Mechanical Science for Technicians

Contents

Preface


1 Principles of Stress-And-Strain Analysis

Classification of Materials

Relationship between Stress and Strain

Volumetric Strain

Relationship between Linear Strain and Volumetric Strain

Bulk Modulus of Elasticity

Relationship between The Elastic Constants E, G, Ky and V

Stresses in Thin-Walled Vessels

Effect of Internal Pressure on the Volume of Thin-Walled Vessels

Complementary Shear Stress

Shear Stress in Beams due to Bending

Complex Stress

Normal and Shear Stresses on Any Plane in an Element Subject to Normal Stresses Only

Normal and Shear Stresses on Any Plane in an Element Subject to Shear Stress Only

Normal and Shear Stresses on Any Plane in a General Two-Dimensional Stress System

Principal Planes and Principal Stresses

Mohr's Circle for Stress

Trigonometric Identities (Proof)


2 Second Moments of Area of Beam Sections

Second Moment of Area

'I' for Common Sections

The Parallel-Axis Theorem


3 Combined Direct and Bending Stresses

Direct Stress

Bending Stress

Values of I and ymax. for Common Sections

Combined Bending and Direct Stress

Core or 'Kern' of Section

The Position of the Neutral Axis

Worked Examples 4 Shear Force and Bending Moment

Introduction

Shear Force

Bending Moment

Relationship between Loading, Shear Force, and Bending Moment

Application of the Mathematical Relationship between Shear Force and Bending Moment to Solution of Problems


5 Slope and Deflection of Beams

Introduction

Elastic Equation for Bending

Sign Convention and Boundary Conditions

Applications of the Elastic Equation for Bending

Principle of Superposition

Macaulay's Method


6 Belt Friction

Power Transmission by Belt Drive

Ratio of Belt Tensions

Maximum Power Transmitted by a Belt

Vee-Belt Drives

Initial Tension in a Belt


7 Velocity Diagrams

Relative Velocities of Points on a Rigid Bar Rotating about One End

Relative Velocities of Points on a Rigid Bar Having Plane Motion

Relative Velocities of Points in a Slider-Crank Mechanism

Relative Velocities of Points in a Quadric Cycle Chain

Relative Velocities of Points in Combinations of Quadric Cycle Chains and Slider-Crank Mechanisms

Velocity Diagrams for Mechanisms Having Combined Sliding and Rotation


8 Flywheels and Turning-Moment Diagrams

Function of a Flywheel

The Energy in a Flywheel

Turning-Moment Diagrams

Coefficient of Fluctuation of Speed

Coefficient of Fluctuation of Energy

Fluctuation of Energy from Turning-Moment Diagrams


9 Oscillations

Periodic Time and Frequency

Displacement and Amplitude

Simple Harmonic Motion

Free Longitudinal Oscillations of a Mass on a Vertical Spring

Free Transverse Oscillation of a Mass on a Cantilever

Free Transverse Oscillation of a Single Mass on a Simply Supported Beam

Torsional Oscillations

Transverse Vibration of a Shaft Carrying a Uniformly Distributed Load Using the Energy or Rayleigh's Method

Transverse Vibration of a Beam Carrying Several Point Loads Using the Energy or Rayleigh's Method

Dunkerley's Method

Whirling of Shafts

Limiting Speeds


10 Balancing Rotating Masses

Static and Dynamic Balance

Balancing Masses Rotating in the Same Plane

Balancing of Masses Rotating in Different Planes

Dynamic Reactions at Bearings due to Out-of-Balance Forces

Index