Keywords: concrete bridges, time-dependent, creep, shrinkage, relaxation, single-step method.

The creep and shrinkage of concrete and the relaxation of cables in prestressed concrete bridges are known to interact with one another. These time-dependent factors can cause the redistribution of internal forces which in turn affect the long-term structural performance. So it is important to predict the time-dependent deformations due to these effects reasonably accurately not only to ensure satisfactory structural performance but also to enable effective structural health monitoring systems to be built.

This paper proposes a single-step method to predict the time-dependent behaviour of concrete structures due to concrete creep, concrete shrinkage and cable relaxation. Firstly, a new relaxation model for steel tendons using an equivalent relaxation function is proposed to enable accurate estimation of the loss of cable forces. Based on this new model, a relaxation-adjusted elasticity modulus is introduced to enable the prestress loss to be analyzed using a single step. Then a general method is established for single-step finite element analysis of the time-dependent deformations of concrete bridges under the effects of concrete creep, concrete shrinkage and cable relaxation, using the age-adjusted elasticity modulus [1], shrinkage-adjusted elasticity modulus [2] and relaxation-adjusted elasticity modulus respectively. In this proposed model, concrete members are modelled using beam elements, while tendons are modelled as bar elements with nodes connected to the beam axis by perpendicular rigid arms [2,3,4,5].

Case studies show that the results from the sing-step (SS) method are always a little greater than those from time integration (TI) method, However the error between results obtained from these two methods is small enough which indicates the SS method is an efficient and reliable method for analyzing concrete structures.

Case studies also show that the concrete creep and concrete shrinkage can increase the cable relaxation in the tendons and that the cable relaxation can reduce the effect of concrete creep and shrinkage on the time-dependent deflections of concrete structures. So the interaction among concrete creep, concrete shrinkage and cable relaxation should be carefully considered for the time-dependent analysis of concrete structures and building an efficient health monitoring system.

1

Z.P. Bazant, "Prediction of concrete creep effects using age-adjusted effective modulus method", ACI Journal, 69(4), 212-217, 1972.

2

F.T.K. Au, C.H. Liu, P.K.K. Lee, "Creep and shrinkage analysis of reinforced concrete frames by history-adjusted and shrinkage-adjusted elasticity moduli", The structural design of tall and special buildings, 18, 13-35, 2009. doi:10.1002/tal.391

3

B.O. Aalami, "Time-dependent analysis of concrete structures", Progress in Structural Engineering and Materials, 1(4), 384-391, 1998. doi:10.1002/pse.2260010407

4

N. Ariyawardena, A. Ghali, "Prestressing with unbonded internal or external tendon: anlysis and computer model", Journal of structural Engineering, 128(12), 1493-1501, 2002. doi:10.1061/(ASCE)0733-9445(2002)128:12(1493)

5

M.M. Elbadry, A. Ghali, "Analysis of time-dependent effects in concrete structures using conventional linear computer programs", Canadian Journal of Civil Engineering, 28(2), 190-200, 2001.

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