This text makes use of symbolic algebra and vector-matrix algebra to demonstrate a new approach to learning statics. Symbolic solutions are obtained, together with the types of solutions covered in other texts, so that students can see the advantages of this new approach.
This innovative text is an extension of second-generation vector Statics courses to a new, third-generation matrix-vector Statics course, a course that addresses deformable as well as rigid bodies and employs MATLAB®.
MATLAB® is used as a “calculator” whose built-in functions are used to solve statics problems. This text uses vectors and matrices to solve both statically determinate rigid body problems and statically indeterminate problems for deformable bodies.
The inclusion of statically indeterminate problems is unique to this text. It is made possible by using symbolic algebra and a new, simplified vector-matrix formulation that combines the equations of equilibrium, the homogeneous solutions to those equations, and a description of the flexibilities found in the deformable elements of a structure to solve directly for the unknown forces/moments.
1 Introduction to Statics and the Concept of Force
1.1 About This Book
1.2 Quantities and Units
1.3 Numerical Calculations
1.4 Forces and Vectors
1.5 Scalars, Vectors, and Matrices
1.6 Unit Vectors and Cartesian (Rectangular) Components
1.7 Oblique Components
1.8 The Dot Product and Direction Cosines
1.9 Position Vectors
1.10 Problems
2 Moments and Couples
2.1 Moment of a Force About a Point
2.2 Couples
2.3 Moment of a Force About a Line
2.4 Problems
3 Equivalent Systems and Resultants
3.1 Resultants of Two-dimensional Force Systems
3.2 Resultants of Three-dimensional Force Systems
3.3 Reduction to a Wrench
3.4 Resultants and the Center of Gravity
3.5 Resultants of Distributed Forces
3.6 Problems
4 Equilibrium
4.1 Free Body Diagrams
4.2 Reaction Forces at Supports
4.3 Solving Equilibrium Problems – I
4.4 Alternate Systems of Equilibrium Equations
4.5 Problems
5 Trusses
5.1 The Method of Pins
5.2 Zero Force Members
5.3 The Method of Sections
5.4 Space Trusses
5.5 Problems
6 Frames and Machines
6.1 Solving Equilibrium Problems – II
6.2 Problems
7 Centroids
7.1 Centroids of Volumes, Areas, and Lines
7.2 Composite Areas
7.3 Distributed Line Loads
7.4 Problems
7.5 Tables of Centroids
8 Beams
8.1 Internal Forces and Moments
8.2 Singularity Functions
8.3 Problems
9 Frictional Forces
9.1 Slipping and Tipping
9.2 Flat Belts or Ropes in Contact with Rough Surfaces
9.3 Wedges
9.4 Problems
10 Statically Indeterminate Structures
10.1 Solving a Statically Indeterminate Problem
10.2 A Matrix-Vector Force-based Method
10.3 Steps in the Force-based Method
10.4 Examples of the Force-based Method
10.5 Problems
11 Area Moments and Mass Moments of Inertia
11.1 Area Moments
11.2 Polar Area Moment and the Radius of Gyration
11.3 Composite Areas
11.4 Rotation of Coordinates
11.5 Principal Area Moments and Principal Axes
11.6 Area Moment Matrices
11.7 Mass Moments of Inertia
11.8 Problems
11.9 Tables of Mass Moments of Inertia and Area Moments
Appendices
A MATLAB® Overview
A.1 Constants, Operations, and Built-in Functions
A.2 Vectors
A.3 Matrices
A.4 Solutions of Simultaneous Linear Equations
A.5 Element-by-Element Operations, Plotting, and Logical Vectors
A.6 Functions and Scripts
A.7 Anonymous Functions
A.8 Symbolic Calculations
B MATLAB® Files
Problem Answers
Index
Biography
Lester W. Schmerr Jr. holds a PhD in Mechanics from the Illinois Institute of Technology and a BS in Aeronautics and Astronautics from MIT. He is Professor Emeritus at Iowa State University, where he taught and conducted research for four decades.
