Engineering mechanics is a professional basic course. It provides a necessary foundation for learning about the subsequent advanced professional courses. And it can be directly applied to solve many engineering problems in the field of aerospace, civil engineering, mechanical engineering, energy and power, etc.
This course introduces the fundamental concepts of mechanics, for example, force/rigid body/equilibrium/friction, stress/strain, strength/rigidity etc. It studies the resultant and decomposition of forces, the equilibrium conditions and equilibrium equation of force system, the friction laws, ans so on. And then this module develops concepts of stresses and strains in basic deformations and how they may be designed to provent failure. It deals with the strength conditions and rigidity conditions of components under tension/compression, shear, torsion and bending. It provide students with a clear and thorough presentation of the physical behaviour of materials under load and then modeling this behaviour to develop the theory.Corresponding applications for real-life design tasks are finally discussed to get insight into basic mechanics-based material selection criteria.
I. General requirements of Statics are to understand the basic concepts, basic theory, and basic method to solve the equilibrium problem of a particle, and a rigid body and rigid body system.
Requirements of each part:
a. Familiar with various of common constraints of simple body system, and drawing the free body diagram.
b. Understanding the concepts and charactors and calculation of the force, moment and force couple.
c. Mastering the method of simplification of all kinds of force system, and the calculating method of principal vector and principal moment of general force system. Mastering force equilibrium condition and equilibrium equations of all kinds of coplanar force system, and skilled application of solving equilibrium problems of single body and simple body system.
d. Understanding the concept and characteristics of sliding friction, and mastering how to solve balance problem when considering sliding friction.
II.The general requirements of materials mechanics: be able to classify, summarize and abstract mechanical models from practical engineering problems; understand the basic concepts of strength, rigidity and stability of members through the force analysis of members; and then have the ability to carry out strength analysis and design of structures.
a. Understanding the derivation of tensile normal stress formula, mastering the strength conditions of tensile and compressive bars; Understanding the concepts of elastic modulus, Poisson's ratio, tensile stiffness and the phenomenon of stress concentration.
b. Mastering the practical calculations of shear and bearing of connecting members, and carrying out strength analysis with the strength conditions of tension (compression), shear and bearing for connecting structures.
c. Understanding the derivation of formulas of shear stress and angle of twist when the circular shaft is in torsion, and mastering the calculation of strength and rigidity of the circular shaft in torsion.
d. Understanding the concepts of bending and plane bending, mastering the drawing of shear and bending moment diagrams; knowing the concepts of pure bending and transverse bending, mastering the derivation of formulas of bending normal stress and shear stress of beams and the distribution of stresses. And designing beams with strength condition and rigidity condition.
Chapter1 : Axioms of Statics and Freebody Diagram
1.1 Basic conception in statics
1.2 Axioms of statics
1.3 Constraints and their reaction forces
1.4 Force analysis and force diagrams
Ch1 Free body diagram
Chapter 2 : Coplanar Fundamental Force Systems
2.1 The graphical method of composition and the equilibrium of a coplanar system of concurrent forces
2.2 The analytical method of composition and the equilibrium of a coplanar system of concurrent forces
2.3 Force couples
Ch2 Fundmental Force system
Chapter 3: General Coplanar Force System
3.1 Moment of a Force about a Point
3.2 Reduction and Resultants of General Coplanar Force Systems
3.3 Equilibrium of a general coplanar force system
Ch 3: General Coplanar Force System
Chapter 4 Equilibrium of a Body System
4.1 The concepts of statically determinate and statically indeterminate problems,the equilibrium of a body system
4.2Analysis of internal force of plane truss
Ch4 Equilibrium of a Body System
Chapter 5 Friction
5.1 Types of Friction
5.2 Theory of Sliding Friction
5.3 Equilibrium problems with friction
Ch5 Friction
Chapter 6 Introduction to Mechanics of Materials
6.1 Tasks of Mechanics of Materials and basic assumptions of deformable bodies
6.2 Some Concepts
Chapter 6 Introduction to Mechanics of Materials
Chapter 7 Axial Tension and Compression
7.1 Axial force and stress
7.2 Properties of mechanics of materials of axially loaded members
7.3 Strength condition
7.4 Deformation of axially loaded bars · Stress concentration
Chapter 7 Axial Tension and Compression
Chapter 8 Shear
8.1 Introduction
8.2 Strength Calculation of connecting members
8.3 Pure shear and Hooke’s Law in Shear
Chapter 8 Shear
Chapter 9 Torsion
9.1 Internal Force and Internal force diagram
9.2 Torsional shear stress of circular shafts
9.3 Torsional deformation · Strength condition and rigidity condition
Chapter 9 Torsion
Chapter 10 Internal Forces in Bending
10.1 Internal forces in Planar Bending
10.2 Drawing of shear force and bending moment diagrams
10.3 Relations among load, shear force and bending moment
Chapter 10 Internal Forces in Bending
Appendix A Moments of Areas
A.1 Static moment of an area and centroid
A.2 Moment of inertia of an area · Product of inertia of an area · Radius of gyration
A.3 Parallel-axis theorem
Appendix A Moments of Areas
Chapter 11 Stresses in Bending
11.1 Normal stress in pure bending
11.2 Extension of normal stress formula · strength condition
11.3 Shear stress in transvers bending · Strength condition
11.4 Design of beams
Chapter 11 Stresses in Bending
Chapter 12 Deflection of Beams
12.1 Differential equation of the deflection curve
12.2 Double integration method
12.3 Method of superposition
12.4 Rigidity condition and Design of beams
Chapter 12 Deflection of Beams
Advanced Mathematics,College Physics
Textbooks:
1. Zhang Juan, etc, Theoretical Mechanics 理论力学(英文版)第2版,Northwestern Polytechnical University Press, 2022.12
2. Zhang Yan, etc, Mechanics of Materials, Tsinghua Press, 2018.05
Reference Books:
1. Hibbler R C. Engineering Mechanics: Statics. 14th ed. Singapore: Pearson Prentice Hall, 2016
2. Zhi Xizhe,Theoretical Mechanics, Higher Education Press, 2017.05