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National Bureau of StarKlards

Library, E-01 Admin. BIdg,

OCT 6 1981

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3 9:1

/oo NBS TECHNICAL NOTE 985

U.S. DEPARTMENT OF COMMERCE/National Bureau of Standards

Fire Effects on Reinforced

Concrete Members

QC

100

.U5753

1^0.985

1979
NATIONAL BUREAU OF STANDARDS

The National Bureau of Standards' was established by an act ot Congress on March 3, 1901. The Bureau's overall goal is to strengthen and advance the Nation's science and technology

and facilitate their effective application for public benefit. To this end, the Bureau conducts

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the Institute for Computer Sciences and Technology.

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'Headquarters and Laboratories at Gaithersburg, MD, unless otherwise noted; mailing address Washington, DC 20234. -Some divisions within the center are located at Boulder. CO 80303.
^EP 13

?9%^"'

Fire Effects on Reinforced

Concrete Members

Bruce Ellingwood

James Shaver

y

Center for Building Technology

National Engineering Laboratory

National Bureau of Standards

Washington, D.C. 20234

HT OF cr

^^tEAV O^ --r^

U.S. DEPARTMENT OF COMMERCE, Juanita M. Kreps, Secretary

Luther H. Hodges, Jr., Under Secretary

Jordan J. Baruch, Assistant Secretary for Science and Technology

i '- NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

Issued August 1979
National Bureau of Standards Technical Note 985

Nat. Bur. Stand. (U.S.), Tech. Note 985 , 42 pages (Aug. 1979) CODEN: NBTNAE

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 1979

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402

Stock No. 003-003-02104-1 Price $2.00

(Add 25 percent additional for other than U.S. mailing).
TABLE OF CONTENTS

Page

Abstract

Notation

1. Introduction

2. Development of Alternate Fire Curves

3. Validation of Thermal Analysis ......

4. Studies of Structural Response

5. Conclusions

6. References

iv

V

1

2

9

17

33

35

111
FIRE EFFECTS ON REINFORCED CONCRETE MEMBERS

Bruce Ellingwood and James Shaver

Fire ratings for structural assemblies in the U, S. are currently measured by endurance of or temperature rise in components subjected to a standard test. Analytical procedures show considerable

promise for alleviating the extensive testing required, and for placing

fire resistant structural design on a limit states basis. In this

study, thermal and structural analyses for reinforced concrete members

are validated using experimental data. Temperature distributions

computed in reinforced concrete members for several realistic fire

exposures are examined and compared to the distributions measured in a

standard test. Parameter studies show the effect of typical variations

in thermal diffusivity, emissivity and conductivity. Structural responses for the different fire exposures are also briefly compared.

Key words: Concrete (reinforced); fire load; fire resistance; fire

tests; structural engineering; temperature; thermal analysis.

IV
NOTATION

Aj, A^- = Floor area, wall area;

A , A^ = Area of opening, total bounding surface area;

h = weighted height of openings;

h^ = conduction coefficient;

k = thermal conductivity;

q, q£ = fire load referenced to total bounding surface area,

floor area, respectively;

T, t = temperature, time, respectively;

e = surface emissivity coefficient;

pC = heat capacity;

a = Stefan - Boltzman constant;

\}) = ventilation or opening factor.

1. INTRODUCTION

Losses due to fire in the U.S. exceed losses from other extreme

environmental factors which are normally considered in structural

design. In the U.S., fire ratings for structural assemblies are

currently based on the time period until structural failure, loss

of integrity, or excessive temperature rise occurs in structural

members subjected to the standard ASTM E119 [14] fire endurance

test. These tests, which form the basis for most code requirements,

are very costly and do not provide a basis for extrapolating to

situations not covered by the limited test data. Moreover, there

is substantial evidence [8-12] to show that the ASTM fire test may

be an inappropriate indicator of performance for many kinds of

realistic fires.

In recognition of these factors, analytical procedures have been

developed and are currently being extended [1, 2, 3, 4, 6] which

show promise in predicting structural behavior under conditions

simulating severe fire exposures. These procedures enable the

effects of various material parameters on thermal and structral

response to be studied without resorting to expensive laboratory

testing. They also make it feasible to consider alternate fire

curves (tirae-temperature histories) for design in addition to ASTM

E119; the necessity for doing this has been recognized by various

standards organizations in Europe.

Numbers in brackets denote references found at the end of this report.

1
Improved analysis procedures, validated by limited experimental

data, make it possible for the designer to consider fire explicitly

as another limit state. The development of fire resistant design

procedures based on identifiable limit states of performance and

realistic fire curves should lead to cost savings in certain structures and result in more uniform reliability for all structures.

The present paper contributes to the data base which is necessary for improved fire resistant design procedures to evolve in the

U.S. Temperature distributions in various reinforced concrete sections are studied as functions of thermal conductivity and heat capacity. Temperature distributions corresponding to alternate fire

exposure curves are also illustrated; these curves were developed

utilizing data from a recent survey of fire and live loads in offices

in the U.S. conducted by the National Bureau of Standards. Finally,

the sensitivity of structural behavior of simple reinforced concrete

members to the different fire curves will be examined briefly. These

parametric studies are necessary to assess the effect of these curves

on the variability in member performance in a realistic fire.

2. DEVELOPMENT OF ALTERNATE FIRE CURVES

The standard ASTM E119 fire test imposes three conditions for

failure for reinforced concrete components: (1) Collapse of the

component or failure to inhibit passage of flame or hot gasses; (2)

Attainment of the limiting average temperature of 593°C (1100°F) in

reinforcement; (3) Rise of 139°C (250°F) in the average temperature

of the unexposed surface of the test component. The applied

2
temperature-time relation (fire curve) is monotonically increasing

during the rating period and is identical for walls, floors, columns

and beams. This test is useful as a standard procedure for comparison purposes, but may not always provide a good indication of how

the component might be expected to behave in an actual fire. Except

for the first failure condition, the test failure criteria are not

directly related to any physically meaningful limit state of performance. Moreover, the use of one unique increasing fire curve fails

to recognize that the amount and composition of material in the

compartment, as well as ventilation effects, will cause variations in

the rate of heat generated and the peak temperature reached.

Finally, structural and heat transmission effects which occur following the rising temperatures during the rating period are not

accounted for [8, 9, 10, 11].

Numerous compartment fire tests have been conducted in recent

years. These indicate that while the fire curves depend on many

factors, the two significant parameters are the fire load q per unit

area (described subsequently) and a ventilation or "opening" factor

defined as il* = A / h/A^^, in which A = total area of window and

door openings, h = weighted average height of openings, and A^ =

total area of compartment bounding surfaces [8-11]. With q and ^

defined, realistic fire curves for design can be generated [11].

The National Bureau of Standards has recently completed a survey

of fire and live loads in office buildings in the U.S. [5]. The fire

loads reported represent the total weight of combustible items within

3
a room converted to equivalent weights of combustibles having a

calorific value of 18.6 MJ/kg (8000 Btu/lb). This was then divided

by the room floor area to obtain the load intensity (load per unit

area) reported. The effects of several factors on the fire load were

•considered. In general, it was found that the fire loads did not

depend on the geographic location, height or age of the building, nor

was there any significant different between government and private

office buildings. On the other hand, the magnitude of room fire loads

appeared to be strongly correlated to the use of the room; moreover,

file, library and storage rooms which tended to have low values of

^ were more heavily loaded than general and clerical offices which

generally had high values of ^. Table 37 of Ref. 5 shows that the

mean and standard deviation of the total fire load (in equivalent

weight; see preceding paragraph) for general clerical offices are

350 N/m^ (7.3 psf) and 211 N/m^ (4.4 psf), respectively; the 95 percentile values is 737 N/m (15.4 psf) according to Fig. 14 of the

1 /2 same reference. The average opening factor was \|) = 0.081 m

'

(0.146 ft^/2) with a standard deviation of 0.07 m^^^ (0.127 ft^^^),

indicating that the scatter in ^ is quite large.

In order to use the method of Ref. 11 to generate fire curves,

the above fire loads must be converted to load per unit area of

bounding surface (wall plus ceiling plus floor). That is, with

q£ = W/A£ reported in Ref. 5,

q = J_= q

1 (1) A, ^f 2 + A^/Af

Table 32 of Ref. 5 may be used to estimate A^/A^; it was found that

(2 + A^/Aj) ranged from about 0.25 to 0.36. For purposes of

1
obtaining a fire curve for general and clerical offices, then,

q » 0.3 q^.

Using a derating factor of 0.9 [5], to reflect the fact that

combustibles enclosed in steel furniture may not be totally consumed

in a fire, we find that for general and clerical offices the mean

value of q is 179 MJ/m and the 95-percentile value is 378 MJ/m with

1 /2 a mean opening factor 0.081 m ' , The mean and 95-percentile short

duration high intensity design fire curves thus obtained (SDHI-M and

SDHI-95) are compared in Fig. 1 to the ASTM E119 fire curve. The

decrease in temperature following the exhaustion of the finite amount

of fuel is characteristic of realistic fire curves [9, 10], but currently is not taken into account in standard fire tests, since performance is only considered during the rising temperature portion.

Similar fire curves can be generated for other room uses.

Lumping the fire load data on file and storage rooms for government

and private offices [5], the mean q^ = 277 MJ/m (13.6 psf) and

1)) = 0.03 m^/2 (0.016 ft^/^). Here, q

* 0.25 q^, as file and storage

rooms tend to be small. The corresponding long duration moderate

intensity fire curve (LDMI-M) using the conservative derating factor

of 0.9 is also compared to the ASTM curve in Fig. 1. In contrast to

the fire curves for general and clerical offices, the curve for file

and storage rooms indicates a lower maximum temperature but a longer

fire duration. This is a reflection of the lower ventilation factor,

which reduces the rate of combustion, as well as the higher fire load.
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These fire curves are quite similar to the temperatures observed in compartment fire tests. For example, recent fire tests have

been conducted at NBS in which the test compartment simulated a

residential recreation room. The equivalent fire load was 225 N/m

1/2 (4.7 psf) referenced to the floor area and ip = 0.05 m ' . A time

history of average upper air compartment temperatures measured

directly during the test is shown in Fig. 2 (curve DATA). The

irregularities in the time-temperature history are typical in fire

tests. Compartment temperatures were only monitored for one hour;

the remaining portion of the curve (dotted line) is estimated. The

trend for the portion of the curve for which data are available is

quite similar to those previously discussed. Curves developed [11]

with q = 100 MJ/m (roughly equivalent to the 4.7 psf fire load on

the floor) and with 'I' = 0.04 m^'^ and i|) = 0.08 m

^'^ are shown in

Fig, 2 for comparison. Considering the inherent scatter in fire

testing, the agreement is quite good.

Conceptually, different fire curves can be generated for any

combination of fire load and opening factor, including the effect of

different bounding surface compositions [11]. Considering the present

state of fire resistance design in the U.S., however, such refinements may not be desirable in the short term or even necessary in

order to obtain more realistic estimates of structural performance

during fires and to foster the adoption of limit states design procedures. The survey of fire loads in offices [5] revealed that

* These data made available courtesy of by Dr. J. B. Fang of the Center

for Fire Research, National Bureau of Standards.
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areas which are more heavily loaded also tend to be poorly ventilated. Thus, it would appear that improvements and potential economies

in fire resistant design for office buildings could be achieved by

initially specifying just two design fire curves; the first for

heavily loaded, poorly ventilated areas such as storage rooms (LDMI),

and the second for lightly loaded, well ventilated areas such as

general offices (SDHI). Additional curves can be specified at a

later time for other occupancies (residences, commercial establishments, warehouses, etc.) by standards writing organizations if they

feel the situation warrants them. In the following sections, the

response of members to such curves is compared with their response

to the ASTM fire curve.

3. VALIDATION OF THERMAL ANALYSIS

A thermal analysis of a non-reinforced rectangular concrete

section was made to study the effect on temperature distribution of

varying the thermal properties of the concrete (conductivity, capacity) and the parameters on the fire boundary (convection, emissivity). The analysis is two dimensional, and it has been assumed

the material is homogenous. There are no phase changes or exothermic

reactions. The possibility of cracking during the fire has been neglected. The results of the analysis are compared with experimental

data from an ASTM Fire Test provided NBS by the Portland Cement

Association (PCA)*.

Data provided courtesy of Mr. M. S. Abrams , Mgr, Fire Research

Station, PCA. A paper entitled, "Temperature Distribution in

Concrete Beams During Fire Tests," by T. D. Lin and M. S. Abrams

documenting these tests is currently in preparation.
The thermal analysis was performed with a computer program*

which solves by forward differences the nonlinear heat conduction

equation:

pCp[T] T + k [T] T = Q [T, t] (2)

in which pC = the heat capacity matrix, k = the conductivity matrix,

Q = the heat input vector, t = time, T = temperature vector and the

dot represents differention with respect to time. Q is defined at

the boundary nodes by,

Q = h^ (T^ - Tg) + ead/ - Tg^) (3)

The first and second terms in Eq. 3 are convection and radiation

components, respectively; h = the convection coefficient, e = the

emissivity coefficient, a = the Stef an-Boltzman constant and, T^»Tg =

absolute air and surface temperatures. The accuracy and stability of

the solution to Eq. 2 is based on a limited time step within each

time interval which is a function of the material properties and

boundary conditions during the time interval.

Figure 3 shows the grid used in the analysis of the 203 mm by

406 mm (8 x 16 in) rectangular cross section and the circles denote

the locations of the thermocouples on the cross-section during the

PCA test. Due to symmetry only half of the cross-section was

analyzed. The ASTM test is simulated analytically by exposing the

bottom and side of the section to the fire while the top is exposed

to the ambient air temperature.

it The computer program was initially developed by Mr. Ulf Wickerstrom

of Lund Institute of Technology, Sweden.

10
TOP OF BEAM

FIRE BOUNDARY

BOnOM OF BEAM

THERMOCOUPLE

GRID LINE

Fig. 3 Non-reinforced Rectangular Concrete Section Used in Thermal

Analysis Validation

11
Temperature changes have a marked effect on the thermal properties of concrete and a wide range of values have been reported by

different investigators. This range is due to the composite nature

of concrete and varies with the properties of the aggregate and cement, their proportions, moisture content and also the history and

age of the concrete. Despite this scatter it has been found that

the conductivity of concrete generally decreases with an increase in

temperature as shown in Fig. 4. The range of values indicated by the

shaded area in Fig. 4 was reported by Bizri [3] and the dashed line

represents the conductivity model used in this study. The other

two conductivity models indicated by the triangle and square were

reported by Anderberg [1] and Petterson [12] , respectively. The heat

capacity of concrete is a function of both the density, p, and the

specific heat, C , of concrete. Although both change with temperature

as might be expected due to drying, dehydration, etc., the product

of the two, PC , remains essentially constant with increase in

temperature. Bizri used pC = 745 W-hr/m-^-°C (40 Btu/ft^-°F) while

Petterson suggested that pC = 590 W-hr/m^-°C (32 Btu/ft-^-°F) between

and 400°C (752°F) and 764 W-hr/m^-°C (41 Btu/ft^-°F) for temperatures

greater than 800°C (1472°F).

Analysis were conducted using the three diffusivlty (k/pC )

relations (numbered for reference in further figures) shown in

Fig. 5 to study the effect that thermal properties and their variability have on temperature distributions. One value for thermal

capacity, pC = 725 W-hr/m-^-°C was used. Thermal diffusivity is an

indication of ability to respond to a sudden temperature change; a

12

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REF. 3 a REF. 12

500 1000 TEMPERATURE ("C)

Fig. 4 Effect of Temperature on Conductivitv of Concrete

1500

500 1000 1500 TEMPERATURE ("C)

Fig. 5 Concrete Diffusivity Functions Used in Thermal Analysis Validation

13
low value such as that of concrete Indicates slow response. Figures

6 and 7 show the computed temperature variation along the crosssection center line for the three diffusivity models along with the

PCA thermocouple data. In comparison to the thermocouple data at

both 2 and 4 hours, all three models over-predict the temperatures

at the fire boundary (bottom of beam) and under-predict the temperature at the unexposed surface (top of beam). It should be noted that

the thermocouple on the fire boundary may not give an accurate reading

of the concrete surface temperature because of the care that is taken

to protect it from damage during the fire test, type of thermal couple

used, method of attachment, etc. Since under-reinforced beams fail

primarily due to loss of steel load carrying capacity the more important region for agreement between measured and predicted temperatures

is between 38 mm (1.5 in) and 102 mm (4.0 in) from the bottom of the

beam where the reinforcing steel would be located. At 64 mm (2.5 in)

which is representative of the reinforcing steel centroid the variation in the predicted value is + 100°C from the measured at 2 hours

while the variation from the measured is + 200°C at 4 hr. Much of

this difference can be explained as a result of the material variability that is inherent to the problem (e.g. Fig. 4), i.e., the actual

k and pC for the PCA test beams are not known.

Because of the difference between the measured and computed

temperature values on the fire boundary a brief study was made of

the effect a variation in fire environment parameters has on the heat

input vector Q. Figure 8 shows a plot of measured and computed

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temperatures as a function of time at the center of the bottom fire

boundary surface. As can be readily seen, there is a significant

difference between the measured surface temperature and the ASTM fire

temperature. However, the predicted temperatures follow the ASTM

fire curve rather closely. A reduction of h has very little effect

after 1 hr, as might be expected from Eq. 3, while a change in emissivity from 0.8 to 0.5 is significant up to about 3 hours.

It has been found [2] that reinforcing bars have a small effect

on the temperature distribution on cross sections when the reinforcement ratio is less than about 0.04. Accordingly, their presence has

been ignored in thermal analysis of the lightly reinforced members

discussed in the following sections.

4. STUDIES OF STRUCTURAL RESPONSE

A series of simply supported beams fabricated with normal weight

concrete and spanning 12.2 m (40 ft) with sections as shown in

Fig. 9 were tested by PCA [7] using the ASTM E119 fire. The available test data enable certain aspects of the present thermal and

structural analysis to be checked.

As an illustration of this, the predicted midspan deflections

of the beam during the first two hours of the ASTM and DATA fires

are compared to observed deflections [7] in Fig. 9. The agreement

between the predicted and test deflections for the ASTM fire is

quite close, the difference being attributable in part to the

slightly higher predicted steel temperatures and accompanying

17
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increased flexibility in the beam. In contrast with the behavior

during the ASTM fire, the beam exposed to the DATA fire shows a

rapid increase in deflection for the first 25 minutes or so but

subsequently its deflection increases very little, due to the

effect of the cooling phase. Comparisons of the predicted and

observed endurance of the beam under the ASTM fire in terms of

ability to carry load were also quite close [6]; predicted endurance ranged from 240 to 370 minutes, depending on material properties, while the test failures range from about 300 to 360 min.

Temperature distributions on the cross section shown in

Fig. 10 were developed using the various fire curves shown in

Fig. 1. This section would correspond, for example, to a section

from a beam-supported slab or waffle slab floor system.

Figure 11 shows how the cross section was descretized to analyze the development of temperatures during the various fires. An

additional division in the flange portion of the section, indicated

by the dashed line, was introduced to examine the effect of mesh

refinement on the temperature distribution in that region. This

additional nodal line produced a change of only about 0.5 percent

in the temperature distribution resulting from the SDHI-M fire

exposures, indicating that a fine mesh is only necessary in regions

of high thermal gradients which occur near the fire boundaries.

The accuracy and stability of the solution of Eq. 2 also

depends on the time increment used during the solution. The

19
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457.2min |18.0|

431.8min |17.0|

406.4mm (16.0)

381.0mm (15.0)

355.8mm |14.0|

297.8mm (11.72)

239.8mm |9.44|

181.8mm (7.157)

123.8mro (4.875)

93.70mm (3.89)

83.50mm (2.5)

31.75mm (1.25)

Fig. 11 Cross-Section Descretization for Beam-Slab Section

21
maximum permissible time increment is determined from a stability

criterion which depends on the thermal properties of the material

and mesh size. Of course, smaller time increments would be expected

to affect the accuracy of the solution. Accordingly, a brief examination was made of the effect that reducing the time increment has

on the temperature distribution in a 102 mm (4 in ) flange exposed

to the SDHI-M fire. A variation in time increment between 30 sec

and 1.5 min produced temperature changes of approximately 0.5 percent. Therefore,* the time increment can be selected simply on the

basis of the stability criterion.

Temperature distributions along vertical sections A-A are compared in Fig. 12 for an exposure period of two hours for the ASTM

and SDHI-95 fire curves, the latter being a severe but realistic

curve. Temperatures are generally higher than they were for the

PCA beam (ASTM fire in both cases) due to the reduced width of the

T-stem. The cooling phase of the SDHI-95 fire curve causes significant differences after the hour of fire, particularly in regions

close to the fire boundary. The interior of the section continues

to heat slowly for a time while the exterior layers are actually

cooling due to the decrease in fire temperature. This is similar

to the inertial effect in dynamics and occurs because concrete is

a relatively poor conductor. Physically, it has the effect of

making the thermal strains on the cross section more uniform.

In contrast to the PCA beam (Fig. 9), the reinforcing bar cover

here is the ACI minimum of 38mm (1-1/2 in). This decrease in bar

22

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cover from 51 mm (2 in) raises the predicted temperature in the lower

corner bar after 2 hr of the ASTM fire from the 360°C (680°F) in the

PCA beam to 501°C (934°F); after 4 hr, the respective values are 580°C

(1076°F) and 757°C (1345°F). The maximum predicted temperature for the

lower corner reinforcing bars and time at which it occurs during a

fire duration of 4 hr are compared in Table 1 for the different fire

curves.

Table 1 - Maximum Reinforcement Temperature

for Cross Section in Fig. 10

Fire Curve Max. Temp °C (°F) Time of Occurance (min)

SDHI-M 276 (529) 92

SDHI-95 408 (766) 114

LDMI 489 (912) 168

ASTM 757 (1395) 240

Only in the case of the ASTM fire does the steel temperature rise

above the 593°C (1100°F) limit which is imposed by ASTM E119 for

reinforced concrete members; this limit is reached at 155 min.

Assuming that the 593°C (1100°F) has some significance from a limit

states viewpoint, this suggests that ratings determined using

ASTM fire curve tests for the structural component in Fig. 10 would

tend to be conservative in terms of structural behavior during an

actual fire.

24

m^BOBtaiSM^BMM
A comparison of maximum temperatures on the unheated surface of

the 102 mm (4 In) slab during fires of 4 hr duration Is shown In Fig.

13. It Is Interesting to compare the time lag between these and the

maximum fire temperatures of Fig. 1. Except for the early part of

the exposure (less than 2 hr) temperatures tend to be higher for the

LDMI than SDHI curves. This Is because of the extended time at elevated temperature coupled with the poor thermal conductivity of concrete. The maximum temperature rise of 139°C (250°?) above the

initial temperature of 20°C (68°F) allowed by ASTM E119 for floor

assemblies is reached at 110 min for the LDMI fire, and is closely

approached by the SDHI-95 fire at 125 min. The maximum allowable

temperature rise with the ASTM fire is reached at about 90 min; the

conventional rating for the slab thus would be 1-1/2 hr, assuming

that heat transmission Is the controlling criterion of failure.

This does not lessen the value of the ASTM test as a basic comparison tool, since the original purpose of limiting the temperature

rise on unexposed surfaces was to prevent the ignition of combustibles in adjoining compartments. However, the face that in approximately 95 percent of the realistic short duration high intensity fire

exposures in offices such temperatures would not develop in common

reinforced concrete construction raises the question of whether some

alternate test procedure ought to be developed for use when evaluating a component's resistance to fire spread in those circumstances.

The use of more realistic curves could lead to less costly fire protection.

25
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The effect of flange thickness on the maximum temperature rise

on the unexposed surface of the flange during the SDHI-94 and SDHIM fires is shown in Fig. 14. Flange thicknesses of 64 mm, 102 mm

and 152 nun (2.5, 4 and 6 in) were chosen as typical of the range of

thicknesses that might be found in practice. The temperatures on

the unexposed surface of the 64 nun (2.5 in) flange are substantially

higher than those for the other two thicknesses due to the insulation provided by the increased mass of concrete. The 102 mm (4 in)

flange barely satisfies the criterion for maximum temperature rise

for the SDHI-95 fire (see also Fig. 13). It follows that a 89 mm

(3.5 in) slab would fail to satisfy this criterion for the SDHI-95

fire but would be satisfactory for the SDHI-M fire. Note also that

differences between the maximum temperatures reached during each

fire decrease with increasing flange thickness.

The inherent scatter in the fire load and associated statistical

variability in the time-temperature curve naturally causes variability in the reinforcement temperatures during the fire. Assuming that

the fire load is normally distributed [5], the standard deviation in

reinforcing bar temperature increases from about 36°C at 1 hr to 73°C

at 4 hrs. This variability is in addition to that in conductivity

(Fig. 4) and other material parameter uncertainties. When this is

viewed along with the scatter in the reduced steel yeild stress at

elevated temperatures [3, 6], it is apparent that the member load

capacity during an actual fire might be quite variable. These

various sources of uncertainty ought to be identified and quantified

27
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28
so that appropriate fire resistant design safety criteria can be

developed. Studies leading toward this objective are currently in

progress at NBS [6].

Finally, the behavior of a simply supported beam spanning

6.1 m (20 ft), with the cross section shown in Fig. 10 was analyzed.

However, in this example, the vertical edges of the flange were

exposed to the fire. This beam carried a uniform load of 43.2 kN/m

(2.96 k/ft); in contrast to the 12.2 m (40 ft) PCA beam previously

studied, the nominal shear stress at room temperature was considerably higher. The beam was fabricated using Grade 60 reinforcement and nominal 4000 psi (27.6 MPa) concrete.

A comparison of the temperature on the unheated surface for the

two flange boundary conditions (vertical edges exposed and unexposed)

is shown in Fig. 15 for the SDHI-95 fire curve. Temperatures along

the centerline (slab and T stem) of the section are virtually the

same in both cases due to the insulating properties of the concrete

mass. The temperatures in the flange are quite responsive to the

fire curve when the flange vertical edge is not insulated. When

this edge is insulated, extending the width of the flange does not

materially change the maximum surface temperature, and this temperature is virtually constant more than 152 mm (6 in) from the centerline.

The nonlinearity of the temperature distribution (e.g. Fig. 12)

has a significant effect on the behavior of bean or column cross

29
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30
sections. The exterior heated portions of the member tend to develop

compressive stresses while the interior, which remains relatively

cool due to the poor thermal conductivity of concrete, tends to go

into tension to equilbrate stresses. This can cause certain portions

of the cross section to crack or crush if the limiting strains of

the concrete are exceeded, as shown in Figs. 16a and 16b for a section at the beam quarter span. The cracked portion at t = is

simply due to normal flexural cracking. As the fire progresses,

portions of the interior of the beam which were previously in compression crack while at the same time elements on the heated boundary

begin to crush. This crushing has also been observed in beams fire

tested by PCA [7]. Although the degradation of the section does not

appear to be as severe for the SDHI-95 fire curve as for the ASTM

fire curve, in both cases relatively little of the section remains

entirely undamaged.

This degradation of the section can have serious consequences in

certain structural members. For very long lightly loaded spans where

the shear-moment (V/M) ratio is small, significant degradation of the

section can be tolerated. In fact, this was demonstrated during the

PCA fire tests [7] where the 12.2 m (40 ft) spans had sufficient rotational capacity in flexure to a form plastic hinge at midspan at failure. However, this may not be possible in shorter spans with higher

V/M, where the extensive cracking or crushing may cause a shear failure before the more gradual flexural failure develops. Cracking of

the section, itself, does not necessarily imply a significant loss

31
t =

CRACKED

CRUSHED

ASTM - t = 30 min ASTM - t = 1 hr

a) ASTM Stress Distribution

SDHI-95 t = 30 min SDHI-95 t = 1

b) SDHI-95 Stress Distribution

Fig. 16 Effect of Stress Distribution on Beam-Slab Section for ASTM and

SDHI-95 Fire Curves

32
of shear capacity, as aggregate interlock or Interface shear transfer

provides a certain amount of shear resistance even in a cracked section. However, when significant portions of the concrete on the

heated boundary crush (e.g. Fig. 16) and subsequently are lost, the

shear reinforcement loses much of its protection against high temperatures and may lose some of the anchorage required for effective shear

resistance. Under these circumstances, extensive cracking of the

core becomes a matter of concern.

Recently published guides for fire resistance design (e.g.,

Ref 13) have emphasized the flexure limit state, wherein the behavior of the structural member is essentially controlled by the

temperature in the longitudinal reinforcing or prestressing steel

[6]. The present study suggests that this procedure generally would

not be sufficient for more heavily loaded structural members; in the

latter case, an analysis which considers thermal strain-induced

cracking and crushing, as well as steel temperatures, should be carried out in a limit states design procedure.

5. CONCLUSIONS

The calculated performance of reinforcement concrete members

exposed to various fire conditions has been examined. Available

test data show that reasonable predictions of structural behavior can

be obtained using analytical methods currently under development at

NBS and elsewhere. Conceptually, therefore, there is no reason why

fire resistant structural design cannot be treated in a limited state

design context provided that realistic fire curves can be developed.

33
In this regard, realistic fire curves have been proposed which are

based on recent load surveys and fire test data. The ASTM fire

curve, represents only one of many possible fire exposures and,

based on heat transfer calculations, generally provides a very

conservative indication of how a structural member will perform in

an actual fire. Design economies could be realized if building standards were to permit the use of realistic fire curves for calculation

of structural behavior in fire resistant structural design.

ACKNOWLEDGEMENT

The comments offered by Mr, Daniel Gross of the Center for Fire

Research, National Bureau of Standards, are gratefully acknowledged.

34
6. REFERENCES

1. Anderberg, Yngve, "Fire-exposed Hyperstatic Concrete Structures,"

National Swedish Building Research Document Dl 1973, Stockholm,

1973.

2. Becker, J. Bresler, B., "FIRE-RC - A Computer Program for the

fire Response of Reinforced Concrete Frames," Dept. or Civil

Engineering, University of California, Berkeley Report UCB 74-3,

July 1974.

3. Bizri, H., "Structural Capacity of Reinforced Concrete Columns

Subjected to Fire Induced Thermal Gradients," Dept. of Civil

Engineering, University of California, Berkeley, Report UC-SESM

73-1, Jan 1973.

4. Bresler, B., "Fire Protection of Modern Buildings: Engineering

Response to New Problems," Dept. of Civil Engr. , Univ. of Calif.,

Berkeley Report UCB FRO WP 77-3, June 1977.

5. Culver, C. G., "Survey Results for Fire Loads and Live Loads in

Office Buildings," National Bureau of Standards Building Science

Series 85, Washington, D.C., May 1976.

6. Ellingwood, B., Shaver, J. R., "Reliability of RC Beams Subjected

to Fire," Journal of the Structural Division , ASCE, Vol. 103,

No. ST5, Proc. Paper 12945, May 1977, pp. 1047 - 1059.

7. Gustaferro, A. H., Abrams, M. S., Salse, E. A. B., "Fire Resistance of Prestressed Concrete Beams, Study C: Structural Behavior During Fire Tests (BID 009. OIB), Portland Cement Association,

1971.

8. Harmarthy, T. Z., "Fire Resistance versus Flame Spread Resistance,'

Fire Technology, Vol. 12, No. 4, November 1976, pp 290 - 302.

9. Lie, T. T., "Characteristic Temperature Curves for Various Fire

Severities," Fire Technology, Vol. 10, No. 4, November 1974,

pp. 315-326.

10. Lie, T. T., Stanzak, W. W. , "Structural Steel and Fire - More

Realistic Analysis," Presented at the April 1974 ASCE National

Structural Engineering Meeting, held in Cincinnati, Ohio

(Preprint 2256).

11. Magnusson, S. E., Thelanderson, S., "Temperature-Time Curves for

the Complete Process of Fire Development," Acta Polytechnica

Scandinavica, Civil Engineering and Building Construction Series

No. 65, Stockholm, 1970.

35
12, Petterson, 0., "Theoretical Design of Fire Exposed Structures,"

Division of Structural Mechanics and Concrete Construction

Bulletin 51, Lund Institute of Technology, Lund, Sweden, 1976,

13, "PCI Design for Fire Resistance of Precast Prestressed Concrete."

prepared for the PCI Fire Committee by A, H. Gustaferro and

L, D, Martin, Prestressed Concrete Institute, 1977,

14, "Standard Methods of Fire Tests of Building Construction and

Materials," (ASTM E-119-76) Annual Book of ASTM Standards , Part 18 , American Society for Testing and Materials, Philadelphia,

PA, 1976,

36
NBS-114A (REV. 9-78)

U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO. NBS TN 985ci^sslon No.

4. TITLE AND SUBTITLE

Fire Effects on Reinforced Concrete Members

Z, m6ipimt$^ M^^9.hi^ ^'^.

5. Publication Date August 1979

W.' Pertenntng Orpnlxatloft Code

7. AUTHOR(S)

Bruce Ellingwood and James Shaver

8. Performing Organ. Report No.

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, DC 20234

*orlt Onft No.

11. Contract/Grant No.

12. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS fS<ree(, City, state. ZIP) 13. Type of Report & Period Covered Final

14, %)onsorinje Agency Code

15. SUPPLEMENTARY NOTES

I I Document describes a computer program; SF-185, FIPS Software Summary, is attached.

16. ABSTRACT (A 200-word or teas tactual summary ot moat signilicanl information. It document includes a signilicent bibliography or

literature survey, mention it here,)

Fire ratings for structural assemblies in the U. S. are currently measured

>y endurance of or temperature rise in components subjected to a standard test.

Analytical procedures show considerable promise for alleviating the extensive

Itesting required, and for placing fire resistant structural design on a limit

[states basis. In this study, thermal and structural analyses for reinforced

Iconcrete members are validated using experimental data. Temperature distribuftions computed in reinforced concrete members for several realistic fire exposures

[are examined and compared to the distributions measured in a standard test.

[Parameter studies show the effect of typical variations in thermal diffusivity,

jemissivity and conductivity. Structural responses for the different fire exposures

[are also briefly compared.

17. KEY WORDS (•'Ik to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper nami

separated by semicolons) Concrete (reinforced) ; fire load; fire resistance; fire tests structural

engineering; temperature; thermal analysis.

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