Tech Ref Reviewer Pages

8/8/2019 Tech Ref Reviewer Pages

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Contents

TOPIC # Chapter

I Background & Support

1 Systerm of Units pp. 1-1 to 1-10 10

1 Introduction p 1-1 Pound unit both for for

2 Common Unit of Mass p 1-1 Gram, pound, kilogra

3 Mass and Weight p 1-1 SI- kilogram (mass ) &4 Acceleration of gravity p 1-2 g = 32.2 ft/sec2 = 9.8

5 Consistent Systems of Units p 1-2 M=Fd is OK& F=ma

6 The English Engineering System p 1-2 Lb-mass & Lb-force ar

7 Other Formulas Affected by Inconsistencies p 1-3 Req's "g" term; Kinetic

8 Wight and Weight Density p 1-3 W=mg/gc; gamma =

9 The English Gravitational Sytem p 1-3 Slug = lbf-sec2/ft = lb

10 The Absolute English System p 1-4 Poundal = 0.03108 lb

11 Metric System of Units p 1-4 Based on meters or a

12 The cgs System p 1-4 Unit of force = g-cm / s

13 SI Units ( The mks System ) p 1-5 Base units: length (m);

Table 1.2 & 1.3 S. I. d

14 Rules for Using SI Units p 1-6 Symbols are NOT plur 15 Primary Dimensions p 1-7 (ML0T),mass(M),lengt

16 Dimensionless Groups p 1-7 Ratio of 2 forces or qu

17 Lineal and Board Foot Measurements p 1-8 Bd. Ft = 12" x 12" x 1"

18 Dimensional Analysis p 1-8 Means of obtaining an

Table 1.8 - Common Dimensionless groups p 1-9 Example of Dimension

1 pp 1 - 20 Units,conversions, Mathematics, Probability

2 pp 21 - 40 Probability, statics, dynamics,mechanics

3 pp 41- 60 Mechanics,Fluid/Hydro, Thermodynamics

4 pp 61- 80 Thermo,heat transfer, transport,biology,chemistry

5 pp 81- 100 Chemistry,materials science,Mesayrements/control,computer,economics, eth

6 pp101- 120 Chemical engineering, civil engineering

7 pp121- 140 Civil engineering8 pp141- 160 Environmental, electrical & computer engineering

9 pp161- 180 Electrical & computer engineering

10 pp181- 200 Electrical & industrial engineering

11 pp201- 220 Mechanical Engineering & Index

1 Vectors p 7. Mathematics


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2 Derivatives & intergrals p 9. Mathematics

3 Areas & volumes p 10 - 11 Mathematics

4 Confidence intervals, value of Za/2 p 19. Probability & Statistics

5 Distribution tables p 20 - 23 Probability & Statistics

6 Centroids & moment of inertia p 27 - 29 Statics

7 Mass & centroid, mass / inertia p 37. Dynamics

8 Beam deflection formulas p 43. Mechanics of Materials9 Fluid measurements p 50 - 51 Fluid Mechanics

10 Properties of water p 53. Fluid Mechanics

11 Moody ( Stanton ) Diagram p 54. Fluid Mechanics

12 Reynolds Number / drag coeff p 55. Fluid Mechanics

13 Phase diagrams p 59. Thermodynamics

14 Thermo cycles/ engines p 61. Thermodynamics

15 Steam tables p 62 - 63 Thermodynamics

16 Refrigerant HFC-134a diagram p 64. Thermodynamics

17 ASHRAE Psychrometric chart p 65 Thermodynamics

18 Heat capacity tables p 66 Thermodynamics

19 Convection / radiation p 71 Heat Transfer

20 Characteristics of sel. Microbial cells p 75 Biology21 Compositon data for biomass p 76 Biology

22 Periodic table p 79 Chemistry

23 Organic compounds p 80 Chemistry

24 Corrosion reaction table p 81 Chemistry

25 Testing methods p 83 Materials Science / Matter

26 Half-life & materials characteristics p 85 Materials Science / Matter

27 Engineering economics table p 92 Engineering Economics

28 Modified ACRS factors p 93 Engineering Economics

29 Factor tables p 94 - 98 Engineering Economics

30 Common names & molecular formulas p 102 Chemical Engineering

31 Typ. Exponents for eqpt cost vs. cap p 109 Chemical Engineering

32 Unified soil classifications p 112 - 113 Civil Engineering33 Reinf. Conc. Design p 115 - 120 Civil Engineering

34 Steel Structures p 121 - 134 Civil Engineering

35 Sewage flow ratio curves p 135 Civil Engineering

36 Hydraulic - elements graph for cir. p 136 Civil Engineering

37 Horizontal Curve formulas p 139 Civil Engineering

38 Highway pavement design p 141 Civil Engineering

39 Cyclone ratio: dim - body diam. p 146 Environmental Engineering

40 Baghouse, air-to-cloth ratio p 147 Environmental Engineering

41 Partiton coeff/steady state reactor p 149 Environmental Engineering

42 Half life, Sampling & monitoring p 151 Environmental Engineering

43 MSDS hazard assessment p 153 Environmental Engineering

44 Hazardous waste compatibilty chart p 154 Environmental Engineering45 Carcinogens & noncarcinogens p 155 Environmental Engineering

46 Exposure & intake rates p 156 - 157 Environmental Engineering

47 Toxicology p 158 Environmental Engineering

48 Water treatment technology p 159 - 166 Environmental Engineering

49 AC power p 171 Electrical & Computer Eng'g

50 Laplace transform p 174 Electrical & Computer Eng'g

51 Digital signals/comm. Theory p 175 Electrical & Computer Eng'g

52 Fourier transform p 176 Electrical & Computer Eng'g


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53 Analog Filter circuits p 179 Electrical & Computer Eng'g

54 band-Phase filters p 180 - 181 Electrical & Computer Eng'g

55 Amplifiers p 182 Electrical & Computer Eng'g

56 Device & schematic symbols p 183 Electrical & Computer Eng'g

57 N-channel JFE Transistors p 184 - 185 Electrical & Computer Eng'g

58 Enhancement MOSFET p 186 Electrical & Computer Eng'g

59 Number systems & codes p 187 Electrical & Computer Eng'g60 Logic operations & Boolean p 187 Electrical & Computer Eng'g

61 Flip-flops p 188 Electrical & Computer Eng'g

62 Queueing models p 190 Industrial Engineering

63 Linear regressions p 192 Industrial Engineering

64 2nd factorial designs p 193 Industrial Engineering

65 Ergonomics p 194 Industrial Engineering

66 anova Tables p 196 Industrial Engineering

67 Probability & density functions p 197 Industrial Engineering

68 Ergonomics table p 200 Industrial Engineering

69 Spring & compression spring p 203 Mechanical Engineering

70 Inter & long columns p 204 Mechanical Engineering

71 Power transmission p 204 Mechanical Engineering72 Rivets & fasteners p 205 Mechanical Engineering

73 Kinematics, dynamics & vibrations p 206 Mechanical Engineering

74 Performance of Components p 211 Mechanical Engineering

75 Cycles & processes p 212 Mechanical Engineering

76 Fluid machines p 215 Mechanical Engineering

77 Refrigeration & HVAC p 217 Mechanical Engineering


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ce & mass in English System ( American )

and slug

Newton ( force ), Wt = mg, mass & wt are NOT the same!1 m / s

si consistent; problems fluid flow & thermo are solved in U.S. w/ inconsistent units.

e different as gallons & feet. Lb-force = Lb-mass / 32.1740 lbm-ft / s2

energy (E=mv2/2g); Potential energy (E=mgz/g ); pressure ( p=pgh/g )= gamma h

/V = rho g / gc; p= gamma h

/gc

orce or 1/32.2

y part of meters, either mks or cgs

ec2 = dyne

mass (kg); time (sec); elect. Current(ampere); temp(K);amt. of substance(mole) & lum.Intensity (candela)

rived units; solid angle =sr = steradian

alized; a period after symbol is NOT used; use prefixesh(L),time(0) & temp(T); ML2/02 (kg-m2)/s2; FML0TQ=engineering dimensional system

antities, notably in fluid mechanics or heat transfer, ie: Reynolds, Mach & Froude numbers

= 144 cubic inches

equation that describes some phenomenon w/out understanding the mechanism of the phenomenon

less Analysis

ics


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Contents

Topic Ch.

# 1 Background & Support

1 System of Units pp. 1-1 to 1-10 10

1 Introduction p 1-1 Pound unit both for force & mass in English System ( American )

2 Common Unit of Mass p 1-1 Gram, pound, kilogram and slug

3 Mass and Weight p 1-1 SI- kilogram (mass ) & Newton ( force ), Wt = mg, mass & wt are NOT the same!

4 Acceleration of gravity p 1-2 g = 32.2 ft/sec2 = 9.81 m / s; Earth's radius = 3 ,960 miles = 6, 370 Km = 6.37 x

5 Consistent Systems of Units p 1-2 M=Fd is OK& F=ma si consistent; problems fluid flow & thermo are solved in U.S

6 The English Engineering System p 1-2 Lb-mass & Lb-force are different as gallons & feet. Lb-force = Lb-mass / 32.1740 lb

7 Other Formulas Affected by Inconsistencies p 1-3 Req's "g" term; Kinetic energy (E=mv2/2g); Potential energy (E=mgz/g ); pressure (

8 Weight and Weight Density p 1-3 W=mg/gc; gamma = W/V = rho g / gc; p= gamma h

9 The English Gravitational Sytem p 1-3 Slug = lbf-sec2/ft = lbm/gc

10 The Absolute English System p 1-4 Poundal = 0.03108 lb force or 1/32.2

11 Metric System of Units p 1-4 Based on meters or any part of meters, either mks or cgs

12 The cgs System p 1-4 Unit of force = g-cm / sec2 = dyne

13 SI Units ( The mks System ) p 1-5 Base units: length (m); mass (kg); t ime (sec); elect. Current(ampere); temp(K);amt.

Table 1.2 & 1.3 S. I. derived units; solid angle =sr = steradian

14 Rules for Using SI Units p 1-6 Symbols are NOT pluralized; a period after symbol is NOT used; use prefixes

15 Primary Dimensions p 1-7 (ML0T),mass(M),length(L),time(0) & temp(T); ML2/02 (kg-m2)/s2; FML0TQ=engine

16 Dimensionless Groups p 1-7 Ratio of 2 forces or quantities, notably in fluid mechanics or heat transfer, ie: Reyno

17 Lineal and Board Foot Measurements p 1-8 Bd. Ft = 12" x 12" x 1" = 144 cubic inches

18 Dimensional Analysis p 1-8 Means of obtaining an equation that describes some phenomenon w/out understan

Table 1.8 - Common Dimensionless groups p 1-9 Example of Dimensionless Analysis

2 Engineering Drawing Practic pp. 2-1 to 2-4 4

1 Normal Views of Lines & Planes p 2-1 True length of a line is viewed and can be measured

2 Intersecting & Paral lel Lines p 2-1 If two or more views show the lines as having the same common point, then the line3 Types of Views p 2-1

4 Principal ( Orthographic ) Views p 2-2 Also planar views, requires at least three (3) principal views & at most 6 principal vi

Plan views & elevations

5 Auxilliary ( Orthographic ) Views p 2-2 Needed when an object has an inclined plane or curved feature. Only 1 of the 3 dim

6 Oblique ( Orthographic ) Views p 2-2 If the object is turned so that 3 dimensions are visible, it can be illustrated by a sing

7 Axonometric ( Orthographic Oblique ) Views p 2-3 Projections: isometric, dimetric & trimetric.

8 Perspective Views p 2-3 Parallel perspective, angular perspective & oblique perspective

9 Sections p 2-3 "Imaginary" cut taken through an object to reveal the shape or interior construction.

10 Tolerances p 2-4 The total permissible variation between the acceptable limits, ie; +/- 0.001

11 Surface Finish p 2-4 Parameters are maximum allowable values. All lesser values are permitted.

3 Algebra pp. 3-1 to 3-12 12

1 Introduction p 3-1 One & first of the mathematical concepts needed by engineers.

2 Symbols used in this book p 3-1 Used to represent variables in the formulas throughout this book, ref. Table 3.2, p. 33 Greek Alphabet p 3-1 Alpha, beta, gamma, delta.omega

4 Types of Numbers p 3-1 Real numbers, rational real & irrational real; imaginary numbers are square roots of

5 Significant Digits p 3-1 Include the leftmost, nonzero digits to the rightmost digit written. See Table 3.3 on p

6 Equations p 3-2 It is a mathematical statement of equality; or variables ( Algebraic); "functional" form

7 Fundamental Algebraic Laws p 3-3 A + B = B + A ( commutative add ); AB=BA ( comm. Multi ); associative & distributiv

8 Polynomials p 3-3 Rational expression, usually the sum of several variable terms; degree is highest po

9 Roots of Quadratic Equations p 3-3 x1 + x2 = - b/a; x1x2 = c/a; x1, x2 = ( -b +/- ( b x b - 4ac ) 1/2) / 2a

10 Roots of General Polynomials p 3-3 Techniques: inspection, graphing, numerical methods, factoring, special case ( New

11 Extraneous Roots p 3-4 Extraneous roots does NOT establish equality in equations.

12 Descartes Rule of Signs p 3-4 Real roots of a polynomial equation.

ortographic, principal, auxilliary, oblique, cavalier projection, cabinet projection, cli

axonometric views, isometric, dimetric, trimetric, perspective views, parallel perspe


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13 Rules for Exponent & Radicals p 3-5 Equality with base & exponents

3 AlgebraCont'd pp. 3-1 to 3-12 12

14 Logarithms p 3-5 log b a = n; b n =a are equivalent.Logarithm is exponent.

15 Logarithm Identities p 3-5 Useful equations, erspecially the solution for ln

16 Partial Fractions p 3-6

17 Simultaneous Linear Equations p 3-7

18 Complex Numbers p 3-7

19 Operations on Complex Numbers p 3-8 Algebraic operations OK, except in equality operators.

20 Limits p 3-9 Value of a function approaches when an independent variable approaches a target

21 Sequences and Progressions p 3-10 A sequence is an ordered progression of numbers. Can be divergent or convergent

22 Standard Sequences p 3-11 Geometric. Arithmetic, harmonic & p-sequence.

23 Series p 3-11 Sum of terms in a sequence. 2 types: finite & infinite series.Performance is based o

24 Tests for Series Convergence p 3-11 Finite series converge. Infinite series convergence can be determined by the limit o

25 Series of Alternating Signs p 3-12 1 diverges

4 Linear Algebra pp. 4-1 to 4-7 7

1 Matrices p 4-1

2 Special types of Matrices p 4-1 cofactor, column, complex, diagonal, echelon ( row-reduced echelon ), identity, null

scalar, singular, skew symmetric, square, symmetrical, triangular, unit ( or identity )

3 Row equivalent matrices p 4-2 if matrix B is obtained by a finite sequence of elementary row operations on A

4 Minors & Cofactors p 4-2 Determinants of submatrices associated with particular entries in the original square

5 Determinants p 4-3 Scalar calculated from a square matrix. See rules.

6 Matrix Algebra p 4-3

7 Matrix addition & subtraction p 4-4 Possible if both matrices have the same numbers of rows & columns.

8 Matrix multiplication p 4-4 Can be by a scalar. With another matrix provided that no. of col of left-hand matrix i

9 Transpose p 4-4

10 Singularity & Rank p 4-5 Singular matrix has zero determinants while nonsingular matrix has nonzero determ

11 Classical adjoint p 4-5 The transpose of the cofactor matrix.12 Inverse p 4-5 Only square matrices have inverses, but NOT all are invertible.Only nonsingula , no

13 Writing simul linear eqs. In matrix forms p 4-6 Coefficient matrix, variable matrix & constant matrix.

14 Solving simul linear eqs. p 4-6 by Gauss-Jordan elimination & Cramer's rule

15 Eigenvalues and Eigenvectors p 4-6

5 Vectors pp. 5-1 to 5-5 5

1 Introduction p 5-1 A scalar has only magnitude. A vector is a directed straight line with a specific mag

Force, momentum, displacement and velocity are examples of vectors.

2 p 5-1 A vector can be spacified in terms of n coordinates of its two endpoints

3 Unit Vectors p 5-2

4 Vector Representation p 5-2 In rectangular form and/or phasor or polar form.

5 Conversion between systems p 5-2 coefficient of transformation, transformation matrix.

6 Vector addition p 5-3 By polygon method, where the sum is the "resultant vector".

7 Multiplication by Scalar p 5-3 Scalar multiplication is distributive.8 Vector DOT Product p 5-3 If 2 vector magnitude characteristic are known, get relative directions by Cauchy-Sc

9 Vector Cross Product p 5-4 Cross product of 2 vectors is a vector that is orthogonal ( perpendicular ) to the plan

10 Mixed Triple Product p 5-4 Mixed triple product of 3 vectors is a scalar qty representing the volume of parallele

11 Vector triple product p 5-5 Vector triple product is defined by Eq. 5.42.

12 Vector Functions p 5-5 A vector can be a function of another parameter, and can be differentiated or integr

To transform a proper polynomial fraction of two polynomials into a sum of simpler

Solution of "consistent system" by: graphing, substitution, reduction or by Cramer's

Combination of real & imaginary numbers. Rectangular of trigonometric form ( a + b

Convenient method of representing a set of numbers. m=rows x n=columns:Bold up

matrix algebra differs from standard algebra. Equality, inequality, comm add'n & as

Atof an m x n matrix A is an n x mthe diagonal is "unchanged".

characteristic values & characteristic vectors of a square matrix are the scalars ka

Vectors in n-SPACE

The unit vector a has the same direction as vectorV but has a length of 1. This un

calculated by dividing the original vectorV by its magnitude/V/


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5 pp 81- 100 Chemistry,materials science,Mesayrements/control,computer,economics, ethics


7 pp121- 140 Civil engineering

8 pp141- 160 Environmental, electrical & computer engineering






3 Areas & volumes p 10 - Mathematics

4 Confidence intervals, value of Za/2 p 19. Probability & Statistics5 Distribution tables p 20 -Probability & Statistics

6 Centroids & moment of inertia p 27 -Statics


8 Beam deflection formulas p 43. Mechanics of Materials

9 Fluid measurements p 50 -Fluid Mechanics






15 Steam tables p 62 -Thermodynamics



18 Heat capacity tables p 66 Thermodynamics

19 Convection / radiation p 71 Heat Transfer 20 Characteristics of sel. Microbial cells p 75 Biology

21 Compositon data for biomass p 76 Biology





26 Half-li fe & materials characteristics p 85 Materials Science / Matter



29 Factor tables p 94 -Engineering Economics


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32 Unified soil classifications p 112Civil Engineering

33 Reinf. Conc. Design p 115Civil Engineering

34 Steel Structures p 121Civil Engineering










44 Hazardous waste compatibilty chart p 154 Environmental Engineering

45 Carcinogens & noncarcinogens p 155 Environmental Engineering

46 Exposure & intake rates p 156Environmental Engineering


48 Water treatment technology p 159Environmental Engineering



51 Digital signals/comm. Theory p 1 75 Electrical & Computer Eng'g



54 band-Phase filters p 180Electrical & Computer Eng'g


56 Device & schematic symbols p 183 Electrical & Computer Eng'g

57 N-channel JFE Transistors p 184Electrical & Computer Eng'g58 Enhancement MOSFET p 186 Electrical & Computer Eng'g

59 Number systems & codes p 187 Electrical & Computer Eng'g

60 Logic operations & Boolean p 187 Electrical & Computer Eng'g











71 Power transmission p 204 Mechanical Engineering

72 Rivets & fasteners p 205 Mechanical Engineering73 Kinematics, dynamics & vibrations p 206 Mechanical Engineering






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n

tion of real & imaginary.

e.


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.

n

the argument


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Contents : ALPHABETICAL ARRANGEMENTTopic Ch.

# 1 Background & Support

1 System of Units pp. 1-1 to 1-10 10

1 Acceleration of gravity p 1-2 g = 32.2 ft/sec2 = 9.81 m / s; Earth's radius = 3,960 miles = 6, 370 Km = 6.37 x 1

2 Common Unit of Mass p 1-1 Gram, pound, kilogram and slug

3 Consistent Systems of Units p 1-2 M=Fd is OK& F=ma si consistent; problems fluid flow & thermo are solved in U.S

4 Dimensional Analysis p 1-8 Means of obtaining an equation that describes some phenomenon w/out understand

Table 1.8 - Common Dimensionless groups p 1-9 Example of Dimensionless Analysis

5 Dimensionless Groups p 1-7 Ratio of 2 forces or quantities, notably in fluid mechanics or heat transfer, ie: Reyno

6 Introduction p 1-1 Pound unit both for force & mass in English System ( American )

7 Lineal and Board Foot Measurements p 1-8 Bd. Ft = 12" x 12" x 1" = 144 cubic inches

8 Mass and Weight p 1-1 SI- kilogram (mass ) & Newton ( force ), Wt = mg, mass & wt are NOT the same!9 Metric System of Units p 1-4 Based on meters or any part of meters, either mks or cgs

10 Other Formulas Affected by Inconsistencies p 1-3 Req's "g" term; Kinetic energy (E=mv2/2g); Potential energy (E=mgz/g ); pressure (

11 Primary Dimensions p 1-7 (ML0T),mass(M),length(L),time(0) & temp(T); ML2/02 (kg-m2)/s2; FML0TQ=engine

12 Rules for Using SI Units p 1-6 Symbols are NOT pluralized; a period after symbol is NOT used; use prefixes

13 SI Units ( The mks System ) p 1-5 Base units: length (m); mass (kg); t ime (sec); elect. Current(ampere); temp(K);amt.

SI Units ( The mks System ) Table 1.2 & 1.3 S. I. derived units; solid angle =sr = steradian

14 The Absolute English System p 1-4 Poundal = 0.03108 lb force or 1/32.2

15 The cgs System p 1-4 Unit of force = g-cm / sec2 = dyne

16 The English Engineering System p 1-2 Lb-mass & Lb-force are different as gallons & feet. Lb-force = Lb-mass / 32.1740 lb

17 The English Gravitational Sytem p 1-3 Slug = lbf-sec2/ft = lbm/gc

18 Weight and Weight Density p 1-3 W=mg/gc; gamma = W/V = rho g / gc; p= gamma h

2 Engineering Drawing Practic pp. 2-1 to 2-4 4

1 Auxilliary ( Orthographic ) Views p 2-2 Needed when an object has an inclined plane or curved feature. Only 1 of the 3 dim

2 Axonometric ( Orthographic Oblique ) Views p 2-3 Projections: isometric, dimetric & trimetric.3 Intersecting & Paral lel Lines p 2-1 If two or more views show the lines as having the same common point, then the line

4 Normal Views of Lines & Planes p 2-1 True length of a line is viewed and can be measured

5 Oblique ( Orthographic ) Views p 2-2 If the object is turned so that 3 dimensions are visible, it can be illustrated by a sing

6 Perspective Views p 2-3 Parallel perspective, angular perspective & oblique perspective

7 Principal ( Orthographic ) Views p 2-2 Also planar views, requires at least three (3) principal views & at most 6 principal vie

Plan views & elevations

8 Sections p 2-3 "Imaginary" cut taken through an object to reveal the shape or interior construction.

9 Surface Finish p 2-4 Parameters are maximum allowable values. All lesser values are permitted.

10 Tolerances p 2-4 The total permissible variation between the acceptable limits, ie; +/- 0.001

11 Types of Views p 2-1

12 Types of Views

3 Algebra pp. 3-1 to 3-12 12

1 Complex Numbers p 3-7

2 Descartes Rule of Signs p 3-4 Real roots of a polynomial equation.3 Equations p 3-2 It is a mathematical statement of equality; or variables ( Algebraic); "functional" form

4 Extraneous Roots p 3-4 Extraneous roots does NOT establish equality in equations.

5 Fundamental Algebraic Laws p 3-3 A + B = B + A ( commutative add ); AB=BA ( comm. Multi ); associative & distributiv

6 Greek Alphabet p 3-1 Alpha, beta, gamma, delta.omega

7 Introduction p 3-1 One & first of the mathematical concepts needed by engineers.

8 Limits p 3-9 Value of a function approaches when an independent variable approaches a target

9 Logarithm Identities p 3-5 Useful equations, erspecially the solution for ln

10 Logarithms p 3-5 log b a = n; b n =a are equivalent.Logarithm is exponent.

11 Operations on Complex Numbers p 3-8 Algebraic operations OK, except in equality operators.

ortographic, principal, auxilliary, oblique, cavalier projection, cabinet projection, clin

axonometric views, isometric, dimetric, trimetric, perspective views, parallel perspe

Combination of real & imaginary numbers. Rectangular of trigonometric form ( a + b


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12 Partial Fractions p 3-6

13 Polynomials p 3-3 Rational expression, usually the sum of several variable terms; degree is highest po

3 AlgebraCont'd pp. 3-1 to 3-12 12

14 Roots of General Polynomials p 3-3 Techniques: inspection, graphing, numerical methods, factoring, special case ( New

15 Roots of Quadratic Equations p 3-3 x1 + x2 = - b/a; x1x2 = c/a; x1, x2 = ( -b +/- ( b x b - 4ac ) 1/2) / 2a

16 Rules for Exponent & Radicals p 3-5 Equality with base & exponents

17 Sequences and Progressions p 3-10 A sequence is an ordered progression of numbers. Can be divergent or convergent

18 Series p 3-11 Sum of terms in a sequence. 2 types: finite & infinite series.Performance is based o

19 Series of Alternating Signs p 3-12 1 diverges

20 Significant Digits p 3-1 Include the leftmost, nonzero digits to the rightmost digit written. See Table 3.3 on p

21 Simultaneous Linear Equations p 3-7

22 Standard Sequences p 3-11 Geometric. Arithmetic, harmonic & p-sequence.

23 Symbols used in this book p 3-1 Used to represent variables in the formulas throughout this book, ref. Table 3.2, p. 3

24 Tests for Series Convergence p 3-11 Finite series converge. Infinite series convergence can be determined by the limit o

25 Types of Numbers p 3-1 Real numbers, rational real & irrational real; imaginary numbers are square roots of

4 Linear Algebra pp. 4-1 to 4-7 7

1 Classical adjoint p 4-5 The transpose of the cofactor matrix.

2 Determinants p 4-3 Scalar calculated from a square matrix. See rules.

3 Eigenvalues and Eigenvectors p 4-6

4 Inverse p 4-5 Only square matrices have inverses, but NOT all are invertible.Only nonsingula , no

5 Matrices p 4-1

6 Matrix addition & subtraction p 4-4 Possible if both matrices have the same numbers of rows & columns.

7 Matrix Algebra p 4-3

8 Matrix multiplication p 4-4 Can be by a scalar. With another matrix provided that no. of col of left-hand matrix i

9 Minors & Cofactors p 4-2 Determinants of submatrices associated with particular entries in the original square

10 Row equivalent matrices p 4-2 if matrix B is obtained by a finite sequence of elementary row operations on A

11 Singularity & Rank p 4-5 Singular matrix has zero determinants while nonsingular matrix has nonzero determ12 Solving simul linear eqs. p 4-6 by Gauss-Jordan elimination & Cramer's rule

13 Special types of Matrices p 4-1 cofactor, column, complex, diagonal, echelon ( row-reduced echelon ), identity, null

Special types of Matrices scalar, singular, skew symmetric, square, symmetrical, triangular, unit ( or identity )

14 Transpose p 4-4

15 Writing simul linear eqs. In matrix forms p 4-6 Coefficient matrix, variable matrix & constant matrix.

5 Vectors pp. 5-1 to 5-5 5

1 Conversion between systems p 5-2 coefficient of transformation, transformation matrix.

2 Introduction p 5-1 A scalar has only magnitude. A vector is a directed straight line with a specific mag

Introduction Force, momentum, displacement and velocity are examples of vectors.

3 Mixed Triple Product p 5-4 Mixed triple product of 3 vectors is a scalar qty representing the volume of parallele

4 Multiplication by Scalar p 5-3 Scalar multiplication is distributive.


Unit Vectors

6 Vector addition p 5-3 By polygon method, where the sum is the "resultant vector".7 Vector Cross Product p 5-4 Cross product of 2 vectors is a vector that is orthogonal ( perpendicular ) to the plan

8 Vector DOT Product p 5-3 If 2 vector magnitude characteristic are known, get relative directions by Cauchy-Sc

9 Vector Functions p 5-5 A vector can be a function of another parameter, and can be differentiated or integr

10 Vector Representation p 5-2 In rectangular form and/or phasor or polar form.

11 Vector triple product p 5-5 Vector triple product is defined by Eq. 5.42.

12 p 5-1 A vector can be spacified in terms of n coordinates of its two endpoints

To transform a proper polynomial fraction of two polynomials into a sum of simpler

Solution of "consistent system" by: graphing, substitution, reduction or by Cramer's

characteristic values & characteristic vectors of a square matrix are the scalars ka

Convenient method of representing a set of numbers. m=rows x n=columns:Bold up

matrix algebra differs from standard algebra. Equality, inequality, comm add'n & as

Atof an m x n matrix A is an n x mthe diagonal is "unchanged".

The unit vector a has the same direction as vectorV but has a length of 1. This un

calculated by dividing the original vectorV by its magnitude/V/

Vectors in n-SPACE


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5 pp 81- 100 Chemistry,materials science,Mesayrements/control,computer,economics, ethics


7 pp121- 140 Civil engineering

8 pp141- 160 Environmental, electrical & computer engineering






3 Areas & volumes p 10 - Mathematics4 Confidence intervals, value of Za/2 p 19. Probability & Statistics

5 Distribution tables p 20 -Probability & Statistics

6 Centroids & moment of inertia p 27 -Statics


8 Beam deflection formulas p 43. Mechanics of Materials

9 Fluid measurements p 50 -Fluid Mechanics






15 Steam tables p 62 -Thermodynamics



18 Heat capacity tables p 66 Thermodynamics19 Convection / radiation p 71 Heat Transfer

20 Characteristics of sel. Microbial cells p 75 Biology

21 Compositon data for biomass p 76 Biology





26 Half-li fe & materials characteristics p 85 Materials Science / Matter




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29 Factor tables p 94 -Engineering Economics



32 Unified soil classifications p 112Civil Engineering

33 Reinf. Conc. Design p 115Civil Engineering

34 Steel Structures p 121Civil Engineering










44 Hazardous waste compatibilty chart p 154 Environmental Engineering

45 Carcinogens & noncarcinogens p 155 Environmental Engineering

46 Exposure & intake rates p 156Environmental Engineering


48 Water treatment technology p 159Environmental Engineering



51 Digital signals/comm. Theory p 1 75 Electrical & Computer Eng'g



54 band-Phase filters p 180Electrical & Computer Eng'g


56 Device & schematic symbols p 183 Electrical & Computer Eng'g57 N-channel JFE Transistors p 184Electrical & Computer Eng'g

58 Enhancement MOSFET p 186 Electrical & Computer Eng'g

59 Number systems & codes p 187 Electrical & Computer Eng'g

60 Logic operations & Boolean p 187 Electrical & Computer Eng'g











71 Power transmission p 204 Mechanical Engineering72 Rivets & fasteners p 205 Mechanical Engineering

73 Kinematics, dynamics & vibrations p 206 Mechanical Engineering






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n

ndela)

the argument


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tion of real & imaginary.

.

n


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Contents

Topic Ch.

# 2 Water Resources

14 Fluid Properties pp. 14-1 to 14-15 15

1 Characterist ics of a Fluid p 14-1 Liquid & gases are "f luids".Compressibility; Shear Resistance = Zero; Shape & Volume (Den

Characteristics of a Fluid Resistance to Motion ( Viscosity ); Molecular Spacing ( kinetic Energy ); Pressure : ( at a pt.

2 Types of Fluid p 14-2 Ideal & Real; ( Newtonian ie; water, air, gas, steam, alcohol... & non-Newtonian ); Pseudopla

3 Fluid Pressure & Vacuum p 14-2 Absolute ( measured w/ respect to true zero pressure ref. ) Gage ( measured w/ respect to a

Pabs = Pgage + Patmos = Patmos - Pvacuum;

4 Density p 14-3 Mass per unit volume; = pressure,p / RT; Water = 62.4 lbm/cu. Ft = 999 kg / cu.m. (in S.I. =

5 Specific Volume p 14-4 Volume occupied by a unit mass of fluid = 1/density; cu. Ft / lbm, cu. m / kg, cu. Ft. / lbmole.

6 Specific Gravity p 14-4 Is a dimensionless ratio of a fluid's density to some standard ref. density. K = C + 273 degre

7 Specific Weight p 14-5 Weight of fluid per unit volume. = lbf / cu.ft.

8 Mole Fraction p 14-5 The mole fraction of component A is the number of moles of that component divided by the t

9 Viscosity p 14-6 It is a measure of fluid's resistance to flow when acted upon by external force such as press

10 Kinematic Viscosity p 14-8

11 Viscosity Conversions p 14-8

12 Viscosity Index p 14-9 Measure of a fluid's sensitivity to change in viscosity w/ changes in temperature. Vis. Is mea

13 Vapor Pressure p 14-9 Vaporization & condensation at constant temperature are equilibrium processes. The equilib

14 Osmotic Pressure p 14-9

15 Surface Tension p 14-10 Tension between 2 points a unit distance apart on the surface; lbf / ft ( ft-lbf / Sq. Ft. ) = F / 2

16 Capillary Action p 14-11 Name given to the behavior of a liquid in a thin-bore tube, caused by surface tension bet.liqu

17 Compressibility p 14-12 Is the fractional change in the vol. of afluid per unit change in pressure in a constant tempera

18 Bulk Modulus p 14-13 Reciprocal of "compressibility", & analogous to the Modulus of Elasticity of a solid. E = stres

19 Speed of Sound p 14-14 = 1, 126 ft / sec @ 20 deg.C in dry air; = 369 m/s @ 66 deg C at std. 20 Properties of Solutions p 14-15

in the combined fluid; xA = nA / ( nA + nB + nC + ). Mole fraction is a no. bet. 0-1.0, Mole

Fluid shear , T = F/A = u( dv/dy); Pseudoplastic, plastic/Bingham; dilatant, Newtonian; u is

v, ratio of abs. viscosity to mass density = u / p, unit = Sq. Ft. / sec, centistokes, cSt

Pls. refer to table 14.5.; u = pv

by these free molecules is known as the vapor pressure orsaturation pressure.

Pi = pgh = MR*T; R* = universal gas constant = 0.08205746 0r 0. 821 Lat/K-mol

= Sq. Rt (E / p )


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# 2 Water Resources

14 Fluid Properties pp. 14-1 to 14-15 15

1 Bulk Modulus p 14-13 Reciprocal of "compressibility", & analogous to the Modulus of Elasticity of a solid. E = stress

2 Capillary Action p 14-11 Name given to the behavior of a liquid in a thin-bore tube, caused by surface tension bet.liqu

3 Characteristics of a Fluid p 14-1 Liquid & gases are "f luids".Compressibility; Shear Resistance = Zero; Shape & Volume (Den

Characteristics of a Fluid Resistance to Motion ( Viscosity ); Molecular Spacing ( kinetic Energy ); Pressure : ( at a pt.

4 Compressibility p 14-12 Is the fractional change in the vol. of afluid per unit change in pressure in a constant tempera

5 Density p 14-3 Mass per unit volume; = pressure,p / RT; Water = 62.4 lbm/cu. Ft = 999 kg / cu.m. (in S.I. =

6 Fluid Pressure & Vacuum p 14-2 Absolute ( measured w/ respect to true zero pressure ref. ) Gage ( measured w/ respect to a

Fluid Pressure & Vacuum Pabs = Pgage + Patmos = Patmos - Pvacuum;

7 Kinematic Viscosity p 14-88 Mole Fraction p 14-5 The mole fraction of component A is the number of moles of that component divided by the t

Mole Fraction

9 Osmotic Pressure p 14-9

10 Properties of Solutions p 14-15

11 Specific Gravity p 14-4 Is a dimensionless ratio of a fluid's density to some standard ref. density. K = C + 273 degree

12 Specific Volume p 14-4 Volume occupied by a unit mass of fluid = 1/density; cu. Ft / lbm, cu. m / kg, cu. Ft. / lbmole.

13 Specific Weight p 14-5 Weight of fluid per unit volume. = lbf / cu.ft.

14 Speed of Sound p 14-14

15 Surface Tension p 14-10 Tension between 2 points a unit distance apart on the surface; lbf / ft ( ft-lbf / Sq. Ft. ) = F / 2

16 Types of Fluid p 14-2 Ideal & Real; ( Newtonian ie; water, air, gas, steam, alcohol... & non-Newtonian ); Pseudopla

17 Vapor Pressure p 14-9 Vaporization & condensation at constant temperature are equi librium processes. The equil ib

Vapor Pressure

18 Viscosity p 14-6 It is a measure of fluid's resistance to flow when acted upon by external force such as pressu

Viscosity

19 Viscosity Conversions p 14-8 = 1, 126 ft / sec @ 20 deg.C in dry air; = 369 m/s @ 66 deg C at std. a20 Viscosity Index p 14-9 Measure of a fluid's sensitivity to change in viscosity w/ changes in temperature. Vis. Is mea

v, ratio of abs. viscosity to mass density = u / p, unit = Sq. Ft. / sec, centistokes, cSt

in the combined fluid; xA = nA / ( nA + nB + nC + ). Mole fraction is a no. bet. 0-1.0, Mole

Pi = pgh = MR*T; R* = universal gas constant = 0.08205746 0r 0. 821 Lat/K-mol

= Sq. Rt (E / p )

by these free molecules is known as the vapor pressure orsaturation pressure.

Fluid shear , T = F/A = u( dv/dy); Pseudoplastic, plastic/Bingham; dilatant, Newtonian; u is

Pls. refer to table 14.5.


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Contents

TopicCh.

# IV Geotechnical

35 Soil Properties & Testing pp. 35-1 to 35-30 30

1 Soil Particle Size Distribution p 35-2 Coarse-grained ( sand & gravel ) & fine-grained ( silt & clay ); Uniformity coeff, Cu =D60/D1

2 Soil Classification p 35-4 Depends mostly on the % of gravel, sand, silt & clay. A-1, A-3, A-2, A-4, A-5, A-6, A-7, & A-

3 AASHTO Soil Classification p 35-5 This is based on: Sieve analysis, l iquid limit & plasticity index. A-1 is best for roadway subg

Group Index, IgEq. 35.23; Tables 35.2, 35.5

4 Unified Soil Classification p 35-5 W=well graded, C=significant amounts of clay, P=poorly graded, M=significant amount of s

5 Mass-Volume Relationship p 35-7

6 Swell p 35-14 Swell occurs when clayey soils are used at lower loadings and/or higher moisture contents

7 Effective stress p 35-14 Sigma = gamma x ht. or pg x ht., consider pore pressure

8 Standardized Soil Testing Procedures p 35-15 List per Table 35.8;

9 Standard Penetration Test ( SPT ) p 35-17 In-situ test w/c is part of drilling & sampling operations.Measures resistance to the penetrat

that is driven by a 140-ldm hammer dropped from a height of 30". N blows req'd to drive sa

10 Cone Penetrometer Test ( CPT ) p 35-17

11 Proctor Test p 35-17

12 Modified Proctor test p 35-18 Similar to "Proctor Test ) but the soil is compacted in 5 layers w/ a 10 lbm hammer falling 1

13 In-Place Density Test p 35-20 Also known as " Field Density Test. A 3 to 5" deep hole with smooth sides is dug into the co

14 Atterberg Limit Tests p 35-21 P.L. = water content corr. transition bet. semi-solid & plastic state; L.L. = bet. Plastic to liqui

15 Permeability Tests p 35-22

16 Consolidation tests p 35-23 Also known as "confined compression tests" or oedometer tests " start w/ a disc of soil conf

17 Direct Shear Tests p 35-24 To determine the relationship of shear strength to consolidation stress.18 Triaxial Stress Test p 35-25 More sophisticated that the direct shear test. Dense & loose curves are plotted along with t

19 Vane-Shear Test p 35-28

consisting of a four-bladed vane on a vertical shaft.

20 Unconfined Compressive Strength Test p 35-28

21 Sensitivity p 35-28 Clay will become softer as it is worked, and clay soil can turn into viscous liquids during con

22 California Bearing Ratio Test p 35-29 CBR = actual load / standard load x 100%. Used to determine the suitability of a soil for use

23 Plate Bearing Value Test p 35-30 "performed on compacted soil in the field. The deflection prior to loading, the final deflectio

24 Hveem's Resistance Value Test p 35-30 To evaluate the suitability of a soil for use inn the pavement section (w/R-values 0 for wa

25 Classification of Rocks p 35-30 Igneous, sedimentary & metamorphic.

36 Shallow Foundation pp. 36-1 to 36-10 10

1 Shallow Foundations p 36-1 Df/B


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12 Rafts on Clay p 36-9 Consider factor of safety ( F ) & clay equations 36.21 & Tables 36.2 & 36.4.

13 Rafts on sand p 36-10TopicCh.

# IV Geotechnical

37 Rigid Retaining Walls pp. 37-1 to 37-8 8

1 Types of Retaining walls p 37-1 Gravity walls, semi-gravity wal ls, Buttress walls, Counterfort walls, Canti lever Walls.

2 Cohesive & Granular Soils p 37-2 The nature of the backfilled or retained soil greatly affects the design of retaining walls, ang

3 Earth Pressure p 37-2 Force per unit area exerted by soil of retaining wall. "Active"(or tensioned or forward ), "Pas

4 Vertical Soil Pressure p 37-3 Caused by the soil's own weight; pv = gammaH

5 Active Soil Pressure p 37-3

By graphical method, see appendix 37.A.

6 Passive soil Pressure p 37-4

7 At-Rest Soil Pressure p 37-48 Graphical Solutions p 37-5 Appendix 37.A; Ra,h = 1/2KhHsquared; Ra,v = 1/2KvHsquared

9 Surcharge Loading p 37-5 An additional force applied at the exposed upper surface of the restrained soil. A surcharge

point, line or strip load. Pq = kaq; Rq = kaqH x (wall width ) acting @ H/2 above the base.A

10 Effective Stress p 37-6 The equivalent specific weight of water behind a retaining wall is taken @ 45 lbf/cu.ft.

11 Cantilever Retaining Walls: Analysis p 37-6 9 steps for reference.

12 Retaining Walls : Design p 37-8 Steps & assumptions to make in the design of retaining wall.

38 Piles and deep Foundationpp. 38-1 to 38-6 8

1 Introduction p 38-1 Piles, slender members that are drilled or jetted into the ground.Ultimate static bearing cap

2 Pile Capacity from Driving Data p 38-2 Safe load ( safe bearing value ) can be calculated empirically using ENR equations: Qa=(2

3 Theoretical Point Bearing Capacity p 38-2 Also known as " Tip resistance & point capacity "; Qp = Ap ( 1/2gammaBNgamma +cNc + g

4 Theoretical Skin Friction Capacity p 38-3 Also known as " Side resistance, skin resistance & shaft capacity "; Qf = Asfs = pfsLe = pfs

5 H-Piles p 38-3 Skin perimeter is the "block" perimeter of the pi le, assuming that the soil between the flages

6 Tensile capacity p 38-5 Tension piles pullout capacity includes the weight of the pile + shaft resistance (or skin frict

7 Capacity of Pile Groups p 38-5 Spacing = 3 - 3.5x the pile dia apart.Qs=2(b+w)Lec1; Qp=9c2bw; Qult = Qs + Qp; Qa = Qu

8 Settlement of Piles & Pile groups p 38-5 Pile in clay may experience significant settling. Can be estimated by assuming that the supp

9 Downdrag and Adfreeze forces p 38-6

10 Micropiles p 38-6 Used when traditional pile driving is prevented by restricted access, usually in urban areas

11 Piers p 38-6 Deep foundation with significant cross-sectional area.

40 Special Soil topics pp. 40-1 to 40-11 11

1 Pressure from Applied Loads: p 40-1 The increase in vertical pressure caused by an application of a point load,P,;pv = (3hcubeP

Boussinesq's Equation when h>2B; pls. refer to Eq. 40.1

2 Pressure from Applied Loads: p 40-2 Delta pv = P/A wher A = area at influence depth "h"

Zone of Influence

3 Pressure from Applied Loads: p 40-2 For footing or mat foundation, pls. see chart on p. 40-3.

Influence Chart

4 Settling p 40-3 Generally due to "consolidation" ( decrease in void fraction ) of the supporting soil. 3 types:

Since settling is greater for higher foundation pressures, specific settlement limits ( e.g. 1")

5 Clay Condition p 40-3 "Consolidation curve" shows a recompression segment and the virgin compression branch.

6 Consolidation Parameters p 40-4 Along the recompression line, the recompression index,Cr, is the logarithmic slope of the re7 Primary Consolidation p 40-4 When clay layers are loaded to a higher pressure, water is squeezed from the voids.Primar

8 Primary Consolidation Rate p 40-5 Consolidation of clay is a continuous process, thothe rate decreases with time. ; t=; Cv=; avecon ary onso a on p -

10 Slope Stability in Saturated Clay p 40-7 "Taylor slope stability chart"; Typesof Slope failures=slope circle; toe circle; base circle.

11 Loads on Buried pipes p 40-8 Ref: factor h/B yields valus of C for each Backfill materials.

12 Allowable Pipe Loads p 40-9 w allowable = (known pipe crushing strength) x (LF/F)

13 Slurry Trench and Walls p 40-9 Slurry trenches are "non-structural" barriers created by chemically solidifying soils: to dewa

contaminants, & hydraulically isolate holding ponds and lagoons.

Slurry walls are reinforced semistructural walls used for more seepage control than can be

Slurry walls are constructedby excavating a trenc h, support it with bentonite slurry to preve

and displacing the slurry with cast-in-place tremie concrete.

14 Cofferdams and Caissons p 40-10 Cofferdam is a temporary structure built to enclose a construction site; Caisson is a perman

15 Geotextiles p 40-10 Also known as filter cloth, reinforcing fabric and support membrane are fabrics used to stab

Well protected against bearing capacity. Settlement will govern in design. Qa=0.22CnN.

ka=coefficient of active earth pressure ( by Coulomb or Rankine ); Ra = 1/2pa H = 1/2 ka g

kp=coefficient of passive earth pressure ( by Coulomb or Rankine ); Rp = 1/2pp H = 1/2 kp

ko=coefficient of earth pressure at rest ( w/c varies from 0.4 to 0.50.; Ro = 1/2 ko gamma H


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16 Soil Nailing p 40-11 It is a slope-stabilization method that involves installing closely spaced nails in the soil/rock

17 Trenchless Methods p 40-11 Trenchless method include pipe jacking, microtunneling, auger boring and impact ramming

18 Liquefaction p 40-11 Is a sudden drop in shear strength that can occur in soils of saturated cohesionless particle

zero, the sand liquefies. In effect, the soil turns into a liquid, allowing everything it previousl


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Contents : ALPHABETICAL ARRANGEMENT

TopicCh.

# IV Geotechnical

35 Soil Properties & Testing pp. 35-1 to 35-30 30

1 AASHTO Soil Classification p 35-5 This is based on: Sieve analysis, l iquid limit & plasticity index. A-1 is best for roadway subg

AASHTO Soil Classification Group Index, IgEq. 35.23; Tables 35.2, 35.5

2 Atterberg Limit Tests p 35-21 P.L. = water content corr. transition bet. semi-solid & plastic state; L.L. = bet. Plastic to liqui

3 California Bearing Ratio Test p 35-29 CBR = actual load / standard load x 100%. Used to determine the suitability of a soil for use

4 Classification of Rocks p 35-30 Igneous, sedimentary & metamorphic.

5 Cone Penetrometer Test ( CPT ) p 35-17

6 Consolidation tests p 35-23 Also known as "confined compression tests" or oedometer tests " start w/ a disc of soil conf

Consolidation tests

7 Direct Shear Tests p 35-24 To determine the relationship of shear strength to consolidation stress.

8 Effective stress p 35-14 Sigma = gamma x ht. or pg x ht., consider pore pressure

9 Hveem's Resistance Value Test p 35-30 To evaluate the suitability of a soil for use inn the pavement section (w/R-values 0 for wa

10 In-Place Density Test p 35-20 Also known as " Field Density Test. A 3 to 5" deep hole with smooth sides is dug into the co

11 Mass-Volume Relationship p 35-7

12 Modified Proctor test p 35-18 Similar to "Proctor Test ) but the soil is compacted in 5 layers w/ a 10 lbm hammer falling 18

13 Permeability Tests p 35-22

14 Plate Bearing Value Test p 35-30 "performed on compacted soil in the field. The deflection prior to loading, the final deflection

15 Proctor Test p 35-17

16 Sensitivity p 35-28 Clay will become softer as it is worked, and clay soil can turn into viscous liquids during con

17 Soil Classification p 35-4 Depends mostly on the % of gravel, sand, silt & clay. A-1, A-3, A-2, A-4, A-5, A-6, A

18 Soil Particle Size Distribution p 35-2 Coarse-grained ( sand & gravel ) & fine-grained ( silt & clay ); Uniformity19 Standard Penetration Test ( SPT ) p 35-17 In-situ test w/c is part of drilling & sampling operations.Measures resistance to the penetrat

Standard Penetration Test ( SPT ) that is driven by a 140-ldm hammer dropped from a height of 30". N blows req'd to drive sa

20 Standardized Soil Testing Procedures p 35-15 List per Table 35.8;

21 Swell p 35-14 Swell occurs when clayey soils are used at lower loadings and/or higher moisture contents

22 Triaxial Stress Test p 35-25 More sophisticated that the direct shear test. Dense & loose curves are plotted along with th

23 Unconfined Compressive Strength Test p 35-28

24 Unified Soi l Classification p 35-5 W=well graded, C=significant amounts of clay, P=poorly graded, M=significant amount of s

25 Vane-Shear Test p 35-28

Vane-Shear Test consisting of a four-bladed vane on a vertical shaft.

36 Shallow Foundation pp. 36-1 to 36-10 10

1 Allowable Bearing Capacity p 36-2

2 Bearing Capacity of Clay p 36-4 Angle of internal friction, phi = 0. Su = c Suc/2; qa = qnet / F = cNc / F; wgere F = total (net)

3 Bearing Capacity of sand p 36-6

4 Bearing Capcity of Rock p 36-7 For most rocks, the design will be based on settlement characteristics, NOT strength.

5 Eccentric Loads on Rectagular Footings p 36-8 eB = MB / P & eL = ML/P; pmin, pmax = (P/BL) (1 +- 6e/B )

6 Effects of Water table on Footing Design p 36-7 May or may not affect bearing capacity. There are three (3) general principles.

7 General Bearing Capacity equation p 36-3

General Bearing Capacity equation

8 General Considerations for Footings p 36-2 Footing is an enlargement at the base of a load-supporting column that is designed to tran

General Considerations for Footings (individual or isolated ); Continuous or wall footing; Combined ; Catilever. Should be safe a

9 General Considerations for Rafts p 36-8 Rafts, or mat, or pad(when spread footing area would constitute 1/2 or more than 50% of

10 Rafts on Clay p 36-9 Consider factor of safety ( F ) & clay equations 36.21 & Tables 36.2 & 36.4.

11 Rafts on sand p 36-10

An alternative to the SPT. Good for classifying both sands & clays. fR = qs/qcx 100 %

The load versus the void ratio for al l increments is ployyed as an e=log p curve.

porosity, void ratio, moisture ( or water ) content, degree of saturation, densitySp. Gr. Of

Measure of continuous voids. (Darcy's law. Q=vAgross; v = Ki); { Hazen's formula ( K = VL

Usually accomplished by placing soil in lifts. RC =pd / p*dx 100 %

OCR =

S = tau = c + sigm

A cylinder of cohesive soil ( usually clay ) is loaded axially to compressive failure. Suc= P/A

The shear strength of a low-strength, homogeneous cohesive soil ( e.g., clay ) can be neas

Also known as "net allowable or safe B. P." ( From Table 36.1, Typ. All. Soil B. P. Ranges

The cohesion, c, =0; qult = (/2)gammaBNgamma + 0 + (pq + gammaDf)Nq ; qnet = qult - pg

Terzaghi-Meyerhof Equation; qult = 1(/2)pgBNgamma + cNc+ (pq +pgDf)Nq = 1(/2)gamma

See Tables 36.4 & 36.5 for Bearing Capacity Factor Multipliers for various values ofB/L

Well protected against bearing capacity. Settlement will govern in design. Qa=0.22CnN.


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12 Sand Versus clay p 36-1 Sand is strong & drains quickly, but behaves poorly in excavations due to lack of cohesion.

13 Shallow Foundations p 36-1 Df/B


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Slurry Trench and Walls Slurry walls are constructedby excavating a trenc h, support it with bentonite slurry to preve

Slurry Trench and Walls and displacing the slurry with cast-in-place tremie concrete.

17 Soil Nailing p 40-11 It is a slope-stabilization method that involves installing closely spaced nails in the soil/rock

18 Trenchless Methods p 40-11 Trenchless method include pipe jacking, microtunneling, auger boring and impact ramming


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Contents

Topic Ch.

# V STRUCTURAL

41 Determinate Statics pp. 41-1 to 41-21 21

1 Introduction to statics p 41-1

2 Internal & External Forces p 41-2 External force is a force acting on a R.B. caused by other bodies; internal F is that hold


4 Concentrated Forces p 41-2

5 Moments p 41-2 Moment is the name given to the tendency of a force to rotate, turn or twist a rigid body

6 Moment of a Force about a Point p 41-2 Moments are vectors. Mo cross product of force F and position vector, r; Mo = r x F x s

7 Varignon's Theorem p 41-3 "The sum of individual moments about a point caused by multiple concurrent forces is

8 Moment of a Force about a Line p 41-3 Most rotating machines, motors, pemps, flywheels, etc, turn or rotate about a line. In p

9 Components of a Moment p 41-3 Mx = Mcosthex; My = Mcosthey; Mz = Mcosthez; Mx =yFz -zFy; My = zFx-xFz; Mz= xF

10 Couples p 41-4 Any pair of equal, opposite & parallel forces constitute a couple; Mo = 2rFsin = Fd

11 Equivalence of Forces & Force-Couple Sy p 41-4 If a force,F, is moved a distance "d" from the original point of application, a couple,M, e

12 Resultant Force-Couple Systems p 41-4 Any collection of forces and moments in three-dimensional space is statically equiv. to

13 Linear Force Systems p 41-4 Is one in w/c all forces are paralle a & applied along a straight line. A straight beam loa

14 Distributed Loads p 41-4 If an object is "continuously" loaded over a portion of its length, it is subject to a "distrib

15 Moment from Distributed Loads p 41-6 M = 1/2 (w) xsq ; = product of the total force and the distance to the centroid of the dist

16 Types of Force Systems p 41-6 Concurrent ( acting on same pt.); Collinear ( share same line of action); parallel; co-pla

17 Condition of Equilibrium p 41-6 An obnject is static when it is stationary; when all of the forces on the object must be in

18 Two & Three force Members p 41-6 In most cases, two-force members are loaded axially, and the lines of action coincides

19 Reactions, types of supports p 41-6 The first step in solving most statics problems is to determine the reaction forces. Conv

20 Determinacy p 41-7 When the equations of equilib are independent, a rigid body force system is "statically d

than are necessary for equilibrium, the force system is said to be statically indetermina

21 Types of Determinate Beams p 41-7 see Fig. 41.8 ( 4 types illustrated ).

22 Free-Body Diagrams (F.B.D.) p 41-7 F.B.D. is a representation of a body in equilibrium. It shows all applied forces, moments

23 Finding Reactions in Two Dimensions p 41-8 There are 9 steps to follow.

24 Couples and Free Moments p 41-9 Once a couple on a body is known, the derivation & source of the couple is irrelevant. T

25 Influence Lines for Reactions p 41-10

Influence diagrams can also be drawn for moments, shears & deflections.

26 Hinges p 41-10 Hinges are added to structures to prevent translation while permitting rotation. A friction

27 Levers p 41-10 Simple mechanical machine/s w/ ability to increase an applied force; The ratio of load-b

28 Pulleys p 41-11 (Also a sheave) is used to change the direction of an applied tensile force.A series of p

29 Axial members p 41-11 Is capable of supporting axial forces only & is loaded only @ its joints/ends. Can be in

30 Forces in Axial Members p 41-11 A horizontal member carries only horizontal loads. It can not carry vertical loads. Simila

31 Trusses p 41-12 A set of pin-connected axial members.For truss to be stable, all of the structural cells m

32 Determinate Trusses p 41-13 No. of members = 2(no. of joints) - 3.

33 Zero-Force Members p 41-13 3rd member framing into a jnt already connecting 2 collinear members carries NO inte

34 Method of Joints p 41-14 This method is useful when most or all truss member forces are to be calculated.

35 Cut-and-Sum Method p 41-15 Method can be used to find forces in inclined mambers. This is strictly an application of

36 Method of Sections p 41-15 It is a direct approach to finding forces in any truss member.

37 Superposition of Loads p 41-16

38 Transverse Truss Member Loads p 41-16 Nontraditional transverse loading can actually occur e.g. ; a truss member's own weigh

39 Cables Carrying Concentrated Loads p 41-16 An ideal cable is assumed to be completely flexible, massless and incapable of elonga

40 Parabolic Cables p 41-17 If the distributed load / unit length, w, on a cable is constant w/ respect to the horiz. axi

41 Cables Carrying Distributed Loads p 41-18

42 Catenary Cables p 41-18 If a distributed load is constant along the length of the cable, as it as w/ a loose cable l

43 Cables with Ends at Different Elevations p 41-19 A cable will be asymmetrical if its ends are at different elevations.

44 Two-Dimensional Mechanisms p 41-19 A two-dimensional mechanism is a nonrigid structure.In order to determine an unknow

45 Equilibrium in Three dimensions p 41-20 There are 5 steps to follow.

46 Tripods p 41-21 It is a simple 3-dimensional truss that consists of 3 axial members.

To be stationary, a rigid body has to be in static equilibriumhas no unbalanced force

It is a vector of unit length directed alonga coordinate axis. In rec. coord. Sys, there ar

x, y& zrespectively. Unit vectors are used in vector equations to indicate direction wit

Also known as a point force, is a vector having magnitude, direction & location; e.g. F

It is a graph of the magnitude of a reaction as a function of the load placement. By con

a moment. Since the moment is zero, a structure can be sectionedat the hinge and th


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Topic Ch.

# V STRUCTURAL

42 Properties of Areas pp. 42-1 to 42- 8 8

1 Centroid of An Area p 42-1 Pls. APP 42.a on page A-74

2 First Moment of the Area p 42-2

3 Centroid of a line p 42-2

4 Theorems of Pappus-Guldinus p 42-3 Surface & volume of revolution.

5 Moment of Inertia of an Area p 42-3 The centroidal moment of inertia, (Icx or Icy ) is the smallest possible moment of inertia

6 Parallel Axis Theorem p 42-4 I parallel axis = Ic + A (d) squared.

7 Polar Moment of Inertia p 42-5 "J" is required in torsional stress calculations.

8 Radius of Gyration p 42-6 The radius of gyration is an imaginary distance from the centroidal axis at w/c the entirethe moment of inertia.; I = r (squared ) A; r square root ( I/A ).

9 Product of Inertia p 42-6

10 Section Modulus, S p 42-7

beam x-section to the extreme fiber is the "distance to the extreme fiber." S combines

11 Rotation of Axes p 42-7

12 Principal Axes p 42-7

13 Mohr's Circle p 42-8

43 Material Properties & Testingpp. 43-1 to 43-16 16

1 Tensile Test p 43-1 Elongation is plotted against the applied load; stress (s) = F/Ao; stain(e) = elongation/L

B-Elastic; C-Yield Point; D-Ultimate Strength; E- Fracture Point; O'-Permanent Set. By

is known as the Modulus of Elasticity, E = s/e; s = Ee; "Lower yield strength" is commo

2 Stress-Strain Char.:Non-Ferrous Metals p 43-3 Non-ferrous metals : aluminum, magnesium, copper & other FCC and HCP metals, no3 Stress-Strain Char.:Brittle Materials p 43-3 Glass, cast-iron and ceramics, can only support small strains before they fail catastrop

4 Secant modulus p 43-4 It is the slope of the straight line connecting the "orogin" and the point of operation.

5 Poisson's Ratio p 43-4

6 Strain Hardening & Necking Down p 43-4 When the applied stress exceeds the yield strength, specimen u/goes plastic deforma

7 True Stress & Strain p 43-5 True stress or physical stress is known as the stress calculated from the instantaneous

areas or diameters, NOT length. E = 2ln ( Do/D); True stress ( sigma ) = K (e to the nth

8 Ductility p 43-5

Percent elongation = (Lf -Lo) / Lo x 100% = ef x 100%. (Reduction in Area = (Ao-Af)

9 Strain Energy p 43-6 Also known as interal work, is the energy per unit volume stored in a deformed materia

10 Resilience p 43-6 Able to absorb & release strain without permanent deformation. It is measured by Mod

11 Toughness p 43-6 A tough material will be able to withstand occasional stresses w/out fracturing. UT = (S

12 Unloading & Reloading p 43-7 The apparent yield stress of reloaded specimen will be higher. This extra strength is th

13 Compressive Strength p 43-7 Compressive strength ( ultimate strength in compression ) of "brittle" materials, e.g. co

tensile strengths, while the comp. strengths of ductile matls such as steel are the same

14 Torsion Test p 43-7 Shear stress, tau, = G(theta); theta is shear strain. Angle of twist ( radians ) = TL/JG =

15 Relationship between the Elastic Constant p 43-8 E=Mod. Of Elasticity; v = Piosson's ratio; G = Shear Modulus or Modulus of Elasticityof

16 Fatigue Testing p 43-8 A material can fail after repeated stress loadings even i f stress level never exceeds the

A specimen is loaded repeatedly to a sp. Stress amplitude,s, & the number of applicati

17 Testing of Plastics p 43-10 Plastic tests are used to determine material specifications, NOT performance specifica

18 Nondestructive Testing p 43-11

eddy current, liquid penetrant, ultrasonic imaging, acoustic emission, infrared testing &

19 Hardness Testing p 43-12 Hardness tests measure the capacity of a surface to resist deformation, to verify heat t

Brinell Hardness Number, BHN = P/pi Dt = (2P) / [ pi D ( D- {Sq. Rt ( Dsquared - dsqu

20 Toughness Testing p 43-14

21 Creep Test p 43-15 Creep or creep starin is the continuous yielding of a material under constant stress. Du

magtitude is applied to a specimen, and the strain is measured as a function of time.

In the analysis of beams, the outer compressive surface is known as the extreme fiber

It is the ratio of the lateral strain (diameter ) to the axial strain (length ), w/c is taken 0.3

A material that deforms & elongates a great deal before failure is a ductile material. Th

Used when it is impractical or uneconimical to perform destructive sampling on manufa

Toughness is a measure of the material's ability to yield & absorb highly localized appl

Charpy Test,falling pendulum striker; IzodTest.


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22 Effects of Impurities & Strain on Mech'l Prop 43-16 These produce stronger materials.

23 Classification of Materials p 43-16 Soft & weak; Strong & tough; Weak & brittle; Hard & strong.

Topic

# V STRUCTURAL

44 Strength of Materials pp. 44-1 to 44-19 19

1 Basic Concepts p 44-2 Stress is force per unit area, s=F/A; With normal stress, the area is normal to the force

2 Hooke's Law p 44-2 Hooke's Law is a relationship between elastic stress & strain; For normal strain, the pr

& for the shear stress, the constant of proportionality is the shear Modulus.

3 Elastic Deformation p 44-2 Since stress is F/A & strain is (elong) "delta"/Lo, Hooke's law can be rearranged; "delta

4 Total Strain Energy p 44-2 below the proportional ity limit, the total strain energy for a member loaded in tension or

5 Stiffness and Rigidity p 44-2

SEE table 44.

6 Thermal Deformation, w/ coeff. List. p 44-3 If the temperature of an object is changed, the object will experience length, area & vol

on the coefficient of linear expansion, "alpha". "delta"L = "alpha"Lo ( T2-T1); "delta" V =

7 Stress Concentrations p 44-4 A geometric stress concentration occurs whenever there is a discontinuity or non-unifo

8 Combined Stresses ( Biaxial Loading ) p 44-5 "normal stress"=1/2(n.stress x + n stress y) = +or- shear stress 1; principal shear stres

9 Mohr's Circle for Stress p 44-6 See 8 steps to draw "Mohr's" circle.

10 Impact Loading p 44-7 If a load is applied to a strcuture suddenly, the structure's response will be composed o

to zero, and a steady-state response. The total change in potential energy of the mass

11 Shear & Moment p 44-7 Shear at a point is the sum of all vertical forces acting on an object. Typical application

point is the total bending moment acting on an object.

12 Shear & Bending Moment Diagrams p 44-8 Maximum moment occurs at the point of zero shear.

13 Shear Stress in Beams p 44-9 Shear stress is NOT the limiting factor in most designs However, it can control in wood

For a rectangular beam; Ss or tau = 3V/2bh; Beam w/ circular x-section = 4V/3pirsqrd;

14 Bending Stress in Beams p 44-10 "sigma"b = Mc/I = M/S; S=bhsqrd/6

15 Strain Energy Due to Bending Moment p 44-11 U =1/(2EI)

16 Eccentric Loading of Axial Members p 44-11 Stress = F/A +or- Mc/I = F/A +or- Fe(c/I) = F/A +or- M/S

17 Beam Deflection: Doub. Integration Metho p 44-13 OKSee example

18 Beam Deflection: Moment Area Method p 44-14

19 Beam Deflection: Strain Energy Method p 44-15

20 Beam Deflection: Conjugate Beam Methodp 44-16

21 Beam Deflection: Table Look-up Method p 44-16 See Appendix 44.A & 47.A

22 Beam Deflection: superposition p 44-16

23 Inflection Points p 44-16 Point of contraflexure

24 Truss Deflection: Strain Energy Method p 44-17 Req'd: All member forces are known!

25 Truss Deflection: Virtual Work Method p 44-17 "delta"=Sum of (SuL / AE )

26 Modes of Beam Failures p 44-18 Excessive deflection or elastic failure; lateral / vertical buckling, web crippling, rotation

27 Curved Beams p 44-19 See Table 44.4 for "correction" factors

28 Composite Structures p 44-19 There are 9 steps to follow. Use "transformed" sections; n = Emax / E weakest

45 Basic Elements of Design pp. 45-1 to 45-19 19

1 Slender Columns p 45-2

GIVEN: E, SyT & rSolve (SR)T by getting Kvalus from Table 45.1. Check if Long Co

2 Intermediate Columns p 45-3

3 Eccentrically Loaded Columns p 45-3 Use secant formula. For a given eccentricity,e, & an assumed buclking load,F, eq. 45.9

"sigma" max = (F/A) / {1 + (ec/rsqrd)sec phi}

4 Thin-walled cylindrical tanks p 45-3

5 Thick-walled cylinders p 45-4

6 Thin-walled spherical tanks p 45-5

7 Interference fits, cylinders w/in cylinders p 45-5 It is the outer pice, while inner pc is called the shrink fit. Idiam=2Iradial=do(inner)-di(out

8 Stress Concentration for Press-Fitted shaftp 45-7 When a shaft carrying apress-fitted hub is loaded in flexure, there will be an increase in

9 Bolts p 45-8 American National (Unified) thread is specified by the sequence of parameters S(xL)-N

(nominal size), L=optional shank length; N=number of threads per inch; F=thread pitch

Stiffness is the amount of force req'd to cause a unit of deformation and is referred to ak= AE/Lo ( normal stress form ), lb / inch.Rigidities have NO units. A ratio of two (2) rig

member is compared to another; Rj = kj / Sum of k(on a joint ).

Sideways buckling failure orCritical load or Euler load.; "sigma"e= Fe/A = (pisqrdE)/(K

W/ reference to "curve-fit" constants a and band Critical slenderness ratio.

Wall thickness-to-internal diam. Ratio; t/diort/2ri< 0.1; St=pr/t; Sa=pr/2t; Sb=Mc/I; I =

Stress =pr/2t


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are optional hand and engagement length designations. Proof load = Proof Streng

10 Rivet & Bolt Connections p 45-10 tension lap : Failure-shear @ connectors: Ss=F/A & n=Ss/allow shear stress; Plate fail

Plate fails in bearing: (bolt bearing area)Sb=F/dt & n=Sb/allow bearing stress; Plate f

11 Bolt preload p 45-11 An effective method of reducing the alternating stress in bolted tension connections. Fb

12 Bolt torque to Obtain Preload p 45-12

13 Fillet welds p 45-13 y=weld size; Stress=F/(bte) where te =0.707y.Weld (filler) m etal should have a strengt

Topic

# V STRUCTURAL

45 Basic Elements of Design pp. 45-1 to 45-19 19

14 Circular shaft design p 45-13 Torsional stress

15 Torsion in thin-walled, non circular shells p 45-14

16 Torsion in Solid, NonCircular members p 45-15 I-beam included.

17 Shear Center of Beams p 45-15 The shear center is a point that does not experience rotation when the beam is in torsio

18 Eccentrically Loaded Bolted Connections p 45-16

19 Eccentrically Loaded Welded Connections p 45-18 Assume: each weld is a line & assuming an arbitrary thickness, "t". Torsional shear stre

20 Flat Plates p 45-18 "Built-in" or simply supported. Find t, bending stress or internal pressure ex : t= sqrt

21 Springs p 45-19 The ideal spring is assumed to be elastic w/in its working range; F=k(delta); k = ( F1-F2

22 Wire Rope p 45-19 n strands x m wires x diameter wire rope

46 Structural analysis pp. 46-1 to 46-13 13

1 Introduction to Indeterminate Statics p 46-1 Equations of statics are NOT sufficient to determine all reactions, momemts & internal

2 Degree of Indeterminacy p 46-1 Is equal to the number of reactions or members that wud have to be removed to make

3 Indeterminate Beams p 46-1 Continuous beams; propped cantilever beam; fixed-end beam

4 Review of Elastic Deformation p 46-1 Deformation= FL/AE = "alpha"Lo (T2-T1)

5 Consistent Deformation Method p 46-2 F=Fc + Fst; Deform"c" = Deform"st"; Fc = F / [( 1 + (AstEst/AcEc)]; Similarly, Fst =

6 Superposition Method p 46-4 There are at least 4 steps to follow.

7 Three-Moment equation p 46-5 M1L1 +2M2(L1+L2) + M3L2 = -6 {A1a/L1 + A2b/L2}; Aa=Ab=Flcube/16 ( Conc.Ld @ m

8 Fixed-End Moments p 46-6 Fixed-end beams are inherently indeterminate. SEE APP 47.A9 Indeterminate Trusses p 46-6 Dummy unit Load method. Draw the truss twice & follow the six steps.

10 Influence Diagrams p 46-7 Shear, moment & reaction influence diagrams (influence lines) can be drawn for any po

Influence Diagram for Beam reactions; Finding Reaction Influence Diagrams Graphical

Shear Influence Diagrams by Virtual displacement; Moment Influence Diagrams by Virt

on Cross-Beam Decks; Influence Diagrams on Cross-Beam Decks; Influence Diagram

11 Moving Loads on Beams p 46-13 There are at least 5 steps to follow.

47 Strength of Materials pp. 47-1 to 47-20 19

1 Introduction to Structural Analysis p 47-1

2 Traditional Methods p 47-2 Indeterminate structural analysis procedures can be classified as either force method o

3 Review of Work & Energy p 47-3 W= PV (linear displacement); W=T0 (rotation); W = U2 - U1.

4 Review of Linear Deformation p 47-3 Deformation = PL/AE.5 Thermal Loading p 47-3 Thermal induced axial load in a constrained member with a uniform temperature chang

or = coeff. Of thermal expansion (T2-T1)AE

6 Dummy Unit Load Method ( D.U.L.M. ) p 47-3

7 Beam Deflections by the D.U.L.M. p 47-4 See example 47.1, with "beam" F.B.D. & deflection - work done by a unit load.

8 Truss Deflections by the D.U.L.M. p 47-4 See example 47.2, with "truss" F.B.D. & deflection - work done by a unit load.

9 Frame Deflections by the D.U.L.M. p 47-5 See example 47.3, with a "frame" F.B.D. & deflection - work done by a unit load.

10 Conjugate Beam Method p 47-6 See example 47.4, with real beam & conjugate beam.

11 Introduction to the Flexibility Method p 47-7 Also known as the method of consistent deformations. ( w/ three-span continuous beam

12 Basic Flexibili ty Method Procedure p 47-7 There are at least 5 steps to follow.

13 Systematic Flexibility Method Procedure p 47-8 There are at least 4 steps to follow.

14 Stiffness Method p 47-10 Solve by Simultaneous Linear Equation.

15 Moment Distribution Method p 47-13 COF-Carry Over factor; DF-Distribution Factor

16 Moment Distribution Procedure: NO Sidesp 47-13 There are at least 8 steps to follow.

17 Structures with Sidesway p 47-15

"Maney formula"; Installation torque,T = KtdboltFi=; tan (theta) = (lead per revolution

Torsional shear stress = Fer/Jto be resolved into "x" & "y" components. Vertical load s

The classical moment distribution & slope deflection methods are displacement - base

displacement method. The flexibility methodis a force-based approach.

Or the energy methodis based on the virtual work principle.


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18 Second Order ( P-V ) Analysis p 47-16

19 Simplified Second-Order Analysis p 47-16

20 Plastic Analysis p 47-17

21 Plastic Analysis of Beams p 47-17

22 Appox. Method : Assumed Inflection Point p 47-18

23 Appox. Method : Moment Coefficients p 47-19

24 Appox. Method : Shear Coefficients p 47-19

25 Appox. Method : Envelope of Max. Shear p 47-20


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# V STRUCTURAL

41 Determinate Statics pp. 41-1 to 41-21 21

1 Axial members p 41-11 Is capable of supporting axial forces only & is loaded only @ its joints/ends. Can be in e

2 Cables Carrying Concentrated Loads p 41-16 An ideal cable is assumed to be completely flexible, massless and incapable of elongat

3 Cables Carrying Distributed Loads p 41-18

4 Cables with Ends at Different Elevations p 41-19 A cable will be asymmetrical if its ends are at different elevations.

5 Catenary Cables p 41-18 If a distributed load is constant along the length of the cable, as it as w/ a loose cable lo

6 Components of a Moment p 41-3 Mx = Mcosthex; My = Mcosthey; Mz = Mcosthez; Mx =yFz -zFy; My = zFx-xFz; Mz= xF

7 Concentrated Forces p 41-2

8 Condition of Equilibrium p 41-6 An obnject is static when it is stationary; when all of the forces on the object must be in

9 Couples p 41-4 Any pair of equal, opposite & parallel forces constitute a couple; Mo = 2rFsin = Fd10 Couples and Free Moments p 41-9 Once a couple on a body is known, the derivation & source of the couple is irrelevant. T

11 Cut-and-Sum Method p 41-15 Method can be used to find forces in inclined mambers. This is strictly an application of

12 Determinacy p 41-7 When the equations of equilib are independent, a rigid body force system is "statically d

Determinacy than are necessary for equilibrium, the force system is said to be statically indeterminat

13 Determinate Trusses p 41-13 No. of members = 2(no. of joints) - 3.

14 Distributed Loads p 41-4 If an object is "continuously" loaded over a portion of its length, it is subject

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