Aisi manual cold formed steel design 2002 edition

The material contained herein has been developed by the American Iron and Steel Institute Committee on Specifications for the Design of ColdFormed Steel Structural Members. The Committee has made a diligent effort to present accurate, reliable, and useful information on coldformed steel design. The Committee acknowledges and is grateful for the contributions of the numerous researchers, engineers, and others who have contributed to the body of knowledge on the subject. With anticipated improvements in understanding of the behavior of coldformed steel and the continuing development of new technology, this material may eventually become dated. It is anticipated that AISI will publish updates of this material as new information becomes available, but this cannot be guaranteed. The materials set forth herein are for general information only. They are not a substitute for competent professional advice. Application of this information to a specific project should be reviewed by a registered professional engineer. Indeed, in most jurisdictions, such review is required by law. Anyone making use of the information set forth herein does so at their own risk and assumes any and all resulting liability arising therefrom.

STEELS - AVAILABILITY AND PROPERTIES

Introduction to Table of Referenced Steels

The referenced steels table serves as a valuable resource for material selection, summarizing the relevant ASTM Standards, categorizing product classifications, and highlighting key material properties.

The North American Specification for the Design of Cold-Formed Steel Structural Members recognizes 15 ASTM Standards for steels, promoting their use in construction While these referenced steels are encouraged, alternative steels can also be utilized in cold-formed steel structures as long as they meet the Specification's requirements.

Of the referenced steels, 5 are for plate and bar, 1 is for plate, 2 are for sheet and strip, 5 are for sheet, and 2 are for tubing products.

ASTM classifies hot-rolled steel products as being either sheet, strip, plate or bar, based on size, as follows:

Product Classification - Hot-Rolled Steel

Thickness, t in. in 0.2300≤t 0.2031≤t≤0.2299 0.1800≤t≤0.2030 0.0470≤t≤0.1799 w≤3-1/2 bar bar strip strip

(1) Strip, only when ordered in coils.

(2) Sheet, only when ordered in coils.

(3) Sheet, only when ordered in coils.

ASTM classifies cold-rolled carbon and high-strength low-alloy (HSLA) sheet steel products, including hot-dip coated, based on size, as follows:

Product Classification - Cold-Rolled Sheet Steel

Thickness, t in. in Carbon Steel HSLA steel

The structural properties critical to cold-formed steel structures include yield point, tensile strength, elongation in 2 inches, and the tensile strength-to-yield point ratio Total elongation in 2 inches reflects the ductility of steel, showcasing its capacity to endure significant plastic or permanent strains prior to fracture Additionally, the tensile strength-to-yield point ratio indicates the material's ability to redistribute stress effectively.

1.2 Summary Of Scope And Principle Tensile Properties,

ASTM Specifications For Referenced Steels

Summary Of Scope And Principle Tensile Properties ASTM Specifications for Referenced Steels

Percent elongation in 2 inches (min)

This specification covers carbon steel shapes, plates and bars for use in riveted, bolted, or welded construction of bridges and buildings, and for general structural purposes.

Supplemental requirements are provided where improved notch toughness is important These shall apply only when specified by the purchaser in the order.

When the steel is to be welded, a welding procedure suitable for the grade of steel and intended use or service will be utilized.

This specification outlines high-strength low-alloy structural steel shapes, plates, and bars designed for welded, riveted, or bolted construction These materials are primarily intended for structural applications where weight reduction and enhanced durability are crucial.

Steel exhibits superior atmospheric corrosion resistance compared to carbon structural steels, whether or not they contain copper When adequately exposed to atmospheric conditions, this steel can be utilized in its bare form for various applications This specification applies to materials with a thickness of up to 4 inches (100 mm), inclusive.

When the steel is to be welded, it is presupposed that a welding procedure suitable for the grade of steel and intended use or service will be utilized.

This specification covers four grades of carbon steel plates for general applications.

This specification outlines the requirements for cold-formed welded and seamless carbon steel structural tubing, available in round, square, rectangular, or special shapes It is intended for use in welded, riveted, or bolted construction of bridges and buildings, as well as for various general structural applications.

This tubing is produced in both welded and seamless sizes with a maximum periphery of 64 in [1626 mm] and a maximum wall of 0.625 in [15.88 mm] Grade D requires heat treatments.

Products made to this specification may not be appropriate for applications involving dynamically loaded components in welded structures, particularly where low-temperature notch-toughness properties are crucial.

This specification covers carbon- manganese steel shapes, plates and bars for use in riveted, bolted, or welded construction of buildings and for general structural purposes.

Material under this specification is available in two grades: Grade 50 for plates to 1 in [25.4 mm] thick and to

12 in [305 mm] wide, bars to 3 1/2 in.

[90 mm] thick, and Group 1 and 2 shapes; Grade 55 for plates to 1 in.

[25.4 mm] thick and to 12 in [305 mm] wide, bars to 3 in [75 mm] thick, and Group 1 and 2 shapes.

When the steel is to be welded, it is presupposed that a welding procedure suitable for the grade of steel and intended use or service will be utilized.

This specification covers five grades of high-strength low-alloy structural steel shapes, plates, sheet piling, and bars Grades 42 [290], 50 [345], and

55 [380] are intended for riveted, bolted, or welded construction.

Grades 60 [415] and 65 [450] are intended for riveted or bolted construction of bridges or for riveted, bolted, or welded construction in other applications.

For applications such as welded bridge construction, where notch toughness is important, notch toughness requirements are to be nego- tiated between the purchaser and the producer.

This specification outlines high-strength low-alloy structural steel shapes, plates, and bars designed for welded, riveted, or bolted construction, primarily for use in welded bridges and buildings where weight savings and durability are crucial This steel offers significantly better atmospheric corrosion resistance compared to carbon structural steels, with or without copper additions When adequately exposed to the atmosphere, it can be utilized unpainted for various applications The specification applies to materials with a maximum thickness of 8 inches (200 mm).

This specification outlines high-strength, low-alloy hot- and cold-rolled sheet and strip products designed for structural and miscellaneous applications, emphasizing weight savings and enhanced durability These steels exhibit improved resistance to atmospheric corrosion and are categorized into two types: Type 2, which contains a minimum of 0.20% copper, and Type 4, which includes additional alloying elements for superior corrosion resistance compared to carbon steels Notably, Type 4 can be utilized in its bare form for various applications when adequately exposed to atmospheric conditions.

Hot Rolled -Annealed Normal- or ized Rolled Cold

This specification outlines the requirements for steel sheets that are either zinc-coated (galvanized) or coated with a zinc-iron alloy (galvannealed) through the hot dip process, available in coils and cut lengths It includes various grades categorized by yield strength, encompassing both structural steel (SS) and high-strength low-alloy steel (HSLAS), with HSLAS sheets offered in Type A and Type B.

HSLAS Type A is intended for applications where improved formability is required compared to SS.

HSLAS Type B is intended for applications where improved formability is required compared to

HSLAS Type A Products furnished under A653/A653M must conform to the latest revision of A924/A924M except as otherwise indicated in the specification.

This specification details 55% aluminum-zinc alloy-coated steel sheet available in coils and cut lengths, produced through the hot-dip process The alloy consists of approximately 55% aluminum, 1.6% silicon, and the remainder zinc, making it ideal for applications demanding enhanced corrosion and heat resistance The aluminum-zinc alloy-coated sheet is offered in grades such as Commercial Steel (CS) and Forming Steel (FS).

Drawing Steel (DS), High Tempera- ture Steel (HTS), and Structural Steel

This specification outlines the requirements for cold-formed welded and seamless high-strength low-alloy structural tubing, available in round, square, rectangular, or special shapes It is designed for welded, riveted, or bolted construction in bridges and buildings, as well as for general structural applications that demand high strength and improved atmospheric corrosion resistance Notably, this steel exhibits significantly better corrosion resistance than carbon steel in most environments, whether or not copper is added.

When properly exposed to the atmosphere, this steel can be used bare

When utilizing this steel in welded construction, it is essential to ensure that the welding procedure is appropriate for both the steel type and its intended application The tubing is available in welded sizes, featuring a maximum perimeter of 64 inches (1626 mm) and a maximum wall thickness of 0.625 inches.

[15.88 mm], and in seamless with a maximum periphery of 32 in [813 mm] and a maximum wall of 0.500 in [12.70 mm].

This specification covers steel sheet, in coils and cut lengths, metallic- coated by the hot-dip process, with zinc-5% aluminum alloy coating.

The Zn-5Al alloy coating includes trace elements beyond zinc and aluminum to enhance processing and product characteristics It is available in two types: Type I, which is a zinc-5% aluminum-mischmetal alloy, and Type II, a zinc-5% aluminum-0.1% magnesium alloy Additionally, the coating is offered in two distinct structures and several designations based on coating weight.

This steel sheet is specifically designed for applications that demand corrosion resistance, formability, and paintability It is available in various designations, types, grades, and classes to meet diverse application requirements effectively.

Material Thickness

Historically, sheet and strip steels have been ordered from the steel producer using one of the following systems to specify thickness:

When ordering steel, a minimum thickness is specified to ensure that all thickness tolerances are above the stated measurement, with no allowance for any reduction This approach is crucial when the design relies on minimum strength requirements, as it guarantees that the sheet product meets the necessary thickness standards.

When steel is ordered to a nominal thickness, the thickness tolerances are evenly split between over and under measurements This practice is common because the equipment used for processing the material is typically designed to accommodate specific thicknesses.

Gauge thickness, once a common method for specifying the thickness of sheet and strip steel, is now considered outdated Gauge numbers provide only a rough estimate of steel thickness and are not reliable for ordering, designing, or specifying steel products.

Hot-dip coated sheet products are defined by their total thickness, which encompasses both the sheet and the coating Relevant ASTM specifications outline the required thickness values for the coating of these various coated sheet products.

When designing with steel, the specified thickness should refer to the uncoated base steel sheet or strip, as coatings like paint or zinc contribute minimal structural strength and should not be factored into the design thickness.

Due to tolerances in the acceptable methods for ordering sheet and strip steel thickness, it is unrealistic to anticipate that the delivered minimum thickness of a cold-formed steel product will precisely match the specified design thickness Specification provisions account for minor negative thickness tolerances, establishing that 95 percent of the design thickness is the minimum acceptable delivered thickness for cold-formed steel products.

If the delivered minimum thickness is below 95 percent of the design thickness, an analysis must be conducted to assess the product's suitability for its intended use Thickness measurements can be taken across the sheet's width, adhering to the minimum distance requirements outlined in relevant ASTM specifications It is important to note that thickness at bends, such as corners, may fall below 95 percent of the design thickness due to cold-forming effects and can still be deemed acceptable.

REPRESENTATIVE COLD FORMED STEEL SECTIONS

Representative versus Actual Sections

The cross-sections outlined in Tables I-1 to I-8 serve as a guide for designing cold-formed steel structural members, reflecting various sections used by manufacturers and fabricators While these sections are beneficial for preliminary design, they may not represent stock items Designers are encouraged to refer to the literature from cold-formed product providers for accurate section property information when specifying products.

The Manual employs two distinct naming conventions: the SSMA naming convention for standard stud and track sections, and an AISI-developed convention for other sections.

2.1.1 SSMA Stud and Track Section Nomenclature

Standard studs and tracks from the Steel Stud Manufacturers Association (SSMA) are recognized in this Manual through a specific SSMA identification code This code is created by combining essential information related to the products.

1 Depth in 1/100th inches For studs, the depth is the outside depth For tracks, the depth is the inside depth (the depth of the stud the track fits over).

2 Style: S =Stud (C-Section with Lips), T = Track (C-Section without Lips)

3 Flange Width in 1/100th inches

5 Minimum base material thickness (95% of design thickness) in 1/1000th inches

The 600S162-54 designation refers to a stud, specifically a C-section with lips, featuring a depth of 6 inches, a flange width of 1 5/8 inches, and a minimum thickness of 0.054 inches Additional specifications, including bend radii and lip lengths, can be located in Tables I-2 and I-3.

This naming convention is an industry standard.

The naming convention for the representative sections was designed to streamline the charts, tables, and example problems in the Manual Each section name is created by combining specific information for clarity and organization.

2 Section Profile: C = C-Section, Z = Z-Section, L = Equal Leg Angle, H = Hat Section

3 Code for Stiffened or Unstiffened Flanges: S = Stiffened, U = Unstiffened

The 9CS3x075 designation refers to a C-Section featuring stiffened lips, measuring 9 inches in depth, 3 inches in flange width, and 0.075 inches in thickness Additional specifications, including bend radii and lip lengths, can be located in Tables I-1 and I-4 through I-8.

This naming convention is not an industry standard Individual manufacturers and industry groups have adopted their own systems, and these systems should be used when specifying actual products.

Notes on Tables

Tabulated section properties are presented with three significant figures, and dimensions are specified to three decimal places; however, due to space constraints, strict adherence to these guidelines may not always be possible.

(b) The weight of these sections is calculated based on a steel weight of 40.8 pounds per square foot per inch thickness.

(c) Where they apply, the algebraic formulae presented in Section 3 of Part I formed the basis of the calculations for these tables.

(d) Tables I-1 to I-8 inclusive are Gross Section Property Tables Effective section properties can be found in Parts II and III for beams and columns, respectively.

(e) In Table I-8, the orientation of the x-axis is vertical to be consistent with the provisions ofSpecificationSection C3.1.2.1 which defines the x-axis as the axis of symmetry for singly-symmetric section.

(f) Section dimensions are defined in the figures provided in each table Sec- tion properties are defined in theSpecification, Symbols and Definitions.

Gross Section Property Tables

TableI-1 Gross S ection Properties C- S ec ti on s W it h Li ps x y x y x m

The article presents detailed dimensions and properties of various full section steel beams, including specifications such as depth, width, thickness, radius, area, and weight per foot For example, the 12CS4x105 beam measures 12 inches in length and 4 inches in width with a thickness of 0.105 inches, yielding a weight of 2.20 lb/ft Similarly, the 10CS2x065 beam is 10 inches long and 2 inches wide, with a thickness of 0.065 inches and a weight of 0.971 lb/ft Each beam's properties, including moment of inertia and section modulus, are essential for structural applications, providing critical data for engineers and architects in selecting appropriate materials for construction projects.

TableI-1(continued) Gross S ection Properties C- S ec ti on s W it h Li ps x y x y x m

The article presents a comprehensive overview of various properties related to full section dimensions of structural components, highlighting critical specifications such as dimensions, weights, and areas For instance, the 9CS2.5x105 model measures 9.000 inches in length and 2.500 inches in width, with a weight of 4 lb/in and an area of 21.5 in² Similarly, the 8CS4x105 variant features dimensions of 8.000 inches by 4.000 inches, a weight of 50.4 lb/in, and an area of 36.7 in² The data further includes variations like the 7CS4x105, which measures 7.000 by 4.000 inches, with a corresponding weight of 38.1 lb/in This detailed analysis serves as a valuable resource for professionals in the field, aiding in the selection and application of appropriate materials based on specific engineering requirements.

TableI-1(continued) Gross S ection Properties C- S ec ti on s W it h Li ps x y x y x m

The article presents detailed specifications of various full section dimensions, including properties such as weight per foot, area, and dimensions in inches Key models discussed include 7CS2.5x105, 6CS4x105, and 4CS2.5x105, each with unique values for thickness, yield strength, and other mechanical properties For instance, the 7CS2.5x105 model features dimensions of 7.000 x 2.500 inches with a weight of 4 lb/in, while the 6CS4x105 model has dimensions of 6.000 x 4.000 inches and a weight of 1.57 lb/in The article emphasizes the importance of these specifications for applications in construction and engineering, providing essential data for professionals in the field The comprehensive table includes various configurations, highlighting the differences in performance metrics such as yield strength and moment of inertia, crucial for structural design considerations.

TableI-2 Gross S ection Properties SSMA S tuds C- S ec ti on s W it h Li ps x y x y x m

The article presents the dimensions and properties of various full section steel beams, including specifications such as depth (D), width (B), thickness (t), and radius (R) Each beam is identified by a unique code, such as "1200S250 -9," and detailed data includes weight per foot, moment of inertia (I), and section modulus (S) For instance, the "1200S250 -9" beam measures 12.000 inches in length and 2.500 inches in width, with a weight of 34.0 lb/ft and a moment of inertia of 32.7 in^4 The article also notes that beams with a height-to-thickness ratio greater than 200 require stiffeners This comprehensive data serves as a valuable resource for engineers and architects in selecting appropriate steel beams for construction projects.

TableI-2(continued) Gross S ection Properties SSMA S tuds C- S ec ti on s W it h Li ps x y x y x m

The article provides detailed specifications of various steel sections, including dimensions, weights, and properties essential for structural analysis Each section is identified by a unique code, such as 800S200 and 600S250, with corresponding dimensions, including width, height, and thickness Key properties include weight per foot, area, and moment of inertia, which are crucial for understanding the section's performance in construction For instance, the 800S200-9 section has a weight of 4 lb/ft and a moment of inertia of 800, while the 600S250-9 section weighs 6 lb/ft with a moment of inertia of 117 The data also highlights variations in properties based on different section sizes, emphasizing the importance of selecting the appropriate section for structural integrity Additionally, the note regarding stiffeners for sections with a height-to-thickness ratio greater than 200 underscores the need for careful design considerations in engineering applications.

The article presents detailed specifications for various steel sections, including dimensions, weight per foot, and area properties For instance, the 600S162 series features dimensions of 6 inches by 1.625 inches, with weights ranging from 4 lb/ft to 2.15 lb/ft and varying area metrics Similarly, the 400S200 series showcases dimensions of 4 inches by 2 inches, with weights from 1.05 lb/ft to 1.70 lb/ft Each section's performance characteristics are meticulously listed, providing essential data for structural applications The 550S162 series, with dimensions of 5.5 inches by 1.625 inches, also demonstrates a range of weights and area properties, crucial for engineers and architects in their design processes Overall, this comprehensive data serves as a valuable resource for professionals in the construction and engineering industries, ensuring informed decisions based on accurate specifications.

This article presents a detailed analysis of various properties of structural dimensions, including full section dimensions and weight per foot It highlights specific measurements such as width, height, and area for multiple profiles, with data points including values for the 362S200, 362S162, 362S137, 350S162, and 250S162 series Each profile is characterized by its dimensions, weight, and related metrics, demonstrating variations in structural properties For instance, the 362S200-6 profile has dimensions of 3.625 in by 2.000 in with a weight of 4 lb/ft, while the 250S137-3 profile measures 2.500 in by 1.375 in and weighs 0.197 lb/ft The article provides essential insights into the mechanical properties and applications of these profiles, making it a valuable resource for engineers and designers in the field.

TableI-3 Gross S ection Properties SSMA Tracks C S ections W ithout Lips x x x y y m

This article presents the dimensional properties of full sections, including key specifications such as depth (D), flange width (B), thickness (t), and radius (R) Each section is identified by unique designations like 1200T200 and 1000T150, with detailed metrics provided for various configurations The data includes values for area, weight per foot, and moment of inertia, essential for structural analysis For instance, the 1200T200-9 section features a depth of 12.356 inches and a weight of 2.000 lb/in, while the 1000T125-6 section has a depth of 10.250 inches and a weight of 1.250 lb/in It is important to note that sections with a height-to-thickness ratio greater than 200 require stiffeners for structural integrity This comprehensive overview aids engineers and architects in selecting appropriate materials for construction projects.

TableI-3(continued) Gross S ection Properties SSMA Tracks C S ections W ithout Lips x x x y y m

The article provides detailed specifications for various steel sections, including dimensions, weights, and properties for models such as 800T200, 800T150, and 600T200 Each model lists critical data such as height, width, weight per foot, and area, along with performance metrics like moment of inertia and section modulus For instance, the 800T200-9 model has dimensions of 8.356 in by 2.000 in and a weight of 4.14 lb/ft, while the 600T200-9 model measures 6.356 in by 2.000 in with a weight of 3.45 lb/ft The data also indicates that models with a height-to-thickness ratio greater than 200 require stiffeners This information is essential for engineers and architects in selecting appropriate materials for construction projects.

This article presents detailed properties and dimensions of various structural sections, including their weights and areas Key specifications include the dimensions such as width and height, as well as critical values like weight per foot and area For instance, the 600T150 series shows a consistent height of 1.500 inches across different configurations, with varying weights and areas, indicating a robust design suitable for various applications The data also highlights the differences in performance metrics across the 600T125 and 550T series, with specific attention to their load-bearing capabilities The inclusion of stiffeners for sections exceeding a certain height-to-thickness ratio ensures structural integrity Overall, this comprehensive analysis serves as a valuable resource for engineers and designers in selecting appropriate materials for construction projects.

The article presents detailed specifications and properties of various full section dimensions, including metrics such as weight per foot, area, and other critical parameters For instance, the 550T125 series highlights dimensions of 5.750 in length and 1.250 in width, with a weight of 4 lb/in and varying properties across different configurations Similarly, the 400T200 series showcases dimensions of 4.250 in length and 2.000 in width, with weight and area metrics that emphasize structural integrity Additional configurations, such as the 400T150 and 400T125 series, further illustrate the diversity in dimensions and properties, catering to specific engineering requirements Each section is meticulously detailed to assist in selecting the appropriate dimensions for various applications, ensuring optimal performance and compliance with engineering standards.

This article presents detailed specifications for various full section dimensions, including properties such as weight per foot, area, and other critical metrics For instance, the 362T200 series features dimensions of 3.875 in by 2.000 in., with a weight of 4 lb/in and an area of 0.0713 ft² Similarly, the 362T150 series showcases dimensions of 3.875 in by 1.500 in., with a weight of 4 lb/in and an area of 0.0713 ft² The 350T200 series, with dimensions of 3.750 in by 2.000 in., also highlights a weight of 4 lb/in and an area of 0.0713 ft² Each series is characterized by specific metrics that contribute to its overall performance, making them suitable for various applications in construction and engineering The data provided offers insights into the physical properties essential for selecting the right materials for structural integrity and efficiency.

The properties of full sections are defined by various dimensions and characteristics, including width, height, and weight per foot For instance, the 350T125 series features dimensions of 3.750 in by 1.250 in., with a weight of 4 lb/in and an area ratio of 1.45 As the series progresses, dimensions and weight per foot decrease, such as the 250T200 series, which has dimensions of 2.750 in by 2.000 in and a weight of 4 lb/in The 250T150 series showcases further reductions in size and weight, highlighting a consistent trend across the sections Additionally, the 162T125 series presents even smaller dimensions and weights, illustrating the diverse range of properties available for various applications Understanding these specifications is crucial for selecting the appropriate section for structural and engineering projects.

TableI-4 Gross S ection Properties Z- S ec ti on s W it h Li ps

The article presents a comprehensive analysis of various dimensions and properties of full sections, detailing specifications such as thickness, radius, and area across different models Key data points include dimensions such as 12.000 inches in length and variations in thickness from 0.059 to 0.105 inches, with corresponding weight per foot and stress values Each entry systematically lists properties like moment of inertia and section modulus, essential for structural engineering applications The analysis covers models like 12ZS3.2 and 10ZS2.2, highlighting their mechanical performance metrics, including yield strength and deflection characteristics This data is crucial for engineers in selecting appropriate materials for construction and design, ensuring optimal performance under load conditions.

TableI-4(continued) Gross S ection Properties Z- S ec ti on s W it h Li ps

The article presents detailed properties of various full section dimensions, including critical parameters such as width, height, and weight per foot for different configurations Each section is characterized by specific dimensions, material properties, and calculated metrics like area and moment of inertia For example, the 9ZS2.25x105 configuration has a width of 9.000 inches, height of 2.250 inches, and a moment of inertia of 0.105, demonstrating its structural capabilities Similarly, the 8ZS3.25x085 variant features a width of 8.000 inches and a moment of inertia of 0.085, indicating its suitability for various engineering applications The data highlights the importance of selecting the appropriate section dimensions based on strength and stability requirements, essential for effective structural design.

TableI-4(continued) Gross S ection Properties Z- S ec ti on s W it h Li ps

Steel Deck

Steel decks are at times used for architectural application; however, they are fundamentally structural products As such, the structural capabilities

(strength and stiffness) are determined using theSpecification, which also provides base steel specifications Design may use either Allowable Strength Design

Load and Resistance Factor Design (LRFD) and Allowable Stress Design (ASD) are key techniques in structural engineering Common steel deck products include roof decks, form decks, and composite floor decks, which not only support gravity and wind uplift loads but also resist in-plane diaphragm loads Section 2.4.1 provides an overview of the most prevalent types of steel decks used in construction.

When selecting deck products, it's crucial to consider their required service life and the environmental conditions they will face For example, when installing insulation boards with fasteners on a roof deck, one must account for potential corrosion of both the fasteners and the deck itself This consideration also extends to form decks and floor decks in humid environments or areas exposed to water Additionally, insurance requirements and fire ratings can influence the choice of finishes for these deck products.

Figure 2.4-1 shows cross sections of industry standard steel deck profiles.

These profiles are merely representative of what is available Consult the literature of manufacturers to obtain further information about these and other available deck profiles.

The different profiles lend themselves to different uses:

Form decks are essential for spanning between floor joists, acting as formwork for cast-in-place concrete floor systems The shallowest available profile is 9/16 inch deep, while deeper profiles can accommodate longer spans and heavier loads Form decks may feature either trapezoidal or sinusoidal flutes, providing versatility for various construction needs.

Narrow Rib Deck (NR) serves as an effective roofing solution in regions with minimal insulation needs Its design features a narrow rib that allows for easy bridging of thin rigid insulation across short spans While it may be the least structurally efficient option, its key advantage lies in the straightforward attachment of roofing materials, as a significant portion of the deck is aligned with the roof plane.

The Intermediate Rib Deck (IR) serves as an effective roof decking solution, offering enhanced structural efficiency compared to the narrow rib deck However, it necessitates thicker insulation to adequately support the wider flute design.

The Wide Rib Deck (WR) is an ideal choice for roof decking in extreme climates, whether hot or cold Its design allows for thick insulation to effectively span the wide flutes, making it the most structurally efficient option among roof deck profiles.

(e) Deep Rib Deck (3DR): Deep rib deck is used where long spans between joists or purlins occur and/or the deck spans are subject to larger loads.

In addition to these industry standard profiles, manufacturers produce proprietary steel deck profiles that provide special functional enhancements, such as acoustical absorption capability and cellular raceway features.

(e) Deep Rib Deck Type 3DR

(d) Wide Rib Deck Type WR

(c) Intermediate Rib Deck Type IR (b) Narrow Rib Deck Type NR (a) 9/16" Form Deck (Representative)

The thickness of steel deck is typically indicated by gage, with minimum design thicknesses specified by the Steel Deck Institute (SDI) in Section 2.4.3 It's important to note that the actual material thicknesses offered by manufacturers may differ.

Recommended Maximum Spans for Construction and Maintenance Loads

Condition Span ft-in Roof Deck Cantilever ft-in.

* Deck section properties are provided in Section 2.4.3

Spans are governed by a maximum stress of 26 ksi and a maximum deflection of L/240 with a 200 pound concentrated load at midspan on a 12 in wide section of deck.

If the designer contemplates loads of greater magnitude, spans shall be de- creased or the thickness of the steel deck increased as required.

All loads shall be distributed by appropriate means to prevent damage to the completed assembly during construction.

Do not walk or stand on deck until it is fastened in accordance with the

Steel Deck Institute Design Manual, Publication No 30.

Construction phase load of 10 psf on adjacent span and cantilever plus 200 pound load at end of cantilever with a stress limit of 26 ksi for ASD.

Service load of 45 psf on adjacent span and cantilever plus 100 pound load at end of cantilever with a stress limit of 20 ksi.

Deflection limited to 1/240 of adjacent span for interior span and deflection at end of cantilever to 1/120 of overhang.

1 Adjacent span: Limited to those spans shown in Section 3.4 of the SDI

Roof Deck Specifications In those instances where the adjacent span is less than 3 times the cantilever span, the individual manufacturer should be consulted for the appropriate cantilever span.

2 Sidelaps must be attached at the end of the cantilever and at a maximum of 12 inches on center from the end.

3 No permanent suspended loads are to be supported by the steel deck.

4 The deck must be completely attached to the supports and at the sidelaps before any load is applied to the cantilever.

The Steel Deck Institute (SDI) utilized the most conservative dimension combinations for each roof deck profile depicted in Figure 2.4-1, excluding the form deck, to determine the section properties presented in the following table.

The values presented are not specific to any single manufacturer but indicate the minimum potential values Consequently, load tables derived from these properties are conservative Form deck profiles differ significantly, and their specifications are not defined by SDI The profile depicted is an actual product from a manufacturer, and while these properties can be seen as indicative, actual values may vary.

In the tables below, the I and S t values given are for compression on the top;

The provided S b values are intended for bottom compression, and the weight listed is solely for dead load calculations, not for ordering purposes These values are calculated based on steel with a yield strength of 33 ksi, except for the form deck values, which are derived from a yield strength of 80 ksi.

Weight lb/ft 2 I in 4 /ft

Type Designation Thickness in Painted Galvanized in 4 /ft in 3 /ft in 3 /ft

CALCULATION OF SECTION PROPERTIES

Linear Method for Computing Properties of Formed Sections

The linear method simplifies the computation of properties for formed sections by concentrating the material along the centerline of the steel sheet and replacing area elements with straight or curved "line elements." The thickness dimension, t, is incorporated after the linear calculations are finalized.

The total area of the section is found from the relation: Area = Lxt, where L is the total length of all line elements.

The moment of inertia of the section, I, is found from the relation:

The moment of inertia of the centerline of the steel sheet is represented as I = I′xt To calculate the section modulus, divide I or I′xt by the distance from the neutral axis to the extreme fiber, rather than to the centerline of the extreme element.

First power dimensions, such as x, y, and r (radius of gyration) are ob- tained directly by the linear method and do not involve the thickness dimension.

Reducing the flat width (w) of a stiffened compression element for design purposes directly influences the calculation of the total effective length (L eff) of the line elements, as the effective design width (b) is utilized in this process.

The linear method can be applied to various sections, primarily consisting of straight lines and circular arcs For easy reference, Section 3.2 provides sketches and equations detailing the moments of inertia and the location of the centroid for these elements.

The equations for line elements are precise because a line has no thickness; however, when calculating the properties of a physical section, where the line element represents a tangible element with thickness, the results become approximate due to various factors.

(1) The moment of inertia of a straight actual element about its longitudinal axis is considered negligible.

The moment of inertia for a straight actual element inclined to the reference axes is marginally greater than that of the corresponding line element However, for elements of equal length, this discrepancy is smaller than the error from disregarding the moment of inertia about the element's longitudinal axis Notably, this error is eliminated when the element is positioned perpendicular to the axis.

When utilizing linear arc properties to determine characteristics of actual corners, small errors may arise; however, these errors are often negligible for typical small corner radii Specifically, the impact on the centroid's location and moment of inertia is minimal In cases where the mean radius of a circular element exceeds four times its thickness, such as in tubular sections and sheets with circular corrugations, these errors become virtually insignificant.

Using the computed values of I x , I y , and I xy the moment of inertia about principal axes of the section can be calculated by the following equation:

2   I x –I 2 y  2 + I xy 2 where I x and I y are the moment of inertia of the section about x- and y-axis, respectively and I xy is the product of inertia.

The angle between the x-axis and the minor principal axis is θ=π

Properties of Line Elements

Moments of inertia of straight line elements can be calculated using the equations given below:

Moments of inertia of circular line elements can be calculated using the equations given below:

R = inside radius r = median radius θ(expressed in radians) = 0.01745θ r

180 (expressed in degrees and decimals thereof)

I 12 = sin 2 θ 2 − 2 sin 2 θ 1 +  sin θ 2 − sin θ θ 2 1 − cosθ 1 θ 2 − cos θ 1   r 3

I 4 = θ 2 − θ 1 − sin θ 2 cos2 θ 2 + sin θ 1 cos θ 1  r 3 I 34 =  sin 2 θ 2 − 2 sin 2 θ 1  r 3

I 1 =  θ + sin 2 θ cos θ − sin θ 2 θ  r 3 I 2 =  θ − sin 2 θ cos θ − (1 − cos θ θ) 2  r 3

Properties of Sections

Section properties of some sections can be calculated using the equations given below The following are to be noted:

In engineering design, three distinct types of dimensions are utilized: capital letters (A) represent outside dimensions, lowercase barred letters (a) denote centerline dimensions, and lowercase letters (a) indicate flat dimensions Flat dimensions are essential for calculating properties like the moment of inertia (I), assuming rounded corners, while centerline dimensions are crucial for determining torsional properties, such as Cw, with the assumption of square corners.

The outside dimensions are shown because they are the dimensions usu- ally given in tables.

All expressions for calculating torsional properties (m, j, and Cw) assume sections have round corners, except for specific cases While these calculations are based on a square corner approximation, round corner values are utilized for area and moment of inertia in the torsional property formulas Nevertheless, the nominal stresses derived from this method are adequately precise for routine engineering design of sections with small corner radius-to-thickness ratios.

In moment of inertia calculations, the moment of inertia of a flat element about its weak axis is typically excluded However, the moments of inertia for corners around their own axis are included to accommodate sections featuring large corner radii.

(4) All expressions are given for the full, unreduced sections.

3.3.1 Equal Leg Angles (Singly-Symmetric) With and Without Lips

3 Distance between centroid and centerlines of webs x c =y c = tA a  a2+r + u(0.363r) + α  c  a + 2 c + 3r  + u(a + 2r)  

* For sections with lips,α= 1.0; for sections without lips,α= 0.

Figure 3.3.1-1 Equal Leg Angle (Singly Symmetric) With Lips

Figure 3.3.1-2 Equal Leg Angle (Singly Symmetric)

4 Distance between centroid and outside of webs x =y = xc+t

5 Moment of inertia about x and y axes

6 Product of inertia about x and y axes

7 Moment of inertia about y 2 -axis

8 Distance between shear center and centerline of square corner m =a c 2 2

11 Distance from centroid to shear center* x o =− x c  +2 m

12 Parameter used to determine elastic critical moment j = 2 t

3.3.2 C-Sections (Singly-Symmetric) With and Without Lips and Hat Sections (Sin- gly-Symmetric) x c

C-Section (Singly Symmetric) With Lips

Figure 3.3.2-2 C-Section (Singly Symmetric) Without Lips b

Figure 3.3.2-3 Hat Section (Singly Symmetric)

* Negative sign indicates x o is measured in negative x 2 direction.

3 Moment of inertia about x-axis

4 Distance between centroid and web centerline  x c = 2t

5 Distance between centroid and outside of web x =xc+t

6 Moment of inertia about y-axis

7 Distance between shear center and web centerline a) Channel: m = b 

** For sections with lips,α= 1.0; for sections without lips,α= 0. c) Hat Section: m = b 

8 Distance between centroid and shear center x o =-(x c + m)*

14 Parameter used in determination of elastic critical moment j = 12Iy βw+β f +β l  −xo

* Negative sign indicates x o is measured in negative x direction.

3.3.3 I-Sections With Unequal Flanges (Singly-Symmetric) and T-Sections (Singly-

Figure 3.3.3-1 I-Section With Unequal Flanges (Singly Symmetric)

4 Distance between centroid and longer flange centerline  x c = 2tAu0.363r+aa∕2+r +α[u(a+1.637r)+c(a+2r)]

5 Distance between centroid and outside of longer flange x =x c + t2

7 Distance between shear center and longer flange centerline m =a 1 − b 3 b + 3 c 3 

8 Distance between shear center and centroid x o =- (x c - m)*

In I-Sections, the value of Cw is double that of each channel when fastened at the center of the webs Conversely, when two channels are continuously welded at both edges of the web to create the I-Section, the warping constants differ for unlipped I-Sections and T-Sections.

For double symmetric, lipped I-Sections: c =length of lip, see Figure 3.3.3-1

* Negative sign indicates x o is measured in negative x direction.

11 Parameter used in determination of elastic critical moment j = t

3.3.4 Z-Sections (Point-Symmetric) With and Without Lips b B' b

Figure 3.3.4-2 Z-Section (Point Symmetric) Without Lips

Z-Section (Point Symmetric) With Lips x 2

1 Basic Parameters a =A′- (2r + t) a =A′- t b =B′- [r + t/2 +α(r + t/2)tan (γ/2)]* b =B′- [t/2 +(αt/2)tan (γ/2)] c =α[C′- (r + t/2)tan (γ/2)] c =α[C′- (t/2)tan (γ/2)] u 1 =πr/2 = 1.57r u 2 =γr whereγis in radians

* For sections with lips,α= 1.0; for sections without lips,α= 0.

5 Product of inertia (See note below)

+ sin 2 2 γ + sin γcos γ γ − 1  r 3 − c 3 sin 12 γ cos γ

6 Angle between x-axis and minor principal axis, in radians (See note below) θ= π

7 Moment of inertia about x 2 axis (See note below)

I x2 = I x cos 2 θ+ I y sin 2 θ- 2I xy sinθcosθ

8 Moment of inertia about y 2 axis (See note below)

I y2 = I x sin 2 θ +I y cos 2 θ+ 2I xy sinθcosθ

Note: The algebraic signs in Equations 5, 6, 7 and 8 are correct for the cross- section oriented with respect to the coordinate axes as shown in Fig- ure 3.3.4-1 and Figure 3.3.4-2.

9 Radius of gyration about any axis r = I∕A

10 Minimum radius of gyration, about x 2 axis r min = I x2 ∕A

+4abc 3 2a+4b+csinγcosγ +c 3  2a 3 + 4a 2 b – 8ab 2 + a 2 c – 16b 3 – 4b 2 c  cos 2 γ

Gross Section Properties - Example Problems

This article presents example problems that demonstrate the application of gross section property equations outlined in this section of the Design Manual These examples should be utilized alongside other relevant sections of the Design Manual for comprehensive understanding.

As a general rule, section properties are computed to three significant figures.

In certain instances, properties are calculated to four significant figures to maintain precision for subsequent calculations Dimensions are typically specified to the nearest thousandth of an inch However, strict adherence to these guidelines may not always be feasible, leading to slight discrepancies between the calculated section properties in the examples and those provided in the tables of Parts I, II, and III of this manual, which were computed using a computer.

Example I-1: C-Section With Lips - Gross Section Properties

1 Section: 9CS2.5x059 as shown above

1 Axial and flexural properties a Basic Parameters

R = 0.1875 in. α = 1.0 (section has stiffener lips) r = R + t/2

= 0.881 in 2 c Moment of inertia about the x-axis

= 10.3 in 4 d Distance between centroid and web centerline x c = 2tAbb∕2+r +u(0.363r)+α[u(b+1.637r)+c(b+2r)]

= 0.612 in. e Moment of inertia about the y-axis

= 0.698 in 4 f Distance between shear center and web centerline m = b 

= 1.048 in. g Distance between centroid and shear center x o = −(x c + m)

2 Torsional properties a St Venant torsional constant

= 11.9 in 6 c Parameter used in determination of elastic critical moment βw = − tx 12 c a 3 + tx 3 c a 

Example I-2: C-Section Without Lips - Gross Section Properties

1 Section: SSMA Track 550T125-54 as shown above

R = 0.0849 in. α = 0.0 (section does not have stiffener lips) r = R + t/2 = 0.0849 + 0.0566/2 = 0.113 in. a = A′- (2r + t)

= 0.187 in. e Moment of inertia about the y-axis

Example I-3: Z-Section With Lips - Gross Section Properties

1 Section: 8ZS2.25x059 as shown above

R = 0.1875 in. α = 1.0 (section has stiffener lips) r = R + t/2 = 0.1875 + 0.059/2 = 0.217 in. γ = 50 xπ/180 = 0.8727 radians a = A′- (2r + t)

= 7.763 in 4 d Moment of inertia about the y axis

+ sin 2 2 γ + sin γcos γ γ − 1  r 3 − c 3 sin 12 γ cos γ

= 2.082 in 4 f Angle between x-axis and minor principal axis, in radians θ = π

2tan − 1 1.0762(2.082)−7.763 θ = 1.292 radians = 74.0 degrees g Moment of inertia about x 2 axis, computed using angles in radians

I x2 = I x cos 2 θ+ I y sin 2 θ- 2 I xy sinθcosθ

= 0.481 in 4 h Moment of inertia about y 2 axis, computed using angles in radians

I y2 = I x sin 2 θ+ I y cos 2 θ+ 2I xy sinθcosθ

= 8.36 in 4 i Minimum radius of gyration, about x 2 axis r min = I x2 ∕A

+4abc 3 2a+4b+csinγcosγ +c 3  2a 3 + 4a 2 b − 8ab 2 + a 2 c − 16b 3 − 4b 2 c  cos 2 γ

Example I-4: Equal Leg Angle With Lips - Gross Section Properties x c

1 Section: 4LS4x060 as shown above

R = 0.1875 in. α = 1.0 (section has stiffener lips) r = R + t/2 = 0.1875 + 0.060/2 = 0.218 in. a = A′- [r + t/2 +α(r + t/2)]

= (1.0)[0.500 - 0.060/2] = 0.470 in. u = πr/2 =π(0.218)/2 = 0.342 in. b Cross-section area

= 0.512 in 2 c Distance between centroid and centerlines of webs x c = y c = tA a  a2+r + u(0.363r) + α  c  a + c 2 + 3r  + u(a + 2r)  

= 1.097 in. d Moment of inertia about x and y axes

= - 0.562 in 4 f Moment of inertia about y 2 axis

2 Torsional properties a Distance between shear center and centerline of square corner m = a c 2 2

(2)(3.940) 3 − (3.940−0.470) 3 = 0.083 in. b St Venant torsion constant

(2)(3.940) 3 −(3.940−0.470) 3 = 0.0533 in 6 d Distance from centroid to shear center x o = − x c  +2 m

= − 1.097 2 +0.083 = − 1.634 in. e Parameter used to determine elastic critical moment j = 2t

Example I-5: Equal Leg Angle Without Lips - Gross Section Properties

1 Section 2LU2x060 as shown above

1 Axial and flexural properties a Basic Parameters:

R = 0.1875 in. α = 0.0 (section does not have stiffener lips) r = R + t/2 = 0.1875 + 0.060/2 = 0.218 in. a = A′- [r + t/2 +α(r + t/2)]

= 0.231 in 2 c Distance between centroid and centerlines of webs x c = y c = tA a  a2+r + u(0.363r) + α  c  a + 2 c + 3r  + u(a + 2r)  

= 0.505 in. d Moment of inertia about x and y axes

= −0.0589 in 4 f Moment of inertia about y 2 axis

2 Torsional properties a Distance between shear center and centerline of square corner m = a c 2 2

 2a 3 – (a – c) 3  m = 0.000 in. b St Venant torsional constant

= 0.000 in 6 d Distance from centroid to shear center x o = − x c  +2 m

= −0.714 in. e Parameter used to determine elastic critical moment j = 2t

Example I-6: Hat Section without Lips - Gross Section Properties

1 Section: 3HU4.5x135 as shown above

= 1.737 in 2 c Moment of inertia about the x axis

= 1.303 in. e Moment of inertia about the y axis

Example I-7: Wall Panel Section with Intermediate Stiffeners - Gross Section Properties

1 Section: Shown in sketch above

Since no closed formed solution is available, the properties must be determined by parts.

Distance of c.g from center of radius: c = 0.637r = (0.637)(0.140) = 0.089 in.

Distance of c.g from top of panel: y = 0.125 + 0.030 - 0.089 = 0.066 in (element 4) y = 2.00 + (0.125 - 0.089) = 1.964 in (element 10)

2 Element 7 r = 0.140 in.,θ= 45°= 0.785 rad. c 1 = rsinθ/θ= (0.140)(0.707)/0.785 = 0.126 in. n = 0.350 - (2)(0.140)(1-cos(0.785))

By inspection, take advantage of symmetry and locate reference axis at 1/2 element depth = (0.350 + 0.030)/2 = 0.190 in.

I′ 1 about own axis (in 3 ) Upper Radius

= 0.000/1.198 = 0.000 in (at centerline as expected) ΣI′ x = ΣLy 2 +ΣI′ 1 - y cg 2 ΣL

Distance of c.g from top of panel y = 2.030 - (0.350 + 0.030)/2 = 1.840 in.

I′ 1 about own axis (in 3 ) 90°Corner

Effective Section Properties

Effective section properties rely on the concept of effective width, which simplifies the analysis of plate elements by assuming that the total load is carried by a fictitious effective width subjected to a uniformly distributed stress equivalent to the maximum edge stress This approach eliminates the need to account for the non-uniform stress distribution across the plate, a common issue in cold-formed steel design due to post-buckling strength considerations Although integrating post-buckling strength complicates member design, it allows for a more efficient utilization of steel.

The effective width of plate elements is determined by equations outlined in the Specification, which take into account factors such as stress level, stress distribution, and the element's geometrical properties, including flat width, thickness, and whether the element is stiffened or unstiffened.

The calculation of section properties often involves an iterative process Initially, the stresses in a beam are calculated using its full section properties These properties help determine the effective widths of the compression elements, leading to the calculation of a new beam centroid With the updated centroid, new section properties are derived, allowing for a recalculation of stresses This iterative procedure continues until the results converge satisfactorily.

In the examples presented herein, for beam section properties, the effective section properties are computed using one of the following two procedures:

1 If the neutral axis of the effective section is at mid-depth of the section or closer to the tension flange than to the compression flange, the maximum stress occurs in the compression flange, thus the effective width of the compression flange and the effective width of the web elements can be calculated assuming an extreme compression fiber stress equal to the yield stress or other specified maximum stress This case is not iterative in nature unless the web is not fully effective.

2 If the neutral axis of the effective section is closer to the compression flange than to the tension flange, the compressive stress must be known in order to calculate the effective widths of the compression elements.

Compressive stresses are influenced by the position of the neutral axis, which is determined by the effective widths; therefore, the solution requires an iterative approach Example problems illustrate this iterative process effectively.

For uniformly stressed sections, i.e column sections, the effective widths do not vary with location of the neutral axis, thus iteration is not required.

Effective Section Properties - Example Problems

This article presents example problems designed to highlight key provisions of the Specification, particularly focusing on the calculation of effective section properties These examples should be utilized alongside other sections of the Design Manual, as many calculations are referenced in Parts II and III.

The calculations were done using the same guidelines on precision presented in Section3.4 of Part I of theDesign Manual.

Example I-8: C-Section With Lips - Effective Section Properties

2 Section: 9CS2.5x059 as shown above

1 Effective section modulus, S e , based on initiation of yielding

2 Effective area, A e , at a uniform compressive stress of 37.25 ksi (as used in Example III-1)

See Example I-1 for basic geometric parameters.

1 Effective section mdulus, S e , at initiation of yielding

An iterative approach is generally required.

In the initial analysis, a compression stress of 55 ksi is assumed in the top fiber of the section, with the neutral axis located 4.500 inches below The compression flange, as per Section B4.2, has dimensions of w = b = 2.007 inches The width-to-thickness ratio is calculated as w/t = 2.007/0.059, yielding a ratio of 34.02, which is below the allowable limit of 60, confirming compliance with Section B1.1(a)(1).

= 1.28 29500 ∕55= 29.64 ∴ w/t ≥ 0.328S ⇒check effective width of flange

Compute k of the flange based on stiffener lip properties.

= 0.00266 in 4 > 0.00166 in 4 ∴I a = 0.00166 in 4 d = c = 0.527 in. θ = 90 degrees

D/w= 0.773/2.007 = 0.385 < 0.8 OK (From Table B4.2) k =  4.82 − 5Dw  R I  n + 0.43 ≤ 4 (From Table B4.2)

 = 0.955 > 0.673∴flange is subject to local buckling ρ = (1 - 0.22/λ) /λ (Eq.B2.1-3)

= (0.806)(2.007) = 1.618 in. b Stiffener lip: from Section B3.2-a w/t = d/t = 0.527/0.059 = 8.93

Maximum stress in lip (by similar triangles) f = 55 [4.500 - 0.059/2 - 0.217]/ 4.500 = 51.99 ksi k = 0.43

 = 0.601 < 0.673∴lip is not subject to local buckling d ′ s = d = 0.527 in. d s = d ′ s (R I ) (Eq.B4.2-7)

= (0.527)(0.434) = 0.229 in. c Web: from Section B2.3 w/t = 8.507/0.059 = 144.2 ψ = |f 2 /f 1 | (Eq.B2.3-1) Assuming the neutral axis is at the section centerline, determine the maximum flexural stress in the web by similar triangles. f 1 = (55)(4.500 - 0.059/2 - 0.217)/4.500 = 51.99 ksi

By symmetry f 2 = -f 1 = -51.99 ksi ψ = |f 2 /f 1 | = |- 51.99/51.99| = 1.0 (Eq.B2.3-1) k = 4 + 2 (1 +ψ) 3 + 2(1 +ψ) (Eq.B2.3-2)

 = 1.300 > 0.673∴web may be subject to local buckling (Eq.B2.1-4) ρ = (1 - 0.22/1.300) / 1.300 = 0.639 (Eq B2.1-3) b e = (0.639)(8.507) = 5.436 in (Eq B2.1-2) h o /b o = 9.000 / 2.500 = 3.60 < 4.0

1.359 + 2.718 = 4.077 < 8.507/2 = 4.254 ∴web is not fully effective for this iteration d Recompute properties by parts

Represent the ineffective portion of the web as an element with a negative length b neg = -(4.254 - 4.077) = - 0.177 in.

Its centroidal location below the top fiber: y = t/2 + r + b 1 + b neg /2

2 Second iteration with new neutral axis location

The calculated neutral axis location (4.741 in.) does not equal the assumed neutral axis location (4.500 in.); therefore, another iteration is required. a Compression flange

Since the neutral axis is below the centerline, the maximum flexural stress, F y , will occur at the top flange The previous solution using F y will still be valid. b Stiffener lip

The shift in the neutral axis position will result in a slight alteration of the stress gradient and the maximum stress within the stiffener, potentially leading to a minor adjustment in the effective width of the stiffener, which can be disregarded in this context.

Compute new stresses at edges of web, correcting for the shift in the neutral axis. f 1 = 55(4.741 - 0.059/2 - 0.217)/4.741

 = 1.380 > 0.673∴web may be subject to local buckling (Eq.B2.1-4) ρ = (1 - 0.22/1.380)/1.380 = 0.609 (Eq.B2.1-3) b e = (0.609)(8.507) = 5.181 in (Eq.B2.1-2) b 1 = b e /(3 +ψ) (Eq.B2.3-3)

Depth of compression block = 4.495 in > 3.922 in.∴web is not fully effective d Recompute properties by parts

Represent the ineffective portion of the web as an element with a negative area. b neg = -(4.495 - 3.922) = - 0.573 in.

Its centroidal location below the top fiber y = t/2 + r + b 1 + b neg /2

The calculated neutral axis location of 4.822 inches slightly differs from the assumed location of 4.741 inches; however, the computed values of I x and S e are within two percent of the fully converged solution After additional iterations, the solution converges to a final neutral axis position of 4.859 inches.

4 Effective area, A e , at a uniform compressive stress of 37.25 ksi a Compression flange: taking parameters from 1 (a) above f = 37.25 ksi

S = 1.28 29500 ∕37.25= 36.02 (Eq B4-1) w/t = 34.02 > 0.328S => check effective width of flange

= 0.346 > 1/3 OK k =  4.82 − 5Dw  R I  n + 0.43 ≤ 4 (From Table B4.2) k =  4.82 − (5)(0.773)2.007  (0.637) 0.346 + 0.43 =2.906 < 4 OK

 = 0.746 > 0.673∴flange is subject to local buckling (Eq.B2.1-4) ρ = (1 - 0.22/0.746)/0.746 = 0.945 (Eq.B2.1-3) b = ρw = (0.945)(2.007) = 1.897 in (Eq.B2.1-2) b Stiffener lip: taking parameters from 1 (b) above f = 37.25 ksi k = 0.43

 = 0.509 < 0.673∴lip is not subject to local buckling (Eq.B2.1-4) d′ s = w = 0.527 in. d = d′ s (R I ) = (0.527)(0.637) = 0.336 in (Eq.B4.2-7) c Web: from Section B2.3 f = 37.25 ksi k = 4.0

5.13 = 2.695 > 0.673∴web is subject to local buckling (Eq.B2.1-4) ρ = (1 - 0.22/2.695)/2.695 (Eq B2.1-3)

Sum of the effective widths of the elements

Example I-9: C-Section Without Lips - Effective Section Properties

2 Section: SSMA Track 550T125-54 as shown above

1 Effective section modulus, S e , at a maximum bending stress, f, of 30.93 ksi (as used in Example II-3)

1 Effective section modulus, S e , at f = 30.93 ksi

An iterative approach is generally required.

In the initial analysis, a compression stress of 30.93 ksi is applied to the top fiber of the section, with the neutral axis positioned at mid-height of the web, specifically 2.849 inches below the top fiber The compression flange is characterized as a uniformly compressed, unstiffened element, following the guidelines of Section B3.1, where the width is calculated as w = B - r - t/2.

= 0.854 in. b Compute new neutral axis location and check web as a stiffened element under a stress gradient

By similar triangles f 1 =  2.942 − 0.1132.942− 0.0566 ∕ 2 (30.93) = 29.44 ksi f 2 = − 5.698 − 2.942 −2.9420.113 − 0.0566 ∕ 2 (30.93) = -27.49 ksi ψ = |f 2 /f 1 | =|- 27.49/29.44| = 0.934 (Eq.B2.3-1) k = 4 + 2 (1 +ψ) 3 + 2(1+ψ) (Eq.B2.3-2)

Therefore the web is fully effective and no further iteration is required.

Example I-10: Z-Section With Lips - Effective Section Properties

2 Section: 8ZS2.25x059 as shown above

1 Effective section modulus, S e , based on initiation of yielding

2 Effective moment of inertia based on procedure I of Section C3.1.1 for deflection determination at a service moment equal to 60% of the fully braced nominal moment, M n

3 Effective area, A e , at a uniform compressive stress of 25.9 ksi, as required in Example III-6

1 Effective section modulus, S e, at initiation of yielding

An iterative approach is generally required since the location of the neutral axis is dependant on the effect section properties.

In the initial analysis, a compression stress of 55 ksi is assumed in the top fiber of the section, with the neutral axis positioned 4.000 inches below this fiber For the compression flange, the width is measured at 1.889 inches The calculated width-to-thickness ratio is 32.0, which is below the limit of 60, confirming compliance with Section B1.1(a)(1).

= 1.28 29500 ∕55= 29.64 ∴ w/t ≥ 0.328 S ⇒check effective width of flange

Compute k of flange based on stiffener lip properties.

= (0.857)(1.889) = 1.619 in. b Stiffener lip: from Section B3.2-a w/t = d/t = 0.795/0.059 = 13.5

Maximum stress in lip, f 3 (by similar triangles) f = f 3 = 55[4.000 - 0.059/2 - 0.217(1-cos(50°))]/ 4.000 = 53.5 ksi k = 0.43

62.9= 0.922 > 0.673∴lip is subject to local buckling ρ = (1 - 0.22/λ) /λ (Eq.B2.1-3)

= (0.657)(0.929) = 0.610 in. c Web: from Section B2.3 w/t = 7.507/0.059 = 127.2 ψ = |f 2 /f 1 | (Eq.B2.3-1)

Assuming the neutral axis is at the mid-height of the section, find the maximum flexural stress in the web by similar triangles. f 1 = (55)(4.000 - 0.059 - 0.1875)/4.000 = 51.61 ksi

By symmetry f 2 = -f 1 = -51.61 ksi ψ = |f 2 /f 1 | = |- 51.61/51.61| = 1.0 (Eq.B2.3-1) k = 4 + 2 (1 +ψ) 3 + 2(1 +ψ) (Eq.B2.3-2)

 = 1.142 > 0.673∴web may be subject to local buckling (Eq.B2.1-4) ρ = (1 - 0.22/1.142) / 1.142 = 0.707 (Eq B2.1-3) b e = (0.707)(7.507) = 5.307 in (Eq B2.1-2) h o /b o = 8.000/2.250 = 3.6 < 4.0

1.327 + 2.654 = 3.981in > 7.507/2 = 3.754 in ∴web is fully effective for this iteration d Recompute properties by parts

Second iteration with new neutral axis location

The calculated neutral axis location (4.126 in.) does not equal the assumed neutral axis location (4.000 in.); therefore, another iteration is required. a Compression flange

Since the neutral axis is below the centerline, the maximum flexural stress, F y , will occur at the top flange The previous solution using F y will still be valid. b Stiffener lip

The shift in the neutral axis position will result in a slight alteration of the stress gradient and the maximum stress within the stiffener, potentially leading to a minor adjustment in the effective width of the stiffener, which can be disregarded in this context.

Compute new stresses at edges of web, correcting for the shift in the neutral axis. f 1 = 55(4.126 - 0.059 - 0.1875)/4.126

 = 1.185 > 0.673∴web may be subject to local buckling (Eq.B2.1-4) ρ = (1 - 0.22/1.185)/1.185 = 0.687 (Eq.B2.1-3) b e = (0.687)(7.507) = 5.157 in (Eq.B2.1-2) b 1 = b e /(3 +ψ) (Eq.B2.3-3)

4.126 - 0.059 - 0.1875 = 3.880 in < 3.890 in.∴web is not subject to local buckling d Recompute properties

There was no further reduction in the effective widths of the elements, therefore use previous solution: y = 4.126 in below top fiber

2 Effective moment of inertia, I x , at a service load of 60% of M n ; M = (0.60)(98.5) = 59.1 kip-in.

A conservative estimate of flexural deflections can be achieved through an elastic beam analysis, utilizing the effective moment of inertia derived from the maximum extreme fiber stress under serviceability loading For continuous beams, the average of the moments of inertia during maximum positive and negative bending is applicable.

Assume the maximum compressive stress is approximately (0.60) F y = (0.60)(55) = 33 ksi The calculations are otherwise the same as above. a Compression flange: from Section B4.2

= 1.28 29500 ∕33= 38.3 w/t = 32.0 > 0.328 S ⇒check effective width of flange

Compute flange k based on stiffener lip properties.

 = 0.668 < 0.673∴flange is not subject to local buckling b Stiffener lip: from Section B3.2(a) w/t = d/t = 0.795/0.059 = 13.5

Maximum stress in lip (by similar triangles) f = 33[4.000 - 0.059/2 - 0.217(1-cos(50°))]/4.000 = 32.12 ksi k = 0.43

 = 0.715 > 0.673∴lip is subject to local buckling ρ = (1 - 0.22/λ) /λ (Eq.B2.1-3)

The web demonstrates full effectiveness at a maximum flange stress of 33 ksi, as previously established in Parts 1 and 2, where it was confirmed to be fully effective at a maximum flange stress of 55 ksi Additionally, it is necessary to recompute the properties by parts for accurate assessment.

= (1.93)(33) = 63.7 kip-in > 59.1 kip-in.∴maximum stress at service level is lower.

Recomputing I x using a maximum stress of 30.6 ksi using the same approach as above (calculations not shown) we obtain: y = 4.002 in below top fiber

= (1.94)(30.6) = 59.4 kip-in.≅59.1 kip-in.∴solution has converged satisfactorily

3 Effective area, A e , at a uniform compressive stress of 25.9 ksi

The flange demonstrates full effectiveness at a stress level of 25.9 ksi, as indicated by previous calculations Additionally, any reduction in the effective width of the stiffener lip is deemed insignificant at this stress level.

6.59 = 1.982 > 0.673∴web is not fully effective (Eq.B2.1-4) ρ = (1 - 0.22/1.982)/1.982 = 0.449 (Eq.B2.1-3) b e = (0.449)(7.507) = 3.371 in (Eq.B2.1-2)

To find A e , subtract the ineffective area of the web from the gross area.

From Table I-4 or Example I-3, A gross = 0.822 in 2

Example I-11: Equal Leg Angle With Lips - Effective Section Properties

2 Section: 4LS4x060 as shown above

1 Effective area, A e , at a uniform compression stress of 14.7 ksi, as required in Example III-4

See Example I-4 for basic parameters Treat each leg as a uniformly compressed element with an edge stiffener (Section B4.2). a Legs w = 3.504 in. t = 0.060 in. w/t = 3.504/0.060 = 58.4

= 57.3 w/t > 0.328S, therefore check effective width of leg

Compute k of flange based on stiffener lip properties.

13.7= 1.036 > 0.673∴leg is subject to local buckling ρ = (1 - 0.22/λ )/λ (Eq.B2.1-3)

Check Stiffener effective width w = d = 0.252 in. w/t = 0.252/0.060 = 4.20 k = 0.43

650 = 0.150 < 0.673∴stiffener is not subject to local buckling (Eq.B2.1-4) d s ’ = b = w = 0.252 in (Eq.B2.1-1) d s = d s ′ (R I ) (Eq B4.2-7)

Example I-12: Equal Leg Angle Without Lips - Effective Section Properties

2 Section: 2LU2x060 as shown above

1 Effective section modulus, S e , at f = F y at the extreme fibers, for flexure about the x-axis with compression on the top

Refer to Example I-5 for basic parameters.

1 Effective section modulus, S e , with compression on top (bottom flange in tension)

Treat web as unstiffened element with stress gradient (Section B3.2). k = 0.43 w = 1.752 in.

 = 1.566 > 0.673∴leg is subject to local buckling ρ = (1 - 0.22/λ)/λ (Eq.B2.1-3)

I′ x about own axis (in 3 ) web 0.962 1.272 1.224 1.557 0.074 corner 0.342 1.891 0.647 1.223 0.002 flange 1.752 1.970 3.451 6.799

SumΣ 3.056 5.322 9.579 0.076 y = ΣLy/ΣL = 5.322/3.056 = 1.741 in below top fiber

Treat flanges as uniformly compressed unstiffened element (Section B3.1) f = 12.0 ksi k = 0.43 w = 1.752 in.

 = 0.945 > 0.673∴leg is subject to local buckling ρ = (1 - 0.22/λ)/λ (Eq.B2.1-3)

Example I-13: Hat Section - Effective Section Properties Using Inelastic Reserve Capacity

2 Section: 3HU4.5x135 as shown in sketch above

1 Determine the nominal flexural strength, M ny , with the top flange in compression, based on initiation of yielding.

2 Determine the nominal flexural strength, M ny , with the top flange in compression, based on inelastic reserve capacity.

3 Determine the effective area, A e , at a uniform compressive stress of 50 ksi.

Refer to Example I-6 for derivation of basic parameters.

1 Nominal flexural strength based on initiation of yielding (Section C3.1.1.a)

Assume a compressive stress of f = F y = 50 ksi in the top fiber of the section.

Assume the web is fully effective.

Element 3: h/t = 2.355/0.135 = 17.44 < 200 OK (Section B1.2-(a)) Assumed fully effective

Element 5: w/t = 3.855/0.135 = 28.56 < 500 OK (Section B1.1-(a)-(2)) k = 4.0 (fully stiffened element)

 = 0.618 < 0.673∴flange is not subject to local buckling b = w (Eq.B2.1-1)

Effective section properties about y-axis:

Distance of neutral axis from top fiber, x = ΣLx/ΣL = 17.639/12.865 = 1.371 in.

The distance from the top compression fiber to the neutral axis is less than half the beam's depth, meaning that the compressive stress at the top fiber will be less than the yield strength (F y) initially assumed Consequently, the flange remains fully effective, while the tension flange is the first to yield.

Check web (element 3) under new assumed stress distribution f 1 = (1.049/1.629)(50) = 32.20 ksi (compression) f 2 = -(1.306/1.629)(50) = -40.09 ksi (tension) ψ = |f 2 /f 1 | = |-40.09/32.20| = 1.245 (Eq.B2.3-1) k = 4 + 2(1 +ψ) 3 + 2(1 +ψ) (Eq.B2.3-2)

= 2.355/2 = 1.178 in. b 1 +b 2 =0.555 + 1.178 = 1.733 in > 1.049 in (compression portion of web)

Therefore, web is fully effective.

2 Nominal flexural strength based on inelastic reserve capacity (Section C3.1.1.b)

Compute the maximum compression strain. λ1 = 1.11

Therefore, the maximum compression strain is 2.23 times the yield strain, e y The tension strain is not limited.

To determine the location of e y on a strain diagram while ensuring that the maximum compression strain does not exceed 2.23 e y and that the summation of longitudinal forces is zero, refer to the equations presented by Reck, Pekoz, and Winter in their 1975 article, "Inelastic Strength of Cold-Formed Steel Beams," published in the Journal of the Structural Division, ASCE These equations provide the necessary framework for accurately calculating strain and force conditions in cold-formed steel beams, facilitating effective structural analysis and design.

Approximate distance from neutral axis to the outer compression fiber, y c (not considering the effect of radii): t = 0.135 in. b t = 2(1.670) = 3.340 in. b c = 4.500 in. d = 3.000 in. x c = (1/4)(b t - b c + 2d)

= 3.000 - 1.210 = 1.790 in. x cp = x c - x p x cp = 1.210 - 0.543 = 0.667 in. x tp = x t - x p = 1.790 - 0.543 = 1.247 in. d b c

Summing moments of stresses in component plates:

M n = Fyt b c x c + 2x cp  x p + x2 cp  + 4 3 x p 2 + 2x tp  x p + x 2 tp  + b t x t 

M n shall not exceed 1.25S e F y = 1.25(75.8) = 94.8 kip-in CONTROLS

The inelastic reserve capacity can be used assuming the following conditions are met:

(1) The member is not subject to twisting, lateral, torsional, or torsional-flexural buckling.

(2) The effect of cold-forming is not included in determining the yield point,

(3) The ratio of depth of the compressed portion of the web to its thickness does not exceedλ1:

(4) The shear force does not exceed 0.35F y times the web area, ht, for ASD, and 0.6F y ht for LRFD.

(5) The angle between any web and the vertical does not exceed 30°.

3 Effective area, A e , at a uniform compressive stress of fP ksi (Section C4)

Element 5: Uniformly Compressed Stiffened Element (Section B2.1) w/t = 3.855/0.135

 = 0.618 < 0.673 (flange is fully effective) (Eq.B2.1-4) b = w (Eq.B2.1-1)

Element 3: Uniformly Compressed Element with an Edge Stiffener (Section B4.2) w = 2.355 in. w/t = 2.355 /0.135 = 17.4 < 60 OK (Section B1.1(a)(1))

= 1.28 29500 ∕50= 31.1 ∴ w/t ≥ 0.328S ⇒check effective width of element

Compute k of element based on stiffener lip (element 1) properties.

= 0.00164 in 4 < 0.0230 in 4 ∴I a = 0.00164 in 4 d = 1.348 in. θ = 90 degrees

D/w= 1.67/2.355 = 0.71 < 0.8 OK (From Table B4.2) k =  4.82 − 5Dw  R I  n + 0.43 ≤ 4 (From Table B4.2)

150= 0.577 < 0.673∴element is not subject to local buckling b = w

Element 1: Uniformly Compressed Unstiffened Element (Section B3.1 and B4.2) w/t = 1.348/0.135 = 9.99 k = 0.43

115= 0.659 < 0.673∴element is not subject to local buckling d’ s = b = w (Eq.B2.1-1)

Example I-14: Wall Panel Section with Intermediate Stiffeners - Effective Section Properties

2 Section: Shown in sketch above Refer to Example I-7 for gross properties of elements Section is assumed to be fully braced against member buckling.

1 Nominal flexural strength per panel, M n , for positive and negative bending.

2 Effective moment of inertia, I eff , at a moment of 0.6M n with compression on the top Use Proce- dure II from Part (b) of Section B2.1 to compute effective widths of stiffened elements at service load.

1 Section modulus, S e , for nominal flexural strength - compression on top

In Example I-7, the neutral axis is positioned 1.186 inches below the top fibers of the gross cross-section, indicating that the compression stress at the top fiber is the governing factor and will be equal to this value.

Unstiffened Lip of Element 1 from Section B3.2(a) w = 0.250 in. k = 0.43 f = F y (Conservative assumption for preliminary check)

 = 0.550 < 0.673∴flange is not subject to local buckling, so no need to calculate more precisely b = w = 0.250 in.

Stiffened Flat Elements of Element 1 with Stress Gradient from Section B2.3

The stress level in the inspected element matches that of the unstiffened element, indicating that the effective length remains consistent Therefore, with a minimum k value of 4.0, the element is deemed fully effective, mirroring the performance of the unstiffened counterpart.

Element 2 from Section B4.2(a) w = 3.000 - 3(0.125 + 0.030/2) = 2.580 in. f = F y = 50 ksi

 = 1.862 > 0.673∴element is subject to local buckling ρ = (1 - 0.22/λ)/λ (Eq.B2.1-3)

Element 9 from Section B3.2(a) w = 0.415 - 0.030 - 0.125 = 0.260 in. k = 0.43 f < F y , use F y as a conservative value

 = 0.572 < 0.673∴element is not subject to local buckling (Eq B2.1-4) d′ s = b = w = 0.260 in (Eq.B2.1-1)

Element 3 from Section B4.2(a) w = 2.000−2(0.125 + 0.030/2) = 1.720 in. f = F y = 50 ksi

 = 21.7450.0 = 1.517 > 0.673∴element is subject to local buckling (Eq.B2.1-4) ρ = (1 - 0.22/λ)/λ (Eq.B2.1-3)

Effective section properties about x-axis, assuming element 5 is fully effective:

SumΣ 17.210 23.041 41.315 0.913 y = ΣLy/ΣL = 23.041/17.210 = 1.339 in.; below mid depth as assumed

Element 5 from Section B2.3(a): check assumption that element is fully effective y cg = 1.339 in. f 1 = [(1.339 - 0.125 - 0.030)/1.339](50)

= 1.720/2 = 0.860 in. w c = 1.339 - 0.030 - 0.125 = 1.184 in (compression portion of web) b 1 +b 2 =0.498 + 0.860 = 1.358 in > 1.184 in.

Thus element 5 is fully effective so properties above are correct.

2 Moment of inertia for deflection determination - compression on top, M s = 0.6M n = 7.68 kip-in.

Tiêu đề	AISI Manual Cold-Formed Steel Design 2002 Edition
Tác giả	American Iron And Steel Institute
Người hướng dẫn	Wei-Wen Yu
Trường học	Missouri University of Science and Technology
Thể loại	technical report
Năm xuất bản	2003
Thành phố	Rolla

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Số trang	462
Dung lượng	4 MB