J. Cent. South Univ. Technol. (2008) 15(s1): 337-341

DOI: 10.1007/s11771-008-376-1

Effect of concrete creep on pre-camber of continuous rigid-frame bridge

HE Guo-jing(贺国京)^{1, 2}, LI Yuan-yuan(李媛媛)¹, ZOU Zhong-quan(邹中权)², DUAN Liang-liang(段靓靓)¹

(1. College of Civil and Architecture and Mechanics, Central South University of Forestry and Technology, Changsha 410004, China;

2. School of Civil and Architectural Engineering, Central South University, Changsha 410075, China)

Abstract: The effect of concrete creep on the pre-camber of a long-span pre-stressed concrete continuous rigid-frame bridge constructed by cantilever casting method was investigated. The difference of creep coefficients calculated with two Chinese codes was discussed. Based on the calculations, the pre-camber of a pre-stressed concrete continuous rigid-frame box bridge was computed for construction control purpose. The results show that the short-term creep coefficient and long-term creep coefficient calculated with the CC-1985 are larger than those calculated with the CC-2004, while the medium-term creep coefficient calculated with the CC-1985 is smaller than that calculated with the CC-2004. The difference of creep deformation calculated with these two codes is small, and the influences of concrete creep on the pre-camber for most of the segments are negligible. The deflections and stresses of the box girder measured during the construction stages agree very well with the predictions.

Key words: creep; pre-stressed concrete; continuous rigid-frame bridge; cantilever casting method; pre-camber

1 Introduction

The creep deformation of concrete is non-elastic and depends on the load and time. It is about 1 to 3 times of the elastic deformation in long-span concrete bridges and is not negligible^[1]. With the development of computational theory and construction technology, the spans of bridges have been increased unceasingly in the past 40 years. It is very difficult to construct bridges crossing great rivers with the traditional method with scaffolds. In 1950, cantilever casting method, one of the existing methods without scaffolds, was firstly adopted by German engineers to build continuous pre-stressed concrete girder bridges^[2]. The girder is constructed on the finished piers and symmetrically hanged out segment by segment along the longitudinal direction. The construction of long-span bridges has been greatly enhanced by the application of this method. However, there are some difficulties in the construction process, such as to determine the changes of secondary internal forces and displacements. In order to ensure the quality and safety of bridge, it is necessary to adjust the pre-camber and pre-stressing force during the construction stages. In the CC-1985^[3], the calculation method for creep deformation was adopted from the Eurocode CEB-FIP1978. The calculation formulae have been revised in the newly issued Chinese code CC-2004^[4]. In this work, the creep coefficients vs time according to the formulae were calculated and compared.  The displacements and internal forces were calculated according to the two codes for a pre-stressed concrete rigid frame bridge. The displacements and stresses of the box girder measured during construction stages agree very well with the predictions.

2 Theory for calculation of concrete creep

The calculation methods for creep are based on effective modulus method, aging theory, elastic creep theory, elastic continuation and plastic flow theory^[5-6]. The most commonly used one was proposed by Bazant-Trost^[7]. According to this theory, the time-dependent stress—strain relationship is given as follows:

     [1+x(t, t₀)(t, t₀)]             (1)

where σ(t₀) is the initial stress; σ(t)-σ(t₀) is the variation of stress; e(t₀) is the initial elastic modulus upon the member which is loaded; (t, t₀) is the creep coefficient of concrete; x(t , t₀) is the aging coefficient.

Based on the aging theory, JIN proposed a simple expression for the aging coefficient x(t, t₀)^[8]:

                   (2)

It is the most important to choose a suitable creep mode in Eqn.(1). Several creep modes have been proposed, such as CEB-FIP1978 mode, BP2 mode and ACI209 mode, etc. In the CC-1985^[3], the specified formula for creep calculation is as follows:

φ(t, τ)=β_α(τ)+0.4β_d(t-τ)+φ_f[β_f(t) -β_f(τ)]           (3)

where β_α(τ) is the initial unrecoverable plastic deformation; 0.4β_d(t-τ) is elastic strain lag dependent on time, andis the plastic strain lag dependent on the age of concrete.

In the CC-1985, the values of the above three items are given in diagrams or tables, which are not convenient for the calculation by computer programs. Therefore, equations that fit the diagrams and tables are proposed as

β_α(τ)=0.8[1-0.7837τ/(4.2+0.85τ)^3/2]               (4)

β_d(t-τ)=0.73[1-exp(-0.01(t-τ))]+0.27             (5)

          (6)

where , is the coefficient of flowing plasticity, and H_f can be found in Ref.[5].

In the newly issued CC-2004^[4], the formulae for calculation of creep deformation are revised as follows:

                          (7)

                         (8)

                      (9)

                     (10)

where  t₀ is the concrete age when it is loaded, d; t is the calculating age of concrete, d; and R is average relative humidity in a year, %, usually adopting 70%. RH₀=100%, t₀=1 d, f_cm0=10 MPa, and f_cm0=0.8 f_{cm, k}+8, is the standard average cubic compressive strength for concrete C20-C50, which are specified in CC-2004.

Man-Tian-Xing Bridge is a pre-stressed concrete continuous rigid-frame box bridge located in Guizhou Province, with a span of 78 m +120 m +78 m and total length of 277.10 m. The heights of the beam at the top of piers and the middle of the span are 7.5 m and 2.8 m, respectively. The pier adopts a reinforced concrete dual-column. Its section dimension is (2-1.6) m×4.1 m, and the distance of the two columns is 4.4 m. The heights of two piers are 75 m and 88 m, respectively. The elevation view and typical sections of the beam are shown in Figs.1 and 2. It is constructed with balanced

Fig.1 Elevation view of Man-Tian-Xing Bridge (unit: m)

Fig.2 Sections of Main-Tian-Xing Bridge (unit: cm): (a) Section at top of pier; (b) Section of mid-span

cantilever casting method. Each cantilever is divided into 10 segments, plus three closure segments in the middle span and the two side spans. The segments in the side span and one half of the middle span for each pier are named A1-A10 and J1-J10, respectively.

The bridge was designed in 2000 according to CC-1985, and was constructed in 2005. To analyze the influence of creep on the construction pre-camber, the concrete creep coefficients were calculated according to the CC-1985 and CC-2004, respectively.

Two cases of loading age were considered, i.e., 7 d and 28 d. Since the exposure length of the girder section to the atmosphere is not clearly defined in CC-2004, the contact acreage coefficient of the box beam was considered to be 1.0 and 0.5, respectively. Calculated results are shown in Figs.3 and 4.

Fig.3 Creep coefficients vs time for loading age of 7 d

Fig.4 Creep coefficients vs time for loading age of 28 d

It can be concluded from the above analysis as follows: 1) when the loading age is 7 d, the creep coefficients calculated from CC-1985 are slightly larger than those from CC-2004; 2) when the loading age is 28 d, the creep coefficients calculated from CC-1985 are slightly less than those from CC-2004 as the calculating age is less than 1 000 d. However, it is slightly larger when the calculating age is more than 1 000 d; 3) The difference of calculated coefficients from the two codes is slight.

3.2 Creep deformation of girder during construction process

    To analyze the influence of concrete creep on the pre-cambers of the girder, the creep deformations of the girder in each construction stage were calculated by using the above two codes. In the analysis, the construction time for each segment was assumed to be 13 d, and the loading age was assumed to be the time of tensioning the prestressing reinforcement. The calculated results of segment No.3 are shown in Fig.5.

Fig.5 Creep deflections of segment No.3 for different construction stages

It can be found from the above diagram that the creep deflection calculated from CC-1985 is smaller than that from CC-2004, while the difference is quite small, and even the total creep deformation is not very large.

3.3 Influence of creep on pre-camber

    Elevation control is one of the key process in construction control for the bridge constructed by cantilever construction method. Improper elevation control will affects the quality and safety of the bridge, even results in an embarrassing situation that the bridge cannot be drawn to closure. The elevation control of the bridge is achieved by adjusting the construction elevation, i.e., setting some pre-cambers. There are three methods for setting pre-camber, i.e., relative deflection method, short-length-method, absolute deflection method. In this work, the absolute deflection method was used to set the pre-cambers.

  Secondary dead load, 1 500 d creep with shrinkage and 1/2 live loads were considered for pre-camber calculation. The equation of objective pre-camber is given by

               (11)            

where  y_mi is the objective pre-camber at point i, while f_si, f_xi, f_2i and f_hi are the creep deflection at 1 500 d, shrinkage deflection at 1 500 d,  deflection of secondary dead load and deflection of live load at point i, respectively.

   The pre-cambers, calculated according to the formulae specified in the CC-2004^[3] and CC-1985^[4], are  shown in Fig.6. It can be concluded that the pre-cambers calculated from CC-1985 are slightly larger than those from CC-2004. The maximum difference arises in the mid-span, which is up to 0.011 m, while differences in other sections are quite small and negligible.

Fig.6 Pre-cambers calculated from two codes

3.4 Measurements of deformation

Deformation measuring is an important work for the elevation control of long-span bridges. It is usually taken when the temperature is relatively steady in a day (often before the sun rises).

The measurements have been taken 7 times for each segment, including formwork installation, before the concrete casting, after the concrete casting, before prestressing, after prestressing, before the moving of hanging basket, after the moving of hanging basket. Furthermore, the measurements have been taken for the bridge in the stages of closuring up at side span and middle span, the construction of bridge decking. The deformations at each stage were measured by the precise level. The deflections of theoretical value and measurement value of typical segment are shown in the Figs.7 and 8.

It can be found that the differences between the theoretical values and the measured values are all within

Fig.7 Comparison of deflections in typical segments before and after concrete casting

Fig.8 Comparison of deflection in typical segments before and after prestressing

10 mm. The parameters adopted for the calculation of construction control are in good accordance with the material properties. The measurements of the deflection are reasonable.

4 Conclusions

1) The creep coefficient is calculated with the formula determined by the CC-1985 and CC-2004. It is shown that the short-term creep coefficient and long-term creep coefficient calculated according to the CC-1985 are larger than those calculated according to CC-2004, while the medium-term creep coefficient calculated according to CC-1985 is smaller than that calculated according to CC-2004.

2) The concrete creep is calculated according to the above two codes to analyze its influence on the pre-camber. The results indicate that the difference of creep deformation calculated with that two codes is small, and its influences on the pre-cambers for most of the segments are negligible.

3) The construction control is performed successively, and the profile of the girder is satisfactory.

References

[1] YANG Feng-lian, WANG Gen-hui. The study of creep deformation during the construction of long-span concrete bridge without bracket [J]. Journal of Lanzhou Jiaotong University, 2003, 32(3): 145-149.

[2] MA Bao-ling. The high-rise pier and long span continuous rigid frame bridge [M]. Beijing: China Communication Press, 2001. (in Chinese)

[3] JTG 023—1985, Code for Design of Highway Reinforced Concrete and Prestressed Concrete Bridges and Culverts. [S].

[4] JTG D62—2004, Code for Design of Highway Reinforced Concrete and Prestressed, Concrete Bridges and Culverts. [S].

[5] HUI Rong-yan, HUANG Guo-xing, YI Bin-ruo. The creep of concrete [M]. Beijing: China Railway Publishing House, 1988. (in Chinese)

[6] ZHOU Lü, CHEN Yong-chun. Creep and shrinkage [M]. Beijing: China Railway Publishing House, 1994. (in Chinese)

[7] BAZANT Z P, PANULA L. Creep and shrinkage characterization for analyzing prestressed concrete structures [J]. PCI Journal, 1980, 25(3): 86-122.

[8] WANG Jun-weng, LI Jian-zhong, SU Mu-biao. Internal forces redistribution and stresses redistribution analysis of continuous and prestressed concrete girder bridges [J]. Journal of Shijiazhuang Railway Institute, 1999, 12(1): 1-6. (in Chinese)

(Edited by YANG Hua)

Foundation item: Project(2008047B) supported by the Funds for Youth of Control South University of Forestry and Technology

Received date: 2008-06-25; Accepted date: 2008-08-05

Corresponding author: LI Yuan-yuan, Master; Tel: +86-731-5623319; E-mail: sweet_yuan@126.com.