Mechanics of Solid Materials

Course ID: Engi 4312, Offered in Spring, Enrollments: 90, Class hours: 3hr/wk

Major Topics

Introduction to Mechanics of Materials and Stress

  • Definition of mechanics; Different types of loads/forces; Review of reactions at supports/connections; Equations of forces/moments in equilibrium state
  • Internal loadings in solid materials for an external load
  • Concept of stress; Average normal stress and average shear stress
  • Allowable stress design for a solid material

Deformation and Strain in Solid Materials

  • Effects of an external force
  • Concept of deformation and strain
  • Concept of axial and shear strain

Mechanical Properties of Materials

  • The tension tests, the stress-strain diagram
  • Detail inspection of stress-strain diagram
  • Concept of Modulus of elasticity (Hook’s law), Yielding, Plastic Deformation, Strain Hardening, Necking
  • Ductile Materials vs. Brittle materials
  • Procedure for Determining Yield Stress for Materials with Non-linear Elastic Behaviors (e.g.; Metal, Plastic)
  • Concepts of Permanent set, Strain Energy, Strain Energy Density, Elastic Strain Energy, Modulus of Resilience, Modulus of Toughness, Poisson Ratio, Creep, Fatigue

Stress and Deformation in Materials under Normal Loading

  • Review of stress distribution and Hooke’s law
  • The Saint-Venant Principle
  • Estimating deformation of an axially loaded member (within the elastic region)
  • The Principle of Superposition
  • Statically indeterminate axially loaded member
  • How to analyze statically indeterminate axially loaded member
  • Concepts of Thermal Stress, Stress Concentration and Residual Stress

Effect of Torsional Forces in Structural Materials

  • Concept of torsional moment or torque
  • A brief overview of torsion test
  • Visualization of torsion force application or torsional effects
  • Understanding and estimation of effect (stress and strain) of torsional force on a circular shaft
  • Review of polar moment of inertia
  • Understanding shear stress distribution in a member and its effects; Relationship between power (rate of work) and torque
  • Estimation of angle of twist for a torsional force; Sign convention in torsion problem

Effect of Bending Loading 

  • Concept of bending/flexural moment
  • Visualization of bending/flexural effects
  • Effects of internal loadings in beams
  • Detail discussion on methods for determining shear and moment in beams: shear and moment functions method and graphical method
  • Understanding of bending deformation in a beam due to bending moment and equation for estimating bending deformation
  • Understanding of bending stress (flexure stress) and equation for bending stress (flexure stress)
  • Procedure for determining bending stress in a beam
  • Concept of unsymmetrical bending and determining bending stress when moment arbitrarily applied

Concepts and Applications of Transverse Shear Forces

  • Concept of transverse and longitudinal shear forces or shear stresses
  • Understanding shear force and shear stress in straight member
  • Visualization of transverse shear effects
  • Estimating the shear stress in the member at the point located a distance y from the neutral axis
  • What will be the shear stress at flange-web junction?
  • Shear stress distribution over the width t at the section
  • Procedure for estimating shear stress distribution
  • Concept of shear flow in a built-up member
  • Estimating spacing of fastener/tie

Effect of Combined Loadings

  • Understanding stresses in pressure vessels or cylinders
  • Estimating Hoop/Circumferential Stress in a thin-wall pressure vessel
  • Estimating Longitudinal Stress in a thin-wall pressure vessel
  • Estimating Circumferential and Longitudinal Stresses in a Spherical Vessel
  • Understanding concept of combined loadings, and the resultant stress from the combined loadings
  • Procedure for analysis to determine stress from combined loadings
  • Application of concepts