Engineering Encyclopedia

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1 Saudi Aramco DeskTop Standards STRUCTURAL STEEL DESIGN DATA, PRINCIPLES, AND TOOLS Note: The source of the technical material in this volume is the Professional Engineering Development Program (PEDP) of Engineering Services. Warning: The material contained in this document was developed for Saudi Aramco and is intended for the exclusive use of Saudi Aramco s employees. Any material contained in this document which is not already in the public domain may not be copied, reproduced, sold, given, or disclosed to third parties, or otherwise used in whole, or in part, without the written permission of the Vice President, Engineering Services, Saudi Aramco. Chapter : Civil and Structural For additional information on this subject, contact File Reference: CSE PEDD Coordinator on

2 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 Definitions, Values, and Significance of Mechanical Properties Tensile and Compressive Strength Yield Strength Shear Strength Elongation Ductility Hardness Chemical Composition Physical Properties Density Thermal Expansion Types of Sections Designation and Dimensioning of Sections Properties of Sections SELECTING DESIGN PRINCIPLES FOR STEEL STRUCTURES Allowable Stress Design (ASD) Basic Concepts Allowable Stresses Factor of Safety (F.S.) Load and Resistance Factor Design (LRFD) Basic Concepts Saudi Aramco DeskTop Standards i

3 Load Factors and Combinations Limit States Design Strengths for Factored Loads and Serviceability Requirements Plastic Design (PD) Basic Concepts Relationships to LRFD Applications and Limitations of ASD, LRFD, and PD Principles SELECTING COMPUTER PROGRAMS FOR STEEL STRUCTURE DESIGNS Types of Computer Programs Available in Saudi Aramco Mainframe Applications PC Applications General Purpose vs. Specialty Computer Programs Supported (Licensed) vs. Unsupported Computer Programs Supported (Licensed) Programs Unsupported Programs Computer-Aided Design Packages When to Use Computer Programs Cautions and Limitations on the Use of Computer Programs PRIMARY CONSIDERATIONS IN THE DESIGN OF STEEL STRUCTURES Factors Affecting Design Safety and Reliability Function and Serviceability Maintenance Economics and Cost Implications and Significance of These Factors SUMMARY GLOSSARY Saudi Aramco DeskTop Standards ii

4 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 iii

5 INTRODUCTION This first module of the course is. 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. Saudi Aramco DeskTop Standards 4

6 STRUCTURAL STEEL TYPES, MECHANICAL AND PHYSICAL PROPERTIES, AND STEEL SECTIONS Types of Steel Ordinary Grades 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. 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 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. Saudi Aramco DeskTop Standards 5

7 Ordinary Grade Steel Steel Type Carbon A36 A529 Availability of Shapes and Bars According to ASTM Structural Steel Specifications F y Minimum Yield Stress (ksi) ASTM Designation F u Tensile Stress a (ksi) c Shapes Group per ASTM A6 To 1/2'' b Incl. Over 1/2'' to 3/4'' Incl. Over 3/4'' to 1 1/4'' Incl. Over Over 1 1/4'' to 1 1/2'' Incl. Plates and Bars 1 1/2'' to 2'' Incl. Over 2'' to 2 1/2'' Incl. Over 2 1/2'' to 4'' Incl. Over 4'' to 5'' Incl. Over 5'' to 6'' Incl. Over 6'' to 8'' Incl. Over 8'' 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 Source: Manual of Steel Construction, page 1-7, copyright 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. Saudi Aramco DeskTop Standards 6

8 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 44x 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 With permission from the American Institute of Steel Construction. Figure 2. ASTM A6 Structural Section Size Groupings Saudi Aramco DeskTop Standards 7

9 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. High - Strength Steel Steel Type ASTM Designation High- Sterngth Low- Alloy A572 Grade A A242 A588 Availability of Shapes and Bars According to ASTM Structural Steel Specifications F y Minimum Yield Stress (ksi) F u Tensile Stress a (ksi) Shapes Group per ASTM A6 To 1/2'' b Incl. Over 1/2'' to 3/4'' Incl. 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. Over 3/4'' to 1 1/4'' Incl. Over Over 1 1/4'' to 1 1/2'' Incl. Plates and Bars 1 1/2'' to 2'' Incl. Over 2'' to 2 1/2'' Incl. Over 2 1/2'' to 4'' Incl. Over 4'' to 5'' Incl. Over 5'' to 6'' Incl. Over 6'' to 8'' Incl. Over 8'' Available Not available Source: Manual of Steel Construction, page 1-7, copyright With permission from the American Institute of Steel Construction. Figure 3. High-Strength Steel Saudi Aramco DeskTop Standards 8

10 Special Purpose Steels 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 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. Saudi Aramco DeskTop Standards 9

11 Availability of Shapes and Bars According to ASTM Structural Steel Specifications Shapes Plates and Bars Special Purpose Steel Steel Type Quenched & Tempered Low- Alloy ASTM Designation A852 d F y Minimum Yield Stress (ksi) F u Tensile Stress a (ksi) Group per ASTM A6 To 1/2'' b Incl. Over 1/2'' to 3/4'' Incl. Over 3/4'' to 1 1/4'' Incl. Over Over 1 1/4'' to 1 1/2'' Incl. 1 1/2'' to 2'' Incl. Over 2'' to 2 1/2'' Incl. Over 2 1/2'' to 4'' Incl. Over 4'' to 5'' Incl. Over 5'' to 6'' Incl. Over 6'' to 8'' Incl. Over 8'' Quenched & Tempered Low- Alloy A514 d a Minimum unless a range is shown. b Includes bar-size shapes. d Plates onlly. Available Not available Source: Manual of Steel Construction, page 1-7, copyright With permission from the American Institute of Steel Construction. 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. Saudi Aramco DeskTop Standards 10

12 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 , 12th printing - March 1982, Figure 5. Steel Selection Checklist Saudi Aramco DeskTop Standards 11

13 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 Tensile and Compressive Strength Chemical composition 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 crosssectional 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. Saudi Aramco DeskTop Standards 12

14 The formulas for computing normal stress and strain are: Normal Stress Strain σ= P A ε= L L o where: = Stress where: e = Strain P = Applied load L = Beam deflection length A = Cross-sectional area L o = Starting length 70 Ultimate Strength 60 Stress, 1000 psi Upper Yield Point Lower Yield Point Proportional Elastic Limit Facture Strain, in. / in. Source: Metals and How to Weld Them, Strain/Stress Figure, by T.B. Jefferson and Gorham Woods, page 21, 1978 edition, Figure 6. Stress/Strain Relationship Saudi Aramco DeskTop Standards 13

15 Yield Strength The yield point is the point, measured in ksi, beyond which the material stretches briefly without an increase in load. For lowand 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 (e u ), 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. Saudi Aramco DeskTop Standards 14

16 The formula for computing elongation is: e u = 100 L u L o L o where: e u = Elongation in percent L u = Length after elongation L o = Starting length Original Distance Between Points, L o 2 in. Original Test Specimen 2 1/2 in. Final Distance, L u, or 25% Elongation in 2 in. Final Test Specimen at Rupture 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. Saudi Aramco DeskTop Standards 15

17 Hardness Chemical Composition 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. 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. Saudi Aramco DeskTop Standards 16

18 Maximum Hardness, Rockwell C Maximum Hardness for Carbon and Alloy Steels Carbon, Percent Equivalent Tensile Strength, ksi Source: Engineering for Steel Construction, page 2-4, copyright With permission from the American Institute of Steel Construction. Figure 8. Chemical Composition Physical Properties Density 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. 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/ft 3 for design purposes. Saudi Aramco DeskTop Standards 17

19 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. Saudi Aramco DeskTop Standards 18

20 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. Saudi Aramco DeskTop Standards 19

21 W Section M Section S Section HP Section C Section MC Section L Section Equal / Unequal Tee Section Pipe Section Tube Section / Square Tube Section / Rectangular Example of Combination Section Figure 9. Common Types of Sections Saudi Aramco DeskTop Standards 20

22 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. t f Flange Y k 1 k Web d X X T t w Root Radius Y b f k where: d = Depth t w = Web thickness k 1 = Distance to root radius from web centerline b f = Flange width t f = Flange thickness T = k = Distance between root radii Distance to root radius from outside face of flange Source: Manual of Steel Construction, page 1-11, copyright With permission from the American Institute of Steel Construction. Figure 10. W Section Dimensioning Saudi Aramco DeskTop Standards 21

23 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. t f Flange Y k 1 k Web d X X T t w Y b f k where: d = Depth t w = Web thickness k 1 = Distance to root radius from web centerline b f t f = Flange width = Flange thickness T = Distance between root radii k = Distance to root radius from outside face of flange Source: Manual of Steel Construction, page 1-35, copyright With permission from the American Institute of Steel Construction. Figure 11. M Section Dimensioning Saudi Aramco DeskTop Standards 22

24 S Sections - The S sections designate American Standard beams and have a slope of approximately 16-2/3% on their inner flange surfaces. t f Y k d X X T t w Y k b f where: d = Depth t w = Web thickness k = Distance to root radius from outside face of flange b f = Flange width t f = Flange thickness T = Distance to root radius between root radii Source: Manual of Steel Construction, page 1-37, copyright With permission from the American Institute of Steel Construction. Figure 12. S Section Dimensioning Saudi Aramco DeskTop Standards 23

25 HP Sections - HP, or bearing pile, sections have essentially parallel flange surfaces and equal web and flange thickness. t f Y k 1 k d X X T t w Y b f k where: d = Depth t w = Web thickness k 1 = Distance to root radius from web centerline b f = Flange width t f = Flange thickness T = Distance between root radii k = Distance to root radius from outside face of flange Source: Manual of Steel Construction, page 1-39, copyright With permission from the American Institute of Steel Construction. Figure 13. HP Section Dimensioning Saudi Aramco DeskTop Standards 24

26 Channel Section (C) - The C designation represents American Standard channels, which have a slope of approximately 16 f(2,3) % on their inner flange surfaces. Y t f k T X X d t w k Y b f where: d = Depth t w = Web thickness k = Distance to root radius from outside face of flange b f = Flange width t f = Flange thickness T = Distance between root radii Source: Manual of Steel Construction, page 1-41, copyright With permission from the American Institute of Steel Construction. Figure 14. Channel Section Dimensioning Saudi Aramco DeskTop Standards 25

27 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 t f k T X X d t w k Y b f where: d = Depth t w = Web thickness k = Distance to root radius from outside face of flange b f = Flange width t f = Flange thickness T = Distance between root radii Source: Manual of Steel Construction, page 1-43, copyright With permission from the American Institute of Steel Construction. Figure 15. MC Channel Dimensioning Saudi Aramco DeskTop Standards 26

28 Angle Sections (L), Equal and Unequal Legs - The L designation indicates equal and unequal leg angle sections. b k t a where: k = Distance to root radius from outside face of leg t = Leg thickness a, b = Leg lengths Source: Manual of Steel Construction, page 1-46, copyright With permission from the American Institute of Steel Construction. Figure 16. Angle Section Dimensioning Saudi Aramco DeskTop Standards 27

29 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. t f b f k d t w where: d = Depth of tee t w = Stem thickness b f = Flange width t f = Flange thickness k = Distance to root radius from outside face of flange Source: Manual of Steel Construction, page 1-55, copyright With permission from the American Institute of Steel Construction. Figure 17. Tee Section Dimensioning Saudi Aramco DeskTop Standards 28

30 Circular Hollow Section (Pipe) - See Figure 18. OD ID t where: OD = Outside diameter ID = Inside diameter t = Wall thickness Source: Manual of Steel Construction, page 1-93, copyright With permission from the American Institute of Steel Construction. Figure 18. Circular Hollow Section (Pipe) Dimensioning Saudi Aramco DeskTop Standards 29

31 Square Hollow Section (Tube) - See Figure 19. t a a where: t = Wall thickness a = Nominal size Source: Manual of Steel Construction, page 1-94, copyright With permission from the American Institute of Steel Construction. Figure 19. Square Hollow Section (Tube) Dimensioning Saudi Aramco DeskTop Standards 30

32 Rectangular Hollow Section (Tube) - See Figure 20. t b a where: t = Wall thickness a, b = Nominal size Source: Manual of Steel Construction, page 1-98, copyright With permission from the American Institute of Steel Construction. Figure 20. Rectangular Hollow Section (Tube) Dimensioning Saudi Aramco DeskTop Standards 31

33 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 X X Y Source: Manual of Steel Construction, page 1-84, copyright With permission from the American Institute of Steel Construction. Figure 21. Example of Combination Section Saudi Aramco DeskTop Standards 32

34 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. Saudi Aramco DeskTop Standards 33

35 For built-up sections, use this formula: I n = I y M 2 A where: I n = 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 = I c 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 = I A Saudi Aramco DeskTop Standards 34

36 SELECTING DESIGN PRINCIPLES FOR STEEL STRUCTURES Allowable Stress Design (ASD) Basic Concepts 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. 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: Q i R n / F.S. Saudi Aramco DeskTop Standards 35

37 The left side of the inequality is the required strength, which is the sum of the load effects, Q i (that is, forces or moments). The right side, the design strength, is the nominal strength or resistance (R n ) 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: Q i = the maximum (absolute value) of the following combinations: D + L I (D + L I + W) x 0.75 (D + L I + E) x 0.75 D W D E L I = L + (L r or R) where: D = Dead load effect L I = Live load effect W = Wind load effect E = Earthquake load effect L = Live load due to occupancy and movable equipment L r = 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. Saudi Aramco DeskTop Standards 36

38 Allowable Stresses Factor of Safety (F.S.) 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. 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. ( b ) 30 ( a ) Applied Load = 20 kips Figure 22. Simple Boom Structure Saudi Aramco DeskTop Standards 37

39 Solution: Allowable Stress Design Problem Determine the design axial force in member (b) by force resolution: Design Axial Load (b) = Yield stress of Grade A36 steel = 36 ksi 20 = 40 kips Sin 30 Determine the allowable stress with a factor of safety (F.S.) of 1.5: Allowable stress = Yield stress F.S. Allowable stress = 36 = 24 ksi 1. 5 Determine the required cross-sectional area: Cross sec tional area = Design axial load Allowable stress Cross sec tional area = 40 = 1.7 in 2 24 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. Saudi Aramco DeskTop Standards 38

40 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 i Q i φr n On the left side of the inequality, the required strength is the sum of the various load effects (Q i ) multiplied by their respective load factors ( i ). The design strength, on the right side, is the nominal strength or resistance (R n ) multiplied by a resistance factor (. i Q i = The maximum of the following combinations. Load Combination Load Combination Factor Formula 1 1.4D 2 1.2D + 1.6L + 0.5(L r or R) 3 1.2D + 1.6(L r or R) + (0.5L or 0.8W) 4 1.2D + 1.3W + 0.5L + 0.5(L r or R) 5 1.2D + 1.5E + 0.5L 6 0.9D (1.3W or 1.5E) Figure 23. Load Combination Factor Formulas Saudi Aramco DeskTop Standards 39

41 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 arbitrarypoint-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 L r 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. Saudi Aramco DeskTop Standards 40

42 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/ft 2. Specified roof loads are 30 lb/ft 2 downward (due to roof live load or rain) and 20 lb/ft 2 upward or downward (due to wind). Solution: Determine the critical loading for LRFD. D = 31 lb/ft + 40 lb/ft 2 x 7.0 ft = 311 lb/ft L = 0 (L r or R) = 30 lb/ft 2 x 7.0 ft = 210 lb/ft W = 20 lb/ft 2 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) (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) (210 lb/ft) = 660 lb/ft 5 1.2(311 lb/ft) = 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. Saudi Aramco DeskTop Standards 41

43 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 Strength (including yielding, rupture, buckling, and transformation into a mechanism) Stability against overturning and sway Fracture due to fatigue Brittle fracture Deflection Serviceability Limit State 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. Saudi Aramco DeskTop Standards 42

44 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 (R n ) 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 Saudi Aramco DeskTop Standards 43

45 Plastic Design (PD) Basic Concepts Relationships to LRFD 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 (P w ) applied, the bending moment at any point is some function of P w. 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 (M p ) 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 ). 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. Saudi Aramco DeskTop Standards 44

46 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. Beam w = 1kip/ft 20 ft Bending Moment Diagram M max = 50 ft kips 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. w u = 1.0(1.70) kips/ft Required M p = 1.7 x 50 = 85 ft-kips Re quired Z = M p F y = 85( 12) = 28.4 in Saudi Aramco DeskTop Standards 45

47 Answer: Using the AISC Manual, pp , Plastic Design Selection Table, select W12 x 22 with Z x = 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. Saudi Aramco DeskTop Standards 46

48 SELECTING COMPUTER PROGRAMS FOR STEEL STRUCTURE DESIGNS Types of Computer Programs Available in Saudi Aramco Mainframe Applications PC Applications 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) 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 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. Saudi Aramco DeskTop Standards 47

49 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. Saudi Aramco DeskTop Standards 48