hand book of mechanical

HANDBOOK
of

MECHANICAL DESIGN



'7S~
/

HANDBOOK
of

MECHANICAL DESIGN
BY

GEORGE

NORDENHOLT

F.

Editor of Product Engineering

JOSEPH KERR
Managing Editor

of Product Engineering

AND

JOHN SASSO
Associate Editor of Product Engineering

First Edition

Third Impression

McGRAW-HILL BOOK COMPANY,
NEW YORK AND LONDON
1942

Inc.


HANDBOOK OP MECHANICAL DESIGN
CksPYRIGHT, 1942, BY THE

McGraw-Hill Book Company,

Inc.

PRINTED IN THE UNITED STATES OF AMERICA
All rights reserved. This book, or
parts thereof,

may not

be reproduced

in any form without permission of
the publishers.

THE MAPLE PRESS COMPANY, YORK,

PA.


PREFACE
Many engineering departments, perhaps most, compile and keep up to date a
manual which may be called the standards book, reference book, engineering department standards, or which may be given some other name. Also, many design
In such books will be found a vast fund
engineers build their own book or manual.
of engineering data and many methods of design procedure not found in existing
handbooks.

When

Product Engineering was launched as a pubhcation to serve the design
was obvious to the editors that a great service could be rendered to the
profession by gathering and publishing data, information, and design procedures such
Thus, the first number of
as are contained in engineering department manuals.
Product Engineering in January, 1930, contained a reference-book sheet for design
Soon
calculations, a feature which has been continued in practically every number.
afterward, there was added to Product Engineering's editorial content another regular

engineers,

it

feature, a two-page spread illustrating standard constructions, possible variations

by

which to achieve a desired result, and similar design standards covering constructions,
drives, and controls.
It was soon found impossible to meet all the requests for additional copies of
reference-book sheets and design standards. The demand continued to increase and
numerous readers suggested that the material be compiled into book form and pubIt was in answer to this demand that the authors compiled this book.
lished.
Other than the major portion of the chapter on materials and a few other pages
that have been added to round out the treatment of certain subjects, all the material
in this book appeared in past numbers of Product Engineering, although some of it has
been condensed or re-edited. Very little of the material in this book can be found in
the conventional handbooks, for this Handbook of Mechanical Design contains practically no explanations of theoretical design.
It confines itself to practical design
methods and procedures that have been in use in engineering design departments.
The authors wiU welcome suggestions from users of this book and especially
desire to be notified of any errors.
We wish to make special acknowledgment of the material on typical designs
appearing in Chapters IV and VI, by Fred Firnhaber, now of Landis Tool Company;
the nomograms by Carl P. Nachod, vice-president of the Nachod & U. S. Signal Co.;
the standard procedure in the design of springs

by W. M.

Griffith of Atlas Imperial

Company; the spring charts by F. Franz; the methods for calculating
and other nomograms by Emory N. Kemler, now associate professor of
mechanical engineering at Purdue University; the nomograms for engineering calculations by M. G. Van Voorhis, now on the editorial staff of Product Engineering; and
to S. A. Kilpatrick and 0. J. Schaefer for their brilliant series of articles, which have
Diesel Engine

belt drives


PREFACE

vi

slightlj^ condensed form, on the design of formed thin-sheet aluminumAcknowledgment is also made here of data on properties of materials
contributed by the Alimiinum Company of America, United States Steel Corporation,
and the American Foundrymen's Association.
Other engineers whose contributions to Product Engineering have been incorporated in this book are H. M. Brayton, 0. E. Brown, E. Cowan, C. Donaldson, R. G. N.
Evans, C. H. Leis, A. D. McKenzie, G. A. Schwartz, A. M. Wasbauer, B. B. Ramey,

been included in

alloy sections.

Harper, H. M. Richardson, G. A. Ruehmling, T. H. Nelson, E. Touceda,
Rigby, R. S. Elberty, Jr., and G. Smiley.
J.

W.

George

F.

Nordenholt,

Joseph Kerr,

John Sasso.
New

York,

April, 1942.

W.

S.


CONTENTS
Pa.qe

Preface

v

CHAPTER

I

Charts and Tables for General Arithmetical Calculations

1

Arc length versus Central Angle. Chordal Height and Length of Chord. Length of Material for Bends.
Volumes in Tanks, Horizontal Round. Volumes in Tanks, Vertical Round. Volume,
Circular Segments.
Weight, and Cost. Weights of Cylindrical Pieces. Chart of Unit and Total Weights. Chart of Weights
and Volumes. Moment of Inertia of Prisms; Flywheels; Gears and Armatures. Radii of Gyration.
Transferring Moments of Inertia to Parallel Axis.
WR^ of Symmetrical bodies. Centrifugal Force.
Mean Cooling Temperature. Solution of
Forces in Toggle Joint. Linear Motion. Rotary Motion.
Ohm's Equations. Total Resistance of Parallel Circuits.

CHAPTER

II

Materials

33

Cast Irons. Alloy Cast Irons. Effect of Nickel and Chromium on Cast Iron.
Malleable Iron Castings. Cast Carbon Steels. High Alloy Cast Steels. Low Alloy Cast Steels. CorroIron-nickel-chromium Alloys. AlumiProperties of Stainless Steel.
sion and Heat-resistant Cast Steels.
num Base Alloys. Magnesium Base Alloys. Insulating Materials. Plastic Materials. Phenolic
Selection of Materials.

Laminated Molded Materials.

Steels for

Automotive Parts.

CHAPTER

III

Beams and Structures

71

Thin Aluminum Sheet

Sections.
Compression Members. Angles in Compression.
Shear Resisting Webs. Diagonal Tension Webs. Hollow
Box Sections Subjected to Torsion. Chart for Determining Bending Moments. Deflection of
Girders.
Variously Loaded Beams. Stresses in Cantilever Beams. Tensile Strength of Round Wires. Rectangular
Stress Calculations for

Shear Members.

Moments

Vertical

Stiffeners

for

of Inertia.

CHAPTER

IV

Latches, Locks and Fastenings

95

Locking Devices. Retaining and Locking Detents. Wire Locks and Snap Rings. Taper- Pin Applications.
Hinges and Pivots. Clamping Shoes and Plugs. Lock Bolts and Indexing Mechanisms. Machine
Clamps. Door and Cover Fastenings. Bolt Diameter, Load, and Stress.

CHAPTER V
Springs

121

Spring Wire Specifications. Design Stresses. Torsional Moduli. Allowable
Based on Endurance Limits. Natural Frequency. Formulas for Helical Springs. Permissible
Manufacturing Tolerances. Form for Design Calculations. Standard Drawings for Springs. Table of
Wire Gages and Diameters, with Their Squares, Cubes, and Fourth Powers. Inspection and Testing of

Designs of Helical Springs.

Stresses

Graphical Solution of Helical Spring Formulas. Helical Spring Charts for Specified Ratio of
Designs of Tension Spring Ends. Graphical Designs of Flat Cantilever Springs.
Graphical Designs of Semielliptic Laminated Springs.

Springs.

Loads and Lengths.

59376

,


CONTENTS

viil

Page

CHAPTER

VI

Power Transmission Elements and Mechanisms
Flexible Couplings.

151

Shaft Diameters for Torsion and Bending.

—

Shaft Diameters for Torsional Deflection.

Shaft Diameters for Lateral Deflection. Shaft Diameters A.S.M.E. Code. Two-bearing Shafts of
Uniform Strength. Stress in Rotating Disk. Velocity Chart for Gears and Pulleys. Flat-belt Length and
Flat-belt Speed-Horsepower Charts.
Belt Horsepower Charts. Flat-belt Horsepower
and V-belt Horsepower Charts. V-belt Lengths. Short-center Belt Drives. Chart for
Calculating Needle Bearings. Thrust Bearing Friction Moments. Bronze Bearing Alloys. Shaft Seals.
Gibs and Guides.
Roller-Bearing Seals. Sleeve-bearing Seals. Safety Gears. Shifting Mechanisms.
Cam Designs. Variable-speed Devices. Transport Mechanisms. Automatic Feed Hoppers. Glueapplying Mechanisms.

Pulley Diameter.
Charts.

Flat

CHAPTER

VII

Drwes and Controls

207

WR^. Analysis of Motor Load. Selection of Motor Type. Inquiry 'Form for Electric

Motors. Winding Connection Diagrams for Multispeed Motors. Electric Control Methods. Electrically
Operated Values. Automatic Timers. Trigger Switch Mountings. Thermostatic Mechanisms. Automatic Stops.
Significance of

CHAPTER

VIII

Design Data on Production Methods
Fusion

Welding.

Welding.
Die Casting.

Resistance

Permanent Mold Casting.

251
Flame Hardening. Centrifugal Casting.
Flame Cutting. Powdered Metal Pressings.

Furnace Brazing.
Forging.


HANDBOOK OF MECHANICAL DESIGN
CHAPTER

I

CHARTS AND TABLES
For General Arithmetical Calculations
The

charts and

nomograms

in this chapter include only those pertaining to

Nomograms,

general arithmetical calculations, as hsted below.
for use in the design of specific

machine elements or structures

and tables
be found in the

charts,

will

chapters devoted to the design of those elements or structures.

Moment

Len^jth

of Inertia, Radius of Gyration,

and

Page

Arc Length vs. Central Angle
Chordal Height and Length of Chord
Length of Material for Bends

WRPage

2

Prisms

16

3

Flywheels, Gears, and Armatures

17

4

Radii of Gyration

Transferring to Parallel Axis

17

WR-

19

Area

of

18

Symmetrical Bodies
Force

Circular Segments

8
Centrifugal

26

Forces in Toggle Joint

27

Volume
Tanks, Horizontal Round

Tanks, Vertical Round
Volume, Weight, and Cost

Force, Velocity,

9
10
11

and Acceleration

Linear Motion

28

Rotary Motion

29

Heat and Temperature

Mean

Weight

Cooling Temperature

,

CyUndrical Pieces

Unit and Total Weight

12
14

Solution of

Weight and Volume

15

Total Resistance of Parallel Circuits

30

Electrical

Ohm's Equations.

31

32


HANDBOOK OF MECHANICAL DESIGN
ARC LENGTH VERSUS CENTRAL ANGLE
(Angle of Bend, Length, and Radius)

Draw

a straight hne through the two

known

points.

The answer

will

at the intersection of this line with the third scale.

Example: For a

6-in. radius

and 45-deg. bend, length

of arc is 4.7 in.

be found


CHARTS AND TABLES
CHORDAL HEIGHT AND LENGTH OF CHORD

^vill be found
a straight line through the two known points. The answer
at the intersection of this line with the third scale.
height h of

Example: Length of chord is 3 in., and radius of circle is 4 in. The

Draw

the chord

is

0.29

in.


HANDBOOK OF MECHANICAL DESIGN
LENGTH OF MATERIAL FOR

90 -DEG.

BENDS

As shown in Fig. 1, when a sheet or flat bar is bent, the position of the neutral plane with respect to the outer and
For a sharp corner,
inner surfaces will depend on the ratio of the radius of bend to the thickness of the bar or sheet.
As the radius of the bend is
the neutral plane will lie one-third the distance from the inner to the outer surface.
This
increased, the neutral plane shifts until it reaches a position midway between the inner and outer surfaces.
factor should be taken into consideration when calculating the developed length of material required for formed pieces.
The table on the following pages gives the developed length of the material in the 90-deg. bend. The following
formulas were used to calculate the quantities given in the table, the radius of the bend being measured as the distance

from the center of curvature to the inner surface of the bend.
For a sharp corner and for any radius of bend up to T, the thickness
1
a 90-deg. bend will be
.

L =
2.

L

for

(«-D

For any radius of bend greater than 2T, the length

L =
3.

1.5708

of the sheet, the developed length

L

for a 90-deg.

bend

will

be

(r +
^^

1..5708

R=

For any radius of bend between IT and 2T, the

T= Stock thickness

Inside radius

value of L as given in the table was found by interpolation
The developed length L of the material in any bend
other than 90 deg. can be obtained from the following

H

^

-M h-

Neutral

1t-5*>2

irl

line

formulas:
1.

For a sharp corner or a radius up to T:
T

L =
2.

0.0175 (li

For a radius

L =

of

+ t) X
2T

degrees of bend

E

Sharp corner

R=Torless

or more:

5(S+|)

X

0.0175

R=iTto2T
Fig.

R= 2T or more

1.

degrees of bend

For double bends as shown

in Fig.

2, if fii

X = V2BiR, +Ri- B/2)
With Ri, Ri, and B known:
flo - B
fl,

""^ ^ =
—rT+rT
L = 0.0175(S, + R2)A
where A is in degrees and L is the developed

-|-

Ss

is

greater than B:

-t-

If

Ri

+

Y =B

Ri

is less

cosec

The value

of

than B, as in Fig.

A —

{Ri

X when B

+
is

fl2)(cosec

A —

cotan A)

greater than Ri

X =B
The

length.

3,

total developed length

L

cot

A

+

Ri

To

be
7S2)

(cosec

A -

cotan A)

+

0.0175(^1 4- R2)A

'

simplify the calculations, the table on this page gives the equations for X, Y, and the developed length for
common angles of bend. The table on following pages gives L for values of R and T for 90-deg. bends.

EQUATIONS FOR
Angle A,
deg.

+

required for the material in the straight section plus that in the two arcs will be

L = Y
various

will

-h {Ri

X, Y,

AND DEVELOPED LENGTHS


CHARTS AND TABLES
DEVELOPED LENGTH IN INCHES OF MATERIAL REQUIRED FOR

90-DEG.

BEND


6

HANDBOOK OF MECHANICAL DESIGN
DEVELOPED LENGTH IN INCHES OF MATERIAL REQUIRED FOR

90-DEG.

BEND

{Continued)


CHARTS AND TABLES
DEVELOPED LENGTH IN INCHES OF MATERIAL REQUIRED FOR

7
90-DEG.

BEND

(Continued)


HANDBOOK OF MECHANICAL DESIGN

8

AREAS OF CIRCULAR SEGMENTS
-50

-7000

-40
5,000

F-2
-

3,000

-

2,000

-30

-

1,000

-20

1^

500

1

0.9

rO.8

A=

-0.7

Note: The ang/e

0.01745 R^arc cos
is

-~

•300
- (R-H)Vh('2R-H)

-200

expressed in degrees
~—

100
10

0.5

0.5

-7

E-30

i-20

•0.4"

o

=-5

<.

10

c

-5
-0.3

=-3

'-2

-0.25

-2
-0.2
hO.5
-0.3
-0.2

-0.15

^0.1

:

h 0.05
0.03

0.1

•=-0.02

Dra'w a straight

line

through the two kno'wn points.

The answer

will

be found

at the intersection of this line with the third scale.

Example: For a
sq. in.

10-in. radius

and

H

=

4.0 in.,

H/R =

0.40

in.

Area

A =

46


CHARTS AND TABLES

VOLUMES

IN

HORIZONTAL ROUND TANKS WITH FLAT ENDS

F-30

/Turning

line

Notes: Shift decimal point on volume
scale two' points for a one-point

sliift

on

diameter scale; one point for a one-point
shift on length scale.

H

= 0.9 ft. H/D = 0.15. Join 0.15 on
Example: Tank is 6 ft. in diameter and 15 ft.' long.
scale with 6 on diameter scale.
From point of intersection with turning line, draw line to
15 ft. on the length scale.
The volume scale shows 300 gal. If D had been 0.6 ft.,
0.09 ft.,
and length the same, the answer would be 3.00 gal.

H/D

H

HANDBOOK OF MECHANICAL DESIGN

10

VOLUMES
10

IN VERTICAL

ROUND TANKS WITH FLAT BOTTOMS

r^'OOO

f-io

-9

^9
r4,000

-8

'-7

r- 3,000

-2,000

-6

r6
- 1,000
800

^5

-5
^600

r80
f-60

-2

40
•30

Draw a straight line through the two known
points.

-20

The answer

•^6

be found at the

In reading the answer on the volume scale,

decimal point on volume scale two places
for one-place shift on diameter scale, and
one place for one-place shift on height scale.
Example: Diameter of tank is 4 ft. Depth
of liquid is 2.5 ft.
Volume as read is 230 gal.
If diameter of tank is 0.4 ft. and depth 2.5 ft.,
shift

r-10

will

intersection of this line with the third scale.

volume

is

2.3 gal.


CHARTS AND TABLES
VOLUME, WEIGHT, AND COST CHART

11


12

HANDBOOK OF MECHANICAL DESIGN


CHARTS AND TABLES
WEIGHTS OF CYLINDRICAL
Diam-

PIECES,

POUNDS PER INCH OF LENGTH

13
(Continued)