University of Architecture, Civil Engineering and Geodesy (UACEG)

Goals and objectives of the subject: Plastic analysis of structures is an elective course for Structural Engineering students in 7-th semester. The subject is organized in 30 lectures hours and finishes with continuous assessment and 2 credit points according to ECTS.
The simplest variant of theory of plasticity - the limit state method – has been considered in detail. It is applied to plane frames and slabs. Students learn also the applied methods for estimation of the bearing capacity of plane frames and continuous beams taking into account the material nonlinearity. Determination of ultimate loads and the relevant failure or collapse mechanisms are also considered along with the use of appropriate specialized software. The yield-line theory for reinforced concrete slabs has been applied for determination of critical loads. The study hours include modelling of plane frame structures according to assumption of concentrated plasticity as well as distributed plasticity in frames and floor slabs and comparisons of the results against basic simplified theories.
Characteristics of the subject: The limit state analysis is the simplest variant of applied theory of plasticity. When all the material yielding in given a section it behaves like a hinge. The plastic hinge arises in a point and has zero length together with the assumption of elastic perfectly-plastic or rigid perfectly-plastic behaviour of the material.
Two basic problems are analysed in the course:
• Calculation of ultimate load for a given frame structure and parametrically assigned loads when due to consecutive formation of plastic hinges the structure becomes mechanism followed by its collapse;
• Design of a frame structure which is able to withstand the applied ultimate external loads.
Determination of critical loads in reinforced concrete slabs is another subject of the current course.
An introduction to the basics of the deformational and incremental theory of plasticity for cases of two- and three-dimensional problems is performed. Equations and relations are formulated in tensor form.
Acquired knowledge: Students become familiar with the behaviour of nonlinear deformation systems taking into account the material nonlinearity for plane frame and slabs. The have knowledge when and under what conditions plastic hinge is formed in the model and how it affects the behaviour of the whole structure. Different methods for determination of ultimate loading are among the acquired knowledge, such as: consecutive elastic solutions; application of appropriate software and respective nonlinear static solution; application of the lower (static) and upper (kinematic) bound theorems of plasticity.
Acquired skills: The students are able to trace the elastic behaviour of the structure until the first plastic hinge is formed, followed by elastic-plastic behaviour of the frame until a local or full collapse mechanism is reached. They are familiar with contemporary software for structural analysis and they are able to assign the parameters and perform nonlinear static analysis in order to obtain ultimate critical load associated with following collapse of the structure.
Preliminary requirements: In order to achieve the level of education put in the current curriculum the students must have knowledge on Statics of structures I-st part as well as fundamental subjects like Mathematics, Physics and Theory of elasticity and plasticity.