Seely F.B. Analytical Mechanics for Engineers

B

^

132

3^3

GIFT

OF

Charles !.!.

Titus

UNIVERSITY

FARM

ANALYTICAL

MECHANICS

FOR ENGINEERS

BY

FRED

B.

SEELY,

M.S.

Professor

of

Theoretical

and

Applied

Mechanics

AND

NEWTON

E.

ENSIGN,

A.B.,

B.S.

Assistant

Professor of

Theoretical

and

Applied

Mechanics

University of

Illinois

TOTAL

ISSUE,

TEN

THOUSAND

NEW

YORK

JOHN

WILEY

&

SONS,

INC

LONDON:

CHAPMAN

&

HALL,

LIMITED

1921

UNIVERSITY OF

CALIFORNIA

LIBRARY

BRANCH

OF

THE

COLLEGE OF

AGRICULTURE

Copyright,

1921,

By

FRED

B.

SEELY

and

NEWTON

E.

ENSIGN

PRESS Of

BRAUNWORTH

& CO.

5/23

BOOK

MANUFACTURERS

BROOKLYN,

N.

Y,

PREFACE

THIS

book,

as

its

name

suggests,

presents

those

principles

of mechanics

that are believed

to be

essential

for the student

of

engineering.

Throughout

the book the

aim

has been

to

make

the

principles

of mechanics

stand

out

clearly

;

to

build them

up

as much

as

pos-

sible

from

common

experience

(the

student's

experience);

to

apply

the

principles

to concrete

problems

of

practical

value;

and to

emphasize

the

physical

rather

than

the

mathematical

interpretation

of the

principles.

Important

equations

are

printed

in bold-faced

type

and the

statements

of

the

more

important

principles

are

italicized.

The book

is divided

into three

parts;

namely,

Statics,

Kine-

matics,

and

Kinetics. Statics

is

presented

first because

of

its

simplicity

and its

direct

relation

to

the student's

experience.

However,

in the

first two

chapters

are

developed

certain

concepts

and

elementary

principles

that

are

fully

as

important

in

kinetics

as in

statics,

and the

authors

feel that it

is

essential

to a

satis-

factory grasp

of

mechanics,

as

a

whole,

that sufficient

time

and

care be taken

to cause these

elementary

concepts

and

principles

to

crystallize

in the student's

mind before the more

general

prin-

ciples

and

problems

are

studied.

The

equilibrium

of

the

various

types

of force

systems

are treated

both

by

the

algebraic

and

by

the

graphical

method.

A

large

number of

problems

involving

the

equilibrium

of

the

simpler

structures

and machines are

given,

and

figures

illustrating

the structures

and machines are

used

freely.

Although

kinematics as

herein

developed

is

mainly

a

prelim-

inary

to

kinetics,

the authors'

experience

indicates

that

the

kinematic

properties

of motion

must be isolated and

developed

with

care

if

they

are to be used with success

in the

study

of the

kinetics

of

the motion.

iii

iv

PREFACE

Both

kinematics

and kinetics have been

developed

with

regard

for

the

increasing

importance

of

dynamics

to

engineers.

The

geometric

and

physical

conceptions

and

interpretations

of

the

quantities

in

kinematics have been

emphasized

rather than

the

mathematical

conceptions.

A treatment of

acceleration is

given

which,

it is

hoped,

will

help

to

overcome some

of

the

difficulties

frequently

found

in

the

use of this

quantity.

The

treatment of

kinetics

has been restricted

to the

more

common

types

of

motion

found in

engineering practice,

but these motions have been

treated

more

fully

than

is usual

in

elementary

texts on mechanics. This

is

particularly

true of

plane

motion. D'Alembert's

principle

(involving

inertia

forces)

has been used for

each

type

of motion

as a second method

of

solution.

The

methods of

procedure

used

in

the

analysis

of kinetics

problems

are

strongly emphasized

both

in

the

general

discussions

and

in

the solutions

of

illustrative

problems.

Illustrative

problems

are

given

at the end

of

the

more

important

articles and

many problems

are offered for solution. Great

care

has been exercised

in

selecting problems

that are

of

practical

interest

and

yet

are

easily

comprehended

and are

free

from

unim-

portant

details

so that the

principles

used

in their solution

will

stand

out

clearly.

The answers to about

one-half

of the

problems

are

given.

Graphical

methods

of

representation

and

of solution have

been

used

frequently

in all three

parts

of the

book.

A

knowledge

of

elementary

calculus

is assumed

although

little

use

is made

of it

in

the first

four

chapters.

The

discussion of centroids

(Chapter

V)

is

developed

directly

from

the

principle

of

moments a

principle

given

much

emphasis

throughout

the book.

Several

special

topics

are discussed

in Section

3

of

Chapter

IX.

They may

be

omitted without

interfering

with the

continuity

of

the

book,

or

any

one

of the

topics

may

be studied

alone

without

studying

the whole

section.

Further,

if

it is desired

to

reduce

the

time

given

to

kinetics,

the

second

method

of

analysis

of the

motion

of rotation

or of

plane

motion

(which

employs

D'Alembert's

principle

and inertia

forces)

in

Section

2 of

Chapter

IX

may

be

omitted.

And,

in

general,

the last

part

of

the

material

in

any

section

or

chapter may

be omitted without

interfering

with

the

student's

progress

in the

first

part

of the next

section

or

chapter.