THERMAL STRESSES IN STEAM-CURED CONCRETE

THERMAL STRESSES IN STEAM-CURED CONCRETE

by

Gy. BAL . .(zs-M. BERENYI-B. SZENTIY . .(NYI Department of Building Materials, Technical University, Budapest

(Received February 15, 1973) Presented by Prof. Dr. J. TALABER

Steam-curing is the most important means to accelerate hardening of precast concrete and reinforced concrete units. Steam-curing is controlled by steam-curing diagrams. It is obvious from the diagrams in Fig. 1 that the steam-curing procedure has four distinct stages: self-curing, heating, isotherm- al curing and cooling periods. Risks of thermal stresses arise especially in the cooling period. Namely the concrete is still plastic when heated, 'whereas in the cooling period - in case of large-size concrete units with uneven tempera- ture distribution - tensile stresses develop because for some time the tempera- ture in the concrete is higher than the ambient temperature, likely to cause cracks in the concrete. Such cracks were observed e.g. in the first tubbing ele- ments for the Metro of Budapest, as soon as removed from the steam-curing space; the steam-curing technology being developed for smaller units [1].

The aim of this project was to determine thermal stresses developing in the cooling period.

A procedure 'was developed to determine the temperature distribution, responsible for thermal stresses in beams of arbitrary cross-section. As beams are much longer than wide, the longitudinal temperature distribution may be considered as uniform. The temperature distribution in cross-sections normal to the longitudinal axis is described by the two-dimensional form of the Fourier differential equation:

8<P ;. ( 8² <P

- - = - - - -

8t cb Yb 8X2

where <P the unknown temperature function, t time

I. - conductivity coefficient of the concrete

Cb specific temperature of the concrete Yb

=

C = cement content

Qc = heat released by setting cement of unit weight per unit time.

122

Applying the so-caned Newton cooling law as boundary condition:

acp Cl

- , - = - -::-(cp - rp)

on ).

°C al max. perm. temp. 85°C

~~5

--- ---;..;;;;:,

.2 ideal-.. - 360

~ max -0- 300

"-

E

'" ^{st~ rage}

~o u

,-" I~

a _c

"- """ ⁰

Vl .0 V> . 0

E ₀ E.9 E _aU a ~I~

'" ^..c: .,

Jl ^{u V;} ~W

0 6 7 time,h

:3⁴⁰ _l-

a 0- ~-gl ⁽⁵

VJ

E .ctSl E ELila

a a I",

Q) -5 !"Vl

i7l

0 3 4 6 7 8 time,h

",,'

.::i 8LO+---u~1 oi

~ ~wl c ru!

Vl CHfl 0 ..c:; air

E "2-flIE - I El

~ 0 ~ "0.,:1' g)

rn

350 360 380

o 2 3 i. 7 time,h

E a

'"

0=)

__ :.~ _!!lE~ E~~~ !.e.c.n.E.j)Q.~~ ______ _

J i

01 El

~! Ill!

, 4

min nour-degr: 350 ideal -,- - H _ 370 390

8 time, h

Fig, 1. Steam-curing diagrams used at present in the factory for: a) Beam F (cement C 500, hour/degrees: 360); b) Precast hall units; column. roof ,lab EP 12, for 12 ^ID main truss beam and reinforced columns (cement C 500. hour/degrees: 360); c) Beam E (cement C 500, hour!

degrees: 420); d) Floor units PE.. PS (cements C 500, C 600: hour/degrees: 370)

STEA.II-CURED CO.YCRETE 123

where 8<P is the derivative of the temperature function normal to the boundary 8n

x heat transfer coefficient between the concrete and the ambient air space q; ambient temperature.

Variation in time of the thermal material characteristics was omitted in the calculations. The Fourier differential equation was solved by a numerical approximation method, i.e., the method of finite elements. The beam cross- section was divided into arbitrary triangular parts and the corner point values of the temperature function in each time interval were considered as unkno"wn.

The temperature within each triangle can be given at every time as a function of these unknowns and the co-ordinates x and y. The three parameters of the condition function

presumed for the temperature distribution ·within each triangle are easily expressed in terms of the three corner temperature values. Solution of the Fourier differential equation can be retraced to the determination of the fol- lowing integral cxpression, yielding the minimum of function <P.

I(<P) =JT{~ . ^~ [( ^~<P)2 , (6<P) 2]

~ 2 Cb 'Yb dx 8y

T

[ C'Qc _ a<p]<PdXdY.

Cc f'b

at

Above can be proved by the variation calculus method.

It follows from the minimizing condition that forming derivatives with respect to the corner values of this integral expl'cssion within each element, and summing the derivatives pertaining to one nodal value, the following

inear differential equation system is obtained:

H· <P,P [8CPJ _ot

Supposing at the starting time the temperature of each point to be kno·wn, the yector

[a<p 1

at .

"<1>

of-^O- to be linear ·withia each period Jt, the differential equation svstem can be

at ..

solved by stepwise integration. Boundary conditions were taken into account by modifying the "rigidity" matrix H and the load vcctor F.

In computing thermal stresses, the customary simplifieations of elas- ticity were used. (The concrete is homogeneous, isotropic, follows the Hooke's law and the Bernoulli-~avier hypothesis.) Modulus of elasticity of the concrete was considered constant in the relatively short cooling interval and the effeet of deformation "was also neglected. For reinfol'ced beams, approximations of

124 BALAzs - BERENYI - SZENTIV ANn

the first stress condition were used. The instationary temperature field creates a stress condition changing as a function of time. According to the Duhamel hypothesis it may be supposed that the acceleration effect can be disregarded and the stress condition changing with time can be considered as a succession of equilibrium positions. The principle applied to determine the thermal stresses was to consider as first approximation the beam as clamped at both ends, each cross-section being in the condition of plane strain. Then on the stresses at both ends of the beam a linear stress distribution is superimposed, balancing a force system of longitudinal stresses at the beam ends, determined from the condition of plane strain. Thereby the condition is satisfied that the beam is not supported at its ends, and the local disturbances resulting from the different distribution of the two force systems vanish in the relatively small region of the beam end, in conformity ·with the Saint Venant principle.

The stresses were also calculated by the finite element method. The tri- angular division applied in the determination of temperature distribution was used; the elements were assumcd to be connected at the corner points only and the nodal displacements became the basic unknown parameters of the problem.

(In this way the continuum problem was traced back to the analysis of a planar structure by the displacement method.) The temperature within each triangle was supposed to be constant, and taken as the arithmetic average of the corner point values. The condition functions considered linear within each element were expressed, similarly to the temperature distribution, as nodal values vs.

x and y. Then expressing the potential energy minimum of the whole system a linear equation system was obtained for determining the nodal displacement values. From these, the stresses of the plane deformation condition are easy to calculate.

The inverse of the force system of longitudinal stresses resulting from the plane strain condition

is reduced to the origin of the co-ordinate system and the matrix equation be- tween deformations and strains is written as

according to the excentric tension, where F is the cross-section area; Sx, Sy its static moments; Ix and Iv secondary moments along axes x and J; CXy is the centrifugal moment along axes x and y; E being the modulus of elasticity.

Soh-ing it for the displacements, the stress superimposed on the longi- tudinal stress obtained from the condition of plane strain is:

STEAJJ-CURED CONCRETE 125

Fig. 2. Concrete temperature development in steam-curing for different heat conductivities (1. I. = 1.8 kcaljm h cC, 2. ). = 0.9 kcaljm h QC, 3. }. = 2.7 kcaljm h QC), on the beam surface

(point 1'\0. 1) and in the centre of the beam (point 1'\0. 25)

I J 1 ^I

_---1--

£- . ...:-.".;;-::':;:::: .... : .. _r··· ·«f:"·)I·~·' _{/ .. / ..} ·l---

K'-"~"

^{.... _} ... +'<,

1I~,'

j / ).. /'

\ ^I

/ /1 ,,'

f / " 1 " ' / ^\~

;,' \ ',',

I ." .. " '-,'"

I /.Y ,.'

\1

1/

90

80

70

60

I it' _I t : /

I \

/ / :

/ ;' i

I .-

It

I

~,

I .. •

I 1/ ~,

if ^//.-' \"

50

/: ^)l/,'

I \

//LI

~

/'/:/1 ~;,;....-:::

1./1 1,0

30 I~ ,~"

~'~~1:

20 o

I

2 3 ^I.

I ^I

5 6 7 8 9 10 h

Fig. 3. Concrete temperature development in steam-curing for different specific heat values (1. Cb = 0.23 kcaljkg QC; 4. cb = 0.19 kcal/kg QC; 5. Cb = 0.27 kcaljkg QC) at the corner

point of the beam (point .;\'0. 1) and in the beam centre (point 1'\0. 25)

126

I -1 I 1

"'-"'-i'-"',··,

90 - - - ; - - - . - - -.. ~, ~~-lr"""""7rl1--~,='"'''' =·"'==·4of-~c:-. -'Ii----t---:--

I -

1 .. ' 1 .~':-'-' I .. .-. '-"-'>."::'"

I ••••• I ____ / l /

I

'. J'.\."

.. ' {' /1

I .

I>.>

80~-~---+--7~--+7-~--~---+-~~~-+-~~r---+--- 70

+--_+---i-tLL_/-,/x11L.4i--:1,-/_:-+I+/_'/_·/.,.fl=-~/_/_/+i ^/_/_/'_i \l...:..~'\-";-\-+---\-\....:.~t-\-'\-;~

L.

^{V / !} "\ \ \ I \

i

/11 / / I

~

60+---~~r·_V---+/~~/L·~~/----+_----+_----~~·_T~----~-:~_T---

: ;' / / 11 / // I

I i \

50+---~+-/L'~/--r-r:--~,-lr/_/--~---+---+_----r-~~~'I~ .~\~----\T7---

:,: ./' .:' / 1/

: / : / \ ~7/25

40+-~:~'~1 --7~r.:/~/-/-'r--~---r--~--~r--~-~~-T~--~,-6-/1-

:y::/

I I \ __

'i : // 1 I ... I

:/~ . . " /' 1 I

30 +1-"-'" .Y· "--b.Lr..-c--t---+---~----t----+_----t-, - - - 7

1:---1,:---+:---

2

0 i-"·G~r...

le...

I 1 1 ^I "'''1'''' I

o 2 3 5 5 8 9 10 h

Fig. 4. Concrete temperature development in steam-curing for different heat transfer coeffi- cients (1. Cl: = 20 kcaljm² h QC; 6. Cl: = 10 kcaljm" h QC; 7. Cl: = 200 kcaljm² h QC) at the exter-

nal corner point of the beam (point )io. I) and in the beam centre (point ~o. 25)

[J+---~----~--,r+---~~--+---~-~---~~---,--­

~"-

, ? .

70+_----+_----~----~-~

. ____ ~i,_'~:~~\~\~ \~i~

11'!23 t J t---i--f.---:----'---j,!.:...J---1·--+---+----'\-+---+--r-

S J t---y--'----,.<;----'---;----t---t----+,----t---t--

-J+-~f.~----'*--_t_-_+---+_--_T----+_-_r~~---t-- 12/1 1/1

~ v +----j----;---i---i----i----+---,---i---+---+-___

h Fig. 5. Development of temperature in steam-curing for different concrete densities (1. ,.' = 2400 kg/m^3; 11. ;J =2300 kgfm^3; 12. y = 2500 kgjm³⁾ at the corner point of the beam (point

~o. I) and in the beam centre (point ~o. 25)

STEA.U-CURED CONCRETE 127

x*, y* being co-ordinates of the triangle's centre of gravity.

Based on the above principles a computer simulation program in FORTRAN language was developed for a SIEMENS 4004 computer. The

'C

I

cO+---~ __ r-~--~~

- laD ⁷

BD '

~

~ 70 a

~60 ~

~ SO

!

^l L

~ ^{- ; 25,0}

200k-~1--~~---~---1~O-'i-m--e,h

Fig. 6. Division and steam-curing diagram used for testing the effect of material character- istics

tested beam may be of any cross-section, the accidentally curved boundaries can be substituted by a straight-sided polygon. The net of arbitrary triangles can be discretionally made denser at the place of expected stress maxima. The steam-curing period was divided into identical time intervals LIt. The program can cope with 360 dividing points, 600 triangular elements and 200 time inter- vals. The Concrete and Reinforced Concrete W-orks granted 5 hours running time for the program.

2 PeI"iodica Polyte:hnica Civil li,i3-·t

128 BALAzs - BEREN YI - SZENTIV ANYI

To determine the input data of the program, both the thermal character- istics of the concrete and the development of hydration heat of the cement had to be examined.

a.

Ni res tst.

thermo - meters

to control

bridge to Whea:s!one

bridge

lid

cement moria r inner heating in pvC tube polythene bag.

copper vEssel thermos metal casin co rk underlay

~======================~~======~

___

b.

c.

voltage stabilizer

ou·ter heating

to heating relais

outer inner

Fig. 7. Sketch of the testing equipment for measuring cement hydration heat and circuit diagram, a) Testing equipment; b) Control bridge of outer heating; c) Control circuit diagram

Thermal characteristics reported in the literature are rather scattered.

Since no relevant tests have been made, the use of statistical relationships obtained from the great many tests described in literature was endeavoured.

They yield the thermal features of the concrete as a function of the composi.

tion, the temperature, etc., neglecting the less important effects. To determine the conductivity and the specific heat, the formula

STEAM-CURED CONCRETE 129 of the US Bureau of Reclamation was used, G_v indicating the percentage by weight of concrete components, f1 and f2 coefficients tabulated for cement and the different aggregates vs. concrete temperature mean. In the heat trans-

I

33 kg

30

I I I I 1 .J:::::::

27

I

I I ^{I I} 4" I

21. 1

I

^V-

21 1 I 1

L 1

18 1

!

, !

/

15

I

12 I

1 / 1

-t

9 1

.Jt ^I

I

/1

5 I

3

I

yr

i ^I

I

~

I I j

Cl' e

12 13 11. 15 16 17 18 19 20 21 ChJ

Qc [keOI]

kgh

10 /"

I

9

1

8

1 Ll I

7

I I / \

6

I V

".

5

I I ^{; /}

I. V ₁

3

L ^~I

2

I V ^~I

1

/1 I _~

d ^I

^{i I}

1 13 ^~iL. 15 16 17 18 19 20 21 [n1

Fig. 8. Development and rate of hydration development of Por!land cement C 500 DCl\!

throughout steam-curing in test 4. (Initial temperature 25.18 oC, final temperature 73.4 CC)

fer test, the effect of the steel shuttering was completely neglected, in conform- ity with the literature. It was established that as long as steam is condensating on the surface of the units in the heat-up period, the conductivity ranges from 100 to 300 kcal/m^{2 •} hour' cC, while it is only 10 to 20 kcal/m2 • hour' °C in the cooling period, depending on the air motion and the relative humidity.

2*

130 BALAzs- BERENYI -SZE1'iTIV ANYI

Because of uncertainties in the determination of thermal characteristics, the effect of varying each factor was checked by computer.

Figs 2, 3, 4 and 5 show variation of specific heat and density of the con- crete not to significantly affect the development of tensile stress maxima,

30 20

h";---~'1 .-

^!:

0:. NI. 2 2

M; NI

®

~ ~r1 ^{2 I} f 3

Cl) 4 f, 18

(f)4 P 14

0956 spiral

CDS'l6

~ ^~26

^~27

nTfl11\

I

!~

• X

Fig. 9. Reinforcement in column

Ne·so

though the conductivity and heat transfer coefficients considerably influenced the stress development. The triangular division and the steam-curing diagram used for the computation are shown in Fig. 6. The concrete heat expansion coefficient adopted was that of P ALOT.{S [2]. Since no adequate data were avail-

STE.·Uf·CURED CONCRETE 131

able in the literature for hydration heat development in steam-curing condi- tions, direct experiments were made, using test equipment shown in Fig. 7.

In Fig. 8 the diagrams of cement hydration heat development and heat release rate are plotted for one of the five tests carried out.

:'~~ ~.

: "'co

~~"'. I_"'.~

< .

"r ^!9

-2:

~

~':§ ,g..~ /

-3,:· ~ ; /

-"oj ~

lcey

Fig. 10. Temperature and stress distribution in the diagonal section of the column 1\'C-80 90 min after taken out of the steam-curing chamber

The computer outputs show a good agreement with test results obtained at the Department of Building :i\Iaterials in 1968.

Stresses due to uneven temperature distribution in two products of the Concrete and Reinforced Concrete Works were tested assuming that the steam- curing diagrams in the technological specification have been observed. The two members (reinforced concrete column Y 46 A and reinforced concrete pile NC-80) were steam-cured according to the same diagram. The thermal stresses obtained by the computer, however, differed very much. This shows that in establishing the technology for some mass-produced unit, optimum cooling conditions should be considered. Computations reveal also damages likely to result from the neglection of technological specifications.

Figs 9, 10 show the reinforced concrete pile NC-80, the applied triangular division and the distribution oftemperaturcs and stresses Uz along the diagonal.

132 BALAZS -BEREiVYI -SZENTIV.4iVYI

Figs 11, 12 show the cross-section of the reinforced concrete column, the applied division and the isotherm lines of the temperature field of the column 1 1/2 h after leaving the chamber. Concrete tensile strength values of the pile and the column were assessed according to ^HELLMANN [3] and it could be stated that the

2

o

'"

!

it

^I:

^cD

SS

2 1

I ; = ' 2

211 13

CD 1.><122

o

0 2 jiJ'12

© ^{40 >J 6}

CD

Fig. 11. Reinforcement in column Y 46 A and triangle division used for calculating the thermal- stresses

tensile strength of the pile was not reached, whereas in the corner region of the reinforced concrete column the tensile stress values were over twice the tensile strength. Here cracks occur by all means. The tests proved to be a good practice not to wet the elements immediately after stripping, because this increased the heat transfer factor and contributed to the uneven heat distribution, likely -to cause stresses many times higher than those due to shrinkage.

The described computerized method lends itself to further improve the steam-curing technology for large-size units; outcomes of the kind would be

STEAM-CURED CONCR£TE 133

()£ special use in developing the technology for the recently installed automatic steam control devices.

Fig. 12. Isotherms of the temperature field in the cross-section of column Y 46 A, 90 min after taken out of the steam-curing chamber

Summary

Determination of thermal stresses arising in precast r. c. products in the cooling period of steam curing has been set as an objective, in order to prevent cracking due to erroneous steam curing parameters. A computerized method has been developed. based on the method of finite elements, to determine the temperature distribution, or better, the thermal stresses in beams of arbitrary cross-section. Computer outputs and conclusions drawn thereof are pre- sented. Thermal characteristics as inputs have been taken from the literature, and the setting heat development process has been experimentally studied.

134 BALAZS-BERENYI-SZK',"TIV ANYI

References

1. BAL-.\ZS, GY.-ZnlOI>YI, Gy.-ZOBEL: Stresses and cracks in precast concrete due to uueven temperature distribution'" :Meiyepitestudomanyi Szemle, 1967, Ko. 6.

2. PALOT . .\S, L.: Inherent concrete stresses due to temperature changes* ~Ieiyepitestudomanyi

Szemle, 1970, No. 8.

3. HELLMANI>: Beziehungen zwischen Zug- und Druckfestigkeit des Betons. Beton, 1969,

No. 2. ~

Ass. Prof. Dr. Gyorgy BAL(ZS, } 1111 B d 1\··1" ^{( T .} k 3

A B'l S ' u apest, - ue_)· et em r p. .

ss. e a ZENTIVANYI ^v

Mik16s BERENYI, section head, 1052 Budapest, Martinelli ter 3. Hungary

* In Hungarian