2019 Fundamentals of Mechanics of Materials B

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Academic unit or major
Undergraduate major in Architecture and Building Engineering
Motoyui Shojiro 
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Course description and aims

This course focuses on the fundamental knowledge of mechanics for building structures. Topics include the calculation method for the deflection of beams, the principal stresses in multi-axial stress field, the concept of the strain energy, and some nonlinear behaviors in building structures.
To design building structures, not only stresses but also deflection and various unstable behaviors should be taken account. The true aim of this course is the acquitting the sense of mechanics while concrete calculation methods for stresses and deflection. Because everyone working in the field of architecture need to understand various mechanical phenomena and explain them by intuition. Students will realize both the usefulness and complication of mechanics.
In This course Curved continua like arches and domes are often applied to actual building structures for indoor sport stadiums. The specific coordinate system which was the most suitable one to the configuration of the target structure was referred to when deriving basic equations for the structure. Consequently, varied expressions of the basic equations were used corresponding to the problem. According to the concept of tensor analysis, the basic equations can be derived in the common form which is independent of the reference coordinate system. Students will realize both the usefulness and complication of tensor analysis. Conversely, students will know we have received the benefit from the Cartesian coordinate system in deriving various equations.

Student learning outcomes

By the end of this course, students will be able to:
1) Calculate the deflection of beams.
2) Find the principal stresses in the multi-axial stress filed.
3) Explain the concept of the strain energy.
4) Explain concept of buckling behavior.


Deflection of beams, Principal stresses, Strain energy, Castigliano's theorem, Principle of virtual work, Buckling

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

At the beginning of each class, solutions to exercise problems that were assigned during the previous class are reviewed. Towards the end of class, students are given exercise problems related to the lecture given that day to solve. Required learning should be completed outside of the classroom for review purposes.

Course schedule/Required learning

  Course schedule Required learning
Class 1 Bernoulli's beam theory History of beam theory and concept of Bernoulli's beam theory
Class 2 Deflection of beams Calculation method for Deflection of beams subjected to external forces
Class 3 Deflection of beams with shear deformation Calculation method for Deflection of beams considering effect of shear deformation
Class 4 strain energy Concept of strain energy
Class 5 Castigliano's theorem Calculation of deflection based on Castigliano's theorem
Class 6 What is "Stress"? Definition of "Stress"
Class 7 Principal stresses in multi-axial stress field Concept of principal stresses and calculation of them
Class 8 Buckling of bars Concept of buckling and calculation of buckling load for bar in compression


Kiso-zairyourikigaku [Revised version] by Yoshihisa Minaguchi et.al., published by Yokendo

Reference books, course materials, etc.

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Assessment criteria and methods

Exercises and exam.

Related courses

  • ARC.S201 : Fundamentals of Mechanics of Materials A
  • ARC.S203 : Structural Mechanics I
  • ARC.S305 : Structural Mechanics II
  • ARC.S306 : Structural Mechanics III

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

Students must have successfully completed Fundamentals of Mechanics of Materials A

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