A course of study in building trade mathematics

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A COURSE OF STUDY IN BUILDING TRADE MATHEMATICS

A Project Presented, to the Faculty of the School of Education The University of Southern California

In Partial Fulfillment of the Requirements for the Degree Master of Science in Education

by Thomas Dee Parry February 1950

UMI Number: EP46009

Ail rights reserved IN F O R M A T IO N T O ALL U S E R S T h e quality of this reproduction is d ependent upon the quality of the copy submitted. In the unlikely event that the author did not send a com plete manuscript and there a re missing pages, these will be noted. Also, if material had to be rem oved, a note will indicate the deletion.

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T h is p r o je c t r e p o r t, w r it t e n u n d e r the d ir e c t io n o f the c a n d id a te ’s a d v is e r a n d a p p r o v e d by h im , has been presen ted to a n d acce p te d by the F a c u lt y o f the S c h o o l o f E d u c a t io n in p a r t i a l f u l f i l l m e n t o f the re q u ire m e n ts f o r the degree

o f M a s te r o f

Science in E d u c a tio n .

A d v is e r

Dean

ii TABLE OP CONTENTS CHAPTER 1.

PAGE

BUILDING PLANS:

HOW TO WORK PROM BLUEPRINTS . . . ♦ .

A*

Goals which you may achieve if you

MOTIVATION:

learn how to read blueprints • • • • • • B.

DIRECTIONS:

LINES:

.........

...............

SYMBOLS:

* .

1

How to construct according to the

principal kinds of lines on a blueprint 2.

1

Key points to guide you in reading

building plans . . . . • • • • 1*

1

...

1

How to build or install fixtures

properly according to symbols that pertain to the building trades • • • • • • • • . • • • 3.

CONVENTIONS:

How to build properly according

to indicated dimensions 4.

4

SCALE REPRESENTATION:

« . . . . » • • . • •

7

How to translate the

drawing into structures of the proper proportions 5.

• • • . . . . . • • • • . • • . • 1 2

SOURCES FOR THIS CHAPTER:

Where to get

further assistance • • • • • . « • . . . . • . C.

ACTIVITY ASSIGNMENTS:

Learning experiences to

help you read blueprints D.

EVALUATION:

..........

FOUNDATIONS:

15

Check-ups which may be applied to

your mastery of blueprint reading 2.

13

. . . . . . . .

15

HOW TO FORM AN ESTIMATE FOR

FOUNDATION W O R K ........................................21

iii CHAPTER A.

PACE MOTIVATION: Advantages of making good estimates for foundation work • • • • • • • • • •

B.

21

DIRECTIONS: Some helpful guides to follow in making a foundation-work survey 1.

EXCAVATION:

21

How to figure the amount of

piek and shovel work needed before laying the foundation 2*

FORMS:

• • • « • • • ............

21

How to determine the approximate

quantities of materials required for wooden forms • . . • ............ 3*

CONCRETE:

22

How to calculate the amounts of

cement, sand and rock needed 4.

COSTS:

. . • • . . « •

How to compute the cost of

foundation w o r k ................ 5.

SOURCES FOR THIS CHAPTER: further assistance

C.

26

ACTIVITY ASSIGNMENTS:

30

Where to get

• • • . . . •

...........

32

Some learning experiences

to enhance your skill in making a foundationwork survey • • • • • • « D.

........

. . . . . . .

EVALUATION: Check-ups which may be applied to your estimates of foundation work

5.

STRUCTURE: A.

32

33

HOW TO ESTIMATE F R A M I N G ................... 35

MOTIVATION: Rewards that come from being able to estimate framing 1 . ............

35

iv CHAPTER B«

PAGE DIRECTIONS:

Suggestions on how to figure the

amounts and cost of framing materials and labor • 1*

UNDERPINNINGS:

35

How to determine the

quantity of lumber needed for a sturdy foundation framework 2*

FLOORS:

35

How to figure the amount of

material needed for floor 3*

WALLS:

36

How to estimate wall framing .....................

lumber 4*

framing

CEILINGS;

41

How to compute the quantity of

lumber needed for the ceiling structure • • • 5.

ROOFS:

How to calculate the amount of I

.

44

needed for framing materials and labor . .

«

48

material required for the roof framework 6.

7.

COSTS:

How to figure the amount of money

SOURCES FOR THIS CHAPTER: further assistance

C.

44

ACTIVITY ASSIGNMENTS:

Where to get

. • • • • • • • • • • • •

50

Projects to perfect your

ability to estimate framing m a t e r i a l s ............. 50 D.

EVALUATION:

Ways in which your mastery of

framing estimating techniques may be checked 4«

FLOOR SURFACES:

. .

52

HOW TO FIGURE MATERIALS AND COST OF

FLOOR S U R F A C E S .......................

55

V

CHAPTER

PAGE

A. MOTIVATION:

Advantages of making accurate

computations for floor surfaces • • • • • • • • • B.

DIRECTIONS:

Guides in calculating materials

for floor surfaces

. . . . . . . . . .

1*

MEASUREMENT:

2.

FLOOR SURFACES:

3.

55



55

of common types of floor coverings required •

56

COSTS:

How to calculate floor areas

55

How to figure the amount

How to compute the expense of

finish flooring and labor . . . . . . . . . . 4.

SOURCES FOR THIS CHAPTER:

m e r e to get

further assistance C.

ACTIVITY ASSIGNMENTS:

63 Projects that will help

you in figuring floor surfaces D.

EVALUATION:

63

Methods which may be employed in

checking your computations for floor surfaces . . 5.

WALL COVERINGS:

MOTIVATION:

1 ........... 66

Outcomes of making good

computations for wall coverings • • • * • • • • • B.

DIRECTIONS:

Some

figuring the cost

LATHING:

How

66

pointers to help you in of materials and labor for

lathing and plastering 1.

64

HOW TO COMPUTE THE COST OF LABOR

AND MATERIALS FOR LATHING AND PLASTERING A.

60

. . . . « • • . • • • • .

66

to calculate the quantity of

materials needed as a base for plaster

...

66

Vi CHAPTER

PAGE 2.

PLASTERING:

How to figure the amount of

materials for plastering 3.

COSTS:

69

How to determine the material and

labor cost of lathing and plastering 4.

SOURCES FOR THIS CHAPTER: further assistance

C.

ACTIVITY ASSIGNMENTS:

. • • •

71

Where to get

. • •

. .

73

Work to do to help you.

in computing materials and labor cost for wall coverings D.

EVALUATION:

. . • • 73 An evaluation instrument which may

be employed in relation to your calculation of wall coverings 6.



73

ROOF COVERINGS:

HOW TO ESTIMATE ROOF COVERINGS . . .

A.

Rewards for being able to figure

MOTIVATION:

the amount and cost of roofing materials B.

DIRECTIONS:

• • • « 76

Steps to follow in calculating

quantities and costs of roof coverings 1.

MEASUREMENT: How to find roof areas

2.

ROOFING: How to estimate

• • • • • 76 . . . .

COSTS:

76

the amount of

materials needed 3.

76

77

How to figure the amount of money

you will have to pay for roofing materials and labor • • • . . ...................

82

vii CHAPTER

PAGE 4.

SOURCES FOR THIS CHAPTER: further assistance

C.

ACTIVITY ASSIGNMENTS:

Where to get

• • • • » • • • • • • • • Projects to help you to

become proficient in estimating roof coverings D.

PROTECTIVE COVERINGS:

........... 85

. . .......... . . .

,

.

88

DIRECTIONS: Practical suggestions on how to estimate painting and paper hanging • • • • • . . 1.

EXTERIOR WORK:

2.

INTERIOR WORK:

WALL PAPER:

the indoor areas

COSTS:

.

. . ♦ 92

How to determine the number of

rolls of wall paper required 4*

• . • . 88

How to calculate the amount

of paint to buy for 3.

88

How to figure the quantity

of paint needed to cover the outside

............... 94

How to estimate the cost of materials

and labor for painting and papering . . . . . 5.

SOURCES FOR THIS CHAPTER: further assistance

C.

88

MOTIVATION: Gains that accrue from accurate figuring of protective coverings

B.

85

HOW TO CALCULATE THE AMOUNT

OF PAINT AND WALL PAPER REQUIRED A.

.

EVALUATION: Check-ups which may be applied to your estimates of roof coverings

7,

84

95

Where to get •

97

compute the cost of painting and papering • • • •

97

ACTIVITY ASSIGNMENTS:

• • • • • • Projects for learning to

viii CHAPTER D.

PAGE EVALUATION:

An evaluation instrument for

checking your figuring for painting and wall papering



BUILDING TRADE MATHEMATICS COLLECTION:

93 A special reserve

shelf for use in building trade mathematics courses,

1G0

ix LIST OP TABLES TABLE I, II* III. IV. V. VI. VII.

PAGE

MATERIALS FOR ONE CUBIC YARD OP C O N C R E T E

*

29

SPACING CONSTANTS FOR JOISTS, STUDS, AND RAFTERS . .

38

CONSTANT TABLE FOR RAFTER LENGTHS

46

NAIL QUANTITIES

. . . . . . . . .

..................

49

APPROXIMATE TIME IN MAN-HOURS FOR F R A M I N G .......... 51 FLOORING DATA

................

58

LABOR HOURS REQUIRED FOR F L O O R I N G ................... 61

VIII.

MATERIALS PER 100 SQ. YD. OF PLASTER AND STUCCO

. .

70

IX.

LABOR HOURS REQUIRED FOR LATHING AND PLASTERING

. .

72

X. XI. XII. XIII. XIV.

CONSTANT TABLE FOR ROOF A R E A S ....................... 78 DATA ON ASPHALT SHINGLES

............ .

81

QUANTITIES OF INGREDIENTS FOR 100 GALLONS OF PAINT .

90

COVERING CAPACITY OF PAINTING M A T E R I A L S .............91 DATA FOR DETERMINING LABOR COSTS OF PAINTING . . . .

-96

X

LIST OP FIGURES FIGURE

PAGE

1.

LINE INDICATIONS

...................................

2.

ARCHITECTURAL SYMBOLS

3.

ARCHITECTURAL SYMBOLS. . . . . . . .

4.

SYMBOLS FOR FIXTURES

5.

SYMBOLS FOR FIXTURES

6.

C O N V E N T I O N S ............... .. .

7.

C O N V E N T I O N S ........ . . . . . . .............. . . . .

11

8.

ARCHITECTS SCALE

14

9.

FOUNDATION PLAN . . . . . . . . . . . . .

...............................

. . . . . .

5

................

............

...

6 8

.

............

2

.........

9 10

. . . . . . . . . . . ..........

16

10.

FLOOR P L A N ............................................ 17

11.

ELEVATION P L A N ...............................

12.

ELEVATION PLAN

13.

BUILDING DETAILS

14.

SECTION THROUGH CONCRETE FORM

15.

GEOMETRIC FIGURES

16.

.

18

...................... . . ..............

19

. . . . . . . .

20

................24 .

FLOOR FRAMING ...............

. . . . . . . . . . . .

27 37

17.

WALL F R A M I N G ............ ........................... 42

18.

ROOF F R A M I N G .......................................... 45

19.

TYPES OF LATH

20.

ROOF AND C O R N I C E ........ ........................... 79

...........

67

xi PREFACE This project was designed to present an integrated course of study in mathematics for the building trades.

The course

was planned as a part of the vocational training program of education for the secondary level.

The material in this

course may also be used in related shop mathematics classes of vocational schools, evening trade classes and apprentice­ ship classes. This syllabus was written primarily to meet the need for a course of instruction for students who plan to specialize in some branch of the building trade.

It is hoped that this

course will help the student to solve the mathematical prob­ lems frequently encountered in construction work.

Whether It

be in calculating quantities of materials to order or laying out framing details the general principles are set forth for the students use.

The student will be introduced to methods

of calculating areas, volumes, board feet, and cost of materials, and proportions of ingredients.

He will be given an over all

view of how to estimate materials and labor for the various trades.

He will also learn the basic arithmetic skills which

are required for the solution of the practical problems in­ volved.

The included information will also be helpful to the

home owner who desires to become familiar with the construction, repair, and upkeep of his house.

It will also help prospective

xii homeowners, to observe building operations intelligently and recognize good and poor building practices. With the experience which the student will receive in this course, it is believed that he will be able to make great­ er progress in his future employment. give him a more well rounded education.

It will also help to Finally it is be­

lieved that this type of course will aid the student in making vocational choices, because he will have an opportunity to see first hand some of the requirements of the several building trades.

1

CHAPTER 1. BUILDING PLANS HOW TO WORK PROM BLUEPRINTS A.

MOTIVATION;

Goals which you may achieve if you learn

how to read blueprints* 1*

SKILLED CRAFTSMAN:

Being able to follow exactly the

directions given on the blueprints will make you independent of other workmen and put you In the group of high-class tradesman# 2#

S.

BETTER INVESTMENTS:

Ability to use blueprints and

specifications will

help you to build or buy wisely#

BETTER BUILT HOMES:

Ability to read blueprints and

follow specifications will enable you to do a better building job. 4#

RAPID PROMOTIONS:

The ambitious young workman who

wants to become a skilled craftsman, or perhaps a foreman or contractor, must learn how to work from blueprints* 5.

EASE IN FINDING EMPLOYMENT:

An important qualification

of an efficient building tradesman is his ability to read and understand architectural drawings# B.

DIRECTIONS:

Key points to guide you in reading building

plans. 1#

LINES:

How to construct according to the principal

kinds of lines on a blueprint, a.

Use Figure I as a guide#

2

I.

B o r d e r L in e

Z.

M a i n O b j e c t .l i n e

3.

D im e n s io n

Line

4.

E x te n s io n

Line

------i

&L 1 ---------

A

5.

S e c tio n

6 .

o 'fM O O L S e c t io n

Lin

A

t __________________T

e

u n e

^

7. B roken Line 8.

In v i s i b l e

9.

Center

i Q.

Lin e Line

STAiR In d i c a t o r

E IO U R F l i n e

- W

!

X'":-::'-

- m —— >

Be able to recognize and interpret the principal kinds of lines* (1)

A border line is a heavy continuous line that outlines the drawing*

(2)

A main object line is a full unbroken line used to outline the main walls on plans*

(3)

A dimension line is a fine solid line, term­ inated by arrowheads and used to indicate distances between points or edges of the building.

The number in the break or top of

the dimension line gives the exact distance between these points* (4)

An extension line is a fine line that shows the extreme limits of a dimension*

It is the

line that the arrowheads of the dimension line touches• (5)

A symbol section line is light and generally solid.

Sometimes section lines, evenly spaced

are used to indicate the materials used. (6)

A broken line has a wavy break in it at inter­ vals and is used to show that parts have been left out or that the full length has not been drawn.

(7)

A dash line, or invisible line, is used to indicate hidden, or invisible parts of a

house.

These lines represent the outline of

parts which may be under the floor level, with­ in walls, or occur beyond or behind elevations# (8)

A center line is made up of alternating long and short dashes and is used to show the center of the axis of an object*

The center of a

round object is shown by two intersecting center lines. (9)

A section line is a light continuous line with an arrowhead at each end pointing in the direction in which the section is to be taken* This line tells you where the section line has been cut through the wall or building.

(10)

A stair indicator is a solid line with an arrowhead pointing the direction of the run of the stairs.

If given as ”up 10-R” it means

that there are 10 risers from floor to floor and that the stairs go up. SYMBOLS:

How to build or install materials and fictures

properly according to symbols that pertain to the building trades. a.

On a large job where many different materials are used, check very carefully with the symbol key. (See Figures 2 and 3.) (1)

You should learn the more common symbols

ATE

° 5 Y M 6 0 k S 0 f o R SECTfON

Ik I E Y A H o ?*

a oA a- A ■*■

« 17 » A <

=

8 " “

=

C o n c re te .

g

=

g

1's' 1 1>' *\ .I " *

(

Rough Lum ber

__

IX b H

~

F in is h

=

v m

R lA iS

L

u

m

b

e

Z E Z ssm s:

r

Concrete.

m

&

^xVvvwi/wv;^

m

f o c k s

F o rth

.h ________£

T^M'TTT i ‘\ i * . »

P /a s te r

=

};~ ; '.'

irjSu/ono

7560^2

n

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