by the curve for displacements versus time step

merging towards the horizontal asymptote by a 1% error. In other

words, a member is considered as failed when it unable to resist

the initially applied gravity loads (Kathryn and Buchanan, 2000;

Almand et al., 2004) which is assumed to be the case when the

response curve becomes too flat.

As is seen in Figs. 12(a) and 13(b), there is a correlation between

the fire resistance rating and the performance levels so that the

fire resistance of the designed frame at the higher performance

level, i.e., IO, is obviously more than the frame designed for the

lower level, i.e., LS performance level. In other words, the PEF

resistance is influenced by the intensity of damage induced in the

frame during the prior earthquake. On the other hand, while in

the first scenario the collapse time for PEF-IO level is around 28

minutes, it increases to about 38 minutes in the fire only situation,

which represents a 26% difference in the fire resistance. By

contract, while the fire resistance of the undamaged frame

designed for LS level is about 32 minutes, it reduces to 25

minutes in case of PEF, which signifies a 22% reduction in the

fire resistance. Although, the fire resistances based on Natural

Fire model for both cases, i.e., IO and LS, are more than those

calculated based on the ISO model, a similarity can be observed

in terms of structural behavior, as shown in Figs. 13(a) and 13(b).

The figures show that the fire resistance of both IO and LS levels

of performance decreases when the structures are subjected to

prior earthquake. While, the fire resistance of undamaged IO and

LS cases is around 51 minutes and 24 minutes, respectively, it

reduces to about 22 minutes and 18 minutes, respectively, in case

of PEF.

The lateral displacement versus time based on ISO834 curve

and scenario 2 is shown in Fig. 14. Similar to Figs. 12 and 13, the

sharp increase and the decrease is due to the loading and

unloading steps during the application of lateral loads to the

structures. It is again evident that both the fire resistance and the

Fig. 12. Fire Resistance based on ISO834 - Scenario 1 (1st Story Lateral Displacement): (a) School (IO Performance Level), (b) Residential

(LS Performance Level)

Fig. 13. Fire Resistance based on Natural Fire - Scenario 1 (1st Story Lateral Displacement): (a) School (IO Performance Level), (b) Resi-

dential (LS Performance Level)



PEF resistance of the frame designed as residential occupancy, is

lower than those of the building designed as school. In case of

fire alone scenario, the designed frame as school occupancy fails

at around 35 minutes, while the designed frame as residential

occupancy fails at around 25 minutes. The PEF resistance of

both frames- the school and the residential- then declines

considerably to around 20 minutes and 16 minutes, respectively.

In is also observed that comparing with the first scenario, i.e.,

when the fire is applied to the first floor, the fire resistance and

the PEF resistance decline. Fig. 15 shows the fire and the PEF

resistance of the frames based on the second scenario and the

application of Natural Fire curves to the frames. Again, the

results show that both fire resistance and PEF resistance of frame

designed as school occupancy is more than that of the frame

designed as residential occupancy. In the case of fire alone

situation, the frame designed as school fails at about 40 minutes,

the frame designed as residential occupancy fails at about 18

minutes. The PEF resistance of the frame designed as school is

around 19 minutes while it is around 13 minutes for the frame

designed as residential.

A comparison between the results of Figs. 14 and 15 with those

of Figs. 12 and 13 shows that there are more reductions in the

resistance of frames in the second scenario than the first scenario.

This could be attributed to the lower stiffness of the frames in the

top story comparing to the first story. It is worth noting that two

types of collapse, global collapse and local collapse were

observed during the analyses. While the global collapse is

defined as a situation in which the frame fails because of

considerable lateral movement of columns, the local collapse

involves the failure of beams mainly. In the studied cases, both

frames, i.e., the school and the residential, and in case of PEF, the

global collapse occurred. However, the local collapse occurred

when the elements are subjected to fire alone. Fig. 16 schematically

show two types of collapse failure in the scenarios considered.

5. Conclusions

Post-Earthquake Fire (PEF) is a reality that has not received

adequate attention in the past. Investigating the effects of PEF on

structures classified as “ordinary” in the codes such as educational

and residential is important, as these buildings comprise a major

part of urban buildings. Design based on performance requires

these buildings to remain within the “life safety” level of

response under the design earthquake. These structures, however,

Fig. 14. Fire Resistance based on ISO834 - Scenario 2 (5th Story Lateral Displacement): (a) School (IO Performance Level), (b) Residential

(LS Performance Level)

Fig. 15. Fire Resistance based on Natural Fire - Scenario 2 (5th Story Lateral Displacement): (a) School (IO Performance Level), (b) Resi-

dential (LS Performance Level)


Vol. 19, No. 1 / January 2015 − 283 −

are more vulnerable if loaded with fire after they are weakened to

some extent by a prior earthquake. In this research, sequential

non-linear analysis is proposed for the PEF analysis of these

structures. Two steel moment resisting frames were selected and

designed at two different occupancy purposes, a school and a

residential building. The structures were then pushed to the

maximum allowable inter-story drift, which is assumed to satisfy

the Immediate Occupancy and Life Safety performance levels.

Pushover curve was then extracted for use in subsequent analysis.

Sequential loading consisting of gravity and lateral loads that

was followed by fire (ISO834 model and Natural fire model)

was a key aspect of the study conducted using the SAFIR

software. In SAFIR, the P-∆ effect and the residual lateral

deformation as well as degradation in stiffness were considered.

Accordingly, the following remarks can be made:

• The sequential analysis is the functional tool to consider the

effects of residual deformations from an earthquake as well

as degradation in stiffness and strength.

• Structures suffered damage from earthquake loads have

lower fire resistance than undamaged structures. This can be

the result of residual lateral displacements and the degrada-

tion of strength and stiffness that exacerbate the effects of

fire.

• Fire resistance calculated based on Natural Fire model is

more than that calculated based on the ISO834 model.

Although, there seems to be consensus worldwide on using

standard fire patterns such as ISO834, using Natural Fire

models are more accurate as several factors are considered

at the same time.

• Two types of collapse mechanisms were observed during

the fire analyses; these being global collapse and local col-

lapse. While, the local collapse occurred in the beams, glo-

bal collapse was represented mostly by considerable lateral

movement in the columns. Interestingly, the majority of fires

only analysis resulted in the local collapse while all PEF

analyses resulted in the global collapse.

• Whilst the investigations performed here were for a certain

class of structures, the results confirm the need for the incor-

poration of PEF in the process of analysis and design. Fur-

ther studies thus need to be performed either numerically or

experimentally on different structures subjected to PEF in

order to develop a better understanding of the issue.

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