mechanical and metal trade handbook 01

8102019 Mechanical and Metal Trade Handbook 01

httpslidepdfcomreaderfullmechanical-and-metal-trade-handbook-01 120



Original title

Tabellenbuch Metall 45th edition 2011

Authors

Ulrich Fischer Dipl-Ing (FH) Reutlingen

Roland Gomeringer Dipl-Gwl Meszligstetten

Max Heinzler Dipl-Ing (FH) Wangen im Allgaumlu

Roland Kilgus Dipl-Gwl Neckartenzlingen

Friedrich Naumlher Dipl-Ing (FH) Balingen

Stefan Oesterle Dipl-Ing Amtzell

Heinz Paetzold Dipl-Ing (FH) Muumlhlacker

Andreas Stephan Dipl-Ing (FH) Marktoberdorf

Editor

Ulrich Fischer Reutlingen

Graphic design

Design office of Verlag Europa-Lehrmittel Ostfildern Germany

The publisher and its affiliates have taken care to collect the information given in this book to the best of their

ability However no responsibility is accepted by the publisher or any of its affiliates regarding its content or

any statement herein or omission there from which may result in any loss or damage to any party using the

data shown above Warranty claims against the authors or the publisher are excluded

Most recent editions of standards and other regulations govern their use

They can be ordered from Beuth Verlag GmbH Burggrafenstr 6 10787 Berlin Germany

The content of the chapter bdquoProgram structure of CNC machines according to PALldquo (page 412 to 424) complies

with the publications of the PAL Pruumlfungs- und Lehrmittelentwicklungsstelle (Institute for the development of

training and testing material) of the IHK Region Stuttgart (Chamber of Commerce and Industry of the Stuttgartregion)

English edition Mechanical and Metal Trades Handbook

3rd edition 2012

6 5 4 3 2 1

All printings of this edition may be used concurrently in the classroom since they are unchanged except for somecorrections to typographical errors and slight changes in standards

ISBN 13 978-3-8085-1914-1

Cover design includes a photograph from TESABrown amp Sharpe Renens Switzerland

All rights reserved This publication is protected under copyright law Any use other than those permitted by law

must be approved in writing by the publisher

copy 2012 by Verlag Europa-Lehrmittel Nourney Vollmer GmbH amp Co KG 42781 Haan-Gruiten Germanyhttpwwweuropa-lehrmittelde

Translation Eva Schwarz 76879 Ottersheim Germany wwwtechnische-uebersetzungen-eva-schwarzde

Typesetting Satz+Layout Werkstatt Kluth GmbH D-50374 Erftstadt Germany wwwslw-kluthde

Printed by M P Media-Print Informationstechnologie GmbH D-33100 Paderborn Germany



3

Preface

The Mechanical and Metal Trades Handbook is well-suited

for shop reference tooling machine building maintenance

and as a general book of knowledge It is also useful for ed-

ucational purposes especially in practical work or curricula

and continuing education programsTarget Groups

bull Industrial and trade mechanics

bull Tool amp die makers

bull Machinists

bull Millwrights

bull Draftspersons

bull Technical Instructors

bull Apprentices in above trade areas

bull Practitioners in trades and industry

bull Mechanical Engineering students

Notes for the user

The contents of this book include tables and formulae in

eight chapters including Tables of Contents Subject Index

and Standards Index

The tables contain the most important guidelines designs

types dimensions and standard values for their subject

areas

Units are not specified in the legends for the formulae if sev-

eral units are possible However the calculation examples

for each formula use those units normally applied in practice

The Table of Contents in the front of the book is expandedfurther at the beginning of each chapter in form of a partial

Table of Contents

The Subject Index at the end of the book (pages 435 ndash 444) is

extensive

The Standards Index (pages 425 ndash 434) lists all the current

standards and regulations cited in the book In many cases

previous standards are also listed to ease the transition from

older more familiar standards to new ones

Changes in the 3rd edition

In the present edition we have updated the cited standards

and restructured updated enhanced or added the follow-ing chapters in line with new developments in engineering

Acknowledgement

Special thanks to Alexander Huter Vocational TrainingSpecialist ndash Tool and Die Ontario for his input into the

English translation of this book His assistance has been

extremely valuable

November 2012 Authors and publisher

M1 Mathematics

9 ndash 28

P2 Physics

29 ndash 50

TD3 Technical

Drawing

51 ndash 110

MS4 Material

Science

111 ndash 200

ME5 Machine

Elements

201 ndash 268

PE6 Production

Engineering

269 ndash 366

A7 Automation and

Information Tech-

nology 367 ndash 424

S8 International Material

Comparison ChartStandards 425ndash 434

ndash Fundamentals of technical

mathematics

ndash Strength of materials

ndash Plastics

ndash Production management

ndash Forming

ndash Welding

ndash PAL programming system

for NC turning and NC

milling

ndash Steel types

ndash Material testing

ndash Machining processes

ndash Injection molding (new)

ndash GRAFCET





5Table of Contents

4 Materials Science (MS) 11141 Materials Material characteristics of solids 112 Material characteristics of liquids

and gases 113 Periodic table of the elements 114

42 Steels designation system Definition and classification of steel 116 Standardization of steel products 117 Designation system for steels 118

43 Steels steel types Overwiew of steel products 123 Unalloyed steels 126 Case hardened steels quenched amp

tempered steels 129 Nitriding steels free cutting steels 131 Tool steels stainless steels 132 Steels for bright steel products 137

44 Steels finished products Sheet and strip metal tubes 138

Profiles 142 Linear mass density and area mass

d e n s i t y 1 5 1

45 Heat treatment Iron-carbon phase diagram 152 Heat treatement of steels 153 Hardening of aluminium alloys 156

46 Cast iron materials Designation and material codes 157 Classification 158 Cast iron 159 Malleable cast iron cast steel 160

47 Foundry technology 1 6 148 Light alloys Overview of aluminum alloys 163 Wrought aluminum alloys 165 Aluminum profiles 168 Magnesium and titanium alloys 171

49 Heavy non-ferrous metals Overview and designation system 172 Copper and refined zinc alloys 174

410 Other metallic materials 176

411 Plastics Overview and designation 178 Thermoset plastics 181 Thermoplastics elastomers 182

Plastics processing testing of plastics 186

3 Technical Drawing (TD) 51

31 Graphs Cartesian coordinate system 52

Graph types 53

32 Basic geometric constructions Lines and angles 54

Tangents circular arcs 55 Inscribed circles ellipses 56

Cycloids involute curves parabolas 57

33 Elements of drawingFonts 58

Preferred numbers radii scales 59

Drawing layout bills of materials 60 Line types 62

34 Representation Projection methods 64 Views 66

Sectional views 68 Hatching 70

35 Dimensioning drawings Dimensioning lines dimension values 71

Dimensioning rules 72 Elements of drawing 73 Tolerance specifications 75 Types of dimensioning 76 Simplified presentation in drawings 78

36 Machine elements representation Gear types 79 Roller bearings 80 Seals 81 Retaining rings springs 82

37 Object elements Bosses object edges 83 Thread runouts thread undercuts 84 Threads screw joints 85 Center holes knurls undercuts 86

38 Welding and soldering Graphical symbols 88 Dimensioning examples 91

39 Surfaces Hardness specifications in drawings 92 Form deviations roughness 93 Surface testing surface indications 94

310 ISO tolerances and fits Fundamentals 98 Basic hole system basic shaft system 102 General tolerances 106 Roller bearing fits 106 Fit recommendations 107 Geometric tolerancing 108





7Table of Contents

81 International material comparisonchart 425

82 Index of cited standards and otherregulations 430

8 Material Chart Standards (S) 425 ndash 434

Subject Index 435 ndash 444

7 Automation and Information Technology (A) 367

71 Control engineering basic terminology

Basic terminology code letters symbols 368 Analog controllers 370 Discontinuous and digital controllers 371

Binary logic 372 Numbering systems 373 Information processing 374

72 Electrical circuits Circuit symbols 375 Designations in circuit plans 377 Circuit diagrams 378 Sensors 379 Safety precautions 380

73 GRAFCET Important basic terms 382 Steps transitions 383 Actions 384 Branchings 386

74 Programmable logical controllers PLC PLC programming languages overview 388 Ladder diagram (LD) 389 Instruction list (IL) 390 PLC programming languages

comparison 391 Programming example 392

75 Hydraulics pneumatics

Circuit symbols 393 Proportional valves 395 Circuit diagrams 396 Pneumatic control 397 Electro-pneumatic control 398 Electro-hydraulic control 399 Hydraulic fluids 400 Pneumatic cylinders 401

Hydraulic pumps 402 Tubes 403

76 Handling and robot systems

Coordinate systems and axes 404 Robot designs 405 Grippers job safety 406

77 CNC technology Coordinate axes 407 Program structure 408 Tool offset and cutter compensation 409 Program structure according to DIN 410 Program structure according to PAL 412 PAL functions for lathes 413 PAL cycles for lathes 414

PAL functions for milling machines 417 PAL cycles for milling machines 418

67 Separation by cutting Cutting force 325 Cutting tool 326

68 Forming Bending 330 Deep drawing 334

69 Injection molding Injection molding tools 338 Shrinkage cooling batching 341

610 Joining Welding processes 343 Weld preparation 345 Gas-shielded welding 346 Arc welding 348 Beam cutting 350 Gas cylinders identification 352

Brazing bonded joints 354

611 Workplace and environmental protection Safety colors 359 Warning signs safety signs 360 Sound and noise 366



8

Standards and other Regulations

Standardization and standards terms

Standardization is the systematic achievement of uniformity of material and non-material objects such as compo-nents calculation methods process flows and services for the benefit of the general public

Types of standards and regulations (selection)

Standards term Example Explanation

Standard DIN 7157 A standard is the published work of standardization e g the selection of particularfits in DIN 7157

Part DIN 30910-2 Standards can comprise several parts associated with each other The part num-bers are appended to the main standard number with hyphens DIN 30910-2describes sintered materials for filters for example whereas Part 3 and 4 deal withsintered materials for bearings and formed parts

Supplement DIN 743Suppl 1

A supplement contains information for a standard however no additional specifi-cations The supplement DIN 743 Suppl 1 for example contains applicationexamples of load capacity calculations for shafts and axles described in DIN 743

Draft E DIN 743(2008-10)

Draft standards are made available to the public for examination and comment-ing The planned new version of DIN 743 on load-bearing calculations of shaftsand axes for example has been published since October 2008 as Draft E DIN 743

Preliminary

standard

DIN V 66304

(1991-04)

A preliminary standard contains the results of standardization which have not

been released as a standard because of certain provisos DIN V 66304 for examplediscusses a format for exchange of standard part data for computer-aided design

Issue date DIN 76-1(2004-06)

Date of publication which is made public in the DIN publication guide this is thedate at which time the standard becomes valid DIN 76-1 which sets undercutsfor metric ISO threads has been valid since June 2004 for example

Type Abbreviation Explanation Purpose and contents

InternationalStandards(ISO standards)

ISO International Organization forStandardization Geneva (O and Sare reversed in the abbreviation)

Simplifies the international exchange ofgoods and services as well as cooperationin scientific technical and economic areas

EuropeanStandards

(EN standards)

EN European Committee for Standardi-zation (Comiteacute Europeacuteen de

Normalisation) Brussels

Technical harmonization and the associatedreduction of trade barriers for the advance-

ment of the European market and the coa-lescence of Europe

GermanStandards(DIN standards)

DIN Deutsches Institut fuumlr Normung eVBerlin (German Institute forStandardization)

National standardization facilitates rational-ization quality assurance environmentalprotection and common understanding ineconomics technology science manage-ment and public relations

DIN EN European standard for which theGerman version has attained thestatus of a German standard

DIN ISO German standard for which an inter-national standard has been adoptedwithout change

DIN EN ISO European standard for which aninternational standard has been

adopted unchanged and the Ger-man version has the status of a Ger-man standard

DIN VDE Printed publication of the VDEwhich has the status of a Germanstandard

VDI Guidelines VDI Verein Deutscher Ingenieure eVDuumlsseldorf (Association of GermanEngineers)

These guidelines give an account of the cur-rent state of the art in specific subject areasand contain for example concrete procedu-ral guidelines for the performing calculationsor designing processes in mechanical orelectrical engineering

VDE printedpublications

VDE Verband Deutscher ElektrotechnikereV Frankfurt (Association forElectrical Electronic amp InformationTechnologies)

DGQpublications DGQ Deutsche Gesellschaft fuumlr QualitaumlteV Frankfurt (German Society forQuality)

Recommendations in the area of qualitytechnology

REFA sheets REFA Association for Work Design Indus-trial Organization and CorporateDevelopment REFA eV Darmstadt

Recommendations in the area of produc-tion and work planning



9Table of Contents

1 Mathematics

M

P

TD

MS

ME

PE

A

S

Quantity SymbolUnit

Name Symbol

Lengths Œ meter m

11 Units of measurement

SI base quantities and base units 10 Derived quantities and their units 11

Non-SI units 12

12 Formulas

Formula symbols mathematical symbols 13 Formulas equations graphs 14

Transformation of formulas 15 Quantities and units 16 Calculation with quantities 17 Percentage and interest calculation 17

13 Angels and triangels

Types of angels sum of angels in a triangle 18 Theorem of intersecting lines 18 Functions of right triangles 19 Functions of oblique triangles 19

14 Lengths

Division of lengths 20Spring wire lengths 21

Rough lengths 21

15 Areas

Angular areas 22 Triangle polygon circle 23 Circular sector circular segment 24 Ellipse 24

16 Volume and surface area

Cube cylinder pyramid 25

Truncated pyramid cone truncated cone sphere 26 Volumes of composite solids 27

17 Mass

General calculations 27 Linear mass density 27 Area mass density 27

18 Centroids

Centroids of lines 28 Centroids of plane areas 28

sine = opposite side hypotenuse

cosine = adjacent side

hypotenuse

tangent = opposite side

adjacent side

xsx

y s

y

S1

S2

S

m inkg

m 1 m

d

A d h d

s = +p

p

middot middot middot middot

24

2

Surface area

AM = p middot d middot h

Lateral surface area



10 11 Units of measurement

M

P

D

S

E

E

A

Units of measurement

SI1) Base quantities and base units cf DIN 1301-1 (2010-10) -2 (1978-02) -3 (1979-10)

Base quantities derived quantities and their units

Length Area Volume Angle

Mechanics

Basequantity

Length Mass TimeElectriccurrent

Thermo-dynamic

temperature

Amount ofsubstance

Luminousintensity

Base

units meter

kilo-

gram second ampere kelvin mole candela

Unitsymbol

m

1) The units for measurement are defined in the International System of Units SI (Systegraveme International drsquoUniteacutes) Itis based on the seven basic units (SI units) from which other units are derived

kg s A K mol cd

Quantity

Symbol

Œ meter m 1 m = 10 dm = 100 cm = 1000 mm1 mm = 1000 microm1 km = 1000 m

1 inch = 254 mmIn aviation and nautical applicationsthe following applies1 international nautical mile = 1852 m

Unit

Name SymbolRelationship

RemarksExamples of application

Length

A S square meter

arehectare

m2

aha

1 m2 = 10 000 cm2

= 1 000 000 mm2

1 a = 100 m2

1 ha = 100 a = 10 000 m2

100 ha = 1 km2

Symbol S only for cross-sectionalareas

Are and hectare only for land

Area

V cubic meter

liter

m3

mdash L

1 m3 = 1000 dm3

= 1 000 000 cm3

1 mdash = 1 L = 1 dm3 = 10 d mdash =0001 m3

1 m mdash = 1 cm

3

Mostly for fluids and gases

Volume

a b g hellip radian

degrees

minutes

seconds

rad

deg

+

1 rad = 1 mm = 572957hellipdeg= 180deg p

1deg = p

rad = 60 180

1 = 1deg60 = 60+1+ = 1 60 = 1deg3600

1 rad is the angle formed by theintersection of a circle around thecenter of 1 m radius with an arc of 1m lengthIn technical calculations instead ofa = 33deg 17 276+ better use is a =33291deg

Planeangle(angle)

asymp steradian sr 1 sr = 1 m2 m2 An object whose extension measures1 rad in one direction and perpendicu-larly to this also 1 rad covers a solidangle of 1 sr

Solid angle

m kilogramgram

megagrammetric ton

kgg

Mgt

1 kg = 1000 g1 g = 1000 mg

1 metric t = 1000 kg = 1 Mg02 g = 1 ct

Mass in the sense of a scale result or aweight is a quantity of the type of mass(unit kg)

Mass for precious stones in carat (ct)

Mass

m kilogramper meter

kgm 1 kgm = 1 gmm For calculating the mass of bars pro-files pipes

Linear massdensity

m+ kilogramper squaremeter

kgm2 1 kgm2 = 01 gcm2 To calculate the mass of sheet metalArea massdensity

r kilogramper cubicmeter

kgm3 1000 kgm3 = 1 metric tm3 = 1 kgdm3

= 1 gcm3

= 1 gml

= 1 mgmm3

The density is a quantity independentof location

Density




M

P

TD

MS

ME

PE

A

S


J kilogram xsquaremeter

kg middot m2 The following applies for ahomogenous bodyJ = r middot r 2 middot V

The moment of inertia (2nd momentof mass) is dependent upon the totalmass of the body as well as its formand the position of the axis of rotation

Momentof inertia 2ndMoment ofmass

Quantities and Units (continued)

Mechanics

F

F G G

newton N1 N = 1

kg middot m= 1

J s2 m

1 MN = 103 kN = 1 000 000 N

The force 1 N effects a change invelocity of 1 ms in 1 s in a 1 kg mass

Force

Weight

M M bT

newton xmeter

N middot m1 N middot m = 1

kg middot m2

s21 N middot m is the moment that a force of1 N effects with a lever arm of 1 m

TorqueBending momTorsionalmom

p kilogram xmeter

per second

kgmiddot ms 1 kg middot ms = 1 N middot s The momentum is the product of themass times velocity It has the direc-

tion of the velocity

Momentum

p

s t

pascal

newtonper squaremillimeter

Pa

Nmm2

1 Pa = 1 Nm2 = 001 mbar1 bar = 100 000 Nm2

= 10 Ncm2 = 105 Pa1 mbar = 1 hPa1 Nmm2 = 10 bar = 1 MNm2

= 1 MPa1 daNcm2 = 01 Nmm2

Pressure refers to the force per unitarea For gage pressure the symbol p g is used (DIN 1314)

1 bar = 145 psi (pounds per squareinch )

Pressure

Mechanicalstress

I meter to thefourth powercentimeterto the fourthpower

m4

cm4

1 m4 = 100 000 000 cm4 Previously Geometrical moment ofinertia

Secondmoment ofarea

E W joule J 1 J = 1 Nmiddot m = 1 Wmiddot s = 1 kgmiddot m2 s2

Joule for all forms of energy kWmiddot hpreferred for electrical energy

Energy WorkQuantity ofheat

PG

watt W 1 W = 1 Js = 1 N middot ms = 1 V middot A = 1 m2 middot kgs3

Power describes the work which isachieved within a specific time

PowerHeat flux

Time

t seconds minuteshoursdayyear

sminhda

1 min = 60 s1 h = 60 min = 3600 s1 d = 24 h = 86 400 s

3 h means a time span (3 hrs)3h means a point in time (3 orsquoclock)If points in time are written in mixedform eg 3h24m10s the symbol mincan be shortened to m

Time Time spanDuration

f v hertz Hz 1 Hz = 1s 1 Hz Dagger 1 cycle in 1 secondFrequency

n 1 per second

1 per minute

1s

1min

1s = 60min = 60 minndash1

1min = 1 minndash1 = 1

60 s

The number of revolutions per unit oftime gives the revolution frequencyalso called rpm

RotationalspeedRotationalfrequency

v meters persecond

meters perminute

kilometers perhour

ms

mmin

kmh

1 ms = 60 mmin= 36 kmh

1 mmin =1 m

60 s

1 kmh =1 m

36 s

Nautical velocity in knots (kn)

1 kn = 1852 kmh

miles per hour = 1 mileh = 1 mph1 mph = 160934 kmh

Velocity

w 1 per second

radians persecond

1s

rads

w = 2 p middot n For a rpm of n = 2s the angular

velocity w = 4 p s

Angular-

velocity

a g meters persecondsquared

ms21 ms2 =

1 ms 1 s

Symbol g only for acceleration due togravity

g = 981 ms2 fi 10 ms2

Acceleration

QuantitySym-bol

Unit






M

P

D

S

E

E

A

Electricity and Magnetism

QuantitySym-bol

Unit

NameRelationship



I

E

R

G

amperevolt

ohm

siemens

AV

O

S

1 V = 1 W1 A = 1 JC

1 O = 1 V1 A

1 S = 1 A1 V = 1 O

The motion of an electrical charge iscalled current The electromotive forceis equal to the potential difference be-tween two points in an electric field Thereciprocal of the electrical resistance iscalled the electrical conductivity

Frequency of public electric utilityEU 50 Hz USACanada 60 Hz

Electric currentElectromotiveforceElectricalresistance

Electricalconductance

r

g k

ohm xmeter

siemensper meter

O middotm

Sm

10ndash6 O middot m = 1 O middot mm2 m r

k= 1 2

in mm

m

Ω middot

kr

= 1

2in

m

mmΩ middot

Specificresistance

Conductivity

f hertz Hz 1 Hz = 1s1000 Hz = 1 kHz

Frequency

In atomic and nuclear physics the uniteV (electron volt) is used

W joule J 1 J = 1 W middot s = 1 N middot m1 kW middot h = 36 MJ1 W middot h = 36 kJ

Electrical energy

The angle between current and voltagein inductive or capacitive load

j ndash ndash for alternating current

cos j = P

U middot I

Phasedifference

In electrical power engineeringApparent power S in V middot A

P watt W 1 W = 1 Js = 1 Nmiddotms = 1 V middot A

Power Effective power

E F

Q C

Q

U Q t = = = middotI

E Q C L

volts per metercoulombfarad

henry

VmCFH

1 C = 1 A middot 1 s 1 A middot h = 36 kC1 F = 1 CV1 H = 1 V middot sA

Elect field strength

Elect chargeElect capacitanceinductance

Quantities and units (continued)


QuantitySym-bol

Unit

NameRelationship


Sym-bol

Non-SI units

T Q

t h

kelvin

degreesCelsius

K

degC

0 K = ndash 27315 degC

0 degC = 27315 K0 degC = 32 degF0 degF = ndash 1777 degC

Kelvin (K) and degrees Celsius (degC) areused for temperatures and tempera-ture differencest = T ndash T 0 T 0 = 27315 Kdegrees Fahrenheit (degF) 18 degF = 1 degC

Thermo-

dynamic

temperature

Celsiustemperature

Q joule J 1 J = 1 W middot s = 1 N middot m1 kW middot h = 3 600 000 J = 36 MJ

1 kcal Dagger 41868 kJQuantity ofheat

H u joule per

kilogramJoule percubic meter

Jkg

Jm3

1 MJkg = 1 000 000 Jkg

1 MJm3 = 1 000 000 Jm3

Thermal energy released per kg fuel

minus the heat of vaporization of thewater vapor contained in the exhaustgases

Net calorific

value

Length Area Volume Mass Energy Power

1 inch (in) = 254 mm

1 foot (ft) = 03048 m

1 yard(yd) = 09144 m

1 nautical

mile = 1852 km1 mile = 16093 km

1 sqin = 6452 cm2

1 sqft = 929 dm2

1 sqyd = 08361 m2

1 acre = 4046856m2

Pressure

1 bar = 145poundin2

1 Nmm2 = 145038poundin2

1 cuin = 1639 cm3

1 cuft = 2832 dm3

1 cuyd = 7646 dm3

1 gallon1 (US) = 3785 mdash

1 gallon1 (UK) = 4546 mdash

1 barrel = 1588 mdash

1 oz = 2835 g

1 lb = 4536 g

1 t = 1000 kg

1 shortton = 9072 kg

1 Karat = 02 g

1 poundin3 = 2768gcm3

1 PSh = 0735 kWh

1 PS = 735 W

1 kcal = 41868 Ws

1 kcal = 1166 Wh

1 kpms = 9807 W

1 Btu = 1055 Ws

1 hp = 7457 W

Sym-bol



1312 Formulas

M

P

TD

MS

ME

PE

A

S

FormulaMeaning

symbol

Œ Length

w Width

h Height

s Linear distance

r R Radius

d D Diameter

A S Area Cross-sectional area

V Volume

a b g Planar angle

W Solid angle

l Wave length

FormulaMeaning

symbol

FormulaMeaning

symbol

Formula symbols Mathematical symbols

Formula symbols cf DIN 1304-1 (1994-03)


t Time Duration

T Cycle duration

n Revolution frequency

Speed

f v Frequency

v u Velocity

w Angular velocity

a Acceleration

g Gravitational acceleration

a Angular acceleration

Qmiddot

V q v Volumetric flow rate

Time

Q Electric charge Quantity ofelectricity

E Electromotive force C Capacitance I Electric current

L Inductance R Resistance r Specific resistance g k Electrical conductivity

X Reactance Z Impedance j Phase difference N Number of turns

Electricity

T Q Thermodynamictemperature

DT Dt Dh Temperature difference t h Celsius temperature

a mdash a Coefficient of linearexpansion

Q Heat Quantity of heat l Thermal conductivity a Heat transition coefficient k Heat transmission

coefficient

G middotQ Heat flow a Thermal diffusivity c Specific heat H net Net calorific value

Heat

E Illuminance f Focal length n Refractive index

I Luminous intensity Q W Radiant energy

Light Electromagnetic radiation

p Acoustic pressurec Acoustic velocity

fi approx equals aroundabout

Dagger equivalent to hellip and so on etc 6 infinity

= equal to Iuml not equal to ==

def is equal to by definition lt less than

permil less than or equal to gt greater than

rsaquo greater than or equal to + plus

ndash minus middot times multiplied by ndash divide over divided by per to S sigma (summation)

proportional an

a to the n-th power the n-th

power of a 0 3

square root of

n0 3 n-th root of

aeligxaelig absolute value of x o perpendicular to oslash is parallel to parallel in the same direction

ordm parallel in the opposite direction angle

trade triangle 9 congruent to

Dx delta x (difference betweentwo values)

percent of a hundred permil per mil of a thousand

log logarithm (general)

lg common logarithm

ln natural logarithm

e Euler number (e = 2718281hellip)

sin sine cos cosine tan tangent cot cotangent

() [] parentheses brackets open and closed

p pi (circle constant =314159 hellip)

AB line segment AB

AB pound arc AB a a+ a prime a double prime a1 a2 a sub 1 a sub 2

LP Acoustic pressure level I Sound intensity

N Loudness LN Loudness level

Acoustics

m Mass

m Linear mass density

m+ Area mass density

r Density

J Moment of inertia

p Pressure

p abs Absolute pressure

p amb Ambient pressure

p g Gage pressure

F Force

F W W Gravitational force WeightM Torque

T Torsional moment

M b Bending moment

s Normal stress

t Shear stress

e Normal strain

E Modulus of elasticity

G Shear modulus

micro f Coefficient of friction

W Section modulus

I Second moment of an area

W E Work Energy

W p E p Potential energy

W k E k Kinetic energy

P Power

n Efficiency

Mechanics

Mathematical symbols cf DIN 1302 (1999-12)

MathSpoken

symbol

MathSpoken

symbol

MathSpoken

symbol

ordm

ordmordm





1512 Formulas

M

P

TD

MS

ME

PE

A

S

Example formula L = Œ1 + Œ2 transformation to find Œ2

Example formula A = Œ middot b transformation to find Œ

Example formula n =

ŒŒ1 + s

transformation to find s

Example formula c =

a2 + b2 transformation to find a

Transformation of formulas


Transformations of sums

Transformations of products

Transformations of fractions

Transformations of roots

Formulas and numerical equations are transformed so that the quantity to be obtainedstands alone on the left side of the equation The value of the left side and right side ofthe formula must not change during the transformation The following rule applies to allsteps of the formula transformation

Changes applied to theleft formula side

=Changes applied to theright formula side

To be able to trace each step of the transformation it is useful to mark it to the right nextto the formula

aeligmiddot t int both sides of the formula are multiplied by t

aelig F int both sides of the formula are divided by F

Formula

P =

F middot s

t

left side right sideof the = of theformula formula

1222222

122222

1

1

1

1

3

3

4

4

2

2

2

2

3

3

4

4

5

5

6

6

L = Œ1 + Œ2 aeligndash Œ1

A = Œ middot b aelig b

n =

ŒŒ1 + s

aeligmiddot (Œ1 + s )

c = a 2 + b 2 aelig( )2

L ndash Œ1 = Œ2

A

b = Œ

n middot Œ1 ndash n middot Œ1 + n middot s = Œ ndash n middot Œ1 aelig n

a 2 = c 2 ndash b 2 aelig12

L ndash Œ1 = Œ1+ Œ2 ndash Œ1

A

b = Œ middot b

b

n middot (Œ1 + s ) = Œ middot (Œ1 + s )

(Œ1 + s )

c 2 = a 2 + b 2 aeligndash b 2

n middot Œ1 + n middot s = Œ aeligndash n middot Œ1

c 2 ndash b 2 = a 2 + b 2 ndash b 2

Œ2 = L ndash Œ1

Œ = A

b

s middot n

n

= Œ ndash n middot Œ1

n

a 2 = c 2 ndash b 2

s =

Œ ndash n middot Œ1n

a = c 2 ndash b 2

subtract Œ1

divide by b

multiply by (Œ1 + s )

square equation

invert both sides

invert both sides

subtractdivide by n

extract the root

performsubtraction

cancel b

cancel (Œ1 + s ) on theright side

solve the term inbrackets

subtract b 2

subtract ndash n middot Œ1

subtractinvert both sides

transformedformula

transformedformula

cancel n

simplify theexpression

transformedformula

transformedformula

122 1222222

1222222



16 12 Formulas

M

P

D

S

E

E

A

Conversion of units

Quantities and units

Decimal multiples or factors of units cf DIN 1301-1 (2004-10)

Conversion factors for units (excerpt)

Numerical values and units

Prefix Powerof ten

Mathematicaldesignation

ExamplesSymbol Name

T tera 1012 trillion 12 000 000 000 000 N = 12 middot 1012 N = 12 TN (teranewtons)

G giga 109 billion 45 000 000 000 W = 45 middot 109 W = 45 GW (gigawatts)

M mega 106 million 8 500 000 V = 85 middot 106 V = 85 MV (megavolts)

k kilo 103 thousand 12 600 W = 126 middot 103 W = 126 kW (kilowatts)

h hecto 102 hundred 500 mdash

= 5 middot 102 mdash

= 5 h mdash

(hectoliters)

da deca 101 ten 32 m = 32 middot 101 m = 32 dam (decameters)

ndash ndash 100 one 15 m = 15 middot 100 m

d deci 10ndash1 tenth 05 mdash = 5 middot 10ndash1 mdash = 5 d mdash (deciliters)

c centi 10ndash2 hundredth 025 m = 25 middot 10ndash2 m = 25 cm (centimeters)

m milli 10ndash3 thousandth 0375 A = 375 middot 10ndash3 A = 375 mA (milliamperes)

micro micro 10ndash6 millionth 0000 052 m = 52 middot 10ndash6 m = 52 microm (micrometers)

n nano 10ndash9 billionth 0000 000 075 m = 75 middot 10ndash9 m = 75 nm (nanometers)

p pico 10ndash12 trillionth 0000 000 000 006 F = 6 middot 10ndash12 F = 6 pF (picofarads)

Quantity Conversion factors e g Quantity Conversion factors e g

Length 1 =

10 mm1 cm

=

1000 mm1 m

=

1 m1000 mm

=

1 km1000 m

Time 1 =

60 min1 h

=

3600 s1 h

=

60 s1 min

=

1 min60 s

Area 1 =

100 mm2

1 cm2 =

100 cm2

1 dm2 =

Angle 1 =

60rsquo1deg

=

60rsquorsquo1rsquo

=

3600rsquorsquo1deg

=

1deg60 s

Volume 1 =

1000 mm3

1 cm3 =

1000 cm3

1 dm3 = Inch 1 inch = 254 mm 1 mm =

1

254 inches

Calculations with physical units are only possible if these units refer to the same base in this calculation Whensolving mathematical problems units often must be converted to basic units e g mm to m s to h mm2 to m2 Thisis done with the help of conversion factors that represent the value 1 (coherent units)

Physical quantities e g 125 mm consist of a

bull numerical value which is determined by measurement or calculation and abull unit e g m kg

Units are standardized in accordance with DIN 1301-1 (page 10)Very large or very small numerical values may be represented in a simplified wayas decimal multiples or factors with the help of prefixes e g 0004 mm = 4 microm

Physical quantity

10 mm

Numerical Unitvalue

Convert volume V = 3416 mm3 to cm3

Volume V is multiplied by a conversion factor Its numerator has the unit cm3 and its denominator the unitmm3

V = 3416 mm3 =1 cm3 middot 3416 mm3

1000 mm3 =

3416 cm3

1000 = 3416 cm 3

The angle size specification a = 42deg 16rsquo is to be expressed in degrees (deg)

The partial angle 16rsquo must be converted to degrees (deg) The value is multiplied by a conversion factor thenumerator of which has the unit degree (deg) and the denominator the unit minute (rsquo)

983137 = 42deg + 16rsquo middot1deg60rsquo

= 42deg +16 middot 1deg

60 = 42deg + 0267deg = 42267deg

1st example

2nd example





aring iquest

b a

c

copy

Sum of angles in a triangle

iquest

para

aring copy

g

g2

g1

18 13 Angels and Triangels

M

P

D

S

E

E

A

b2

a2

c2

abc

G 0 3

P1 X

Z

P2

RK I

Types of angles Theorem of intersecting lines Angles in a triangle Pythagorean theorem

Types of angles

Theorem of intersecting lines

Pythagorean theorem

D d

a2

daggerto

daggerti

a1

b 1

b 2

g straight line

g 1 g 2 parallel straight lines

a b corresponding angles

b d opposite anglesa d alternate angles

a g adjacent angles

If two parallels are intersected by a straight line thereare geometrical interrelationships between the resultingangles

If two intersecting lines are intercepted by a pair ofparallels the resulting segments form equal ratios

a = b

Corresponding angles

b = d

Opposite angles

a = d

Alternate angles

a + g = 180deg

Adjacent angles

a

b

a

b

1

1

2

2

=

b

d

b

D

1 2=

a

a

b

b

d

D

1

2

1

2

2

2

= =

Theorem ofintersecting lines

a + b + g = 180deg

Sum of angles ina triangle

In every triangle thesum of the interiorangles equals 180deg

D = 40 mm d = 30 mmtta = 135 Nmm2 tti =

Example

a = 21deg b = 95deg g =

983143 = 180deg ndash a ndash b = 180deg ndash 21deg ndash 95deg = 64deg

Example

t

t

t

tti

to

tito

= rArr =

=

d

D

d

D

middot

135 Nmm middot 30 mm

4

2

00 mm= 101 Nmm225

tto outer torsional stress

tti inner torsional stress

a b c sides of the triangle

a b g angles in the triangle

c a b

c a

=

=

35 mm = 21 mm =

= mm)2 2b ndash ( ndash2 35 ((21 mm)2= 28mm

1st example

c 2 = a 2 + b 2

Length of thehypotenuse

In a right triangle the square on the hypotenuse is equalto the sum of the squares on the sides meeting the rightangle

a sideb sidec hypotenuse

CNC programm with R = 50 mm and I = 25 mmK =

2nd example

c a b

R K

K R

2 2 2

2 2 2

2 2 2 250 25

= +

= +

= =

=

I

I ndash ndashmm mm2 2

K 433mm

c a b = +2 2

Square on thehypotenuse

a c b = 2 2ndash

b c a = 2 2ndash

Length of the sides

meeting the right angle



1913 Angels and Triangels

M

P

TD

MS

ME

PE

A

S

Functions of triangles

c hypotenuse

b adjacent side of aring

a adjacentside of aringaring

b opposite side of iquest

aadjacentside of iquest

iquestc hypotenuse

F

L3=140mm

L

L

1 = 1 5 0 m

m

L

2 = 3 0 m m

aring

szlig

copy

aring iquest

b a

c

Fd

Fz

F

4 0

1 2

szlig = 3 8

aring = 4 0

1 2

copy = 1 0

2

Fd

Fz

F

Diagram of forces

Functions of right triangles (trigonometric functions)

Functions of oblique triangles (law of sines law of cosines)

sine = opposite side

hypotenuse

cosine = adjacent side hypotenuse


adjacent side

Trigonometric functionsc hypotenuse (longest side)

a b sidesndash b is the adjacent side of a ndash a is the opposite side of a

a b g angles in the triangle g = 90deg

sin notation of sine

cos notation of cosine

tan notation of tangent

sina sine of angle a

According to the law of sines the ratios of

the sides correspond to the sine of theiropposite angles in the triangle If one sideand two angles are known the other valuescan be calculated with the help of thisfunction

Side a int opposite angle sinaSide b int opposite angle sinbHypothenuse c int opposite angle sing

The calculation of an angle in degrees (deg)

or as a circular measure (rad) is done withthe help of inverse trigonometric functionse g arcsine

L1 = 150 mm L2 = 30 mm L3 = 140 mmangle a =

Angle 983137 = 52deg

1st example

tan a =+

= =L L

L

1 2

3

1 286180 mm

140 mm

L1 = 150 mm L2 = 30 mm a = 52degLength of the shock absorber L =

2nd example

L =+

= =L L1 2

sina

180 mm

sin 52deg22842mm

F = 800 N a = 40deg b = 38deg F z = F d =

The forces are calculated with the help

of the forces diagram

Example

F F F

F

sin sin

middot sin

sina b

b

a= rArr =

=

zz

800 N middot sin38degF z

ssin40deg= 76624 N

F F F

F

sin sin

middot sin

sina g

g

a= rArr =

=

dd

800 N middot sin102F d

degdeg

sin40deg= 121738 N

Relations applying to angle a

sina =

a

c cosa =

b

c tana =

a

b

Relations applying to angle b

sinb =

b

c cosb =

a

c tanb =

b

a

There are many transformationoptions

a =

b middot sinasinb

=

c middot sinasing

b =

a middot sinbsina

=

c middot sinbsing

c =

a middot singsina

=

b middot singsinb

Law of sines

a b c = sina sinb sing

a

sina =

b

sinb =

c

sing

Law of cosines

a 2 = b 2 + c 2 ndash 2 middot b middot c middot cosab 2 = a 2 + c 2 ndash 2 middot a middot c middot cosbc 2 = a 2 + b 2 ndash 2 middot a middot b middot cosg

The calculation of an angle indegrees (deg) or as a circularmeasure (rad) is done with thehelp of inverse trigonometricfunctions e g arcsine

Transformation e g

cosa =

b 2 + c 2 ndash a 2

2 middot b middot c



20 14 Lengths

Division of lengths Arc length Composite length

Œ total length n number of holesp spacing

Spacing

Spacing

Sub-dividing lengths

Arc length

L = Œ1 + Œ2 + hellip

Composite length

D outside diameter d inside diameterd m mean diameter t thicknessŒ1 Œ2 section lengths L composite lengtha angle at center

Composite length

D = 360 mm t = 5 mm a = 270deg Œ2 = 70 mmd m = L =

Example (composite length picture left)

Edge distance = spacing

Edge distance) spacing

Example

Œ total length n number of holesp spacing a b edge distances

Example

Number of pieces

Subdividing into pieces Œ bar length s saw cutting widthz number of pieces Œr remaining lengthŒs piece length

Example

Œr = Œ ndash z middot (Œs + s )

Remaining length

Example Torsion spring Œa arc length a angle at centerr radius d diameter

Example

Arc length

M

P

D

S

E

E

A



Original title

Tabellenbuch Metall 45th edition 2011

Authors

Ulrich Fischer Dipl-Ing (FH) Reutlingen

Roland Gomeringer Dipl-Gwl Meszligstetten

Max Heinzler Dipl-Ing (FH) Wangen im Allgaumlu

Roland Kilgus Dipl-Gwl Neckartenzlingen

Friedrich Naumlher Dipl-Ing (FH) Balingen

Stefan Oesterle Dipl-Ing Amtzell

Heinz Paetzold Dipl-Ing (FH) Muumlhlacker

Andreas Stephan Dipl-Ing (FH) Marktoberdorf

Editor

Ulrich Fischer Reutlingen

Graphic design

Design office of Verlag Europa-Lehrmittel Ostfildern Germany

The publisher and its affiliates have taken care to collect the information given in this book to the best of their

ability However no responsibility is accepted by the publisher or any of its affiliates regarding its content or

any statement herein or omission there from which may result in any loss or damage to any party using the

data shown above Warranty claims against the authors or the publisher are excluded

Most recent editions of standards and other regulations govern their use

They can be ordered from Beuth Verlag GmbH Burggrafenstr 6 10787 Berlin Germany

The content of the chapter bdquoProgram structure of CNC machines according to PALldquo (page 412 to 424) complies

with the publications of the PAL Pruumlfungs- und Lehrmittelentwicklungsstelle (Institute for the development of

training and testing material) of the IHK Region Stuttgart (Chamber of Commerce and Industry of the Stuttgartregion)

English edition Mechanical and Metal Trades Handbook

3rd edition 2012

6 5 4 3 2 1

All printings of this edition may be used concurrently in the classroom since they are unchanged except for somecorrections to typographical errors and slight changes in standards

ISBN 13 978-3-8085-1914-1

Cover design includes a photograph from TESABrown amp Sharpe Renens Switzerland

All rights reserved This publication is protected under copyright law Any use other than those permitted by law

must be approved in writing by the publisher

copy 2012 by Verlag Europa-Lehrmittel Nourney Vollmer GmbH amp Co KG 42781 Haan-Gruiten Germanyhttpwwweuropa-lehrmittelde

Translation Eva Schwarz 76879 Ottersheim Germany wwwtechnische-uebersetzungen-eva-schwarzde

Typesetting Satz+Layout Werkstatt Kluth GmbH D-50374 Erftstadt Germany wwwslw-kluthde

Printed by M P Media-Print Informationstechnologie GmbH D-33100 Paderborn Germany



3

Preface








bull Machinists

bull Millwrights

bull Draftspersons





Notes for the user



and Standards Index



areas





Table of Contents


extensive








Acknowledgement



extremely valuable


M1 Mathematics

9 ndash 28

P2 Physics

29 ndash 50

TD3 Technical

Drawing

51 ndash 110

MS4 Material

Science

111 ndash 200

ME5 Machine

Elements

201 ndash 268

PE6 Production

Engineering

269 ndash 366

A7 Automation and

Information Tech-





mathematics


ndash Plastics


ndash Forming

ndash Welding



milling

ndash Steel types




ndash GRAFCET





5Table of Contents








d e n s i t y 1 5 1










Graph types 53




















7Table of Contents




























8










Draft E DIN 743(2008-10)


Preliminary

standard

DIN V 66304

(1991-04)









EuropeanStandards

(EN standards)























9Table of Contents

1 Mathematics

M

P

TD

MS

ME

PE

A

S

Quantity SymbolUnit

Name Symbol

Lengths Œ meter m



Non-SI units 12

12 Formulas





14 Lengths


Rough lengths 21

15 Areas





17 Mass


18 Centroids




hypotenuse


adjacent side

xsx

y s

y

S1

S2

S

m inkg

m 1 m

d

A d h d

s = +p

p


24

2

Surface area






M

P

D

S

E

E

A





Mechanics

Basequantity


Thermo-dynamic

temperature

Amount ofsubstance

Luminousintensity

Base

units meter

kilo-


Unitsymbol

m


kg s A K mol cd

Quantity

Symbol



Unit



Length

A S square meter

arehectare

m2

aha

1 m2 = 10 000 cm2

= 1 000 000 mm2

1 a = 100 m2

1 ha = 100 a = 10 000 m2

100 ha = 1 km2



Area

V cubic meter

liter

m3

mdash L

1 m3 = 1000 dm3

= 1 000 000 cm3


1 m mdash = 1 cm

3


Volume

a b g hellip radian

degrees

minutes

seconds

rad

deg

+


1deg = p

rad = 60 180

1 = 1deg60 = 60+1+ = 1 60 = 1deg3600


Planeangle(angle)


Solid angle

m kilogramgram

megagrammetric ton

kgg

Mgt

1 kg = 1000 g1 g = 1000 mg

1 metric t = 1000 kg = 1 Mg02 g = 1 ct



Mass

m kilogramper meter


Linear massdensity





= 1 gcm3

= 1 gml

= 1 mgmm3


Density




M

P

TD

MS

ME

PE

A

S







Mechanics

F

F G G

newton N1 N = 1

kg middot m= 1

J s2 m

1 MN = 103 kN = 1 000 000 N


Force

Weight

M M bT

newton xmeter


kg middot m2



p kilogram xmeter

per second



Momentum

p

s t

pascal


Pa

Nmm2

1 Pa = 1 Nm2 = 001 mbar1 bar = 100 000 Nm2





Pressure

Mechanicalstress


m4

cm4


Secondmoment ofarea




PG



PowerHeat flux

Time


sminhda

1 min = 60 s1 h = 60 min = 3600 s1 d = 24 h = 86 400 s




n 1 per second

1 per minute

1s

1min



60 s



v meters persecond

meters perminute

kilometers perhour

ms

mmin

kmh


1 mmin =1 m

60 s

1 kmh =1 m

36 s


1 kn = 1852 kmh


Velocity

w 1 per second

radians persecond

1s

rads


velocity w = 4 p s

Angular-

velocity


ms21 ms2 =

1 ms 1 s


g = 981 ms2 fi 10 ms2

Acceleration

QuantitySym-bol

Unit






M

P

D

S

E

E

A


QuantitySym-bol

Unit

NameRelationship



I

E

R

G

amperevolt

ohm

siemens

AV

O

S

1 V = 1 W1 A = 1 JC

1 O = 1 V1 A

1 S = 1 A1 V = 1 O





r

g k

ohm xmeter

siemensper meter

O middotm

Sm


k= 1 2

in mm

m

Ω middot

kr

= 1

2in

m

mmΩ middot

Specificresistance

Conductivity


Frequency



Electrical energy



cos j = P

U middot I

Phasedifference




E F

Q C

Q

U Q t = = = middotI

E Q C L


henry

VmCFH






QuantitySym-bol

Unit

NameRelationship


Sym-bol

Non-SI units

T Q

t h

kelvin

degreesCelsius

K

degC




Thermo-

dynamic

temperature

Celsiustemperature



H u joule per


Jkg

Jm3

1 MJkg = 1 000 000 Jkg

1 MJm3 = 1 000 000 Jm3



Net calorific

value



1 foot (ft) = 03048 m

1 yard(yd) = 09144 m

1 nautical

mile = 1852 km1 mile = 16093 km

1 sqin = 6452 cm2

1 sqft = 929 dm2

1 sqyd = 08361 m2

1 acre = 4046856m2

Pressure

1 bar = 145poundin2


1 cuin = 1639 cm3

1 cuft = 2832 dm3

1 cuyd = 7646 dm3




1 oz = 2835 g

1 lb = 4536 g

1 t = 1000 kg


1 Karat = 02 g


1 PSh = 0735 kWh

1 PS = 735 W

1 kcal = 41868 Ws

1 kcal = 1166 Wh

1 kpms = 9807 W

1 Btu = 1055 Ws

1 hp = 7457 W

Sym-bol



1312 Formulas

M

P

TD

MS

ME

PE

A

S

FormulaMeaning

symbol

Œ Length

w Width

h Height

s Linear distance

r R Radius

d D Diameter


V Volume

a b g Planar angle

W Solid angle

l Wave length

FormulaMeaning

symbol

FormulaMeaning

symbol




t Time Duration

T Cycle duration


Speed

f v Frequency

v u Velocity

w Angular velocity

a Acceleration



Qmiddot


Time





Electricity





coefficient


Heat












proportional an


power of a 0 3

square root of

n0 3 n-th root of







lg common logarithm






AB line segment AB




Acoustics

m Mass



r Density

J Moment of inertia

p Pressure



p g Gage pressure

F Force


T Torsional moment

M b Bending moment

s Normal stress

t Shear stress

e Normal strain


G Shear modulus


W Section modulus


W E Work Energy



P Power

n Efficiency

Mechanics


MathSpoken

symbol

MathSpoken

symbol

MathSpoken

symbol

ordm

ordmordm





1512 Formulas

M

P

TD

MS

ME

PE

A

S



Example formula n =

ŒŒ1 + s


Example formula c =














Formula

P =

F middot s

t


1222222

122222

1

1

1

1

3

3

4

4

2

2

2

2

3

3

4

4

5

5

6

6



n =

ŒŒ1 + s


c = a 2 + b 2 aelig( )2

L ndash Œ1 = Œ2

A

b = Œ




A

b = Œ middot b

b


(Œ1 + s )




Œ2 = L ndash Œ1

Œ = A

b

s middot n

n


n

a 2 = c 2 ndash b 2

s =


a = c 2 ndash b 2

subtract Œ1

divide by b


square equation

invert both sides

invert both sides

subtractdivide by n

extract the root

performsubtraction

cancel b



subtract b 2



transformedformula

transformedformula

cancel n


transformedformula

transformedformula

122 1222222

1222222



16 12 Formulas

M

P

D

S

E

E

A

Conversion of units





Prefix Powerof ten


ExamplesSymbol Name







= 5 h mdash

(hectoliters)










Length 1 =

10 mm1 cm

=

1000 mm1 m

=

1 m1000 mm

=

1 km1000 m

Time 1 =

60 min1 h

=

3600 s1 h

=

60 s1 min

=

1 min60 s

Area 1 =

100 mm2

1 cm2 =

100 cm2

1 dm2 =

Angle 1 =

60rsquo1deg

=

60rsquorsquo1rsquo

=

3600rsquorsquo1deg

=

1deg60 s

Volume 1 =

1000 mm3

1 cm3 =

1000 cm3


1

254 inches





Physical quantity

10 mm

Numerical Unitvalue



V = 3416 mm3 =1 cm3 middot 3416 mm3

1000 mm3 =

3416 cm3

1000 = 3416 cm 3





60 = 42deg + 0267deg = 42267deg

1st example

2nd example





aring iquest

b a

c

copy


iquest

para

aring copy

g

g2

g1


M

P

D

S

E

E

A

b2

a2

c2

abc

G 0 3

P1 X

Z

P2

RK I


Types of angles


Pythagorean theorem

D d

a2

daggerto

daggerti

a1

b 1

b 2

g straight line




a g adjacent angles



a = b


b = d

Opposite angles

a = d

Alternate angles

a + g = 180deg

Adjacent angles

a

b

a

b

1

1

2

2

=

b

d

b

D

1 2=

a

a

b

b

d

D

1

2

1

2

2

2

= =


a + b + g = 180deg




Example

a = 21deg b = 95deg g =


Example

t

t

t

tti

to

tito

= rArr =

=

d

D

d

D

middot


4

2

00 mm= 101 Nmm225





c a b

c a

=

=

35 mm = 21 mm =


1st example

c 2 = a 2 + b 2





2nd example

c a b

R K

K R

2 2 2

2 2 2

2 2 2 250 25

= +

= +

= =

=

I


K 433mm

c a b = +2 2


a c b = 2 2ndash

b c a = 2 2ndash

Length of the sides





M

P

TD

MS

ME

PE

A

S


c hypotenuse





iquestc hypotenuse

F

L3=140mm

L

L

1 = 1 5 0 m

m

L

2 = 3 0 m m

aring

szlig

copy

aring iquest

b a

c

Fd

Fz

F

4 0

1 2

szlig = 3 8

aring = 4 0

1 2

copy = 1 0

2

Fd

Fz

F

Diagram of forces




hypotenuse



adjacent side















1st example

tan a =+

= =L L

L

1 2

3

1 286180 mm

140 mm


2nd example

L =+

= =L L1 2

sina

180 mm

sin 52deg22842mm

F = 800 N a = 40deg b = 38deg F z = F d =



Example

F F F

F

sin sin

middot sin

sina b

b

a= rArr =

=

zz


ssin40deg= 76624 N

F F F

F

sin sin

middot sin

sina g

g

a= rArr =

=

dd


degdeg

sin40deg= 121738 N


sina =

a

c cosa =

b

c tana =

a

b


sinb =

b

c cosb =

a

c tanb =

b

a


a =

b middot sinasinb

=

c middot sinasing

b =

a middot sinbsina

=

c middot sinbsing

c =

a middot singsina

=

b middot singsinb

Law of sines


a

sina =

b

sinb =

c

sing

Law of cosines



Transformation e g

cosa =

b 2 + c 2 ndash a 2

2 middot b middot c



20 14 Lengths



Spacing

Spacing


Arc length


Composite length


Composite length





Example


Example

Number of pieces


Example


Remaining length


Example

Arc length

M

P

D

S

E

E

A



3

Preface








bull Machinists

bull Millwrights

bull Draftspersons





Notes for the user



and Standards Index



areas





Table of Contents


extensive








Acknowledgement



extremely valuable


M1 Mathematics

9 ndash 28

P2 Physics

29 ndash 50

TD3 Technical

Drawing

51 ndash 110

MS4 Material

Science

111 ndash 200

ME5 Machine

Elements

201 ndash 268

PE6 Production

Engineering

269 ndash 366

A7 Automation and

Information Tech-





mathematics


ndash Plastics


ndash Forming

ndash Welding



milling

ndash Steel types




ndash GRAFCET





5Table of Contents








d e n s i t y 1 5 1










Graph types 53




















7Table of Contents




























8










Draft E DIN 743(2008-10)


Preliminary

standard

DIN V 66304

(1991-04)









EuropeanStandards

(EN standards)























9Table of Contents

1 Mathematics

M

P

TD

MS

ME

PE

A

S

Quantity SymbolUnit

Name Symbol

Lengths Œ meter m



Non-SI units 12

12 Formulas





14 Lengths


Rough lengths 21

15 Areas





17 Mass


18 Centroids




hypotenuse


adjacent side

xsx

y s

y

S1

S2

S

m inkg

m 1 m

d

A d h d

s = +p

p


24

2

Surface area






M

P

D

S

E

E

A





Mechanics

Basequantity


Thermo-dynamic

temperature

Amount ofsubstance

Luminousintensity

Base

units meter

kilo-


Unitsymbol

m


kg s A K mol cd

Quantity

Symbol



Unit



Length

A S square meter

arehectare

m2

aha

1 m2 = 10 000 cm2

= 1 000 000 mm2

1 a = 100 m2

1 ha = 100 a = 10 000 m2

100 ha = 1 km2



Area

V cubic meter

liter

m3

mdash L

1 m3 = 1000 dm3

= 1 000 000 cm3


1 m mdash = 1 cm

3


Volume

a b g hellip radian

degrees

minutes

seconds

rad

deg

+


1deg = p

rad = 60 180

1 = 1deg60 = 60+1+ = 1 60 = 1deg3600


Planeangle(angle)


Solid angle

m kilogramgram

megagrammetric ton

kgg

Mgt

1 kg = 1000 g1 g = 1000 mg

1 metric t = 1000 kg = 1 Mg02 g = 1 ct



Mass

m kilogramper meter


Linear massdensity





= 1 gcm3

= 1 gml

= 1 mgmm3


Density




M

P

TD

MS

ME

PE

A

S







Mechanics

F

F G G

newton N1 N = 1

kg middot m= 1

J s2 m

1 MN = 103 kN = 1 000 000 N


Force

Weight

M M bT

newton xmeter


kg middot m2



p kilogram xmeter

per second



Momentum

p

s t

pascal


Pa

Nmm2

1 Pa = 1 Nm2 = 001 mbar1 bar = 100 000 Nm2





Pressure

Mechanicalstress


m4

cm4


Secondmoment ofarea




PG



PowerHeat flux

Time


sminhda

1 min = 60 s1 h = 60 min = 3600 s1 d = 24 h = 86 400 s




n 1 per second

1 per minute

1s

1min



60 s



v meters persecond

meters perminute

kilometers perhour

ms

mmin

kmh


1 mmin =1 m

60 s

1 kmh =1 m

36 s


1 kn = 1852 kmh


Velocity

w 1 per second

radians persecond

1s

rads


velocity w = 4 p s

Angular-

velocity


ms21 ms2 =

1 ms 1 s


g = 981 ms2 fi 10 ms2

Acceleration

QuantitySym-bol

Unit






M

P

D

S

E

E

A


QuantitySym-bol

Unit

NameRelationship



I

E

R

G

amperevolt

ohm

siemens

AV

O

S

1 V = 1 W1 A = 1 JC

1 O = 1 V1 A

1 S = 1 A1 V = 1 O





r

g k

ohm xmeter

siemensper meter

O middotm

Sm


k= 1 2

in mm

m

Ω middot

kr

= 1

2in

m

mmΩ middot

Specificresistance

Conductivity


Frequency



Electrical energy



cos j = P

U middot I

Phasedifference




E F

Q C

Q

U Q t = = = middotI

E Q C L


henry

VmCFH






QuantitySym-bol

Unit

NameRelationship


Sym-bol

Non-SI units

T Q

t h

kelvin

degreesCelsius

K

degC




Thermo-

dynamic

temperature

Celsiustemperature



H u joule per


Jkg

Jm3

1 MJkg = 1 000 000 Jkg

1 MJm3 = 1 000 000 Jm3



Net calorific

value



1 foot (ft) = 03048 m

1 yard(yd) = 09144 m

1 nautical

mile = 1852 km1 mile = 16093 km

1 sqin = 6452 cm2

1 sqft = 929 dm2

1 sqyd = 08361 m2

1 acre = 4046856m2

Pressure

1 bar = 145poundin2


1 cuin = 1639 cm3

1 cuft = 2832 dm3

1 cuyd = 7646 dm3




1 oz = 2835 g

1 lb = 4536 g

1 t = 1000 kg


1 Karat = 02 g


1 PSh = 0735 kWh

1 PS = 735 W

1 kcal = 41868 Ws

1 kcal = 1166 Wh

1 kpms = 9807 W

1 Btu = 1055 Ws

1 hp = 7457 W

Sym-bol



1312 Formulas

M

P

TD

MS

ME

PE

A

S

FormulaMeaning

symbol

Œ Length

w Width

h Height

s Linear distance

r R Radius

d D Diameter


V Volume

a b g Planar angle

W Solid angle

l Wave length

FormulaMeaning

symbol

FormulaMeaning

symbol




t Time Duration

T Cycle duration


Speed

f v Frequency

v u Velocity

w Angular velocity

a Acceleration



Qmiddot


Time





Electricity





coefficient


Heat












proportional an


power of a 0 3

square root of

n0 3 n-th root of







lg common logarithm






AB line segment AB




Acoustics

m Mass



r Density

J Moment of inertia

p Pressure



p g Gage pressure

F Force


T Torsional moment

M b Bending moment

s Normal stress

t Shear stress

e Normal strain


G Shear modulus


W Section modulus


W E Work Energy



P Power

n Efficiency

Mechanics


MathSpoken

symbol

MathSpoken

symbol

MathSpoken

symbol

ordm

ordmordm





1512 Formulas

M

P

TD

MS

ME

PE

A

S



Example formula n =

ŒŒ1 + s


Example formula c =














Formula

P =

F middot s

t


1222222

122222

1

1

1

1

3

3

4

4

2

2

2

2

3

3

4

4

5

5

6

6



n =

ŒŒ1 + s


c = a 2 + b 2 aelig( )2

L ndash Œ1 = Œ2

A

b = Œ




A

b = Œ middot b

b


(Œ1 + s )




Œ2 = L ndash Œ1

Œ = A

b

s middot n

n


n

a 2 = c 2 ndash b 2

s =


a = c 2 ndash b 2

subtract Œ1

divide by b


square equation

invert both sides

invert both sides

subtractdivide by n

extract the root

performsubtraction

cancel b



subtract b 2



transformedformula

transformedformula

cancel n


transformedformula

transformedformula

122 1222222

1222222



16 12 Formulas

M

P

D

S

E

E

A

Conversion of units





Prefix Powerof ten


ExamplesSymbol Name







= 5 h mdash

(hectoliters)










Length 1 =

10 mm1 cm

=

1000 mm1 m

=

1 m1000 mm

=

1 km1000 m

Time 1 =

60 min1 h

=

3600 s1 h

=

60 s1 min

=

1 min60 s

Area 1 =

100 mm2

1 cm2 =

100 cm2

1 dm2 =

Angle 1 =

60rsquo1deg

=

60rsquorsquo1rsquo

=

3600rsquorsquo1deg

=

1deg60 s

Volume 1 =

1000 mm3

1 cm3 =

1000 cm3


1

254 inches





Physical quantity

10 mm

Numerical Unitvalue



V = 3416 mm3 =1 cm3 middot 3416 mm3

1000 mm3 =

3416 cm3

1000 = 3416 cm 3





60 = 42deg + 0267deg = 42267deg

1st example

2nd example





aring iquest

b a

c

copy


iquest

para

aring copy

g

g2

g1


M

P

D

S

E

E

A

b2

a2

c2

abc

G 0 3

P1 X

Z

P2

RK I


Types of angles


Pythagorean theorem

D d

a2

daggerto

daggerti

a1

b 1

b 2

g straight line




a g adjacent angles



a = b


b = d

Opposite angles

a = d

Alternate angles

a + g = 180deg

Adjacent angles

a

b

a

b

1

1

2

2

=

b

d

b

D

1 2=

a

a

b

b

d

D

1

2

1

2

2

2

= =


a + b + g = 180deg




Example

a = 21deg b = 95deg g =


Example

t

t

t

tti

to

tito

= rArr =

=

d

D

d

D

middot


4

2

00 mm= 101 Nmm225





c a b

c a

=

=

35 mm = 21 mm =


1st example

c 2 = a 2 + b 2





2nd example

c a b

R K

K R

2 2 2

2 2 2

2 2 2 250 25

= +

= +

= =

=

I


K 433mm

c a b = +2 2


a c b = 2 2ndash

b c a = 2 2ndash

Length of the sides





M

P

TD

MS

ME

PE

A

S


c hypotenuse





iquestc hypotenuse

F

L3=140mm

L

L

1 = 1 5 0 m

m

L

2 = 3 0 m m

aring

szlig

copy

aring iquest

b a

c

Fd

Fz

F

4 0

1 2

szlig = 3 8

aring = 4 0

1 2

copy = 1 0

2

Fd

Fz

F

Diagram of forces




hypotenuse



adjacent side















1st example

tan a =+

= =L L

L

1 2

3

1 286180 mm

140 mm


2nd example

L =+

= =L L1 2

sina

180 mm

sin 52deg22842mm

F = 800 N a = 40deg b = 38deg F z = F d =



Example

F F F

F

sin sin

middot sin

sina b

b

a= rArr =

=

zz


ssin40deg= 76624 N

F F F

F

sin sin

middot sin

sina g

g

a= rArr =

=

dd


degdeg

sin40deg= 121738 N


sina =

a

c cosa =

b

c tana =

a

b


sinb =

b

c cosb =

a

c tanb =

b

a


a =

b middot sinasinb

=

c middot sinasing

b =

a middot sinbsina

=

c middot sinbsing

c =

a middot singsina

=

b middot singsinb

Law of sines


a

sina =

b

sinb =

c

sing

Law of cosines



Transformation e g

cosa =

b 2 + c 2 ndash a 2

2 middot b middot c



20 14 Lengths



Spacing

Spacing


Arc length


Composite length


Composite length





Example


Example

Number of pieces


Example


Remaining length


Example

Arc length

M

P

D

S

E

E

A





5Table of Contents








d e n s i t y 1 5 1










Graph types 53




















7Table of Contents




























8










Draft E DIN 743(2008-10)


Preliminary

standard

DIN V 66304

(1991-04)









EuropeanStandards

(EN standards)























9Table of Contents

1 Mathematics

M

P

TD

MS

ME

PE

A

S

Quantity SymbolUnit

Name Symbol

Lengths Œ meter m



Non-SI units 12

12 Formulas





14 Lengths


Rough lengths 21

15 Areas





17 Mass


18 Centroids




hypotenuse


adjacent side

xsx

y s

y

S1

S2

S

m inkg

m 1 m

d

A d h d

s = +p

p


24

2

Surface area






M

P

D

S

E

E

A





Mechanics

Basequantity


Thermo-dynamic

temperature

Amount ofsubstance

Luminousintensity

Base

units meter

kilo-


Unitsymbol

m


kg s A K mol cd

Quantity

Symbol



Unit



Length

A S square meter

arehectare

m2

aha

1 m2 = 10 000 cm2

= 1 000 000 mm2

1 a = 100 m2

1 ha = 100 a = 10 000 m2

100 ha = 1 km2



Area

V cubic meter

liter

m3

mdash L

1 m3 = 1000 dm3

= 1 000 000 cm3


1 m mdash = 1 cm

3


Volume

a b g hellip radian

degrees

minutes

seconds

rad

deg

+


1deg = p

rad = 60 180

1 = 1deg60 = 60+1+ = 1 60 = 1deg3600


Planeangle(angle)


Solid angle

m kilogramgram

megagrammetric ton

kgg

Mgt

1 kg = 1000 g1 g = 1000 mg

1 metric t = 1000 kg = 1 Mg02 g = 1 ct



Mass

m kilogramper meter


Linear massdensity





= 1 gcm3

= 1 gml

= 1 mgmm3


Density




M

P

TD

MS

ME

PE

A

S







Mechanics

F

F G G

newton N1 N = 1

kg middot m= 1

J s2 m

1 MN = 103 kN = 1 000 000 N


Force

Weight

M M bT

newton xmeter


kg middot m2



p kilogram xmeter

per second



Momentum

p

s t

pascal


Pa

Nmm2

1 Pa = 1 Nm2 = 001 mbar1 bar = 100 000 Nm2





Pressure

Mechanicalstress


m4

cm4


Secondmoment ofarea




PG



PowerHeat flux

Time


sminhda

1 min = 60 s1 h = 60 min = 3600 s1 d = 24 h = 86 400 s




n 1 per second

1 per minute

1s

1min



60 s



v meters persecond

meters perminute

kilometers perhour

ms

mmin

kmh


1 mmin =1 m

60 s

1 kmh =1 m

36 s


1 kn = 1852 kmh


Velocity

w 1 per second

radians persecond

1s

rads


velocity w = 4 p s

Angular-

velocity


ms21 ms2 =

1 ms 1 s


g = 981 ms2 fi 10 ms2

Acceleration

QuantitySym-bol

Unit






M

P

D

S

E

E

A


QuantitySym-bol

Unit

NameRelationship



I

E

R

G

amperevolt

ohm

siemens

AV

O

S

1 V = 1 W1 A = 1 JC

1 O = 1 V1 A

1 S = 1 A1 V = 1 O





r

g k

ohm xmeter

siemensper meter

O middotm

Sm


k= 1 2

in mm

m

Ω middot

kr

= 1

2in

m

mmΩ middot

Specificresistance

Conductivity


Frequency



Electrical energy



cos j = P

U middot I

Phasedifference




E F

Q C

Q

U Q t = = = middotI

E Q C L


henry

VmCFH






QuantitySym-bol

Unit

NameRelationship


Sym-bol

Non-SI units

T Q

t h

kelvin

degreesCelsius

K

degC




Thermo-

dynamic

temperature

Celsiustemperature



H u joule per


Jkg

Jm3

1 MJkg = 1 000 000 Jkg

1 MJm3 = 1 000 000 Jm3



Net calorific

value



1 foot (ft) = 03048 m

1 yard(yd) = 09144 m

1 nautical

mile = 1852 km1 mile = 16093 km

1 sqin = 6452 cm2

1 sqft = 929 dm2

1 sqyd = 08361 m2

1 acre = 4046856m2

Pressure

1 bar = 145poundin2


1 cuin = 1639 cm3

1 cuft = 2832 dm3

1 cuyd = 7646 dm3




1 oz = 2835 g

1 lb = 4536 g

1 t = 1000 kg


1 Karat = 02 g


1 PSh = 0735 kWh

1 PS = 735 W

1 kcal = 41868 Ws

1 kcal = 1166 Wh

1 kpms = 9807 W

1 Btu = 1055 Ws

1 hp = 7457 W

Sym-bol



1312 Formulas

M

P

TD

MS

ME

PE

A

S

FormulaMeaning

symbol

Œ Length

w Width

h Height

s Linear distance

r R Radius

d D Diameter


V Volume

a b g Planar angle

W Solid angle

l Wave length

FormulaMeaning

symbol

FormulaMeaning

symbol




t Time Duration

T Cycle duration


Speed

f v Frequency

v u Velocity

w Angular velocity

a Acceleration



Qmiddot


Time





Electricity





coefficient


Heat












proportional an


power of a 0 3

square root of

n0 3 n-th root of







lg common logarithm






AB line segment AB




Acoustics

m Mass



r Density

J Moment of inertia

p Pressure



p g Gage pressure

F Force


T Torsional moment

M b Bending moment

s Normal stress

t Shear stress

e Normal strain


G Shear modulus


W Section modulus


W E Work Energy



P Power

n Efficiency

Mechanics


MathSpoken

symbol

MathSpoken

symbol

MathSpoken

symbol

ordm

ordmordm





1512 Formulas

M

P

TD

MS

ME

PE

A

S



Example formula n =

ŒŒ1 + s


Example formula c =














Formula

P =

F middot s

t


1222222

122222

1

1

1

1

3

3

4

4

2

2

2

2

3

3

4

4

5

5

6

6



n =

ŒŒ1 + s


c = a 2 + b 2 aelig( )2

L ndash Œ1 = Œ2

A

b = Œ




A

b = Œ middot b

b


(Œ1 + s )




Œ2 = L ndash Œ1

Œ = A

b

s middot n

n


n

a 2 = c 2 ndash b 2

s =


a = c 2 ndash b 2

subtract Œ1

divide by b


square equation

invert both sides

invert both sides

subtractdivide by n

extract the root

performsubtraction

cancel b



subtract b 2



transformedformula

transformedformula

cancel n


transformedformula

transformedformula

122 1222222

1222222



16 12 Formulas

M

P

D

S

E

E

A

Conversion of units





Prefix Powerof ten


ExamplesSymbol Name







= 5 h mdash

(hectoliters)










Length 1 =

10 mm1 cm

=

1000 mm1 m

=

1 m1000 mm

=

1 km1000 m

Time 1 =

60 min1 h

=

3600 s1 h

=

60 s1 min

=

1 min60 s

Area 1 =

100 mm2

1 cm2 =

100 cm2

1 dm2 =

Angle 1 =

60rsquo1deg

=

60rsquorsquo1rsquo

=

3600rsquorsquo1deg

=

1deg60 s

Volume 1 =

1000 mm3

1 cm3 =

1000 cm3


1

254 inches





Physical quantity

10 mm

Numerical Unitvalue



V = 3416 mm3 =1 cm3 middot 3416 mm3

1000 mm3 =

3416 cm3

1000 = 3416 cm 3





60 = 42deg + 0267deg = 42267deg

1st example

2nd example





aring iquest

b a

c

copy


iquest

para

aring copy

g

g2

g1


M

P

D

S

E

E

A

b2

a2

c2

abc

G 0 3

P1 X

Z

P2

RK I


Types of angles


Pythagorean theorem

D d

a2

daggerto

daggerti

a1

b 1

b 2

g straight line




a g adjacent angles



a = b


b = d

Opposite angles

a = d

Alternate angles

a + g = 180deg

Adjacent angles

a

b

a

b

1

1

2

2

=

b

d

b

D

1 2=

a

a

b

b

d

D

1

2

1

2

2

2

= =


a + b + g = 180deg




Example

a = 21deg b = 95deg g =


Example

t

t

t

tti

to

tito

= rArr =

=

d

D

d

D

middot


4

2

00 mm= 101 Nmm225





c a b

c a

=

=

35 mm = 21 mm =


1st example

c 2 = a 2 + b 2





2nd example

c a b

R K

K R

2 2 2

2 2 2

2 2 2 250 25

= +

= +

= =

=

I


K 433mm

c a b = +2 2


a c b = 2 2ndash

b c a = 2 2ndash

Length of the sides





M

P

TD

MS

ME

PE

A

S


c hypotenuse





iquestc hypotenuse

F

L3=140mm

L

L

1 = 1 5 0 m

m

L

2 = 3 0 m m

aring

szlig

copy

aring iquest

b a

c

Fd

Fz

F

4 0

1 2

szlig = 3 8

aring = 4 0

1 2

copy = 1 0

2

Fd

Fz

F

Diagram of forces




hypotenuse



adjacent side















1st example

tan a =+

= =L L

L

1 2

3

1 286180 mm

140 mm


2nd example

L =+

= =L L1 2

sina

180 mm

sin 52deg22842mm

F = 800 N a = 40deg b = 38deg F z = F d =



Example

F F F

F

sin sin

middot sin

sina b

b

a= rArr =

=

zz


ssin40deg= 76624 N

F F F

F

sin sin

middot sin

sina g

g

a= rArr =

=

dd


degdeg

sin40deg= 121738 N


sina =

a

c cosa =

b

c tana =

a

b


sinb =

b

c cosb =

a

c tanb =

b

a


a =

b middot sinasinb

=

c middot sinasing

b =

a middot sinbsina

=

c middot sinbsing

c =

a middot singsina

=

b middot singsinb

Law of sines


a

sina =

b

sinb =

c

sing

Law of cosines



Transformation e g

cosa =

b 2 + c 2 ndash a 2

2 middot b middot c



20 14 Lengths



Spacing

Spacing


Arc length


Composite length


Composite length





Example


Example

Number of pieces


Example


Remaining length


Example

Arc length

M

P

D

S

E

E

A





7Table of Contents




























8










Draft E DIN 743(2008-10)


Preliminary

standard

DIN V 66304

(1991-04)









EuropeanStandards

(EN standards)























9Table of Contents

1 Mathematics

M

P

TD

MS

ME

PE

A

S

Quantity SymbolUnit

Name Symbol

Lengths Œ meter m



Non-SI units 12

12 Formulas





14 Lengths


Rough lengths 21

15 Areas





17 Mass


18 Centroids




hypotenuse


adjacent side

xsx

y s

y

S1

S2

S

m inkg

m 1 m

d

A d h d

s = +p

p


24

2

Surface area






M

P

D

S

E

E

A





Mechanics

Basequantity


Thermo-dynamic

temperature

Amount ofsubstance

Luminousintensity

Base

units meter

kilo-


Unitsymbol

m


kg s A K mol cd

Quantity

Symbol



Unit



Length

A S square meter

arehectare

m2

aha

1 m2 = 10 000 cm2

= 1 000 000 mm2

1 a = 100 m2

1 ha = 100 a = 10 000 m2

100 ha = 1 km2



Area

V cubic meter

liter

m3

mdash L

1 m3 = 1000 dm3

= 1 000 000 cm3


1 m mdash = 1 cm

3


Volume

a b g hellip radian

degrees

minutes

seconds

rad

deg

+


1deg = p

rad = 60 180

1 = 1deg60 = 60+1+ = 1 60 = 1deg3600


Planeangle(angle)


Solid angle

m kilogramgram

megagrammetric ton

kgg

Mgt

1 kg = 1000 g1 g = 1000 mg

1 metric t = 1000 kg = 1 Mg02 g = 1 ct



Mass

m kilogramper meter


Linear massdensity





= 1 gcm3

= 1 gml

= 1 mgmm3


Density




M

P

TD

MS

ME

PE

A

S







Mechanics

F

F G G

newton N1 N = 1

kg middot m= 1

J s2 m

1 MN = 103 kN = 1 000 000 N


Force

Weight

M M bT

newton xmeter


kg middot m2



p kilogram xmeter

per second



Momentum

p

s t

pascal


Pa

Nmm2

1 Pa = 1 Nm2 = 001 mbar1 bar = 100 000 Nm2





Pressure

Mechanicalstress


m4

cm4


Secondmoment ofarea




PG



PowerHeat flux

Time


sminhda

1 min = 60 s1 h = 60 min = 3600 s1 d = 24 h = 86 400 s




n 1 per second

1 per minute

1s

1min



60 s



v meters persecond

meters perminute

kilometers perhour

ms

mmin

kmh


1 mmin =1 m

60 s

1 kmh =1 m

36 s


1 kn = 1852 kmh


Velocity

w 1 per second

radians persecond

1s

rads


velocity w = 4 p s

Angular-

velocity


ms21 ms2 =

1 ms 1 s


g = 981 ms2 fi 10 ms2

Acceleration

QuantitySym-bol

Unit






M

P

D

S

E

E

A


QuantitySym-bol

Unit

NameRelationship



I

E

R

G

amperevolt

ohm

siemens

AV

O

S

1 V = 1 W1 A = 1 JC

1 O = 1 V1 A

1 S = 1 A1 V = 1 O





r

g k

ohm xmeter

siemensper meter

O middotm

Sm


k= 1 2

in mm

m

Ω middot

kr

= 1

2in

m

mmΩ middot

Specificresistance

Conductivity


Frequency



Electrical energy



cos j = P

U middot I

Phasedifference




E F

Q C

Q

U Q t = = = middotI

E Q C L


henry

VmCFH






QuantitySym-bol

Unit

NameRelationship


Sym-bol

Non-SI units

T Q

t h

kelvin

degreesCelsius

K

degC




Thermo-

dynamic

temperature

Celsiustemperature



H u joule per


Jkg

Jm3

1 MJkg = 1 000 000 Jkg

1 MJm3 = 1 000 000 Jm3



Net calorific

value



1 foot (ft) = 03048 m

1 yard(yd) = 09144 m

1 nautical

mile = 1852 km1 mile = 16093 km

1 sqin = 6452 cm2

1 sqft = 929 dm2

1 sqyd = 08361 m2

1 acre = 4046856m2

Pressure

1 bar = 145poundin2


1 cuin = 1639 cm3

1 cuft = 2832 dm3

1 cuyd = 7646 dm3




1 oz = 2835 g

1 lb = 4536 g

1 t = 1000 kg


1 Karat = 02 g


1 PSh = 0735 kWh

1 PS = 735 W

1 kcal = 41868 Ws

1 kcal = 1166 Wh

1 kpms = 9807 W

1 Btu = 1055 Ws

1 hp = 7457 W

Sym-bol



1312 Formulas

M

P

TD

MS

ME

PE

A

S

FormulaMeaning

symbol

Œ Length

w Width

h Height

s Linear distance

r R Radius

d D Diameter


V Volume

a b g Planar angle

W Solid angle

l Wave length

FormulaMeaning

symbol

FormulaMeaning

symbol




t Time Duration

T Cycle duration


Speed

f v Frequency

v u Velocity

w Angular velocity

a Acceleration



Qmiddot


Time





Electricity





coefficient


Heat












proportional an


power of a 0 3

square root of

n0 3 n-th root of







lg common logarithm






AB line segment AB




Acoustics

m Mass



r Density

J Moment of inertia

p Pressure



p g Gage pressure

F Force


T Torsional moment

M b Bending moment

s Normal stress

t Shear stress

e Normal strain


G Shear modulus


W Section modulus


W E Work Energy



P Power

n Efficiency

Mechanics


MathSpoken

symbol

MathSpoken

symbol

MathSpoken

symbol

ordm

ordmordm





1512 Formulas

M

P

TD

MS

ME

PE

A

S



Example formula n =

ŒŒ1 + s


Example formula c =














Formula

P =

F middot s

t


1222222

122222

1

1

1

1

3

3

4

4

2

2

2

2

3

3

4

4

5

5

6

6



n =

ŒŒ1 + s


c = a 2 + b 2 aelig( )2

L ndash Œ1 = Œ2

A

b = Œ




A

b = Œ middot b

b


(Œ1 + s )




Œ2 = L ndash Œ1

Œ = A

b

s middot n

n


n

a 2 = c 2 ndash b 2

s =


a = c 2 ndash b 2

subtract Œ1

divide by b


square equation

invert both sides

invert both sides

subtractdivide by n

extract the root

performsubtraction

cancel b



subtract b 2



transformedformula

transformedformula

cancel n


transformedformula

transformedformula

122 1222222

1222222



16 12 Formulas

M

P

D

S

E

E

A

Conversion of units





Prefix Powerof ten


ExamplesSymbol Name







= 5 h mdash

(hectoliters)










Length 1 =

10 mm1 cm

=

1000 mm1 m

=

1 m1000 mm

=

1 km1000 m

Time 1 =

60 min1 h

=

3600 s1 h

=

60 s1 min

=

1 min60 s

Area 1 =

100 mm2

1 cm2 =

100 cm2

1 dm2 =

Angle 1 =

60rsquo1deg

=

60rsquorsquo1rsquo

=

3600rsquorsquo1deg

=

1deg60 s

Volume 1 =

1000 mm3

1 cm3 =

1000 cm3


1

254 inches





Physical quantity

10 mm

Numerical Unitvalue



V = 3416 mm3 =1 cm3 middot 3416 mm3

1000 mm3 =

3416 cm3

1000 = 3416 cm 3





60 = 42deg + 0267deg = 42267deg

1st example

2nd example





aring iquest

b a

c

copy


iquest

para

aring copy

g

g2

g1


M

P

D

S

E

E

A

b2

a2

c2

abc

G 0 3

P1 X

Z

P2

RK I


Types of angles


Pythagorean theorem

D d

a2

daggerto

daggerti

a1

b 1

b 2

g straight line




a g adjacent angles



a = b


b = d

Opposite angles

a = d

Alternate angles

a + g = 180deg

Adjacent angles

a

b

a

b

1

1

2

2

=

b

d

b

D

1 2=

a

a

b

b

d

D

1

2

1

2

2

2

= =


a + b + g = 180deg




Example

a = 21deg b = 95deg g =


Example

t

t

t

tti

to

tito

= rArr =

=

d

D

d

D

middot


4

2

00 mm= 101 Nmm225





c a b

c a

=

=

35 mm = 21 mm =


1st example

c 2 = a 2 + b 2





2nd example

c a b

R K

K R

2 2 2

2 2 2

2 2 2 250 25

= +

= +

= =

=

I


K 433mm

c a b = +2 2


a c b = 2 2ndash

b c a = 2 2ndash

Length of the sides





M

P

TD

MS

ME

PE

A

S


c hypotenuse





iquestc hypotenuse

F

L3=140mm

L

L

1 = 1 5 0 m

m

L

2 = 3 0 m m

aring

szlig

copy

aring iquest

b a

c

Fd

Fz

F

4 0

1 2

szlig = 3 8

aring = 4 0

1 2

copy = 1 0

2

Fd

Fz

F

Diagram of forces




hypotenuse



adjacent side















1st example

tan a =+

= =L L

L

1 2

3

1 286180 mm

140 mm


2nd example

L =+

= =L L1 2

sina

180 mm

sin 52deg22842mm

F = 800 N a = 40deg b = 38deg F z = F d =



Example

F F F

F

sin sin

middot sin

sina b

b

a= rArr =

=

zz


ssin40deg= 76624 N

F F F

F

sin sin

middot sin

sina g

g

a= rArr =

=

dd


degdeg

sin40deg= 121738 N


sina =

a

c cosa =

b

c tana =

a

b


sinb =

b

c cosb =

a

c tanb =

b

a


a =

b middot sinasinb

=

c middot sinasing

b =

a middot sinbsina

=

c middot sinbsing

c =

a middot singsina

=

b middot singsinb

Law of sines


a

sina =

b

sinb =

c

sing

Law of cosines



Transformation e g

cosa =

b 2 + c 2 ndash a 2

2 middot b middot c



20 14 Lengths



Spacing

Spacing


Arc length


Composite length


Composite length





Example


Example

Number of pieces


Example


Remaining length


Example

Arc length

M

P

D

S

E

E

A



8










Draft E DIN 743(2008-10)


Preliminary

standard

DIN V 66304

(1991-04)









EuropeanStandards

(EN standards)























9Table of Contents

1 Mathematics

M

P

TD

MS

ME

PE

A

S

Quantity SymbolUnit

Name Symbol

Lengths Œ meter m



Non-SI units 12

12 Formulas





14 Lengths


Rough lengths 21

15 Areas





17 Mass


18 Centroids




hypotenuse


adjacent side

xsx

y s

y

S1

S2

S

m inkg

m 1 m

d

A d h d

s = +p

p


24

2

Surface area






M

P

D

S

E

E

A





Mechanics

Basequantity


Thermo-dynamic

temperature

Amount ofsubstance

Luminousintensity

Base

units meter

kilo-


Unitsymbol

m


kg s A K mol cd

Quantity

Symbol



Unit



Length

A S square meter

arehectare

m2

aha

1 m2 = 10 000 cm2

= 1 000 000 mm2

1 a = 100 m2

1 ha = 100 a = 10 000 m2

100 ha = 1 km2



Area

V cubic meter

liter

m3

mdash L

1 m3 = 1000 dm3

= 1 000 000 cm3


1 m mdash = 1 cm

3


Volume

a b g hellip radian

degrees

minutes

seconds

rad

deg

+


1deg = p

rad = 60 180

1 = 1deg60 = 60+1+ = 1 60 = 1deg3600


Planeangle(angle)


Solid angle

m kilogramgram

megagrammetric ton

kgg

Mgt

1 kg = 1000 g1 g = 1000 mg

1 metric t = 1000 kg = 1 Mg02 g = 1 ct



Mass

m kilogramper meter


Linear massdensity





= 1 gcm3

= 1 gml

= 1 mgmm3


Density




M

P

TD

MS

ME

PE

A

S







Mechanics

F

F G G

newton N1 N = 1

kg middot m= 1

J s2 m

1 MN = 103 kN = 1 000 000 N


Force

Weight

M M bT

newton xmeter


kg middot m2



p kilogram xmeter

per second



Momentum

p

s t

pascal


Pa

Nmm2

1 Pa = 1 Nm2 = 001 mbar1 bar = 100 000 Nm2





Pressure

Mechanicalstress


m4

cm4


Secondmoment ofarea




PG



PowerHeat flux

Time


sminhda

1 min = 60 s1 h = 60 min = 3600 s1 d = 24 h = 86 400 s




n 1 per second

1 per minute

1s

1min



60 s



v meters persecond

meters perminute

kilometers perhour

ms

mmin

kmh


1 mmin =1 m

60 s

1 kmh =1 m

36 s


1 kn = 1852 kmh


Velocity

w 1 per second

radians persecond

1s

rads


velocity w = 4 p s

Angular-

velocity


ms21 ms2 =

1 ms 1 s


g = 981 ms2 fi 10 ms2

Acceleration

QuantitySym-bol

Unit






M

P

D

S

E

E

A


QuantitySym-bol

Unit

NameRelationship



I

E

R

G

amperevolt

ohm

siemens

AV

O

S

1 V = 1 W1 A = 1 JC

1 O = 1 V1 A

1 S = 1 A1 V = 1 O





r

g k

ohm xmeter

siemensper meter

O middotm

Sm


k= 1 2

in mm

m

Ω middot

kr

= 1

2in

m

mmΩ middot

Specificresistance

Conductivity


Frequency



Electrical energy



cos j = P

U middot I

Phasedifference




E F

Q C

Q

U Q t = = = middotI

E Q C L


henry

VmCFH






QuantitySym-bol

Unit

NameRelationship


Sym-bol

Non-SI units

T Q

t h

kelvin

degreesCelsius

K

degC




Thermo-

dynamic

temperature

Celsiustemperature



H u joule per


Jkg

Jm3

1 MJkg = 1 000 000 Jkg

1 MJm3 = 1 000 000 Jm3



Net calorific

value



1 foot (ft) = 03048 m

1 yard(yd) = 09144 m

1 nautical

mile = 1852 km1 mile = 16093 km

1 sqin = 6452 cm2

1 sqft = 929 dm2

1 sqyd = 08361 m2

1 acre = 4046856m2

Pressure

1 bar = 145poundin2


1 cuin = 1639 cm3

1 cuft = 2832 dm3

1 cuyd = 7646 dm3




1 oz = 2835 g

1 lb = 4536 g

1 t = 1000 kg


1 Karat = 02 g


1 PSh = 0735 kWh

1 PS = 735 W

1 kcal = 41868 Ws

1 kcal = 1166 Wh

1 kpms = 9807 W

1 Btu = 1055 Ws

1 hp = 7457 W

Sym-bol



1312 Formulas

M

P

TD

MS

ME

PE

A

S

FormulaMeaning

symbol

Œ Length

w Width

h Height

s Linear distance

r R Radius

d D Diameter


V Volume

a b g Planar angle

W Solid angle

l Wave length

FormulaMeaning

symbol

FormulaMeaning

symbol




t Time Duration

T Cycle duration


Speed

f v Frequency

v u Velocity

w Angular velocity

a Acceleration



Qmiddot


Time





Electricity





coefficient


Heat












proportional an


power of a 0 3

square root of

n0 3 n-th root of







lg common logarithm






AB line segment AB




Acoustics

m Mass



r Density

J Moment of inertia

p Pressure



p g Gage pressure

F Force


T Torsional moment

M b Bending moment

s Normal stress

t Shear stress

e Normal strain


G Shear modulus


W Section modulus


W E Work Energy



P Power

n Efficiency

Mechanics


MathSpoken

symbol

MathSpoken

symbol

MathSpoken

symbol

ordm

ordmordm





1512 Formulas

M

P

TD

MS

ME

PE

A

S



Example formula n =

ŒŒ1 + s


Example formula c =














Formula

P =

F middot s

t


1222222

122222

1

1

1

1

3

3

4

4

2

2

2

2

3

3

4

4

5

5

6

6



n =

ŒŒ1 + s


c = a 2 + b 2 aelig( )2

L ndash Œ1 = Œ2

A

b = Œ




A

b = Œ middot b

b


(Œ1 + s )




Œ2 = L ndash Œ1

Œ = A

b

s middot n

n


n

a 2 = c 2 ndash b 2

s =


a = c 2 ndash b 2

subtract Œ1

divide by b


square equation

invert both sides

invert both sides

subtractdivide by n

extract the root

performsubtraction

cancel b



subtract b 2



transformedformula

transformedformula

cancel n


transformedformula

transformedformula

122 1222222

1222222



16 12 Formulas

M

P

D

S

E

E

A

Conversion of units





Prefix Powerof ten


ExamplesSymbol Name







= 5 h mdash

(hectoliters)










Length 1 =

10 mm1 cm

=

1000 mm1 m

=

1 m1000 mm

=

1 km1000 m

Time 1 =

60 min1 h

=

3600 s1 h

=

60 s1 min

=

1 min60 s

Area 1 =

100 mm2

1 cm2 =

100 cm2

1 dm2 =

Angle 1 =

60rsquo1deg

=

60rsquorsquo1rsquo

=

3600rsquorsquo1deg

=

1deg60 s

Volume 1 =

1000 mm3

1 cm3 =

1000 cm3


1

254 inches





Physical quantity

10 mm

Numerical Unitvalue



V = 3416 mm3 =1 cm3 middot 3416 mm3

1000 mm3 =

3416 cm3

1000 = 3416 cm 3





60 = 42deg + 0267deg = 42267deg

1st example

2nd example





aring iquest

b a

c

copy


iquest

para

aring copy

g

g2

g1


M

P

D

S

E

E

A

b2

a2

c2

abc

G 0 3

P1 X

Z

P2

RK I


Types of angles


Pythagorean theorem

D d

a2

daggerto

daggerti

a1

b 1

b 2

g straight line




a g adjacent angles



a = b


b = d

Opposite angles

a = d

Alternate angles

a + g = 180deg

Adjacent angles

a

b

a

b

1

1

2

2

=

b

d

b

D

1 2=

a

a

b

b

d

D

1

2

1

2

2

2

= =


a + b + g = 180deg




Example

a = 21deg b = 95deg g =


Example

t

t

t

tti

to

tito

= rArr =

=

d

D

d

D

middot


4

2

00 mm= 101 Nmm225





c a b

c a

=

=

35 mm = 21 mm =


1st example

c 2 = a 2 + b 2





2nd example

c a b

R K

K R

2 2 2

2 2 2

2 2 2 250 25

= +

= +

= =

=

I


K 433mm

c a b = +2 2


a c b = 2 2ndash

b c a = 2 2ndash

Length of the sides





M

P

TD

MS

ME

PE

A

S


c hypotenuse





iquestc hypotenuse

F

L3=140mm

L

L

1 = 1 5 0 m

m

L

2 = 3 0 m m

aring

szlig

copy

aring iquest

b a

c

Fd

Fz

F

4 0

1 2

szlig = 3 8

aring = 4 0

1 2

copy = 1 0

2

Fd

Fz

F

Diagram of forces




hypotenuse



adjacent side















1st example

tan a =+

= =L L

L

1 2

3

1 286180 mm

140 mm


2nd example

L =+

= =L L1 2

sina

180 mm

sin 52deg22842mm

F = 800 N a = 40deg b = 38deg F z = F d =



Example

F F F

F

sin sin

middot sin

sina b

b

a= rArr =

=

zz


ssin40deg= 76624 N

F F F

F

sin sin

middot sin

sina g

g

a= rArr =

=

dd


degdeg

sin40deg= 121738 N


sina =

a

c cosa =

b

c tana =

a

b


sinb =

b

c cosb =

a

c tanb =

b

a


a =

b middot sinasinb

=

c middot sinasing

b =

a middot sinbsina

=

c middot sinbsing

c =

a middot singsina

=

b middot singsinb

Law of sines


a

sina =

b

sinb =

c

sing

Law of cosines



Transformation e g

cosa =

b 2 + c 2 ndash a 2

2 middot b middot c



20 14 Lengths



Spacing

Spacing


Arc length


Composite length


Composite length





Example


Example

Number of pieces


Example


Remaining length


Example

Arc length

M

P

D

S

E

E

A



9Table of Contents

1 Mathematics

M

P

TD

MS

ME

PE

A

S

Quantity SymbolUnit

Name Symbol

Lengths Œ meter m



Non-SI units 12

12 Formulas





14 Lengths


Rough lengths 21

15 Areas





17 Mass


18 Centroids




hypotenuse


adjacent side

xsx

y s

y

S1

S2

S

m inkg

m 1 m

d

A d h d

s = +p

p


24

2

Surface area






M

P

D

S

E

E

A





Mechanics

Basequantity


Thermo-dynamic

temperature

Amount ofsubstance

Luminousintensity

Base

units meter

kilo-


Unitsymbol

m


kg s A K mol cd

Quantity

Symbol



Unit



Length

A S square meter

arehectare

m2

aha

1 m2 = 10 000 cm2

= 1 000 000 mm2

1 a = 100 m2

1 ha = 100 a = 10 000 m2

100 ha = 1 km2



Area

V cubic meter

liter

m3

mdash L

1 m3 = 1000 dm3

= 1 000 000 cm3


1 m mdash = 1 cm

3


Volume

a b g hellip radian

degrees

minutes

seconds

rad

deg

+


1deg = p

rad = 60 180

1 = 1deg60 = 60+1+ = 1 60 = 1deg3600


Planeangle(angle)


Solid angle

m kilogramgram

megagrammetric ton

kgg

Mgt

1 kg = 1000 g1 g = 1000 mg

1 metric t = 1000 kg = 1 Mg02 g = 1 ct



Mass

m kilogramper meter


Linear massdensity





= 1 gcm3

= 1 gml

= 1 mgmm3


Density




M

P

TD

MS

ME

PE

A

S







Mechanics

F

F G G

newton N1 N = 1

kg middot m= 1

J s2 m

1 MN = 103 kN = 1 000 000 N


Force

Weight

M M bT

newton xmeter


kg middot m2



p kilogram xmeter

per second



Momentum

p

s t

pascal


Pa

Nmm2

1 Pa = 1 Nm2 = 001 mbar1 bar = 100 000 Nm2





Pressure

Mechanicalstress


m4

cm4


Secondmoment ofarea




PG



PowerHeat flux

Time


sminhda

1 min = 60 s1 h = 60 min = 3600 s1 d = 24 h = 86 400 s




n 1 per second

1 per minute

1s

1min



60 s



v meters persecond

meters perminute

kilometers perhour

ms

mmin

kmh


1 mmin =1 m

60 s

1 kmh =1 m

36 s


1 kn = 1852 kmh


Velocity

w 1 per second

radians persecond

1s

rads


velocity w = 4 p s

Angular-

velocity


ms21 ms2 =

1 ms 1 s


g = 981 ms2 fi 10 ms2

Acceleration

QuantitySym-bol

Unit






M

P

D

S

E

E

A


QuantitySym-bol

Unit

NameRelationship



I

E

R

G

amperevolt

ohm

siemens

AV

O

S

1 V = 1 W1 A = 1 JC

1 O = 1 V1 A

1 S = 1 A1 V = 1 O





r

g k

ohm xmeter

siemensper meter

O middotm

Sm


k= 1 2

in mm

m

Ω middot

kr

= 1

2in

m

mmΩ middot

Specificresistance

Conductivity


Frequency



Electrical energy



cos j = P

U middot I

Phasedifference




E F

Q C

Q

U Q t = = = middotI

E Q C L


henry

VmCFH






QuantitySym-bol

Unit

NameRelationship


Sym-bol

Non-SI units

T Q

t h

kelvin

degreesCelsius

K

degC




Thermo-

dynamic

temperature

Celsiustemperature



H u joule per


Jkg

Jm3

1 MJkg = 1 000 000 Jkg

1 MJm3 = 1 000 000 Jm3



Net calorific

value



1 foot (ft) = 03048 m

1 yard(yd) = 09144 m

1 nautical

mile = 1852 km1 mile = 16093 km

1 sqin = 6452 cm2

1 sqft = 929 dm2

1 sqyd = 08361 m2

1 acre = 4046856m2

Pressure

1 bar = 145poundin2


1 cuin = 1639 cm3

1 cuft = 2832 dm3

1 cuyd = 7646 dm3




1 oz = 2835 g

1 lb = 4536 g

1 t = 1000 kg


1 Karat = 02 g


1 PSh = 0735 kWh

1 PS = 735 W

1 kcal = 41868 Ws

1 kcal = 1166 Wh

1 kpms = 9807 W

1 Btu = 1055 Ws

1 hp = 7457 W

Sym-bol



1312 Formulas

M

P

TD

MS

ME

PE

A

S

FormulaMeaning

symbol

Œ Length

w Width

h Height

s Linear distance

r R Radius

d D Diameter


V Volume

a b g Planar angle

W Solid angle

l Wave length

FormulaMeaning

symbol

FormulaMeaning

symbol




t Time Duration

T Cycle duration


Speed

f v Frequency

v u Velocity

w Angular velocity

a Acceleration



Qmiddot


Time





Electricity





coefficient


Heat












proportional an


power of a 0 3

square root of

n0 3 n-th root of







lg common logarithm






AB line segment AB




Acoustics

m Mass



r Density

J Moment of inertia

p Pressure



p g Gage pressure

F Force


T Torsional moment

M b Bending moment

s Normal stress

t Shear stress

e Normal strain


G Shear modulus


W Section modulus


W E Work Energy



P Power

n Efficiency

Mechanics


MathSpoken

symbol

MathSpoken

symbol

MathSpoken

symbol

ordm

ordmordm





1512 Formulas

M

P

TD

MS

ME

PE

A

S



Example formula n =

ŒŒ1 + s


Example formula c =














Formula

P =

F middot s

t


1222222

122222

1

1

1

1

3

3

4

4

2

2

2

2

3

3

4

4

5

5

6

6



n =

ŒŒ1 + s


c = a 2 + b 2 aelig( )2

L ndash Œ1 = Œ2

A

b = Œ




A

b = Œ middot b

b


(Œ1 + s )




Œ2 = L ndash Œ1

Œ = A

b

s middot n

n


n

a 2 = c 2 ndash b 2

s =


a = c 2 ndash b 2

subtract Œ1

divide by b


square equation

invert both sides

invert both sides

subtractdivide by n

extract the root

performsubtraction

cancel b



subtract b 2



transformedformula

transformedformula

cancel n


transformedformula

transformedformula

122 1222222

1222222



16 12 Formulas

M

P

D

S

E

E

A

Conversion of units





Prefix Powerof ten


ExamplesSymbol Name







= 5 h mdash

(hectoliters)










Length 1 =

10 mm1 cm

=

1000 mm1 m

=

1 m1000 mm

=

1 km1000 m

Time 1 =

60 min1 h

=

3600 s1 h

=

60 s1 min

=

1 min60 s

Area 1 =

100 mm2

1 cm2 =

100 cm2

1 dm2 =

Angle 1 =

60rsquo1deg

=

60rsquorsquo1rsquo

=

3600rsquorsquo1deg

=

1deg60 s

Volume 1 =

1000 mm3

1 cm3 =

1000 cm3


1

254 inches





Physical quantity

10 mm

Numerical Unitvalue



V = 3416 mm3 =1 cm3 middot 3416 mm3

1000 mm3 =

3416 cm3

1000 = 3416 cm 3





60 = 42deg + 0267deg = 42267deg

1st example

2nd example





aring iquest

b a

c

copy


iquest

para

aring copy

g

g2

g1


M

P

D

S

E

E

A

b2

a2

c2

abc

G 0 3

P1 X

Z

P2

RK I


Types of angles


Pythagorean theorem

D d

a2

daggerto

daggerti

a1

b 1

b 2

g straight line




a g adjacent angles



a = b


b = d

Opposite angles

a = d

Alternate angles

a + g = 180deg

Adjacent angles

a

b

a

b

1

1

2

2

=

b

d

b

D

1 2=

a

a

b

b

d

D

1

2

1

2

2

2

= =


a + b + g = 180deg




Example

a = 21deg b = 95deg g =


Example

t

t

t

tti

to

tito

= rArr =

=

d

D

d

D

middot


4

2

00 mm= 101 Nmm225





c a b

c a

=

=

35 mm = 21 mm =


1st example

c 2 = a 2 + b 2





2nd example

c a b

R K

K R

2 2 2

2 2 2

2 2 2 250 25

= +

= +

= =

=

I


K 433mm

c a b = +2 2


a c b = 2 2ndash

b c a = 2 2ndash

Length of the sides





M

P

TD

MS

ME

PE

A

S


c hypotenuse





iquestc hypotenuse

F

L3=140mm

L

L

1 = 1 5 0 m

m

L

2 = 3 0 m m

aring

szlig

copy

aring iquest

b a

c

Fd

Fz

F

4 0

1 2

szlig = 3 8

aring = 4 0

1 2

copy = 1 0

2

Fd

Fz

F

Diagram of forces




hypotenuse



adjacent side















1st example

tan a =+

= =L L

L

1 2

3

1 286180 mm

140 mm


2nd example

L =+

= =L L1 2

sina

180 mm

sin 52deg22842mm

F = 800 N a = 40deg b = 38deg F z = F d =



Example

F F F

F

sin sin

middot sin

sina b

b

a= rArr =

=

zz


ssin40deg= 76624 N

F F F

F

sin sin

middot sin

sina g

g

a= rArr =

=

dd


degdeg

sin40deg= 121738 N


sina =

a

c cosa =

b

c tana =

a

b


sinb =

b

c cosb =

a

c tanb =

b

a


a =

b middot sinasinb

=

c middot sinasing

b =

a middot sinbsina

=

c middot sinbsing

c =

a middot singsina

=

b middot singsinb

Law of sines


a

sina =

b

sinb =

c

sing

Law of cosines



Transformation e g

cosa =

b 2 + c 2 ndash a 2

2 middot b middot c



20 14 Lengths



Spacing

Spacing


Arc length


Composite length


Composite length





Example


Example

Number of pieces


Example


Remaining length


Example

Arc length

M

P

D

S

E

E

A




M

P

D

S

E

E

A





Mechanics

Basequantity


Thermo-dynamic

temperature

Amount ofsubstance

Luminousintensity

Base

units meter

kilo-


Unitsymbol

m


kg s A K mol cd

Quantity

Symbol



Unit



Length

A S square meter

arehectare

m2

aha

1 m2 = 10 000 cm2

= 1 000 000 mm2

1 a = 100 m2

1 ha = 100 a = 10 000 m2

100 ha = 1 km2



Area

V cubic meter

liter

m3

mdash L

1 m3 = 1000 dm3

= 1 000 000 cm3


1 m mdash = 1 cm

3


Volume

a b g hellip radian

degrees

minutes

seconds

rad

deg

+


1deg = p

rad = 60 180

1 = 1deg60 = 60+1+ = 1 60 = 1deg3600


Planeangle(angle)


Solid angle

m kilogramgram

megagrammetric ton

kgg

Mgt

1 kg = 1000 g1 g = 1000 mg

1 metric t = 1000 kg = 1 Mg02 g = 1 ct



Mass

m kilogramper meter


Linear massdensity





= 1 gcm3

= 1 gml

= 1 mgmm3


Density




M

P

TD

MS

ME

PE

A

S







Mechanics

F

F G G

newton N1 N = 1

kg middot m= 1

J s2 m

1 MN = 103 kN = 1 000 000 N


Force

Weight

M M bT

newton xmeter


kg middot m2



p kilogram xmeter

per second



Momentum

p

s t

pascal


Pa

Nmm2

1 Pa = 1 Nm2 = 001 mbar1 bar = 100 000 Nm2





Pressure

Mechanicalstress


m4

cm4


Secondmoment ofarea




PG



PowerHeat flux

Time


sminhda

1 min = 60 s1 h = 60 min = 3600 s1 d = 24 h = 86 400 s




n 1 per second

1 per minute

1s

1min



60 s



v meters persecond

meters perminute

kilometers perhour

ms

mmin

kmh


1 mmin =1 m

60 s

1 kmh =1 m

36 s


1 kn = 1852 kmh


Velocity

w 1 per second

radians persecond

1s

rads


velocity w = 4 p s

Angular-

velocity


ms21 ms2 =

1 ms 1 s


g = 981 ms2 fi 10 ms2

Acceleration

QuantitySym-bol

Unit






M

P

D

S

E

E

A


QuantitySym-bol

Unit

NameRelationship



I

E

R

G

amperevolt

ohm

siemens

AV

O

S

1 V = 1 W1 A = 1 JC

1 O = 1 V1 A

1 S = 1 A1 V = 1 O





r

g k

ohm xmeter

siemensper meter

O middotm

Sm


k= 1 2

in mm

m

Ω middot

kr

= 1

2in

m

mmΩ middot

Specificresistance

Conductivity


Frequency



Electrical energy



cos j = P

U middot I

Phasedifference




E F

Q C

Q

U Q t = = = middotI

E Q C L


henry

VmCFH






QuantitySym-bol

Unit

NameRelationship


Sym-bol

Non-SI units

T Q

t h

kelvin

degreesCelsius

K

degC




Thermo-

dynamic

temperature

Celsiustemperature



H u joule per


Jkg

Jm3

1 MJkg = 1 000 000 Jkg

1 MJm3 = 1 000 000 Jm3



Net calorific

value



1 foot (ft) = 03048 m

1 yard(yd) = 09144 m

1 nautical

mile = 1852 km1 mile = 16093 km

1 sqin = 6452 cm2

1 sqft = 929 dm2

1 sqyd = 08361 m2

1 acre = 4046856m2

Pressure

1 bar = 145poundin2


1 cuin = 1639 cm3

1 cuft = 2832 dm3

1 cuyd = 7646 dm3




1 oz = 2835 g

1 lb = 4536 g

1 t = 1000 kg


1 Karat = 02 g


1 PSh = 0735 kWh

1 PS = 735 W

1 kcal = 41868 Ws

1 kcal = 1166 Wh

1 kpms = 9807 W

1 Btu = 1055 Ws

1 hp = 7457 W

Sym-bol



1312 Formulas

M

P

TD

MS

ME

PE

A

S

FormulaMeaning

symbol

Œ Length

w Width

h Height

s Linear distance

r R Radius

d D Diameter


V Volume

a b g Planar angle

W Solid angle

l Wave length

FormulaMeaning

symbol

FormulaMeaning

symbol




t Time Duration

T Cycle duration


Speed

f v Frequency

v u Velocity

w Angular velocity

a Acceleration



Qmiddot


Time





Electricity





coefficient


Heat












proportional an


power of a 0 3

square root of

n0 3 n-th root of







lg common logarithm






AB line segment AB




Acoustics

m Mass



r Density

J Moment of inertia

p Pressure



p g Gage pressure

F Force


T Torsional moment

M b Bending moment

s Normal stress

t Shear stress

e Normal strain


G Shear modulus


W Section modulus


W E Work Energy



P Power

n Efficiency

Mechanics


MathSpoken

symbol

MathSpoken

symbol

MathSpoken

symbol

ordm

ordmordm





1512 Formulas

M

P

TD

MS

ME

PE

A

S



Example formula n =

ŒŒ1 + s


Example formula c =














Formula

P =

F middot s

t


1222222

122222

1

1

1

1

3

3

4

4

2

2

2

2

3

3

4

4

5

5

6

6



n =

ŒŒ1 + s


c = a 2 + b 2 aelig( )2

L ndash Œ1 = Œ2

A

b = Œ




A

b = Œ middot b

b


(Œ1 + s )




Œ2 = L ndash Œ1

Œ = A

b

s middot n

n


n

a 2 = c 2 ndash b 2

s =


a = c 2 ndash b 2

subtract Œ1

divide by b


square equation

invert both sides

invert both sides

subtractdivide by n

extract the root

performsubtraction

cancel b



subtract b 2



transformedformula

transformedformula

cancel n


transformedformula

transformedformula

122 1222222

1222222



16 12 Formulas

M

P

D

S

E

E

A

Conversion of units





Prefix Powerof ten


ExamplesSymbol Name







= 5 h mdash

(hectoliters)










Length 1 =

10 mm1 cm

=

1000 mm1 m

=

1 m1000 mm

=

1 km1000 m

Time 1 =

60 min1 h

=

3600 s1 h

=

60 s1 min

=

1 min60 s

Area 1 =

100 mm2

1 cm2 =

100 cm2

1 dm2 =

Angle 1 =

60rsquo1deg

=

60rsquorsquo1rsquo

=

3600rsquorsquo1deg

=

1deg60 s

Volume 1 =

1000 mm3

1 cm3 =

1000 cm3


1

254 inches





Physical quantity

10 mm

Numerical Unitvalue



V = 3416 mm3 =1 cm3 middot 3416 mm3

1000 mm3 =

3416 cm3

1000 = 3416 cm 3





60 = 42deg + 0267deg = 42267deg

1st example

2nd example





aring iquest

b a

c

copy


iquest

para

aring copy

g

g2

g1


M

P

D

S

E

E

A

b2

a2

c2

abc

G 0 3

P1 X

Z

P2

RK I


Types of angles


Pythagorean theorem

D d

a2

daggerto

daggerti

a1

b 1

b 2

g straight line




a g adjacent angles



a = b


b = d

Opposite angles

a = d

Alternate angles

a + g = 180deg

Adjacent angles

a

b

a

b

1

1

2

2

=

b

d

b

D

1 2=

a

a

b

b

d

D

1

2

1

2

2

2

= =


a + b + g = 180deg




Example

a = 21deg b = 95deg g =


Example

t

t

t

tti

to

tito

= rArr =

=

d

D

d

D

middot


4

2

00 mm= 101 Nmm225





c a b

c a

=

=

35 mm = 21 mm =


1st example

c 2 = a 2 + b 2





2nd example

c a b

R K

K R

2 2 2

2 2 2

2 2 2 250 25

= +

= +

= =

=

I


K 433mm

c a b = +2 2


a c b = 2 2ndash

b c a = 2 2ndash

Length of the sides





M

P

TD

MS

ME

PE

A

S


c hypotenuse





iquestc hypotenuse

F

L3=140mm

L

L

1 = 1 5 0 m

m

L

2 = 3 0 m m

aring

szlig

copy

aring iquest

b a

c

Fd

Fz

F

4 0

1 2

szlig = 3 8

aring = 4 0

1 2

copy = 1 0

2

Fd

Fz

F

Diagram of forces




hypotenuse



adjacent side















1st example

tan a =+

= =L L

L

1 2

3

1 286180 mm

140 mm


2nd example

L =+

= =L L1 2

sina

180 mm

sin 52deg22842mm

F = 800 N a = 40deg b = 38deg F z = F d =



Example

F F F

F

sin sin

middot sin

sina b

b

a= rArr =

=

zz


ssin40deg= 76624 N

F F F

F

sin sin

middot sin

sina g

g

a= rArr =

=

dd


degdeg

sin40deg= 121738 N


sina =

a

c cosa =

b

c tana =

a

b


sinb =

b

c cosb =

a

c tanb =

b

a


a =

b middot sinasinb

=

c middot sinasing

b =

a middot sinbsina

=

c middot sinbsing

c =

a middot singsina

=

b middot singsinb

Law of sines


a

sina =

b

sinb =

c

sing

Law of cosines



Transformation e g

cosa =

b 2 + c 2 ndash a 2

2 middot b middot c



20 14 Lengths



Spacing

Spacing


Arc length


Composite length


Composite length





Example


Example

Number of pieces


Example


Remaining length


Example

Arc length

M

P

D

S

E

E

A




M

P

TD

MS

ME

PE

A

S







Mechanics

F

F G G

newton N1 N = 1

kg middot m= 1

J s2 m

1 MN = 103 kN = 1 000 000 N


Force

Weight

M M bT

newton xmeter


kg middot m2



p kilogram xmeter

per second



Momentum

p

s t

pascal


Pa

Nmm2

1 Pa = 1 Nm2 = 001 mbar1 bar = 100 000 Nm2





Pressure

Mechanicalstress


m4

cm4


Secondmoment ofarea




PG



PowerHeat flux

Time


sminhda

1 min = 60 s1 h = 60 min = 3600 s1 d = 24 h = 86 400 s




n 1 per second

1 per minute

1s

1min



60 s



v meters persecond

meters perminute

kilometers perhour

ms

mmin

kmh


1 mmin =1 m

60 s

1 kmh =1 m

36 s


1 kn = 1852 kmh


Velocity

w 1 per second

radians persecond

1s

rads


velocity w = 4 p s

Angular-

velocity


ms21 ms2 =

1 ms 1 s


g = 981 ms2 fi 10 ms2

Acceleration

QuantitySym-bol

Unit






M

P

D

S

E

E

A


QuantitySym-bol

Unit

NameRelationship



I

E

R

G

amperevolt

ohm

siemens

AV

O

S

1 V = 1 W1 A = 1 JC

1 O = 1 V1 A

1 S = 1 A1 V = 1 O





r

g k

ohm xmeter

siemensper meter

O middotm

Sm


k= 1 2

in mm

m

Ω middot

kr

= 1

2in

m

mmΩ middot

Specificresistance

Conductivity


Frequency



Electrical energy



cos j = P

U middot I

Phasedifference




E F

Q C

Q

U Q t = = = middotI

E Q C L


henry

VmCFH






QuantitySym-bol

Unit

NameRelationship


Sym-bol

Non-SI units

T Q

t h

kelvin

degreesCelsius

K

degC




Thermo-

dynamic

temperature

Celsiustemperature



H u joule per


Jkg

Jm3

1 MJkg = 1 000 000 Jkg

1 MJm3 = 1 000 000 Jm3



Net calorific

value



1 foot (ft) = 03048 m

1 yard(yd) = 09144 m

1 nautical

mile = 1852 km1 mile = 16093 km

1 sqin = 6452 cm2

1 sqft = 929 dm2

1 sqyd = 08361 m2

1 acre = 4046856m2

Pressure

1 bar = 145poundin2


1 cuin = 1639 cm3

1 cuft = 2832 dm3

1 cuyd = 7646 dm3




1 oz = 2835 g

1 lb = 4536 g

1 t = 1000 kg


1 Karat = 02 g


1 PSh = 0735 kWh

1 PS = 735 W

1 kcal = 41868 Ws

1 kcal = 1166 Wh

1 kpms = 9807 W

1 Btu = 1055 Ws

1 hp = 7457 W

Sym-bol



1312 Formulas

M

P

TD

MS

ME

PE

A

S

FormulaMeaning

symbol

Œ Length

w Width

h Height

s Linear distance

r R Radius

d D Diameter


V Volume

a b g Planar angle

W Solid angle

l Wave length

FormulaMeaning

symbol

FormulaMeaning

symbol




t Time Duration

T Cycle duration


Speed

f v Frequency

v u Velocity

w Angular velocity

a Acceleration



Qmiddot


Time





Electricity





coefficient


Heat












proportional an


power of a 0 3

square root of

n0 3 n-th root of







lg common logarithm






AB line segment AB




Acoustics

m Mass



r Density

J Moment of inertia

p Pressure



p g Gage pressure

F Force


T Torsional moment

M b Bending moment

s Normal stress

t Shear stress

e Normal strain


G Shear modulus


W Section modulus


W E Work Energy



P Power

n Efficiency

Mechanics


MathSpoken

symbol

MathSpoken

symbol

MathSpoken

symbol

ordm

ordmordm





1512 Formulas

M

P

TD

MS

ME

PE

A

S



Example formula n =

ŒŒ1 + s


Example formula c =














Formula

P =

F middot s

t


1222222

122222

1

1

1

1

3

3

4

4

2

2

2

2

3

3

4

4

5

5

6

6



n =

ŒŒ1 + s


c = a 2 + b 2 aelig( )2

L ndash Œ1 = Œ2

A

b = Œ




A

b = Œ middot b

b


(Œ1 + s )




Œ2 = L ndash Œ1

Œ = A

b

s middot n

n


n

a 2 = c 2 ndash b 2

s =


a = c 2 ndash b 2

subtract Œ1

divide by b


square equation

invert both sides

invert both sides

subtractdivide by n

extract the root

performsubtraction

cancel b



subtract b 2



transformedformula

transformedformula

cancel n


transformedformula

transformedformula

122 1222222

1222222



16 12 Formulas

M

P

D

S

E

E

A

Conversion of units





Prefix Powerof ten


ExamplesSymbol Name







= 5 h mdash

(hectoliters)










Length 1 =

10 mm1 cm

=

1000 mm1 m

=

1 m1000 mm

=

1 km1000 m

Time 1 =

60 min1 h

=

3600 s1 h

=

60 s1 min

=

1 min60 s

Area 1 =

100 mm2

1 cm2 =

100 cm2

1 dm2 =

Angle 1 =

60rsquo1deg

=

60rsquorsquo1rsquo

=

3600rsquorsquo1deg

=

1deg60 s

Volume 1 =

1000 mm3

1 cm3 =

1000 cm3


1

254 inches





Physical quantity

10 mm

Numerical Unitvalue



V = 3416 mm3 =1 cm3 middot 3416 mm3

1000 mm3 =

3416 cm3

1000 = 3416 cm 3





60 = 42deg + 0267deg = 42267deg

1st example

2nd example





aring iquest

b a

c

copy


iquest

para

aring copy

g

g2

g1


M

P

D

S

E

E

A

b2

a2

c2

abc

G 0 3

P1 X

Z

P2

RK I


Types of angles


Pythagorean theorem

D d

a2

daggerto

daggerti

a1

b 1

b 2

g straight line




a g adjacent angles



a = b


b = d

Opposite angles

a = d

Alternate angles

a + g = 180deg

Adjacent angles

a

b

a

b

1

1

2

2

=

b

d

b

D

1 2=

a

a

b

b

d

D

1

2

1

2

2

2

= =


a + b + g = 180deg




Example

a = 21deg b = 95deg g =


Example

t

t

t

tti

to

tito

= rArr =

=

d

D

d

D

middot


4

2

00 mm= 101 Nmm225





c a b

c a

=

=

35 mm = 21 mm =


1st example

c 2 = a 2 + b 2





2nd example

c a b

R K

K R

2 2 2

2 2 2

2 2 2 250 25

= +

= +

= =

=

I


K 433mm

c a b = +2 2


a c b = 2 2ndash

b c a = 2 2ndash

Length of the sides





M

P

TD

MS

ME

PE

A

S


c hypotenuse





iquestc hypotenuse

F

L3=140mm

L

L

1 = 1 5 0 m

m

L

2 = 3 0 m m

aring

szlig

copy

aring iquest

b a

c

Fd

Fz

F

4 0

1 2

szlig = 3 8

aring = 4 0

1 2

copy = 1 0

2

Fd

Fz

F

Diagram of forces




hypotenuse



adjacent side















1st example

tan a =+

= =L L

L

1 2

3

1 286180 mm

140 mm


2nd example

L =+

= =L L1 2

sina

180 mm

sin 52deg22842mm

F = 800 N a = 40deg b = 38deg F z = F d =



Example

F F F

F

sin sin

middot sin

sina b

b

a= rArr =

=

zz


ssin40deg= 76624 N

F F F

F

sin sin

middot sin

sina g

g

a= rArr =

=

dd


degdeg

sin40deg= 121738 N


sina =

a

c cosa =

b

c tana =

a

b


sinb =

b

c cosb =

a

c tanb =

b

a


a =

b middot sinasinb

=

c middot sinasing

b =

a middot sinbsina

=

c middot sinbsing

c =

a middot singsina

=

b middot singsinb

Law of sines


a

sina =

b

sinb =

c

sing

Law of cosines



Transformation e g

cosa =

b 2 + c 2 ndash a 2

2 middot b middot c



20 14 Lengths



Spacing

Spacing


Arc length


Composite length


Composite length





Example


Example

Number of pieces


Example


Remaining length


Example

Arc length

M

P

D

S

E

E

A




M

P

D

S

E

E

A


QuantitySym-bol

Unit

NameRelationship



I

E

R

G

amperevolt

ohm

siemens

AV

O

S

1 V = 1 W1 A = 1 JC

1 O = 1 V1 A

1 S = 1 A1 V = 1 O





r

g k

ohm xmeter

siemensper meter

O middotm

Sm


k= 1 2

in mm

m

Ω middot

kr

= 1

2in

m

mmΩ middot

Specificresistance

Conductivity


Frequency



Electrical energy



cos j = P

U middot I

Phasedifference




E F

Q C

Q

U Q t = = = middotI

E Q C L


henry

VmCFH






QuantitySym-bol

Unit

NameRelationship


Sym-bol

Non-SI units

T Q

t h

kelvin

degreesCelsius

K

degC




Thermo-

dynamic

temperature

Celsiustemperature



H u joule per


Jkg

Jm3

1 MJkg = 1 000 000 Jkg

1 MJm3 = 1 000 000 Jm3



Net calorific

value



1 foot (ft) = 03048 m

1 yard(yd) = 09144 m

1 nautical

mile = 1852 km1 mile = 16093 km

1 sqin = 6452 cm2

1 sqft = 929 dm2

1 sqyd = 08361 m2

1 acre = 4046856m2

Pressure

1 bar = 145poundin2


1 cuin = 1639 cm3

1 cuft = 2832 dm3

1 cuyd = 7646 dm3




1 oz = 2835 g

1 lb = 4536 g

1 t = 1000 kg


1 Karat = 02 g


1 PSh = 0735 kWh

1 PS = 735 W

1 kcal = 41868 Ws

1 kcal = 1166 Wh

1 kpms = 9807 W

1 Btu = 1055 Ws

1 hp = 7457 W

Sym-bol



1312 Formulas

M

P

TD

MS

ME

PE

A

S

FormulaMeaning

symbol

Œ Length

w Width

h Height

s Linear distance

r R Radius

d D Diameter


V Volume

a b g Planar angle

W Solid angle

l Wave length

FormulaMeaning

symbol

FormulaMeaning

symbol




t Time Duration

T Cycle duration


Speed

f v Frequency

v u Velocity

w Angular velocity

a Acceleration



Qmiddot


Time





Electricity





coefficient


Heat












proportional an


power of a 0 3

square root of

n0 3 n-th root of







lg common logarithm






AB line segment AB




Acoustics

m Mass



r Density

J Moment of inertia

p Pressure



p g Gage pressure

F Force


T Torsional moment

M b Bending moment

s Normal stress

t Shear stress

e Normal strain


G Shear modulus


W Section modulus


W E Work Energy



P Power

n Efficiency

Mechanics


MathSpoken

symbol

MathSpoken

symbol

MathSpoken

symbol

ordm

ordmordm





1512 Formulas

M

P

TD

MS

ME

PE

A

S



Example formula n =

ŒŒ1 + s


Example formula c =














Formula

P =

F middot s

t


1222222

122222

1

1

1

1

3

3

4

4

2

2

2

2

3

3

4

4

5

5

6

6



n =

ŒŒ1 + s


c = a 2 + b 2 aelig( )2

L ndash Œ1 = Œ2

A

b = Œ




A

b = Œ middot b

b


(Œ1 + s )




Œ2 = L ndash Œ1

Œ = A

b

s middot n

n


n

a 2 = c 2 ndash b 2

s =


a = c 2 ndash b 2

subtract Œ1

divide by b


square equation

invert both sides

invert both sides

subtractdivide by n

extract the root

performsubtraction

cancel b



subtract b 2



transformedformula

transformedformula

cancel n


transformedformula

transformedformula

122 1222222

1222222



16 12 Formulas

M

P

D

S

E

E

A

Conversion of units





Prefix Powerof ten


ExamplesSymbol Name







= 5 h mdash

(hectoliters)










Length 1 =

10 mm1 cm

=

1000 mm1 m

=

1 m1000 mm

=

1 km1000 m

Time 1 =

60 min1 h

=

3600 s1 h

=

60 s1 min

=

1 min60 s

Area 1 =

100 mm2

1 cm2 =

100 cm2

1 dm2 =

Angle 1 =

60rsquo1deg

=

60rsquorsquo1rsquo

=

3600rsquorsquo1deg

=

1deg60 s

Volume 1 =

1000 mm3

1 cm3 =

1000 cm3


1

254 inches





Physical quantity

10 mm

Numerical Unitvalue



V = 3416 mm3 =1 cm3 middot 3416 mm3

1000 mm3 =

3416 cm3

1000 = 3416 cm 3





60 = 42deg + 0267deg = 42267deg

1st example

2nd example





aring iquest

b a

c

copy


iquest

para

aring copy

g

g2

g1


M

P

D

S

E

E

A

b2

a2

c2

abc

G 0 3

P1 X

Z

P2

RK I


Types of angles


Pythagorean theorem

D d

a2

daggerto

daggerti

a1

b 1

b 2

g straight line




a g adjacent angles



a = b


b = d

Opposite angles

a = d

Alternate angles

a + g = 180deg

Adjacent angles

a

b

a

b

1

1

2

2

=

b

d

b

D

1 2=

a

a

b

b

d

D

1

2

1

2

2

2

= =


a + b + g = 180deg




Example

a = 21deg b = 95deg g =


Example

t

t

t

tti

to

tito

= rArr =

=

d

D

d

D

middot


4

2

00 mm= 101 Nmm225





c a b

c a

=

=

35 mm = 21 mm =


1st example

c 2 = a 2 + b 2





2nd example

c a b

R K

K R

2 2 2

2 2 2

2 2 2 250 25

= +

= +

= =

=

I


K 433mm

c a b = +2 2


a c b = 2 2ndash

b c a = 2 2ndash

Length of the sides





M

P

TD

MS

ME

PE

A

S


c hypotenuse





iquestc hypotenuse

F

L3=140mm

L

L

1 = 1 5 0 m

m

L

2 = 3 0 m m

aring

szlig

copy

aring iquest

b a

c

Fd

Fz

F

4 0

1 2

szlig = 3 8

aring = 4 0

1 2

copy = 1 0

2

Fd

Fz

F

Diagram of forces




hypotenuse



adjacent side















1st example

tan a =+

= =L L

L

1 2

3

1 286180 mm

140 mm


2nd example

L =+

= =L L1 2

sina

180 mm

sin 52deg22842mm

F = 800 N a = 40deg b = 38deg F z = F d =



Example

F F F

F

sin sin

middot sin

sina b

b

a= rArr =

=

zz


ssin40deg= 76624 N

F F F

F

sin sin

middot sin

sina g

g

a= rArr =

=

dd


degdeg

sin40deg= 121738 N


sina =

a

c cosa =

b

c tana =

a

b


sinb =

b

c cosb =

a

c tanb =

b

a


a =

b middot sinasinb

=

c middot sinasing

b =

a middot sinbsina

=

c middot sinbsing

c =

a middot singsina

=

b middot singsinb

Law of sines


a

sina =

b

sinb =

c

sing

Law of cosines



Transformation e g

cosa =

b 2 + c 2 ndash a 2

2 middot b middot c



20 14 Lengths



Spacing

Spacing


Arc length


Composite length


Composite length





Example


Example

Number of pieces


Example


Remaining length


Example

Arc length

M

P

D

S

E

E

A



1312 Formulas

M

P

TD

MS

ME

PE

A

S

FormulaMeaning

symbol

Œ Length

w Width

h Height

s Linear distance

r R Radius

d D Diameter


V Volume

a b g Planar angle

W Solid angle

l Wave length

FormulaMeaning

symbol

FormulaMeaning

symbol




t Time Duration

T Cycle duration


Speed

f v Frequency

v u Velocity

w Angular velocity

a Acceleration



Qmiddot


Time





Electricity





coefficient


Heat












proportional an


power of a 0 3

square root of

n0 3 n-th root of







lg common logarithm






AB line segment AB




Acoustics

m Mass



r Density

J Moment of inertia

p Pressure



p g Gage pressure

F Force


T Torsional moment

M b Bending moment

s Normal stress

t Shear stress

e Normal strain


G Shear modulus


W Section modulus


W E Work Energy



P Power

n Efficiency

Mechanics


MathSpoken

symbol

MathSpoken

symbol

MathSpoken

symbol

ordm

ordmordm





1512 Formulas

M

P

TD

MS

ME

PE

A

S



Example formula n =

ŒŒ1 + s


Example formula c =














Formula

P =

F middot s

t


1222222

122222

1

1

1

1

3

3

4

4

2

2

2

2

3

3

4

4

5

5

6

6



n =

ŒŒ1 + s


c = a 2 + b 2 aelig( )2

L ndash Œ1 = Œ2

A

b = Œ




A

b = Œ middot b

b


(Œ1 + s )




Œ2 = L ndash Œ1

Œ = A

b

s middot n

n


n

a 2 = c 2 ndash b 2

s =


a = c 2 ndash b 2

subtract Œ1

divide by b


square equation

invert both sides

invert both sides

subtractdivide by n

extract the root

performsubtraction

cancel b



subtract b 2



transformedformula

transformedformula

cancel n


transformedformula

transformedformula

122 1222222

1222222



16 12 Formulas

M

P

D

S

E

E

A

Conversion of units





Prefix Powerof ten


ExamplesSymbol Name







= 5 h mdash

(hectoliters)










Length 1 =

10 mm1 cm

=

1000 mm1 m

=

1 m1000 mm

=

1 km1000 m

Time 1 =

60 min1 h

=

3600 s1 h

=

60 s1 min

=

1 min60 s

Area 1 =

100 mm2

1 cm2 =

100 cm2

1 dm2 =

Angle 1 =

60rsquo1deg

=

60rsquorsquo1rsquo

=

3600rsquorsquo1deg

=

1deg60 s

Volume 1 =

1000 mm3

1 cm3 =

1000 cm3


1

254 inches





Physical quantity

10 mm

Numerical Unitvalue



V = 3416 mm3 =1 cm3 middot 3416 mm3

1000 mm3 =

3416 cm3

1000 = 3416 cm 3





60 = 42deg + 0267deg = 42267deg

1st example

2nd example





aring iquest

b a

c

copy


iquest

para

aring copy

g

g2

g1


M

P

D

S

E

E

A

b2

a2

c2

abc

G 0 3

P1 X

Z

P2

RK I


Types of angles


Pythagorean theorem

D d

a2

daggerto

daggerti

a1

b 1

b 2

g straight line




a g adjacent angles



a = b


b = d

Opposite angles

a = d

Alternate angles

a + g = 180deg

Adjacent angles

a

b

a

b

1

1

2

2

=

b

d

b

D

1 2=

a

a

b

b

d

D

1

2

1

2

2

2

= =


a + b + g = 180deg




Example

a = 21deg b = 95deg g =


Example

t

t

t

tti

to

tito

= rArr =

=

d

D

d

D

middot


4

2

00 mm= 101 Nmm225





c a b

c a

=

=

35 mm = 21 mm =


1st example

c 2 = a 2 + b 2





2nd example

c a b

R K

K R

2 2 2

2 2 2

2 2 2 250 25

= +

= +

= =

=

I


K 433mm

c a b = +2 2


a c b = 2 2ndash

b c a = 2 2ndash

Length of the sides





M

P

TD

MS

ME

PE

A

S


c hypotenuse





iquestc hypotenuse

F

L3=140mm

L

L

1 = 1 5 0 m

m

L

2 = 3 0 m m

aring

szlig

copy

aring iquest

b a

c

Fd

Fz

F

4 0

1 2

szlig = 3 8

aring = 4 0

1 2

copy = 1 0

2

Fd

Fz

F

Diagram of forces




hypotenuse



adjacent side















1st example

tan a =+

= =L L

L

1 2

3

1 286180 mm

140 mm


2nd example

L =+

= =L L1 2

sina

180 mm

sin 52deg22842mm

F = 800 N a = 40deg b = 38deg F z = F d =



Example

F F F

F

sin sin

middot sin

sina b

b

a= rArr =

=

zz


ssin40deg= 76624 N

F F F

F

sin sin

middot sin

sina g

g

a= rArr =

=

dd


degdeg

sin40deg= 121738 N


sina =

a

c cosa =

b

c tana =

a

b


sinb =

b

c cosb =

a

c tanb =

b

a


a =

b middot sinasinb

=

c middot sinasing

b =

a middot sinbsina

=

c middot sinbsing

c =

a middot singsina

=

b middot singsinb

Law of sines


a

sina =

b

sinb =

c

sing

Law of cosines



Transformation e g

cosa =

b 2 + c 2 ndash a 2

2 middot b middot c



20 14 Lengths



Spacing

Spacing


Arc length


Composite length


Composite length





Example


Example

Number of pieces


Example


Remaining length


Example

Arc length

M

P

D

S

E

E

A





1512 Formulas

M

P

TD

MS

ME

PE

A

S



Example formula n =

ŒŒ1 + s


Example formula c =














Formula

P =

F middot s

t


1222222

122222

1

1

1

1

3

3

4

4

2

2

2

2

3

3

4

4

5

5

6

6



n =

ŒŒ1 + s


c = a 2 + b 2 aelig( )2

L ndash Œ1 = Œ2

A

b = Œ




A

b = Œ middot b

b


(Œ1 + s )




Œ2 = L ndash Œ1

Œ = A

b

s middot n

n


n

a 2 = c 2 ndash b 2

s =


a = c 2 ndash b 2

subtract Œ1

divide by b


square equation

invert both sides

invert both sides

subtractdivide by n

extract the root

performsubtraction

cancel b



subtract b 2



transformedformula

transformedformula

cancel n


transformedformula

transformedformula

122 1222222

1222222



16 12 Formulas

M

P

D

S

E

E

A

Conversion of units





Prefix Powerof ten


ExamplesSymbol Name







= 5 h mdash

(hectoliters)










Length 1 =

10 mm1 cm

=

1000 mm1 m

=

1 m1000 mm

=

1 km1000 m

Time 1 =

60 min1 h

=

3600 s1 h

=

60 s1 min

=

1 min60 s

Area 1 =

100 mm2

1 cm2 =

100 cm2

1 dm2 =

Angle 1 =

60rsquo1deg

=

60rsquorsquo1rsquo

=

3600rsquorsquo1deg

=

1deg60 s

Volume 1 =

1000 mm3

1 cm3 =

1000 cm3


1

254 inches





Physical quantity

10 mm

Numerical Unitvalue



V = 3416 mm3 =1 cm3 middot 3416 mm3

1000 mm3 =

3416 cm3

1000 = 3416 cm 3





60 = 42deg + 0267deg = 42267deg

1st example

2nd example





aring iquest

b a

c

copy


iquest

para

aring copy

g

g2

g1


M

P

D

S

E

E

A

b2

a2

c2

abc

G 0 3

P1 X

Z

P2

RK I


Types of angles


Pythagorean theorem

D d

a2

daggerto

daggerti

a1

b 1

b 2

g straight line




a g adjacent angles



a = b


b = d

Opposite angles

a = d

Alternate angles

a + g = 180deg

Adjacent angles

a

b

a

b

1

1

2

2

=

b

d

b

D

1 2=

a

a

b

b

d

D

1

2

1

2

2

2

= =


a + b + g = 180deg




Example

a = 21deg b = 95deg g =


Example

t

t

t

tti

to

tito

= rArr =

=

d

D

d

D

middot


4

2

00 mm= 101 Nmm225





c a b

c a

=

=

35 mm = 21 mm =


1st example

c 2 = a 2 + b 2





2nd example

c a b

R K

K R

2 2 2

2 2 2

2 2 2 250 25

= +

= +

= =

=

I


K 433mm

c a b = +2 2


a c b = 2 2ndash

b c a = 2 2ndash

Length of the sides





M

P

TD

MS

ME

PE

A

S


c hypotenuse





iquestc hypotenuse

F

L3=140mm

L

L

1 = 1 5 0 m

m

L

2 = 3 0 m m

aring

szlig

copy

aring iquest

b a

c

Fd

Fz

F

4 0

1 2

szlig = 3 8

aring = 4 0

1 2

copy = 1 0

2

Fd

Fz

F

Diagram of forces




hypotenuse



adjacent side















1st example

tan a =+

= =L L

L

1 2

3

1 286180 mm

140 mm


2nd example

L =+

= =L L1 2

sina

180 mm

sin 52deg22842mm

F = 800 N a = 40deg b = 38deg F z = F d =



Example

F F F

F

sin sin

middot sin

sina b

b

a= rArr =

=

zz


ssin40deg= 76624 N

F F F

F

sin sin

middot sin

sina g

g

a= rArr =

=

dd


degdeg

sin40deg= 121738 N


sina =

a

c cosa =

b

c tana =

a

b


sinb =

b

c cosb =

a

c tanb =

b

a


a =

b middot sinasinb

=

c middot sinasing

b =

a middot sinbsina

=

c middot sinbsing

c =

a middot singsina

=

b middot singsinb

Law of sines


a

sina =

b

sinb =

c

sing

Law of cosines



Transformation e g

cosa =

b 2 + c 2 ndash a 2

2 middot b middot c



20 14 Lengths



Spacing

Spacing


Arc length


Composite length


Composite length





Example


Example

Number of pieces


Example


Remaining length


Example

Arc length

M

P

D

S

E

E

A



16 12 Formulas

M

P

D

S

E

E

A

Conversion of units





Prefix Powerof ten


ExamplesSymbol Name







= 5 h mdash

(hectoliters)










Length 1 =

10 mm1 cm

=

1000 mm1 m

=

1 m1000 mm

=

1 km1000 m

Time 1 =

60 min1 h

=

3600 s1 h

=

60 s1 min

=

1 min60 s

Area 1 =

100 mm2

1 cm2 =

100 cm2

1 dm2 =

Angle 1 =

60rsquo1deg

=

60rsquorsquo1rsquo

=

3600rsquorsquo1deg

=

1deg60 s

Volume 1 =

1000 mm3

1 cm3 =

1000 cm3


1

254 inches





Physical quantity

10 mm

Numerical Unitvalue



V = 3416 mm3 =1 cm3 middot 3416 mm3

1000 mm3 =

3416 cm3

1000 = 3416 cm 3





60 = 42deg + 0267deg = 42267deg

1st example

2nd example





aring iquest

b a

c

copy


iquest

para

aring copy

g

g2

g1


M

P

D

S

E

E

A

b2

a2

c2

abc

G 0 3

P1 X

Z

P2

RK I


Types of angles


Pythagorean theorem

D d

a2

daggerto

daggerti

a1

b 1

b 2

g straight line




a g adjacent angles



a = b


b = d

Opposite angles

a = d

Alternate angles

a + g = 180deg

Adjacent angles

a

b

a

b

1

1

2

2

=

b

d

b

D

1 2=

a

a

b

b

d

D

1

2

1

2

2

2

= =


a + b + g = 180deg




Example

a = 21deg b = 95deg g =


Example

t

t

t

tti

to

tito

= rArr =

=

d

D

d

D

middot


4

2

00 mm= 101 Nmm225





c a b

c a

=

=

35 mm = 21 mm =


1st example

c 2 = a 2 + b 2





2nd example

c a b

R K

K R

2 2 2

2 2 2

2 2 2 250 25

= +

= +

= =

=

I


K 433mm

c a b = +2 2


a c b = 2 2ndash

b c a = 2 2ndash

Length of the sides





M

P

TD

MS

ME

PE

A

S


c hypotenuse





iquestc hypotenuse

F

L3=140mm

L

L

1 = 1 5 0 m

m

L

2 = 3 0 m m

aring

szlig

copy

aring iquest

b a

c

Fd

Fz

F

4 0

1 2

szlig = 3 8

aring = 4 0

1 2

copy = 1 0

2

Fd

Fz

F

Diagram of forces




hypotenuse



adjacent side















1st example

tan a =+

= =L L

L

1 2

3

1 286180 mm

140 mm


2nd example

L =+

= =L L1 2

sina

180 mm

sin 52deg22842mm

F = 800 N a = 40deg b = 38deg F z = F d =



Example

F F F

F

sin sin

middot sin

sina b

b

a= rArr =

=

zz


ssin40deg= 76624 N

F F F

F

sin sin

middot sin

sina g

g

a= rArr =

=

dd


degdeg

sin40deg= 121738 N


sina =

a

c cosa =

b

c tana =

a

b


sinb =

b

c cosb =

a

c tanb =

b

a


a =

b middot sinasinb

=

c middot sinasing

b =

a middot sinbsina

=

c middot sinbsing

c =

a middot singsina

=

b middot singsinb

Law of sines


a

sina =

b

sinb =

c

sing

Law of cosines



Transformation e g

cosa =

b 2 + c 2 ndash a 2

2 middot b middot c



20 14 Lengths



Spacing

Spacing


Arc length


Composite length


Composite length





Example


Example

Number of pieces


Example


Remaining length


Example

Arc length

M

P

D

S

E

E

A





aring iquest

b a

c

copy


iquest

para

aring copy

g

g2

g1


M

P

D

S

E

E

A

b2

a2

c2

abc

G 0 3

P1 X

Z

P2

RK I


Types of angles


Pythagorean theorem

D d

a2

daggerto

daggerti

a1

b 1

b 2

g straight line




a g adjacent angles



a = b


b = d

Opposite angles

a = d

Alternate angles

a + g = 180deg

Adjacent angles

a

b

a

b

1

1

2

2

=

b

d

b

D

1 2=

a

a

b

b

d

D

1

2

1

2

2

2

= =


a + b + g = 180deg




Example

a = 21deg b = 95deg g =


Example

t

t

t

tti

to

tito

= rArr =

=

d

D

d

D

middot


4

2

00 mm= 101 Nmm225





c a b

c a

=

=

35 mm = 21 mm =


1st example

c 2 = a 2 + b 2





2nd example

c a b

R K

K R

2 2 2

2 2 2

2 2 2 250 25

= +

= +

= =

=

I


K 433mm

c a b = +2 2


a c b = 2 2ndash

b c a = 2 2ndash

Length of the sides





M

P

TD

MS

ME

PE

A

S


c hypotenuse





iquestc hypotenuse

F

L3=140mm

L

L

1 = 1 5 0 m

m

L

2 = 3 0 m m

aring

szlig

copy

aring iquest

b a

c

Fd

Fz

F

4 0

1 2

szlig = 3 8

aring = 4 0

1 2

copy = 1 0

2

Fd

Fz

F

Diagram of forces




hypotenuse



adjacent side















1st example

tan a =+

= =L L

L

1 2

3

1 286180 mm

140 mm


2nd example

L =+

= =L L1 2

sina

180 mm

sin 52deg22842mm

F = 800 N a = 40deg b = 38deg F z = F d =



Example

F F F

F

sin sin

middot sin

sina b

b

a= rArr =

=

zz


ssin40deg= 76624 N

F F F

F

sin sin

middot sin

sina g

g

a= rArr =

=

dd


degdeg

sin40deg= 121738 N


sina =

a

c cosa =

b

c tana =

a

b


sinb =

b

c cosb =

a

c tanb =

b

a


a =

b middot sinasinb

=

c middot sinasing

b =

a middot sinbsina

=

c middot sinbsing

c =

a middot singsina

=

b middot singsinb

Law of sines


a

sina =

b

sinb =

c

sing

Law of cosines



Transformation e g

cosa =

b 2 + c 2 ndash a 2

2 middot b middot c



20 14 Lengths



Spacing

Spacing


Arc length


Composite length


Composite length





Example


Example

Number of pieces


Example


Remaining length


Example

Arc length

M

P

D

S

E

E

A




M

P

TD

MS

ME

PE

A

S


c hypotenuse





iquestc hypotenuse

F

L3=140mm

L

L

1 = 1 5 0 m

m

L

2 = 3 0 m m

aring

szlig

copy

aring iquest

b a

c

Fd

Fz

F

4 0

1 2

szlig = 3 8

aring = 4 0

1 2

copy = 1 0

2

Fd

Fz

F

Diagram of forces




hypotenuse



adjacent side















1st example

tan a =+

= =L L

L

1 2

3

1 286180 mm

140 mm


2nd example

L =+

= =L L1 2

sina

180 mm

sin 52deg22842mm

F = 800 N a = 40deg b = 38deg F z = F d =



Example

F F F

F

sin sin

middot sin

sina b

b

a= rArr =

=

zz


ssin40deg= 76624 N

F F F

F

sin sin

middot sin

sina g

g

a= rArr =

=

dd


degdeg

sin40deg= 121738 N


sina =

a

c cosa =

b

c tana =

a

b


sinb =

b

c cosb =

a

c tanb =

b

a


a =

b middot sinasinb

=

c middot sinasing

b =

a middot sinbsina

=

c middot sinbsing

c =

a middot singsina

=

b middot singsinb

Law of sines


a

sina =

b

sinb =

c

sing

Law of cosines



Transformation e g

cosa =

b 2 + c 2 ndash a 2

2 middot b middot c



20 14 Lengths



Spacing

Spacing


Arc length


Composite length


Composite length





Example


Example

Number of pieces


Example


Remaining length


Example

Arc length

M

P

D

S

E

E

A



20 14 Lengths



Spacing

Spacing


Arc length


Composite length


Composite length





Example


Example

Number of pieces


Example


Remaining length


Example

Arc length

M

P

D

S

E

E

A

mechanical and metal trade handbook 01

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