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Engineering Encyclopedia Saudi Aramco DeskTop Standards

STRUCTURAL STEEL DESIGN DATA, PRINCIPLES, AND TOOLS

Engineering Encyclopedia Analysis and Design of Steel Structures

Structural Steel Design Data, Principles, and Tools

Saudi Aramco DeskTop Standards i

MODULE COMPONENT PAGE

INTRODUCTION............................................................................................................. 4

STRUCTURAL STEEL TYPES, MECHANICAL AND PHYSICAL PROPERTIES, AND STEEL SECTIONS ........................................................................ 5

Types of Steel....................................................................................................... 5 Ordinary Grades ........................................................................................ 5 High-Strength Steels.................................................................................. 8 Special Purpose Steels.............................................................................. 9 Factors Affecting Choice.......................................................................... 10

Definitions, Values, and Significance of Mechanical Properties ......................... 12 Tensile and Compressive Strength.......................................................... 12 Yield Strength .......................................................................................... 14 Shear Strength......................................................................................... 14 Elongation................................................................................................ 14 Ductility .................................................................................................... 15 Hardness ................................................................................................. 16 Chemical Composition ............................................................................. 16

Physical Properties............................................................................................. 17 Density..................................................................................................... 17 Thermal Expansion .................................................................................. 18 Types of Sections .................................................................................... 19 Designation and Dimensioning of Sections.............................................. 21 Properties of Sections.............................................................................. 33

SELECTING DESIGN PRINCIPLES FOR STEEL STRUCTURES............................... 35

Allowable Stress Design (ASD) .......................................................................... 35 Basic Concepts........................................................................................ 35 Allowable Stresses................................................................................... 37 Factor of Safety (F.S.) ............................................................................. 37

Load and Resistance Factor Design (LRFD) ...................................................... 39 Basic Concepts........................................................................................ 39



Saudi Aramco DeskTop Standards ii

Load Factors and Combinations .............................................................. 40 Limit States .............................................................................................. 42 Design Strengths for Factored Loads and Serviceability Requirements .......................................................................................... 43

Plastic Design (PD) ............................................................................................ 44 Basic Concepts........................................................................................ 44 Relationships to LRFD............................................................................. 44

Applications and Limitations of ASD, LRFD, and PD Principles ......................... 46

SELECTING COMPUTER PROGRAMS FOR STEEL STRUCTURE DESIGNS ...................................................................................................................... 47

Types of Computer Programs Available in Saudi Aramco.................................. 47 Mainframe Applications............................................................................ 47 PC Applications ....................................................................................... 47

General Purpose vs. Specialty Computer Programs .......................................... 47 Supported (Licensed) vs. Unsupported Computer Programs ............................. 48

Supported (Licensed) Programs .............................................................. 48 Unsupported Programs............................................................................ 49

Computer-Aided Design Packages..................................................................... 49 When to Use Computer Programs...................................................................... 50 Cautions and Limitations on the Use of Computer Programs............................. 51

PRIMARY CONSIDERATIONS IN THE DESIGN OF STEEL STRUCTURES.............. 52

Factors Affecting Design .................................................................................... 52 Safety and Reliability ............................................................................... 52 Function and Serviceability ...................................................................... 52 Maintenance ............................................................................................ 52 Economics and Cost ................................................................................ 52

Implications and Significance of These Factors.................................................. 53

SUMMARY.................................................................................................................... 54

GLOSSARY .................................................................................................................. 55



Saudi Aramco DeskTop Standards iii

LIST OF FIGURES

Figure 1. Ordinary Grades of Steel ...............................................................................6 Figure 2. ASTM A6 Structural Section Size Groupings .................................................7 Figure 3. High-Strength Steel........................................................................................8 Figure 4. Special Purpose Steel ..................................................................................10 Figure 5. Steel Selection Checklist..............................................................................11 Figure 6. Stress/Strain Relationship ............................................................................13 Figure 7. Elongation ....................................................................................................15 Figure 8. Chemical Composition .................................................................................17 Figure 9. Common Types of Sections .........................................................................20 Figure 10. W Section Dimensioning ............................................................................21 Figure 11. M Section Dimensioning.............................................................................22 Figure 12. S Section Dimensioning .............................................................................23 Figure 13. HP Section Dimensioning...........................................................................24 Figure 14. Channel Section Dimensioning ..................................................................25 Figure 15. MC Channel Dimensioning.........................................................................26 Figure 16. Angle Section Dimensioning ......................................................................27 Figure 17. Tee Section Dimensioning .........................................................................28 Figure 18. Circular Hollow Section (Pipe) Dimensioning .............................................29 Figure 19. Square Hollow Section (Tube) Dimensioning.............................................30 Figure 20. Rectangular Hollow Section (Tube) Dimensioning .....................................31 Figure 21. Example of Combination Section ...............................................................32 Figure 22. Simple Boom Structure ..............................................................................37 Figure 23. Load Combination Factor Formulas ...........................................................39 Figure 24. Load Factors ..............................................................................................40 Figure 25. Examples of Limit States............................................................................42 Figure 26. Beam/Bending Moment..............................................................................45



Saudi Aramco DeskTop Standards 4

INTRODUCTION

This first module of the Analysis and Design of Steel Structures course is Structural Steel Design Data, Principles, and Tools. This module focuses on the application of design principles and Saudi Aramco design considerations in the design of steel structures. It also covers the types of structural steel and steel sections with their mechanical and physical properties. In addition, the module covers allowable stress, load and resistance factor, and plastic design principles. Selection of the most suitable computer program for the design of a given steel structure and the rationale for that selection are also discussed. An overview of the primary considerations in the design of steel structures is given.




STRUCTURAL STEEL TYPES, MECHANICAL AND PHYSICAL PROPERTIES, AND STEEL SECTIONS

Structural steel is typically described according to the type of steel; the mechanical properties of the steel; the physical properties of the steel; and, the shape and dimensions of the steel.

Types of Steel

When designing steel structures, the engineer will primarily work with three types of steel:

• Ordinary grades

• High-strength

• Special purpose

The American Society of Testing and Materials (ASTM) has developed standardized specifications for these steels. The American Institute of Steel Construction (AISC) Manual of Steel Construction refers to the ASTM grades of structural steel in its charts and tables.

Ordinary Grades

Ordinary grades of steel are also called “carbon” steels and have specified minimum yield points up to about 40 ksi. The principal strengthening agents in these steels are carbon and manganese. Ordinary grades of steel are normally selected for Saudi Aramco construction. Grade A36 is the grade of steel most used within Saudi Aramco. See Figure 1.




Availability of Shapes and Bars According toASTM Structural Steel Specifications

Shapes

Group perASTM A6

Mini-mumYield

Stress(ksi)

ASTMDes-igna-tion

a Minimum unless a range is shown.b Includes bar-size shapes.c For shapes over 426 lbs./ ft., minimum of 58 ksi only applies.

Available

Not available

58-8032A36

A529

Carbon

Ord

inar

y G

rade

Ste

el

58-80c

60-85

36

42

SteelType

Fy

Ten-sile

Stressa

(ksi)

FuOver1/2''to

3/4''Incl.

Over3/4''to

1 1/4''Incl.

Over1 1/4''

to1 1/2''Incl.

Over1 1/2''

to2''

Incl.

Over 2''to

2 1/2''Incl.

Over2 1/2''

to4''

Incl.

Over4''to5''

Incl.

Over5''to6''

Incl.

Over6''to8''

Incl.Over

8''

To1/2''Incl.2 3 4 5b1

Plates and Bars

Source: Manual of Steel Construction, page 1-7, copyright 1989. With permission from the American Institute of Steel Construction.

Figure 1. Ordinary Grades of Steel

Grade A36 Low-Alloy Carbon Steel - Grade A36 steel is available in minimum yield stress points of 32 and 36 ksi. The tensile strength at minimum yield point of 36 ksi is 58 to 80 ksi. Material at this rating is available in all five ASTM A6 sections (Figure 2), including plates and bars up to and including 8 in. The minimum yield stress available for material over 8 in. is reduced to 32 ksi with tensile strengths at 58 to 80 ksi.




Structural Section Size Groupings for Tensile Property Classification

Structural Sections Group 1 Group 2 Group 3 Group 4 Group 5

W Sections M Sections S Sections HP Sections American Standard Channels (C) Miscellaneous Channels (MC) Angles (L) Structural Bar-size

W 24x55,62 W 21x44 to 57 incl. W 18x35 to 71 incl. W 16x26 to 57 incl. W 14x22 to 53 incl. W 12x14 to 58 incl. W 10x12 to 45 incl. W 8x10 to 48 incl. W 6x9 to 25 incl. W 5x16, 19 W 4x13 to 37.7 lb/ft incl. to 35 lb/ft incl. to 20.7 lb/ft incl. to 28.5 lb/ft incl. to 1/2 in. incl.

W 44x198, 224 W 40x149 to 268 incl. W 36x135 to 210 incl. W 33x118 to 152 incl. W 30x90 to 211 incl. W 27x84 to 178 incl. W 24x68 to 162 incl. W 21x62 to 147 incl. W 18x76 to 143 incl. W 16x67 to 100 incl. W 14x61 to 132 incl. W 12x65 to 106 incl. W 10x49 to 112 incl. W 8x58, 67 to 102 lb/ft incl. over 20.7 lb/ft over 28.5 lb/ft over 1/2 to 3/4 in. incl.

W 44x248 285 W 40x227 to 328 incl. W 36x230 to 300 incl. W 33x201 to 291 incl. W 30x235 to 261 incl. W 27x194 to 258 incl. W 24x176 to 229 incl. W 21x166 to 223 incl. W 18x158 to 192 incl. W 14x145 to 211 incl. W 12x120 to 190 incl. over 102 lb/ft over 3/4 in.

W 40x362 to 655 incl. W 36x328 to 798 incl. W 33x318 to 619 incl. W 30x292 to 581 incl. W 27x281 to 539 incl. W 24x250 to 492 incl. W 21x248 to 402 incl. W 18x211 to 311 incl. W 14x233 to 550 incl. W 12x210 to 336 incl.

W 36x848 W 14x605 to 730 incl.

Notes: Structural tees from W, M, and S sections fall into the same group as the structural section from which they are cut.

Group 4 and Group 5 sections are generally contemplated for application as columns or compression components. When used in other applications (e.g., trusses) and when thermal cutting or welding is required, special material specification and fabrication procedures apply to minimize the possibility of cracking.

Source: Manual of Steel Construction, page 1-8, copyright 1989. With permission from the

American Institute of Steel Construction.

Figure 2. ASTM A6 Structural Section Size Groupings




High-Strength Steels

High-strength steels are used when the design specification requires better strength properties than provided by the ordinary grades of steel. ASTM has established a standard specification for these steels. Grade A441 is typically specified when the design requirements exceed the strength limits of Grade A36 carbon steel. Grade A242 is used when improved corrosion resistance is an additional design requirement and is the most commonly used high-strength steel in Saudi Aramco. See Figure 3.


Shapes

Group perASTM A6

Mini-mumYield

Stress(ksi)

ASTMDes-igna-tion

a Minimum unless a range is shown.b Includes bar-size shapes.c For shapes over 426 lbs./ ft., minimum of 58 ksi only applies.

Available

Not available

40

A441

A242

A588

High-Sterngth

Low-Alloy

Hig

h -

Str

engt

hS

teel

A57

2 G

rade

42

46

50

42

50

60

65

42

46

50

42

46

50

60

63

67

70

60

65

75

80

63

67

70

63

67

70

42

50

60

65

SteelType

Fy

Ten-sile

Stressa

(ksi)

FuOver1/2''to

3/4''Incl.

Over3/4''to

1 1/4''Incl.

Over1 1/4''

to1 1/2''Incl.

Over1 1/2''

to2''

Incl.

Over 2''to

2 1/2''Incl.

Over2 1/2''

to4''

Incl.

Over4''to5''

Incl.

Over5''to6''

Incl.

Over6''to8''

Incl.Over

8''

To1/2''Incl.2 3 4 5b1

Plates and Bars


Figure 3. High-Strength Steel




Grade A441 High-Strength Steel - Grade A441 is a general purpose high-strength specification available in sections or plates and bars at minimum yield points of 40 to 50 ksi. Tensile strengths range from 60 to 70 ksi. Plates and bars are available in thicknesses up to and including 8 in.

Grade A242 High-Strength Steel - Grade A242 provides the same strengths as Grade A441 but with improved corrosion resistance. Grade A242 is limited in plate and bar thickness to 4 in.

Special Purpose Steels

Special purpose grades of steels are typically used when unusually high loads are encountered, particularly in tension members. Their increased strength is gained by the addition of different elements and in the steel manufacturing processes. Steels in this classification are quenched and tempered with minimum yield points ranging from 70 to 100 ksi and tensile stresses of 90 to 130 ksi. See Figure 4.





Shapes

Group perASTM A6

Mini-mumYield

Stress(ksi)

ASTMDes-igna-tion

a Minimum unless a range is shown.b Includes bar-size shapes.d Plates onlly.

Available

Not available

A852d

A514d

70 90-110

100-130

100-130

Quenched&

Tem-peredLow-Alloy

Quenched&

Tem-peredLow-AlloyS

peci

al P

urpo

seS

teel

90

100

SteelType

Fy

Ten-sile

Stressa

(ksi)

FuOver1/2''to

3/4''Incl.

Over3/4''to

1 1/4''Incl.

Over1 1/4''

to1 1/2''Incl.

Over1 1/2''

to2''

Incl.

Over 2''to

2 1/2''Incl.

Over2 1/2''

to4''

Incl.

Over4''to5''

Incl.

Over5''to6''

Incl.

Over6''to8''

Incl.Over

8''

To1/2''Incl.2 3 4 5b1

Plates and Bars


Figure 4. Special Purpose Steel

Factors Affecting Choice

The use of high-strength steels usually results in a reduced structural weight. If the weight reduction lowers the cost of foundations, supporting structures, or handling, transportation, or erection costs, then the high-strength steels can and should be used to advantage.




Figure 5 illustrates some of the considerations for selecting a high-strength steel as opposed to an ordinary grade steel.

CHECKLIST FOR USE OF HIGH-STRENGTH STEEL

In structural steel design, A36 is generally the most versatile and economical of the construction steels. However, there are occasions where the judicious use of high-strength steels can result in overall cost and weight savings, such as:

Tensions Members High-strength steels can usually be used to advantage in tension members except when the members are relatively small in section or when holes (i.e., for bolts or rivets) substantially reduce the net section of the member.

Beams a. When steel dead load is a major

portion of design load b. When deflection limitations are not a

major factor in determining section.

c. When deflections can be reduced through design features such as continuity or composite design.

d. When weight is important. e. When fabricating costs can be

reduced. f. When architectural considerations limit

the beam dimensions.

Columns and Compression Members a. When steel dead load is a major

portion of design load. b. When the slenderness ration (l/r) of the

member is small. c. When weight is important. d. When fabricating costs can be

reduced. e. When architectural considerations limit

the column dimensions.

Source: Design of Welded Structures, Checklist for Use of High-Strength Steel, by O.W. Blodgett, page 7.1-12, 12th printing - March 1982, © 1966.

Figure 5. Steel Selection Checklist




Definitions, Values, and Significance of Mechanical Properties

The mechanical properties of a steel relate to how the material behaves when loads are applied. This section covers:

• Tensile and compressive strength

• Yield strength

• Shear strength

• Elongation

• Ductility

• Hardness

• Chemical composition

Tensile and Compressive Strength

Tensile strength, sometimes called the ultimate strength (�u), is the resistance of a material to a force that is acting to pull it apart. Tensile strength is one of the most important properties in evaluating steels.

The tensile strength is determined by testing a steel specimen, that is, machined and ground, under specified conditions. It is calculated by dividing the maximum load the specimen sustains during the tensile test, by the specimen’s original cross-sectional area. The tensile test applies and measures stress on the specimen, and strain is the physical effect of the applied stress. The test results are shown as stress (�) in pounds per square inch (psi). The elongation of the specimen represents the strain (�) expressed as inches per inch of length (in./in.) or as a percentage of length. Figure 6 illustrates the stress/strain relationship.

Compressive strength is the point at which a material under load experiences crush failure. In normal design practice, compressive strength for steel is assumed to be equal to the tensile strength. The compression test uses a short specimen and applies a load from two directions in axial opposition. Depending on the material being tested, the compressive strength may be somewhat greater than the tensile strength.




The formulas for computing normal stress and strain are:

Normal Stress Strain

σ = P

A ε = ∆L

Lo

where: � = Stress where: e = Strain

P = Applied load ∆L = Beam deflection length

A = Cross-sectional area Lo = Starting length

Upper Yield

00.025

70

60

50

40

30

20

10

00.050

0.0750.100

0.125

Strain, in. / in.

Str

ess,

100

0 ps

i

0.1500.175

0.2000.225

Lower YieldPoint

PointProportional

Elastic Limit

Ultimate Strength

Facture

Source: Metals and How to Weld Them, Strain/Stress Figure, by T.B. Jefferson and Gorham Woods, page 21, 1978 edition, ©1962.

Figure 6. Stress/Strain Relationship




Yield Strength

The yield point is the point, measured in ksi, beyond which the material stretches briefly without an increase in load. For low- and medium-carbon steels, the stress at the yield point is considered to be the material’s tensile yield strength (�y). For other metals, the yield strength is the stress required to strain the specimen by a specified small amount beyond the elastic limit.

Shear Strength

Shear strength is the resistance to tearing or ripping of the material. There are no recognized standard testing methods for shear. Shear strength can, however, be obtained from an actual shearing of the metal. Pure shear loads are seldom encountered in structural members, but shear stress frequently develops as a by-product of principal stresses or the application of transverse forces.

When it is not practical to physically determine shear strength, the ultimate shear strength for most structural steels is generally assumed to be three-quarters of the material’s tensile strength.

The formula for computing shear stress is:

τ = V

A

where: � = Shear stress

V = Applied shear force

A = Cross-sectional area

Elongation

Elongation (eu), a measure of the amount of deformation that occurs in a loaded material specimen before it ruptures, is measured during the tensile test. Elongation is generally expressed as a percentage of the material’s starting length.

See Figure 7.




The formula for computing elongation is:

e u = 100

Lu − L oL o

where: eu = Elongation in percent

Lu = Length after elongation

Lo = Starting length

2 in.

2 1/2 in.

Original DistanceBetween Points, Lo

Original TestSpecimen

Final TestSpecimenat Rupture

Final Distance, Lu, or 25%Elongation in 2 in.

Figure 7. Elongation

Ductility

Ductility is the ability of a material to stretch and become permanently deformed without breaking or cracking. Ductility can be measured by the material’s elongation percentage and the reduction of area percentage. Materials with a large elongation are said to be ductile. Ductility is usually a desirable property in a structural member because the elongation warns of potential failure.




Hardness

Hardness is the ability of a material to resist indentation or penetration and is measured by a hardness tester. Steel hardness is typically measured using the “resistance to indentation by a particular shape of indenter” method. The Brinell test uses a steel ball and measures the diameter of the indentation to determine the hardness rating. The Rockwell test uses steel balls of various diameters or a diamond cone and automatically indicates the depth of the penetration on a dial. Both tests are reliable, but the data cannot be converted between the two tests.

Hardness measurements provide a quick and rough indication of the mechanical properties of a metal.

Chemical Composition

The chemical composition of steel defines the nature and quantity of alloy added, as a percentage of weight. Low-carbon steel consists primarily of iron, carbon, and manganese. Other elements may be present but are in the form of impurities. In structural steels, carbon content is the most significant factor. Carbon content, as illustrated by Figure 8, affects the hardness and tensile strength of the material. As the carbon content increases in steel, the:

• Hardness and tensile strength increase.

• Ductility of the material decreases.




0 0.20 0.40 0.60 0.80 1.0

70

60

50

40

30

255

180

140

20

10

Carbon, Percent

Max

imum

Har

dnes

s, R

ockw

ell C

Equ

ival

ent T

ensi

le S

tren

gth,

ksi

Maximum Hardness for Carbonand Alloy Steels

Source: Engineering for Steel Construction, page 2-4, copyright 1989. With permission from the American Institute of Steel Construction.

Figure 8. Chemical Composition

By adding selected alloys to low-carbon steel, yield strength and ductility can be improved. In addition, alloying elements can improve corrosion resistance while maintaining the advantages of strength, hardness, and ductility.

Physical Properties

Density

Density is expressed as mass per unit volume and may be referred to as specific weight. Density is often used to determine loads due to self-weight, or dead load weight, of materials.

Density = Mass (Mass )

Volume (V)

The density of steel is typically 490 lb/ft3 for design purposes.




Thermal Expansion

Most materials expand when heated and contract when cooled. Temperature changes affect the deflection (movement) or stress in a structure. The coefficient of thermal expansion is used to determine the strain of a structural member.

strain = ��T

where: � = Coefficient of thermal expansion

∆T = Change in temperature

The coefficient of linear thermal expansion is the strain per unit change in temperature.

e = ��T L

where: e = Change in length

L = Original length

For steel design purposes, � is typically 11.7 x 10-6 (°C)-1.




Types of Sections

The main types of sections used in structural design are as follows:

• W sections: sections having parallel flanges

• M sections: sections that cannot be classified as W, HP, or S

• S sections: American Standard beams

• HP sections: bearing pile section

• Channel Section (C): American Standard channel section

• Miscellaneous channel sections (MC): channel sections that cannot be classified as C sections

• Equal angle section (L)

• Unequal angle section (L)

• Tee section (WT or ST)

• Circular hollow section (pipe)

• Square hollow section (tube)

• Rectangular hollow section (tube)

• Combination sections: two or more sections used together

Figure 9 illustrates the different sections.




Tube Section / Square

Tube Section / Rectangular

L SectionEqual / Unequal

Tee Section

W Section M Section

S Section HP Section

C Section MC Section

Pipe Section

Example ofCombination Section

Figure 9. Common Types of Sections




Designation and Dimensioning of Sections

W Section - The W section is designated by the nominal depth and weight per foot. (For example, W18 x 97 is nominally 18 in. deep and weighs 97 lb per ft.) W sections have essentially parallel flange surfaces.

Y

Y

X

RootRadius

tf

bf

tw

X

Web

Flange

Td

k

kk1

where: d = Depth tw = Web thickness

k1 = Distance to root radius from web centerline

bf = Flange width

tf = Flange thickness

T = Distance between root radii k = Distance to root radius from outside face of

flange


Figure 10. W Section Dimensioning




M Sections - The M designation applies to sections that cannot be classified as W, HP, or S. Due to the unusualness of M sections, they may be difficult to obtain, and the dimensions may vary depending on the producer.

Y

Y

X

tf

bf

tw

X

Web

Flange

Td

k

kk1



bf = Flange width


T = Distance between root radii k = Distance to root radius from outside face of flange



Figure 11. M Section Dimensioning




S Sections - The S sections designate American Standard beams and have a slope of approximately 16-2/3% on their inner flange surfaces.

Y

Y

tf

bf

tw

X X Td

k

k


k = Distance to root radius from outside face of flange bf = Flange width


T = Distance to root radius between root radii


Figure 12. S Section Dimensioning




HP Sections - HP, or bearing pile, sections have essentially parallel flange surfaces and equal web and flange thickness.

Y

Y

X

tf

bf

tw

X Td

k

kk1



bf = Flange width


T = Distance between root radii k = Distance to root radius from outside face of flange



Figure 13. HP Section Dimensioning




Channel Section (C) - The C designation represents American Standard channels, which have a slope of approximately 16f(2,3)% on their inner flange surfaces.

Y

Y

X

tf

bf

tw

XT d

k

k




T = Distance between root radii


Figure 14. Channel Section Dimensioning




Miscellaneous Channel (MC) Sections - The MC section designation represents channel sections that cannot be classified as American Standard channel (C) sections. Due to the unusualness of MC sections, they may be difficult to obtain, and the dimensions may vary depending on the producer.

Y

Y

X

tf

bf

tw

XT d

k

k




T = Distance between root radii


Figure 15. MC Channel Dimensioning




Angle Sections (L), Equal and Unequal Legs - The L designation indicates equal and unequal leg angle sections.

a

b

kt

where: k = Distance to root radius from outside face of leg t = Leg thickness

a, b = Leg lengths


Figure 16. Angle Section Dimensioning




Tee Sections (WT or ST) - Tee sections are typically cut from W or S sections and conform to the flange specifications of the W or S section.

tf bf

tw

d

k

where: d = Depth of tee tw = Stem thickness

bf = Flange width


k = Distance to root radius from outside face of flange


Figure 17. Tee Section Dimensioning




Circular Hollow Section (Pipe) - See Figure 18.

OD

ID

t

where: OD = Outside diameter ID = Inside diameter t = Wall thickness



Figure 18. Circular Hollow Section (Pipe) Dimensioning




Square Hollow Section (Tube) - See Figure 19.

a

a

t

where: t = Wall thickness a = Nominal size



Figure 19. Square Hollow Section (Tube) Dimensioning




Rectangular Hollow Section (Tube) - See Figure 20.

a

b

t

where: t = Wall thickness a, b = Nominal size



Figure 20. Rectangular Hollow Section (Tube) Dimensioning




Combination Sections - Standard rolled sections are frequently combined to produce structural members for special applications. When sized and connected to satisfy the design and specification criteria, combination members may be used as struts, lintels, eave struts, and light crane and trolley runways.

Y

Y

XX


Figure 21. Example of Combination Section




Properties of Sections

Steel sections have certain geometric properties depending on the sections and sizes of the cross sections.

The properties that are most important for design purposes are:

• Area of the section (A) • Moment of inertia (�) • Section modulus (S) • Radius of gyration (r)

Area of Section (A) - The area of a member’s cross section is used in calculating simple tension, compression, and shear. Area is expressed in square inches.

Moment of Inertia (I) - The moment of inertia of the cross section of a structural member measures the resistance to rotation offered by the section’s geometry and size. It is used to solve design problems involving a bending moment. The moment of inertia is expressed in inches to the fourth power (in.4).

When working with a section’s moment of inertia, you must locate the neutral axis (NA) of the section. To compute the neutral axis, (1) compute the moment of each element of the section, about a reference axis, and (2) divide the total of the moments by the total area of the section. The result is the distance (n) of the neutral axis from the reference axis.

There are four methods for computing the moment of inertia:

• Use the simplified formulas given for typical sections. • Break the whole section into rectangular elements.

Find the neutral axis for the whole section first. Then compute the moment of inertia for each element about its own centroid or center of gravity (c.g.).

In addition, there is a much greater moment of inertia for each element because of the distance of its center of gravity to the neutral axis of the whole section. This moment of inertia is equal to the area of the element multiplied by the distance of its c.g. to the neutral axis squared.

Thus, the moment of inertia of the entire section about its neutral axis equals the sum of the two moments of inertia of the individual elements.




• For built-up sections, use this formula:

In = I y –

M2

A

where: In = Moment of inertia of whole section about its neutral axis, n-n

Iy = Sum of the moments of inertia of all elements about a common reference axis, y-y

M = Sum of the moments of all elements about the same reference axis, y-y

A = Total area, or sum of the areas of all elements of section

• Refer to the steel tables found in the AISC handbook and other steel handbooks. The values in these tables are for standard steel sections.

Section Modulus (S) - The section modulus is found by dividing the moment of inertia (�) by the distance (c) from the neutral axis to the outermost fiber of the section.

S =

Ic

Radius of Gyration - The radius of gyration (r) is the distance from the neutral axis of a section to an imaginary point where the whole area of the section could be concentrated and still have the same moment of inertia. This property is used primarily in solving column problems.

r =

IA




SELECTING DESIGN PRINCIPLES FOR STEEL STRUCTURES

Three basic design principles are used in the design of structural members or assemblies. These are:

• Allowable stress design (ASD)

• Load and resistance factor design (LRFD)

• Plastic design (PD)

Selecting the correct principle of design for the application is essential to safe design. The applications, limitations, and uses of the three principles are reviewed in this section.

Allowable Stress Design (ASD)

Basic Concepts

The allowable stress design (ASD) principle is generally used by Saudi Aramco for the design of structures and is based on elastic theory. It states that when complete external loading is applied to a structure, the stresses that arise must not exceed certain allowable values.

At the design stage it may not be possible to predict all the applied loads. Some of the uncertainties are:

• An overload applied in the life of the structure.

• Defects in the materials used.

• Poor workmanship during construction.

• Differential settlement of supports.

If a structure is designed to a stress that is close to the elastic limit, the yield stress may be exceeded in the life of the structure. However, if a suitable safety factor is introduced, the design stress will be well below the yield stress.

The ASD principle of design can be represented by the following inequality:

∑Qi ≤ Rn / F.S.




The left side of the inequality is the required strength, which is the sum of the load effects, Qi (that is, forces or moments). The right side, the design strength, is the nominal strength or resistance (Rn) divided by a factor of safety (F.S.). When divided by the appropriate section property (for example, area or section modulus), the two sides of the inequality become the actual stress (left side) and allowable stress (right side).

The left side of the inequality can be expanded as follows:

∑Qi = the maximum (absolute value) of the following combinations:

D + LI

(D + LI + W) x 0.75

(D + LI + E) x 0.75 D – W D – E

LI = L + (Lr or R)

where: D = Dead load effect

LI = Live load effect W = Wind load effect E = Earthquake load effect L = Live load due to occupancy and

movable equipment Lr = Roof live load

R = Nominal load due to initial rainwater exclusive of ponding contribution

0.75 = The reciprocal of 1.33, which represents the 1/3 increase in allowable stress when wind or earthquake is taken simultaneously with live load

ASD, then, is characterized by the use of unfactored “working” loads in conjunction with a single factor of safety applied to the resistance.




Allowable Stresses

The engineer needs to proportion all structural members, connections, and connectors so the stresses, due to the working loads, do not exceed the specified allowable stresses. The specified allowable stresses are compared with the stresses determined by the analysis of the design load effects on the structure. The specified allowable stresses do not apply to peak stresses in regions of connections. In some cases, highly localized peak stresses may exceed allowable stresses. You need to exercise engineering judgment in this situation.

Factor of Safety (F.S.)

The ratio of the material’s yield stress to the allowable stress is called the safety factor (factor of safety). In a structure made from a linearly elastic material, the safety factor is also the ratio of the load required to produce this yield stress to the working load. A typical safety factor ratio for steel is about 1.5.

Sample Problem: Allowable Stress Design Problem

Given: Select a suitable tubular member (b) to carry a load of 20 kips, as shown, in Grade A36 steel using the allowable stress design approach, with a factor of safety of 1.5.

( a )

Applied Load = 20 kips

( b )

30°

Figure 22. Simple Boom Structure




Solution: Allowable Stress Design Problem

Determine the design axial force in member (b) by force resolution:

Design Axial Load (b) = 20

Sin 30° = 40 kips

Yield stress of Grade A36 steel = 36 ksi

Determine the allowable stress with a factor of safety (F.S.) of 1.5:

Allowable stress = Yield stress

F.S.

Allowable stress = 36

1. 5 = 24 ksi

Determine the required cross-sectional area:

Cross − sec tional area =

Design axial loadAllowable stress

Cross − sec tional area = 40

24 = 1.7 in 2

Using the determined cross-sectional area, 1.7 in.2, and the AISC Manual of Steel Construction, select the tube section dimension that most closely approximates the required cross-sectional area.

Answer:

Reference the AISC Manual of Steel Construction, p. 1-96, the Square Structural Tube section chart. A 2 x 2 in. section with a wall thickness of 5/16 in. has a cross-sectional area of 1.86 in.2.




Load and Resistance Factor Design (LRFD)

Basic Concepts

Load and resistance factor design (LRFD) is the principle of proportioning structures so that no applicable limit state is exceeded when the structure is subjected to all appropriate factored load combinations. Although not widely used at this time, LRFD is gradually becoming the design standard of the future.

LRFD uses separate factors for each load and for the resistance. Because the different factors reflect the degree of uncertainty of different loads and combinations of loads and the accuracy of predicted strength, a more uniform reliability is possible than with the ASD principle.

The LRFD principle may be summarized by the following inequality:

Σγ iQ i ≤ φRn

On the left side of the inequality, the required strength is the sum of the various load effects (Qi) multiplied by their respective load factors (�i). The design strength, on the right side, is the nominal strength or resistance (Rn) multiplied by a resistance factor (�.

��iQi = The maximum of the following combinations.

Load Combination Load Combination Factor Formula

1 1.4D

2 1.2D + 1.6L + 0.5(Lr or R)

3 1.2D + 1.6(Lr or R) + (0.5L or 0.8W)

4 1.2D + 1.3W + 0.5L + 0.5(Lr or R)

5 1.2D + 1.5E + 0.5L

6 0.9D – (1.3W or 1.5E)

Figure 23. Load Combination Factor Formulas




Load Factors and Combinations

The load factors (1 through 6) recognize that when several loads act in conjunction, only one assumes its maximum lifetime value at a time. Other loads are at their “arbitrary-point-in-time” (APT) values. Each combination models the total design loading condition when a different load is at its maximum.

Load Combination Load at Its Lifetime (50-Yr) Maximum

1 D (during construction; other loads not present)

2 L

3 Lr or R (a roof load)

4 W (acting in direction of D)

5 E (acting in direction of D)

6 W or E (opposing D)

Figure 24. Load Factors

The APT loads have mean values considerably lower than the lifetime maximums. To achieve a uniform reliability, every factored load (lifetime maximum or APT) is higher than its mean value by an amount depending on its variability.

In general, the resistance factors are less than one (�<1). Several representative LRFD �factors for steel members are:

�t � 0.90 for tensile yielding

�t = 0.75 for tensile fracture

�c = 0.85 for compression

�b = 0.90 for flexure

�v = 0.90 for shear yielding

Resistance factors for other member and connection limit states are given in the AISC LRFD Specification.

An example of a load combination problem follows.




Sample Problem: Determining Load Combinations

Determine which load factor combination is the critical loading.

Given:

Roof beams W16 x 31, spaced 7.0 ft center-to-center, support a superimposed dead load of 40 lb/ft2. Specified roof loads are 30 lb/ft2 downward (due to roof live load or rain) and 20 lb/ft2 upward or downward (due to wind).

Solution:

Determine the critical loading for LRFD.

D = 31 lb/ft + 40 lb/ft2 x 7.0 ft = 311 lb/ft

L = 0

(Lr or R) = 30 lb/ft2 x 7.0 ft = 210 lb/ft

W = 20 lb/ft2 x 7.0 ft = 140 lb/ft

E = 0

Load Combination Factor Loads

1 1.4(311 lb/ft) = 435 lb/ft

2 1.2(311 lb/ft) + 0 + 0.5(210 lb/ft) = 478 lb/ft

3 1.2(311 lb/ft) + 1.6(210 lb/ft) + 0.8(140 lb/ft) = 821 lb/ft

4 1.2(311 lb/ft) + 1.3(140 lb/ft) + 0 + 0.5(210 lb/ft) = 660 lb/ft

5 1.2(311 lb/ft) + 0 + 0 = 373 lb/ft

6 0.9(311 lb/ft) – 1.3(140 lb/ft) = 98 lb/ft

Answer:

The critical factored load combination for design is the third (3), with a total factored load of 821 lb/ft.




Limit States

Limit states are strength or serviceability conditions that represent a limit of structural usefulness. Limit states may be dictated by functional requirements such as maximum deflection. They can also be conceptual, such as plastic hinge or mechanism formation. They may also represent the actual collapse of the whole or part of the structure.

The two main limit states are:

• The ultimate limit state when the structure becomes incapable of carrying the applied loads.

• The serviceability limit state when the structure becomes unusable from the owner’s point of view.

See Figure 25.

Ultimate Limit State Serviceability Limit State

Strength (including yielding, rupture, buckling, and transformation into a mechanism)

Stability against overturning and sway

Fracture due to fatigue

Brittle fracture

Deflection

Vibration (for example, wind-induced oscillation)

Repairable damage due to fatigue

Corrosion and durability

Figure 25. Examples of Limit States

Ultimate limit states are related to safety and load carrying capacity. Serviceability limit states relate to performance under normal service conditions. Typically, a structural member will have several limit states. For a beam, as an example, the limit states include flexural strength, shear strength, vertical deflection.

Because the primary concern is safety, ultimate limit states are generally emphasized. The load combinations for determining the required strength are given in expressions 1 through 6, as shown in Figure 23. Other load combinations with different values of � are appropriate for serviceability.




Design Strengths for Factored Loads and Serviceability Requirements

The design strength of each structural component or assembly must equal or exceed the required strength based on the factored nominal loads. The design strength (�Rn) is calculated for each applicable limit state. The required strength is determined for each applicable load combination.

The overall structure and the individual members, connections, and connectors should be checked for serviceability. The four items shown in the right column of Figure 25 should be considered for serviceability.

Deflection, or deformation, is an essential limit check in structural design. During design, definitive values cannot always be given for each situation met. Situations may arise when the published limits are either too strict or, more likely, too lenient. In these cases the designer has to use his judgment. When calculating deflections, he uses unfactored imposed and wind loads and carries out the analysis on an elastic basis.

The vibration limit state may not be clearly defined for a given situation. Modifying the natural frequency of the structure is recommended when vibration is a critical factor. Designing to a higher load factor does not always correct the situation and can possibly make it worse.

The limit state of repairable damage due to fatigue covers those cases where a fatigue crack can be found and repaired without risking major structural damage.

The approach to the corrosion and durability limit state is to consider the various factors involved in the deterioration of steel and ensure that the structure has a reasonable life expectancy.

Factors affecting corrosion and durability are the:

• Environment • Degree of exposure • Shape of the members and structural detailing • Protective measures applied, if any, to the surface of

the steel • Possibility of future maintenance




Plastic Design (PD)

Basic Concepts

In some cases a design based on elastic theory (ASD or LRFD) is conservative and wasteful. An alternative is the plastic design (PD) principle. The plastic design principle is based on calculating the load required to produce sufficient plastic hinges in the structure to turn it, or at least part of it, into a mechanism. This load is then divided by the load factor (rather than the safety factor) and the value of the working load is determined. In practice, of course, the problem is presented the other way around. The approximate working loads are known, and the sections of the various members are determined for a particular load factor.

If instability may occur or if the design requires that deflections be kept to a minimum, it may not be possible to use the plastic design principle.

If a statically determinate structure has a set of working loads (Pw) applied, the bending moment at any point is some function of Pw. If the loads are all increased by the same factor (� all the bending moments increase by � since the structure is statically determinate). When the fully plastic bending moment (Mp) is reached at any point on the structure, a hinge forms, the structure becomes a mechanism, and collapse occurs. The value of � that causes collapse is called the collapse load factor (�c).

Relationships to LRFD

Plastic design is a special case of limit-state design, which requires the limit state for strength to be the attainment of plastic strength. This limit precludes having limit states based on instability, fatigue, or brittle fracture. In plastic design, the inherent ductility of steel is recognized and used. In LRFD ductility is not considered, and only the elastic property is used.

The following sample problem illustrates the selection of a steel section using the plastic design principle.




Sample Problem: Beam Selection Using Plastic Design

Given:

Using the plastic design principle, select the Grade A36 steel section to carry a uniformly distributed superimposed load of 1 kip/ft on a 20-ft simply supported span, using a load factor of 1.7.

Solution:

The compression flange of the beam is fully supported against lateral movement.

20 ft

Mmax = 50 ft kips

w = 1kip/ft

Bending Moment Diagram

Beam

Figure 26. Beam/Bending Moment

The load factor 1.7 is applied to the service load first, and the required plastic moment is then computed.

wu = 1.0(1.70) kips/ft

Required Mp = 1.7 x 50 = 85 ft-kips

Re quired Z =

MpFy

=85 12( )

36 = 28.4 in.3




Answer: Using the AISC Manual, pp. 28-29, Plastic Design Selection Table, select W12 x 22 with Zx = 29.3 in.3.

Applications and Limitations of ASD, LRFD, and PD Principles

Saudi Aramco typically uses the ASD principle for structural design. ASD uses unfactored working loads in conjunction with a single factor of safety applied to the resistance. Because of the greater variability and unpredictability of live loads and other loads in comparison with the dead load, uniform reliability is not possible.

The major advantage to using ASD is its simplicity: it has no load factors to apply to loading. The major disadvantage is that ASD may be conservative and result in a waste of material.

LRFD is gradually becoming accepted as the best design approach. The major advantage to using LRFD is that it provides a more uniform reliability than ASD. This reliability is achieved by applying different load factors, reflecting the degree of uncertainty of different loads (combinations of loads) and the accuracy of predicted strength. The major disadvantage of LRFD is that it is more time consuming than ASD because load and resistance factors must be applied to each load combination.

Plastic design (PD) is the least used design principle. However, when it is appropriate, it can produce the most economical designs in terms of weight. Some disadvantages of PD are that it:

• Requires an understanding of where plastic hinges and their mechanisms will form in the structure.

• Requires consideration of different collapse mechanisms to determine which will occur first.

• Depends on the inherent ductility of the steel. • Requires that structural sections be capable of

developing the full plastic moment (plastic hinge formation).

If instability may occur or if the design requires that the deflections be kept to a minimum, it may not be possible to use the plastic principle of design.




SELECTING COMPUTER PROGRAMS FOR STEEL STRUCTURE DESIGNS Types of Computer Programs Available in Saudi Aramco

Saudi Aramco uses a variety of computer software to support its structural engineering applications. The computer programs can be classed by the type of hardware on which they are run:

• Mainframe applications (for example, Oceans, Strudyl)

• Personal computer (PC) applications (for example, STAAD III, Algor, ANSYS)

Mainframe Applications

Typically, installation of mainframe computers requires a large space and certain environmental considerations. Mainframes have a large storage capacity and allow multiple users to work simultaneously. Because of their large storage capacity, mainframe systems are well suited to working with large structural problems that are beyond the capability of smaller PC systems. Depending on the number of users, the mainframe computer system may be either slower or faster than a PC system for a particular application.

PC Applications

PC systems are smaller than mainframes and are generally considered desktop computers. In some situations the PCs may be linked by a local area network (LAN), allowing information exchange via the computer network. Even though the PC is user dedicated, it has limited storage capacity due to its size and supporting hardware limitations. This storage limitation may restrict the use of PCs on large, complex structural problems.

Some software applications are designed for mainframe use only and some for PC use only. Other applications may be compatible with either.

General Purpose vs. Specialty Computer Programs

General purpose programs (for example, STAAD III) are capable of dealing with a large variety of structures. Specialty programs are written specifically to analyze particular types of structures or parts of a structure.




Some types of specialty program applications are:

• Finite element programs for plate/shell structures

• Marine structure analysis programs

• Foundation analysis programs

Although general purpose programs may be capable of simulating special types of structures, they usually require simplifying assumptions that result in a less accurate solution. The analysis of certain complex or unusual structures may require a specialty program.

STAAD III is a general purpose structural analysis program used by Saudi Aramco. STAAD III allows both frame and plate/shell elements to be modeled and analyzed. It also provides dynamic analysis, including the calculation of the natural frequencies of a structure and response spectrum analysis.

STAAD III has design capabilities for steel sections. For steel design STAAD III compares actual stresses with allowable stresses as defined by the American Institute of Steel Construction (AISC) code.

Supported (Licensed) vs. Unsupported Computer Programs

Supported (Licensed) Programs

Programs of this type are commercially available and are accompanied by a full range of support functions such as:

• User manuals

• Telephone help lines (voice or fax)

• Upgrades when published

An advantage of using these programs is that the software has been verified to perform within the limitations published in the supporting documentation. When used appropriately, applications of this type of software provide a high degree of reliability.




Unsupported Programs

Unsupported programs are generally written in-house and are sometimes referred to as “home-grown” programs. These programs are primarily for in-house company use and are not commercially available. Typically, they have only a limited number of users and are poorly supported by documentation.

A disadvantage to using unsupported programs is that they may not be properly verified. The information provided by these programs must be considered suspect if proper verification of the program has not been carried out.

Computer-Aided Design Packages

Computer-Aided Design (CAD) packages are sophisticated drafting tools for the design engineer. Using a CAD system permits greater flexibility in the design process and replaces the traditional drawing board.

CAD applications allow drafting to become easier and quicker with more flexibility in scaling, layout, copying, and presentation. Being able to access the drawing for changes without having to start over is an improvement over the board method. CAD programs can also perform certain computational functions, such as determining material quantities and component weights from the drawings produced. Combined with the 3-D modeling capabilities of some packages, CAD has made model building redundant in some cases. In addition, interference, or “clash” checks, can be performed from 3-D models to identify and eliminate conflicts between components such as pipe routing and cable trays.




When to Use Computer Programs

A computer program can assist the designer when:

• The complexity of a problem prohibits manual calculation methods. When manual calculations take too long, a computer program can speed up the process. Often a more accurate solution is required; manual calculations may require a gross simplification of the problem resulting in a less accurate solution.

• A large number of repetitive calculations and analyses are required. When dealing with a large number of repetitive calculations, using a computer program reduces the time required for analysis significantly.

• Fine tuning an analysis or design initially performed by manual calculation. Computer analysis of a previous problem solved by hand calculation provides more accurate results and can be used as a verification procedure. Computer programs are also suitable when analyzing modifications to an existing design.




Cautions and Limitations on the Use of Computer Programs

When the correct application is selected and used properly, computer programs provide a valuable service to the engineer. The following, however, are some common pitfalls to be avoided in the use of computer applications:

• Incorrect simulation of the problem. To create a computer model of a structure, the user must have some idea of how a structure will behave. With this knowledge, the designer can make the correct assumptions regarding the analysis. A lack of understanding of the problem usually results in wrong assumptions and, therefore, incorrect simulations (for example, wrong loading, locations, intensities, etc.).

• Input error. Carelessness or lack of follow-up checking usually results in inputting the wrong parameters into the model. Input files should always undergo a thorough check, preferably by another engineer, before the program is run. The results will only be as good as the information entered into the program.

• Incorrect interpretation of output. The user needs to be aware of the nature of the computer output, what the output represents, and how the output relates to the behavior of the structure (for example, the basis of design code checks performed, sign conventions used, etc.).

• Lack of understanding of the program being used. The user needs to be aware of the limitations of the program and the conditions under which the program results would be unreliable. The output should be viewed with the limitations of the program in mind.




PRIMARY CONSIDERATIONS IN THE DESIGN OF STEEL STRUCTURES

Factors Affecting Design

For a given design problem involving a steel structure, it is normally not possible to optimize all of the design factors simultaneously. Design is always a compromise within the constraints. Some of the factors to be considered in the design process are:

• Safety and reliability • Function and serviceability • Maintenance • Economics and cost

Safety and Reliability

The structure must be capable of sustaining the design loading safely and reliably. It must have the required integrity against collapse or partial collapse.

Function and Serviceability

The structure must be capable of performing its required function within the desired serviceability requirements. For example, the limiting deflection must be considered.

Maintenance

Future maintenance requirements should be considered in the initial design of the structure. This consideration may require provisions for access to inspect and perform periodic maintenance on the structure. To reduce maintenance, corrosion control should be considered.

Economics and Cost

The design should always keep costs as low as possible. All the following have direct relationships to the cost of a structure:

• Materials (selection of the appropriate type and grade)

• Construction methods (including labor, transportation, etc.)

• Fabrication methods (bolted or welded connections)




Implications and Significance of These Factors

The design of any structure is always a compromise of the individual design factors. For each project, the designer must prioritize design considerations and proceed accordingly. For a low-budget project, cost may be the priority, provided safety is not compromised. Where parts of a structure are difficult to access, maintenance considerations may be the priority.




SUMMARY

In this first module in the Analysis and Design of Steel Structures course, the Participant has reviewed material required for the practical application of structural analysis and design to steel buildings and process plant steel structures.

The Participant was introduced to the types of structural steel and steel sections most commonly used within Saudi Aramco along with their mechanical and physical properties. Allowable Stress Design, Load and Resistance Factor Design, and Plastic Design principles were also presented with examples illustrating these principles.

The Participant was introduced to the use and selection of computer programs and the rationale for deciding which programs to use in designing steel structures. Also presented were the cautions and limitations of using computer programs for analyzing and designing steel structures.

Finally, the Participant was introduced to the primary design considerations for steel structures and the factors affecting structural designs. The implications and significance of these design factors was discussed.

In the evaluation the Participant will be asked to answer a series of questions that represent the knowledge gained from this module. Some questions will also require the Participant to select data from the tables found in the AISC Manual of Steel Construction.




GLOSSARY

allowable stress Material strength divided by the factor of safety.

compressive strength The material stress at which crush failure occurs.

dead load A fixed position gravity service load, for example, weight of structure.

density The weight per unit volume of a material.

ductility The ability of a metal to stretch and become permanently deformed without breaking or cracking.

elongation The lengthening of a material when stress is applied.

factor of safety Ratio of the nominal strength to nominal design load.

hardness The ability of a material to resist indentation or penetration.

limit states Conditions that represent a limit of structural usefulness.

live load Gravity load acting when the structure is in service, but varying in magnitude and location (for example, movable equipment, vehicles).

load factor Factor applied to nominal load to reflect the degree of uncertainty of the load.

plastic flow The condition beginning at yield point and continuing to the point of failure.

resistance factor Factor applied to material strength to reflect the degree of accuracy of predicted strength.

shear strength The material stress at which a tear or rip failure occurs.

tensile strength The material stress at which tensile fracture occurs.

thermal expansion The change in length of a material as a result of exposure to heat or cold.

working stress Material stress arising from unfactored loads.

yield point The material stress at which plastic flow starts.

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