ANSIAISC 36016 An American National Standard

This Preface is not part of ANSIAISC 36016, Specification for Structural Steel Buildings, but is included for informational purposes only.) This Specification is based upon past successful usage, advances in the state of knowledge, and changes in design practice. The 2016 American Institute of Steel Construction’s Specification for Structural Steel Buildings provides an integrated treatment of allowable strength design (ASD) and load and resistance factor design (LRFD), and replaces earlier Specifications. As indicated in Chapter B of the Specification, designs can be made accord ing to either ASD or LRFD provisions. This ANSIapproved Specification has been developed as a consensus document using ANSIaccredited procedures to provide a uniform practice in the design of steelframed buildings and other structures. The intention is to provide design criteria for routine use and not to provide specific criteria for infrequently encountered problems, which occur in the full range of structural design. This Specification is the result of the consensus deliberations of a committee of structural engineers with wide experience and high professional standing, representing a wide geo graphical distribution throughout the United States. The committee includes approximately equal numbers of engineers in private practice and code agencies, engineers involved in research and teaching, and engineers employed by steel fabricating and producing compa nies. The contributions and assistance of more than 50 additional professional volunteers working in task committees are also hereby acknowledged. The Symbols, Glossary, Abbreviations and Appendices to this Specification are an inte gral part of the Specification. A nonmandatory Commentary has been prepared to provide background for the Specification provisions and the user is encouraged to consult it. Additionally, nonmandatory User Notes are interspersed throughout the Specification to provide concise and practical guidance in the application of the provisions.

Seismic Applications

The AISC Seismic Provisions for Structural Steel Buildings (ANSI/AISC 341) are essential for designing seismic force-resisting systems in structural steel or composite systems with reinforced concrete, unless explicitly exempted by the relevant building code.

According to ASCE/SEI 7 (Table 12.2-1, Item H), structural steel systems in seismic design categories B and C are exempt from the AISC Seismic Provisions for Structural Steel Buildings if designed per this Specification and utilizing a seismic response modification factor, R, of 3; however, this exemption does not extend to composite systems Additionally, the Seismic Provisions for Structural Steel Buildings are not applicable in seismic design category A.

Nuclear Applications

The design, fabrication, and erection of nuclear structures must adhere to this Specification, incorporating the stipulations outlined in the AISC Specification for Safety-Related Steel Structures for Nuclear Facilities (ANSI/AISC N690).

A2 REFERENCED SPECIFICATIONS, CODES AND STANDARDS

The following specifications, codes and standards are referenced in this Specification:

ACI 318-14 Building Code Requirements for Structural Concrete and Com - mentary

ACI 318M-14 Metric Building Code Requirements for Structural Concrete and Commentary

ACI 349-13 Code Requirements for Nuclear Safety-Related Concrete Struc tures and Commentary

ACI 349M-13 Code Requirements for Nuclear Safety-Related Concrete Struc - tures and Commentary (Metric)

(b) American Institute of Steel Construction (AISC)

ANSI/AISC 303-16 Code of Standard Practice for Steel Buildings and

ANSI/AISC 341-16 Seismic Provisions for Structural Steel Buildings

ANSI/AISC N690-12 Specification for Safety-Related Steel Structures for Nuclear Facilities

ANSI/AISC N690s1-15 Specification for Safety-Related Steel Structures for

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(c) American Society of Civil Engineers (ASCE)

ASCE/SEI 7-16 Minimum Design Loads and Associated Criteria for Buildings and Other Structures

ASCE/SEI/SFPE 29-05 Standard Calculation Methods for Structural Fire Pro tection

(d) American Society of Mechanical Engineers (ASME)

ASME B18.2.6-10 Fasteners for Use in Structural Applications

ASME B46.1-09 Surface Texture, Surface Roughness, Waviness, and Lay

(e) American Society for Nondestructive Testing (ASNT)

ANSI/ASNT CP-189-2011 Standard for Qualification and Certification of Non - destructive Testing Personnel

Recommended Practice No SNT-TC-1A-2011 Personnel Qualification and Cer tification in Nondestructive Testing

A6/A6M-14 Standard Specification for General Requirements for Rolled Struc - tural Steel Bars, Plates, Shapes, and Sheet Piling

A36/A36M-14 Standard Specification for Carbon Structural Steel

A53/A53M-12 Standard Specification for Pipe, Steel, Black and Hot-Dipped, Zinc-Coated, Welded and Seamless

A193/A193M-15 Standard Specification for Alloy-Steel and Stainless Steel Bolt - ing Materials for High Temperature or High Pressure Service and Other Special Purpose Applications

A194/A194M-15 Standard Specification for Carbon Steel, Alloy Steel, and Stain - less Steel Nuts for Bolts for High Pressure or High Temperature Service, or Both

A216/A216M-14e1 Standard Specification for Steel Castings, Carbon, Suitable for Fusion Welding, for High-Temperature Service

A242/A242M-13 Standard Specification for High-Strength Low-Alloy Struc - tural Steel

A283/A283M-13 Standard Specification for Low and Intermediate Tensile Strength Carbon Steel Plates

A307-14 Standard Specification for Carbon Steel Bolts, Studs, and Threaded Rod, 60,000 PSI Tensile Strength

User Note:ASTM A325/A325M are now included as a Grade within ASTM F3125.

A354-11 Standard Specification for Quenched and Tempered Alloy Steel Bolts, Studs, and Other Externally Threaded Fasteners

A370-15 Standard Test Methods and Definitions for Mechanical Testing of Steel Products

A449-14 Standard Specification for Hex Cap Screws, Bolts and Studs, Steel, Heat Treated, 120/105/90 ksi Minimum Tensile Strength, General Use

User Note:ASTM A490/A490M are now included as a Grade within ASTM F3125.

Sect A2.] REFERENCED SPECIFICATIONS, CODES AND STANDARDS 16.1-3

A500/A500M-13 Standard Specification for Cold-Formed Welded and Seam - less Carbon Steel Structural Tubing in Rounds and Shapes

A501/A501M-14 Standard Specification for Hot-Formed Welded and Seamless Carbon Steel Structural Tubing

A502-03 (2015) Standard Specification for Rivets, Steel, Structural

A514/A514M-14 Standard Specification for High-Yield-Strength, Quenched and Tempered Alloy Steel Plate, Suitable for Welding

A529/A529M-14 Standard Specification for High-Strength Carbon-Manganese Steel of Structural Quality

A563-15 Standard Specification for Carbon and Alloy Steel Nuts

A563M-07(2013) Standard Specification for Carbon and Alloy Steel Nuts (Metric)

A568/A568M-15 Standard Specification for Steel, Sheet, Carbon, Structural, and High-Strength, Low-Alloy, Hot-Rolled and Cold-Rolled, General Require - ments for

A572/A572M-15 Standard Specification for High-Strength Low-Alloy Colum - bium-Vanadium Structural Steel

A588/A588M-15 Standard Specification for High-Strength Low-Alloy Struc - tural Steel, up to 50 ksi [345 MPa] Minimum Yield Point, with Atmos pheric Corrosion Resistance

A606/A606M-15 Standard Specification for Steel, Sheet and Strip, High-Strength, Low-Alloy, Hot-Rolled and Cold-Rolled, with Improved Atmos pheric Cor - rosion Resistance

A618/A618M-04(2015) Standard Specification for Hot-Formed Welded and Seamless High-Strength Low-Alloy Structural Tubing

A668/A668M-15 Standard Specification for Steel Forgings, Carbon and Alloy, for General Industrial Use

A673/A673M-07(2012) Standard Specification for Sampling Procedure for Im - pact Testing of Structural Steel

A709/A709M-13a Standard Specification for Structural Steel for Bridges

A751-14a Standard Test Methods, Practices, and Terminology for Chemical Analysis of Steel Products

A847/A847M-14 Standard Specification for Cold-Formed Welded and Seam - less High-Strength, Low-Alloy Structural Tubing with Improved Atmospheric Corrosion Resistance

A913/A913M-15 Standard Specification for High-Strength Low-Alloy Steel Shapes of Structural Quality, Produced by Quenching and Self-Tempering Process (QST)

A992/A992M-11(2015) Standard Specification for Structural Steel Shapes

A1011/A1011M-14 Standard Specification for Steel, Sheet and Strip, Hot-Rolled, Carbon, Structural, High-Strength Low-Alloy, High-Strength Low-Alloy with Improved Formability, and Ultra-High Strength

A1043/A1043M-14 Standard Specification for Structural Steel with Low Yield to Tensile Ratio for Use in Buildings

A1065/A1065M-15 Standard Specification for Cold-Formed Electric-Fusion (Arc) Welded High-Strength Low-Alloy Structural Tubing in Shapes, with 50 ksi [345 MPa] Minimum Yield Point

16.1-4 REFERENCED SPECIFICATIONS, CODES AND STANDARDS [Sect A2.

Sect A2.] REFERENCED SPECIFICATIONS, CODES AND STANDARDS 16.1-5

A1066/A1066M-11(2015)e1 Standard Specification for High-Strength Low- Alloy Structural Steel Plate Produced by Thermo-Mechanical Controlled Process (TMCP)

A1085/A1085M-13 Standard Specification for Cold-Formed Welded Carbon Steel Hollow Structural Sections (HSS)

C567/C567M-14 Standard Test Method for Determining Density of Structural Lightweight Concrete

E119-15 Standard Test Methods for Fire Tests of Building Construction and Materials

E165/E165M-12 Standard Practice for Liquid Penetrant Examination for Gen eral Industry

E709-15 Standard Guide for Magnetic Particle Examination

F436-11 Standard Specification for Hardened Steel Washers

F436M-11 Standard Specification for Hardened Steel Washers (Metric)

F606/F606M-14a Standard Test Methods for Determining the Mechanical Prop - erties of Externally and Internally Threaded Fasteners, Washers, Direct Tension Indicators, and Rivets

F844-07a(2013) Standard Specification for Washers, Steel, Plain (Flat), Un - hardened for General Use

F959-15 Standard Specification for Compressible-Washer-Type Direct Tension Indicators for Use with Structural Fasteners

F959M-13 Standard Specification for Compressible-Washer-Type Direct Ten - sion Indicators for Use with Structural Fasteners (Metric)

F1554-15 Standard Specification for Anchor Bolts, Steel, 36, 55, and 105-ksi Yield Strength

User Note:ASTM F1554 is the most commonly referenced specification for anchor rods Grade and weldability must be specified.

User Note:ASTM F1852 and F2280 are now included as Grades within ASTM F3125.

F3043-14e1 Standard Specification for “Twist Off” Type Tension Control Struc - tural Bolt/Nut/Washer Assemblies, Alloy Steel, Heat Treated, 200 ksi Mini mum Tensile Strength

F3111-14 Standard Specification for Heavy Hex Structural Bolt/Nut/Washer Assemblies, Alloy Steel, Heat Treated, 200 ksi Minimum Tensile Strength

F3125/F3125M-15 Standard Specification for High Strength Structural Bolts, Steel and Alloy Steel, Heat Treated, 120 ksi (830 MPa) and 150 ksi (1040 MPa) Minimum Tensile Strength, Inch and Metric Dimensions

AWS A5.1/A5.1M:2012 Specification for Carbon Steel Electrodes for Shielded Metal Arc Welding

AWS A5.5/A5.5M:2014 Specification for Low-Alloy Steel Electrodes for ShieldedMetal Arc Welding

AWS A5.17/A5.17M:1997 (R2007) Specification for Carbon Steel Electrodes and Fluxes for Submerged Arc Welding

AWS A5.18/A5.18M:2005 Specification for Carbon Steel Electrodes and Rods for Gas Shielded Arc Welding

AWS A5.20/A5.20M:2005 (R2015) Specification for Carbon Steel Electrodes for Flux Cored Arc Welding

AWS A5.23/A5.23M:2011 Specification for Low-Alloy Steel Electrodes and Fluxes for Submerged Arc Welding

AWS A5.25/A5.25M:1997 (R2009) Specification for Carbon and Low-Alloy Steel Electrodes and Fluxes for Electroslag Welding

AWS A5.26/A5.26M:1997 (R2009) Specification for Carbon and Low-Alloy Steel Electrodes for Electrogas Welding

AWS A5.28/A5.28M:2005 (R2015) Specification for Low-Alloy Steel Elec - trodes and Rods for Gas Shielded Arc Welding

AWS A5.29/A5.29M:2010 Specification for Low-Alloy Steel Electrodes for Flux Cored Arc Welding

AWS A5.32/A5.32M:2011 Welding Consumables—Gases and Gas Mixtures for Fusion Welding and Allied Processes

AWS A5.36/A5.36M:2012 Specification for Carbon and Low-Alloy Steel Flux Cored Electrodes for Flux Cored Arc Welding and Metal Cored Electrodes for Gas Metal Arc Welding

AWS B5.1:2013-AMD1 Specification for the Qualification of Welding In - spectors

AWS D1.1/D1.1M:2015 Structural Welding Code—Steel

AWS D1.3/D1.3M:2008 Structural Welding Code—Sheet Steel

(h) Research Council on Structural Connections (RCSC)

Specification for Structural Joints Using High-Strength Bolts, 2014

ANSI/SDI QA/QC-2011 Standard for Quality Control and Quality Assurance for Installation of Steel Deck

Structural Steel Materials

Material test reports from fabricators or testing laboratories provide adequate proof of compliance with ASTM standards specified in Section A3.1a For hot-rolled structural shapes, plates, and bars, testing must adhere to ASTM A6/A6M, while sheets require compliance with ASTM A568/A568M Additionally, tubing and pipe must meet the relevant ASTM standards for their specific product forms.

Structural steel material conforming to one of the following ASTM specifications is approved for use under this Specification:

16.1-6 REFERENCED SPECIFICATIONS, CODES AND STANDARDS [Sect A2.

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ASTM A606/A606M ASTM A1011/A1011M SS, HSLAS, AND HSLAS-F

Unidentified steel can be utilized in structural components only if its failure does not compromise the overall or local strength of the structure This application requires the approval of the engineer of record to ensure safety and compliance.

Unidentified steel can be utilized for components such as curb plates and shims, where specific mechanical properties and weldability are not critical.

ASTM A6/A6M defines hot-rolled shapes with a flange thickness greater than 2 inches (50 mm) as rolled heavy shapes These shapes, which are subjected to primary tensile forces from tension or flexure and are connected using complete-joint-penetration groove welds, must adhere to specific requirements Structural design documents must mandate that these shapes come with Charpy V-notch (CVN) impact test results per ASTM A6/A6M, Supplementary Requirement S30 The impact test should achieve a minimum average absorbed energy of 20 ft-lb (27 J) at a maximum temperature of +70°F (+21°C).

The requirements outlined in this section are not applicable when splices and connections are created through bolting However, when a rolled heavy shape is welded to another shape using groove welds, the requirements only pertain to the shape that has weld metal fused throughout its cross section.

User Note: Additional requirements for rolled heavy-shape welded joints are given in Sections J1.5, J1.6, J2.6 and M2.2.

Built-up heavy shapes, defined as cross sections with plates thicker than 2 inches (50 mm), are utilized in structural applications where they experience primary tensile forces from tension or flexure These members must be spliced or connected using complete-joint-penetration groove welds that penetrate the full thickness of the plates Structural design documents should mandate that the steel is accompanied by Charpy V-notch impact test results in accordance with ASTM A6/A6M, Supplementary Requirement S5 The impact tests must follow ASTM A673/A673M, Frequency P, ensuring a minimum average absorbed energy of 20 ft-lb (27 J) at a maximum temperature of +70°F (+21°C).

When welding a built-up heavy shape to another member with groove welds, it is essential to note that the requirements pertain solely to the shape that has the weld metal fused throughout its cross section.

User Note: Additional requirements for built-up heavy-shape welded joints are given in Sections J1.5, J1.6, J2.6 and M2.2.

Steel Castings and Forgings

Steel castings and forgings must meet ASTM standards for structural applications, ensuring they possess adequate strength, ductility, weldability, and toughness Compliance with these standards is demonstrated through test reports generated according to ASTM reference guidelines.

Bolts, Washers and Nuts

Bolt, washer and nut material conforming to one of the following ASTM specifications is approved for use under this Specification:

User Note: ASTM F3125 is an umbrella standard that incorporates Grades A325, A325M, A490, A490M, F1852 and F2280, which were previously separate standards.

(d) Compressible-Washer-Type Direct Tension Indicators

Manufacturer’s certification shall constitute sufficient evidence of conformity with the standards.

Anchor Rods and Threaded Rods

Anchor rod and threaded rod material conforming to one of the following ASTM specifications is approved for use under this Specification:

User Note: ASTM F1554 is the preferred material specification for anchor rods.

ASTM A449 material is permitted for high-strength anchor rods and threaded rods of any diameter.

Threads on anchor rods and threaded rods shall conform to the Unified Standard Series of ASME B18.2.6 and shall have Class 2A tolerances

Consumables for Welding

Filler metals and fluxes shall conform to one of the following specifications of the American Welding Society:

Headed Stud Anchors

Steel headed stud anchors shall conform to the requirements of the Structural

Manufacturer’s certification shall constitute sufficient evidence of conformity with AWS D1.1/D1.1M.

A4 STRUCTURAL DESIGN DRAWINGS AND SPECIFICATIONS

The structural design drawings and specifications shall meet the requirements of the

The Code of Standard Practice refers to "design documents" instead of "design drawings" to encompass both traditional paper drawings and electronic models Additionally, the term "fabrication documents" is employed to provide a broader understanding of the relevant materials.

“shop drawings,” and “erection documents” is used in place of “erection drawings.” The use of “drawings” in this standard is not intended to create a conflict.

User Note: Provisions in this Specification contain information that is to be shown on design drawings These include:

• Section A3.1c: Rolled heavy shapes where alternate core Charpy V-notch tough - ness (CVN) is required

• Section A3.1d: Built-up heavy shapes where CVN toughness is required

• Section J3.1: Locations of connections using pretensioned bolts

Other information needed by the fabricator or erector should be shown on design drawings, including:

• Fatigue details requiring nondestructive testing

• Indication of complete-joint-penetration (CJP) groove welds subject to tension (Chapter N)

This chapter addresses general requirements for the design of steel structures applicable to all chapters of this Specification

The chapter is organized as follows:

B6 Quality Control and Quality Assurance

The design of members and connections shall be consistent with the intended behav- ior of the framing system and the assumptions made in the structural analysis.

The loads, nominal loads, and load combinations must adhere to the relevant building code If no building code is available, these specifications should align with the Minimum Design Loads guidelines.

Associated Criteria for Buildings and Other Structures(ASCE/SEI 7).

User Note: When using ASCE/SEI 7 for design according to Section B3.1

(LRFD), the load combinations in ASCE/SEI 7 Section 2.3 apply For design according to Section B3.2 (ASD), the load combinations in ASCE/SEI 7 Section 2.4 apply.

Design shall be such that no applicable strength or serviceability limit state shall be exceeded when the structure is subjected to all applicable load combinations.

Design for strength shall be performed according to the provisions for load and resistance factor design (LRFD) or to the provisions for allowable strength design (ASD).

User Note: The term “design”, as used in this Specification, is defined in the

DESIGN REQUIREMENTS

Design for Strength Using Load and Resistance Factor Design (LRFD) 12 2 Design for Strength Using Allowable Strength Design (ASD)

Designing in accordance with load and resistance factor design (LRFD) meets the requirements outlined in this Specification, provided that the design strength of each structural component is equal to or greater than the required strength calculated from the LRFD load combinations All aspects of this Specification, with the exception of Section B3.2, are applicable.

Design shall be performed in accordance with Equation B3-1:

R u =required strength using LRFD load combinations

R n =nominal strength φ =resistance factor φR n ign strength

The nominal strength, R n , and the resistance factor, φ, for the applicable limit states are specified in Chapters D through K.

2 Design for Strength Using Allowable Strength Design (ASD)

Designing in accordance with allowable strength design (ASD) meets the criteria outlined in this Specification when the allowable strength of each structural component is equal to or greater than the required strength calculated using ASD load combinations All sections of this Specification, with the exception of Section B3.1, are applicable.

Design shall be performed in accordance with Equation B3-2:

R a =required strength using ASD load combinations

The nominal strength, R n , and the safety factor, Ω, for the applicable limit states are specified in Chapters D through K.

Required Strength

The required strength of structural members and connections shall be determined by structural analysis for the applicable load combinations as stipulated in Section B2.

Design by elastic or inelastic analysis is permitted Requirements for analysis are stipulated in Chapter C and Appendix 1.

The flexural strength required for indeterminate beams with compact sections, which carry only gravity loads and meet the unbraced length criteria outlined in Section F13.5, can be calculated as 90% of the negative moments at the support points These moments are generated by gravity loading and must be determined through an elastic analysis that adheres to the standards set in Chapter.

C, provided that the maximum positive moment is increased by one-tenth of the average negative moment determined by an elastic analysis This moment redistribution is not permitted for moments in members with F y exceeding 65 ksi (450 MPa), for moments produced by loading on cantilevers, for design using partially restrained (PR) moment connections, or for design by inelastic analysis using the provisions of Appendix 1 This moment redistribution is permitted for design according to Section B3.1 (LRFD) and for design according to Section B3.2 (ASD) The required axial strength shall not exceed 0.15φ c F y A g for LRFD or 0.15F y A g /Ω c for ASD, where φ c and Ω c are determined from Section E1, A g =gross area of member, in 2 (mm 2 ), and

F y =specified minimum yield stress, ksi (MPa).

Design of Connections and Supports

Connection elements shall be designed in accordance with the provisions of Chapters

In designing connections, the forces and deformations must align with the expected performance and design assumptions of the structure Self-limiting inelastic deformations are acceptable for connections Additionally, beams, girders, and trusses must be secured against rotation at support points unless analytical evidence demonstrates that such restraint is unnecessary.

User Note:Section 3.1.2 of the Code of Standard Practice addresses communi- cation of necessary information for the design of connections.

A simple connection transmits minimal moments and is assumed to permit unrestricted relative rotation between connected framing elements during structural analysis It must possess adequate rotation capacity to accommodate the necessary rotation determined by this analysis.

Two types of moment connections, fully restrained and partially restrained, are permitted, as specified below.

(a) Fully Restrained (FR) Moment Connections

A fully restrained (FR) moment connection effectively transfers moments while minimizing rotation between connected members In structural analysis, this connection is treated as having no relative rotation To ensure structural integrity, an FR connection must possess adequate strength and stiffness to preserve the initial angle between the connected members at strength limit states.

(b) Partially Restrained (PR) Moment Connections

Partially restrained (PR) moment connections are designed to transfer moments while allowing for some rotation between connected members, making it essential to consider their force-deformation response characteristics in structural analysis The documentation of a PR connection's response characteristics can be found in technical literature or established through analytical and experimental methods Additionally, it is crucial that the component elements of a PR connection possess adequate strength, stiffness, and deformation capacity to meet the requirements at strength limit states.

Design of Diaphragms and Collectors

Diaphragms and collectors must be engineered to withstand forces arising from specified loads in Section B2 Their design should adhere to the guidelines outlined in Chapters C through K, as relevant.

Design of Anchorages to Concrete

Anchorage between steel and concrete acting compositely shall be designed in accordance with Chapter I The design of column bases and anchor rods shall be in accordance with Chapter J.

Design for Stability

The structure and its elements shall be designed for stability in accordance withChapter C.

Design for Serviceability

The overall structure and the individual members and connections shall be evaluated for serviceability limit states in accordance with Chapter L.

Design for Structural Integrity

When design for structural integrity is required by the applicable building code, the requirements in this section shall be met.

(a) Column splices shall have a nominal tensile strength equal to or greater than

D +Lfor the area tributary to the column between the splice and the splice or base immediately below, where

Beam and girder end connections must possess a minimum nominal axial tensile strength that is either two-thirds of the vertical shear strength required for design under Section B3.1 (LRFD) or equal to the vertical shear strength required for design under Section B3.2 (ASD), with a minimum threshold of 10 kips in both scenarios.

End connections of bracing column members must possess a nominal tensile strength that meets or exceeds 1% of two-thirds of the required axial strength of the column for LRFD design, as outlined in Section B3.1, or at least 1% of the required axial strength for ASD design, as specified in Section B3.2.

The strength requirements for structural integrity must be assessed independently from other criteria To meet these requirements, connections utilizing bearing bolts with short-slotted holes aligned with the tension force direction and allowing for inelastic deformation are acceptable.

Design for Ponding

A structural analysis of the roof system is essential to verify its strength and stability, particularly under ponding conditions, unless the roof design effectively prevents water accumulation.

Methods of evaluating stability and strength under ponding conditions are provided in Appendix 2.

Design for Fatigue

Fatigue should be evaluated as outlined in Appendix 3 for members and their connections that experience repeated loading However, it is not necessary to account for fatigue in relation to seismic effects or wind loading on standard lateral force-resisting systems and building enclosure components.

Design for Fire Conditions

Appendix 4 outlines two design methods for fire conditions: (a) analysis and (b) qualification testing Adhering to the fire-protection requirements specified in the relevant building code will fulfill the criteria set forth in Appendix 4.

This section is not intended to create or imply a contractual requirement for the engineer of record responsible for the structural design or any other member of the design team.

Design by qualification testing is the standard method outlined in building codes, with architects typically responsible for specifying and coordinating fire protection requirements in most projects In contrast, design by analysis represents a modern engineering approach to fire safety Determining who is accountable for fire condition design is a contractual issue that must be clarified for each individual project.

Design for Corrosion Effects

Where corrosion could impair the strength or serviceability of a structure, structural components shall be designed to tolerate corrosion or shall be protected against corrosion.

Classification of Sections for Local Buckling

Members subjected to axial compression are categorized into nonslender and slender-element sections Nonslender-element sections must adhere to specific width-to-thickness ratios for their compression elements, which should not exceed the limits outlined in Table B4.1a.

If the width-to-thickness ratio of any compression element exceeds λ r , the section is a slender-element section.

Sections subject to flexure are categorized into compact, noncompact, or slender-element classifications A section is deemed compact if its flanges are continuously connected to the web and the width-to-thickness ratios of its compression elements do not surpass the limiting ratios, λ p, specified in Table B4.1b If any compression element's width-to-thickness ratio exceeds λ p but remains below λ r, the section is classified as noncompact Conversely, if the width-to-thickness ratio of any compression element exceeds λ r, the section is identified as a slender-element section.

For unstiffened elements supported along only one edge parallel to the direction of the compression force, the width shall be taken as follows:

(a) For flanges of I-shaped members and tees, the width, b, is one-half the full-flange width, b f

(b) For legs of angles and flanges of channels and zees, the width, b, is the full leg or flange width.

(c) For plates, the width, b, is the distance from the free edge to the first row of fasteners or line of welds.

(d) For stems of tees, d is the full depth of the section.

User Note: Refer to Table B4.1 for the graphic representation of unstiffened element dimensions.

For stiffened elements supported along two edges parallel to the direction of the compression force, the width shall be taken as follows:

In rolled section webs, the clear distance between the flanges is defined as 'h', which excludes the fillet at each flange Additionally, 'h c' represents twice the distance from the centroid to the inside face of the compression flange, also accounting for the fillet or corner radius.

In built-up section webs, the parameter 'h' represents the distance between adjacent fastener lines or the clear space between flanges when welding is utilized The term 'h c' denotes twice the distance from the centroid to the nearest fastener line at the compression flange or its inside face, while 'h p' indicates twice the distance from the plastic neutral axis to the nearest fastener line at the compression flange or its inside face when welds are employed.

TABLE B4.1a Width-to-Thickness Ratios: Compression Elements

Members Subject to Axial Compression

Limiting Width-to-Thickness Ratio ␭ r

I-shaped sections, plates projecting from rolled I-shaped sections, outstanding legs of pairs of angles connected with continuous contact, flanges of channels, and flanges of tees

I-shaped sections and plates or angle legs projecting from built-up I-shaped sections

Legs of single angles, legs of double angles with separators, and all other unstiffened elements

Webs of doubly symmetric rolled and built-up I-shaped sections and channels

Flange cover plates and diaphragm plates between lines of fasteners or welds

Stiff ened Elements Unstiff ened Elements

[a] k c = 4兾 h t / w , but shall not be taken less than 0.35 nor greater than 0.76 for calculation purposes

TABLE B4.1b Width-to-Thickness Ratios: Compression Elements

Limiting Width-to-Thickness Ratio

I-shaped sections, channels, and tees

Flanges of doubly and singly symmetric

I-shaped sections and channels in flexure about the minor axis

(c) For flange or diaphragm plates in built-up sections, the width, b, is the distance between adjacent lines of fasteners or lines of welds.

For rectangular hollow structural sections (HSS), the flange width (b) is defined as the clear distance between the webs, minus the inside corner radius on both sides The web height (h) is the clear distance between the flanges, also reduced by the inside corner radius on each side If the corner radius is unknown, it should be calculated as the outside dimension minus three times the wall thickness, which is determined according to Section B4.2 In the case of box sections and other stiffened elements, the width (b) refers to the clear distance between the stiffening elements.

(f) For perforated cover plates, bis the transverse distance between the nearest line of fasteners, and the net area of the plate is taken at the widest hole.

TABLE B4.1b (continued) Width-to-Thickness Ratios: Compression Elements

Limiting Width-to-Thickness Ratio

Width-to- Thick- ness Ratio

Webs of doubly symmetric I- shaped sections and channels

Flange cover plates and diaphragm plates between lines of fasteners or welds

[a] k c = 4 兾 , shall not be taken less than 0.35 nor greater than 0.76 for calculation purposes

For slender web I-shaped members and major-axis bending of compact and noncompact web built-up I-shaped members with a section modulus ratio (S xt /S xc) of 0.7 or greater, the formula is F L = 0.7F y In contrast, for major-axis bending of compact and noncompact web built-up I-shaped members with a section modulus ratio of less than 0.7, the formula is F L = F y S xt /S xc, which must be at least 0.5F y Here, S xc and S xt represent the elastic section moduli for compression and tension flanges, respectively, expressed in mm³.

[c] M y is the moment at yielding of the extreme fiber M p = F y Z x , plastic bending moment, kip-in (N-mm), where

Z x = plastic section modulus taken about x-axis, in 3 (mm 3 ).

E = modulus of elasticity of steel = 29,000 ksi (200 000 MPa) ENA = elastic neutral axis

F y = specified minimum yield stress, ksi (MPa) PNA = plastic neutral axis h t / w h h

User Note:Refer to Table B4.1 for the graphic representation of stiffened element dimensions.

For tapered flanges of rolled sections, the thickness is the nominal value halfway between the free edge and the corresponding face of the web.

Design Wall Thickness for HSS

The design wall thickness, denoted as t, is crucial for calculations related to the wall thickness of hollow structural sections (HSS) For box sections and HSS manufactured in compliance with ASTM A1065/A1065M or ASTM A1085/A1085M, the design wall thickness is equivalent to the nominal thickness However, for HSS produced under other approved standards, the design wall thickness should be calculated as 0.93 times the nominal wall thickness.

According to this Specification, a pipe can be designed for round HSS sections, provided it meets the requirements of ASTM A53/A53M Grade B and adheres to the relevant limitations outlined in this Specification.

Gross and Net Area Determination

The gross area, A g , of a member is the total cross-sectional area.

The net area, A n , of a member is the sum of the products of the thickness and the net width of each element computed as follows:

In computing net area for tension and shear, the width of a bolt hole shall be taken as 1 /16in (2 mm) greater than the nominal dimension of the hole.

To calculate the net width of a part with a series of holes arranged in a diagonal or zigzag pattern, subtract the total diameter or slot dimensions of all holes from the gross width Additionally, for each gage space in the chain, add 2/4g, where g represents the transverse center-to-center spacing (gage) between fastener gage lines, and s denotes the longitudinal center-to-center spacing (pitch) of consecutive holes.

For angles, the gage for holes in opposite adjacent legs shall be the sum of the gages from the back of the angles less the thickness.

When calculating the net area (A n) for slotted hot-rolled steel (HSS) welded to a gusset plate, it is essential to consider the gross area and subtract the area removed to create the slot This removal is determined by multiplying the thickness of the material by the total width of the slot.

Sect B7.] EVALUATION OF EXISTING STRUCTURES 16.1-21

In determining the net area across plug or slot welds, the weld metal shall not be considered as adding to the net area.

For members without holes, the net area, A n , is equal to the gross area, A g

Shop drawings, fabrication, shop painting and erection shall satisfy the requirements stipulated in Chapter M

B6 QUALITY CONTROL AND QUALITY ASSURANCE

Quality control and quality assurance activities shall satisfy the requirements stipulated in Chapter N.

The evaluation of existing structures shall satisfy the requirements stipulated inAppendix 5.

DESIGN FOR STABILITY

Direct Analysis Method of Design

The direct analysis method for design is applicable to all structures, utilizing either elastic or inelastic analysis When employing elastic analysis, required strengths must be determined per Section C2, while available strengths are calculated according to Section C3 For advanced analysis design, compliance with Section 1.1 and either Section 1.2 or 1.3 of Appendix 1 is essential.

Sect C2.] CALCULATION OF REQUIRED STRENGTHS 16.1-23

Alternative Methods of Design

The effective length method and the first-order analysis method, outlined in Appendix 7, utilize elastic analysis and serve as acceptable alternatives to the direct analysis method for structures meeting the specified limitations.

In the direct analysis method of design, component strengths must be established through an elastic analysis as outlined in Section C2.1 This analysis should also account for initial imperfections per Section C2.2 and incorporate adjustments to stiffness as specified in Section C2.3.

General Analysis Requirements

The analysis of the structure shall conform to the following requirements:

The analysis must account for flexural, shear, and axial deformations of members, along with any component and connection deformations affecting structural displacements It is essential to include reductions in all stiffnesses that impact the stability of the structure, as outlined in Section C2.3.

The analysis must be a second-order analysis that takes into account both P-Δ and P-δ effects However, the P-δ effect can be disregarded if certain conditions are met: the structure primarily supports gravity loads through vertical columns, walls, or frames; the ratio of maximum second-order drift to maximum first-order drift is 1.7 or less for all stories; and no more than one-third of the total gravity load is supported by columns within moment-resisting frames in the direction of interest It is essential to consider these factors in all cases.

P-δeffects in the evaluation of individual members subject to compression and flexure

User Note:A P-Δ-only second-order analysis (one that neglects the effects of

P-δon the response of the structure) is permitted under the conditions listed.

To account for P-δ effects in assessing individual members, it is essential to apply the B1 multiplier, as outlined in Appendix 8, to determine the necessary flexural strength of the member.

Use of the approximate method of second-order analysis provided in Appendix 8 is permitted

(c) The analysis shall consider all gravity and other applied loads that may influence the stability of the structure

16.1-24 CALCULATION OF REQUIRED STRENGTHS [Sect C2.

When analyzing structural integrity, it is crucial to account for all gravity loads, including those on leaning columns and other components not involved in the lateral force-resisting system.

In LRFD design, second-order analysis must be performed using LRFD load combinations Conversely, for ASD design, second-order analysis should be conducted using 1.6 times the ASD load combinations, with the final results divided by 1.6 to determine the necessary component strengths.

Consideration of Initial System Imperfections

The stability of a structure is influenced by initial imperfections at the intersection points of its members This can be addressed through direct modeling of these imperfections during analysis, as outlined in Section C2.2a, or by applying notional loads in accordance with Section C2.2b.

In structural analysis, it is essential to consider system imperfections, particularly the out-of-plumbness of columns, which are critical in typical building structures While initial out-of-straightness of individual members is not required in this analysis, it is addressed in the compression member design provisions outlined in Chapter E, provided it remains within the limits established by the Code of Standard Practice Additionally, Appendix 1, Section 1.2 offers an extension to the direct analysis method that incorporates the modeling of member imperfections, ensuring a comprehensive approach to structural integrity.

In structural analysis, it is essential to account for initial system imperfections by incorporating them directly into the evaluation This involves analyzing the structure with member intersections that are shifted from their nominal positions The design must consider the maximum extent of these initial displacements, ensuring that the displacement pattern chosen creates the most significant destabilizing impact on the structure.

When modeling imperfections, it is essential to consider initial displacements that resemble both loading-induced displacements and expected buckling modes The size of these initial displacements should align with the permissible construction tolerances outlined in the relevant Code.

Standard Practiceor other governing requirements, or on actual imperfections if known.

Sect C2.] CALCULATION OF REQUIRED STRENGTHS 16.1-25

In the analysis of gravity load-supporting structures utilizing vertical columns, walls, or frames, if the ratio of maximum second-order story drift to maximum first-order story drift is 1.7 or less across all stories, initial system imperfections may be incorporated in the analysis for gravity-only load combinations However, these imperfections should not be included in analyses involving applied lateral loads.

2b Use of Notional Loads to Represent Imperfections

In structures that primarily bear gravity loads through vertical columns, walls, or frames, it is acceptable to utilize notional loads to account for initial system imperfections at the intersections of members These notional loads should be applied to a model of the structure that reflects its nominal geometry.

The notional load concept applies universally to various structures and addresses imperfections at both member intersection points and along members However, the specific requirements outlined in Sections C2.2b(a) through C2.2b(d) are relevant only to the designated class of structures and the identified types of system imperfections.

Notional loads must be applied as lateral loads at every level and are additive to other lateral loads These loads should be included in all load combinations, except as specified in Section C2.2b(d) The specific magnitude of the notional loads will be determined accordingly.

N i =notional load applied at level i, kips (N)

Y i =gravity load applied at level ifrom the LRFD load combination or ASD load combination, as applicable, kips (N)

Using notional loads can introduce minor fictitious base shears in a structure To accurately determine the horizontal reactions at the foundation, it is essential to apply an additional horizontal force at the base, equal and opposite to the total of all notional loads This force should be distributed among the vertical load-carrying elements in proportion to the gravity loads they support Moreover, while notional loads may cause fictitious base shears, they can also result in real overturning effects that must be considered.

The notional load at each level, denoted as N i, must be distributed in alignment with the gravity load for that level These notional loads should be applied in the direction that creates the most significant destabilizing impact.

For building structures, the notional load direction requirements can be met by considering two orthogonal directions of notional load application for load combinations without lateral loading, applying both positive and negative loads in the same direction at all levels In cases where lateral loading is included, all notional loads should be applied in the direction of the resultant of the combined lateral loads.

The notional load coefficient of 0.002 in Equation C2-1 is derived from a nominal initial story out-of-plumbness ratio of 1/500 If a different maximum out-of-plumbness ratio is warranted, it is acceptable to proportionally adjust the notional load coefficient accordingly.

According to the Code of Standard Practice, a maximum tolerance of 1/500 is allowed for column plumbness, but in certain situations, stricter tolerances related to the plan location of columns may take precedence, necessitating a tighter plumbness standard.

For structures with a maximum second-order drift to maximum first-order drift ratio of 1.7 or less, determined using LRFD or adjusted ASD load combinations, the notional load (N i) may be applied solely in gravity-only load combinations, excluding any scenarios that involve additional lateral loads.

Adjustments to Stiffness

The analysis of the structure to determine the required strengths of components shall use reduced stiffnesses, as follows:

To enhance structural stability, a reduction factor of 0.80 will be applied to all relevant stiffnesses This reduction can be uniformly implemented across all stiffness components within the structure.

Applying stiffness reduction selectively to certain structural members may lead to artificial distortion and unintended force redistribution under load To prevent these issues, it is advisable to apply stiffness reduction uniformly across all members, including those that do not significantly contribute to the structure's stability.

An additional factor, τ b, will be applied to the flexural stiffnesses of all members that contribute to the stability of the structure For noncomposite members, τ b is defined in accordance with specific guidelines outlined in Section I1.5, which also includes definitions for composite members.

16.1-26 CALCULATION OF REQUIRED STRENGTHS [Sect C2.

Sect C3.] CALCULATION OF AVAILABLE STRENGTHS 16.1-27

(2) When αP r /P ns >0.5 τ b =4(αP r /P ns )[1−(αP r /P ns )] (C2-2b) where α =1.0 (LRFD); α =1.6 (ASD)

P r =required axial compressive strength using LRFD or ASD load combinations, kips (N)

P ns =cross-section compressive strength; for nonslender-element sections, P ns

= F y A g , and for slender-element sections, P ns = F y A e , where A e is as defined in Section E7, kips (N)

In the analysis of structural steel members, it is essential to apply 0.8 times the nominal elastic flexural stiffness and 0.8 times other nominal elastic stiffness values, as stipulated in Sections (a) and (b).

In structures governed by Section C2.2b, it is allowed to use τ b = 1.0 for all noncomposite members instead of τ b < 1.0 when αP r /P ns > 0.5, provided a notional load of 0.001αY i is applied at all levels as defined in Section C2.2b(a) This load must be directed according to Section C2.2b(b) and included in all load combinations Additionally, these notional loads are to be incorporated alongside any loads addressing initial imperfections at member intersections and are exempt from the stipulations outlined in Section C2.2b(d).

When components made from materials other than structural steel are deemed essential for the stability of a structure, any applicable codes and specifications that mandate increased reductions in stiffness must be enforced for those components.

For the direct analysis method of design, the available strengths of members and connections shall be calculated in accordance with the provisions of Chapters D through

K, as applicable, with no further consideration of overall structure stability The effective length for flexural buckling of all members shall be taken as the unbraced length unless a smaller value is justified by rational analysis

Bracing intended to define the unbraced lengths of members shall have sufficient stiffness and strength to control member movement at the braced points

User Note: Methods of satisfying this bracing requirement are provided in

Appendix 6 The requirements of Appendix 6 are not applicable to bracing that is included in the design of the lateral force-resisting system of the overall structure

DESIGN OF MEMBERS FOR TENSION

This chapter applies to members subject to axial tension

User Note:For cases not included in this chapter, the following sections apply:

• Chapter H Members subject to combined axial tension and flexure

• J4.3 Block shear rupture strength at end connections of tension members

There is no maximum slenderness limit for members in tension.

User Note:For members designed on the basis of tension, the slenderness ratio,

L /r, preferably should not exceed 300 This suggestion does not apply to rods or hangers in tension.

The design tensile strength, φ t P n, and the allowable tensile strength, P n /Ω t, for tension members must be determined by the lower value derived from the limit states of tensile yielding in the gross section and tensile rupture in the net section.

(a) For tensile yielding in the gross section

P n =F y A g (D2-1) φ t =0.90 (LRFD) Ω t =1.67 (ASD) (b) For tensile rupture in the net section

DESIGN OF MEMBERS FOR TENSION

Tensile Strength

The design tensile strength (φ t P n ) and allowable tensile strength (P n /Ω t ) for pin-connected members must be determined by the lower value resulting from the limit states of tensile rupture, shear rupture, bearing, and yielding.

TABLE D3.1 Shear Lag Factors for Connections to Tension Members

Case Shear Lag Factor, U Example

All tension members where the tension load is transmitted directly to each of the cross-sectional elements by fasteners or welds (except as in Cases 4, 5 and 6).

Tension members, excluding Hollow Structural Sections (HSS), transmit tension loads through fasteners or a combination of longitudinal and transverse welds to some, but not all, cross-sectional elements Additionally, Case 7 is applicable for Wide Flange (W) sections.

M, S and HP shapes (For angles, Case 8 is permitted to be used.)

All tension members where the tension load is transmitted only by transverse welds to some but not all of the cross-sectional elements.

Plates, angles, channels with welds at heels, tees, and W-shapes with connected elements, where the tension load is transmitted by longitudinal welds only See Case 2 for definition of x –.

Round HSS with a single concentric gusset plate through slots in the HSS.

Rectangular HSS with a single concentric gusset plate with two side gusset plates

W-, M-, S- or HP- shapes, or tees cut from these shapes.

(If U is calculated per Case 2, the larger value is permitted to be used.)

(If U is calculated per Case 2, the larger value is permitted to be used.)

A n = area of the directly connected elements x x x x

Flange connections should utilize three or more fasteners per line aligned with the loading direction Additionally, web connections must have four or more fasteners per line in the same direction If there are fewer than three fasteners per line aligned with the loading direction, refer to Case 2 for guidance.

In structural engineering, key dimensions for hollow structural sections (HSS) are critical for accurate design and analysis The overall width (B) of a rectangular HSS member is measured at a 90° angle to the connection plane, while the outside diameter (D) is applicable for round HSS The overall height (H) of the rectangular member is taken in the plane of the connection, and the depth of the section (d) is essential, particularly for tees, where it refers to the depth from which the tee was cut Additionally, the length of the connection (l), the width of the plate (w), and the eccentricity of the connection (x) are vital parameters to consider in structural calculations.

[a] , where l 1 and l 2 shall not be less than 4 times the weld size.

1 AISC_PART 16_A_Spec A-D (1-32).qxp_15th_Ed._2016 2019-02-26 10:43 AM Page 30

(a) For tensile rupture on the net effective area

P n =F u (2tb e ) (D5-1) φ t =0.75 (LRFD) Ω t =2.00 (ASD) (b) For shear rupture on the effective area

P n =0.6F u A sf (D5-2) φ sf =0.75 (LRFD) Ω sf =2.00 (ASD) where

In shear failure analysis, the area on the shear failure path is denoted in square millimeters (mm²) The shortest distance from the edge of the pin hole to the edge of the member, measured parallel to the force direction, is represented as 'a' in inches (mm) The effective edge distance, 'b_e', is calculated using the formula 2t + 0.63 inches (or 2t + 16 mm), but it should not exceed the actual distance from the edge of the hole to the edge of the part, measured perpendicular to the applied force The diameter of the pin is denoted as 'd' in inches (mm), while 't' represents the thickness of the plate in millimeters For bearing on the projected area of the pin, refer to Section J7.

(d) For yielding on the gross section, use Section D2(a).

Dimensional Requirements

Pin-connected members shall meet the following requirements:

(a) The pin hole shall be located midway between the edges of the member in the direction normal to the applied force.

(b) When the pin is expected to provide for relative movement between connected parts while under full load, the diameter of the pin hole shall not be more than

1/32in (1 mm) greater than the diameter of the pin

The width of the plate at the pin hole must be at least 2b e + d, and the minimum extension, denoted as 'a', beyond the bearing end of the pin hole, parallel to the member's axis, should not be less than 1.33b e.

Corners beyond the pin hole may be cut at a 45° angle to the member's axis, as long as the net area beyond the pin hole, measured on a plane perpendicular to the cut, meets or exceeds the area required parallel to the member's axis.

The available tensile strength of eyebars shall be determined in accordance with Section D2, withA g taken as the cross-sectional area of the body.

For calculation purposes, the width of the body of the eyebars shall not exceed eight times its thickness.

Eyebars shall meet the following requirements:

Eyebars must maintain a consistent thickness and should not feature reinforcements at the pin holes Additionally, they should have circular heads that are concentric with the pin holes It is essential that the radius of the transition between the circular head and the body of the eyebar is at least equal to the diameter of the head.

The pin diameter must be at least seven-eighths the width of the eyebar body, while the pin-hole diameter should not exceed the pin diameter by more than 1/32 inch (1 mm).

(d) For steels having F y greater than 70 ksi (485 MPa), the hole diameter shall not exceed five times the plate thickness, and the width of the eyebar body shall be reduced accordingly.

(e) A thickness of less than 1 /2in (13 mm) is permissible only if external nuts are provided to tighten pin plates and filler plates into snug contact.

The distance from the edge of the hole to the edge of the plate, measured perpendicular to the applied load, must exceed two-thirds and, for calculation purposes, should not exceed three-fourths of the width of the eyebar body.

DESIGN OF MEMBERS FOR COMPRESSION

This chapter addresses members subject to axial compression

E3 Flexural Buckling of Members without Slender Elements

E4 Torsional and Flexural-Torsional Buckling of Single Angles and Members without Slender Elements

• H1 – H2 Members subject to combined axial compression and flexure

• H3 Members subject to axial compression and torsion

• J4.4 Compressive strength of connecting elements

The design compressive strength, φ c P n , and the allowable compressive strength,

The nominal compressive strength, P n , shall be the lowest value obtained based on the applicable limit states of flexural buckling, torsional buckling, and flexural-torsional buckling φ c =0.90 (LRFD) Ω c =1.67 (ASD)

TABLE USER NOTE E1.1 Selection Table for the Application of

Sections in Limit Sections in Limit Chapter E States Chapter E States

Unsymmetrical shapes other than single angles

FB = flexural buckling, TB = torsional buckling, FTB = flexural-torsional buckling, LB = local buckling, N/A = not applicable

Without Slender Elements With Slender Elements

2 AISC_PART 16_A_Spec E-F (33-69)_15th_Ed._2016 2016-11-14 1:20 PM Page 34 (Black plate)

Sect E3.] FLEXURAL BUCKLING OF MEMBERS WITHOUT SLENDER ELEMENTS 16.1-35

The effective length, L c , for calculation of member slenderness, L c /r,shall be determined in accordance with Chapter C or Appendix 7, where

L c =KL ective length of member, in (mm)

L =laterally unbraced length of the member, in (mm) r =radius of gyration, in (mm)

User Note: For members designed on the basis of compression, the effective slenderness ratio, L c /r, preferably should not exceed 200

User Note:The effective length, L c , can be determined through methods other than those using the effective length factor, K

E3 FLEXURAL BUCKLING OF MEMBERS WITHOUT

This section applies to nonslender-element compression members, as defined in Section B4.1, for elements in axial compression.

User Note:When the torsional effective length is larger than the lateral effective length, Section E4 may control the design of wide-flange and similarly shaped columns.

The nominal compressive strength, P n , shall be determined based on the limit state of flexural buckling:

The critical stress, F cr , is determined as follows:

A g =gross cross-sectional area of member, in 2 (mm 2 )

E =modulus of elasticity of steel ),000 ksi (200 000 MPa)

16.1-36 FLEXURAL BUCKLING OF MEMBERS WITHOUT SLENDER ELEMENTS [Sect E3.

F e = elastic buckling stress determined according to Equation E3-4, as specified in Appendix 7, Section 7.2.3(b), or through an elastic buckling analysis, as applicable, ksi (MPa)

F y =specified minimum yield stress of the type of steel being used, ksi (MPa) r =radius of gyration, in (mm)

User Note: The two inequalities for calculating the limits of applicability of Sections E3(a) and E3(b), one based on L c /rand one based on F y /F e , provide the same result for flexural buckling.

E4 TORSIONAL AND FLEXURAL-TORSIONAL BUCKLING OF SINGLE ANGLES AND MEMBERS WITHOUT SLENDER ELEMENTS

This section addresses singly symmetric and unsymmetric members, as well as specific doubly symmetric members like cruciform or built-up types It is applicable when the torsional unbraced length surpasses the lateral unbraced length, provided that there are no slender elements present Additionally, these provisions extend to single angles with a width-to-thickness ratio greater than a specified limit.

, where bis the width of the longest leg and tis the thickness.

The nominal compressive strength, P n , shall be determined based on the limit states of torsional and flexural-torsional buckling:

The critical stress, F_cr, is calculated using Equation E3-2 or E3-3, which incorporates the torsional or flexural-torsional elastic buckling stress, F_e This calculation applies specifically to doubly symmetric members that twist about the shear center.

(b) For singly symmetric members twisting about the shear center where yis the axis of symmetry

User Note:For singly symmetric members with the x-axis as the axis of symmetry, such as channels, Equation E4-3 is applicable with F ey replaced by F ex

(c) For unsymmetric members twisting about the shear center, F e is the lowest root of the cubic equation

F F e ey ez ey ez ey e

2 AISC_PART 16_A_Spec E-F (33-69)_15th_Ed._2016 2016-11-14 1:20 PM Page 36 (Black plate) where

G =shear modulus of elasticity of steel ,200 ksi (77 200 MPa)

I x , I y =moment of inertia about the principal axes, in 4 (mm 4 )

K x ective length factor for flexural buckling about x-axis

K y ective length factor for flexural buckling about y-axis

K z ective length factor for torsional buckling about the longitudinal axis

L cx = K x L x ective length of member for buckling about x-axis, in (mm)

L cy =K y L y ective length of member for buckling about y-axis, in (mm)

L cz =K z L z ective length of member for buckling about longitudinal axis, in (mm)

L x , L y , L z =laterally unbraced length of the member for each axis, in (mm)

⫺r o =polar radius of gyration about the shear center, in (mm)

⫺r o 2 = (E4-9) r x =radius of gyration about x-axis, in (mm) r y =radius of gyration about y-axis, in (mm) x o , y o =coordinates of the shear center with respect to the centroid, in (mm)

User Note:For doubly symmetric I-shaped sections, C w may be taken as

I y h o 2 /4, where h o is the distance between flange centroids, in lieu of a more precise analysis For tees and double angles, omit the term with C w when computing F ez and take x o as 0.

(d) For members with lateral bracing offset from the shear center, the elastic buckling stress, F e , shall be determined by analysis.

User Note:Members with lateral bracing offset from the shear center are suscep- tible to constrained-axis torsional buckling, which is discussed in the Commentary

Sect E4.] TORSIONAL AND FLEXUAL-TORSIONAL BUCKLING 16.1-37

16.1-38 SINGLE-ANGLE COMPRESSION MEMBERS [Sect E5.

The nominal compressive strength (P n) of single-angle members is determined by the lowest value derived from the limit states of flexural buckling, as outlined in Section E3 or E7, or from flexural-torsional buckling according to Section E4 It is important to note that flexural-torsional buckling does not need to be taken into account when the ratio of width to thickness (b/t) is less than or equal to a specified limit.

Eccentricity effects on single-angle members can be disregarded, allowing for evaluation as axially loaded members, using effective slenderness ratios outlined in Section E5(a) or E5(b), provided specific requirements are satisfied.

(1) Members are loaded at the ends in compression through the same one leg.

(2) Members are attached by welding or by connections with a minimum of two bolts.

(3) There are no intermediate transverse loads.

(4) L c /ras determined in this section does not exceed 200.

(5) For unequal leg angles, the ratio of long leg width to short leg width is less than 1.7.

Single-angle members failing to meet the criteria outlined in Section E5(a) or (b) will be assessed for combined axial load and flexural effects according to the guidelines specified in Chapter H.

(a) For angles that are individual members or are web members of planar trusses with adjacent web members attached to the same side of the gusset plate or chord

(1) For equal-leg angles or unequal-leg angles connected through the longer leg (i) When

(2) For unequal-leg angles connected through the shorter leg, L c /r from Equations E5-1 and E5-2 shall be increased by adding 4[ (b l /b s ) 2 −1] , but

L c /rof the members shall not be taken as less than 0.95L/r z

(b) For angles that are web members of box or space trusses with adjacent web members attached to the same side of the gusset plate or chord

(1) For equal-leg angles or unequal-leg angles connected through the longer leg (i) When

DESIGN OF MEMBERS FOR COMPRESSION

Compressive Strength

This section pertains to built-up members that can be either (a) interconnected through bolts or welds, or (b) have at least one open side linked by perforated cover plates or lacing with tie plates Connections at the ends must be made using welding or pretensioned bolts with Class A or B faying surfaces.

When designing a bolted end connection for a built-up compression member, it is essential to account for the full compressive load using bolts in bearing and shear strength considerations, with the requirement that the bolts be pretensioned In built-up compression members, like double-angle struts in trusses, even a minor relative slip between elements can greatly diminish the strut's compressive strength Consequently, it is crucial to design the connections at the ends of built-up members to effectively resist slip.

The nominal compressive strength of built-up members, made of two interconnected shapes via bolts or welds, should be determined per Sections E3, E4, or E7, with a specific modification Instead of a more precise analysis, if the buckling mode leads to relative deformations causing shear forces in the connectors between the shapes, Lc/r is substituted with (Lc/r)m, calculated as follows: (a) for snug-tight bolted intermediate connectors.

(b) For intermediate connectors that are welded or are connected by means of pretensioned bolts with Class A or B faying surfaces

=modified slenderness ratio of built-up member

=slenderness ratio of built-up member acting as a unit in the buckling direction being addressed

L c ective length of built-up member, in (mm)

K i =0.50 for angles back-to-back

=0.75 for channels back-to-back

=0.86 for all other cases a =distance between connectors, in (mm) r i =minimum radius of gyration of individual component, in (mm)

Built-up members shall meet the following requirements:

Compression members made of multiple shapes must be connected at specified intervals to ensure that the slenderness ratio of each component does not exceed 75% of the governing slenderness ratio for the entire built-up member When calculating this slenderness ratio, the smallest radius of gyration for each component should be utilized.

At the ends of compression members supported on base plates or finished surfaces, all contacting components must be securely connected This can be achieved through welding, with the weld length being at least equal to the maximum width of the member, or by using bolts that are spaced no more than four diameters apart over a specified distance.

1 1 /2times the maximum width of the member.

In built-up compression members, the longitudinal spacing of intermittent welds or bolts must ensure sufficient strength between end connections For specific limitations on fastener spacing between continuously contacting elements, such as a plate and a shape or two plates, refer to Section J3.5 Additionally, when a component includes an outside plate, the maximum spacing should not surpass 0.75 times the thickness of the thinner outside plate or 12 inches, provided the ratio a r is less than or equal to 40.

When intermittent welds are used along the edges of components or when fasteners are installed on all gage lines at each section, the maximum spacing of staggered fasteners on each gage line must not exceed 1.12 times the thickness of the thinner outside plate or 18 inches.

Open sides of compression members constructed from plates or shapes must include continuous cover plates with a series of access holes The unsupported width of these plates at the access holes is considered to enhance the available strength, provided that specific requirements outlined in Section B4.1 are satisfied.

(1) The width-to-thickness ratio shall conform to the limitations of Section B4.1.

When analyzing Case 7 in Table B4.1a, it is advisable to apply a conservative limiting width-to-thickness ratio, using the width (b) as the transverse distance between the closest fastener lines The net area of the plate should be calculated at the widest hole Alternatively, this limiting width-to-thickness ratio can also be established through analytical methods.

(2) The ratio of length (in direction of stress) to width of hole shall not exceed 2.

(3) The clear distance between holes in the direction of stress shall be not less than the transverse distance between nearest lines of connecting fasteners or welds.

(4) The periphery of the holes at all points shall have a minimum radius of

Lacing with tie plates is an acceptable alternative to perforated cover plates, with tie plates positioned at the ends and at any interrupted points along the lacing End tie plates must be located as close to the ends as possible and should have a length equal to at least the distance between the fasteners or welds that attach them to the member components Intermediate tie plates should be at least half this length The thickness of tie plates must be no less than one-fiftieth of the distance between the welds or fasteners In welded constructions, the total weld length on each tie plate connection should be a minimum of one-third of the plate's length For bolted constructions, tie plate spacing should not exceed six diameters, with a requirement of at least three fasteners connecting each plate to the member segments.

Lacing elements, such as flat bars, angles, and channels, must be spaced to ensure that the length-to-radius of gyration (L/r) ratio of the flange section between connections does not exceed three-fourths of the governing slenderness ratio for the entire member Additionally, lacing should be designed to provide a shear strength perpendicular to the member's axis that is equal to 2% of the member's available compressive strength For lacing bars configured in single systems, the L/r ratio must not exceed specified limits.

140 For double lacing, this ratio shall not exceed 200 Double laci ng bars shall be joined at the intersections For lacing bars in compression, Lis permitted to be

In built-up members, the unsupported length of the lacing bar between welds or fasteners is defined as the distance for single lacing, while for double lacing, it is calculated as 70% of that distance.

For optimal structural integrity, lacing bars should ideally be positioned at an angle of no less than 60º for single lacing and 45º for double lacing Additionally, when the spacing between welds or fasteners in the flanges exceeds 15 inches (380 mm), it is recommended to use double lacing or angles for enhanced support.

For additional spacing requirements, see Section J3.5.

This section applies to slender-element compression members, as defined in Section B4.1 for elements in axial compression.

The nominal compressive strength, Pn, is defined as the minimum value determined by the relevant limit states, which include flexural buckling, torsional buckling, and the combined effects of flexural-torsional buckling interacting with local buckling.

A e =summation of the effective areas of the cross section based on reduced ef - fective widths, b e , d e or h e , or the area as given by Equations E7-6 or E7-7, in 2 (mm 2 ).

F cr =critical stress determined in accordance with Section E3 or E4, ksi (MPa). For single angles, determine F cr in accordance with Section E3 only.

User Note: The effective area, A e , may be determined by deducting from the gross area, A g , the reduction in area of each slender element determined as (b −b e )t.

Slender Element Members Excluding Round HSS

The effective width, b e , (for tees, this is d e ; for webs, this is h e ) for slender elements is determined as follows:

Members with slender elements are defined by their effective width and width-to-thickness ratio, where the width (b) varies based on the type of element—using depth (d) for tees and height (h) for webs The effective width imperfection adjustment factor (c1) is derived from Table E7.1, while the width-to-thickness ratio (λ) is specified in Section B4.1 Additionally, the limiting width-to-thickness ratio (λr) is outlined in Table B4.1a, ensuring compliance with structural design standards.

=elastic local buckling stress determined according to Equation E7-5 or an elastic local buckling analysis, ksi (MPa)

Round HSS

The effective area, A e, is determined as follows:

D=outside diameter of round HSS, in (mm) t =thickness of wall, in (mm)

TABLE E7.1 Effective Width Imperfection Adjustment Factors, c 1 and c 2

(a) Stiffened elements except walls of square and rectangular HSS 0.18 1.31

(b) Walls of square and rectangular HSS 0.20 1.38

DESIGN OF MEMBERS FOR FLEXURE

This chapter focuses on members experiencing simple bending around a principal axis In simple bending scenarios, the member is subjected to loads in a plane that aligns with a principal axis, which either intersects the shear center or is fixed against twisting at load points and supports The organization of the chapter is clearly outlined for better understanding.

F2 Doubly Symmetric Compact I-Shaped Members and Channels Bent about Their Major Axis

F3 focuses on doubly symmetric I-shaped members featuring compact webs and noncompact or slender flanges that are bent around their major axis In contrast, F4 addresses other I-shaped members, which may have either compact or noncompact webs, also bent about their major axis.

F5 Doubly Symmetric and Singly Symmetric I-Shaped Members with Slender Webs Bent about Their Major Axis

F6 I-Shaped Members and Channels Bent about Their Minor Axis

F7 Square and Rectangular HSS and Box Sections

F9 Tees and Double Angles Loaded in the Plane of Symmetry

F13 Proportions of Beams and Girders

• Chapter G Design provisions for shear

• H1–H3 Members subject to biaxial flexure or to combined flexure and axial force

• H3 Members subject to flexure and torsion

• Appendix 3 Members subject to fatigue

For guidance in determining the appropriate sections of this chapter to apply, Table User Note F1.1 may be used.

Chap F] DESIGN OF MEMBERS FOR FLEXURE 16.1-45

Section in Cross Flange Web Limit

Chapter F Section Slenderness Slenderness States

F12 Unsymmetrical shapes, All limit other than single angles N/A N/A states

Y = yielding, CFY = compression flange yielding, LTB = lateral-torsional buckling, FLB = flange local buckling, WLB = web local buckling, TFY = tension flange yielding, LLB = leg local buckling, LB = local buckling,

C = compact, NC = noncompact, S = slender, N/A = not applicable

TABLE USER NOTE F1.1 Selection Table for the Application of Chapter F Sections

The design flexural strength, φ b M n, and the allowable flexural strength, M n /Ω b ,shall be determined as follows:

(a) For all provisions in this chapter φ b =0.90 (LRFD) Ω b =1.67 (ASD) and the nominal flexural strength, M n , shall be determined according to Sections F2 through F13.

This chapter assumes that the support points for beams and girders are fixed against rotational movement along their longitudinal axis It applies to singly symmetric members with single curvature as well as all doubly symmetric members.

The lateral-torsional buckling modification factor, C b , for nonuniform moment diagrams when both ends of the segment are braced is determined as follows:

M max solute value of maximum moment in the unbraced segment, kip-in. (N-mm)

M A solute value of moment at quarter point of the unbraced segment, kip-in (N-mm)

M B solute value of moment at centerline of the unbraced segment, kip-in (N-mm)

M C solute value of moment at three-quarter point of the unbraced segment, kip-in (N-mm)

For doubly symmetric members without transverse loading between brace points, Equation F1-1 simplifies to 1.0 for equal end moments of opposite sign (uniform moment), 2.27 for equal end moments of the same sign (reverse curvature bending), and 1.67 when one end moment is zero In contrast, a more comprehensive analysis for singly symmetric members is detailed in the Commentary, which offers additional equations for C b to better characterize the effects of various member boundary conditions.

For cantilevers where warping is prevented at the support and where the free end is unbraced, C b =1.0.

In singly symmetric members experiencing reverse curvature bending, it is essential to verify the lateral-torsional buckling strength for each flange The flexural strength must meet or exceed the maximum moment that induces compression in the flange being analyzed.

DESIGN OF MEMBERS FOR FLEXURE

Yielding

F y =specified minimum yield stress of the type of steel being used, ksi (MPa)

Z x =plastic section modulus about the x-axis, in 3 (mm 3 )

Lateral-Torsional Buckling

(a) When L b ≤L p , the limit state of lateral-torsional buckling does not apply. (b) When L p 25, the provisions of Chapter E apply; where

L c =KL = effective length, in (mm)

L =laterally unbraced length of the member, in (mm)

When calculating the compressive strengths of connecting elements, it's important to consider the effective length factors, which depend on the type of end restraint provided These factors may not always be assumed as unity, particularly when using the direct analysis method.

Strength of Elements in Flexure

The flexural strength of affected elements will be determined by the lowest value derived from the limit states of flexural yielding, local buckling, flexural lateral-torsional buckling, and flexural rupture.

4 AISC_PART 16_A_Spec J (113-148)_15th Ed._2016 2016-11-30 2:46 PM Page 138 (Black plate)

Fillers in Welded Connections

When fillers are needed in joints to transfer applied force, they and the associated welds must meet the criteria outlined in Section J5.1a or Section J5.1b, depending on the specific requirements.

Fillers with a thickness of less than 1/4 inch (6 mm) should not be utilized for stress transfer If the filler is either less than 1/4 inch (6 mm) thick or at least 1/4 inch (6 mm) but inadequate for transferring the applied force between connected components, it must be flush with the edge of the outer connected part Additionally, the weld size must be increased by an amount that matches the thickness of the filler.

For effective force transfer between connected components, the filler must extend beyond the edges of the outer base metal The welds that connect the outer base metal to the filler should be robust enough to transmit the applied force, ensuring that the filler can withstand the stress without overstressing Additionally, the welds linking the filler to the inner base metal must also adequately transfer the applied force.

Fillers in Bolted Bearing-Type Connections

When a load-bearing bolt passes through fillers that are 1/4 inch (6 mm) thick or thinner, its shear strength remains unchanged However, if the bolt goes through fillers thicker than 1/4 inch (6 mm), specific requirements must be met.

(a) The shear strength of the bolts shall be multiplied by the factor

1 ⫺0.0154(t ⫺6) (S.I.) but not less than 0.85, where t is the total thickness of the fillers.

Fillers must be welded or extended beyond the joint and secured with bolts to ensure an even distribution of the total force across the combined cross-section of both the connected element and the fillers.

(c) The size of the joint shall be increased to accommodate a number of bolts that is equivalent to the total number required in (b).

Groove-welded splices in plate girders and beams must achieve the nominal strength of the smaller spliced section, while other splice types in these structures should meet the strength requirements dictated by the forces at the splice location.

The design bearing strength (φR n) and allowable bearing strength (R n /Ω) for surfaces in contact must be calculated for the limit state of bearing, specifically local compressive yielding For Load and Resistance Factor Design (LRFD), the factor φ is set at 0.75, while for Allowable Stress Design (ASD), the safety factor Ω is established at 2.00 The nominal bearing strength (R n) is to be determined accordingly.

(a) For finished surfaces, pins in reamed, drilled, or bored holes, and ends of fitted bearing stiffeners

A pb =projected area in bearing, in 2 (mm 2 )

F y =specified minimum yield stress, ksi (MPa) (b) For expansion rollers and rockers

(J7-3M) where d =diameter, in (mm) l b =length of bearing, in (mm)

J8 COLUMN BASES AND BEARING ON CONCRETE

Provisions shall be made to transfer the column loads and moments to the footings and foundations.

In the absence of code regulations, the design bearing strength (φc Pp) and the allowable bearing strength (Pp/Ωc) for concrete crushing can be defined with φc set at 0.65 for LRFD and Ωc at 2.31 for ASD The nominal bearing strength, Pp, is calculated accordingly.

Sect J9.] ANCHOR RODS AND EMBEDMENTS 16.1-141

(a) On the full area of a concrete support

(b) On less than the full area of a concrete support

A 1 =area of steel concentrically bearing on a concrete support, in 2 (mm 2 )

A 2=maximum area of the portion of the supporting surface that is geometrically similar to and concentric with the loaded area, in 2 (mm 2 ) f c ′ =specified compressive strength of concrete, ksi (MPa)

Anchor rods must be engineered to effectively resist loads at the base of columns, including the net tensile forces from bending moments as outlined in Section B2 Additionally, their design should adhere to the specifications for threaded components detailed in Table J3.2.

Design of anchor rods for the transfer of forces to the concrete foundation shall satisfy the requirements of ACI 318 (ACI 318M) or ACI 349 (ACI 349M).

When designing column bases, it is essential to account for their ability to bear against concrete elements, especially when they need to withstand horizontal forces at the base plate For detailed guidelines on column base design, refer to the AISC Design Guide 1, Base Plate and Anchor Rod Design, Second Edition.

When anchor rods are used to resist horizontal forces, hole size, anchor rod setting tolerance, and the horizontal movement of the column shall be considered in the design.

Oversized and slotted holes in base plates are acceptable if sufficient bearing is ensured for the nut by utilizing ASTM F844 washers or plate washers to span the hole.

According to the AISC Steel Construction Manual and ASTM F1554, the allowable hole sizes, washer dimensions, and nuts are specified ASTM F1554 anchor rods can be provided with a body diameter smaller than the nominal diameter as per product specifications It is essential to calculate load effects, including bending and elongation, using the minimum diameters allowed by these specifications For further details, refer to ASTM F1554 and the table titled “Applicable ASTM Specifications for Various Types of Structural Fasteners” found in Part 2 of the AISC.

16.1-142 ANCHOR RODS AND EMBEDMENTS [Sect J9.

User Note: See ACI 318 (ACI 318M) for embedment design and for shear fric- tion design See OSHA for special erection requirements for anchor rods.

J10 FLANGES AND WEBS WITH CONCENTRATED FORCES

This section addresses the application of single and double concentrated forces acting perpendicular to the flanges of wide-flange sections and similar built-up shapes A single concentrated force can be either tensile or compressive, while double concentrated forces consist of one tensile and one compressive force, creating a couple on the same side of the loaded member.

When the required strength surpasses the available strength for specified limit states, it is essential to incorporate stiffeners and/or doublers These reinforcements must be appropriately sized to bridge the gap between the required and available strength for the relevant limit state Additionally, stiffeners must comply with the design criteria outlined in Section J10.8, while doublers should adhere to the standards set in Section J10.9.

User Note: See Appendix 6, Section 6.3 for requirements for the ends of canti - lever members.

Stiffeners are required at unframed ends of beams in accordance with the requirements of Section J10.7.

User Note:Design guidance for members other than wide-flange sections and similar built-up shapes can be found in the Commentary.

Flange Local Bending

This section applies to tensile single-concentrated forces and the tensile component of double-concentrated forces.

The design strength, φR n , and the allowable strength, R n /Ω, for the limit state of flange local bending shall be determined as:

F yf =specified minimum yield stress of the flange, ksi (MPa) t f =thickness of the loaded flange, in (mm)

If the length of loading across the member flange is less than 0.15b f , where b f is the member flange width, Equation J10-1 need not be checked.

When the concentrated force to be resisted is applied at a distance from the member end that is less than 10t f , R n shall be reduced by 50%.

When required, a pair of transverse stiffeners shall be provided.

Web Local Yielding

This section applies to single-concentrated forces and both components of double- concentrated forces.

The available strength for the limit state of web local yielding shall be determined as follows: φ =1.00 (LRFD) Ω =1.50 (ASD) The nominal strength, R n , shall be determined as follows:

(a) When the concentrated force to be resisted is applied at a distance from the member end that is greater than the full nominal depth of the member, d,

When a concentrated force is applied at a distance from the end of a member that is equal to or less than its full nominal depth, denoted as 'd', it creates specific resistance challenges that must be addressed in structural analysis and design.

The specified minimum yield stress of the web material (F yw) is measured in ksi (MPa), while the distance from the outer face of the flange to the web toe of the fillet (k) is expressed in inches (mm) Additionally, the length of bearing (l b) must not be less than k for end beam reactions, also measured in inches (mm) The thickness of the web (t w) is another critical dimension, indicated in inches (mm) When necessary, a pair of transverse stiffeners or a doubler plate should be included to enhance structural integrity.

Web Local Crippling

This section applies to compressive single-concentrated forces or the compressive component of double-concentrated forces.

The available strength for the limit state of web local crippling shall be determined as follows: φ =0.75 (LRFD) Ω =2.00 (ASD) The nominal strength, R n , shall be determined as follows:

(a) When the concentrated compressive force to be resisted is applied at a distance from the member end that is greater than or equal to d /2

(b) When the concentrated compressive force to be resisted is applied at a distance from the member end that is less than d /2

Sect J10.] FLANGES AND WEBS WITH CONCENTRATED FORCES 16.1-143

16.1-144 FLANGES AND WEBS WITH CONCENTRATED FORCES [Sect J10.

(J10-5b) where d =full nominal depth of the member, in (mm)

Q f =1.0 for wide-flange sections and for HSS (connecting surface) in tension

=as given in Table K3.2 for all other HSS conditions

When required, a transverse stiffener, a pair of transverse stiffeners, or a doubler plate extending at least three quarters of the depth of the web shall be provided.

Web Sidesway Buckling

This section pertains specifically to compressive single-concentrated forces exerted on members where there is no restriction on lateral movement between the loaded compression flange and the tension flange at the force application point.

The available strength of the web for the limit state of sidesway buckling shall be determined as follows: φ =0.85 (LRFD) Ω =1.76 (ASD) The nominal strength, R n , shall be determined as follows:

(a) If the compression flange is restrained against rotation

(2) When (h / t w )/(L b / b f ) >2.3, the limit state of web sidesway buckling does not apply.

When the web's required strength surpasses its available strength, it is essential to implement local lateral bracing at the tension flange Alternatively, one can use either a pair of transverse stiffeners or a doubler plate to enhance structural integrity.

(b) If the compression flange is not restrained against rotation

Sect J10.] FLANGES AND WEBS WITH CONCENTRATED FORCES 16.1-145

(2) When (h / t w )/(L b / b f ) >1.7, the limit state of web sidesway buckling does not apply.

When the required strength of the web exceeds the available strength, local lateral bracing shall be provided at both flanges at the point of application of the concentrated forces.

In Equations J10-6 and J10-7, the following definitions apply:

C r 0,000 ksi (6.6 ×10 6 MPa), when M u

Tiêu đề	Specification for Structural Steel Buildings
Trường học	American Institute of Steel Construction
Chuyên ngành	Structural Engineering
Thể loại	Standard
Năm xuất bản	2016
Thành phố	United States of America

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Số trang	680
Dung lượng	9,59 MB