108 Mechanical and Structural Theory

For whom intended  This course is intended for individuals whose primary formal training is not in the field of mechanical or structural engineering. Mechanical and structural considerations are fundamental to almost every technical activity, and all technical personnel have to deal, at least to some extent, with some aspects of mechanical engineering. A basic understanding of mechanical principles is essential to better perform their main function.

Objectives  To help participants to understand basic mechanical and structural concepts and terminology. It is not an in-depth mechanical engineering course but rather a course aimed at individuals who require an intensive review of basic principals, without the assumption of any prior knowledge of the topic. The course is fast paced and as non-mathematical as possible.

Brief Course Description  The course covers basic concepts of mechanical theory, starting with basic mathematics and conversion factors. To fully comprehend sinusoidal and non-sinusoidal waveforms, a basic understanding of complex algebra is required. The instructor reviews this topic as it applies to mechanical technology.

The instructor next introduces the basics of mechanical and structural theory, such as measurement of mass, displacement, acceleration and velocity, before moving into somewhat greater depth on dynamics theory. Single and multiple degree-of-freedom systems are considered, in regard to spring stiffness, dynamic properties of different materials, natural frequency and damping.

The Rayleigh and Dunkerley methods of calculating the first natural frequency of systems are briefly considered, with examples. Forced vibration and loading effects are also included in the dynamics theory section.

Moving on to structural design fundamentals, the instructor addresses the concepts of stress and strain; moment of inertia and the torsional shape factor. Useful formulas are provided for calculating stiffness and stress, also tables for determining moments of inertia and torsional shape factors. The instructor discusses the dynamic characteristics of structural elements such as compression members, flanges and beams. Finally, the course provides useful tables and formulas for the calculation of beam stiffness and resonant frequency, as well as resonances of plates and columns.

Related Courses   TTi Course 310, Mechanical Design for Product Reliability, which is available as an OnDemand Complete Internet Course, contains all the theory contained in this course, plus advanced examples and exercises in applying the theory.

Diploma Programs This may be used as an optional course for any Specialist Diploma Program.

Prerequisites  There are no definite prerequisites. However, this course is aimed toward individuals involved in various technical fields. An understanding of basic algebra will be useful.

Text  Each student will receive 180 days access to the on-line electronic course workbook. Renewals and printed textbooks are available for an additional fee

Course Hours, Certificate and CEUs  Class hours/days for on-site courses can vary from 14-35 hours over 2-5 days as requested by our clients. Upon successful course completion, each participant receives a certificate of completion and one Continuing Education Unit (CEU) for every ten class hours.

Click for a printable course outline (pdf).

Course Outline

Chapter 1 - Review of Mathematics

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  • Math Reference
    • Fractions, Powers, Exponents and Roots
    • Mathematical symbols, Conversions
    • Calculator exponential notation
    • Useful Constants, Trigonometric ratios
    • Scientific and Engineering Notation
    • Greek Letter Symbols
  • Algebra
    • Constants and Variables, Equations, Terms
    • Proportionality
    • Exponential, Linear and Quadratic Equations
    • Graphs
  • Geometry and Trigonometry
    • Arcs and Circles, Radians, Angles, Chords
  • Vectors
    • Angular Frequency, Phase Difference, Critical Functions
    • Linear Coordinates of a Rotating Vector
  • Complex Algebra
    • Rectangular and Polar Coordinates, Vector in Complex Plane
    • Complex Number operations (Addition, Subtraction, Multiplication and Division)
  • Calculus
    • Differentiation, Curve Drawing in Differential Calculus
    • Integration; Calculating the area under a curve
    • Differential Equations

Chapter 2 - Introduction to Vibration

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  • Design and Testing for Vibration and Shock
  • Rotational Unbalance Example—Automobile engine
  • Vibration and Shock Examples
  • Natural Frequency (Resonance)
  • Forcing Frequency
  • Prolonged Excitation of Natural Frequency
  • Tacoma Narrows Bridge
  • Natural and Resonant Frequencies
  • Effects of Shock and Vibration
  • Dynamic Inputs
  • Fragility
  • Effect of Failures

Chapter 3 - Introduction to Mechanical Terms and Material Properties

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  • Laws of Motion
  • Weight, Mass and Gravity
  • Units
  • Specific Weight and Density
  • Definitions of Common Mechanical Terms
  • Friction and Wear
  • Work, Power
  • Energy
  • Engineering Materials: Metals
  • Stress and Strain
  • Definition of Stress
  • Shear Stress and Tensile Stress
  • Examples of Stress:
    • Simple Tension or Compression
    • Pure Shear
  • Strain
  • Shear Strain
  • Elasticity—Definitions and Laws
  • Stress-Strain Relationship
  • Tensile Strength
  • Non-linear Elastic and Anelastic Solid Material
  • Non-Elastic (or Plastic) Load-Extension (F/u) Curves
  • Torque (T)
  • Tangential Acceleration (at )
  • The Mass Moment of Inertia (IM)
  • Radius of Gyration (rho)
  • Mass Moments of Inertia
  • The Area Moment of Inertia (IA)
  • Relative Stiffness (k) of Structural Members
  • Shearing Torques/Twisting Torques
  • Torsional Stiffness of an Open Cross-Section

Chapter 4 - Application of Vibration Theory

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  • Principles of Analysis
  • Fundamentals of Dynamics
  • Stiffness
  • Mass
  • A Simple Dynamic System
  • Degrees of Freedom
  • Single-Degree-of-Freedom (SDoF)
  • Undamped Vibrations—Single Degree of Freedom Systems
  • Sinusoidal Waveform
  • SDoF—Sinusoidal Relationships
  • Relationship between Displacement, Velocity and Acceleration
  • Sinusoidal Relationships
  • Undamped Vibrations in SDoF Systems
  • Natural Frequency
  • Decaying Sinusoidal Vibration
  • Undamped MDoF System Vibration
  • Dimensionless Ratio Graph for 2DoF Systems
  • Complex Systems
  • Spring Stiffness, in Parallel and in Series
  • Multi-Degree-of-Freedom (MDoF) Modeling
  • Rayleigh’s Method
  • Dunkerley’s Method
  • Forced Vibration for SDoF System
  • Transmissibility
  • Plotting Permissibility vs. Frequency Ratio
  • Isolation

Chapter 5 - Materials and Beams

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  • Material Selection in Engineering Design
    • Overall Material Properties
    • Design-Limiting Material Properties
    • Deriving Application-Specific Material Properties
    • Properties of Materials
    • Dynamic Response
  • Simple Beam
  • Bending Moment
  • Elastic Deflection of a Simply Supported Beam (with center load)
  • Sandwich Structures
  • Bending Strengths
  • Structural Beams
  • Bending Stiffness of a Beam Kb
  • Simple Uniformly Loaded Beam
  • Finding Stiffness of a Composite Beam
  • Beam Instability—Twisting
  • Compression Member Instability
  • Instability of Flanges
  • Flange Buckling
  • Structure Buckling
  • Resonant Frequencies of Flanges

Chapter 6 - Frequency and Stiffness Considerations

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  • Designing for Stiffness vs. Strength
  • Frequency Oscillation of a Rod
  • Natural Frequency of a Simply Supported Beam
  • Natural Frequency of a Cantilever
  • Effective Mass
  • Effective Mass of a Beam: Example
  • Natural Frequency of Simply Supported Plate
  • Beam Formulas
  • Stiffness of Gussets—with End load
  • Effective Stiffness of Gusset
  • Beam Formulas
  • Plate Frequency Equation
  • Plate Frequency Parameters
  • Column Resonance
  • Axial Resonance
  • Example: Determining Stress in a Loaded Beam

Appendix A - Glossary of Symbols and Units

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Appendix B - Index of Equations

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Appendix C - Dynamic Force and Motion

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  • Weight, Specific Weight and Density
  • Relative Density or Specific Gravity
  • Common Units of Force—Comparison
  • SDoF — Sinusoidal Relationships
  • Calculating Peak X, V and A
  • Undamped Vibrations in Single Degree of Freedom Systems
  • Calculating Natural Frequency
  • Calculating Stiffness
  • Example—Damped Resonant System

Appendix D - Index of Graphs and Tables

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Award of Certificates for sucessful completion

Click for a printable course outline (pdf).

Revised 6/7/2018