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1、Load and Resistance Factor Design Specification for Single-Angle Members November 10, 2000 Supersedes the Specification for Load and Resistance Factor Design of Single-Angle Members dated December 1, 1993 Prepared by the American Institute of Steel Construction, Inc. Under the Direction of the AISC
2、Committee on Specifications and approved by the AISC Board of Directors AMERICAN INSTITUTE OF STEEL CONSTRUCTION, INC. One East Wacker Drive, Suite 3100 Chicago, IL 60601-2001 LRFD Specification for the Design of Single-Angle Members, November 10, 2000 AMERICANINSTITUTE OFSTEELCONSTRUCTION ii PREFAC
3、E The intention of the AISC Specification is to cover the common everyday design cri- teria in routine design office usage. It is not feasible to also cover the many special and unique problems encountered within the full range of structural design practice. This separate Specification and Commentar
4、y addresses one such topicsingle- angle membersto provide needed design guidance for this more complex struc- tural shape under various load and support conditions. The revised single-angle design criteria were developed through a consensus process by the AISC Task Committee 12 on Single Angles: Jam
5、es M. Fisher, Chairman Leroy A. Lutz, Vice-Chairman Mohamed Elgaaly Shu-Jin Fang Theodore V. Galambos Subhash Goel Charlotte S. Harman Todd Helwig Donald W. White Sergio Zoruba, Secretary The full AISC Committee on Specifications has reviewed and approved this Specification. A non-mandatory Commenta
6、ry provides background for the Specification provi- sions and the user is encouraged to consult it. The principal changes in this edition include: Revisions to flexural design strength criteria a. For the limit state of local buckling when the angle leg is in compression b. For the limit state of yi
7、elding when the tip of an angle leg is in tension c. For the limit state of lateral-torsional buckling d. For bending about geometric axes The reader is cautioned that professional judgment must be exercised when data or recommendations in this Specification are applied. The publication of the mater
8、ial contained herein is not intended as a representation or warranty on the part of the American Institute of Steel Construction, Inc.or any other person named herein that this information is suitable for general or particular use, or freedom from infringement of any patent or patents. Anyone making
9、 use of this information assumes all liability arising from such use. The design of structures is within the scope of expertise of a competent licensed structural engineer, architect, or other licensed professional for the application of principles to a particular structure. LRFD Specification for t
10、he Design of Single-Angle Members, November 10, 2000 AMERICANINSTITUTE OFSTEELCONSTRUCTION iii LRFD Specification for the Design of Single-Angle Members, November 10, 2000 AMERICANINSTITUTE OFSTEELCONSTRUCTION iv Load and Resistance Factor Design Specification for Single-Angle Members November 10, 2
11、000 1.SCOPE This document contains Load and Resistance Factor Design (LRFD) criteria for hot-rolled, single-angle members with equal and unequal legs in tension, shear, compression, flexure, and for combined forces. It is intended to be com- patible with, and a supplement to, the 1999 AISC Load and
12、Resistance Factor Design Specification for Structural Steel Buildings and repeats some common criteria for ease of reference. For design purposes, the conservative simplifi- cations and approximations in the Specification provisions for single angles are permitted to be refined through a more precis
13、e analysis. As an alternative to this Specification, the 1989 AISC Specification for Allowable Stress Design of Single-Angle Members is permitted. The Specification for single-angle design supersedes any comparable but more general requirements of the AISC LRFD. All other design, fabrication, and er
14、ection provisions not directly covered by this document shall be in compli- ance with the AISC LRFD. For design of slender, cold-formed steel angles, the AISI LRFD Specification for the Design of Cold-Formed Steel Structural Members referenced in Section A6 of the AISC LRFD is applicable. 2.TENSION
15、The tensile design strength ?tPnshall be the lower value obtained according to the limit states of yielding, ?t? 0.9, Pn? FyAg, and fracture, ?t? 0.75, Pn? FuAe. a.For members connected by bolting, the net area and effective net area shall be determined from AISC LRFD Specification Sections B1 to B3
16、 inclusive. b.When the load is transmitted by longitudinal welds only or a combina- tion of longitudinal and transverse welds through just one leg of the angle, the effective net area Aeshall be: Ae? AgU(2-1) LRFD Specification for the Design of Single-Angle Members, November 10, 2000 AMERICANINSTIT
17、UTE OFSTEELCONSTRUCTION 1 where Ag? gross area of member U ?1 ? x l ? 0.9 x? connection eccentricity l? length of connection in the direction of loading c.When a load is transmitted by transverse weld through just one leg of the angle, Aeis the area of the connected leg and U ? 1. For members whose
18、design is based on tension, the slenderness ratio l/r prefer- ably should not exceed 300. Members in which the design is dictated by ten- sion loading, but which may be subject to some compression under other load conditions, need not satisfy the compression slenderness limits. 3.SHEAR For the limit
19、 state of yielding in shear, the shear stress, fuv, due to flexure and torsion shall not exceed: fuv? ?v0.6Fy ?v?0.9(3-1) 4.COMPRESSION The design strength of compression members shall be ?cPn where ?c? 0.90 Pn? AgFcr a.For ?c?Q? 1.5 Fcr? Q(0.658Q?c 2)F y (4-1) b.For ?c?Q? 1.5 Fcr? ?Fy (4-2) where ?
20、c? r K ? l ? F E y ? ? Fy? specified minimum yield stress of steel Q ? reduction factor for local buckling 0.877 ? ?c 2 2 LRFD Specification for the Design of Single-Angle Members, November 10, 2000 AMERICANINSTITUTE OFSTEELCONSTRUCTION The reduction factor Q shall be: when ? b t ? 0.446 ? F E y ?:
21、Q = 1.0(4-3a) when 0.446 ? F E y ? ? ? b t ? 0.910 ? F E y ? ?: Q = 1.34 ? 0.761 ? b t ? F E y ? ? (4-3b) when ? b t ? 0.910 ? F E y ? ?: Q ?(4-3c) where b ? full width of longest angle leg t ? thickness of angle For members whose design is based on compressive force, the largest effective slenderne
22、ss ratio preferably should not exceed 200. 5.FLEXURE The flexure design strengths of Section 5.1 shall be used as indicated in Sections 5.2 and 5.3. 5.1.Flexural Design Strength The flexural design strength shall be limited to the minimum value ?bMn determined from Sections 5.1.1, 5.1.2, and 5.1.3,
23、as applicable, with ?b? 0.9. 5.1.1. For the limit state of local buckling when the tip of an angle leg is in compression: when ? b t ? 0.54 ? F E y ? ?: Mn= 1.5 FySc(5-1a) 0.534E ? Fy? b t ? 2 3 LRFD Specification for the Design of Single-Angle Members, November 10, 2000 AMERICANINSTITUTE OFSTEELCON
24、STRUCTION when 0.54 ? F E y ? ? ? b t ? 0.91 ? F E y ? ?: Mn? FySc ? 1.5 ? 0.93? 1?(5-1b) when ? b t ? 0.91 ? F E y ? ?: Mn? 1.34QFySc(5-1c) where b ? full width of angle leg with tip in compression Q ? reduction factor per Equation 4-3c Sc? elastic section modulus to the tip in compression relative
25、 to axis of bending E ? modulus of elasticity 5.1.2. For the limit state of yielding when the tip of an angle leg is in tension Mn? 1.5My(5-2) where My= yield moment about the axis of bending 5.1.3. For the limit state of lateral-torsional buckling: when Mob? My: Mn? 0.92 ? 0.17Mob/MyMob(5-3a) when
26、Mob?My: Mn? 1.92 ? 1.17?My/Mo?b?My? 1.5My(5-3b) where Mob? elastic lateral-torsional buckling moment, from Section 5.2 or 5.3 as applicable 5.2.Bending about Geometric Axes 5.2.1. a.Angle bending members with lateral-torsional restraint along the length shall be designed on the basis of geometric ax
27、is bending with the nominal flexural strength Mnlimited to the provisions of Sections 5.1.1 and 5.1.2. b/t ? 0.54? F E y ? ? 4 LRFD Specification for the Design of Single-Angle Members, November 10, 2000 AMERICANINSTITUTE OFSTEELCONSTRUCTION b.For equal-leg angles if the lateral-torsional restraint
28、is only at the point of maximum moment, the required moment shall be limit- ed to ?bMnper Section 5.1. Myshall be computed using the geometric axis section modulus and Mobshall be substituted by using 1.25 times Mob computed from Equation 5-4. 5.2.2. Equal-leg angle members without lateral-torsional
29、 restraint subjected to flexure applied about one of the geometric axes are permitted to be designed considering only geometric axis bending provided: a.The yield moment shall be based on use of 0.80 of the geomet- ric axis section modulus. b.With maximum compression of the angle-leg tips, the nomin
30、al flexural strength Mnshall be determined by the provisions in Section 5.1.1 and in Section 5.1.3, where Mob? 0.66E l2 b4tCb ?1 ? 0.?78(lt/b?2)2? 1?(5-4) l ? unbraced length Cb? 1.5 where Mmax? absolute value of maximum moment in the unbraced beam segment MA? absolute value of moment at quarter poi
31、nt of the unbraced beam segment MB? absolute value of moment at centerline of the unbraced beam segment MC? absolute value of moment at three-quarter point of the unbraced beam segment c.With maximum tension at the angle-leg tips, the nominal flexur- al strength shall be determined according to Sect
32、ion 5.1.2 and in Section 5.1.3 using Mobin Equation 5-4 with ?1 being replaced by ?1. 5.2.3. Unequal-leg angle members without lateral-torsional restraint subject- ed to bending about one of the geometric axes shall be designed using Section 5.3. 12.5Mmax ? 2.5Mmax? 3MA? 4MB? 3MC 5 LRFD Specificatio
33、n for the Design of Single-Angle Members, November 10, 2000 AMERICANINSTITUTE OFSTEELCONSTRUCTION 5.3.Bending about Principal Axes Angles without lateral-torsional restraint shall be designed considering principal-axis bending, except for the alternative of Section 5.2.2, if appropri- ate. Bending a
34、bout both of the principal axes shall be evaluated as required in Section 6. 5.3.1. Equal-leg angles: a.Major-axis bending: The nominal flexural strength Mnabout the major principal axis shall be determined by the provisions in Section 5.1.1 and in Section 5.1.3, where Mob? Cb? 0.46E l b2t2 ?(5-5) b
35、.Minor-axis bending: The nominal design strength Mnabout the minor principal axis shall be determined by Section 5.1.1 when the leg tips are in com- pression, and by Section 5.1.2 when the leg tips are in tension. 5.3.2. Unequal-leg angles: a.Major-axis bending: The nominal flexural strength Mnabout
36、 the major principal axis shall be determined by the provisions in Section 5.1.1 for the compression leg and in Section 5.1.3, where Mob? 4.9E? l I 2 z ?Cb ?2 w? 0?.052(lt ?/rz)2? ?w?(5-6) Iz? minor principal axis moment of inertia rz? radius of gyration for minor principal axis ?w? I 1 w ? A zo(w2?
37、 z2)dA? 2zo, special section property for unequal-leg angles, positive for short leg in com- pression and negative for long leg in compression (see Commentary for values for common angle sizes). If the long leg is in compression anywhere along the unbraced length of the member, the negative value of
38、 ?wshall be used. 6 LRFD Specification for the Design of Single-Angle Members, November 10, 2000 AMERICANINSTITUTE OFSTEELCONSTRUCTION zo? coordinate along z axis of the shear center with respect to centroid Iw? moment of inertia for major principal axis b.Minor-axis bending: The nominal design stre
39、ngth Mnabout the minor principal axis shall be determined by Section 5.1.1 when leg tips are in com- pression and by Section 5.1.2 when the leg tips are in tension. 6.COMBINED FORCES The interaction equation shall be evaluated for the principal bending axes either by addition of all the maximum axia
40、l and flexural terms, or by consid- ering the sense of the associated flexural stresses at the critical points of the cross section, the flexural terms are either added to or subtracted from the axial load term. 6.1.Members in Flexure and Axial Compression 6.1.1. The interaction of flexure and axial
41、 compression applicable to specific locations on the cross section shall be limited by Equations 6-1a and 6-1b: For ? ? P P u n ? 0.2 ? ? P P u n ? 8 9 ? ? M bM uw nw ? ? M bM uz nz ? 1.0(6-1a) For ? ? P P u n ? 0.2 ? 2? P P u n ? ? M bM uw nw ? ? M bM uz nz ? 1.0(6-1b) where Pu? required compressiv
42、e strength Pn? nominal compressive strength determined in accordance with Section 4 Mu? required flexural strength Mn? nominal flexural strength for tension or compression in accordance with Section 5, as appropriate. Use section modu- lus for specific location in the cross section and consider the
43、type of stress. ? ? ?c? resistance factor for compression ? 0.90 ?b? resistance factor for flexure ? 0.90 w ? subscript relating symbol to major-axis bending z? subscript relating symbol to minor-axis bending 7 LRFD Specification for the Design of Single-Angle Members, November 10, 2000 AMERICANINST
44、ITUTE OFSTEELCONSTRUCTION In Equations 6-1a and 6-1b when Mnrepresents the flexural strength of the compression side, the corresponding Mushall be multiplied by B1. B1? 1.0(6-2) where Cm? bending coefficient defined in AISC LRFD Pe1? elastic buckling load for the braced frame defined in AISC LRFD 6.
45、1.2. For members constrained to bend about a geometric axis with nominal flexural strength determined per Section 5.2.1, the radius of gyration r for Pe1shall be taken as the geometric axis value. The bending terms for the principal axes in Equations 6-1a and 6-1b shall be replaced by a single geome
46、tric axis term. 6.1.3. Alternatively, for equal-leg angles without lateral-torsional restraint along the length and with bending applied about one of the geometric axes, the provisions of Section 5.2.2 are permitted for the required and design bending strength. If Section 5.2.2 is used for Mn, the r
47、adius of gyration about the axis of bending r for Pe1shall be taken as the geo- metric axis value of r divided by 1.35 in the absence of a more detailed analysis. The bending terms for the principal axes in Equations 6-1a and 6-1b shall be replaced by a single geometric axis term. 6.2.Members in Fle
48、xure and Axial Tension The interaction of flexure and axial tension shall be limited by Equations 6-1a and 6-1b where Pu? required tensile strength Pn? nominal tensile strength determined in accordance with Section 2 Mu? required flexural strength Mn? nominal flexural strength for tension or compres
49、sion in accor- dance with Section 5, as appropriate. Use section modulus for specific location in the cross section and consider the type of stress. ? ?t? resistance factor for tension ? 0.90 ?b? resistance factor for flexure ? 0.90 For members subject to bending about a geometric axis, the required bending strength evaluation shall be in accordance with Sections 6.1.2 and 6.1.3. Second-order effects due to axial tension and bending interaction are permit- ted to be considered in the determination of Mufor use in F