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Mechanics of Materials - University of Chinese Academy of Sciences

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Mechanics of Materials

Course Title: Mechanics of Materials

Course Attribute: Specialized Elective Course

Hours/credits: 40 hours/2 credits                                 

Purpose and Requirements:

Through the study of this course the student should be able to:

(1) Understand the concept of stress, strain, stiffness, strength;

(2) Apply linear elastic material laws to calculate deformations of deformable bodies;

(3) Integrate deformable body concepts with static equilibrium to solve statically problems;

(4) Model simple bars and beams (axial loading, torsion, bending);

(5) Design a structural component including the concept of factor of safety;

(6) Interpret two dimensional stresses and strains;

(7) Calculate maximum normal/shear stresses and strains.

Course summary:

Chapter 1: Introduction (1 hour)

1-1 Task for the course of Mechanics of Materials

1-2 Basic assumptions for deformable bodies

1-3 External force and its types

1-4 Internal force, section method and concept of stress

1-5 Deformation and strain

1-6 Basic ways for beam deformation

Chapter 2: Tension, compression and shear (9 hours)

2-1Concepts and examples for axial tension and compression

2-2 Internal force and stress on the cross-section under axial tension and compression

2-3 Stress on an inclined plane for a straight bar under axial tension and compression

2-4 Mechanical properties of materials under tension

2-5 Mechanical properties of materials under compression

2-6Failure, factor of safety and strength calculation

2-7 Deformation under axial tension/compression

2-8 Strain energy under axial tension/compression

2-9 Thermal stress and initial stress after assembling

2-10Concept of stress concentration

Chapter 3: Torsion (5 hours)

3-1Concepts and examples of torsion

3-2 Calculation of torque and torque diagram under external couple moment

3-3Pure shear

3-4 Stress distribution in a circular rod under torsion

3-5 Deformation and twist angle in a circular rod under torsion

3-6 Concept of torsion in a non-circular bar

3-7 Free torsion in a thin-walled tube

Chapter4: Beam bending: internal force (4 hours)

4-1 Concepts and examples of bending

4-2 Simplification of bending beams

4-3 Shear force and bending moment

4-4 Equations and diagrams for shear force and bending moment

4-5 Relationship of external loading, shear force and bending moment

Chapter 5: Beam bending: internal stress (4 hours)

5-1 Pure bending

5-2 Normal stress under pure bending

5-3 Normal stress under nonuniform bending

5-4 Shear stress under bending

5-5 Basic assumptions for bending theory

5-6 Strategies for improving bending strength

Chapter 6: Beam bending: deflection and deformation (5 hours)

6-1 Problems of bending deformation in engineering applications

6-2 Differential equation for deflection curve

6-3 Calculation of bending deformation by integration method

6-4 Calculation of bending deformation by superposition method

6-5 Strategies for improving bending stiffness

Chapter 7: Analysis of stress and strain, Hooke's law and failure criteria

7-1 Concepts of stress state

7-2 Examples of plane-stress state and triaxial-stress state

7-3 Analysis of plane-stress state: analytic method

7-4 Analysis of plane-stress state: method using Mohr's circle

7-5 Triaxial-stress state

7-6 Components of displacement and strain

7-7 Analysis of plane-strain state

7-8 Generalized Hooke's law

7-9 Four common failure criteria

Chapter 8: Combined deformation (4 hours)

8-1 Combined deformation and superposition theory

8-2 Combined deformation by tension/compression and bending

8-3 Eccentric tension/compression and core of cross section

8-4 Combined deformation by torsion and bending

Text book: James M. Gere and Barry J. Goodno, Mechanics of Materials, seventh edition, Cengage learning

Grading: Homework & quiz (20%) + Midterm exam (30%) + Final exam (50%)