Fire resistance of rectangular hollow steel sections filled with bar-reinforced concrete

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Fire resistance of rectangular hollow steel sections filled with bar-reinforced concrete

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Internal Report No. 631 Date of issue: July 1992

de recherches Canada

Institute for lnstitut de Research in recherche en Construction construction

M o w

Steel Sections

by T.T. Lie and R.J. Irwin

J

I n t e r l ' a l re-pnzsrt : I n s t z t u t e f o r Fesearc h i n C o n s t r u c t I on

C a n a d a _ANALYZE#

This is an internal report of the Institute for Research in Construction. Although not intended for general distribution, it may be cited as a reference in other publications.

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FIRE RESISTANCE OF RECTANGULAR HOLLOW STEEL SECTIONS FILLED WITH BAR-REINFORCED CONCRETE

ABSTRACT

Experimental and theoretical studies have been carried out to predict the fire resistance of rectangular hollow steel columns filled with bar-reinforced concrete. A mathematical model to calculate the temperatures, deformations and the fm resistance of the columns is presented.

Calculated results are compared with those measured. The results indicate that the model is capable of predicting the fm resistance of rectangular hollow steel columns, filled with bar-reinforced concrete, with an accuracy that is adequate for practical purposes.

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FlRE RESISTANCE OF RECTANGULAR HOLLOW STEEL SECTIONS FILLED

WITH BAR-REINFORCED CONCRETE

1 INTRODUCTION

Steel Hollow Structural Sections (HSS) are very efficient structural sections in resisting compression loads. By f m g these sections with concrete, a substantial increase in load-bearing capacity can be achieved. Also, fire resistance can be obtained without the necessity of external

fire protection for the steel section

For a number of years, the National Fire Laboratory of the W t u t e for Research in Construction, National Research Council of Canada, has also been engaged in studies to develop methods for predicting the fire resistance of these composite columns.- Thcsc studies were supported by the Canadian Steel Construction Council and the American Iron and Steel Institute. Amulti-ph& program, which involves mathematical modelling andexperiments, was set up.

In the fust phase, HSS filled only with plain concrete were studied. These studies showed that substantial reductions in the loads on the columns have to be made to obtain reproducible and predictable fire resistances. If the concrete is reinforced, however, the fire resistances remain predictable, even when very high loads are applied, as shown in studies on steel-bar reinforced concrete columns with and without steel encasing [1,2].

In this report, a mathematical model for the prediction of the fire resistance of rectangular HSS columns, filled with bar-reinforced concrete, is presented and the results produced by this

model and those from tests are discussed. 2 CALCULATION PROCEDURE

The calculation of the fire resistance of columns is canied out in various steps. It involves the calculation of the temperatures in the column and its deformations and strength during the exposure to fire.

2.1 Temperatures of Column

The column temperatures are calculated by a finite difference method 131. This method has been previously applied to the calculation of temperatures of various building components exposed

to fire [4,5]. Because the method of deriving the heat transfer equations and of calculating the temperatures is described in detail in those studies, it will not be discussed here; only the equations for the calculation of the column temperatures and calculated results will be given

2.1.1 Division of cross-section into elemenQ

The cross-sectional area of the colurhn is subdivided into a number of elements, arranged in a triangular network (Fig. 1). The elements are

square

inside the steel and the concrete and

b g u l a r at the column surface and along the boundary between the concrete and the steel. The steel elements are one-half the width of the concrete elements. For the

square

elements, the temperature at the centre is taken as representative of the entire element For the triangular elements, the representative points are located on the centre of each hypotenuse.

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For reasons of symmetry, only one-qu-r of the section needs to be considered when calculating the temperature distribution in columns with square or rectangular cross-section. As illustrated in Fig. 1, in an x-y co-ordinate system, a point pm,n has the co-ordinates x=(n-1)&24 and y=(m-1)~5*/4.

2.1.2 -tion$ for the fire-steel boundary

It is assumed that the columns are exposed on all sides to the heat of a fire whose

temperature course follows that of the standard fire described in ASTM-El19

[a

or ULC-S101

[7]. This temperature course can be approximately described by the following expression:

where t is the time in hours and T is the fire temperature in "C at time t=jAt

The temperature rise in the layer can be derived by creating a heat balance for each element In the following, all calculations will be canied out for a unit length of the column. For the

elements at the surface of the column along the x-axis, the temperature at time t=(j+l)At is given by the expression:

For the elements at the surface of the column along the y-axis, the temperature at the time t=(i+l)At is given by:

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2.1.3 Eauation for inside the steel

For the elements in the steel, except for the surface elements and the elements at the boundary of the steel and concrete, the temperature at time, t=(j+l)At is given by:

2.1.4 Eauations for the steel-concrete boundary

For the elements along the x-axis at the boundary between the steel and the concrete, the temperature at time, t=(j+l)At is given by:

For the elements along the y-axis at the boundary between the steel and the concrete, the temperature at time, t=(j+l)At is given by:

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2.1.5 m-uation for inside the concrete

For the elements in the concrete, except for the elements at the boundary of the concrete and the steel, the temperahue at time t=(j+l)At is given by:

To calculate the temperatures along the y-axis across the lines of symmetry A-E and E-D,

the temperature has to satisfy the following symmetry conditions:

line A-E

line E-D

Simiily, to calculate the temperatures along the x-axis across the lines of symmetry D-G and

G-C,

the temperature has to satisfy the conditions: line G-C

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line

D-G

2.1.7 Effect of Moistm

The effect of moisture is taken into account by assuming that in each element, the moisture starts to evaporate when the temperature of the element reaches 100°C. During the period of

evaporation, a l l the heat supplied ta an element is used for the evaporation of the moisture, until the element is dry.

For the elements at the boundary between steel and concrete along the x-axis, the initial volume of moisture is given by:

From a heat balance equation it can be derived that, per unit length of the column, the volume AVmevaporated in the time At from the concrete elements at the steel-concrete boundary along the x - m , IS:

For the elements at the boundary between steel and concrete along the y-axis, the initial

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From a heat balance equation it can be derived that, per unit length of the column, the volume A Vevaporated ~ in the time At from the concrete elements at the steel-concrete boundary along the y-axis is:

For the concrete elements inside the column, except for the elements at the boundary between the steel and the concrete, the initial volume of moisture is given by:

Similarly, as for the concrete boundary elements, it can be derived that, per unit length of the column, the volume AV,,,,~, evaporated in the time At &om these elements is:

2.1.8 Stabilitv criterion

In order to ensure that any error existing in the solution at some time level will not be amplified in subsequent calculations, a stab'ity criterion has to be satisfied which, for a selected value of

g,

limits the maximum of time step At. Following the method described in reference [I],

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it can be derived that, for the fire-exposed column, the criterion of the stability is most restrictive along the boundary between fire and concrete. It is given the condition:

where the maximum value of the coefficient of heat transfer during exposure to the standard fue

(hmax) is approximately 675 W/m2"C.

2 . 2 Strength of Column During Fire 2.2.1 Transformation into souare network

To calculate the deformations and stresses in the column, and its strength, the triangular network is transformed into a square network. In Fig. 2, a quarter section of this network,

consisting of square elements arranged parallel to the x- and y-axis of the section, are shown. The amngement of the elements in the three other quarter sections is identical to this. The width of each steel element of this network

is

~€,<2/4, one half the width of a concrete element. The temperatures, deformations and stresses of each element are represented by those of the centre of the element. The temperature at the centre of each element is obtained by averaging the

temperatures of the elements in the triangular network.

Thus,

the representative temperature for a steel element is:

and for a concrete element is:

where the subscripts "square" and "triangular" refer to the elements of the square and triangular network.

For the steel reinforcing bars also, a representative bar temperature can be indicrued. Measurements at various locations during fire tests showed that the differences in temperature in the bar and sections are small [41. A cl& approximation of the average bar tempera& is

obtained by considering the column as consisting entirely of concrete and selecting the temperature at the location of the centre of the bar section as the representative bar temperature. Thus, for a steel reinforcing bar, the centre of whose section is located in an element &, the representative temperature is equal to that of

m,n,

which is given by Eq. (22).

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Similarly, it is assumed that the stresses and deformations at the centre of an element are representative of those of the whole element.

lation of stre

2.2.2 Assum~tions in the calcu nmh during firt;

During exposure to fue, the strength of the column decreases with the duration of exposure. The strength of the column can be calculated by a method based on a load deflection

In this method, the columns, which are fixed at the ends during the tests, are idealized as in-ended columns of length KL (Fig. 3). The load on the column is intended to be concentric.

bue to imperfections of &e ~ o l ~ n s ~ a n d the loading device, a small eccentricity exists. The loading system and the test columns were made with high precision, however. Therefore, in the calculations, a very small initial load eccentricity will be assumed. The real eccentricity, however, is unknown. After calculations showed that for eccentricities up to 3 mm the influence on fue resistance is small, an arbitrary value of 0.2 mm, reflecting a nearly concentric load, has been selected for the initial eccentricity. lie selection of a finite value for the initial eccentricity is needed in order to make the computer program work.

The curvature of the column is assumed to vary from pin-end to mid-height according to a straight line relation, as illustrated in Fig. 3. For such a relation, the deflection at mid-height Y, in terms of curvature

x

_{of the column at}this height, can be given by:

For any given curvature, and thus for any given deflection at mid-height, the axial strain is varied

until the internal moment at the mid-section is in equilibrium with the applied moment given by the product:

load x (deflection

+

eccentricity)

In this way, a load deflection curve can be calculated for smc times during the exposure to fire. From these curves, the strength of the column, i.e., the maximum load that the column can carry, can be determined for each time. In the calculation of column strength, the following assumptions were further made:

1. The properties of the concrete and steel are those described in the Appendix.

2. Concrete has no tensile strength. 3. Plane sections remain plane.

4. There is no slip between steel and concrete.

5 . There is no composite action between the steel and the concrete.

6 . _{The reduction in column length before exposure}_{to fire,}_{consisting of free shrinkage of the}

concrete, creep, and shortening of the column due to load, is negligible. This reduction can be eliminated by selecting the length of the shortened column as initial length from which the changes during exposure to

fire

are determined.

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Based on these assumptions, the column strength during exposure to fire was calculated. In the calculations, the network of elements shown in Fig. 2 was used. Because the strains and stresses of the elements are not symmetrical with respect to the y-axis, the calculations were performed for both the network shown and an identical network at the left of the y-axis. The load that the column can carry and the moments in the section were obtained by adding the loads carried by each element and the moments contributed by them.

The equations used in the calculation of strength of the column during exposure to fire are given below.

2.2.3 m t i o n s for the concrete

The strain in the concrete for the elements at the right of the y-axis (Fig. 2) can be given by:

and for the elements at the left of the y-axis by:

where ( Q ) ~ = the thermal expansion of the concrete (m m-I) E = the axial strain of the column (m m-l)

x, = the horizontal distance from the centre of the elements to the vertical plane

through the y-axis of the column section (m)

p = the radius of curvature (m)

The stresses in the elements are calculated using the same stress-strain relations for

concrete, given in Reference 151. These relations are given by the Eqs. (30)-(35) in the Appendix.

2.2.4 Eauations for the steel reinforcement

The strain in the steel reinforcing bars can be given as the sum of the thermal expansion of the steel bar (eB)*, the axial strain of the column E and the strain due to bending of the colunin xdp, where xg is the horizontal distance of the centre of the section of steel bar to the vertical plane through the y-axis of the column section and p is the radius of curvature. For the steel bars at the right of the y-axis, the strain (EB)R is given by:

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For the steel bars at the left of the y-axis, the strain (EB)L is given by:

The stresses in the steel are calculated using the same stress-strain relations for steel, given in Reference

[q.

These relations are given by the Eqs. (47)-(51) in the Appendix.

2.2.5 muations for the steel

The strain in an element of steel can be given as the sum of the thermal expansion of the steel (&, the axial strain of the column E and the strain due to bending of the column xdp, where

x, is the horizontal displacement of the steel element to the vertical plane through the y-axis of the column section and p is the radius of curvature. For the steel elements to the right of the y-axis, the strain ( E ~ ) ~ is given by:

For the steel elements for the left of the y-axis, the strain (&)L

is given by:

The stresses in the steel are calculated using the same stress-strain relations for steel, given in Reference

[R.

These relations are given by the Eqs. (47)-(51) in the Appendix.

2.2.6 Procedure for calculation of column strength

With the aid of Eqs. (24)-(29), (30>(35) and (47)-(51), the stresses at mid-section in the concrete elements and in the steel bars can be calculated for any value of the axial strain E and

curvature 110. From these stresses. the load that each element and each reinforcing bar carries and its contribution to the internal moment at mid-section can be derived. By adding tb loads and moments, the load that the column carries and the total internal moment at mid-section can be

calculated

The fire resistance of the column is derived by calculating the strength, i.e., the maximum load that the column can cany at several consecutive times during the exposure to fire. This

strength gradually reduces with time. At a certain point, the strength becomes so low that it is no longer sufficient to support the load, and the column fails. The time to reach this point is the fire resistance of the column.

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3 . TEST SPECIMENS

Over the years, various test specimens consisting of circular and square hollow steel columns, filled with bar-reinforced concrete, were tested to verify the mathematical models that have been developed for the calculation of the fire resistance of HSS, filled with bar-reinforced

concrete. These specimens are described in detail in Reference 2.

For the purpose of verification of the model given in this paper, the results of tests on three square columns with different cross section sizes, one small, one medium and one large, will be used for comparison

with

calculated results. The columns were fiued with carbonate aggregate concrete with bars of various dimensions. The specimens are illustrated in Figs. 4-6.

AH

columns were 3810 mm long from end plate to end plate. The outside width of the columns ranged from 203.2 mm to 304.8 mm. The steel wall thickness of all three sections was 6.35 mm.

The steel end plates measured 508 mm wide by 610 mm long by 25 mm thick for all columns.

The steel columns were fabricated by cutting the steel to appropriate lengths. Steel and end plates were then welded at the column extremities. Centering and perpendicularity of the end plates were given special attention to ensure a high degree of accuracy. Before welding the end plates, a hole with a width 25.4 mm smaller than the inner width of the hollow steel section was cut in each plate. The smaller width of the holes created, after welding, a lip of 13 mm, as shown in Figure 7.

Four small holes were also drilled in the steel wall to provide vent holes for water vapour produced during the experiment Two of the holes were located opposite one another at 1448 mm above midheight of the column The other two were also located opposite to one another at 1448 mm below midheight of the column.

The steel of the column was manufactured according to CSA Standard CAN3-G40.20-M81 [9], Class H and had a specified yield strength of 350 m a .

Deformed bars, meeting the CSA Standard G30.12-M77 [lo] with a minimum yield strength of 400 MPa, were used for the main reinforcing and tie bars. The diameter of the main reinforcing bars varied from 16 mm to 25.2 mm. The diameters of the ties were 6.4 mm and 9.5 _mm.

The main reinforcing bars were tied together to complete the steel cage. Tbe main bars were cut 10 mm shorter than the column length. The steel cage was then placed into the column with special care to ensure appropriate centering.

The concrete was poured in the column through the top opening. Its composition, per cubic metre of concrete mix, was as follows:

Cement 439 kg

Water 161 kg

Fme Aggregate 621 kg Coarse Aggregate 1128 kg

The average 28-day cylinder strength was approximately 42 MPa. The average cylinder strength at

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Chromel-alumel thermocouples with a thickness of 0.91 mm were installed at midheight of the column for measuring the temperatures of the steel, reinforcement bars and concrete at different locations in the cross-section The locations of the thermocouples are described in detail in

Reference 2.

4 . TEST APPARATUS

These tests were carried out by exposing the columns to heat in a column test furnace. The test furnace was designed to produce the conditions to which a member might be subjected during a fie. It consists of a steel framework supported by four steel columns, with the fumace chamber inside the framework. The characteristics and instrumentation of the furnace, which has a loading capacity of 1000 t, are described in detail in Reference 11.

5 TEST CONDITIONS AND PROCEDURES

5 . 1 End conditions

All tests were carried out with both ends of the columns fixed, i.e., restrained against rotation and horizontal translation. For this purpose, eight 19 mm bolts spaced regularly around the column were used at each end to bolt the end plates to the loading head at the top and the hydraulic jack at the bottom.

5 . 2 Loading

All columns were tested under a concentric load. The applied load ranged from 22 to 82% of the factored compressive resistance of the columns (C,) or 70 to 192% of the factored

compressive resistance of the concrete core

(w,

determined according to CSA Standard

CSAICAN-S16.1-M89 [12]. The factored compressive resistances of each column, as well as the applied loads, are given in Table 1. The effective length factors, K, used in the calculation of the factored compressive resistances were those recommended in CSAICAN-S16.1-M89 for the given end condition, i.e., 0.65. The effective length of the columns,

KL

was thus assumed to be

2.48 m.

The load was applied approximately 45 min before the start of the test, until a condition was reached at which no further increase of the axial deformation could be measured. This

condition was selected as the initial condition for the column axial deformation The load was maintained constant throughout the test.

5 . 3 Fire exposure

The ambient temperature at the start of each test was approximately 20°C. During the test, the column was exposed to heating controlled in such a way that the average tempemure in the furnace followed as closely as possible the ASTM-El19 [6] or CANNLCClOl [7] standard temperature-time curve.

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5 . 4 Failure criterion

The columns were considered to have failed, and the tests terminated, when the hydraulic jack, which has a maximum speed of 76 mm/min, could no longer maintain the load.

5 . 5 Recording of results

The furnace, concrete and steel t e m p e r a m , as well as the axial deformations of the columns were recorded at Zminute intervals.

6 . RESULTS AND DISCUSSION

Using the mathematical model described in this paper, the temperatures, axial deformations and strengths of the columns were calculated. In the calculations, the thermal and mechanical propertie; of the concrete and steel and the specifics of the colu& furnace given in the Appendix, were used.

In Figs. 8-10, calculated temperatures are compared with the temperatures measured at the steel surface on a centreline of the steel section, and the temperatures at various depths in the concrete. It can be seen that, with the exception of the temperatures measured at an early stage deeper in the specimen, there is a good agreement between calculated and measured column

temperatures. The temperatures measured deeper inside the column show initially arelatively rapid rise, followed by a period of relatively slow rate of temperature rise. This temperature behaviour may be the result of thermally induced migration of the moisture towards the centre of the column where, as shown in previous tests [5] the influence of migration is most pronounced. Although the model takes into account evaporation of moisture, it does not take into account the migration of the moisture towards the centre. That migration appears to account for the deviation between calculated and measured temperatures at the earlier stages of fire exposure. At a later stage,

however, which is the important stage from the point of view of predicting the fue resistance of the columns, there is a good agreement between calculated and measured temperatures.

In Figs. 11-13, the calculated and measured axial deformations of the columns during exposure to fire are shown. It can be seen that there is reasonably good agreement in the trend of deformations between calculated and measured results. There are some differences, however, between the actual values of the calculated and measured deformations.

It must be noted that the column deforms axially as a result of several factors, namely, load, thermal expansion, bending and creep, which cannot be completely tahen into account in the calculations. Since the axial deformations, which are on the order of 20 mm, are for columns with a length of about 3800 mm, small inaccuracies in these factors may cause noticeable differences between calculated and measured axial deformations. A difference of 10% between the theoretical and actual coefficients of thermal expansion of steel, for example, will cause a difference of

approximately 5 mm in the axial deformations. The effect of creep, which is more pronounced at a later stage of the fire exposure, may be even greater. This was particularly the casewith Column No. 1. Whereas the model defines the failure point as the point at which the column can no longer support the applied load and assumes that f a i l k at thii pdint is instantaneous, during the test, the column, which was relatively slender, contracted considerably, avvarentlv as a result of continued _.. loss of strength and creep, &fore it was crushed.

In Fig. 14, calculated column strengths as a function of the fire exposure time are shown, together with the calculated and measured fire resistances for the test loads given in Table 1. The strength decreases with time until it becomes so low that the column can no longer support the

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load The time to reach this point is the fm resistance of the column. The calculated fire

resistances of the columns are also given in Table 1 together with the measured fire resistances. It can be seeh that there is good agreement between caldated and measured fm resistances for Columns Nos. 2 and 3, but the calculated fire resistance of Column No. 1 is about 30% lower than

that measured, due to considerable contraction of the column, which the model can only partly take into account.

7 . CONCLUSIONS

Based on the results of this study, the following conclusions can be drawn:

1. The mathematical model employed in this study is capable of predicting the fire resistance of rectangular columns, made of HSS Nled with bar-reinforced concrete, with an accuracy that

is adequate for practical purposes

2. The model will enable the expansion of existing data on the fire resistance of concrete filled steel columns, which at present consists predominantly of data for circular columns, with that for rectangular columns.

3. Using the model, the fire resistance of rectangular concrete filled steel columns can be

evaluated for any value of the significant parameters, such as load, column section dimensions, column length and percentage of reinforcing steel, without the necessity of testing.

4. The model can also be used for the calculation of the fire resistance of columns made with

concretes other than those investigated in this study, for example lightweight or siliceous aggregate concretes, if the relevant material properties are known.

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REFERENCES

Lie, T.T., Fire Resistance of Reinforced Concrete Columns: A Parametric Study, Journal of Fire Protection Engineering, Vol.1, No.4, 1989, pp. 121-130.

Chabot, M. and Lie, T.T., Experimental Studies on the Fire Resistance of Hollow Steel Columns Filled with Bar-Reinforced Concrete, IRC Internal Report No. 628, Institute for Research in Construction, National Research Council of Canada, Ottawa, April 1992. Dusinberre, G.M., Heat Transfer Calculations by Finite Differences, International Textbook Company, Scranton, PA, 1961.

Lie, T.T., Temperature Distributions in Fire-Exposed Building Columns, Journal of Heat Transfer, Vol. 99, Series

i=,

No. 1, 1977, p.113-119.

Lie. T.T. and Irwin, R.J., Evaluation of the Fire Resistance of Reinforced Concrete c o i m n s with Rectangular Cross-Section, IRC Internal Report No. 601, Institute for Research in Construction, National Research Council of Canada, Ottawa, 1990.

Standard Methods of Fire Test of Building Construction and Materials, ASTM E119-83, American Society for Testing Materials, Philadelphia, PA, 1983.

Standard Methods of

Fire

Endurance Tests of Building Construction and Materials, CAN4-

S101-M82, Underwriters' Laboratories of Canada, Scarborough, Ontario, 1982.

Allen, D.E. and Lie, T.T., Further Studies of the Fire Resistance of Reinforced Concrete Columns, National Research Council of Canada, Division of Building Research,

NRCC 14047, Ottawa, Ontario, 1974.

General Requirement for Rolled or Welded Quality Steel CAN3-G.40.20-M81, Canadian Standards Association, Toronto, Ontario, 1981.

Billet-Steel Bars for Concrete Reinforcement, CAN3-G30.12-M77, Canadian Standards Association, Toronto, Ontario, 1977.

Lie, T.T., "New Facility to Determine the Fire Resistance of Columns", Canadian Journal of Civil Engineering, Vol. 7, No. 3, 1980, p. 551-558.

Limit States Design of Steel Structures - CANICSA-S16.1-M89, Canadian Standards Association, Toronto, Ontario, 1989.

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NOTATION fco f~ f ~ o h j k K specific heat (~kg-~"C-l)

compressive strength of concrete at temperature T (MPa) cylinder strength of concrete at temperature T (MPa) cylinder strength of concrete at room temperature (MPa) strength of steel at temperature T (MPa)

yield strength of steel at room temperature @Pa)

coefficient of heat transfer at fm exposed surface ( w ~ - ~ O C - ~ )

0, 1, 2,

...

thermal conductivity ( ~ m - l " C - ~ ) effective length factor

length of column used in the calculation of axial deformation (m) unsupported length of column (m)

number of points along y-axis number of points along x-axis point time (h) ~emperature (OC) volume of moisture (m3) coordinate (m) coordinate (m)

lateral deflection of column at mid-height (m) coefficient of thermal expansion (T-l)

increment mesh width (m)

emissivity, strain (m m-1) heat of vaporization (Jkgl)

density (kgm-3). radius of curvature (m) Stefan-Bolmann constant ( W m - 2 ~ 4 ) concentration of moisture (fraction of volume) curvature of column at mid-height (m-1)

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Subscripts C f

mM

max min n,N L R of steel reinforcement at room temperature of concrete of the fue

at the points m, M in a column maximum

minimum

at the points n, N in a row left of the x-axis

right of the x-axis

pertaining to proportional stress-strain relation of steel pertaining to temperature of water at the points 1,2 Superscripts j at t =@t

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APPENDIX MATERIAL PROPERTIES AND SPECIFICS OF COLUMNS AND FURNACE

The values of the material properties used in this study are the same as those used in Reference 5 for the calculation of the fire resistance of reinforced concrete columns with the

exception of the thermal properties of the concrete. These properties, which in Reference 5 apply to siliceous aggregate concrete, have been replaced by those of carbonate aggregate concrete, which have been measured recently.

CONCRETE PROPERTIES Stress-strain relations where & = 0.0025

+

(6.0T

+

0.0412) x 10-6 and for O°C < T < 450°C fc = fco for 450°C

<

T I 874OC fc =

fc,

[2.011 - 2.353 -

( 1 1 1

for T > 874OC

fc=o

Thermal capacity for 0 I T I 400°C pccc = 2.566

x

lo6 J m-3OC-I for 400 < T

<

410°C pccc = (0.1765T - 68.034)

x

lo6 J m-3OC-I for 410 < T 1445OC pCcc = (-0.05043T

+

25.00671)

x

lo6

J m-3OC-1

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for 445 < T S _500°C pccc = 2.566 x lo6 J rn-3OC-I for 500 < T 1 635OC pccc = (0.01603T - 5.44881) x lo6 J rnJ0C-I for 635 < T 1715OC pccc

=

(0.16635T - 100.90225)

x

lo6 J

m-30~-1

for 715 < T S 785OC pccc = (-0.22103T

+

176.07343)

x

lo6 J rnSOC-I for T > 785OC pccC = 2.566 x lo6 J rn"OC-l Thermal conductivity for 0 T 1293OC k, = 1.355 W rn-lOc-' for T > 293OC k, = -0.001241T

+

1.7162 W m-I0c'

Coefficient of thermal expansion

STEEL PROPERTIES Stress-strain relations where Ep = 4 X fyo and f(T.001) = (50 - 0.04T)

x

[l - ex&-30

+

o . o ~ T ) ~ ) ]

x

6.9

(24)

where

fiT,(~, - ep

+

0.001)) = (50

-

0.04T) x[l - exp((-30 + 0.03T)i(~s - E, + 0-001))1 x 6.9 (51) Thermal capacity for O°C I T I 650°C pscs = (0.004T

+

3.3) x lo6 J maOC-' for 650°C < T 1725OC p,c, = (0.068T

+

38.3)

x

lo6 J m-3'c-l for 725OC < T 1 800°C pscs = (-0.086T

+

73.35) x

lo6

J m-3°C-' for T > 8W°C p,cs = 4.55 x lo6 J m-3OC-' Thermal conductivity for O°C I T I 9W°C k, = - 0.022T

+

48 W m-1°C-' for T > 9W°C k, = 28.2 W m-'OC-'

Coefficient of thermal expansion

for T < 1000°C as = (0.004T

+

12) X ~o-~OC-' for T 2 1000°C & = 16

x

10-60~-' WATER PROPERTIES Thermal capacity p 4 , = 4.2 x lo6 J mJOC-' Heat of vaporization h, = 2.3

x

lo6 J kg-'

(25)

SPECIFICS

OF

COLUMN

AND

FIRE

&f

=

emissivity of fire: 0.75

Q

=

emissivity of steel: 0.80

KL = effecitve length of columns: 2.0 m for fire msistame cdculations

1 = length of column that contributes to axial deformation: 3.5 m

(26)

Table 1. Summary of test parameters and results

Factored Resistance*:

C'r = Factored compressive resistance of concrete core of column according to CAN3-S16.1-M89 Crc = Factored compressive resistance of concrete-filled HSS column according to CAN3-S16.1 -Ma9

Test Load C (kN) 500 1440 2000 Factored Resistance* C'r Crc (kN) (kN) 717 2258 1223 3186 1775 4154 Column No. I 2 3 Load Intensity CIC'r CICrc 0.70 0.22 1.18 0.45 1.13 0.48 Steel Bars (%) 2.2 2.1 2.3 HSS Dimensions (mm) 203.2 x 203.2 x 6.35 254.0 x 254.0 x 6.35 304.8 x 304.8 x 6.35 Fire Resistance (hr:min) Calculated Measured 1 :55 2:30 2:04 1:53 3 3 4 332 Concrete Strength 28 days test date

(MPa) (MPa) 41.3 47.0 42.3 48.1 41.3 47.0

(27)

INDEX

OF

FIGURES Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8

Thermal network in 114 section Stress-strain network in 114 section Load deflection analysis

Elevation and cross section of Column No. 1 (203.2 x 203.2 x 6.35 mm)

Elevation and cross section of Column No. 2 (254 x 254 x 6.35 mm) Elevation and cross section of Column No. 3 (304.8 x 304.8 x 6.35 mm) End plate connection details

Temperatures at various depths along centreline of Column No. 1 (203 x

203 x 6.35 mm) as a function of exposure time

Figure 9 Temperatures at various depths along centreline of Column No. 2 (254 x

254 x 6.35 mm) as a function of exposure time

Figure 10 Temperatures at various depths along centreline of Column No. 3 (304.8 x

304.8 x 6.35 mm) as a function of exposure time

Figure 11 Calculated and measured axial deformations of Column No. 1 (203.2 x

203.2 x 6.35 mm) as a function of exposure time

Figure 12 Calculated and measured axial deformations of Column No. 2 (254 x 254 x 6.35 mm) as a function of exposure time

Figure 13 Calculated and measured axial deformations of Column No. 3 (304.8 x

304.8 x 6.35 mm) as a function of exposure time

Figure 14 Calculated column strengths as a function of time and calculated and measured fire resistances

(28)

(N- 1)A(d2/4 x=(n-I)A(d2/4 ----mi

C

i

(29)

(30)

(31)

23 _mrn_{COVER TO MAIN}

/

REINFORCING BARS 16 rnrn BARS 203.2 _rnrn

u

203.2 _rnrn

,

127 rnm TIES = 254

Figure

4.

Elevation and cross section of Column No. 1

(203.2

(32)

23 rnrn COVER TO MAIN

/

REINFORCING BARS 19.5 rnm BARS

I

254 mm

u

254 rnrn ,135 rnm

Figure

5. Elevation and cross section

of

Column No.

2 (254

x

254 x 6.35

mm)

(33)

26 mm COVER TO MAIN

1

_{REINFORCING BARS} 25.2 mm BARS 304.8 mm TIES = 380

Figure

6. Elevation and cross section of Column No.

3 (304.8

(34)

(35)

-

Calculated

-

- -

Measured

-

column surface

- -

0

20

40

60

80

100 120 140 160 180 200

TIME,

min

Figure 8.

_{Temperatures at various depths along centreline of}

Column No.

1 (203.2

x

203.2 x

6.35 mm) as a

function of exposure time

(36)

-

Calculated

-

- -

Measured

-

_*

-

column surface

- 60

mm depth

I 0 20 40 60 80 100 120 140

TIME,

min

Figure 9.

Temperatures at various depths along centreline

of

Column No. 2 (254 x 254

x

6.35 mm) as a function

of exposure time

(37)

0

50

100

150

200

250

300 TIME, min

-

Calculated

-

Measured

-

column surface

-

Figure

10. Temperatures at various depths along centreline of

Column No.

3

(304.8

x

304.8 x

6.35 mm)

as

a

(38)

TIME, min

30 Figure

11. Calculated and measured axial deformations of

Column No.

1 (203.2

x

203.2 x

6.35 mm) as a

function of exposure time

20 -

Calculated

- -

Measured

-

\ \ \

-10

-

\ _\ \ \

-20

- _\

-30

\ - \ \

-40

I I I I I I I

0

20

40

60

80 100 120 140 160

(39)

-

Calculated

- -

Measured

- CI

I

_I

- I

_I

\ \ \ - \ \ \ \ - \ \

,

I I I I I I

TIME, min

Figure

12. Calculated and measured axial deformations of

Column No.

2 (254

x

254 x

6.35 mm) as a function

of exposure time

(40)

-

_Calculated

-

_Measured

\

-.

-

\ \ - \ \ \ - \ \ \ - I I I I I

15

10 E

E

5 i

0

5

0

2 CT

-5

0

U. W

-10

<

3 -15

-20

-25

0

40

80

120

160

200 Figure

13. Calculated and measured axial deformations of

Column No.

3 (304.8

x

304.8 x

6.35 mm) as a

function of exposure time

240

(41)

TIME, min

Calculated fire resistance

o Measured fire resistance

Column No. 3

Column No. 2

-

Column No. 1

(203 x 203 x 6.35 mm)

I I I t