Abstract
This paper presents a general procedure for a rate-type creep analysis (based on the use of the continuous retardation spectrum) which avoids the need of recalculating the Kelvin chain stiffness elements at each time step. In this procedure are incorporated three different creep constitutive relations, two recommended by national codes such as the ACI (North-American) and EC2 (European) building codes and one by the RILEM research association. The approximate expressions of the different creep functions with the corresponding Dirichlet series are generated using the continuous retardation spectrum approach based on the Post–Widder formula. The proposed rate-type formulation is implemented into a 3D finite element code and applied to study the long-term deflections of a prestressed concrete bridge built in Romania, which crosses a wide artificial channel that connects the Danube river to the port of Constanta in the Black Sea.
Highlights
An accurate simulation of creep and shrinkage behavior is necessary for certain types of structures such as long-span prestressed box girders; cable-stayed or arch bridges; large bridges built sequentially in stages by joining parts; nuclear containments and vessels; large gravity, arch or buttress dams; cooling towers; large roof shells; and very tall buildings [1,2]
In order to validate the numerical formulation of the rate type creep model and its implementation into a three-dimensional finite element code, the mid-span deflection in time obtained from the finite element analysis is compared with its analytical calculation resulting from the Effective Modulus Method (EMM) [36] applied to the type of load history considered
The procedure is based on the approximation of an aging compliance function through a Dirichlet series, which transforms the classical Volterra integral equation of creep into a rate-type formulation, governed by an aging Kelvin chain whose coefficients are obtained directly from the coefficients of the Dirichlet series approximation of the compliance function
Summary
An accurate simulation of creep and shrinkage behavior is necessary for certain types of structures such as long-span prestressed box girders; cable-stayed or arch bridges; large bridges built sequentially in stages by joining parts; nuclear containments and vessels; large gravity, arch or buttress dams; cooling towers; large roof shells; and very tall buildings [1,2]. The purpose of this paper is to formulate a general procedure, based on the use of the continuous retardation spectrum, capable of readily converting the integral creep problem into a rate-type one without the recalculation of the Kelvin chain stiffness elements at each time step. This procedure is particularized with reference to three different creep constitutive relations, two important because recommended by professional associations in USA and Europe (ACI and CEB-Euro-Code) and one important for its diffusion in the research community, the RILEM B3 model. For general constitutive formulations that starts from early-ages, an interested reader can refer to the formulations presented in [17,18,19,20,21]
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