Practical Mechanics and Strength of Materials
Charles Wilbur Leigh, B.s.
Professor Emeritus of Analytic Mechanics at Illinois Institute
Of Technology; Coauthor,“ Plane and
John Frederic Mangold, B.e., C.e.
Associate Professor of Mechanics at Illinois Institute
Of Technology; Licensed Structural Engineer
Preface to the Third Edition
Preface to the Second Edition
Chapter I. The Three Simple Stresses
Introduction – Force, Action, Mass – Unit Measure of Force
– Properties of a Force – Vectors and Scalars – External
and Internal Forces – Concentrated and Distributed Forces
– Resultant of Two Forces in the Same Straight Line –
Equilibrium – Action and Reaction – Tension and Compression Stress – Stress – Tensile and Root Area of Bolts – Shear
– Shear in a Bolt – Safe Working Stress – Ultimate Strength
– Selection of Safe Working Stress – Stresses in
Thin Pipes or Cylinders – Longitudinal Tension – Stresses
in Hollow Spheres – Pressure of Water in a Tank.
CHAPTER II. WELDED AND RIVETED JOINTS
– Riveted Joints – Stresses in a
– Single Shear – Double Shear – Bearing Stress
– Failure of Riveted Joints – Notation – Strength of Riveted
– Pitch and Back Pitch – Ultimate and Working
– Efficiencies – Net and Gross Areas – Riveted Joints
of Maximum Efficiency – Derivations – Practical Considerations
– Stress Relations – Working Stresses for Structural
CHAPTER III. MECHANICAL PROPERTIES OF MATERIALS 66
Basis of Design – Alloys – Elastic Properties of Steel –
Elongation Modulus of Elasticity – Elastic Limit – Selection
of Working Stress – Hooke’s Law – Poisson’s Ratio – Biaxial
– Temperature Stresses – Members Composed of
Two Materials – Actual Stress.
CHAPTER IV. RESULTANT AND EQUILIBRANT OF FORCES 84
– Types of Force Systems – Resultant – Equilibrium
– Principle of Concurrence – Methods of Solving –
Resultant of Two Forces Algebraically – Free Body –
Analysis of a Simple Structure – Components of a Force
– Rectangular Components ix of ,a Force – Inclined Plane
Resultant of More than Two Forces in a Plane
of More than Two Forces – Resultant of Concurrent Forces
by Summation – Equilibrium of Concurrent Forces –
Moments – Sign of Moments – The Moments of Concurrent
– Moments and Equilibrium – Design of Members
in Simple Structures – Resume of Methods.
CHAPTER V. – PARALLEL FORCES AND MOMENTS
Definitions and Illustrations – Resultant of Parallel Forces –
Resultant of More than Two Parallel Forces
– Couple –
CHAPTER VI. – STATIC AND KINETIC FRICTION
– Friction on an Inclined Plane – Force
Necessary to Move a Body on a Rough Plane – Least Force
– Cone of Friction – Wedge Action – Journal Friction –
Rolling Resistance – Jaekscrew.
– CONCURRENT, NONCOPLANAR FORCES
Resultant – Equilibrium – Condition for Equilibrium.
CHAPTER VIII. – NONCURRENT COPLANAR FORCES
– General Method – Graphical Method – Multipleforce Body – Hinge and Pin Reactions – Algebraic Solution –
CHAPTER IX. – FRAMED STRUCTURES, ROOF AND BRIDGE TRUSSES 197
– General Types – Definitions – Best Support for Loads – Snow and Dead Loads – Wind Loads –
Stresses in Members of a Roof Truss
– Stresses Due to Wind
Loads – King Post Trusses – Truss with Ceiling Loads – The
Equilibrium Polygon – Reactions – Fixed Ends – Wind-load
Stresses by Graphical Method – Fink Roof Truss.
– STABILITY AND CENTER OF GRAVITY
– Center of Gravity by Experiment and Balancing – Center of Gravity of an Area – Practical Applications –
Center of Gravity of Weights and Volumes – Areas and
Solids by Revolution – Stability of a Body – Stability against
CHAPTER XI. MOMENT OF INERTIA
Theory – Illustrations – Radius of Gyration – Transfer Formula – Principal Axes – Built Sections.
CHAPTER XII. – BEAMS AND BEAM DESIGN
Elements of Theory – Shear and Shear Diagrams – Bending
Moment Diagram – Maximum Bending Moments for Various Types of Beams – Bending Moment from the Area under
the Shear Diagram – Maximum Bending Moment Due to a
Load Increasing Uniformly to the Center of the Beam –
Moving Loads – Resisting Moment for a Rectangular Section
– Live Load and Moisture Effect – Nominal and Real Sizes
– Section Modulus – Strength of a Beam –
Illustrations – Bending in Oblique Planes – Simple Beams
with Load Increasing Uniformly from One End.
CHAPTER XIII. HORIZONTAL AND VERTICAL SHEAR
Horizontal Shear – Unit Horizontal and Vertical Shear at
Any Point in a Beam Are Equal – Formulas for Horizontal
Shear – Tension – or Compression Due to Shea
and Minimum Stresses-
– Shearing Stress in 1 Beams –
Shear in I Beams – Plate Girders.
CHAPTER XIV. DEFLECTION, TYPICAL CASES
Discussion – Radius of Curvature in Terms of Bending
Moment – Formulas for Deflection – Cantilever with a
Concentrated London the Free End
– Cantilever with a Load
Not at the End
– Cantilever with a Uniformly Distributed
Load – Simple Beam with a Concentrated Load at the Center
– Simple Beam with a Uniformly Distributed Load – Simple
Beam with a Load Not at the Center – Combined Loads –
Simple Beam with Equal Concentrated Loads at the Third
– Simple Beam with Equal Concentrated Loads at the
Quarter Points – Deflection Due to Oblique Loading.
CHAPTER XV. COMBINED STRESSES, SHORT COLUMNS 355
Direct and Bending Stresses – Derivation – Short Columns –
Eccentric Loads on Short Columns – Location of the True
– Circular Columns – Eccentric Riveted Connections
– The Middle Third in Dams – Shear Due to
Tension or Compression.
CHAPTER XVI. INDETERMINATE BEAMS, CONCRETE BEAMS 379
– Beam Fixed at One End and Supported at the
Other – Beam with Fixed Ends, Carrying a Uniformly
– Beam Resting on Three Supports
Equally Spaced – General Moment Equation – Continuous
– Three-moment Theorem – Theorem of Three MoXll CONTENTS
ments for Concentrated Loads – Computation of Reactions –
•Reinforced Concrete – Ideal Steel Ratio – Moment of Inertia
Method – T Beams – Shear and Diagonal Tension.
CHAPTER XVII. – METAL, TIMBER, AND CONCRETE COLUMNS 409
– Selecting a Column – Hound Columns –
Straight-line Formulas – Radius of Gyration – Cast-iron
– Alloy Columns – Il-section Columns – Plate and
Channel Columns – Rankine’s Formula – Derivation of Rankine’s Formula
– The Forest Products Laboratory Formula
– Reinforced Concrete Columns – Eccentric Loads on I <ong
– Compression Flange as a Column – Column
Action in the Web of an I Beam.
CHAPTER XVIII. – TORSION, SHAFTS AND COUPLINGS
Torsion – Shearing Stress in Terms of Torque – Angle of
Twist – Work – Tension Due to Shear – Combined Torsion
and Bending – Shaft Couplings.
APPENDIX TABLES 465
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Practical Mechanics and Strength of Materials