INFLUENCE OF GIRDER AGE AT CONTINUITY AND CONSTRUCTION SEQUENCE ON THE TIME DEPENDENT RESTRAINT MOMENTS IN CONTINUOUS PRESTRESSED CONCRETE GIRDER BRIDGES.
ABSTRACT: One of the alternate to minimize the expansion joints in prestressed concrete bridges is to use continuous bridges in place of simply supported bridges by connecting the ends of the girders over the supports with a continuity connection. More continuity means shallow sections or longer spans which will consequently reduce the total cost of the bridge. Unlike the simply supported bridges, the design and construction of continuous bridges connected with the continuity connection require some additional consideration due to time-dependent restraint moments. Restraint moments are developed at the continuity connection due to creep and shrinkage effects which makes the design of continuous bridges different from conventional bridges. In this study, the construction stage time dependent analysis method is proposed using age adjusted effective modulus method (AEMM).
In the proposed method of analysis, firstly, the change in curvature at number of sections due to creep, shrinkage and relaxation is calculated. Secondly, the long-term deflections and rotations are determined by numerical integration of curvatures for a number of sections along the length of the member. Once the long term deflections and rotations are determined, the restraint moments are calculated by the force method of structural analysis. A parametric investigation is then carried out to study girder age at continuity and different construction scenarios on the time dependent restraint moments. By delaying girder age at continuity connection and casting of the deck concrete over the span leads to lower positive restraint moments and more continuity.
Key words: Continuous Prestressed Concrete Bridge, Restraint Moment, Creep and Shrinkage.
It is common practice, in current concrete bridge design, to include joints in the bridges. The elimination or minimizing of joints is important as they are expensive to buy, install, maintain and repair. Some times repair costs can be as high as replacement costs. Beginning in the late 1950's, the advantages of making a multi-span, simply supported prestressed girder bridge continuous by connecting the ends of the girders over the supports with a continuity diaphragm connection began to be investigated. Continuity of precast girders can be achieved by providing continuous reinforcement in the deck over the piers and a concrete diaphragm between the ends of the girders at interior supports (Freyermuth,1969).
This type of connection has been used successfully in several states for many years. The girders act as simple span members for dead loads, before the continuity connection is cast. Once the continuity diaphragm and deck are cast, the composite girder/deck section will carry live loads and superimposed dead loads as a continuous structure (Mirmiran et al, 2001). Unlike the simply supported bridges, the design and construction of continuous bridges require some additional considerations, due to time-dependent restraint moments which make the design of jointless bridges different from other conventional bridges (Peterman et al., 1998). Consequently a good understanding of the behavior of continuous bridges under the time-dependent restraint moment is essential in order to appropriately design the continuity connection reinforcement.
Restraint Moments: In continuous composite precast girders bridges, the precast girders are often cast several days before they are installed. Therefore, most of the concrete shrinkage in these members will have occurred before the cast in place (CIP) concrete is cast. As the fresh C1P concrete cures, its shrinkage will then be partially restrained by the precast members to which, it has been connected. In the case of continuous construction, the continuous ends are not allowed to rotate and a negative restraint moment is produced (figure1).
The effect of creep due to prestressing has the opposite effect as that due to differential shrinkage between the precast girders and CIP. For prestressed concrete bridge girders, the center of the prestress force generally lies lower than the neutral axis of the section. This eccentricity of force causes the members to camber upwards and will produce rotations at the member ends. This camber will generally increase due to creep of the concrete under the sustained, eccentric prestressing force. When these members are made continuous in the field, additional end rotations due to creep are restrained and positive moments result at the interior piers as shown in figure2. Also, for continuous construction using precast concrete members, forces resulting from the restraint of creep deformations due to gravity loads acting on the precast members will be in the same direction as the forces which would be produced if the same loads had been applied after the structure was made continuous.
Thus, the restraint of creep deformations due the weight of the precast panels and CIP topping will produce negative moments at interior piers (figure1).
Calculation of Restraint Moment by Proposed Method of Analysis: The proposed method of analysis is
a) Calculate change in curvature at number of sections due to creep, shrinkage and relaxation (ACI, 2002).
b) Calculate the long-term deflections and rotations by numerical integration of curvatures for a number of sections along the length of the member (ACI, 2003).
c) Calculate restraint moments by the force method of structural analysis.
(b) Calculate the long-term deflections and rotations by numerical integration of curvatures for a number of sections along the length of the member: Long-term deflections and rotations can be calculated by numerical integration of long term curvatures for a number of sections along the length of the member.
The following equations derived by virtual work can be used to calculate the translation in any direction and rotation at any section with any variation of (c) Calculation of Restraint Moments from Long Term Deflection and Rotations: Once the long term deflections and rotations are determined by the procedure outlined above, the statically indeterminate bridge beam can be solved by any method of structural analysis (such as force method).
Effect of Girder Age at Continuity on Restraint Moment: In this section the effect of girder ages at continuity on restraint moments is investigated. Restraint moments are computed for girder ages of 15, 30, 60 and 90 days at the time of continuity. These girder ages are selected assuming that 15 days is the earliest practical girder age for smaller bridges, and 90 days is the earliest practical girder age for large bridges.
It can be seen that with the increase in the girder age at continuity there is less negative moment to offset the future positive moment resulting in the decrease of the positive restraint moments at the later age of establishing continuity. Higher number of strands can be used with the increase of the age of establishing continuity to increase positive restraining moments due to creep under pre-stressing that help reducing negative restraining moments from differential shrinkage.
Since the restraint moments are a function of age of the precast girders when continuity is established, so during the design stage it is very important that the designer should consider the precast girders' age at which the continuity connection will be established. However due to practical considerations, the age of the beam at the time the continuity connection can not be determined with high certainty at the time of the design so to overcome this uncertainty consider creep and shrinkage using the extreme cases for girder age at continuity.
Effect of Different Construction Scenario on Restraint Moment: Different construction scenarios are investigated. In the first construction scenario the deck and diaphragm are casted simultaneously. In the second construction scenario the deck concrete is poured initially on the girder spans, but not over the piers. After the first pour has cured, the remaining deck is poured over the piers. In the third construction scenario continuity is established by casting concrete over the pier, and then after the diaphragm concrete cures deck concrete is poured.
It can be concluded that for the second construction scenario by delaying the casting of the deck concrete over the pier the negative restraint moments are decreased while the positive restraint moments are increased and this is due to the reason that before casting the concrete over the pier the girder ends are free to rotate when the deck is first placed, no restraint moments develop due to deck shrinkage initially, which otherwise would cause a negative restraint moment over the piers. Therefore, the tendency for deck cracking over the piers is reduced. However, this means there is less negative restraint moment to offset future positive restraint moments that will develop.
For the third construction scenario, delaying the casting of the deck concrete over the span the negative restraint moments are increased while the positive restraint moments are decreased. Hence the third construction scenario leads to lower positive restraint moments and greater continuity. However, it would require greater negative moment reinforcement to prevent negative restraint moment cracking. Consequently different construction scenario can be considered to be one of the most effective and critical parameters in design, as it directly affects time-dependent restraining moments due to creep and differential shrinkage, which in turn affects stress distribution in sections along the beam.
Conclusions and Recommendations: Following are the conclusions and recommendations based on the work carried out and the results of the parametric analyses.
1 - Analysis shows that both positive and negative restraint moments can occur. Positive restraint moments can have significant effect on the design of precast/prestressed concrete girders made continuous. While the negative restraint moments are temporary.
2 - With the increase in the girder age at continuity there is less negative restraint moment to offset the future positive restraint moment resulting in the decrease of the positive restraint moments at the later age of establishing continuity.
3 - Since the restraint moments are a function of age of the precast girders when continuity is established. However due to practical considerations, the age of the beam at the time the continuity connection can not be determined with high certainty at the time of the design, so to overcome this uncertainty consider creep and shrinkage using the extreme cases for girder age at continuity.
4 - Third construction scenario i.e., delaying the casting of the deck concrete over the span leads to lower positive restraint moments and greater continuity.
ACI 209R-92. Prediction of Creep, Shrinkage and Temperature Effects in Concrete Structures. American Concrete Institute Manual of Concrete Practice Farmington Hills, Michigan. (2002).
ACI 435R-95. American Concrete Institute. Control of Deflection in Concrete Structures. Farmington Hills, Michigan (2003).
Bazant, Z. P. Prediction of Concrete Creep Effects Using Age-Adjusted Effective Modulus Method. ACI Journal, 69, 212-217 (1975).
Ghali, A., R. Favre and M. M. Elbadry. Concrete Structures: Stresses and Deformations. 3rd Ed. Spon Press. London, UK and New York, NY: (2002).
Freyermuth, C. L. Design of Continuous Highway Bridges with Precast, Prestressed Concrete Girders. Journal of the Prestressed Concrete Institute, Vol. 14, No.2. (1969).
Mirmiran, A., S. Kulkarni, R. Castrodale, R. Miller, and M. Hastak. Nonlinear Continuity Analysis of Precast Prestressed Girders with Cast-In-Place Decks and Diaphragms. PCI Journal, Vol. 46, No.5, pp.60-80 (2001).
Peterman, R. J. and J. A. Ramirez. Restraint Moments in Bridges with Full-Span Prestressed Concrete Form Panels. PCI journal, January-February, pp.54-73. (1998).
Department of Civil Engineering, University of Engineering and Technology, Lahore Professor, College of Civil Engineering, Chongqing Jiaotong University, China Corresponding Author: email@example.com
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|Publication:||Pakistan Journal of Science|
|Date:||Mar 31, 2013|
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