The lecture examines elastic and plastic behaviors of the concrete and steel commonly used in reinforced concrete buildings. In particular, the three-dimensional stress and strain, the three-dimensional constitutive laws (Hooke’s law), the three-dimensional plasticity theory of steel, and the failure criteria of concrete under multiaxial stresses are discussed to acquire an appropriately evaluating knowledge of an analytical result by a three-dimensional FEM. The basic knowledge on nonlinear behavior of concrete and steel is developed to understand the nonlinear flexural behavior of reinforced concrete beams and columns.
Students learn the elastic and plastic behaviors of the concrete and steel in a three dimensional field. Knowledge on the yield criteria of steel and failure criteria of concrete are obtained. They will obtain skills to numerically analyze nonlinear flexural behavior of reinforced concrete beams and columns.
three dimensions, stress, strain, constitutive law, yield criteria of steel, failure criteria of concrete, nonlinear flexural behavior or RC members
|✔ Specialist skills||✔ Intercultural skills||Communication skills||Critical thinking skills||✔ Practical and/or problem-solving skills|
The instructor gives lectures with some interaction with students. Solutions to the homeworks are discussed in the beginning of each class to review the last lectures. Then new topics are introduced for the remaining time.
|Course schedule||Required learning|
|Class 1||Behavior of elasto-plastic materials||Behavior of elasto-plastic materials|
|Class 2||Stress tensor||Stress|
|Class 3||Principal stress and stress invariant||Meaning of principal stresses|
|Class 4||Mohr's stress circle||Obtaining Mohr's stress circle|
|Class 5||Failure criterion||Mohr-Coulomb failure criterion, Mises's yield criterion|
|Class 6||Strain tensor||Strain|
|Class 7||Mohr's strain circle and Strain gauges||Rosette strain gauges|
|Class 8||Fundametals for design of reinforced concrete structures||Reading assignment on seismic design of reinforced concrete buildings|
|Class 9||Mechanical properties of concrete and reinforcement||Failure of concrete and yielding of reinforcement|
|Class 10||Stress-strain relations of concrete||Stress-strain relation of concrete|
|Class 11||Stress-strain relations of reinforcement||Stress-strain relation of reinforcement|
|Class 12||Review of mechanical properties of materials||Numerical furmulation of stress-strain relations|
|Class 13||Modelling of nonlinear flexural behavior of RC beams/columns||Section analysis of reinforced concrete section ＃1|
|Class 14||Numerical analysis on nonlinear flexural behavior of RC beams/columns||Section analysis of reinforced concrete section ＃2|
To enhance effective learning, students are encouraged to spend approximately 60 minutes preparing for class and another 60 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course materials.
Reinforced Concrete Structures (Park and Paulay)
Plasticity in Reinforced Concrete (W. F. Chen)
Homeworks, final exams and attendance are considered.
Susumu Kono （kono.s.ae[at]m.titech.ac.jp）(045-924-5384)