2021 Nonlinear Behavior of Concrete and Concrete Members

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Academic unit or major
Graduate major in Urban Design and Built Environment
Kono Susumu  Nishimura Koshiro 
Course component(s)
Lecture    (ZOOM)
Day/Period(Room No.)
Mon1-2()  Thr1-2()  
Course number
Academic year
Offered quarter
Syllabus updated
Lecture notes updated
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Course description and aims

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.

Student learning outcomes

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

Competencies that will be developed

Specialist skills Intercultural skills Communication skills Critical thinking skills Practical and/or problem-solving skills

Class flow

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

  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

Out-of-Class Study Time (Preparation and Review)

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.



Reference books, course materials, etc.

Reinforced Concrete Structures (Park and Paulay)
Plasticity in Reinforced Concrete (W. F. Chen)

Assessment criteria and methods

Homeworks, final exams and attendance are considered.

Related courses

  • Disaster mitigation for building structures

Prerequisites (i.e., required knowledge, skills, courses, etc.)


Contact information (e-mail and phone)    Notice : Please replace from "[at]" to "@"(half-width character).

Susumu Kono (kono.s.ae[at]m.titech.ac.jp)(045-924-5384)
Koshiro Nishimura(nishimura.k.ac[at]m.titech.ac.jp)(045-924-5326)

Office hours

Appointment recommended.

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