Mechanics of Materials
 
 
Subject Code: EME3046
Aim of Subject: To further increase the students' knowledge in mechanics of materials.
Learning Outcome of Subject: At the completion of the subject, students should be able to :
  • Develop an understanding of how the theory of elasticity can be applied to model some mechanical and structural behaviors
  • Carry out two and three-dimensional stress and strain transformation
  • Apply various failure criteria to predict the behavior of materials under multiaxial stress states
  • Calculate the deflection of statically determinate and statically indeterminate structures using energy methods.
  • Determine the critical loading of columns with different end conditions before buckling takes place
  • Analyze the stress distribution of a prismatic bar under torsion.
  • Conduct, under supervision, fatigue testing and determine the endurance limit of various engineering materials
Programme Outcomes:
  • Ability to acquire and apply fundamental principles of science and engineering(50%)
  • Capability to communicate effectively(5%)
  • Acquisition of technical competence in specialised areas of engineering discipline(5%)
  • Ability to identify, formulate and model problems and find engineering solutions based on a systems approach(15%)
  • Ability to conduct investigation and research on engineering problems in a chosen field of study(10%)
  • Understanding of the importance of sustainability and cost-effectiveness in design and development of engineering solutions(10%)
  • Ability to work effectively as an individual, and as a member/leader in a team(5%)
Assessment Scheme:
  • Lab Experiments - work in groups, lab report writing, oral assessment at the end of lab (10%)
  • Tutorial / Assignment - group assignment,focus group discussion at tutorial,to enhance understanding of basic concepts in lecture(15%)
  • Test Quiz - written exam (15%)
  • Final Exam - written exam (60%)
Teaching and Learning Activities: 54 hours (lectures,tutorials and laboratory experiment)
Credit Hours: 3
Pre-Requisite: EME1066 Strength of Materials
References:
  • A. Boresi, R. Schmidt, “Advanced Mechanics of Materials,” 6th ed., John Wiley & Sons, Inc., 2003.
  • M. Vable, “Intermediate Mechanics of Materials, ”
  • Oxford University Press, 2008
  • A. C. Ugural and S. K. Fenster, “Advanced Strength and Applied Elasticity,” Prentice Hall, 2003.
  • F. Beer, "Mechanics of Materials",4th ed., McGraw-Hill, 2005.
  • R. C. Hibbeler, "Mechanics of Materials", 6th ed., Prentice Hall, 2005

Subject Contents

  • Theories of Stress and Strain

    • Definition and notation of stress at a point. Stress acting on arbitrary planes. Normal stress and shear stress on an oblique plane. Transformation of stress. Determination of principal stress and principal directions using the concept of stress invariants. Mohr’s circle in three dimensions. Differential equation of motion of a deformable body. Strain theory. Small displacement theory. Transformation of strain. Principal strains. Strain Compatibility relations. Strain Measurement and strain Rosettes.
     
  • Three-Dimensional Linear Theory of Elasticity

    • Elasticity and internal-energy density. Elasticity and complementary internal-energy density. A brief introduction to anisotropic elasticity. Linear isotropic elasticity. Strain-displacement relations for linear elastic isotropic materials. Strain-stress relations for linear elastic isotropic materials. Hooke’s law for linear elastic isotropic materials.
     
  • Two-Dimensional Linear Theory of Elasticity

    • Plane stress and plane strain problems. Airy stress function. Applications to Problems in rectangular and polar coordinates.
     
  • Inelastic Material Behavior

    • Nonlinear material response. Yield criteria: maximum Principal stress criterion, maximum principal strain criterion, strain-energy density criterion, maximum shear-stress (Tresca) criterion, distortional energy density (von-Mises) criterion. General yielding: Elastic-plastic bending, fully plastic moment.
     
  • Energy Method

    • Principle of Stationary Potential Energy. Castigliano’s theorem on deflections for linear load-deflection relations. Deflections of statically determinate structures: dummy load method and unit dummy load method. Deflections of statically indeterminate structures.
     
  • Torsion of Prismatic Bars

    • Saint Venant’s semi-inverse method. Prandtl’s membrane analogy. Torsion of narrow rectangular cross section. Torsion of sections comprised of thin rectangles. Torsion of hollow thin-walled sections. Torsion of multi-compartment thin-walled sections. Torsion of thin-walled sections with end restraints. Inelastic torsion.
     
  • Buckling of Columns

    • Critical load. Buckling of pin-ended columns. Columns with other end conditions. Classification of columns: short, intermediate and long. Eccentrically loaded columns. Design formulae
     

Laboratory

1. Buckling of Struts
2. Fatigue Testing