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.
Author(s): Lester W Schmerr
Publisher: CRC Pressr
Year: 2024
Language: English
Pages: 433
Cover
Half Title
Series Page
Title Page
Copyright Page
Contents
Preface
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
1.8.1 The Dot Product
1.8.2 Direction Cosines
1.9 Position Vectors
1.10 Problems
1.10.1 Review Problems
2. Moments and Couples
2.1 Moment of a Force about a Point
2.1.1 The Vector Cross Product
2.2 Couples
2.3 Moment of a Force about a Line
2.4 Problems
2.4.1 Review 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
3.6.1 Review 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
4.5.1 Review Problems
5. Trusses
5.1 The Method of Pins
5.1.1 Summary
5.2 Zero-Force Members
5.3 The Method of Sections
5.4 Space Trusses
5.5 Problems
5.5.1 Review Problems
6. Frames and Machines
6.1 Solving Equilibrium Problems - II
6.2 Problems
6.2.1 Review Problems
7. Centroids
7.1 Centroids of Volumes, Areas, and Lines
7.1.1 Integration with Strips
7.2 Composite Areas
7.3 Distributed Line Loads
7.4 Problems
7.4.1 Review Problems
7.5 Tables of Centroids
8. Beams
8.1 Internal Forces and Moments
8.2 Singularity Functions
8.3 Problems
8.3.1 Review 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
9.4.1 Review 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
10.5.1 Review Problems
11. Area Moments and Mass Moments of Inertia
11.1 Area Moments
11.2 Polar Area Moment and the Radius of Gyration
11.2.1 Polar Area Moment
11.2.2 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
11.7.1 Parallel Axis Theorem
11.7.2 Radius of Gyration
11.8 Problems
11.8.1 Review 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.4.1 Numerical Solution
A.4.2 Symbolic Solution in Terms of Numerical Variables
A.4.3 Symbolic Solution in Terms of Symbolic Variables
A.5 Element-by-Element Operations, Plotting, and Logical Vectors
A.5.1 Element-by-Element Operations
A.5.2 Plotting
A.5.3 Logical Vectors
A.5.4 Constants eps and inf
A.6 Functions and Scripts
A.7 Anonymous Functions
A.8 Symbolic Calculations
A.8.1 Symbolic Integration
A.8.2 Symbolic Differentiation
A.8.3 Substitution
B MATLAB® Files
Problem Answers
Index
