CC BY
54
УДК 624.21.01:624.012.35
K. FLAGA, M. PANTAK (Cracow University of Technology, Poland)
THERMAL STRESSES IN COMPOSITE STEEL-CONCRETE BRIDGES DURING CONSTRUCTION STAGE
In the paper the analysis of stresses in concrete deck of steel-concrete composite bridges due to cumulative impacts of cement heat of hydration and ambient temperature have been presented. Examples of analyses of thermal conditions and thermal stresses in construction stage of composite road bridge have been shown. Keyword: steel-concrete composite bridges, thermal conditions, thermal stresses
Genesis of the problem
The case study
One of the most characteristic features of the steel-concrete composite bridges is a two-stage process of their erection. In the first phase (Phase I) acting loads are transferred by steel girders appropriately to the static scheme compatible with the construction method. After the erection of the bridge deck (Phase II) loads are transferred by steel-concrete composite cross section.
The period between phases I and II is a period of curing of concrete slab. In this period a series of chemical and physical processes start and run, among which the process of emission of cement heat of hydration is very important. Due to the emission of cement heat of hydration in erected composite cross-sections an additional thermal load occurs. During simultaneous impact of the cement heat of hydration and the ambient temperature in erected composite cross-sections arises the temperature difference caused by large differences in thermal inertia of steel and concrete. The temperature differences induce an additional stresses in concrete slab and steel beams.
The complexity of the stresses analysis in described stage consist in the necessity of taking into account the changes in mechanical properties and strength of the curing concrete (e.g. modulus of elasticity, compressive and tensile strength). The strength characteristics of the composite cross-section (equivalent cross-section) depend on the time. The cross-sectional area, the moment of inertia and the position of the center of gravity of the cross-section depends on changing in time modulus of elasticity of the curing concrete.
For the purpose of further analysis it is necessary to determine the amount of the heat of hydration which can emit cement used in the concrete and the ambient temperature at which the composite section is erected. These issues will be presented on the examples of two composite road bridges within the A4 motorway over Ship Canal Gliwice in Southern Poland.
In two composite bridges D(Mo)10, D(Mo)11 at the A4 motorway, within a short time after the concreting, significant cracks in concrete deck has occurred. The cracks were parallel, perpendicular and diagonal to the objects axis. The crack width was up to 1 mm and the depth of most of % to '/2 of the deck thickness. Some of the cracks passed throughout the deck. The number of the cracks was up to 358 in the area of 100 m2 in the object D(Mo)010, and 120 in the area of 100 m2 in the object D(Mo)011.
The deck in the object D(Mo)010, with design thickness d = 220 mm (230 mm the real thickness), was concreted on 09/03/2002 at the ambient temperatures: at 700 a.m. - 13 °C, at 100 p.m. -27 °C, at 900 p.m. - 20 °C. The deck of the object D(Mo)011 was concreted on 16/09/2002 at the much lower ambient temperatures: at 700 a.m. -2 °C, at 100 p.m. - 14 °C, at 900 p.m. - 12 °C.
The temperatures were confirmed by the Institute of Meteorology and Water Management (IMGW) branch in Katowice. In the nearby meteorological station Zakrzów and Katowice, they were: 03/09/2002 T = 26,2 °C, Tmin = 9,7 °C,
lIldA y y II11I1 y y
Tmean = 17,4 °C, 16/09/2002 Tmax = 15,2 °C, Tnin = 8,7 °C, Tmea„ = 10,8 °C.
The night temperature drops after the decks concreting amounted respectively for:
- D(Mo)010 ATout = Tmax -Tnm = 16,5 °C,
- D(Mo)011 ATout = 6,5 °C.
The number of the cracks formed at the observed temperature drops indicated the thermal reason of the cracks.
The deck plate with the thickness of d = 0,23 m is characterized by a massive factor m equal
m - — - - -
V d 0,23
•-8,7
(1)
© Flaga K., Pantak М., 2012
where F - the outer surface of the element by which the heat transfer with the environment takes place [m2], V - volume of the element, [m3], d - thickness of the plate.
With the m = 8,7 m"1 the deck belongs to the medium-thick (medium-massive) concrete elements (2 < m < 15) in which, for the concrete class C25/30 and higher, the self-heating due to the cement heat of hydration can reach Atself = 3...35 °C
[1], depending on external conditions, the type of the cement and the water-cement ratio in the concrete. This value of the self-heating arises during the so-called thermal shock, i.e. in the first 50.. .80 hours (2-3 days) of curing of concrete.
In concrete mixture in both structures the cement Warta CEM I NA MSR 42,5 has been used. This cement has a relatively high heat of hydration. In isothermal conditions after 72 hours the cement Warta releases heat of hydration of Q72 = 246 kJ/kg (58,7 kcal/kg) [1]. Inthe first 24 hours of curing of concrete the cement Warta releases Q24 = 166 kJ/kg (39,6 kcal/kg).
In case of bridge D(Mo)010 constructed at Tmean = 17,4 °C the rate of emission of the heat of hydration was lower than at 20 °C in the calorimeter.
Assuming that the heat Q24 self-heating the bridge slab in the first 24 hours of curing of concrete, according to E. Rastrup function the self-heating of the slab would amount:
Kj (17,4) = 2 10 -k(2q) = 0,84
(2)
At
adiab
= K
C • Q
24
• la
= 0,84 •
365 • 39,6 0,23 • 2300
; 23,0, (3)
where: C - cement content in concrete [kg/m3], Q24 - amount of the heat of hydration emitted in the calorimeter after 24 hours [kcal/kg], cc - specific heat of concrete [kcal/(kg°C)], y c - density of concrete [kg/m3]
Because of the simultaneous heat dissipation by the external surfaces the temperature of the self-heating of the deck Atsh will be lower:
Atsh = l • At adiab = 0,5 • 23,0 = 11,5,
(4)
where: y = 0,5 is accepted on the basis of experiences for massive factor m = 8,7 m-1 [1].
In case of the initial temperature of the concrete mix adopted approximately for the bridge D(Mo)010 as equal Tmean = 17,4 °C (average am-
bient temperature) the temperature of the concrete slab, after 24 hours of curing, will be:
Can = Tmean + At» = 17,4 +11,5 * 29,0 (5)
At night the ambient temperature in the case of the D(Mo)010 bridge declined to Tmin = 9,7 °C. Steel beams quickly cooled down to ambient temperature. Therefore in the composite section could arise the temperature difference equal:
At = t™an -Tmin = 29,0-9,7 = 19,3. (6)
Using the same procedure for estimation of the heat of hydration and the self-heating of concrete after 72 hour the temperature difference will achieve:
CQ
365 • 58,7
Atadab=K1-^=o,84• ;;; «34,0; (7)
Ca • la
0,23•2300
Atsh = 0,5-34,0 = 17,0;
t^n = 17,4 +17,0 « 34,4;
At = 34,4-9,7 = 24,7 .
(8)
(9) (10)
According to the above estimates in the D(Mo)010 bridge during the night temperature drop the temperature differences between the concrete slab and steel girders At = 20...25 °C could occur.
In case of the D(Mo)011 bridge obtained results are as follows:
- after 24 hours of curing of concrete:
10,8-20
K
(10,8) = 2"
• K
(20) = 0,53 (11)
At
adiab
0,53 0,84 ^
23,0 « 14,5
Atsh = 0,5 • 14,5 = 7,2
t™an = 10,8 + 7,2 « 18,0 At = 18,0 - 8,7 = 9,3
- after 72 hours of curing of concrete:
0,53
At
adiab
0,84
-•34,4 « 21,7:
Atsh = 0,5 • 21,7 = 10,8; t™an = 10,8 +10,8 « 21,6; At = 21,6 - 8,7 = 12,9.
(12)
(13)
(14)
(15)
(16)
(17)
(18) (19)
In the bridge D(Mo)011 the temperature difference between concrete slab and steel girder could achieve At = 9,0...13,0 °C.
Additionally, the cement used in both bridges have a much better characteristics than it appear from the information provided by the manufactur-
17,4-20
er. Therefore in both bridges a greater heat of hydration and self-heating of concrete has occurred. Concrete strengths after 7 and 28 days reached the values:
- D(Mo)010
fcd 7 = 43,7 MPa, fcd28 = 59,8 MPa;
- D(Mo)011
fcd 7 = 42,3 MPa, fcd 28 = 55,8 MPa.
Concrete class required in both bridges (C25/30) was achieved already after 7 days. After 28 days concrete class was much higher than required and reached C35/45. Undoubtedly it was an additional factor which increased the destructive thermal cracks of the decks in both bridges because of the large amount and higher rate of emission of heat of hydration.
Analysis of the bridge D(Mo)010
The detailed calculations for the D(Mo)010 bridge were carried out. The geometry of the bridge, its cross-sections and static schema during construction stage are shown in Fig. 1 (dimensions in [cm]).
Fig. 1. Cross section and plan view of the D(Mo)010 bridge
The supports no. 2, 3, 4, 5 were temporary supports on which the precambering was realized.
As a result of the temperature difference between slab and steel girders in the structure a thermal bending moment MT has occurred. Under the action of the MT the structure had a tendency to lifting up and breaking away from the temporary supports.
Fig. 2. Static schema during construction stage and beam cross-section of the D(Mo)010 bridge
Fig. 3. The D(Mo)010 beams deflections due to the thermal bending moments for At < 15 °C and At > 15 °C
The calculations of internal forces and stresses during construction stage was carried out for At = 10,15 and 20 °C taking into account a time of
concrete maturation xT = 1,2,...,5 days. Where xT the temperature is adjusted concrete age taking into account influence of elevated temperature of curing of concrete on faster maturation of concrete:
=1 *
i=1
-(4000/[273+T(Axni )]-13,65 ^
(20)
where: Axni - is the number of days where a temperature T prevails, T (Axni ) - is the temperature in °C during the time period Axni [2].
For example, for the first three days of maturation of concrete, in which the temperature of the concrete (mean value) were as shown in Fig. 4, the equivalent time is
X = g-(4000/[273+23,2]-13,65) 1 + -(4000/[273+30,4]-13,65) 1 +
+e
+e
-(4000/[273+33,1]-13,65) 1 =
= 1,2 +1,6 +1,8 = 4,6
(21)
x
XT [days]
Fig. 4. The temperature of the concrete maturation tmean and the temperature adjusted concrete age xT
Stress and deformation characteristics for concrete were determined in accordance with EC2 [2] formulas (Tab. 1):
fcm (xT
•E„
E (xT ) =
cm \ T f
fcm (xT ) = Pcc (xT ) • fcm ; fctm (xT ) = [Pcc (xT • fctm ;
28
pcc (XT ) = eXP <!5 1 -'
/ \1/2 ne 1
Vxt J
(22)
(23)
(24)
(25)
Table 1
The secant modulus of elasticity of concrete Ecm (xt ) and the mean value of axial tensile
strength of concrete fctm (xt ) in each days of maturation
Age of concrete XT, [days] Ecm (XT ) [GPa] fctm (xT ) [MPa]
1 27,681 1,094
2 29,143 1,612
3 30,052 1,914
4 30,688 2,121
5 31,166 2,274
Table 2
Exemplary results of stresses in top fibers of the concrete slab for xt- = 2 days and At = 10,15, 20 °C
At [°C] (xt ) [MPa]
10 1,42
15 2,34
20 2,95
where: Ecm - is the secant modulus of elasticity of concrete, fcm - is the mean compressive strength at 28 days, fctm - is the mean value of axial tensile strength of concrete at 28 days, Pcc (xt ) - is a coefficient which depends on the age of the concrete xT , xT - age of the concrete in days, a = 1,0 for xt < 28, 5 - is a coefficient which depends on the type of cement: s = 0, 20 for rapid hardening high strength cements (R) (CEM 42,5R, CEM 52,5), 5 = 0,25 for normal and rapid hardening cements (N) (CEM 32,5R, CEM 42,5), 5 = 0,38 for slow hardening cements (S) (CEM 32,5) [2].
After determining the internal forces caused by cumulative action of thermal bending moment and dead loads (using the nonlinear static analysis) the stresses in the phase Ia in top fibers of concrete slab, in critical support sections no. 2, 3, 4, 5 have been calculated (Tab. 2).
Then the value of ratio of the atocf (xt) and fctm (xt ) showing the elastic effort of top fibers of the cross-section was calculated K (xt) (Fig. 5 -solid line):
a0 (XT )
K (xt ) =
fctm (xT )
(26)
The critical range of the stresses is for K(xt )> 1,0. In Fig. 5 can be seen that for At = 10 °C concrete slab during the thermal shock ( xt = 2...3 days) is not exposed to cracking. For At = 15 °C dangerous period is xt = 1...7 days. The top of the concrete slab can crack. For At > 20 °C the slab can crack during the 28 days of maturation period.
In first step calculations were performed assuming an elastic work of the concrete until the scratch (index K (xt )). The value of index K (xt )
will be lower due to the elastic-plastic nature of concrete work.
K'(xT ) = ^^ = = 0,588K(xT ) , (27)
X
1.7
where: X - is the coefficient corresponding to the border deformation of the concrete equal ecil = 1,0 -10-4.
At = 10°c
zT [days]
Fig. 5. Values of indexes of elastic K (xT ) and elastic-plastic K '(tt ) effort of the top fibers in the deck slab
for At = 10,15,20 °C
In the early stage of concrete maturity sct1 can be reduced up to 0,4 10-4 and during thermal shock is equal sct1 =(0,7...0,9)-10"4 [3, 4]. It means that
in period of concrete maturity considered in this article (2-3 days) value X = 1,7 should be considered as a top border of reduction coefficient.
In Fig. 5 the dashed lines indicates the elastic-plastic index of slab effort K '(xT) and the region
above 1,0 is a critical period of work of the concrete slab.
Values of K '(xT) presented in Fig. 5 indicates that during the temperature difference At = 10 °C concrete slab is not exposed to thermal cracking, at At = 15 °C can be damaged by cracking in the most strained regions for xT < 1,5 days, and for At = 20 °C the critical period of the construction work relates to xT < 2,5 days and covers the period of the thermal shock. This means that in case of the At > 15 °C in the first 2-3 days of curing of concrete the thermal cracks can occur due to the temperature differences caused by the cumulative impacts of daily temperature variations and self-heating of concrete by the heat of hydration of cement.
In the analyses the impact of creep and shrinkage in early age concrete and susceptibility of the shear connectors have not been taken into account.
Conclusions
In the paper the possibility of cracking of the upper surface of the deck in composite steel-concrete bridges due to temperature differences between concrete slab and steel girders, resulting from daily temperature variations and self-heating of concrete by the heat of hydration in the first days after concreting, has been proved and described.
In characterized composite bridge the temperature difference (mean value) between the concrete slab and steel girders of At > 15 °C was sufficient reason for cracking of the deck slab at critical cross sections over the supports and temperature difference At > 20 °C was a reason of slab cracking on the entire length of the deck, also in span.
REFERENCES
1. Flaga, K. Guidelines for concreting technology of the superstructure of the road viaduct over the Street. Sucharski in Gdansk - report (typescript) [Text] / K. Flaga P. Witakowski, T. Rudka - Institute of Building Materials and Structures, Cracow University of Technology/ - Cracow, 2001.
2. Eurocode 2: Design of concrete structures - Part 1: General rules and rules for buildings [Text] - CEN European Committee for Standardization, 2004.
3. Byfors, J. Plain concrete at early eages [Text] / J. Byfors. - Swedish Cement and Concrete Research Institute at the Institute of Technology. -Stockholm, 1980.
4. Мурашев, В. И. Трещиноустойчивость, жесткость и прочность железобетона [Текст] / В. И. Мурашев - М.: Стройиздат, 1950. - 268 с.
Received by editors' board: July 03, 2012. Approved for publication: July 23, 2012.
К. ФЛАГА, М. ПАНТАК (Кракiвський технолопчний унiверситет, Польща)
ТЕРМ1ЧН1 НАПРУГИ У СТАЛЕЗАЛ1ЗОБЕТОННИХ МОСТАХ У СТАДП БУД1ВНИЦТВА
В доповщ обговорюеться вплив дп тепла пдратацп цементу 1 температуры навколишнього середовища на напруження бетонно! плити пропно! частини в сталебетонных мостах. Представлено приклади анал1зу терм1чних умов, а також анал1зу напруження перер1зу викликане терм1чним впливом в стади буд1вництва моста.
Ключовi слова: сталебетонний м1ст, терм1чш умови, терм1чне напруження К. ФЛАГА, М. ПАНТАК (Краковский технологический университет, Польша)
ТЕРМИЧЕСКИЕ НАПРЯЖЕНИЯ В СТАЛЕЖЕЛЕЗОБЕТОННЫХ МОСТАХ В СТАДИИ СТРОИТЕЛЬСТВА
В докладе обсуждается влияние воздействия тепла гидратации цемента и температуры окружающей среды на натяжение бетонной плиты проезжей части в сталебетонных мостах. Представлено примеры анализа термических условий, а также анализа натяжения сечения вызванного термическим влиянием в стадии строительства моста.
Ключевые слова: сталежелезобетонные мосты, термические условия, термическое натяжение
