Modelling steel behaviour

Fire Safety Journal, 13 ( 1 9 8 8 ) 17 - 2 6

17

Modelling Steel Behaviour YNGVE ANDERBERG

Division o f Building Fire Safety and Technology, Lund Institute o f Technology, Lund (Sweden)

SUMMARY

When modelling material mechanical behaviour, an analytical description is required o f the relationship between stresses and strains. A computer-oriented mechanical behaviour model for steel is described. The model is based on the fact that the deformation process at transient high temperature conditions can be described by three strain c o m p o n e n t s which are separately f o u n d in different steadystate tests. It is s h o w n that a behaviour model based on steady-state data satisfactorily predicts behaviour in transient tests under given fire process, load and strain history. The test m e t h o d used for determining strength properties is o f great importance for the obtained result. B y using the model a procedure is s h o w n o f h o w to couple steady-state and transient-state results and make them comparable for design. S o m e t i m e s the behaviour model for design purposes is simplified by using constructed stress--strain curves based on transient-state results. This means that creep from the transient test is included in an approximate way in the stress-strain curves. The consequence o f this simplification in a computation is illustrated for steel structures approaching creep failure under fire attack.

BACKGROUND

When developing an analytical behaviour model of steel at high temperatures one needs a great a m o u n t of data on the stress and deformation characteristics at different temperature histories. The model must be based on reliable and well-documented results from tests carried out under well
ferently in m a n y ways and therefore hotrolled and cold-worked reinforcing steel, structural steel and prestressed steel must be separated. It is important to have in mind the different test procedures for determining the mechanical properties. There exist two main groups of tests, steady-state tests and transient-state tests. Material properties measured are closely rel a t e d to the test method used. It is therefore of great importance that the test conditions are well defined. During a fire situation, the material is normally subjected to transient processes with varying temperature and stress, and to understand this, transient-state tests are needed. Mechanical properties of steel can be estabfished by following a number of different test procedures. The three main test parameters axe the heating process, application and control of load, and control of strain. These can have constant values or be varied during testing, giving steady-state or transient-state conditions depending on the heating procedure. Six practical regimes which can be used for determining mechanical properties are illustrated in Fig. 1. Properties in these regimes are as follows: steady-state tests • stress-strain relationship {stress rate control) • stress-strain relationship (strain rate control) • creep • relaxation. transient-state tests • failure temperatures, total deformation (stress control) • restraint forces, total forces (strain control). Steady-state tests are characterized by a heating period and a period of time during which the temperature of the specimen is stabilized before any load is applied. The © Elsevier S e q u o i a / P r i n t e d in T h e N e t h e r l a n d s

18 ct~ 12

[TRANSIENT STATE TESTSJ

/

[ ESTRA,NT FORCES [

\

10

FA,LU E ,EMPER,, R Tota deforn~t on

OB 06

/

04 02

ISIEADY STALE TESTSI

0

J 200

/

Strain r a t e - c o n t r o l l e d

~00

.~TempOC 600 700

Fig. 2. Thermal strain (expansion) for structural steel as a function of temperature. (1) St 37-2, J. Ruge and O. Winkelmann [3]; (2) Steel 37, D. H. Skinner [4]; (3) A 36, T. Z. Harmathy [5]; (4) C. Stirland [6].

ISTEAOVSTATETESTSI

FTRESS-S|RAIN RFLATIONSHIP| I

J

7

\

ISTRESS-STRAINRELATIONSHIPI | Stress r a t e - c o n t r o l l e d I

Fig. 1. Different testing regimes for determining mechanical properties [ 1 ].

strain measured before the load is applied corresponds to the thermal expansion. Transient-state tests or non-steady-state tests are characterized by a varying temperature and a simultaneous load. The load can be applied before heating or developed during heating by restraint against thermal expansion. These two types of transient tests are carried out with load and strain control, respectively.

T h e r m a l strain

The thermal strain or thermal expansion is measured on unloaded specimens in a transient test. Investigations published in literature indicate small deviations for structural and prestressed steels. Type of steel and strength characteristics seem to have no significant influence. In Fig. 2 the thermal strain for structural steel is taken from four different sources. The curves are relatively close together. A linear relationship is most often used in analytical modelling. I n s t a n t a n e o u s stress-related strain

GENERAL MODEL

It is generally agreed that the deformation process of steel at transient high temperatures can be described by three strain components defined by the constitutive equation e = eth(T ) + e o ( o , T ) + ecr(o,T,t)

(1)

where eth = thermal strain 6o = instantaneous, stress-related strain based on stress-strain relations obtained under constant, stabilized temperature ecr = creep strain or time~lependent strain. A c o m p u t e r ~ r i e n t e d mechanical behaviour model for steel, based on eqn. (1), was developed by Anderberg [2]. The strains are found separately in different steady-state tests. It is shown that a behaviour model based on steady-state data satisfactorily predicts behaviour in transient tests under any given fire process, load and strain history.

The o-6 relationship can be measured under stress rate or strain rate control. The stressstrain relationship must be obtained at a high rate of loading or high rate of strain in order to avoid the influence of creep, which is of importance above about 400 °C for ordinary steel (for cold-worked or prestressed steel above about 250 °(3). The influence of creep results in a displaced o-6 curve and in a lower ultimate (rupture) strength. The o-e curves can be used to establish compressive or tensile strength, modulus of elasticity and ultimate strain. Experimental results published by Anderberg [7] indicate that reinforcing and structural steel have a similar dimensionless 0 - 6 relationship as illustrated in Fig. 3 at 400 °C and 600 °C. An analytical description of the o-6 curve as a function of temperature can be made in different ways. The experimental curve can be approximated by a number of straight lines

19 0

o

fo-2.2oOC I,O

~

I f0.22.0oC

C

L

....

+

/

/i

! .

o.e

02 ~c , f u

"" "~'~- ---..

r

v - - e n.atyticla+t r

o's

~

s

~'s

i

-

°/o

or b y a modified expression of Ramberg and Osgood [8] used b y Magnusson [9] as follows: eo = o / E ( T ) + 3/7 × f o a T / E ( T ) × (a/fOaT) re(T)

(2) where 6 <. m ( T ) < 50 E ( T ) = modulus of elasticity at temperature T fO.:T = 0.2% p r o o f stress at temperature T.

In this paper the dimensionless a - e relationship is described b y a straight line followed b y an elliptic branch and a straight line as illustrated in Fig. 4. The parameters a, ~ and el are dependent on temperature level and t y p e of steel [10]. The analytical expressions are: R e i n f o r c i n g and structural steel

0 ~< e° ~< el

(3)

o = 2fl + b[1 -- ( 0 . 0 3 - - ea/a):] 1/2 el < eo < 2~

(4)

a = b + 2~(eo -- 0.03)/(0.0123 -- 0.00085T) e° < 2~

(5)

0 < e° < e I

(6)

Prestressed steel o = eoE(T)

o = 2/3 + b [ 1 - - ( 2 ~ - - eo/a)2] 1/2

a = b + 2/3

.

.

I

~///

b

5a

co+

Fig. 3. Dimensionless a - e relationship for four different kinds of reinforcing steel at 400 °C and 600 °C. The theoretical curve is also shown.

a = eoE(T)

.

e I <~ e° ~ 2 a

(7)

eo < 2 ~

(8)

The curve fitting for reinforcing and structural steel at 400 °C and 600 °C is illustrated in Fig. 3.

Fig. 4. Principal model of dimensionless ship.

a-e

relation-

CREEP STRAIN

Creep behaviour is unique for every t y p e of steel and a c o m m o n description is hard to find. This is due to the fact that the chemical composition and the degree of processing strongly influences this. The creep tendency seems not to be related to the 0.2% p r o o f stress or other strength characteristics at r o o m temperature. Therefore the absolute value of stress is used when describing creep analytically. The creep strain can only be directly measured in steady-state tests and if the stress is kept constant it can be separated into t w o phases, primary and secondary phase. However, the creep from steady-state tests can be used in order to predict the creep process in transient tests, which will be illustrated. Models of creep are in most cases based on a concept put forward b y Dorn [11] in which the effect of variable temperatures is considered. The extension of the model to be applicable to variable stress can, for instance, be based on the strain hardening rule. The creep strain modelled in this paper is assumed to be dependent on the magnitude of stress and on the temperature-compensated time evaluated from the expression t ) e ( x p~AH -~ 0 = ~'~-

dt

(h)

o

where AH = activation energy of creep, J / m o l R = gas constant, J / m o l K t = time.

(9)

2O Ecr

ecr = ec~,o2(ZO/ecr, o) 1/2

0 ~< 0 ~< 0o (10)

ecr = ecr,0[1 + (ZOlecr, o)] 1/2 0 >10o where

d ECSF- Z

0 o = ecr,0/Z

(11)

Harmathy [12] has derived an analytical expression between ecr and the parameters 0, Z and ecr,0 as follows:

Ecr, O

ear = (eer,0/ln 2) arcosh(2Z°/Ccr, o) 00

Temperature--compensated

=- 8 time

This formula is not that practical and is unnecessarily complicated. Creep parameters for different kinds of steels and used in calculations are collected in Table 5.1 in gilem [1]. The following equations are governing Z and ecr, o :

Fig. 5. Principal creep curve for the steel according to Dorn's theory.

The relation between creep strain, ec~, and temperature-compensated time, 0, at a given stress level is shown principally in Fig. 5. The change from the curved branch to the straight line (primary and secondary phase) is denoted 00 and the intersection between the straight line and the creep axis is called e~,0. The slope of the straight line is called Z. The primary phase is defined by a parabolic equation and the secondary phase by a linear slope. The transfer occurs at time 00. The mathematical formula is

Ecr,'/o

(12)

ear,0

(13)

Ao B

=

}Co D Z = ( H exp(Fo)

iron< S I G 1 } if a > SlG 1

(14)

In ref. 7, the modified version of the D o r n Harmathy theory, described above, has been used and the concordance between test and calculation is shown in Fig. 6. A simplified w a y is to approximate the creep curve by t w o straight branches with

0.22

O"

601"C

II'.... ~" Tf0="2'-603°C Cal Measur 20°C cuLateed'd- ~i////t / / / / ~ / /

--'I"1

0.02 r

/

/

//

/ f

f

0

j

/

~

T L L

j

583oc

J

J

f

_J

f

~ j 602°C --

I

-

>

0.15

0.15 588°C

f

0.5

0.22

>

.

J

/ 0.01

i

i

,

1.0

Ti me, h

Fig. 6. Measured and predicted creep (modified Dorn-Harmathy theory) at different stress levels. Reinforcing steel Ks 60 ~8, f0.2,20°c = 710 MPa, Anderberg [7 ].

21 RELAXATION

Ecr

A relaxation test is closely related to a creep test but is carried o u t at constant strain and t e m p e r a t u r e (Fig. 1) and t he stress decrease is studied as a f u n c t i o n o f time. T he relaxation process can analytically be f o u n d b y using t he f o r m u l a t i o n o f creep and t he instantaneous stress-related strain as follows. The total strain is constant, which means t hat the sum of eo and ecr is constant. The increase in creep must be followed by the same decrease in ca. The stress must t herefore decrease with time in such a way t hat ea decreases as ecr increases.

Zpl I

tt 4' 4" Primary phase

Time

{?tot = const

=

eo(a,T) + e¢~(a,T,t)

(18)

4' Secondary

phase Fig. 7. Measured creep curve approximated by two straight branches with slopes Zp and Zs, Anderberg [ 7 ]. slopes Zp and Zs [7] as illustrated in Fig. 7. The creep strain is an explicit f u n c t i o n of time, t e m p e r a t u r e and stress, where ecr(t,T,a) = t Z ( T , o )

(15)

ecr = Zp(T, G)

if 0 <<. t <<. t t t

ec~ = Zs(T, a)

if t > tt

Dimensionless relaxation curves measured and predicted for reinforcing steel are compared in Fig. 8. The agreement is very good. o

f0.2: 20°C

1.0

(16)

08

Nomograms for the rate o f creep in primary and secondary phase for reinforcing steel Ks 40 ~b8 are published in ref. 7. These nom ograms including th e d e t e r m i n a t i o n of t he transition time, tt, facilitate an estimation of t he magnitude o f creep. In Japan, creep formulations also are developed and Fur a m ur a et al. [13] present a f o r m ul a for structural steel SS 41 as follows

0.6

ecr = 10 (a/T+ b)G(c/T + d)t(eT + f)

- ....

Test

Catculotion Ks60 f0.2,20,C =710 MPo 300 'C

....

F" . . . . .

q. . . . . .

I

O2 t .

-

~oo

500 --~-22=2

s50

3

4 Time.h

60O

0 0

1

2

Fig. 8. Measured and predicted relaxation curves for reinforcing steel [7 ].

(17)

where a = - - 7 .2 1 X 103 b = 3.26 c = 1.55 X l 0 s d = 2.25 e = 8.98 X 104 f = - - 3 . 3 0 X 10 -1 T = absolute t e m p e r a t u r e t = time in minutes a = stress k g /mm 2 e¢~ = creep strain %. T h e ef f ect o f variable stress and t e m p e r a t u r e is solved b y using a modification of t he strain hardening rule.

Total strain The behaviour model is based on steadystate data, but the creep can be predicted at varying load and t e m p e r a t u r e (transient process) by using t he strain hardening rule. This means t hat any test can be simulated by using the com pl et e behaviour m odel as expressed above. The t ot al d e f o r m a t i o n as a f u n c t i o n of t e m p e r a t u r e measured in a transient test, T = 10 °C/min, is calculated and t he comparison is illustrated in Fig. 9. There is a good agreement bet w een test and calculation. However, there is a discrepancy at

22 0

Temp'*C

500

f0.2,20"C"

i

L

0

~.,.. .

.

.

.

--~.

---, .

2.0

25

.

.

.

.

.

.

.

.

.

O.

~

//

0.5

1.0

1.5

3.0

35

/,.0

Fig. 9. Measured a n d p r e d i c t e d t o t a l d e f o r m a t i o n as a f u n c t i o n of t e m p e r a t u r e at d i f f e r e n t load levels in a t r a n sient process, T = 10 °C/rain. R e i n f o r c i n g steel Ks 60 ~b8, f0.2,20Oc = 7 1 0 MPa [ 1 4 ] .

the load level o / f o . 2 , 2 o o c = 0.9 and temperature region 100 - 300 °C. This is due to an instability p h e n o m e n o n in the material called 'thermal activated flow', which only occurs in transient tests. This characteristic feature has been observed in m a n y experimental investigations and sometimes the deformation results from two identical tests m a y differ very much in the temperature region 100 - 300 °C. This is due to a more pronounced thermal-activated flow in one of the tests.

the stress at which the strain is 4%, the thermal strain excluded. In the analytical modelling, the strain and stress rate in a steady-state procedure to give the same ultimate strength as under transientstate conditions is found, if the rate of heating is chosen to be 10 °C/min. The result is shown in Fig. 12(d) for a specific reinforcing steel (Ks 60, f0.2,2ooc = 710 MPa). The strain and stress rates obtained by computation are thus = 20(%0 )/min

HOW T O C O U P L E S T E A D Y - S T A T E A N D TRANSIENT-STATE RESULTS

Analytical modelling illustrated above makes it possible to couple steady-state tests and transient-state tests. For instance, the strain or stress rate can be determined in steady-state tests to give the same ultimate strength as occurs in a transient test for a given rate of heating. The predicted influence of stress and strain rates on the stress-strain relationship under steady-state conditions can be studied in Figs. 10 and 11. From such curves the ultimate strength as a function of temperature can be evaluated. In Fig. 12 (a) and (b), the influence of stress and strain rates on the ultimate strength under steady-state conditions is illustrated. The influence of rate of temperature under transient-state conditions is given in Fig. 12(c). The ultimate strength is defined by

and 6 = 0.20 MPa/s = 12 MPa/min These values, as shown in Table 1, vary somewhat depending on the type of steel: (a) structural steel 1411, f0.2,20Oc = 340 MPa (b) hot-rolled reinforcing steel Ks 40, f0.:,20Oc = 456 MPa (c) hot-rolled reinforcing steel Ks60, f0.2,20Oc = 710 MPa TABLE 1 T y p e of steel

Steel1411 Ks 40 Ks 60 ASTM A 421-65

T (°C/rain)

(~ (MPa/s)

((%o)/min)

10 10 10 10

0.20 0.20 0.20 0.50

10 10 20 10

23 f 0.2,20~

1.2 I

(~:3.50MPo/s --0:0.07 MPa/s

1.0

300 'C ~ . ~

~ " ~ " ~

'

f

400

0.8

500 0.6

600

0./.,.

.

.

.

.

.

_

700

0.2

0

-----~,,,-

0.5

0

10

1.5

2.0

2.5

30

3.5

E,%

Z.,.O

Fig. 10. Predicted o-e curves at different stress rates for reinforcing steel (Ks 60, fo.2,2o°c = 710 MPa) [14].

(0.2.20°C

12

i : ?00'/./rain C : - - - -- 2 5 ' / . / r n i n

10~ 300°C

08_)

400

06-

SIMPLIFIED MODEL 500

0/~-

___)

02-

600

- -

__) 700 o

the measured ultimate strength should be corrected downwards. The rate of stress or strain in a steady-state test and the rate of temperature increase in a transient test are governing the development of creep which causes the change in the ultimate strength. The influence of creep for these procedures is fully illustrated in ref. 14.

"S-- -I ....... 0 2

4

6

8

10

12

Fig. 11. Predicted G-e curves at different strain rates for prestressed steel (ASTM A 421-65, f0.2,20Oc = 1470 MPa) [14].

(d) prestressed steel ASTM A 421-65, f0.2.:0Oc = 1470 MPa. For steels in addition to those in Table 1, the results of computation are given in diagrams in ref. 14. Such diagrams can be used for design as illustrated in ref. 14. If the strength-temperature curve, based on the transient-state conditions where for instance ~ = 10 °C/min is accepted as a reference curve, test results can be directly interpreted and, thus, are comparable. If the rates and ~ are below the values mentioned above,

For design purposes a simplified model is used in practice, where the creep strain in an approximate way is incorporated in the stressstrain relationship. The model is solely based on transient-state tests and the procedure to construct the a - e relationship is as follows. The total deformation measured in a transient test at a constant stress and increasing temperature until failure occurs, minus the thermal strain as a function of temperature, is illustrated in Fig. 13. From these curves, a - e relationships can be constructed in which the creep strain corresponding to a specified heating rate is included. In Fig. 14, o - e curves from steady-state and transient-state tests at different temperatures are compared to each other. Agreement between calculations and measurements is also close. The curve of the steady-state conditions contains no creep due to the high stress rate. In the curve of the transient-state conditions, the influence of creep is, however,

24

fo.2, 20°C f02,20oc

t

12-

1.0

08

06

i ........

........

04 3 5 0 MPo/s

200 °/~/rnin 50

0.2 fo2,20~C__710MPo

20

10

~ ___ - - 0.07 I

o .-.~-3oo ~oo

~ .L_! i_ --,--T~r~p°C ~oo ~oo 700

i ~--li~ 300

400

500

....... nL_~___~i~TempoC

600

700

(b)

(a)

o f 0 2 , 20°C

1 2-~--

f o 21~20°C

i

lo

'

~ ",

i

F

i\\i .......... - -

02 . i

- ~f02.20oc 0

. 300

.

=?IOMPe .

L00

- ~

. 500

2 ~

500

0 : 0 2 MPa/s i" : 10 °C/rain . .

- N

. Ks 60 ~ f02,20oc = 710 MPo

.

•

Ternp °C

700

Temp

300

&O0

500

600

°C

700

(d) Fig. 12. Predicted ultimate strength versus temperature for reinforcing steel [14]. (a) Steady-state, stress-ratecontrolled ; (b) steady-state, strain-rate-controlled, (c) transient state; (d) comparison between steady state and transient state. (c)

o f importance. The difference b e t w e e n the curves at e > 2% and the decrease in ultimate strength at 5 0 0 °C and 6 0 0 °C a m o u n t to a b o u t 15% o f f0.2,20Oc. This difference also is very m u c h d e p e n d e n t o n the heating rate in the transient test; compare with Fig. 1 2 ( c ) . When using constructed o - e curves for design, one obtains s o m e w h a t conservative values w h i c h are thus o n the safe side. In an analytical study of fire-exposed structures, it

is o f t e n t o o a p p r o x i m a t e to use the simplified m o d e l because the real temperature and stress history is n o t a c c o u n t e d for. The influence o f creep o n the d e f o r m a t i o n behaviour for a fire-exposed steel beam is illustrated in Fig. 15. The studied case illustrates creep failure under fire attack. If creep is n o t considered, the collapse time is increased from a b o u t 17 min to 20 min and the failure temperature from 7 0 0 °C to 7 6 0 °C.

25

Temperature

i

o; T;

Temp

-Vo

oC

mm

2O ;

~

N

IPE BO

Fire II ii:o II ii:o

a;

BOO 75S 700

I . . . . ider~ - 6O0 rl(~ . . . . not ....

i

q

10

-

(a)

4.00

£total- £th= £0 +Ecr - 2 O0

Stress

Jv[

>

Time Hin

Fig. 15. Predicted d e f l e c t i o n o f f i r e - e x p o s e d simply s u p p o r t e d beams.

The principal importance of the stress history on the total strain in a transient process, where the rate of heating ~c is constant, is illustrated in Fig. 16. Curve 1 corresponds to a constant stress o0 during heating up to temperature T2 and curve 2 to a stress a0/2 up to temperature T 1 and then a stress o0 until temperature T2 is reached. The difference in total strain is due to the different stress history and a different creep strain developed during the transient process.

(b) Ea * £cr Fig. 13. Transient tests w i t h load c o n t r o l : (a) typical o - T curves at different stress levels; (b) c o n s t r u c t e d o - e curves at different temperatures.

For fire-exposed slender steel columns, the influence of creep can be even further pronounced.

fo.2, 20"C

1.0

"'IT=400°C -4

0.8

I

0.6f f

0.4

_ _

I

I /

-

I I

o o

o.s

T=600

L.

L~

,.o

J

= d

,.s

2.o

-

~o

(I}

EO+ Ecr EO*Ecr

(3)

(2)

l 3.0

I

3.5

•

E,'h

4.0

Fig. 14. Measured and predicted o - e curves f r o m steady-state and transient-state tests [ 14 ]. (1) Steady-state test, stress-controlled, o = 3.5 MPa/s; (2) transient-state test, c o n s t r u c t e d curve, ~h = 10 °C/rain; (3) transient process, curve derived analytically, ~h = 10 °C/rain.

26

Difference due to stress i~istor y

6

7

// J

*

TO

TI

Temp

8

T2

Fig. 16. Principal influence on total strain at different stress histories at a transient process. Curve l : o = a0 T 0 < T < T2 Curve2:o=o0/2 T 0 < T < T1 o = o0 T 1 ~< T ~< T 2

9

REFERENCES 10 1 RILEM 44-PHT (Properties o f Materials at High Temperatures), Y. Anderberg, Behaviour of Steel at High Temperatures, Division of Building Fire Safety and Technology, Lund, Sweden, February, 1983. 2 Y. Anderberg, Fire-Exposed Hyperstatic Concrete Structures -- A n Experimental and Theoretical Study, Division of Structural Mechanics and Concrete Construction, Lund Institute of Technology, Bulletin 55, Lund, 1976. 3 J. Ruge and O. Winkelmann, Deformation Behaviour of Reinforcing and Structural Steel at High Temperatures, Sonderforschungsbereich 148, Part H, Braunschweig, June, 1980, Brandverhalten yon Bauteilen, Arbeitsbericht, 80 (1978) 147 - 192. 4 D. H. Skinner, Measurement o f High Temperature Properties of Steel, MRL 6/10, Melbourne Research l~aboratories, May, 1972. 5 T. Z. Harmathy and W. W. Stanzak, Elevated Temperature Tensile and Creep Properties o f Some Structural and Prestressing Steels, Research

11

12

13

14

Paper No. 424, National Research Council of Canada, Ottawa, 1970. C. Stirland, Steel Properties at Elevated Temperatures for Use in Fire Engineering Calculations, Document ISO/TC92/WG15, No. 14, British Steel Corporation, Teesside Laboratories, U.K., September, 1980. Y. Anderberg, Mechanical Properties o f Reinforcing Steel at Elevated Temperatures (Armeringsstitls mekaniska egenskaper vid h6ga temperaturer), Tekniska Meddelanden Nr. 36, Halmstad J~/rnverk AB, Lund, 1978. In Swedish with an English summary. W. Ramberg and W. Osgood, Description of Stress-Strain Curves by Three Parameters, NACA Technical Note No. 902, National Advisory Committee Aeronautics (now NASA), U.S.A., 1943. S. E. Magnusson, Structural Beahviour and Loadbearing Capacity o f Fire-Exposed Steel Columns, Safety Problem o f Fire-Exposed Steel Structures (St~lpelares verkningssa'tt och bh'rfiJrmllga vid brand. Siikerhetsproblemet vid brandp~verkade sMlkonstruktioner), Division of Structural Mechanics and Concrete Construction, Lund Institute of Technology, Lund, 1974, in Swedish. S. Dounas and B. Golrang, Mechanical Properties at High Temperatures -- Further Development o f Steel Behaviour Model (SMls mekaniska egenshaper vid h6ga temperaturer), Division of Building Fire Safety and Technology, Lund Institute of Technology, Lund, 1982. In Swedish. J. E. Dorn, Some fundamental experiments on high temperature creep, J. Mech. Phys. Solids, 3 (1954) 35. T. Z. Harmathy, Deflection and Failure o f Steel Supported Floors and Beams in Fire, A S T M No. 422, American Society for Testing and Materials, 1967. F. Furumura et al., Nonlinear elasto-plastic creep behaviour of structural steel under continuously varying stress and temperature, J. Struct. Constr. Eng., 353 (July) (1985) 92 - 100. (Tokyo Institute of Technology, Japan.) Y. Anderberg, Predicted Fire Behaviour o f Steels and Concrete Structures, Division of Building Fire Safety and Technology, Lund Institute of Technology, Lund, 1983.