Factors affecting the fire resistance of square hollow steel columns filled with plain concrete

(1)

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Factors affecting the fire resistance of square hollow steel columns

filled with plain concrete

(2)

National Research

Conseil national

de recherches Canada

Institute for

lnstitut de

Research in

recherche en

construction

Steel Columns Filled with

Plain Concrete

by T.T.

Lie and I.

Dawod

Internal Report No.

633

Date of issue: ~ u g u s t

1992

AidriiYZED

C I S T I / I C I S T NRC/CNRC

I R C Ser

~~~~i ved otl: 0'7-28-93

~

,

t

r e p a r t : I n % t i t u t e

~

a

l

f o r R e s g a r c h i t i C u t i s t r u c t i o n

This is an internal report of the lnstitute for Research in Construction. Although not

intended for general distribution, it

may be cited as a reference in other publications.

(3)

(4)

FACTORS AFFECTING THE FIRE RESISTANCE OF SOUARE HOLLOW

STEEL COLUMNS FILLED WITH PLAIN CONCRETE

ABSTRACT

Experimental and theoretical studies have been canied out to predict the

fire

resistance of hollow steel sections filled with various concretes. This repon deals with

square

steel columns filled with plain concrete. Using a computer pro*,

the influence

of the various study variables on the fire resistance of these columns, namely, column

section size, steel wall thickness, load, effective length of the column, concrete strength

and type of aggregate, were investigated The results are described and the influence of the

various study variables

is

discussed.

(5)

FACTORS AFFECTING THE FIRE RESISTANCE O F SOUARE HOLLOW

STEEL COLUMNS FILLED WITH PLAIN CONCRETE

1 INTRODUCTION

For a number of years, the National Research Council of Canada (NRCC)

has

carried out research on the

fire

resistance of concrete-ffled steel columns. Both

experimental and theoretical studies to develop methods for the prediction of the fm

reiistance of these columns were conducted.

-

As

patt of these studies, mathematical models were developed for the calculation of

the fue resistance of hollow steel sections (HSS) filled

with

concrete. Columns of various

steel sizes and shapes filled

with

various concrete types were studied. Full-scale tests for

the validation of the models were canied out

At present, the research has reached a stage at which sufficient

data,

suitable for

release, have been produced. This report contains the data showing the influence of the

important factors on the fire resistance of square steel columns f i e d with plain concrete.

The data, generated by a mathematical model [I] programmed for computer processing,

will enable the assessment of the

fire

resistance of the columns

as

a function of the

variables that determine

it

The model was developed at the National Fire

Laboratory

of the Institute for

Research in Construction,

NRCC

with the support of the Canadian Steel Construction

Council and the American Iron and Steel Institute.

2 STUDY VARIABLES

2 . 1

Column Size of the Steel Section

AU

square

columns, listed

in

the CISC Handbook of Steel Construction 121 and

whose outside dimensions were

equal

to or greater than 101.6

mm,

were considered. The

outside dimension of 101.6

mm

was regarded

as the

smallest column size still suitable for

concrete filling. The selected sizes, in total seven,

are

shown

in

the Tables 1 to 18.

2 . 2

Thickness

of the steel

wall

To

assess

the

effect of

the

steel wall thickness on the fire resistance of the columns,

the extreme values of wall thicknesses for each column

size equal

to

or greater than

101.6 m m

were selected for further study. The selected wall thicknesses

are

given

in

Tables 1 to 18.

. .

2.3 Load

The influence of

the

load on the

fire

resistance of the column was evaluated by

calculating

the

skngth of

the

column, ie., the maximum load that the column

can

support

as a function of time during the exposure

to

fm. S i ,

by defdtion, the

fire

resistance of

the column

is

equal

to the time during which the column can support a specific load, the

fire

resistance can be determined for any load using the strength versus time relations. In this

(6)

study, the strength of the column was calculated at 10 minute intervals during the exposure

to fire.

2.4 Effective Length

To study the influence of

the

effective length of the column on its

fire

resistance,

calculations of the strength of the column, during the exposure to

fire,

were carried out for

column effective lengths of 2.5,3 and 4.5 m.

2.5 Concrete Strength

The influence of the strength of the concrete filling on the

fire

resistance of the

column was studied for concrete compressive strengths of 20,35 and 55 MPa.

2.6 Type of Aggregates

Two concrete types, made with different aggregates, were considered

in

this

study,

namely, siliceous and carbonate..

The

influence of

the type

of aggregate was evaluated by

using, in the mathematical model, the relevant material properties of

the

two types of

concretes. These properties

are

given

in the Appendix.

3 CALCULATION METHOD

The calculation of

the

fire

resistance of

the

columns was carried out according

to the

method described

in

Reference [I].

In

this

method,

the

calculation

of

fire

resistance

is

performed in three steps:

1. Calculation of the

fire

tempemure.

2. Calculation of the temperature

in

the column.

3. Calculation of the strength of

the

column during the exposure

to

f a ,

including

an

analysis of stress and

s&

distribution.

-

A

flow chaa of the calculation procedure is shown in Figure 1.

3.1 Fire Temperature

It

is

assumed that

the

entire surface

area

of the column was exposed to the heat of a

fire. whose ternDerature. course follows

that

of

the

standard

fire

described in

ASTM

EI

19 [3] or ~ h 4 - ~ 1 0 1 [ 4 ] .

This

temperature

course can

be approximately described by

the

following expression:

(7)

3.2 Temperature of Column During Fire Exposure

The column temperatures

are

calculated by a fmite difference method. Because the

finite

difference heat transfer equations for the column are given in detail in Reference [I],

only a description of the method

will

be given in

this

report.

In this method, the cross-sectional area of the column

is

subdivided into a number

of elements, arranged in a triangular network. The elements are diamond-shaped inside the

steel and the concrere, and triangular

at

the column surface and along the

boundary

between

the concrete and the steel. The temperature rise in an element can be derived by creating a

heat balance for the element. By solving the heat balance equations for each element, the

temperature history of the column can be calculated, using the temperature-dependent

thermal properties of the concrete and steel.

These

properties are given in the Appendix.

The effect of moisture in the concrete on the column temperatures was taken into

account by assuming

that,

in each element, the moisture starts to evaporate when the

temperature reaches 100°C.

In

the

period

of evaporation,

all

the heat suppIied to an element

is considered to

be

used for evaporation until the element

is dry.

3 . 3

Strength of Column During Fire Exposure

In

order to calculate the strains and stresses in the column and its strength, the

cross-sectional area of the'column

is

divided into a number of diamond-shaped elements.

The temperatures,

stresses and strains at the centre of each element are representative of the

entire element

The strain in a steel element

can

be given

as

the

sum of the thermal expansion of the

steel, the axial strain of the column due to compression and the strain due to bending of the

column. A similar calculation is performed for the concrete elements.

To simplify

the

strength calculations, the following assumptions are made:

1 .

The curvature of the column varies from pinends to midheight linearly.

2. Concrete has no tensile strength.

3. There is a slip-free surface between steel and concrete.

4. There

is

no composite action between steel and concrete.

With

these

assumptions and with

the

aid of

the

stress-strain relations given

in

the

A ~ ~ t ? n d k .

the stresses at mid-section in

the

steel and concrete can be calculated for any

vzue of

strain and

curvature.

From these stresses, the load that each element canies

and

its

contribution

to

the

intemal moment at mid-section can

be

derived By adding the

loads and moments, the loads that the column carries and the intemal moment at mid-

section can be calculated

The strength of the column, during exposure

to

fire,

can

be

determined by

successive iterations of the axial strain and curvature until the internal moment

at

mid-

section

is

in equilibrium with the applied moment

The

fm

resistance of the column is derived by calculating

the

strength of

the

column a s a function of the time of exposure

to

fire.

This strength reduces gradually with

time. At a ceaain point, the strength becomes so low that it

is

no longer ~ ~ c i e n t

to

support the load. At this

point,

the column becomes unstable and is assumed to have

failed The time

to

reach

this

failure point is the fire

resistance

of

the

column.

(8)

4 RESULTS AND DISCUSSION

Using

the

mathematical model described in Reference [I] and the material properties

given in the Appendix, the strength of the column during exposure

to

fire

was calculated

for the values of the study variables mentioned in Section 2. The results are given in

Tables 1 to 18,

The influence of the various study variables were assessed by comparing the

fire

resistances calculated for the various conditions studied,

with that

of a reference column.

For

this

purpose, the column with an outside dimension of 177.8 mm, a steel wall

thickness of 12.7

mm,

an

effective length of 2.5

m

and siliceous concrete fiUing with a

strength of 35 MPa was selected as the reference column Two reference loads were

selected for

the

fire

resistance comparisons, namely 330

kN

and 1150 kN, the same loads

that were selected

in

Reference [5].

The influence of the various study variables is shown

in

Figures

2 to

7 and is

discussed below.

4 . 1

Outside

Dimension

of the Steel

Section

In Figure 2, the

fire

resistance of the columns is shown as a function of the steel

outside dimension for the two selected reference loads of 330

kN

and 1150

kN.

The

c w e s in

this

figure and the tabulated values in Table

2 for siliceous aggregate concrete

filling and in Table 11 for carbonate aggregate concrete filling, indicate

that

the

column

outside dimension, which is a measure of the column section size, has a great influence on

the

fire

resistance of the column.

The

curves

in

Figure

2 show that the fue resistance of the

column i n c r e w more

than

quadratically with an

increase

in

the

column outside

dimension.

4.2 Thickness

of

the

Steel

Wall

In Figure 3, the graphs representing the influence of wall thickness on the

fire

resistance of the column show

that,

for columns with outside dimensions smaller

than

203 mm, the fire resistance tends

to

increase with

an

increase in the wall thickness. On the

other hand, for columns with outside dimensions greater than 203

mm,

the

fire

resistance

of the column tends

to

deaease

with

the increase. in

the

wall thickness of the column.

However, the influence of wall thickness

is small

in comparison with the influence of the

column

size.

Practically. tbe influence of wall thickness on the

fue resistance of

the

column could

be

neglected.

4.3 Load

In Figure

4,

the

fm

resistances of the columns

are

shown

as

a function of the load

for

three

different

sizes.

For

fire

resistances above

45 minutes, which lie

in

the practical

region, the

fire

resistance of the columns decreases steeply

with

increasing load.

The

influence of load on

fire

resistance

is

relatively hieher for the

lareer columns. For a column

with an outside dimension of 304.8

mm,

for &a&ple, a

mixti&

in load of about

52%

from 3600 kN

to

1745

kN

will

double

the

fire

resistance of

the

column

h m

50 min

to

100 min. For

an

intermediate-sized column, which has an outside dimension of

152.4 mm, the load has to be reduced by 87%

to

double the

fire

resistance from 50 min to

100 min.

(9)

4.4 Effective Length

In

Figure

5,

the fire resistances of the columns are shown as a function of

their

effective lengths for the two selected reference loads of 330

kN

and 1150 irN and two

strengths of concrete filling, namely, 20 MPa and 35

MPa

The curves show

that,

in the

range of effective lengths of 2.5 m

to 4.5

m, the fm resistance

is

approximately inversely

proportional to the effective length.

The influence of the effective length

is

greater for low loads than for higher loads.

The influence of the compressive strength is higher for the shorter columns.

It

can

be

seen

in Figure 5 that, for longer columns, the influence of the compressive strength on the

fire

resistance of the column is minimal.

4.5 Concrete Strength

In

Figure 6, the fm resistances of the columns

are

shown

as

a function of the

concrete compressive strength for the selected reference loads of 330

kN

and 1150

kN.

The curves show a moderate influence of concrete strength on the

fire

resistance of the

column.

4.6 Type

of Aggregates

In

7, the

fm

resistance

is

shown, for siliceous and carbonate aggregate

concrete fillings,

as

a function of the load on two columns; the reference column with an

outside dimension of 177.8

mm

and the largest column

with

an outside dimension of

304.8 mm. The curves show that, for smaller column sizes, the aggregate

type has very

little influence on the

fm

resistance of

the

column. For larger column sizes,

the

fm

resistances of columns filled

with

carbonate aggregateare higher

than

those for columns

filled with siliceous aggregate concrete. In the region of

fire

resistances above

45 minutes,

the difference in fm resistance between carbonate aggregate and siliceous aggregate

concrete filling varies from approximately 10%

to 50%.

The difference in

fire

resistance

tends

to

increase with lower loads or higher

fire

resistances.

This

tendency

is

also

shown

in Tables 1-18 for other column section sizes, steel wall thicknesses, column effective

lengths and concrete strengths.

4.7 Limitations

Comparisons of calculated

fire

mistances

with

test results [6] show that the

calculated

fm

resistances

are,

in general lower or close

to those measured, provided

limitations

are

set

with

regard to load,

fm

resistance time and concrete strength. However,

there

are

instances in which

the

measured

fm

resistance

is

lower than that calculated.

When the load

is high

or

the test duration very long,

the

column failure time

is

no

longer reproducible and the

fm

resistance

is

unpredictable using

this

method.

This is

also

the

case

for columns with concrete filling

with

a strength higher

than

approximately

40 MPa [6].

One uossible reason for

the

unpredictable failures

is

the

creation, during

the

test, of

local excesshe stresses and

cracks,

which propagate through the concrete core due to the

absence of steel reinforcement and lack of containment of the concrete.

In the case of

(10)

higher strength concrete filling, increased concrete brittleness associated with higher

concrete strengths may also

be

a contributing factor.

If

limits

are set with regard to the load,

fire

resistance time and concrete strength,

the fire resistance of the column

is

reasonably predictable and the information given in this

report can

be

wed for the evaluation of the

fm

resistance of square HSS columns fdled

with plain concrete. Until further studies, now in progress at

IRC,

are completed, it is

recommended that the following limitations not

be

exceeded in using the information

contained in

this

report:

a)

The loads be not greater than the factored resistance of the concrete core determined in

accordance

with

CANICSA-S16.1-M89

[7].

b)

The

f r e resistance not be greater than 2 hours.

C)

The

concrete strength not

be

greater than

40 MPa, specified compressive strength at

28 days.

With these limitations, predicted fu-e resistances are, in general, not more

than

about 30%

lower than those measured and,

in

a few cases, not more

than

10% higher.

Fire resistances for other conditions or configurations than those given in

Tables 1-18 or

in

Figures 2-7, can

be

derived by linear interpolation between tabulated or

plotted values.

REFERENCES

1. Lie,

T.T.

and

Invin,

RJ.,

"Fire Resistance of Rectangular Hollow Steel Sections

Filled with Bar-Reinforced Concrete

',

IRC

Internal

Report No. 631, Institute for

Research in Construction, National Research Council of Canada, Onawa, 1992.

2. Handbook of Steel Construction, Canadian Institute of Steel Construction,

Willowdale, Ontario, 1991.

3. Standard Methods of Fire

Tests

of

Building

Construction and

Materials, ASTM

E l 19-83, American Society for

Testing

and Materials, Philadelphia, PA, 1983.

4. Standard Methods of

Fire

Endurance

Tests

of Building Construction and Materials,

CAN4-S101-M89, Underwriters' Laboratories of Canada, Scarborough, Ontario,

_-

1982.

5 .

_Lie.

_T.T..

_Irwin.

_{RJ. and Chabot M.. "Factors Affecting the Eke Resistance of}

Ciiular Hollow Steel Columns '11ed

with

Plain concrekn, IRC Internal Report

No. 612, Institute for Research in Construction, National Research Council of

Canada,

Ottawa,

1991.

6. Lie,

T.T.

and Chabot,

M.,

"Experimental Studies on the Fire Resistance of Hollow

Steel Columns Filled

with

Plain Concrete". IRC Internal Rewrt No.611, Institute for

Research in Construction, National Research Council of ~ G a d a ,

Ottawq1991

7. Limit

State

Design

of Steel Structures. CAN/CSA-S16.1-M89.

Canadian

Standard

Association, Rexdale, Ontario. 1989.

(11)

NOMENCLATURE

Notations

c

specific heat [JkgPC]

f

stress FIpa]

f '

cylinder strength of concrete at temperature

T

w a ]

fco

cylinder strength of concrete at room temperature FIpa]

f,

snength of steel at temperature

T

m a ]

k

thermal conductivity W I m 0 q

K

effective length factor

L

unsupported length of the column [m]

T

temperature

[ O C J

Greek

Letters

a

coefficient of thermal expansion [l/'T]

E

emissivity, strain [mlm]

?.

heat of vaporization [Jkg]

P

density ikg/m3],

radius

of curvature [m]

pc

thermal capacity [J/m3°C]

7

time

N

0 concentration of moisture

Subscripts

0 at

room temperature

c

of concrete

f

of

fue

max

maximum

P

pertaining to proportional stress-strain relation

S

of steel

(12)

TABLE

1

:

STRENGTH (KN) OF COLUMNS DURING FIRE VERSUS TIME FOR VARIOUS SIZES AND WALL THICKNESSES.

-

TYPE OF CONCRETE: SILICEOUS.

-

CONCRETE STRENGTH:

20 MPa.

-

EFFECTIVE LENGTH OF COLUMN: 2.5

m.

Column Size (mm) Wall Thickness (mm) Time (min) 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 152.4 4.78 1123.26 808.87 445.69 256.09 166.35 106.92 74.7 53.33 38.25 26.61 17.24 9.82 3.62

-

--

-

.- 177.8 4.78 1632.43 1348.92 932.2 521.37 376.43 260.94 190.57 142.1 106.94 79.03 55.84 37.43 25.07 15.15 8.85 5.27 2.85 1.36 0.54 0.14 0.01

X

152.4 12.70 2465.26 1992.86 1284.33 789.4 500.78 350.56 210.4 142.24 99.55 69.46 45.55 26.35 10.55

-

--

X 177.8 12.70 3096.78 2625.24 1763.39 1145.04 740.7 541.7 347.69 240.36 172.45 123.32 85.6 54.78 29.15 6.42 2.01 0.82 0.27 0.04 0 0 0 203.2 6.53 2330.38 1991.74 1450.46 1020.33 738.4 477.3 357.41 273.1 1 215.31 168.89 129.39 95.69 67.58 44.56 29.08 20.45 13.88 9.03 5.62 3.12 1.59 191.6 4.78 689.8 419.62 219.7 117.98 72.35 43.64 29.86 20.81 14.43 9.54 5.71 2.61 0.09

-

.-

-

--

-

--

X 203.2 12.70 3763.66 3236.04 2273.91 1537.42 1052.4 797.57 555.08 393.79 292.51 217.82 158.64 108.26 66.96 30.48 16.11 10.5 6.38 3.7 1.89 0.83 0.26 127.0 4.78 893.79 594.03 301.1 164.52 105.99 65.76 45.67 32.41 22.83 15.43 9.69 5 1.09

-

--

-

X 101.6 9.53 1012.53 715.65 413.5 215.94 131.55 69.57 44.05 29.99 20.48 13.4 7.87 3.4 0

-

--

-

--

254.0 6.53 3269.51 2929.37 2349.73 1840.98 1483.19 1220.08 997.95 832.69 697.76 582.58 486.29 409.06 333.58 270.19 216.44 176.32 145.99 119.08 96.12 77.04 60.75

X

127.0 11.13 1832.24 1409.88 869.66 515.72 324.16 209.95 125.74 85.6 59.34 40.3 13.9 6.51 0.41

--

-

--

-

--

-*

--

X

254.0 12.70 5220.12 4652.69 3709.84 2782.01 2078.36 1637 1259.29 958.62 769.49 613.53 493.54 387.68 303.18 226.2 165.7 126.55 101.24 79.9 62.98 48.73 37.18 304.8 6.53 4304.15 3914.23 3268.24 2673.6 2261.88 1957.49 1703.56 151 1.33 1351.88 1210.59 1086.21 968.1 858.64 757.51 666.09 588.96 525.69 468.45 417.66 372.57 327.25 X 304.8 12.70 6763.13 6110.91 5082.06 4030.19 3195.11 2656.75 2188.06 1788.32 1517.8 1299.9 1119.02 958.2 816.29 686.55 574.42 486.86 424.65 378.7 330.49 288.35 247.66

(13)

TABLE

2

:

STRENGTH (KN) OF COLUMNS DURING FIRE VERSUS TIME FOR VARIOUS SIZES AND WALL THICKNESSES.

-

TYPE OF CONCRETE: SILICEOUS.

-

CONCRETE STRENGTH335 MPa.

J

-

EFFECTIVE LENGTH OF COLUMN: 2.5 m.

Column Size (mm) WallThickueas(mm) Time (min) 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200

-

254.0 6.53 4104.51 3779.15 3175.01 2607.94 2173.52 1840.47 1541.49 1308.52 1111.22 936.48 788.29 672.1 558.48 458.99 377.58 308.55 255.48 208.39 168.22 134.81 106.32 X 254.0 12.70 5941.94 5405.91 4465.58 3503.57 2726.99 2212.24 1748.24 1372.82 1109.09 913.1 740.34 598.04 475.45 369.16 281.64 221.41 177.17 139.82 110.22 85.27 65.06 304.8 6.53 5530.95 5167.75 4491.83 3846.95 3361.65 2985.97 2657.08 2402.92 2179.41 1978 1792.82 1618.55 1454.75 1299.3 1155.59 1030.96 919.96 819.78 730.9 651.99 572.68 177.8 4.78 2038.96 1750.67 1289.63 906.57 639.96 431.54 307.47 227 169.04 122.08 87.41 61.7 41.34 25.68 15.49 9.22 5 2.39 0.95 0.25 0.02 203.2 6.53 2834.6 2503.8 1927.3 1427.38 1072.65 810.2 596.89 456.54 352.94 271 206.46 151.93 110.07 75.24 51.34 35.79 24.29 15.8 9.84 5.47 2.78 X 304.8 12.70 7838.73 7239.38 6213.66 5133.63 4242.13 3623.8 3088.08 2607.61 2271.5 1989.1 1744.06 1523.11 1323.89 1142.67 981.71 847.91 743.13 662.73 578.36 504.61 433.4 101.6 4.78 793.78 454.2 219.98 117.98 72.35 43.65 29.86 20.81 14.43 9.54 5.71 2.61 0.09

-

X 177.8 12.70 3406.03 2895.26 1956.45 1275.79 832.62 610.98 393.35 269.31 193.03 136.9 94.6 60.95 32.52 7.89 3.51 1.44 0.47 0.06 0 0 0 X 203.2 12.70 4201.77 3664.74 2732.36 1763.73 1237.71 949.21 660.25 469.84 347.46 257.54 187.79 129.75 76.04 49.79 28.47 18.37 11.16 6.48 3.31 1.45 0.46

X

101.6 9.53 1077.09 714.76 409.95 216.48 131.06 69.5 44.13 30.06 20.5 13.41 7.87 3.4 0

-

--

-

-* 127.0 4.78 1054.34 667.99 345.91 182.86 115.17 71.16 48.89 34.16 23.6 15.79 9.72 5 1.1

-

X

127.0 11.13 1987.9 1502 880.23 518.97 327.01 211.23 126.59 86.1 59.77 40.32 25.43 13.56 3.73

-

--

152.4 4.78 1356.38 1000.6 536.92 303.46 194.26 122.98 84.97 60.03 42.31 29.26 18.85 10.69 3.91

-

X

152.4 12.70 2668.35 2136.39 1355.77 827.27 525.41 365.4 221.43 148.97 104.34 71.99 47.15 27.02 10.77

-

--

-

--

(14)

TABLE 3

:

STRENGTH

(KN)

OF COLUMNS DURING FIRE VERSUS TIME FOR VARIOUS SIZES AND WALL THICKNESSES.

-

TYPE OF CONCRETE: SILICEOUS.

-

CONCRETE STRENGTH: 55 MPa.

-

EFFECTIVE LENGTH OF COLUMN:

2.5 m.

Column

She

(mm) Wall Thickness (mm) Time (min) 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 152.4 4.78 1659.99 1270.54 783.54 361 227.29 141.61 96.73 67.58 47.59 32.26 20.64 11.51 4.24

--

-

--

127.0 4.78 1267.6 847.38 403.66 207.25 128.4 77.89 52.75 36.38 25.06 16.35 9.89 5 1.09

-

X 152.4 12.70 2612.58 1651.03 1023.19 609.46 373.04 252.02 146.82 96.41 67.08 45.99 30.11 17.34 6.89

-

--

-

--

101.6 4.78 931.83 519.46 230.24 118 72.36 43.65 29.86 20.81 14.43 9.54 5.71 2.61 0.09

-

X

127.0 11.13 2187.93 1635.76 939.64 534.31 334.24 215.84 128.98 87.61 60.48 40.49 25.44 13.56 3.73

-

X 101.6 9953 1160.95 726.2 413.5 215.94 131.55 69.57 44.05 29.99 20.48 13.4 7.87 3.4 0

--

-

--

177.8 4.78 2582.63 2280.82 1755.81 1278.55 938.33 653.79 476.94 348.39 259.49 188.57 134.29 92.36 62.46 39.28 24.34 14.5 7.85 3.75 1.49 0.39 0.03 X 177.8 12.70 3821.38 3265.07 2224.84 1463.33 962.11 696.49 444.07 303.25 215.05 152.38 104.48 68.18 36.43 12.44 5.51 2.26 0.73 0.1 0 0 0 203.2 6.53 3129.5 2773.28 2154.17 1581.82 1165.69 842.54 610.36 456.9 341.99 254.97 184.5 129.91 90.62 59.12 37.19 23.73 14.48 7.98 3.84 1.52 0.43 X 203.2 12.70 4784.99 4244.24 3278.78 2378.88 1628.16 1133.41 792.62 562.33 387.63 300.07 225.56 165.5 115.74 73.6 44.48 28.87 17.54 10.18 5.2 2.28 0.73 254.0 6.53 5226.83 4899.75 4265.73 3630.37 3093.15 2655.75 2268.05 1940.88 1657.98 1410.87 1198.65 1023.31 857.12 715.46 588.51 484.86 401.46 327.46 264.34 211.85 167.07 X 254.0 12.70 6927.48 6418.02 5451.43 4446.98 3578.14 2959.31 2402.46 1926.87 1571.81 1288.62 1069.83 875.47 704.68 556.15 439.39 347.88 278.41 219.71 173.2 133.99 102.24 304.8 6.53 7194.16 6839.52 6133.86 5407.26 4826.5 4355.59 3934.31 3595.03 3286.49 3005.84 2734.78 2486.29 2248.73 2016.6 1809.98 1618.25 1445.66 1288.23 1148.56 1024.56 899.93 X 304.8 12.70 9320.76 8758.09 7725.48 6613.93 5610.76 4916.64 4285.57 3700.27 3267 2903.71 2575.07 2279.49 2003.53 1751.89 1522.41 1328.03 1167.78 1041.43 908.85 792.96 681.06

(15)

TABLE 4

:

STRENGTH (KN) O F COLUMNS DURING FIRE VERSUS TIME FOR VARIOUS SIZES AND WALL THICKNESSES.

-

TYPE OF CONCRETE: SILICEOUS.

-

CONCRETE STRENGTH:

20 MPa.

-

EFFECTIVE LENGTH OF COLUMN:

3.0 m.

Column Size (mm) Wall Thickness (mm) Time (min) 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 304.8 6.53 4230.61 3843.11 3171.49 2569.62 2149.65 1838.1 1 1568.82 1371.99 1205.69 1058.55 930.86 815.49 708.37 615.69 534.8 475.76 418.96 370.81 325.56 284.86 248.28 101.6 4.78 678.26 391.26 208.11 109.41 66.56 39.M 27.16 18.87 12.99 8.59 5.14 2.34 0.07

-

X 304.8

-

12.70 6597.11 5952.14 4869.83 3800.65 2959.17 2422.04 1967.76 1581.02 1315.82 1107.87 933.56 784.89 655.83 552.44 460.5 386.22 333.24 290.84 251.31 216.85 185.54 X 101.6 9.53 966.55 682.88 393.4 202.62 123.18 65.32 41.61 28.49 19.4 12.72 7.49 3.22 0

-

127.0 4.78 856.74 507.42 269.94 148.61 94.06 57.8 39.67 28.12 19.78 13.49 8.4 4.32 0.94

-

..

-

..

-

X 127.0 11.13 1760.9 1293.13 808.96 473.89 293.05 187.15 111.16 75.27 51.8 35.05 22.07 11.76 3.22

-

152.4 4.78 1072.47 705.04 356.24 194.76 126.92 80.08 56.28 40.2 29.05 20.16 13.19 7.49 2.72

-

X 152.4 12.70 2352.54 1832.83 1168.28 716.42 448.12 307.72 183.19 121.25 85.06 58.72 38.38 22.13 8.76

-

--

-

--

-

--

177.8 4.78 1576.52 1204.74 676.22 412.18 275.42 182.77 130.28 96.3 71.69 52.71 37.29 24.49 13.71 9.32 6.05 3.59 1.98 0.96 0.37 0.1 0.01 X 177.8 12.70 2974.29 2453.11 1570.14 978.21 611.25 436.86 274.45 186.25 133.26 94.64 65.49 41.79 21.68 4.27 1.35 0.56 0.18 0.02 0 0 0 203.2 6.53 2246.72 1826.89 1231.29 711.56 499.12 349.6 ' 246.65 183.99 139.64 104.82 76.35 52.71 32.74 28.38 20.15 14.15 9.69 6.24 3.9 2.23 1.12 254.0 6.53 3195.06 2817.07 2186.31 1667.6 1309.94 1046.58 835.08 677.55 563.56 459.35 377.65 310.48 253.47 202.25 161.29 130.36 106.93 86.29 69.59 55.31 43.39 X 203.2 12.70 3631.59 3025.02 2046.99 1328.29 876.76 645.44 427.98 296.86 216.72 158.87 114.34 77.75 46.3 19.05 10.94 7.28 4.41 2.53 1.34 0.57 0.18 X 254.0 12.70 5049.74 4446.15 3390.73 2402.87 1574.95 1218.01 915.93 675.7 523.82 410.87 317.67 271.97 217.07 166.02 120.57 91.99 73.4 57.03 44.76 34.77 26.34

(16)

TABLE

5

:

STRENGTH (KN) OF COLUMNS DURING FIRE VERSUS TIME FOR VARIOUS SIZES AND WALL THICKNESSES.

-

TYPE OF CONCRETE: SILICEOUS.

-

CONCRETE STRENGTH:

35 MPa.

-

EFFECTIVE LENGTH OF COLUMN:

3.0 m.

Column Size (mm) Wall Thickness (mm) Time (min) 0 10 20 30 40 50 60 70 SO 90 100 110 120 130 140 150 160 170 180 190 200 203.2 6.53 2728.03 2304.98 1682.99 1 177.25 628.45 433.19 304.43 227.62 170.41 128.31 94.11 86.08 68.17 50.07 35.07 24.76 16.96 10.92 6.82 3.89 1.96 X 203.2 12.70 4045.29 3372.4 2288.91 1495.17 1008.15 739.72 489.28 336.25 244.65 180.24 129.29 87.52 53.17 22.65 18.99 12.75 7.73 4.43 2.34 t 0.32 152.4 4.78 1289.66 823.24 410.93 218.01 138.35 86.64 60.13 42.96 30.86 21.17 13.88 7.73 2.82

-

--

127.0 4.78 1007.42 573.38 269.96 148.61 94.07 57.84 39.68 28.12 19.78 13.49 8.41 4.32 0.94

-

--

254.0 6.53 4017.8 3633.73 2983.12 2390.9 1943.02 1595.59 1299.05 1072.68 896.16 745.9 620.97 515.18 424.06 344.77 279.21 228.12 187.13 151.02 121.78 96.79 75.93 X 152.4 12.70 2556.27 1953.5 1170.94 7 16.63 448.49 308.24 183.41 121.34 85.07 58.74 38.38 22.13 8.77

-

--

-

--

177.8 4.78 1960.96 1570.04 1083.07 515.26 336.14 221.6 156.16 115.42 84.71 62.23 43.74 29.16 20.33 16.44 10.58 6.29 3.47 1.68 0.65 0.17 0.01 X 127.0 11.13 1902.07 1347.25 809.09 473.91 293.06 187.16 111.17 75.27 51.8 35.05 22.07 11.76 3.22

--

-

*-

--

-

101.6 4.78 775.9 394.69 208.11 109.41 66.56 39.84 27.16 18.87 12.99 8.59 5.14 2.34 0.07

-

--

-

X 254.0 12.70 5777.76 5181.27 4122.92 31 33.76 2363.76 1849.53 1444.28 1096.73 845.42 681.32 548.97 441.31 348.16 271.16 206.47 160.92 128.45 99.81 78.33 60.85 46.1 X 177.8 12.70 3274.7 2698.54 1706.76 1059.64 654.91 470.7 293.97 199.19 140.88 100.43 69.34 44.46 23.18 4.73 2.37 0.98 0.31 0.04 0 0 0 304.8 6.53 5461.08 5085.75 4382.28 371 5.05 3212.45 2821.68 2472.74 2189.39 1952.54 1737.31 1539.96 1364.33 1206.22 1058.15 923.32 830.25 733.18 648.91 569.74 498.5 434.49 X 101.6 9.53 1022.66 692.02 393.4 202.62 123.18 65.52 41.64 28.49 19.4 12.72 7.49 3.22 0

-

--

-

--

X 304.8 12.70 7694.9 7086.7 6003.21 4895.98 3972.76 3352.15 2803.41 2333.01 1983.83 1707.14 1464.09 1257.39 1071.91 922.21 786.87 672.05 583.17 508.98 439.79 379.48 324.69

(17)

TABLE 6

:

STRENGTH

(KN)

OF COLUMNS DURING FIRE VERSUS TIME FOR VARIOUS SIZES AND WALL THICKNESSES.

-

TYPE OF CONCRETE: SILICEOUS.

-

CONCRETE STRENGTH: 55 MPa

-

EFFECTIVE LENGTH OF COLUMN:

3.0 m.

Column Size (mm) WallThickness(mm)

Time

(min) 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 101.6 4.78 893.1 405.61 208.11 109.41 66.56 39.84 27.16 18.87 12.99 8.59 5.14 2.34 0.07

-

--

-

X 101.6 9.53 1071.01 700.42 393.4 202.62 123.18 65.52 41.64 28.49 19.4 12.72 7.49 3.22 0

--

-

--

127.0 4.78 1204.43 665.07 270 148.61 94.09 57.88 39.68 28.12 19.78 13.49 8.4 4.32 0.94

-

X

127.0 11.13 2091.09 1433.09 809.26 473.94 293.06 187.16 111.2 75.28 51.8 35.05 22.07 11.76 3.22

-

--

-

--

152.4 4.78 1573.06 1063.49 484.58 248.64 155.34 95.24 65.86 46.34 32.78 22.56 14.58 8.08 2.93

-

X 152.4 12.70 2815.27 2114.46 1237.53 720.15 449.72 309.3 183.7 122.35 85.09 58.77 38.38 22.13 8.77

-

--

177.8 4.78 2477.94 2045.34 1490.93 1021.83 414.98 268.65 187.57 137.67 100.44 73.26 51.95 50.28 37.73 26.19 16.63 9.88 5.45 2.63 1.02 0.27 0.02 X 177.8 12.70 3668.67 2993.52 1891.9 1185.04 730.45 516.81 320.18 215.95 151.86 108.02 73.84 47.52 25.04 5.13 3.72 1.54 0.49 0.07 0 0 0 203.2 6.53 3382.18 2929.62 2253.1 1645.72 1220.97 815.37 582.89 433.09 335.58 260.88 199.07 147.98 109.28 77.63 54.74 38.91 26.64 17.15 10.72 6.12 3.08 X 203.2 12.70 4604.42 3891.15 2816.19 1739.04 1171.68 849.32 561.11 381.71 279.08 203.13 145.9 99.34 61.05 43.98 30.24 20.03 12.14 6.96 3.67 1.58 0.51 254.0 6.53 5122.27 4730.7 4033.25 3348.63 2775.19 2314.31 1922.74 1603.24 1334.54 11 19.67 943.04 784.38 649.31 536.55 437.97 358.46 294.06 237.31 191.37 152.1 119.33 X 254.0 12.70 6758.08 6149.93 5079.5 4024.07 3133.43 2507.22 1985.71 1568.45 1236.35 994.37 806.18 655.25 525.13 412.09 322.35 252.83 201.85 156.84 123.09 95.62 72.44 304.8 6.53 7108.73 6737.87 5991.09 5250.38 4622.46 4130.53 3669.6 3281.89 2950.98 2639.07 2356.7 2099.47 1859.49 1642.42 1453.51 1302.95 1152.14 1019.72 895.3 783.36 682.77 X 304.8 12.70 9176.06 8603.82 7492.71 6326.83 5307.89 4569.31 3917.36 3329.11 2875.73 2498.05 2167.27 1885.31 1629.39 1398.45 1213.68 1051.81 916.41 799.82 691.1 596.33 510.23

(18)

TABLE

7

:

STRENGTH (KN) OF COLUMNS DURING FIRE VERSUS TIME FOR VARIOUS SIZES AND WALL THICKNESSES.

-

TYPE OF CONCRETE: SILICEOUS.

-

CONCRETE STRENGTH:

20 MPa.

-

EFFECTIVE LENGTH OF COLUMN:

4.5

in.

Column Size (mm) Wall Thickness (mm) Time (mitt) 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 < 177.8 4.78 1425.76 835.94 428.09 243.67 158.01 101.77 71.1 51.84 38.18 27.58 18.98 12.11 6.29 1.7 1.77 1.12 0.64 0.32 0.13 0.03 0 101.6 4.78 433.55 282.23 149.15 78.22 47.23 27.81 19.03 13.3 9.06 6.07 3.58 1.63 0.07

-

X 177.8 12.70 2755.45 2053.43 1321.01 817.32 493.09 343.08 206.2 136.34 95.76 67.32 45.71 28.49 14.28 2.71 0.39 0.19 0.06 0.01 0 0 0 X 101.6 9.53 505.3 382.15 216.55 113.51 69.37 35.65 22.82 15.73 10.68 6.96 4.07 1.72 0

-

--

-

--

-

--

203.2 6.53 2038.19 1369.82 701.29 414.05 268.44 178.52' 120.82 88.53 65.46 47.97 33.83 22.38 12.63 4.6 5.67 4.4 3.1 2.09 1.32 0.76 0.4 127.0 4.78 719.16 425.58 219.61 117.85 74.1 45.84 31.99 22.78 16.17 11.06 6.86 3.57 0.77

-

X 203.2 12.70 3304.96 2497.92 1593.41 1004.34 629.01 443.67 280.43 185.95 133.26 96.05 66.9 44.09 24.93 8.92 2.84 2.19 1.38 0.83 0.44 0.19 0.07 152.4 4.78 993.36 537.54 291.01 159.29 101.7 63.61 44.16 31.6 22.72 15.87 10.34 5.86 2.15

-

--

-

--

X 127.0 11.13 1609.7 1145.21 697.28 393.54 242.61 153.47 90.42 61.5 42.9 29.13 8.73 4.01 0.23

-

--

-

254.0 6.53 2940.58 2282.37 1299.42 804.51 529.34 362.32 250.39 187.61 142.61 108.73 81.2 58.25 38.52 50.31 59.64 50.96 40.87 32.17 26.13 20.7 16.59 X 152.4 12.70 2245.26 1607.77 1023.19 609.46 373.04 252.02 146.82 96.41 67.08 45.99 30.11 17.34 6.89

-

--

X 254.0 12.70 4638.97 3771.75 2444.39 1536.84 999.65 719.65 490.87 332.16 243.97 181.63 133.91 95.44 62.52 33.82 11.11 32.67 25.84 20 16.03 12.37 9.7 304.8 6.53 3967.24 3399.17 2628.1 1 2025 1604.2 1315.79 1079.9 898.82 756.73 619.09 507.17 429.57 368.9 321.17 276.22 237.42 206.81 182 158.88 138.12 117.33 X 304.8 12.70 6123.08 5227.05 3835.39 2429.59 1693.54 1283.75 937.28 659.29 495.1 382.78 292.79 220.23 157.1 236.47 213.79 184.58 159.44 137.01 118.14 99.92 83.59

(19)

TABLE 8

:

STRENGTH (KN) OF COLUMNS DURING FIRE VERSUS TIME FOR VARIOUS SIZES AND WALL THICKNESSES.

-

TYPE OF CONCRETE: SILICEOUS.

-

CONCRETE STRENGTH:

35 MPa.

-

EFFECTIVE LENGTH OF COLUMN:

4.5 m.

Column Size (mm) WallThickness(mm) Time (min) 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 304.8 6.53 5122.84 4551.76 3722.23 3007.15 2471.07 2064.16 1721.2 1461.34 1253.58 1056.97 897.42 746.37 643.68 555.28 481.12 415.32 361.92 318.5 278.04 241.71 205.33 X 304.8 12.70 7181.64 6256.84 4891.61 3749.53 2877.76 2305.42 1790.06 803.09 604.12 464.47 628.24 565.05 502.88 432.85 374.02 323.61 279.02 239.77 206.74 174.86 146.28 254.0 6.53 3696.68 2971.99 2223.19 1624.5 641.8 433.76 297.71 221.47 167.24 127.78 95.42 69.44 124.42 122.9 106.97 89.18 71.52 56.29 45.73 36.23 29.03 X 254.0 12.70 5316.28 4281.91 2768.21 1754.49 1136.35 806.64 544.92 366.36 269.55 201.02 148.37 106.07 70.12 38.33 60.27 57.12 45.22 35.01 28.05 21.64 16.97 101.6 4.78 465.11 282.3 149.15 78.22 47.23 27.81 19.03 13.3 9.06 6.07 3.58 1.63 0.07

-

X 101.6 9.53 524.29 382.43 216.55 113.51 69.37 35.65 22.82 15.73 10.68 6.96 4.07 1.72 0

-

127.0 4.78 1007.42 573.38 269.96 148.61 94.07 57.84 39.68 28.12 19.78 13.49 8.41 4.32 0.95

-

--

-

X

127.0 11.13 1713.18 1149.05 697.28 393.54 242.61 153.47 90.42 61.5 42.9 29.13 18.38 9.73 2.66

-

--

-

--

-

--

152.4 4.78 1153.82 544.49 291.01 159.29 101.7 63.61 44.16 31.6 22.72 15.87 10.34 5.86 2.15

-

--

-

X 152.4 12.70 2422.1 1 1624.53 1023.19 609.46 373.04 252.02 146.82 96.41 67.08 45.99 30.11 17.34 6.89

-

--

177.8 4.78 1763.36 a 995.95 428.11 243.67 158.02 101.77 71.1 51.84 38.18 27.58 18.98 12.11 6.29 1.7 3.09 1.95 1.12 0.57 0.23 0.06 0.01 203.2 6.53 2465.97 1640.41 828.48 414.12 269.48 178.79 123.9 88.69 67.52 49.66 35.42 23.61 13.64 4.6 10.13 7.7 5.43 3.65 2.3 1.33 0.7 X 177.8 12.70 3023.37 2152.64 1321.11 817.32 493.09 343.08 206.2 136.34 95.76 67.32 45.71 28.49 14.28 2.71 0.69 0.33 0.1 0.02 0 0 0 X 203.2 12.70 3681.05 2698.85 1593.76 1004.37 629.06 443.68 280.54 185.96 133.27 96.05 66.9 44.09 24.93 8.92 5.34 3.84 2.42 1.46 0.78 0.34 0.11

(20)

TABLE

9

:

STRENGTH (KN) OF COLUMNS DURING FIRE VERSUS TIME FOR VARIOUS SIZES AND WALL THICKNESSES.

-

TYPE OF CONCRETE: SILICEOUS.

.

CONCRETE STRENGTH:

55 MPa.

-

EFFECT1,VE LENGTH OF COLUMN: 4.5

m.

Column S i (mm) WallThickness(mm) Time (min) 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 127.0 4.78 872.77 427.98 219.61 117.85 74.1 45.84 31.99 22.78 16.17 11.06 6.86 3.57 0.77

-

--

-

101.6 4.78 516.7 282.42 149.15 78.22 47.23 27.81 19.03 13.3 9.06 6.07 3.58 1.63 0.07

-

--

-

--

-

X

127.0 11.13 1786.45 1159.84 697.28 393.54 242.61 153.47 90.42 61.5 42.9 29.13 8.73 4.01 023

--

-

--

-

--

-

.-

X 101.6 9.53 550.47 382.81 216.55 113.51 69.37 35.65 22.82 15.73 10.68 6.96 4.07 1.72 0

-

--

-

152.4 4.78 1345.24 552.67 291.01 159.29 101.7 63.61 44.16 31.6 22.72 15.87 10.34 5.86 2.15

-.

.-

--

-.

--

X 152.4 12.70 2612.58 1651.03 1023.19 609.46 373.04 252.02 146.82 96.41 67.08 45.99 30.11 17.34 6.89

--

-

--

-

-*

--

177.8 4.78 2208.82 1365.06 428.13 243.67 158.02 101.77 71.1 51.84 38.18 27.58 18.98 12.11 6.29 1.7 4.86 3.07 1.77 0.89 0.35 0.1 0.01 X 177.8 12.70 3375.22 2300.85 1326.89 817.32 493.09 343.08 206.2 136.34 95.76 67.32 45.71 28.49 14.28 2.71 1.08 0.52 0.16 0.03 0 0 0 203.2 6.53 3023.47 2092.8 975.98 494.56 307.37 198.48 133.54 97.8 72.36 53.08 37.82 25.32 14.64 4.6 16.23 12.1 8.54 5.74 3.62 2.09 1.11 X 203.2 12.70 4164.93 3018.96 1698.69 1004.4 629.13 443.69 280.68 186.4 133.29 96.06 66.9 44.09 24.93 8.92 8.54 6.03 3.8 2.29 1.22 0.54 0.18 254.0 6.53 4693.09 3910.25 3042.93 2335.9 1771.91 520.02 353.11 262.12 198.83 348.62 308.84 273.43 236.73 203.64 169.9 140.12 112.39 88.46 71.87 56.93 45.61 X 254.0 12.70 6199.94 5024.71 3611.45 2045.19 1297.31 911.34 607.04 409.58 298.62 222.01 164.45 117.98 78.59 43.66 103.59 89.72 71.06 55.01 44.08 34.01 26.67 304.8 6.53 6670.34 6057.59 5150.6 4296.08 3578.01 3042.74 2588.42 2208.66 1900.2 1630.88 1392.61 1159.57 1011.94 870.94 748.53 660.9 568.73 500.5 436.91 379.83 322.66 X 304.8 12.70 8583.9 7629.17 6223.7 4951.34 3940.19 3225.63 2624.1 2151.69 1755.55 1342.45 11 17.32 940.48 797.88 685.49 588.76 507.28 438.47 376.79 324.88 274.78 229.88

(21)

TABLE 10

:

STRENGTH (KN) OF COLUMNS DURING FIRE VERSUS TIME FOR VARIOUS SIZES AND WALL THICKNESSES.

-

TYPE OF CONCRETE: CARBONATE.

-

CONCRETE STRENGTH: 20 MPa.

-

EFFECTJVE LENGTH OF COLUMN: 2.5 m.

Column Size (mm) WallThickness(mm) Time (min) 0 10 20 30

40

50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 304.8 6.53 4304.15 3923.15 3282.62 2671.69 2282.77 2025.1 1792.76 1617.18 1471.33 1348.94 1238 1139.54 1046.74 959.59 881.92 815.7 760.26 713.49 668.73 625.11 584.24 X 304.8 12.70 6763.13 6125.35 5102.61 4035.52 3199.1 2715.3 2298.16 1893.51 1646.6 1454.38 1282.91 1127.28 995.4 881.81 778.37 694.94 635.87 590.28 547.14 508.21 472.06 203.2 6.53 2330.38 2003.03 1465.86 1030.47 768.54 548.27 435.13 354.92 293.9 242.52 199.17 162.54 131.24 105.82 85.68 72.98 63.97 56.59 49.9 44.28 39.59 X 203.2 12.70 3763.66 3259.86 2289.98 1536.62 1061.52 834.97 603.96 437.58 341.22 264 197.79 146.29 110.83 83.91 59.43 48.51 42.07 36.7 32.53 28.42 25.04 254.0 6.53 3269.51 2942.79 2365.32 1842.5 1515.7 1282.22 1082.25 929.93 805.24 700.49 611.78 533.16 464.55 410.26 359.68 317.45 285.08 257.98 233.06 210.93 192.46 101.6 4.78 689.8 421.87 220.83 119.66 81.3 51.1 36 25.53 18.43 12.86 8.58 4.96 1.95

-

X 254.0 12.70 5220.12 4681 .I4 3726.99 2795.61 2094.91 1699.17 1350.87 1054.17 869.22 735.33 612.38 509.13 425.01 351.48 289.02 242.11 214.51 191.87 171.88 154.45 140.33 X 101.6 9.53 1012.53 721.61 418.06 218.67 145.8 79.13 52.05 38.59 26.72 17.91 11.63 6.22 1.61

-

127.0 4.78 893.79 597.76 303.38 164.24 114.21 77.18 53.98 39.59 28.66 20.59 14.21 8.81 4.37

-

X

127.0 11.13 1760.9 1300.27 815.6 472.38 300.64 208.3 126.82 89.15 62.38 44.27 19.76 11.35 4.64

-

--

-* 152.4 4.78 1123.26 819.8 448.93 255.79 178.88 120.05 87.86 65.35 48.49 35.75 25.64 17.12 9.76

--

X 152.4 12.70 2465.26 1993.93 1293.17 789.32 506.71 373.16 232.44 165.59 120.52 86.03 60.43 40.26 22.59

-

--

-

--

177.8 4.78 1632.43 1363.87 944.85 617.9 394 98 288.42 218.32 170.27 150.43 126.02 103.28 83.3 67.34 53.1 42.85 36.42 31.75 27.66 24.15 21.19 18.62 X 177.8 12.70 .3096.78 2641.62 1775.88 1138.94 757.17 592.51 399.88 253.92 188.41 146.54 111.96 80.81 50.72 24.47 18.98 16.58 14.52 12.56 10.07 8.47 7.24

(22)

TABLE 11

:

STRENGTH (KN) OF COLUMNS DURING FIRE VERSUS TIME FOR VARIOUS SIZES AND WALL THICKNESSES.

-

TYPE OF CONCRETE: CARBONATE.

-

CONCRETE STRENGTH: 35 MPa.

-

EFFECTIVE LENGTH OF COLUMN: 2.5

m.

Column Sue (mm) Wall Thickness (mm) Time (min) 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200

.

101.6 4.78 793.78 465.2 220.84 119.67 81.3 51.1 36 25.53 18.43 12.86 8.58 4.96 1.95

-

--

-

X

101.6 9.53 1077.1 727.77 418.06 218.67 145.8 79.13 52.05 38.59 26.72 17.91 11.63 6.22 1.61

--

-

127.0 4.78 1054.34 672.67 348.66 182.44 126.33 83.77 59.24 42.81 30.9 22.14 15.27 9.56 4.73

-

X

127.0 11.13 1987.9 1513.69 887.95 517.59 333.36 234.62 144.14 102.17 72.56 51.72 19.76 11.35 4.64

-

152.4 4.78 1356.38 1012.21 540.97 303.33 210.19 139.34 101.89 74.9 55.71 41.26 29.54 19.81 21.7

-

--

177.8 4.78 2038.96 1763.95 1304.82 922.9 679.19 490.06 385.67 313.24 252.64 206.26 165.72 135.12 109.96 89.89 74.61 63.73 55.56 48.4 42.26 37.09 32.58

X

152.4 12.70 2668.35 2154.95 1365.42 827.12 531.69 393.45 248.18 176.53 128.53 91.43 64.57 43.57 24.81

--

-

--

-

--

X

177.8 12.70 3406.03 2916.79 1970.05 1273.95 858.74 667.2 450.39 287.59 215.7 166.69 127.94 93.14 59.65 47.54 33.06 29.02 25.41 21.99 17.63 14.82 12.67 203.2 6.53 2541.03 2210.04 1654.24 1175.06 867.49 621.34 483.87 391.4 321.45 263.46 317.1 262.8 215.68 177.62 148.28 127.72 111.94 99.04 87.32 77.5 69.29

X

203.2 12.70 4201.77 3683.38 2757.1 1762.04 1238.92 986.34 720.51 532.2 414.04 297.33 265.5 216.53 172.51 132.75 102.07 84.89 73.62 64.23 56.92 49.73 43.82 254.0 653 4104.51 3786.66 3187.58 2617.73 2213.96 1926.83 1666.46 1461.97 1286.12 1133.64 998.88 885.09 781.5 700.15 620.11 554.51 498.88 451.46 407.85 369.13 336.8

X

254.0 12.70 5941.94 5439.93 4488.01 3526.15 2757.22 2285.54 1870.56 1514.05 1277.78 1086.21 925.77 793.98 678.36 578.81 489.62 421.36 375.38 335.78 300.78 270.29 245.58 304.8 6.53 5530.95 5177.66 4509.25 3848.67 3393.47 3080.07 2785.73 2567.68 2373.39 2205.84 2047.33 1909.35 1771.89 1644.89 1529.8 1423.23 1330.46 1248.6 1170.28 1093.94 1022.42

X

304.8 12.70 7838.73 7254.19 6235.87 5161 .I 4252.49 3703.95 3227.19 2759.44 2464.81 2220.39 1999.61 1801.67 1626.74 1470.26 1327.32 1208.75 1112.77 1032.99 957.5 889.38 826.11

(23)

TABLE 12

:

STRENGTH (KN) OF COLUMNS DURING FIRE VERSUS TIME FOR VARIOUS SIZES AND WALL THICKNESSES.

-

TYPE OF CONCRETE: CARBONATE

-

CONCRETE STRENGTH: 55 MPa.

-

EFFECTIVE LENGTH OF COLUMN: 2.5 m.

Column Size (mm) Wall Thickness (mm) Time (miu) 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 101.6 4.78 931.83 526.74 232.61 119.69 81.31 51.1 36 25.53 18.43 12.86 8.58 4.96 1.95

-

X 101.6 9.53 1077.1 727.77 418.06 218.67 145.8 79.13 52.05 38.59 26.72 17.91 11.63 6.22 1.61

--

-

--

-

--

-

--

*- 127.0 4.78 1267.61 858.72 405.71 209.2 142.96 91.09 65.45 46.02 33.6 24.06 16.58 10.43 5.22

-

X 127.0 11.13 2187.93 1642.28 945.55 533.49 343.14 239.81 151.24 107.28 75.55 54.1 19.76 11.35 4.61

-

152.4 4.78 1659.99 1287.02 803.69 360.05 247.27 162.23 118.09 86.75 63.49 47.35 34.33 41.45 33.01

--

-

177.8 4.78 2582.63 2295.04 1778.27 1300.82 983.42 737.91 577.81 463.34 375.56 306.15 247.78 205.1 167.42 138.99 117.06 100.15 87.31 76.06 66.41 58.28 51.2 X 152.4 12.70 2941.49 2371.27 1498.26 907.44 582.25 428.35 268.98 190.52 138.51 99.01 69.78 47.24 27.12

-

--

X 177.8 12.70 3821.38 3296.71 2237.87 1445.45 984.23 764.28 515.55 328.97 245.81 191.24 148.6 107.97 93.99 69.6 52.48 45.61 39.93 34.55 27.7 23.28 19.91 203.2 6.53 3522.12 3188.47 2590.62 1989.49 1564.15 1250 1011.58 823.27 678.99 564.21 470.61 393.46 328.46 275.45 231.7 200.71 175.91 155.63 137.22 121.78 108.88 X 203.2 12.70 4784.99 4272.36 3311.21 2395.05 1697.82 1187.78 859.73 711.6 582.4 475.4 381.04 309.4 250.59 198.37 157.65 133.4 115.69 100.93 89.45 78.15 68.86 254.0 6.53 5226.83 4907.92 4280.61 3633.95 3152.12 2775.75 2441.98 2168.87 1922.43 1712.08 1519.55 1351.51 1205.27 1089.93 970.97 870.59 783.96 709.44 640.9 580.06 529.26 X 254.0 12.70 6927.48 6429.88 5493.51 4476.71 3612.19 3058.7 2564.21 2121.81 1816.89 1565.85 1342.86 1174.71 1017.56 878.47 761.22 660.39 589.89 527.66 472.66 424.74 385.91 304.8 6.53 7194.16 6850.35 6147.78 5413.74 4871.89 4484.3 41 16.56 3823.93 3573.16 3345.84 3135.13 2935.19 2742.12 2561.92 2389.9 2233.27 2090.72 1962.08 1839.01 1719.05 1606.65 X 304.8 12.70 9320.76 8773.39 7749.71 6626.75 5627.91 4997.29 4451.39 3914.77 3546.85 3238.59 2958.32 2695.96 2463.49 2257.99 2059.98 1890.89 1748.63 1623.27 1504.64 1397.59 1298.17

(24)

TABLE 13

:

STRENGTH (KN) OF COLUMNS DURING FIRE VERSUS TIME FOR VARIOUS SIZES AND WALL THICKNESSES.

-

TYPE OF CONCRETE: CARBONATE.

-

CONCRETE STRENGTH: 20 MPa.

-

EFFECTIVE LENGTH OF COLUMN: 3.0 m.

Column Size (mm) Wall Thickness (mm) Time (min) 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 101.6 478 678.26 395.6 208.6 110.94 74.94 46.75 32.75 23.22 16.72 11.62 7.7 4.43 1.75

-

152.4 4.78 1072.47 716.26 358.97 194.17 135.66 89.29 64.82 47.61 34.74 25.37 17.86 11.59 6.29

--

-

--

-

.-

--

X

101.6 9.53 966.55 692.81 394.28 205.3 137.69 75.23 49.15 36.44 25.18 16.92 10.97 5.87 1.52

--

-

--

127.0 4.78 856.74 509.77 272.66 148.02 101.33 66.89 46.27 33.41 24.14 17.15 11.58 7.13 3.35

-

--

-

X

152.4 12.70 2352.54 1845.94 1176.54 713.89 453.61 332.01 200.19 140.64 100.27 70.58 48.61 31.35 16.91

-

--

X

127.0 11.13 1760.9 1300.27 815.6 472.38 300.64 208.3 126.82 89.15 62.38 44.27 17.73 10.18 4.17

--

-

--

177.8 4.78 1576.52 1224.58 685.2 411.13 291.09 203.78 150.17 114.77 87.14 66.25 49.9 36.01 45.58 37.83 30.49 26.16 22.67 19.82 17.24 15.02 12.86

X

177.8 12.70 2974.29 2474.42 1581.35 969.04 626.9 483.05 316.06 193.95 142.22 109.44 82.69 58.55 35.7 15.76 13.25 11.51 10.12 8.67 6.96 5.98 5 203.2 6.53 2246.72 1840.4 1245.03 708.68 513.89 381.09 279.36 214.47 166.05 129.43 99.26 108.84 93.01 76.4 62.15 52.6 45.9 40.84 36 31.83 28.32

X

203.2 12.70 3631.59 3027.72 2061.41 1327.49 885.28 677.79 468.73 331.07 252.06 191.72 139.45 100.4 68.38 38.51 42.53 34.72 30.22 26.16 23.12 20.29 17.69 254.0 6.53 3195.06 2822.31 2210.3 1680.57 1342.19 1107.83 915.5 770.39 653.68 566.75 447.81 385.44 330.34 283.85 244.64 214.88 191.47 171.69 154.12 138.84 125.73

X

254.0 12.70 5049.74 4472.43 3423 2436.3 1573.68 1257.46 977.93 729.3 589.83 529.71 452.88 385.15 322.02 266.99 217.41 181.16 159.96 141.96 126.89 114 103.33 304.8 6.53 4230.61 3851.73 3184.99 2573.82 2175.31 1907.15 1663.33 1480.86 1330.5 1199.13 1084.85 982.83 890.25 804.82 730.53 667.86 617.96 571.23 538.48 502.3 469.02

X

304.8 12.70 6597.11 5987.42 4903.06 3814.82 2985.17 2488.62 2079.46 1689.71 1445.58 1260.13 1092.77 948.67 823.37 721.32 628.55 556.77 510.64 475.21 437.89 403.17 372