On the physically non‐linear analysis of cyclic loaded reinforced concrete cross‐sections with mathematical optimisation

Abstract

In the paper, experimental results of tension member tests are used as a basis from which to develop an extended tension stiffening model for reinforced concrete, with emphasis on the specific concrete damage and the developments of residual deformations depending on the structural loading. Two characteristics are contained in the proposed model: one describes the residual deformation behaviour along the reinforcement accounting for the cracks that cannot be closed completely, while the other describes the degradation of the concrete stiffness. Within context of non‐linear analysis, the model is incorporated into an analytical approach, based on the LAG RANGE principle of minimum of total potential energy. The mechanical problem is solved with the application of the mathematical optimisation, using energy principles formulated as a kinematic formulation and transforming them into non‐linear optimisation problems. It was demonstrated, that this approach is eminently suitable for analysing pre‐damaged or pre‐loaded reinforced concrete cross‐sections under cyclic loading.

Santrauka

Pateikti tempiamuju gelžbetoniniu elementu eksperimentiniu tyrimu rezultatai. Remiantis šiais rezultatais pasiūlytas su‐pleišejusio tempiamojo betono modelis, kuriame ivertinama betono pažaidu ir liekamuju deformaciju didejimo itaka tem‐piamuju gelžbetoniniu elementu elgsenai. Modelis susideda iš dvieju komponentu: pirmasis aprašo išilginiu liekamuju de‐formaciju armatūroje kitima, o antrasis betono itakos elemento skerspjūvio deformacijoms mažejima. Netiesine analize atliekama taikant analizini algoritma, kuris pagristas Lagranžo potencines energijos minimalumo principu. Mechanine problema išspresta taikant matematini optimizavima ir energinius principus. Pastarieji aprašyti kinematinemis formulu‐otemis jas perkeliant i netiesinio optimizavimo uždavinio algoritmus. Parodyta, kad pasiūlytas algoritmas gerai tinka cik‐line apkrova veikiamiems gelžbetoniniams elementams analizuoti.

Keywords:

• tension member test
• degradation of concrete stiffness
• residual deformations
• cross‐section analysis
• mathematical optimisation

Reikšminiai žodžiai::

• tempiamu elementu bandymai
• betono standumo mažejimas
• liekamosios deformacijos
• skerspjūvio analize
• matematinis optimizavimas