単位数: 2. 担当教員: 山口 健, 山本 剛. 開講年度: 2024. 科目ナンバリング: TMA-MEE215E. 開講言語: English.
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Google Classroomのクラスコードは工学部Webページにて確認すること。
学部シラバス・時間割(https://www.eng.tohoku.ac.jp/edu/syllabus-ug.html)
Google Classroom will be used in this course.
Class code is "mrvbajs".
Please visit Google Classroom and enter the class code.
The class code for Google Classroom can be found on the Web site of
the School of Engineering:
https://www.eng.tohoku.ac.jp/edu/syllabus-ug.html (JP Only)
１．Class subject
Mechanics of Materials utilizes models that drastically simplify the geometry of structures/components to be designed and the loading modes acting on them, while retaining their essential feature. On the basis of the simplified models the fundamental and necessary knowledge of their mechanical responses is derived and provided for the design of the structures/components. This course is intended as an introduction in mechanics of solids offered to engineering students, and presents the underlying theories and formulations for the description of stress/strain and deformations under various types of loading.
２．Object and summary of class
Mechanics of Materials II discusses the loading mode of bending in addition to tension/compression and torsion treated in Mechanics of Materials I. In particular, beams subjected to bending moments are extensively analyzed. The topics covered in the course of Mechanics of Materials II includes; (1) theory of beams which allows us to calculate bending/shear stresses in beams and their deflections; (2) energy methods such as Castigliano’s theorem; and (3) compression-induced failure such as buckling.
３．Goal of study
At the end of the course, students should be able to calculate the stresses and deformation, and to determine the condition of buckling in simple structures/components such as beams and frames.
It is assumed that the students studying in this course will have some experience in elementary statics (mechanics of rigid bodies) and mathematics (such as differentiation, integration and differential equations).
1. Introduction: Design of structures and approach of Mechanics of Materials
Bending moment and shear force in beams: Types of supports and loads in beams
2. Bending moment and shear force in beams:Bending moment diagram and shear force diagram
3. Stresses in beams: Bending stress and curvature, geometrical parameters of cross section
4. Stresses in beams: Shear stress, composite beams, and combined bending and torsional loads
5. Deflection of beams: Differential equation of the elastic curve, and end conditions
6. Deflection of beams: Deflections by superposition
7. Deflection of beams: Deflections by shear forces
8. Statically indeterminate beams: Compatibility of deformation, method of superposition
9. Summary and Examination-1
10. Strain energy and energy methods: Formulations of strain energy, Castigliano’s theorem
11. Strain energy and energy methods: Application to statically indeterminate beams:
12. Strain energy and energy methods: Maxwell’s reciprocal theorem
13. Column: Failure due to axial compression, Buckling, Euler’s formula of buckling loads
14. Column: Effects of end conditions on buckling loads, semi-empirical formulas
15. Summary and Examination-2
The session time is limited and therefore self-directed learning is important. Students are required to prepare and review for each class.
The students are requested to study the fundamental items described in the textbook before and after each class, and to elaborate the part(s) designated by the lecturer in the class. Several assignments will be provided in the course, and the students are asked to solve them and hand in their solutions as a report.
1. Assignments: 20%
2. Examinations-1 & 2 (Closed book and no notes): 80% (40% each)
The students are welcome to contact the lecturer in order to arrange an meeting for questions.
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