# Graphic statics

GRAPHIC STATICS

BY T. ALEXANDER,
PROFESSOR OF ENGINEERING, TRINITY COLLEGE, DUBLIN

AND

A. W. THOMSON,
PROFESSOR OF ENGINEERING, COLLEGE OF SCIENCE, POONA.

A graduated series of problems and practical examples, with numerous diagrams all drawn to scale.

LONDON; MACMILLAN AND CO., 1904

PREFACE.

In our "Elementary Applied Mechanics" much of the work is done by Graphic Methods; but for want of space, the subject Graphic Statics is not treated systematically. The following problems and applications are intended to form an introduction to our larger work; but as they are complete in themselves, they may be studied as a separate subject.

For many years Graphic Statics has formed an important part of the regular work done by the students who have attended our classes; we find the subject exceedingly useful, readily followed, and easily understood by all.

Many problems, for the solution of which the analytical methods are laborious and difficult to follow, are easily solved by drawing; and students have a better appreciation of many of these problems after they have solved them by graphic methods. The best results are often obtained by using analytical (and graphic methods on the same problem; part of the work being done by one method, part by the other. Frequently a large number of results are obtained by drawing; and the accuracy of the whole drawing may sometimes be tested by checking one of these results by calculation.

The authors have prepared a more advanced set of Graphical Exercises, drawn on a large scale, on sheets of quarter double elephant size: many of them in two colours. These exercises are nearly ready for publication.

CONTENTS

INTRODUCTION

PROBLEMS
Problem I. Given - A plane set of forces acting at a point. Find - The simplest equivalent set

Problem II. Given - A plane set of forces acting at a point. Find - A simpler equivalent set of two forces acting at the same point, whose lines of action are given

Problem III. Given - A plane parallel set of forces. Find - A balancing set of two forces whose lines of action are given

Problem IV. Given- A plane set consisting of a force and a couple. Find - The simplest equivalent set

Problem V. Given - A plane set of forces, for which the force polygon closes. Find - The simplest equivalent set

Problem VI. Given - A plane set of forces. Find an equivalent set of two forces; the line of action of one, and a point in the line of action of the other being given.

Problem VII. Given - A plane parallel set of forces. Find the simplest equivalent set

Problem VIII. Given - A plane parallel set of forces. Find - An equivalent set of two forces ; a point in the line of action of each being given

Problem IX. Given - A plane symmetrical set of equal forces at equal intervals apart. Find - The form of the link polygon

Problem X. Given a plane set of parallel forces. Find - The centre of the forces

Problem XI. Given - A plane area. Find - The centre of gravity of the area

Problem XII. Given - A plane set of parallel forces. Find - The moments of the forces about a given point

Problem XIII. Given - A plane set of parallel forces. Find - The moments of the forces about a given point

Problem XIV. Given - A plane set of parallel forces. Find - The moments of the forces about any point ^the centre of forces; and moments about the centre 16

Problem XV. Given - A beam supporting loads. Find - The supporting forces; the centre of gravity of the loads; and draw the bending moment diagram. 16

Problem XVI. Given - A cross section consisting of rectangles. Find - The neutral axis; geometrical moment; and moment of inertia

PRACTICAL APPLICATIONS.
Example I. King Post Truss, with symmetrical vertical loads
Example II. King Post Truss with unsymmetrical vertical loads
Example III. King Post Truss, distorted; with unsymmetrical vertical loads
Example V. Queen Post Truss with equal symmetrical vertical loads
Example VI. Queen Post Truss with irregular vertical loads
Example X. Warren Girder
Example XI. Flanged Girder with right angled bracing
Example XII. Bowstring Girder
Example XIII. Masonry Retaining Wall supporting water
Example XIV. Masonry Retaining Wall supporting earthwork
Example XV. Wrought Iron Plate Girder
Example XVI. Masonry Bridge. Arch ring for segmental arch with vertical loading
Example XVII. Masonry Bridge. Abutments, piers, and abutment

INTRODUCTION.

In the examples given in the following pages, a Force is represented by two lines; one, a line of indefinite length to represent the line of action of the force; the other, a line drawn parallel to it, whose length gives the magnitude of the force upon a scale which appears on the drawing. For accuracy, these lines should be drawn as thin as possible; the direction of the force should be indicated by an arrow head; and the point of the arrow should indicate the end of the line which represents the magnitude of the force.

A number of forces which act simultaneously upon a body is called a "set of forces;" and when the lines of action of these forces are all in one plane, they are called a "plane set of forces."

A plane set of forces cannot produce change of motion, or tendency to change of motion, normal to their plane. Two sets of forces which produce the same tendency to change of motion are called "equivalent sets." Of two equivalent sets of forces that which consists of the fewer number of forces is called the "simpler;" and of all equivalent sets, that which consists of the fewest forces is called the simplest equivalent set.

In some cases the simplest equivalent set consists of one force - the resultant force; in others, it consists of two forces, - the resultant couple.

In numbering and arranging the forces, we will take them in cyclic order; that is - the numbers will follow each other as the figures on a watch dial; this is frequently of much importance.

The diagrams given have all been drawn to a large scale and reduced  for accuracy of work, large scale drawings are essential.