1st Edition

# Engineering Statics with MATLAB®

By Lester W. Schmerr Jr. Copyright 2024
432 Pages 235 B/W Illustrations
by Chapman & Hall

432 Pages 235 B/W Illustrations
by Chapman & Hall

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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

1.2 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

7.4 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