Evaluation of concrete linear creep in determination of stress state and steel prestress losses in concrete members/Betono tiesinio valkšnumo įvertinimas, nustatant gelžbetoninių elementų įtempimų būvį ir armatūros išankstinio įtempimo nuostolius
Determination of stress-strain state imposed by concrete linear creep and specification of steel prestress losses in linear prestressed concrete member is discussed in this article. Particularities of regulations of the Code acting in Lithuania  and of Eurocode  are analysed and a modified method for calculation of steel prestress losses due to concrete linear creep in prestressed concrete linear members suitable for assessment of Code regulations is presented. Also, the method is used for analysis of results of long-term tests of reinforced concrete members.
In Lithuania, a code based on investigations of prestressed concrete members is used for calculation of steel prestress losses due to concrete creep. Therefore calculation of losses is associated with stress-strain state of the member in time t in empirical way only and time dependent stress-strain state is adjusted by additional coefficients to take into consideration concrete creep. Analogous calculations of steel prestress losses by Eurocode are presented in a more general form and are based on creep theory. It is clear that in the first  and the second  cases the same change in stress-state is evaluated by different parameters. Therefore it is important to create a general method based on concrete creep characteristics.
General case of eccentrically reinforced prestressed concrete linear member under the action of prestressing forces changing with time in relation to prestress losses due to concrete creep is analysed (Fig 1).
Stress-strain time dependent state of such member with the changing concrete stress σ b (t) and σ′ b (t) is determined using well-known equations of equilibrium (1–4) and integral differential equations (7–8) for evaluation of concrete creep deformations [4–8]. These equations are solved by numerical method (9–10) dividing time period considered in intervals. In reference  a more particular solution method evaluating variation of interval magnitude in relation to accuracy of solution is presented.
In such a way it is possible to assess reduction of concrete stress (13–14) at time moment t when loss of steel prestress due to concrete creep takes place (33–34).
There are many experiments performed for investigating concrete creep and determinating time dependent stress-strain state of reinforced concrete members. Various methods are applied for analysis of these data. Assumptions of these methods influence the conclusions of the analysis. In this article there is presented a general method giving opportunity to assess creep of concrete members by the same characteristics, when specific creep (51) or coefficient of creep (52) is determined by tests on eccentrically prestressed linear members (the case of axially prestressed members is presented in ). Pure specific creep C* (t,t 0) values determined according to the method proposed in this article and results of experimental investigations  of prestress in steel of eccentrically prestressed concrete members and also according to data of analysis  of the Code  are presented in Fig 2.
Using the same creep characteristics method of the Code EC-2 and proposed in this article losses of prestress in steel due to concrete creep were calculated according to EC-2 and the method proposed. Values of these losses and their ratio are presented in Fig 3 and 4.
In Fig 5, losses of prestress in steel due to creep predicted after 70 years were calculated in accordance with data of the Code SNiP  analysis  and regulations of the Code EC-2 .
Relationships (62) including (63), (64) formulas are modified EC-2 method for regulation of steel prestress loss due to concrete creep calculation for doubly reinforced members are proposed in the article.
Results of analysis of regulations of Eurocode EC-2 and the Code SNiP indicate that design according to Code  method for steel prestress loss due concrete creep calculation in all cases gives increased values of stiffness and crack resistance characteristics of the structure, but larger amount of steel is to be used in comparison with the design according to SNiP .
First Published Online: 26 Jul 2012
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