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@.
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.
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:
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
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
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
338
Based on the aging theory, JIN proposed a simple expression for the aging coefficient x(t, t0)[8]:
χ
(t
,
t
0
)
=
1
−
e
1
−φ
(t
,t0
)
−
φ
1
(t, t0
)
(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:
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
φ(t, τ)=βα(τ)+0.4βd(t−τ)+φf[βf(t) −βf(τ)]
(3)
where βα(τ) is the initial unrecoverable plastic deformation; 0.4βd(t−τ) is elastic strain lag dependent on time, and φ f [β f (t) − β f (τ )] is the plastic strain lag dependent on the age of concrete.