Review of the methods for analysis of flat slabs

Abstract

The paper analyzes the results of reinforced concrete flat slabs, using different methods based on the theory of elasticity and theory of plasticity. Were considered three methods: stripe method, method according to Hillerborg and Wiesinger and Yield Line theory. The stripe method based on the theory of elasticity and is one of the most commonly used methods for calculation flat slabs, which are recommended by many regulations for calculation reinforced concrete structures. This paper also presents two methods based on the theory of plasticity, the method according to Hillerborg and Wiesinger - lower bound and Yield Line theory - upper bound, which uses a solutions of Johansen. Solutions obtained by these methods define limits interval of critical load. Review the basic theoretical hypothesis of all these methods and their application to flat slabs. Conducted calculation according to Eurocode 2 with a regular arrangement of pillars, analyzed the results and commented differences that occur as a result of the adoption of various hypothesis.

U radu su analizirani rezultati proračuna armiranobetonskih ploča direktno oslonjenih na stubove, koristeći različite metode koje se zasnivaju na teoriji elastičnosti i teoriji plastičnosti. Razmatrane su tri metode: metoda ekvivalentnih traka, metoda prema Hillerborg-u i Wiesinger-u i metoda linija loma. Metoda ekvivalentnih traka zasniva se na teoriji elastičnosti i jedna je od najčešće primenjivanih metoda za proračun ploča direktno oslonjenih na stubove, koju preporučuju mnogi propisi za proračun armiranobetonskih konstrukcija. U radu su predstavljene i dve metode koje se zasnivaju na teoriji plastičnosti, metoda prema Hillerborg-u i Wiesinger-u teorija donje granice i metoda linija loma (Yield Line theory) teorija gornje granice, koja koristi rešenja Johansen-a. Rešenja dobijena ovim metodama definišu granice intervala kritičnog opterećenja. Prikazane su osnovne teorijske pretpostavke svih navedenih metoda kao i njihova primena na ploče direktno oslonjene na stubove. Sproveden je proračun ploče prema Evrokodu 2 sa pravilnim rasporedom stubova, analizirani su rezultati i komentarisane razlike koje se javljaju kao posledica usvajanja različitih pretpostavki.