Đang tải... (xem toàn văn)
COLD-FORMED STEEL DESIGN
SECTION 10 COLD-FORMED STEEL DESIGN R L Brockenbrough, P.E President, R L Brockenbrough & Associates, Inc., Pittsburgh, Pennsylvania This section presents information on the design of structural members that are cold-formed to cross section shape from sheet steels Cold-formed steel members include such products as purlins and girts for the construction of metal buildings, studs and joists for light commercial and residential construction, supports for curtain wall systems, formed deck for the construction of floors and roofs, standing seam roof systems, and a myriad of other products These products have enjoyed significant growth in recent years and are frequently utilized in some shape or form in many projects today Attributes such as strength, light weight, versatility, non-combustibility, and ease of production, make them cost effective in many applications Figure 10.1 shows cross sections of typical products 10.1 DESIGN SPECIFICATIONS AND MATERIALS Cold-formed members for most application are designed in accordance with the Specification for the Design of Cold-Formed Steel Structural Members, American Iron and Steel Institute, Washington, DC Generally referred to as the AISI Specification, it applies to members coldformed to shape from carbon or low-alloy steel sheet, strip, plate, or bar, not more than 1in thick, used for load carrying purposes in buildings With appropriate allowances, it can be used for other applications as well The vast majority of applications are in a thickness range from about 0.014 to 0.25 in The design information presented in this section is based on the AISI Specification and its Commentary, including revisions being processed The design equations are written in dimensionless form, except as noted, so that any consistent system of units can be used A synopsis of key design provisions is given in this section, but reference should be made to the complete specification and commentary for a more complete understanding The AISI Specification lists all of the sheet and strip materials included in Table 1.6 (Art 1.4) as applicable steels, as well several of the plate steels included in Table (A36, A242, A588, and A572) A283 and A529 plate steels are also included, as well as A500 structural tubing (Table 1.7) Other steels can be used for structural members if they meet the ductility requirements The basic requirement is a ratio of tensile strength to yield stress not less than 1.08 and a total elongation of at least 10% in in If these requirements cannot be met, alternative criteria related to local elongation may be applicable In addition, certain steels that not meet the criteria, such as Grade 80 of A653 or Grade E of A611, can be used 10.1 10.2 SECTION TEN FIGURE 10.1 Typical cold-formed steel members for multiple-web configurations (roofing, siding, decking, etc.) provided the yield stress is taken as 75% of the specified minimum (or 60 ksi or 414 MPa, if less) and the tensile stress is taken as 75% of the specified minimum (or 62 ksi or 428 MPa if less) Some exceptions apply Suitability can also be established by structural tests 10.2 MANUFACTURING METHODS AND EFFECTS As the name suggests, the cross section of a cold-formed member is achieved by a bending operation at room temperature, rather than the hot rolling process used for the heavier structural steel shapes The dominant cold forming process is known as roll-forming In this process, a coil of steel is fed through a series of rolls, each of which bends the sheet progressively until the final shape is reached at the last roll stand The number of roll stands may vary from to 20, depending upon the complexity of the shape Because the steel is fed in coil form, with successive coils weld-spliced as needed, the process can achieve speeds up to about 300 ft / and is well suited for quantity production Small quantities may be produced on a press-brake, particularly if the shape is simple, such as an angle or channel cross section In its simplest form, a press brake consists of a male die which presses the steel sheet into a matching female die In general, the cold-forming operation is beneficial in that it increases the yield strength of the material in the region of the bend The flat material between bends may also show an increase due to squeezing or stretching during roll forming This increase in strength is attributable to cold working and strain aging effects as discussed in Art 1.10 The strength increase, which may be small for sections with few bends, can be conservatively neglected Alternatively, subject to certain limitations, the AISI Specification includes provisions for using a section-average design yield stress that includes the strength increase from coldforming Either full section tension tests, full section stub column tests, or an analytical method can be employed Important parameters include the tensile-strength-to-yield-stress COLD-FORMED STEEL DESIGN 10.3 TABLE 10.1 Safety Factors and Resistance Factors Adopted by the AISI Specification Category Tension members Flexural members (a) Bending strength Sections with stiffened or partially stiffened compression flanges Sections with unstiffened compression flanges Laterally unbraced beams Beams having one flange through-fastened to deck or sheathing (C- or Z-sections) Beams having one flange fastened to a standing seam roof system (b) Web design Shear strength controlled by yielding (Condition a, Art 10.12.4) Shear strength controlled by buckling (Condition b or c, Art 10.12.4) Web crippling of single unreinforced webs Web crippling of I-sections Web crippling of two nested Z-sections Stiffeners (a) Transverse stiffeners (b) Shear stiffeners Concentrically loaded compression members Combined axial load and bending (a) Tension component (b) Compression component (c) Bending component Cylindrical tubular members (a) Bending (b) Axial compression Wall studs (a) Compression (b) Bending Diaphragm construction Welded connections (a) Groove welds Tension or compression Shear, welds Shear, base metal (b) Arc spot welds Shear, welds Shear, connected part Shear, minimum edge distance Tension (c) Arc seam welds Shear, welds Shear, connected part (d) Fillet welds Welds Connected part, longitudinal loading Weld length / sheet thickness ⬍25 Weld length / sheet thickness ⱖ25 Connected part, transverse loading ASD safety factor, ⍀ LRFD resistance factor, 1.67 0.95 1.67 1.67 1.67 1.67 1.67 0.95 0.90 0.90 0.90 0.90 1.50 1.67 1.85 2.00 1.80 1.00 0.90 0.75 0.80 0.85 2.00 1.50 / 1.67 1.80 0.85 1.00 / 0.90 0.85 1.67 1.80 1.67 0.95 0.85 0.90 / 0.95 1.67 1.80 0.95 0.85 1.80 1.67 2.00 / 3.00 0.85 0.90 / 0.95 0.50 / 0.65 250 2.50 2.50 0.90 0.80 0.90 2.50 2.50 2.50 2.50 0.60 0.50 / 0.60 0.60 / 0.70 0.60 2.50 2.50 0.60 0.60 2.50 0.60 2.50 2.50 2.50 0.60 0.55 0.60 10.4 SECTION TEN TABLE 10.1 Safety Factors and Resistance Factors Adopted by the AISI Specification (Continued ) Category (e) Flare groove welds Welds Connected part, longitudinal loading Connected part, transverse loading (f ) Resistance welds Bolted connections (a) Minimum spacing and edge distance* When Fu / Fsy ⱖ 1.08 When Fu / Fsy ⬍ 1.08 (b) Tension strength on net section With washers, double shear connection With washers, single shear connection Without washers, double or single shear (c) Bearing strength (d) Shear strength of bolts (e) Tensile strength of bolts Screw connections ASD safety factor, ⍀ LRFD resistance factor, 2.50 2.50 2.50 2.50 0.60 0.55 0.55 0.65 2.00 2.22 0.70 0.60 2.00 2.22 2.22 2.22 2.40 2.00 / 2.25 3.00 0.65 0.55 0.65 0.55 / 0.70 0.65 0.75 0.50 * Fu is tensile strength and Fsy is yield stress ratio of the virgin steel and the radius-to-thickness ratio of the bends The forming operation may also induce residual stresses in the member but these effects are accounted for in the equations for member design 10.3 NOMINAL LOADS The nominal loads for design should be according to the applicable code or specification under which the structure is designed or as dictated by the conditions involved In the absence of a code or specification, the nominal loads should be those stipulated in the American Society of Civil Engineers Standard, Minimum Design Loads for Buildings and Other Structures, ASCE The following loads are used for the primary load combinations in the AISI Specification: D ⫽ Dead load, which consists of the weight of the member itself, the weight of all materials of construction incorporated into the building which are supported by the member, including built-in partitions; and the weight of permanent equipment E ⫽ Earthquake load L ⫽ Live loads due to intended use and occupancy, including loads due to movable objects and movable partitions and loads temporarily supported by the structure during maintenance (L includes any permissible load reductions If resistance to impact loads is taken into account in the design, such effects should be included with the live load.) COLD-FORMED STEEL DESIGN Lr S Rr W ⫽ ⫽ ⫽ ⫽ 10.5 Roof live load Snow load Rain load, except for ponding Wind load The effects of other loads such as those due to ponding should be considered when significant Also, unless a roof surface is provided with sufficient slope toward points of free drainage or adequate individual drains to prevent the accumulation of rainwater, the roof system should be investigated to assure stability under ponding conditions 10.4 DESIGN METHODS The AISI Specification is structured such that nominal strength equations are given for various types of structural members such as beams and columns For allowable stress design (ASD), the nominal strength is divided by a safety factor and compared to the required strength based on nominal loads For Load and Resistance Factor Design (LRFD), the nominal strength is multiplied by a resistance factor and compared to the required strength based on factored loads These procedures and pertinent load combinations to consider are set forth in the specification as follows 10.4.1 ASD Requirements ASD Strength Requirements A design satisfies the requirements of the AISI Specification when the allowable design strength of each structural component equals or exceeds the required strength, determined on the basis of the nominal loads, for all applicable load combinations This is expressed as R ⱕ Rn / ⍀ (10.1) where R ⫽ required strength Rn ⫽ nominal strength (specified in Chapters B through E of the Specification) ⍀ ⫽ safety factor (see Table 10.1) Rn / ⍀ ⫽ allowable design strength ASD Load Combinations In the absence of an applicable code or specification or if the applicable code or specification does not include ASD load combinations, the structure and its components should be designed so that allowable design strengths equal or exceed the effects of the nominal loads for each of the following load combinations: D D ⫹ L ⫹ (Lr or S or Rr) D ⫹ (W or E ) D ⫹ L ⫹ (Lr or S or Rr) ⫹ (W or E ) Wind or Earthquake Loads for ASD When the seismic load model specified by the applicable code or specification is limit state based, the resulting earthquake load (E ) is permitted to be multiplied by 0.67 Additionally, when the specified load combinations include wind or earthquake loads, the resulting forces are permitted to be multiplied by 0.75 However, no decrease in forces is permitted when designing diaphragms 10.6 SECTION TEN Composite Construction under ASD For the composite construction of floors and roofs using cold-formed deck, the combined effects of the weight of the deck, the weight of the wet concrete, and construction loads (such as equipment, workmen, formwork) must be considered 10.4.2 LRFD Requirements LRFD Strength Requirements A design satisfies the requirements of the AISI Specification when the design strength of each structural component equals or exceeds the required strength determined on the basis of the nominal loads, multiplied by the appropriate load factors, for all applicable load combinations This is expressed as Ru ⬍ Rn where Ru Rn Rn ⫽ ⫽ ⫽ ⫽ (10.2) required strength nominal strength (specified in chapters B through E of the Specification) resistance factor (see Table 10.1) design strength LRFD Load Factors and Load Combinations In the absence of an applicable code or specification, or if the applicable code or specification does not include LRFD load combinations and load factors, the structure and its components should be designed so that design strengths equal or exceed the effects of the factored nominal loads for each of the following combinations: 1.4D 1.2D 1.2D 1.2D 1.2D 0.9D ⫹ ⫹ ⫹ ⫹ ⫹ ⫺ L 1.6L ⫹ 0.5(Lr or S or Rr) 1.6(Lr or S or Rr) ⫹ (0.5L or 0.8W ) 1.3W ⫹ 0.5L ⫹ 0.5(Lr or S or Rr) 1.5E ⫹ 0.5L ⫹ 0.2S (1.3W or 1.5E ) Several exceptions apply: The load factor for E in combinations (5) and (6) should equal 1.0 when the seismic load model specified by the applicable code or specification is limit state based The load factor for L in combinations (3), (4), and (5) should equal 1.0 for garages, areas occupied as places of public assembly, and all areas where the live load is greater than 100 psf For wind load on individual purlins, girts, wall panels and roof decks, multiply the load factor for W by 0.9 The load factor for Lr in combination (3) should equal 1.4 in lieu of 1.6 when the roof live load is due to the presence of workmen and materials during repair operations Composite Construction under LRFD For the composite construction of floors and roofs using cold-formed deck, the following additional load combination applies: 1.2DS ⫹ 1.6CW ⫹ 1.4C (10.3) where DS ⫽ weight of steel deck CW ⫽ weight of wet concrete C ⫽ construction load (including equipment, workmen, and form work but excluding wet concrete COLD-FORMED STEEL DESIGN 10.5 10.7 SECTION PROPERTY CALCULATIONS Because of the flexibility of the manufacturing method and the variety of shapes that can be manufactured, properties of cold-formed sections often must be calculated for a particular configuration of interest rather than relying on tables of standard values However, properties of representative or typical sections are listed in the Cold-Formed Steel Design Manual, American Iron and Steel Institute, 1996, Washington, DC (AISI Manual ) Because the cross section of a cold-formed section is generally of a single thickness of steel, computation of section properties may be simplified by using the linear method With this method, the material is considered concentrated along the centerline of the steel sheet and area elements are replaced by straight or curved line elements Section properties are calculated for the assembly of line elements and then multiplied by the thickness, t Thus, the cross section area is given by A ⫽ L ⫻ t, where L is the total length of all line elements; the moment of inertia of the section is given by I ⫽ I ⬘ ⫻ t, where I ⬘ is the moment of inertia determined for the line elements; and the section modulus is calculated by dividing I by the distance from the neutral axis to the extreme fiber, not to the centerline of the extreme element As subsequently discussed, it is sometimes necessary to use a reduced or effective width rather than the full width of an element Most sections can be divided into straight lines and circular arcs The moments of inertia and centroid location of such elements are defined by equations from fundamental theory as presented in Table 10.2 10.6 EFFECTIVE WIDTH CONCEPT The design of cold-formed steel differs from heavier construction in that elements of members typically have large width-to-thickness (w / t) ratios and are thus subject to local buckling Figure 10.2 illustrates local buckling in beams and columns Flat elements in compression that have both edges parallel to the direction of stress stiffened by a web, flange, lip or stiffener are referred to as stiffened elements Examples in Fig 10.2 include the top flange of the channel and the flanges of the I-cross section column To account for the effect of local buckling in design, the concept of effective width is employed for elements in compression The background for this concept can be explained as follows Unlike a column, a plate does not usually attain its maximum load carrying capacity at the buckling load, but usually shows significant post buckling strength This behavior is illustrated in Fig 10.3, where longitudinal and transverse bars represent a plate that is simply supported along all edges As the uniformly distributed end load is gradually increased, the longitudinal bars are equally stressed and reach their buckling load simultaneously However, as the longitudinal bars buckle, the transverse bars develop tension in restraining the lateral deflection of the longitudinal bars Thus, the longitudinal bars not collapse when they reach their buckling load but are able to carry additional load because of the transverse restraint The longitudinal bars nearest the center can deflect more than the bars near the edge, and therefore, the edge bars carry higher loads after buckling than the center bars The post buckling behavior of a simply supported plate is similar to that of the grid model However, the ability of a plate to resist shear strains that develop during buckling also contributes to its post buckling strength Although the grid shown in Fig 10.3a buckled into only one longitudinal half-wave, a longer plate may buckle into several waves as illustrated in Figs 10.2 and 10.3b For long plates, the half-wave length approaches the width b After a simply supported plate buckles, the compressive stress will vary from a maximum near the supported edges to a minimum at the mid-width of the plate as shown by line of 10.8 SECTION TEN TABLE 10.2 Moment of Inertia for Line Elements Source: Adapted from Cold-Formed Steel Design Manual, American Iron and Steel Institute, 1996, Washington, DC COLD-FORMED STEEL DESIGN 10.9 FIGURE 10.2 Local buckling of compression elements (a) In beams; (b) in columns (Source: Commentary on the Specification for the Design of ColdFormed Steel Structural Members, American Iron and Steel Institute, Washington, DC, 1996, with permission.) Fig 10.3c As the load is increased the edge stresses will increase, but the stress in the midwidth of the plate may decrease slightly The maximum load is reached and collapse is initiated when the edge stress reaches the yield stress—a condition indicated by line of Fig 10.3c The post buckling strength of a plate element can be considered by assuming that after buckling, the total load is carried by strips adjacent to the supported edges which are at a uniform stress equal to the actual maximum edge stress These strips are indicated by the dashed lines in Fig 10.3c The total width of the strips, which represents the effective width of the element b, is defined so that the product of b and the maximum edge stress equals the actual stresses integrated over the entire width The effective width decreases as the applied stress increases At maximum load, the stress on the effective width is the yield stress Thus, an element with a small enough w / t will be able to reach the yield point and will be fully effective Elements with larger ratios will have an effective width that is less than the full width, and that reduced width will be used in section property calculations The behavior of elements with other edge-support conditions is generally similar to that discussed above However, an element supported along only one edge will develop only one effective strip Equations for calculating effective widths of elements are given in subsequent articles based on the AISI Specification These equations are based on theoretical elastic buckling theory but modified to reflect the results of extensive physical testing 10.10 SECTION TEN FIGURE 10.3 Effective width concept (a) Buckling of grid model; (b) buckling of plate; (c) stress distributions ... singly-, doubly-, and point-symmetric sections is given by Eq 10. 25 These provisions apply to I-, Z-, C-, and other singly-symmetric sections, but not to multiple-web decks, U- and box sections... testing 10. 10 SECTION TEN FIGURE 10. 3 Effective width concept (a) Buckling of grid model; (b) buckling of plate; (c) stress distributions COLD-FORMED STEEL DESIGN 10. 7 10. 11 MAXIMUM WIDTH-TO-THICKNESS... singly-, doubly-, and point symmetric sections: Me ⫽ Cbro A兹eyt for bending about the symmetry axis (10. 29) 10. 18 SECTION TEN Me ⫽ Cs ⫽ Cs ⫽ ex ⫽ ey ⫽ t ⫽ For singly-symmetric sections, x-axis