Practical Geometry and Engineering Graphics: A Textbook for Engineering and Other Students

353 Pages·1971·17.28 MB·English

PRACTICAL GEOMETRY
AND ENGINEERING
GRAPHICS
by thesame author
.. The Dimensioning of Engineering Drawings"
.. Machine Drawing and Design"
..Perspective", etc., etc.
EIGHTH EDITION
PRACTICAL GEOMETRY
AND ENGINEERING
GRAPHICS
•
A TEXTBOOK FOR ENGINEERING AND
OTHER STUDENTS
by W. ABBOTT
C.M.G., O.B.E., Ph.D., B.Sc., M.I.Mech.E., M.R.I.
Formerly DirectorofStudies, Federation of British
Industries and H.M. StaffInspectorofEngineering,
Ministry ofEducation
This bookis availablein Portuguese,from Editora GertumCarneiro,
Rio de]aneif'o
•
Springer Science+Business Media, LLC
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ISBN978-0-216-89450-1 ISBN978-94-017-2742-6(eBook)
DOI 10.1007/978-94-017-2742-6
©
by W. ABBOTT
Originallypublishedby B1ackie& SonLimited in 1971.
C.M.G..OB.E..PhD..B.Sc..M.l.M.ch.E.•M.R.I
FirstAllanEdition 1961
•
MACHINE DRAWING AND DESIGN
A Textbook of Intermediate Standard for Engineering Students
Eighth Edition
•
THE DIMENSIONING OF ENGINEERING DRAWINGS
Thisisacompanionvolume to Machi~ Drawing mul Designand
deals panicuIarlywith the applicationoftolerances.
•
TECHNICAL DRAWING
A complete course for use in Secondary and TechnicaI Schools
•
PERSPECTIVE
A comprehensive wnrk for the architecr, artist and designer
S.B.N.216.89450•6
PREFACE
T
HIS BOOKIS INTENDEDTO PROVIDEACOURSEINPRACTICAL
Geometry for engineering students who have already received some
instruction in elementary plane geometry, graph plotting, and the use
of vectors. It also covers the requirements of Secondary School pupils
taking Practical Geometry at the Advanced Level.
The grouping adopted, in which Plane Geometry is dealt with in Part I, and
Solid or Descriptive Geometry in Part II, is artificial,and itis the intentionthat
the two parts should be read concurrently. The logical treatment of the subject
presents many difficulties and the sequence of the later chapters in both parts
is necessarily a compromise; as an illustration, certain of the more easy inter
sections and developments might with advantage be taken at an earlier stage
than thatindicated.
In Part I considerable space has been devoted to Engineering Graphics,
particularly to the applications of graphical integration. The use of graphical
methods of computation is fully justified in most engineering problems of a
practical nature-especially where analytical methods would prove laborious
-the results obtained being as accurate as the data warrant.
The scope of the course in Descriptive Geometry has been designed to be in
keeping with the relative importance of the subject in an engineering curri
culum; for, although its educational and practical values have long been recog
nized, the time allocated to its study is usually limited. The earlier chapters in
Part II have been arranged with special regard to the difficulties experienced
by students in dealing with three-dimensional geometry for the first time; with
these difficulties in view the problems of the straight line and plane have been
dealt with after the orthographic and isometric projection of solids, the students
being then more accustomed to think in space. In the treatment of the various
solids, grouping has been based upon identity of principle rather than simi
larity of form. A systematic use has been made of auxiliary projections in the
solution of problems, typical applications being given in Problems 220, 242, and
323; this powerful method does not seem to have been developed to the extent
that it deserves, and by its use many standard problems become merely exer
cises involving a knowledge of a few fundamental constructions. The numerous
pictorial viewsincluded are intended to aid visualization, and thestudentshould
be encouraged to rely upon this kind of sketchrather than to resort to models.
The subject-matter on each page is self-contained, and arranged so that the
text and corresponding diagrams are always adjacent to each other. To facili
tate cross reference a consistent notation has been used throughout and suffixes
only have been given to the lettering, thus obviating the difficulty of locating
a point al' among others marked al and a'.
3
PREFACE
4
In preparing the work the author has been guided by the syllabuses and
past examination papers of the various university and other Examinations
Boards. The examples included have been limited to about six hundred, and
bear directly on the text; most of them are original and of the appropriate
standard, and types having little but their difficulty to recommend them have
been excluded. The questions set by the examining bodies furnish therefore
a furthersupplyfrom whichthestudentmaydraw. Answers have been appended
to a large numberof theexamples; in the geometry portion manyof the answers
have been designed to serve simply as checks upon the accuracy of the con
structions involved.
The author's thanks are due to Mr. A. S. Ritchie, B.Sc., for kindly under
taking the reading of the draft and final proofs of the book, to Mr. F. F. P.
Bisacre, O.B.E., M.A., B.Sc., for advice and guidance during the preparation
of the book and its passage through the press, and to many other friends for
usefulcriticism.
The author will be grateful to receive notification of any errors, ambiguities,
orobscuritieswhich may haveescapednotice.
Seventh Edition. New material on velocity and acceleration diagrams has
been included, and various small improvements made.
W.A.
1963.
ABBREVIATIONS
The followingisa list ofthe abbreviations and symbols used herein:
St. line Straightline. 0" Circumference.
6 Triangle. Rad, Radius.
Parm Parallelogram. Diam. Diameter.
Pari Parallel. -l-ve Positive.
Perp. Perpendicular. -ve Negative.
Rt. L Rightangle. Approx. Approximately.
and otherobvious contractions.
The followingGreeklettersare used:
ex (alpha),f3 (beta), y (gamma), 8 (delta), 8 (theta),1:, a (sigma),'" (phi),
(pi),'" (psi), (omega).
1T (II
EDITOR'S NOTE ON METRIC WORKING
This book is mainly concerned with Ex. I. Take numerical values from fig.
geometry, and the constructions given I; scales m=4, h= 2
are true regardless of units. However, Ex. 2. Take
the exercises do involve drawing to to 2040 60 80 100 120 140 seconds
scaleand thestudentwill wantto do his so 22 98 241 402 536 634 707 metres
work in metric units. In the vast major Ans. 4'2 ra]«,- 0'055 m/s2
ity ofexamples the difficulty can be got Ex. 3, Take length as 2 m, moment
round by the following simple expedi (M)given by M = 4[2kN m
ent: Ex. 4.Take length as 4 m.
MkNm '3 2'4 8'2 19'4 38'0 65'9
Take I inch as 2 centimetres. lm '67 1'33 2'oo 2.673'334'00
All numerical data will then convert by
simply doubling the figure, and the Page 78
same will apply to the answers. The Ex. I. 6 em radius. Ans. 72 crrr', 254
drawings will be somewhat smaller em", 3'59 ern
than the author intended. (Students Ex, 2. Data, P, bar, 10 9 8
who possess larger-than-average draw V, m3/kg '194 '215 '243
ing-boardsmayconvertat 3centimetres P, 7 6 5 4'5 4'0 3'5
to the inch.) V, '277 '323 '388 '430 '486 '555
The above general rule will be pre P, 3'0 2'5 2'0
sumed and the exceptions to it are V, '648 '776 '970
listedasfollows:
Page 6 Expansion from 10 bar to 2 bar. Ans,
Ex. 4.Scale 100 mm »: 0'2 mm 312, 200 J. Stage pressures 5'90 and
Page 30 3"45 bar
Ex. 3. 2'00 m x 1'50 rn, scale 1:10 Ex. 3. Minor radius of cam 31'7 mm,
Page 50 major4I'3mm; form ofall acceleration
Ex. 2. Pitch circles 288 mm and 384 - time graph correct. Ans. I'83 m]«,
457 m/s2
mm dia., addendum 12mm, dedendum
13 rnm, tooth numbers 24 and 32
Page 80
Page 56
Ex. 2. Read metres for feet, answers in
Ex. I to 6. Take 2 ern as the unit secondsandmetres
Page 60
Ex. 1. Amplitudes 4'5 em and 3'5 em Page 82
Ex. 2. Amplitudes 3'5 em and 2'1 cm Ex. Ia. Accept data as given, convertto
Ex. 3. OQ =6 em, travel 9 em 51 units, give power in kilowatts. Ans.
Page 74 118o 1360 1380 II80 790.
Section 93. Read centimetre for inch Ex. lb. Use actual data, butdraw in SI
throughout units. Ans. 385 x 106J
Page 84 Ex. 5. Take form of loading as given,
Ex. 2. Work in inches span 10 m, ordinate scale I em = 10
kN/m, EI in N m", Ans. 3'35 X 1061
Page 86 EI m, '20 m rightofcentre
Problem 105. Initialvelocity 120ftls
Ex. 5. Accept data asgiven and express Page 106
answers in SI units. Ans. I'02 X 10-4 Ex. I. Take 3 ft. as I metre, ordinate
k m2/N, '49 X 10-4 scale I unit = 600 kN/m.Ans. 200 kN,
Ex. p. 80, NO.3. Convert data exactly, 13'3m, 2100kNm, 21'7m, 940kNm
then workin metres Ex. 2. Dimensions 30 m X 12m X 4'5
m, depth3m
Page 92
Ex. I. For pounds read newtons. Page 108
Ex. 2. Take 3 tons as 30 kN, 5 ft. as Ex. I. Read metres for feet, loads each
1'50 m, Ans. 49'1 and 59'8 kN. I kN
Ex.2-3.Anyunits
Page 94
Ex. I. For pounds read newtons, take Page IIO
I in. as2em. Ans. I I N, '21 N m Ex. I. Loads 40 kN and20 kN, scale I
Ex. 2. Side 2 em, forces in N. Ans. em = 5 kN. Ans. 10times given values
2'45N,+'29 N m Ex. 2. Span 16 m, rise 0·64 m, loads in
Ex. 3. Side 6 em, forces In N. Ans. newtons. Scale I em = 200 N. Ans.
5,14 N, 3,6 em; 33'5° in newtons
Page 96 Ex. 3. Take 3 ft. as I metre, loads 20
and 30 kN. Assume supports free to
All forces in N, distances In m, nu move laterally. Ans. in kN, 10 times
merical answers unaffected
values given
Page 98 Ex. 4.Take loadsas 3and 5kN
Ex. I and2.Take I in. as 2 em
Ex. 3.Takefeet asmetres Page II2
Ex. 1-4. Loads in kN. Ans. in kN.
Ex. 4. Convert all data at 3 ft. = I m,
I ton = 1000 kg, answers correspond. Page 114
Note, the answers given for the height Ex. I. Loads in N
of the c.g. are correct but must be Ex. 2. Span 13m, rise 0'975 m
treated with caution. For some stability
calculations it is necessary to place the Page II6
load at the point of the jib, regardless Ex. 1-2. ReadkN for tons
ofits actualheight
Page II8
Page 100 Length 10 m, load 200 kN. Ans. 250
Ex. 1-4. Forces in newtons, distances kN m, 75 kN
in metres, numericalanswersunaffected
Page 120
Page 102 Ex. I. Read kN for tons
Ex. 1-5. Lengths in metres, loads in
kN, numerical answers are then correct Page 122
Ex. I. Take elongations as being in
Page 104 centimetres,drawdiagramtwentytimes
Ex. 1-3. Any units full size
Ex. 4. Take form of loading graph as Ex. 2. Take data for SliP as being in
given, span 6 m, ordinate scale I GIll m/N X 10-6, load 40 kN.
5kN/m,EIinNrn".Ans. 267,000/EI m, Ans, x = '3 mm, Y = 1'3 mm. Hori
0'1 m to right of centre zontal force = 68 kN, deflection -Smrn
Page 124 Ex. 3.Take I inch as 2 cm. Ans. (I) D
Ex. I. Panel size 2 m, load 20 kN,f = 1,83, E '225 m/s. (2) D 2'26, E 1'13
80 MN/m2, E = 200GN/m2•Ans. 13'6 (3) D 2'14, E 3'28 m/s;9'92 rad/s
mm.
Page 146
Ex. 2. Panel size 3m, loads at 10kN = Ex. I. Take I inch as 2 ern. Ans, 47'3,
I tonf.Ans.19'2 mm. 41'52, 26,64, 7'68, -21'12, - 26,64,
Ex. 3. Panel size 3m,f top 80, bottom
- 28'32, -28'32 m/s2
100, vertical 60, inclined 80 MN/m2• Ex.3. Take I inch as 2ern, Ans. 36'72,
E = 200 GN/m2•Ans.49'Smm 26,88 m/s2
Page 136
Page 184
Ex. 1-10. For ft. read metres, for tons
Ex. 2. Take 3 feet as I metre. Scale I:
read kN, answers correspond
100. Ans. 6'5 m
Page 138
Page 192
Ex. I. Work in centimetres, converting
lengths at 2 em to I inch. Ans. twice Ex. 4. Take 3 feet as I metre. Scale I :
20
given values
Ex.2.Initialsteamspeed467 tti]«,blade Page 194
speed ISO m/s. Ans. (a) 330 mis, 135 Ex. I.Take3feet as I metre. Scale 1:10
m/s Page 296
Ex. 3. Dimensions OP 0'5 m.,OQ I m.
Example. Set off aerofoil shapes for
Ans. 25'4 m/s
root and tip, taking chord lengths of
Page 140 3'55 and 1'14 m, and anglesofincidence
Ex. I. Take I inch as 2 em, velocity of of S°and 3°as in fig. 3. Determine the
Q3 m/s. aerofoil shape on a plane three quarters
Ans.3'3 tn]«,55 rad/s, 23'4 rad/s. along tip to root