### 2020　Mechanics of Materials and Members

Font size  SML

Academic unit or major
Undergraduate major in Civil and Environmental Engineering
Instructor(s)
Hirose Sohichi
Class Format
Lecture    (ZOOM)
Media-enhanced courses
Day/Period(Room No.)
Tue3-4(M114)  Fri3-4(M114)
Group
-
Course number
CVE.A201
Credits
2
2020
Offered quarter
1Q
Syllabus updated
2020/9/18
Lecture notes updated
-
Language used
Japanese
Access Index

### Course description and aims

This course gives the fundamentals of mechanics for materials and structural members. Topics include stress, force, strain and displacement of structural members subjected to various loads like axial force, torsion, bending moment and shear force. Also this course covers transformation of stress and strain, structural design based on stress values, fracture criteria, and deformation of structural members expressed in terms of differential equations.

So far students have learned mechanics in a class of physics, in which theories are mainly applied to particles and rigid bodies, and no deformation of bodies is taken into account. However, real structures show deformation when subjected to external forces. Therefore, deformation as well as force and stress plays an important role in the design of structures. This course provides students with a systematic approach for deformable bodies where deformation can be described in terms of differential equations by combining an equilibrium equation with stress-strain relation and strain-displacement relation. The systematic approach will be applied to the subsequent classes including Structural Mechanics, Hydraulics, Geomechanics and Concrete Structures.

### Student learning outcomes

By the end of this course, students will be able to:
1. Explain the relations among force, stress, strain and displacement.
2. Explain stress distributions in structural members subjected to axial force, torsion, bending moment and shear force.
3. Determine principal stress and strain by understanding the transformation of stress and strain.
4. Explain the role of stress in structural design.
5. Explain structural deformation expressed by differential equations.

### Keywords

stress, strain, displacement, torsion, bending, shear, principal stress, principal strain, elasticity, elastoplasticity, safety factor, design, fracture criteria, buckling

### Competencies that will be developed

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

### Class flow

This course will be mainly provided in lecture style. However, students may not obtain fully knowledge and skills on relevant subjects from only lectures. Hence assignment will be given at every class, and their answer will be explained for review in the following lecture time.

### Course schedule/Required learning

Course schedule Required learning
Class 1 Concept of force, stress and equilibrium Explain the concept of force, stress and allowable stress design method. Determine stress using free body diagrams.
Class 2 Relation between normal stress and normal strain, and mechanics of bars subjected to axial force Explain the relation between normal stress and normal strain, and obtain the displacement of bars subjected to axial force. Solve indeterminate problems of bars.
Class 3 General relationship between stress and strain, stress concentration, non-elastic behavior and so on Explain general relationship between stress and strain, and explain stress concentration, elastoplastic deformation, residual deformation and residual stress.
Class 4 Stress and deformation of structural members subjected to torsion Determine stress and deformation of structural members subjected to torsion.
Class 5 Stress and deformation of structural members subjected to pure bending Determine stress and deformation of structural members subjected to pure bending.
Class 6 Topics related to pure bending, including composite materials, elastoplastic behavior, residual stress, unsymmetric bending Explain stress and displacement of pure bending members made of composite or elastoplastic materials.
Class 7 Analysis of beams for bending - Shear and bending moment diagrams Explain the relation between shear and bending moment. Draw shear and bending moment diagrams of beams.
Class 8 Shear stresses in beams Determine shear stresses in beams.
Class 9 Shear stresses in thin wall members Determine shear stresses in thin wall members.
Class 10 Transformations of stress - plane stress; principal stress, maximum shear stress, and Mohr's circle for stress Expalin what plane stress state is. Determine principal stress, maximum shear stress, and Mohr's circle for stress.
Class 11 Transformations of stress and strain - 3D stress, fracture criteria, stresses in thin wall members, and transformation of strain Explain 3D stress, fracture criteria, stresses in thin wall members, and transformation of strain.
Class 13 Deflection of beams Derive a differential equation for beam deflection and determine deflection of beams.
Class 14 Columns Explain unstable phenomenon of columns, and obtain buckling loads.

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

To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.

### Textbook(s)

Handout will be distributed.

### Reference books, course materials, etc.

Mechanics of Materials: F. P. Beer, E. R. Jonston Jr., J.T. Dewolf and D. F. Mazurek, 7th edition, McGrawHill
Vector Mechanics for Engineers: F. P. Beer and E. R. Jonston Jr.著, McGrawHill

### Assessment criteria and methods

Assignment 50% Quiz in class 50%

### Related courses

• CVE.A202 ： Structural Mechanics I
• CVE.A301 ： Structural Mechanics II

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

Students must have successfully completed Fundamentals of Mechanics 1 (LAS.P101) or have equivalent knowledge.