# Reinforced Concrete Structures - Design and Analysis using Theory of Plasticity

**ID: C205**

The course gives the participant an introduction to the fundamental basis of the theory of plasticity as well as a survey of a large number of standardized plasticity methods for calculation and design of reinforced concrete structures.

Kurset varer ialt 3 dage.

- Description of course content
- Agenda
- Teachers
- Practical

The course gives the participant an introduction to the fundamental basis of the theory of plasticity as well as a survey of a large number of standardized plasticity methods for calculation and design of reinforced concrete structures. The purpose is to enable the participant to apply the theory in practice and in particular to analyze non‐standard cases, which are not fully covered by standards and codes.

The theory of plasticity for reinforced concrete structures represents a general and consistent framework for solving problems in the ultimate limit state. A number of calculation models based on this framework are already a part of the Eurocode 2; for instance, model for shear reinforced beams and formulas for tension reinforcement for plane stress conditions. There are two main advantages of the plasticity approach. First and foremost, the approach makes it possible to work with physically simple and understandable structural models, which give the engineers knowledge of both the flow of forces within the structure as well as the collapse mechanism. Secondly, great flexibility in the layout of the reinforcement can be achieved by plasticity methods, which is beneficial for the execution phase.

The first part of the course covers the fundamental basis of the theory of plasticity for structural concrete and aims at making the participant familiar with the concept. The second part is dedicated to a thorough treatment of calculation methods applicable for various types of structural problems and structural members. The aim here is to make the participants able of developing their own solutions to the problems they meet in practice.

The purpose is to enable the participant to apply the theory in practice and in particular to analyze non‐standard cases, which are not fully covered by standards and codes.

Design engineers

**1 ^{st} day**

- Fundamental basis of theory of rigid‐plasticity, including lower‐ and upper bound theorem
- Reinforcement and concrete properties
- Concrete, failure criteria, dissipation and effectiveness factor
- Plane stress fields, yield conditions and reinforcement design
- Slabs, yield conditions and reinforcement design
- Ductility and redistributions

**2 ^{nd} day**Stringer method, Strut and tie models and homogeneous stress fields

- Yield lines
- Anchorage/lap, construction joints
- Holes and concentrated forces
- Frame corners and corbels
- Three-dimensional stress fields, reinforcement design
- Beams, bending/normal force, shear (non-shear reinforcement and shear reinforced members, torsion and combined actions

**3 ^{nd} day**

- Slabs, strip method, yield line theory, membrane actions
- Slabs, shear and punching shear
- Disks and deep beams
- Numerical methods
- Serviceability limit state

### Bent Feddersen

### Linh C. Hoang

The course is based on presentations made for the course, which include both theory as well as a large number of examples from practice. The book ‘M. P. Nielsen and Linh C. Hoang, Limit Analysis and Concrete Plasticity’ will functioning as a basic reference for the participant who wishes to study any of the scheduled subjects in deeper details.