2019 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)
Day/Period(Room No.)
Mon1-2(G511)  Thr1-2(G511)  
Course number
Academic year
Offered quarter
Syllabus updated
Lecture notes updated
Language used
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Course description and aims

The elastic and plastic behaviors of the concrete and steel currently most extensively used as structural materials of a high-rise building are explained. 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 behavior of reinforced concrete beams and columns.

Student learning outcomes

Students learn the elastic and plastic behaviors of the concrete and steel in three dimension field. Knowledge on the yield criteria of steel and failure criteria of concrete are obtained. Nonlinear behavior of reinforced concrete beams and columns can be understood.


three dimensions, stress, strain, constitutive law, yield criteria of steel, failure criteria of concrete, flexural behavior or RC members, shear behavior or RC members

Competencies that will be developed

Intercultural skills Communication skills Specialist skills Critical thinking skills Practical and/or problem-solving skills
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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 recent lectures. Then new topics are introduced for the rest of the class.

Course schedule/Required learning

  Course schedule Required learning
Class 1 Materials characteristics of concrete and steel Differnece between concrete and steel
Class 2 Stress in three dimensional field Stress
Class 3 Principal stresses and axes Meaning of principal stresses
Class 4 Strain in three dimensional field Obtaining strain from displacement field
Class 5 Stress-strain relation of elastic materials Constitutive law in one, two and three dimensions
Class 6 Governing equations of elastic materials and basics of finite element analysis Equilibrium equations
Class 7 Stress functions Application of stress functions
Class 8 Yield criteria and nonlinear stress-strain relation of steel Judging yielding of steel members using the yield criteria
Class 9 Failure criteria of concrete Judging failure of concrete members using the failure criteria
Class 10 Confining effect of concrete and numerical model Stress-strain relation of confined concrete
Class 11 Nonlinear behavior of RC members Seismic damage of RC structures in the past earthquakes
Class 12 Nonlinear flexural behavior of RC beams Reading assignment 1
Class 13 Nonlinear flexural behavior of RC columns Reading assignment 2
Class 14 Decomposition of nonlinear deformation of RC members Flexural analysis of RC members
Class 15 Seismic behavior of RC members in past earthquakes Stress and strain conditions of RC members



Reference books, course materials, etc.

Reinforced Concrete Structures (Park and Paulay)

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[at]serc.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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