Mechanics of Materials is a basic technical course for engineering major in colleges and universities, and it is a bridge to the basic and professional courses. Mechanics of Materials is a necessary knowledge for civil engineering, mechanical engineering, road and bridge engineering, aerospace engineering, material engineering and other disciplines. The aim of this course is to provide students with the basic concepts and essential knowledge of the strength, stiffness, and stability of the components in the engineering structure. And to cultivate students' ability to analyze and calculate mechanics in engineering design and to solve practical problems in engineering. The course provides the necessary theoretical basis for students to further study basic and professional courses in other subjects
The main contents of Mechanics of Material including: basic deformation of member, stress state analysis, strength theory, combined deformation, stability of compressive column, energy method, Statically indeterminate problems, dynamic load and alternating stress, etc.
Advanced Mathematics, Theoretical Mechanics
1. Introduction
1.1 The Tasks of Mechanics of Materials
1.2 Basic Concepts and Contents of Mechanics of Material
Unit Test of Chapter 1
2. Axial tension compression and shear
2.1 Internal Forces and Stresses of Axial Tension
2.2 Mechanical Properties of Plastic Materials in Tension
2.3 Mechanical Properties of Materials in Compression and Strength Condition
2.4 Deformation of Axial Tension and Compression
2.5 Statically Indeterminate Problems in Tension or Compression
2.6 Shearing
supplementary 1: Axial tensile experiment of low carbon steel
supplementary 2: Axial tensile experiment of cast iron
supplementary 3: Axial compression experiment of cast iron
Unit Test of Chapter 2
3. Torsion
3.1 Internal force of the Circular Shaft in Torsion
3.2 Stresses of the Circular Shaft in Torsion
3.3 Strength Condition and Stiffness Condition of the Circular Shaft in Torsion
Unit Test of Chapter 3
4. Geometric Properties of the Section
4.1 Geometric Properties of section 1
4.2 Geometric Properties of Section 2
Unit Test of Chapter 4
5. Internal force in Bending
5.1 Internal Force in Bending
5.2 Shear Force and Bending Moment Diagrams 1
5.3 Shear Force and Bending Moment Diagrams 2
5.4 Internal Force Diagrams of Continuous beam, Plane rigid Frame and Bending bar
Unit Test of Chapter 5
6. Stress in bending
6.1 Normal Stress in Bending
6.2 Shear Stress in Bending
6.3 Strength Conditions of Beam in Bending
Unit Test of Chapter 6
7. Deformation of Beam
7.1 Deformation of Beam and Approximately Differential Equation of the Deflection Curve
7.2 Deformation of Beam by Integration Method
7.3 Deformation of Beam by Superposition Method
7.4 Simple Statically Indeterminate Beams
Unit Test of Chapter 7
8.Stress State Analysis and Strength Theory
8.1 Introduction of Stress State
8.2 Analysis of Plane Stress—Analytical Method
8.3 Analysis of Plane Stress—Mohr’s Circle
8.4 Triaxial Stress State
8.5 Generalized Hooke’s Law
8.6 Strain Energy Density in Triaxial Stress State
8.7 Strength Theories
Unit Test of Chapter 8
9.Combined Deformation
9.1 Introduction of Combined Deformation
9.2 Skew Bending
9.3 Combination of Axial Loading and Bending
9.4 Eccentric Compression or Tension Core of Section
9.5 Combined Deformation of Bending and Torsion
Unit Test of Chapter 9
10.Stability of Compressive Columns
10.1 Introduction to Stability of Compressive Columns
10.2 Euler’s Formula of the Critical Pressure of Slender Compressive Columns
10.3 Application Range of Euler’s Formula · Empirical Formula
10.4 Stability Check of Compressive columns
10.5 Measures to Improve the Stability of Compressive Column
Unit Test of Chapter 10
11. Energy Method
11.1 Work Done by External Forces and Strain Energy
11.2 Complementary Energy Theorem
11.3 Castigliano’s Second Theorem
11.4 Principle of Virtual Work
11.5 Dummy-load method
11.6 Mohr Integral
11.7 Reciprocal theorem
Unit Test of Chapter 11
12.Statically Indeterminate problems
12.1 Introduction of Statically Indeterminate Structures
12.2 The Application of Castigliano’s Second Theorem in Solving Statically Indeterminate Problem
12.3 The Application of Mohr's Integral in Solving Statically Indeterminate Problems
12.4 Canonical Equation of the Force Method
12.5 The Application of Symmetric and Antisymmetric Properties
Unit Test of Chapter 12
13.Dynamic load
13.1 Introduction of Dynamic Load
13.2 Application of D'Alembert's Principle in Dynamic Load
13.3 Application of Energy Method in Impact Problem
Unit Test of Chapter 13
14. Alternative Stress
14.1 Alternative Stress and Fatigue Failure
Unit Test of Chapter 14
Reference
1. R. C. Hibbeler. Mechanics of Materials (8th edn). Pearson Prentice Hall: Upper Saddle River , 2010.
2. James M. Gere, Barry J. Goodno .Mechanics of Materials, SI Edition. Cengage Learning: Boston , 2012