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10.1

SECTION 10COLD-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-formedto cross section shape from sheet steels. Cold-formed steel members include such productsas purlins and girts for the construction of metal buildings, studs and joists for light com-mercial and residential construction, supports for curtain wall systems, formed deck for theconstruction 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 utilizedin 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 manyapplications. 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 Specificationfor 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 cold-formed to shape from carbon or low-alloy steel sheet, strip, plate, or bar, not more than 1-in thick, used for load carrying purposes in buildings. With appropriate allowances, it canbe used for other applications as well. The vast majority of applications are in a thicknessrange from about 0.014 to 0.25 in.

The design information presented in this section is based on the AISI Specification andits Commentary, including revisions being processed. The design equations are written indimensionless form, except as noted, so that any consistent system of units can be used. Asynopsis of key design provisions is given in this section, but reference should be made tothe 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 1 (A36, A242,A588, and A572). A283 and A529 plate steels are also included, as well as A500 structuraltubing (Table 1.7). Other steels can be used for structural members if they meet the ductilityrequirements. The basic requirement is a ratio of tensile strength to yield stress not less than1.08 and a total elongation of at least 10% in 2 in. If these requirements cannot be met,alternative criteria related to local elongation may be applicable. In addition, certain steelsthat do not meet the criteria, such as Grade 80 of A653 or Grade E of A611, can be used

10.2 SECTION TEN

FIGURE 10.1 Typical cold-formed steel members.

for multiple-web configurations (roofing, siding, decking, etc.) provided the yield stress istaken as 75% of the specified minimum (or 60 ksi or 414 MPa, if less) and the tensile stressis taken as 75% of the specified minimum (or 62 ksi or 428 MPa if less). Some exceptionsapply. 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 bendingoperation at room temperature, rather than the hot rolling process used for the heavier struc-tural steel shapes. The dominant cold forming process is known as roll-forming. In thisprocess, a coil of steel is fed through a series of rolls, each of which bends the sheetprogressively until the final shape is reached at the last roll stand. The number of roll standsmay vary from 6 to 20, depending upon the complexity of the shape. Because the steel isfed in coil form, with successive coils weld-spliced as needed, the process can achieve speedsup to about 300 ft /min and is well suited for quantity production. Small quantities may beproduced on a press-brake, particularly if the shape is simple, such as an angle or channelcross section. In its simplest form, a press brake consists of a male die which presses thesteel sheet into a matching female die.

In general, the cold-forming operation is beneficial in that it increases the yield strengthof the material in the region of the bend. The flat material between bends may also showan increase due to squeezing or stretching during roll forming. This increase in strength isattributable to cold working and strain aging effects as discussed in Art. 1.10. The strengthincrease, which may be small for sections with few bends, can be conservatively neglected.Alternatively, subject to certain limitations, the AISI Specification includes provisions forusing a section-average design yield stress that includes the strength increase from cold-forming. Either full section tension tests, full section stub column tests, or an analyticalmethod 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

ASDsafety

factor, �

LRFDresistancefactor, �

Tension members 1.67 0.95

Flexural members(a) Bending strength

Sections with stiffened or partially stiffened compression flanges 1.67 0.95Sections with unstiffened compression flanges 1.67 0.90Laterally unbraced beams 1.67 0.90Beams having one flange through-fastened to deck or sheathing (C- or Z-sections) 1.67 0.90Beams having one flange fastened to a standing seam roof system 1.67 0.90

(b) Web designShear strength controlled by yielding (Condition a, Art. 10.12.4) 1.50 1.00Shear strength controlled by buckling (Condition b or c, Art. 10.12.4) 1.67 0.90Web crippling of single unreinforced webs 1.85 0.75Web crippling of I-sections 2.00 0.80Web crippling of two nested Z-sections 1.80 0.85

Stiffeners(a) Transverse stiffeners 2.00 0.85(b) Shear stiffeners 1.50 /1.67 1.00 /0.90

Concentrically loaded compression members 1.80 0.85

Combined axial load and bending(a) Tension component 1.67 0.95(b) Compression component 1.80 0.85(c) Bending component 1.67 0.90 /0.95

Cylindrical tubular members(a) Bending 1.67 0.95(b) Axial compression 1.80 0.85

Wall studs(a) Compression 1.80 0.85(b) Bending 1.67 0.90 /0.95

Diaphragm construction 2.00 /3.00 0.50 /0.65

Welded connections(a) Groove welds

Tension or compression 250 0.90Shear, welds 2.50 0.80Shear, base metal 2.50 0.90

(b) Arc spot weldsShear, welds 2.50 0.60Shear, connected part 2.50 0.50 /0.60Shear, minimum edge distance 2.50 0.60 /0.70Tension 2.50 0.60

(c) Arc seam weldsShear, welds 2.50 0.60Shear, connected part 2.50 0.60

(d) Fillet weldsWelds 2.50 0.60Connected part, longitudinal loading

Weld length / sheet thickness �25 2.50 0.60Weld length / sheet thickness �25 2.50 0.55

Connected part, transverse loading 2.50 0.60

10.4 SECTION TEN

TABLE 10.1 Safety Factors and Resistance Factors Adopted by the AISI Specification (Continued )

Category

ASDsafety

factor, �

LRFDresistancefactor, �

(e) Flare groove weldsWelds 2.50 0.60Connected part, longitudinal loading 2.50 0.55Connected part, transverse loading 2.50 0.55

(f ) Resistance welds 2.50 0.65

Bolted connections(a) Minimum spacing and edge distance*

When Fu /Fsy � 1.08 2.00 0.70When Fu /Fsy � 1.08 2.22 0.60

(b) Tension strength on net sectionWith washers, double shear connection 2.00 0.65With washers, single shear connection 2.22 0.55Without washers, double or single shear 2.22 0.65

(c) Bearing strength 2.22 0.55 /0.70

(d) Shear strength of bolts 2.40 0.65

(e) Tensile strength of bolts 2.00 /2.25 0.75

Screw connections 3.00 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 operationmay also induce residual stresses in the member but these effects are accounted for in theequations for member design.

10.3 NOMINAL LOADS

The nominal loads for design should be according to the applicable code or specificationunder which the structure is designed or as dictated by the conditions involved. In the absenceof a code or specification, the nominal loads should be those stipulated in the AmericanSociety of Civil Engineers Standard, Minimum Design Loads for Buildings and Other Struc-tures, ASCE 7. The following loads are used for the primary load combinations in the AISISpecification:

D � Dead load, which consists of the weight of the member itself, the weight of allmaterials of construction incorporated into the building which are supported by the mem-ber, including built-in partitions; and the weight of permanent equipmentE � Earthquake loadL � Live loads due to intended use and occupancy, including loads due to movable objectsand movable partitions and loads temporarily supported by the structure during mainte-nance. (L includes any permissible load reductions. If resistance to impact loads is takeninto account in the design, such effects should be included with the live load.)


Lr � Roof live loadS � Snow load

Rr � Rain load, except for pondingW � Wind load

The effects of other loads such as those due to ponding should be considered when signif-icant. Also, unless a roof surface is provided with sufficient slope toward points of freedrainage or adequate individual drains to prevent the accumulation of rainwater, the roofsystem 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 varioustypes 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 strengthbased on nominal loads. For Load and Resistance Factor Design (LRFD), the nominalstrength is multiplied by a resistance factor and compared to the required strength based onfactored loads. These procedures and pertinent load combinations to consider are set forthin the specification as follows.

10.4.1 ASD Requirements

ASD Strength Requirements. A design satisfies the requirements of the AISI Specificationwhen the allowable design strength of each structural component equals or exceeds therequired strength, determined on the basis of the nominal loads, for all applicable loadcombinations. This is expressed as

R � R /� (10.1)n

where R � required strengthRn � 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 theapplicable code or specification does not include ASD load combinations, the structure andits components should be designed so that allowable design strengths equal or exceed theeffects of the nominal loads for each of the following load combinations:

1. D2. D � L � (Lr or S or Rr)3. D � (W or E )4. D � L � (Lr or S or Rr) � (W or E )

Wind or Earthquake Loads for ASD. When the seismic load model specified by theapplicable code or specification is limit state based, the resulting earthquake load (E ) ispermitted to be multiplied by 0.67. Additionally, when the specified load combinations in-clude 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 roofsusing cold-formed deck, the combined effects of the weight of the deck, the weight of thewet concrete, and construction loads (such as equipment, workmen, formwork) must beconsidered.

10.4.2 LRFD Requirements

LRFD Strength Requirements. A design satisfies the requirements of the AISI Specificationwhen the design strength of each structural component equals or exceeds the requiredstrength determined on the basis of the nominal loads, multiplied by the appropriate loadfactors, for all applicable load combinations. This is expressed as

R � �R (10.2)u n

where Ru � required strengthRn � nominal strength (specified in chapters B through E of the Specification)� � resistance factor (see Table 10.1)

�Rn � design strength

LRFD Load Factors and Load Combinations. In the absence of an applicable code orspecification, or if the applicable code or specification does not include LRFD load combi-nations and load factors, the structure and its components should be designed so that designstrengths equal or exceed the effects of the factored nominal loads for each of the followingcombinations:

1. 1.4D � L2. 1.2D � 1.6L � 0.5(Lr or S or Rr)3. 1.2D � 1.6(Lr or S or Rr) � (0.5L or 0.8W )4. 1.2D � 1.3W � 0.5L � 0.5(Lr or S or Rr)5. 1.2D � 1.5E � 0.5L � 0.2S6. 0.9D � (1.3W or 1.5E )

Several exceptions apply:

1. The load factor for E in combinations (5) and (6) should equal 1.0 when the seismic loadmodel specified by the applicable code or specification is limit state based.

2. The load factor for L in combinations (3), (4), and (5) should equal 1.0 for garages, areasoccupied as places of public assembly, and all areas where the live load is greater than100 psf.

3. For wind load on individual purlins, girts, wall panels and roof decks, multiply the loadfactor for W by 0.9.

4. The load factor for Lr in combination (3) should equal 1.4 in lieu of 1.6 when the rooflive 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:

1.2D � 1.6C � 1.4C (10.3)S W

where DS � weight of steel deckCW � weight of wet concrete

C � construction load (including equipment, workmen, and form work but excludingwet concrete


10.5 SECTION PROPERTY CALCULATIONS

Because of the flexibility of the manufacturing method and the variety of shapes that can bemanufactured, properties of cold-formed sections often must be calculated for a particularconfiguration of interest rather than relying on tables of standard values. However, propertiesof 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 ofsteel, computation of section properties may be simplified by using the linear method. Withthis method, the material is considered concentrated along the centerline of the steel sheetand area elements are replaced by straight or curved line elements. Section properties arecalculated 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 ofinertia determined for the line elements; and the section modulus is calculated by dividingI by the distance from the neutral axis to the extreme fiber, not to the centerline of theextreme element. As subsequently discussed, it is sometimes necessary to use a reduced oreffective width rather than the full width of an element.

Most sections can be divided into straight lines and circular arcs. The moments of inertiaand centroid location of such elements are defined by equations from fundamental theory aspresented in Table 10.2.

10.6 EFFECTIVE WIDTH CONCEPT

The design of cold-formed steel differs from heavier construction in that elements of mem-bers typically have large width-to-thickness (w / t) ratios and are thus subject to local buck-ling. Figure 10.2 illustrates local buckling in beams and columns. Flat elements in com-pression 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 topflange 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 isemployed for elements in compression. The background for this concept can be explainedas follows.

Unlike a column, a plate does not usually attain its maximum load carrying capacity atthe buckling load, but usually shows significant post buckling strength. This behavior isillustrated in Fig. 10.3, where longitudinal and transverse bars represent a plate that is simplysupported along all edges. As the uniformly distributed end load is gradually increased, thelongitudinal bars are equally stressed and reach their buckling load simultaneously. However,as the longitudinal bars buckle, the transverse bars develop tension in restraining the lateraldeflection of the longitudinal bars. Thus, the longitudinal bars do not collapse when theyreach their buckling load but are able to carry additional load because of the transverserestraint. The longitudinal bars nearest the center can deflect more than the bars near theedge, and therefore, the edge bars carry higher loads after buckling than do the center bars.

The post buckling behavior of a simply supported plate is similar to that of the gridmodel. However, the ability of a plate to resist shear strains that develop during bucklingalso contributes to its post buckling strength. Although the grid shown in Fig. 10.3a buckledinto only one longitudinal half-wave, a longer plate may buckle into several waves as illus-trated in Figs. 10.2 and 10.3b. For long plates, the half-wave length approaches the widthb.

After a simply supported plate buckles, the compressive stress will vary from a maximumnear the supported edges to a minimum at the mid-width of the plate as shown by line 1 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.


FIGURE 10.2 Local buckling of compression elements. (a) In beams; (b) incolumns. (Source: Commentary on the Specification for the Design of Cold-Formed 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 mid-width of the plate may decrease slightly. The maximum load is reached and collapse isinitiated when the edge stress reaches the yield stress—a condition indicated by line 2 ofFig. 10.3c.

The post buckling strength of a plate element can be considered by assuming that afterbuckling, the total load is carried by strips adjacent to the supported edges which are at auniform stress equal to the actual maximum edge stress. These strips are indicated by thedashed lines in Fig. 10.3c. The total width of the strips, which represents the effective widthof the element b, is defined so that the product of b and the maximum edge stress equalsthe actual stresses integrated over the entire width. The effective width decreases as theapplied stress increases. At maximum load, the stress on the effective width is the yieldstress.

Thus, an element with a small enough w / t will be able to reach the yield point and willbe fully effective. Elements with larger ratios will have an effective width that is less thanthe 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 thatdiscussed above. However, an element supported along only one edge will develop only oneeffective strip.

Equations for calculating effective widths of elements are given in subsequent articlesbased on the AISI Specification. These equations are based on theoretical elastic bucklingtheory 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 ofplate; (c) stress distributions.


10.7 MAXIMUM WIDTH-TO-THICKNESS RATIOS

The AISI Specification gives certain maximum width-to-thickness ratios that must be adheredto.

For flange elements, such as in flexural members or columns, the maximum flat width-to-thickness ratio, w/t, disregarding any intermediate stiffeners, is as follows:

Stiffened compression element having one longitudinal edge connected to a web or flangeelement, the other stiffened by(a) a simple lip, 60(b) other stiffener with IS � Ia, 90(c) other stiffener with IS � Ia, 90Stiffened compression element with both longitudinal edges connected to other stiffenedelements, 500Unstiffened compression element, 60

In the above, IS is the moment of inertia of the stiffener about its centroidal axis, parallel tothe element to be stiffened, and Ia is the moment of inertia of a stiffener adequate for theelement to behave as a stiffened element. Note that, although greater ratios are permitted,stiffened compression elements with w / t � 250, and unstiffened compression elements withw/t � 30 are likely to develop noticeable deformations at full design strength, but ability todevelop required strength will be unaffected.

For web elements of flexural members, the maximum web depth-to-thickness ratio, h/ t,disregarding any intermediate stiffeners, is as follows:

Unreinforced webs, 200Webs with qualified transverse stiffeners that include (a) bearing stiffeners only, 260(b) bearing and intermediate stiffeners, 300

10.8 EFFECTIVE WIDTHS OF STIFFENED ELEMENTS

10.8.1 Uniformly Compressed Stiffened Elements

The effective width for load capacity determination depends on a slenderness factor � definedas

1.052 w ƒ� � (10.4)� � �t E�k

where k � plate buckling coefficient (4.0 for stiffened elements supported by a web alongeach longitudinal edge; values for other conditions are given subsequently)

ƒ � maximum compressive stress (with no safety factor applied)E � Modulus of elasticity (29,500 ksi or 203 000 MPa)

10.12 SECTION TEN

FIGURE 10.4 Illustration of uniformly compressed stiffened element. (a) Actual element; (b) stress oneffective element. (Source: Specification for the Design of Cold-Formed Steel Structural Members, Amer-ican Iron and Steel Institute, Washington, DC, 1996, with permission.)

For flexural members, when initial yielding is in compression, ƒ � Fy , where Fy is the yieldstress; when the initial yielding is in tension, ƒ � the compressive stress determined on thebasis of effective section. For compression members, ƒ � column buckling stress.

The effective width is as follows:

when � � 0.673, b � w (10.5)

when � � 0.673, b � �w (10.6)

where the reduction factor � is defined as

� � (1 � 0.22/�) /� (10.7)

Figure 10.4 shows the location of the effective width on the cross section, with one-halflocated adjacent to each edge.

Effective widths determined in this manner, based on maximum stresses (no safety factor)define the cross section used to calculate section properties for strength determination. How-ever, at service load levels, the effective widths will be greater because the stresses aresmaller, and another set of section properties should be calculated. Therefore, to calculateeffective width for deflection determination, use the above equations but in Eq. 10.4, sub-stitute the compressive stress at design loads, ƒd.

10.8.2 Stiffened Elements with Stress Gradient

Elements with stress gradients include webs subjected to compression from bending aloneor from a combination of bending and uniform compression. For load capacity determination,the effective widths b1 and b2 illustrated in Fig. 10.5 must be determined. First, calculatethe ratio of stresses

� � ƒ /ƒ (10.8)2 1

where ƒ1 and ƒ2 are the stresses as shown, calculated on the basis of effective section, withno safety factor applied. In this case ƒ1 is compression and treated as �, while ƒ2 can beeither tension (�) or compression (�). Next, calculate the effective width, be, as if theelement was in uniform compression (Art. 10.8.1) using ƒ1 for ƒ and with k determined asfollows:

3k � 4 � 2(1 � � ) � 2(1 � �) (10.9)

Effective widths b1 and b2 are determined from the following equations:


FIGURE 10.5 Illustration of stiffened element with stress gradient. (a) Actual element; (b) stress on ef-fective element varying from compression to tension; (c) stress on effective element with non-uniform com-pression. (Source: Specification for the Design of Cold-Formed Steel Structural Members, American Ironand Steel Institute, Washington, DC, 1996, with permission.)

b � b / (3 � �) (10.10)1 e

b � b /2 (10.11)2 e

The sum of b1 and b2 must not exceed the width of the compression portion of the webcalculated on the basis of effective section.

Effective width for deflection determination is calculated in the same manner except thatstresses are calculated at service load levels based on the effective section at that load.

10.14 SECTION TEN

FIGURE 10.6 Illustration of uniformly compressed unstiffened element. (a) Actual element; (b) stresson effective element. (Source: Specification for the Design of Cold-Formed Steel Structural Members,American Iron and Steel Institute, Washington, DC, 1996, with permission.)

10.9 EFFECTIVE WIDTHS OF UNSTIFFENED ELEMENTS

10.9.1 Uniformly Compressed Unstiffened Elements

The effective widths for uniformly compressed unstiffened elements are calculated in thesame manner as for stiffened elements (Art. 10.8.1), except that k in Eq. 10.4 is taken as0.43. Figure 10.6 illustrates the location of the effective width on the cross section.

10.9.2 Unstiffened Elements and Edge Stiffeners with Stress Gradient

The effective width for unstiffened elements (including edge stiffeners) with a stress gradientis calculated in the same manner as for uniformly loaded stiffened elements (Art. 10.9.1)except that (1) k in Eq. 10.4 is taken as 0.43, and (2) the stress ƒ3 is taken as the maximumcompressive stress in the element. Figure 10.7 shows the location of ƒ3 and the effectivewidth for an edge stiffener consisting of an inclined lip. (Such lips are more structurallyefficient when bent at 90, but inclined lips allow nesting of certain sections.)

10.10 EFFECTIVE WIDTHS OF UNIFORMLY COMPRESSEDELEMENTS WITH EDGE STIFFENER

A commonly encountered condition is a flange with one edge stiffened by a web, the otherby an edge stiffener (Fig. 10.7). To determine its effective width for load capacity determi-nation, one of three cases must be considered. The case selection depends on the relationbetween the flange flat width-to-thickness ratio, w/t, and the parameter S defined as

S � 1.28�E /ƒ (10.12)

For each case an equation will be given for determining Ia, the moment of inertia requiredfor a stiffener adequate so that the flange element behaves as a stiffened element, IS is themoment of inertia of the full section of the stiffener about its centroidal axis, parallel to theelement to be stiffened. A�S is the effective area of a stiffener of any shape, calculated bymethods previously discussed. The reduced area of the stiffener to be used in section propertycalculations is termed AS and its relation to A�S is given for each case. Note that for edgestiffeners, the rounded corner between the stiffener and the flange is not considered as partof the stiffener in calculations. The following additional definitions for a simple lip stiffenerillustrated in Fig. 10.7 apply. The effective width dS� is that of the stiffener calculated ac-cording to Arts. 10.9.1 and 10.9.2. The reduced effective width to be used in section property


FIGURE 10.7 Illustration of element with edge stiffener. (a) Actual element; (b) stress on effective element andstiffener. (Source: Specification for the Design of Cold-Formed Steel Structural Members, American Iron and SteelInstitute, Washington, DC 1996, with permission.)

calculations is termed dS and its relation to dS� is given for each case. For the inclined stiffenerof flat depth d at an angle as shown in Fig. 10.7,

3 2I � (d t sin ) /12 (10.13)S

A� � d �t (10.14)S S

Limit d / t to 14.

Case I: w / t � S /3

For this condition, the flange element is fully effective without an edge stiffener so b �w, Ia � 0, dS � dS�, AS � A�S.

Case II: S /3 � w / t � S

4 3I � 399t {[(w / t) /S] � �k /4} (10.15)a u

where ku � 0.43. The effective width b is calculated according to Art. 10.8.1 using thefollowing k:

10.16 SECTION TEN

nk � C (k � k ) � k (10.16)2 a u u

where n � 1/2, C2 � IS / Ia, and C1 � 2 � C2. The coefficients C1 and C2 give the proportionof the effective width to be placed along either edge of the flange, Fig. 10.7. The platebuckling coefficient ka and other terms are determined as follows:

For a simple lip stiffener with 140 � � 40 and D /w � 0.8 (see Fig. 10.7),

k � 5.25 � 5(D /w) � 4.0 (10.17)a

d � C d � (10.18)S 2 S

For other stiffeners,

k � 4.0 (10.19)a

A � C A � (10.20)S 2 S

Case III: w / t � S

4I � t {[115(w / t) /S] � 5} (10.21)a

The following are calculated as for Case II, but with n � 1/3: C1, C2, b, k, dS, and AS.For all cases, effective width for deflection determination is calculated in the same manner

except that stresses are calculated at service load levels based on the effective section at thatload.

10.11 TENSION MEMBERS

The nominal tensile strength, Tn, of an axial loaded tension member is the smallest of threelimit states: (1) yielding in the gross section, Eq. 10.22; (2) fracture in the net section awayfrom the connections, Eq. 10.23; and (3) fracture in the net section at connections (Art.10.18.2)

T � A F (10.22)n g y

T � A F (10.23)n n u

where Ag is the gross cross section area, An is the net cross section area, Fy is the designyield stress and Fu is the tensile strength.

As with all of the member design provisions, these nominal strengths must be dividedby a safety factor, �, for ASD (Art. 10.4.1) or multiplied by a resistance factor, �, forLRFD (Art. 10.4.2). See Table 10.1 for � and � values for the appropriate member orconnection category.

10.12 FLEXURAL MEMBERS

In the design of flexural members consideration must be given to bending strength, shearstrength, and web crippling, as well as combinations thereof, as discussed in subsequentarticles. Bending strength must consider both yielding and lateral stability. In some appli-cations, deflections are also an important consideration.


10.12.1 Nominal Strength Based on Initiation of Yielding

For a fully braced member, the nominal strength, Mn, is the effective yield moment basedon section strength:

M � S F (10.24)n e y

where Se is the elastic section modulus of the effective section calculated with the extremefiber at the design yield stress, Fy. The stress in the extreme fiber can be compression ortension depending upon which is farthest from the neutral axis of the effective section. Ifthe extreme fiber stress is compression, the effective width (Art. 10.8–10.10) and the effectivesection can be calculated directly based on the stress Fy in that compression element. How-ever, if the extreme fiber stress is tension, the stress in the compression element depends onthe effective section and, therefore, a trial and error solution is required (Art. 10.22).

10.12.2 Nominal Strength Based on Lateral Buckling

For this condition, the nominal strength, Mn, of laterally unbraced segments of singly-, dou-bly-, 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.Also, beams with one flange fastened to deck, sheathing, or standing seam roof systems aretreated separately. The nominal strength is

M � S M /S (10.25)n c c ƒ

where Sƒ � Elastic section modulus of the full unreduced section for the extreme compres-sion fiber

Sc � Elastic section modulus of the effective section calculated at a stress Mc /Sƒ inthe extreme compression fiber

Mc � Critical moment calculated as follows:

For Me � 2.78 My

M � M (10.26)c y

For 2.78 My � Me � 0.56My

10M10 yM � M 1 � (10.27)� �c y9 36Me

For Me � 0.56My

M � M (10.28)c e

where My � Moment causing initial yield at the extreme compression fiber of the full section� SƒFy

Me � Elastic critical moment calculated according to (a) or (b) below:(a) For singly-, doubly-, and point symmetric sections:

M � C r A�� for bending about the symmetry axis. (10.29)e b o ey t

10.18 SECTION TEN

For singly-symmetric sections, x-axis is the axis of symmetry oriented suchthat the shear center has a negative x-coordinate. For point-symmetric sec-tions, use 0.5 Me.Alternatively, Me can be calculated using the equation for doubly-symmetricI-sections or point-symmetric sections given in (b).

Me � Cs A�ex[ j � C s ] /CT F for bending (10.30)2 2� j � r (� /� )o t ex

about the centroidal axis perpendicular to the symmetry axis for singly-symmetric sections only

Cs � �1 for moment causing compression on the shear center side of the centroidCs � �1 for moment causing tension on the shear center side of the centroid

�ex �2� E

2(K L /r )x x x (10.31)

�ey �2� E

2(K L /r )y y y (10.32)

�t �21 � ECwGJ �� 2 2Ar (K L )o t t (10.33)

A � Full cross-sectional area

Cb �12.5Mmax

2.5M � 3M � 4M � 3Mmax A B C (10.34)

where Mmax � absolute value of maximum moment in the unbraced segmentMA � absolute value of moment at quarter point of unbraced segmentMB � absolute value of moment at centerline of unbraced segmentMC � absolute value of moment at three-quarter point of unbraced segment Cb is

permitted to be conservatively taken as unity for all cases.For cantilevers or overhangs where the free end is unbraced, Cb � 1.0. Formembers subject to combined compressive axial load and bending moment(Art. 10.15), Cb � 1.0.

E � Modulus of elasticity

CT F � 0.6 � 0.4 (M1 /M2) (10.35)

whereM1 is the smaller and M2 the larger bending moment at the ends of theunbraced length in the plane of bending, and where M1 /M2, the ratio of endmoments, is positive when M1 and M2 have the same sign (reverse curvaturebending) and negative when they are of opposite sign (single curvature bend-ing). When the bending moment at any point within an unbraced length islarger than that at both ends of this length, and for members subject to com-bined compressive axial load and bending moment (Art. 10.15), CT F � 1.0.

ro � Polar radius of gyration of the cross section about the shear center

ro � (10.36)2 2 2�r � r � xx y o

rx , ry � Radii of gyration of the cross section about the centroidal principal axesG � Shear modulus (11,000 ksi or 78 000 MPa)

Kx , Ky , Kt � Effective length factors for bending about the x- and y-axes, and for twistingLx , L y , L t � Unbraced length of compression member for bending about the x- and y-axes,

and for twistingxo � Distance from the shear center to the centroid along the principal x-axis, taken

as negativeJ � St. Venant torsion constant of the cross section

Cw � Torsional warping constant of the cross section


TABLE 10.3 R values for Simple Spans(See Eq. 10.40)

Section depth, d, in Profile R*

d � 6.5 C or Z 0.706.5 � d � 8.5 C or Z 0.658.5 � d � 11.5 Z 0.508.5 � d � 11.5 C 0.40

* For simple spans, multiply R by the correctionfactor r to account for the effects of compressedinsulation between the sheeting and the member:For uncompressed batt insulation of thickness ti, thefactor is r � 1.00 � 0.01ti (in), or r � 1.00 �0.004ti (mm).

j � (10.37)1 3 2[� x dA � � xy dA] � xA A o2Iy

(b) For I- or Z-sections bent about the centroidal axis perpendicular to the web (x-axis): Inlieu of (a), the following equations may be used to evaluate Me :

Me � for doubly-symmetric I-sections (10.38)2� EC dIb yc

2L

� for point-symmetric Z-sections (10.39)2� EC dIb yc

22L

d � Depth of sectionL � Unbraced length of the member

Iyc � Moment of inertia of the compression portion of a section about the gravityaxis of the entire section parallel to the web, using the full unreduced section

Other terms are defined in (a).

10.12.3 Beams (C- or Z- Section) Having One Flange Through-Fastened toDeck or Sheathing

If the tension flange of a beam is screwed to deck or sheathing and the compression flangeis unbraced, such as a roof purlin or wall girt subjected to wind suction, the bending strengthlies between that for a fully braced member and an unbraced member. This is due to therotational restraint provided by the spaced connections. Therefore, based on numerous tests,the AISI Specification gives the nominal strength in terms of a reduction factor R applied tothe nominal strength for the fully braced condition (Art. 10.12.1):

M � RS F (10.40)n e y

For continuous spans, R � 0.60 for C-sections, and 0.70 for Z-sections. For simple spans,R is given in Table 10.3.

The provisions do not apply for the region adjacent to a support between inflection pointsin a continuous beam. Numerous physical conditions are imposed, including member and

10.20 SECTION TEN

panel characteristics, span length (33 ft maximum), fasteners, and fastener spacing (12 inmaximum).

10.12.4 Beams (C- or Z- Section) Having One Flange Fastened to aStanding Seam Roof System

If the flange of a supporting beam is fastened to a standing seam roof system, the bendingstrength generally lies between that for a fully braced member and an unbraced member, butmay equal that for a fully braced member. The strength depends on the details of the system,as well as whether the loading is gravity or uplift, and cannot be readily calculated. There-fore, the AISI Specification allows the nominal strength to be calculated by Eq. 10.40, butwith the reduction factor R determined by representative tests of the system. Test specimensand procedures are detailed in the ‘‘Base Test Method’’ given in the AISI Manual. Alterna-tively, the rules for discrete point bracing (Art. 10.12.2) can be used.

10.12.5 Nominal Shear Strength

The AISI specification gives three equations for nominal shear strength of beam webs forthree categories or conditions of increasing web slenderness. Condition (a) is based on yield-ing, condition (b) is based on inelastic buckling, and condition (c) is based on elastic buck-ling.

(a) For h / t � 0.96 �Ek /Fv y

V � 0.60F ht (10.41)n y

(b) For 0.96 �Ek /F � h / t � 1.415 �Ek /Fv y v y

2V � 0.64t �k F E (10.42)n v y

(c) For h / t � 1.415 �Ek /Fv y

2 3� Ek tv 3V � � 0.905Ek t /h (10.43)n v212(1 � )h

where vn � Nominal shear strength of beamt � Web thicknessh � Depth of the flat portion of the web measured along the plane of the web

kv � Shear buckling coefficient determined as follows:

1. For unreinforced webs, kv � 5.342. For beam webs with transverse stiffeners satisfying AISI requirements

when a /h � 1.0

5.34k � 4.00 � (10.44)v 2(a /h)

when a /h � 1.0

4.00k � 5.34 � (10.45)v 2(a /h)

where a � the shear panel length for unreinforced web element� the clear distance between transverse stiffeners for reinforced web elements.


For a web consisting of two or more sheets, each sheet is considered as a separate elementcarrying its share of the shear force.

10.12.6 Combined Bending and Shear

Combinations of bending and shear may be critical at locations such as near interior supportsof continuous beams. To guard against this condition, the AISI Specification provides tradi-tional interaction equations, which depend on whether the beam web is unreinforced ortransversely stiffened. Although similar in concept, for clarity, separate equations are givenfor ASD and LRFD. Symbols have common definitions except as noted.

ASD Method. For beams with unreinforced webs, the required flexural strength, M, andrequired shear strength, V, must satisfy the following:

2 2� M � Vb v� � 1.0 (10.46)� � � �M Vnxo n

For beams with transverse web stiffeners, the required flexural strength, M, and requiredshear strength, V, shall not exceed Mn/�b and Vn/�v , respectively. When �bM/Mnxo � 0.5and �vV/Vn � 0.7, then M and V must satisfy the following interaction equation:

� M � Vb v0.6 � � 1.3 (10.47)� � � �M Vnxo n

where �b � factor of safety for bending (Table 10.1)�v � factor of safety for shear (Table 10.1)Mn � nominal flexural strength when bending alone exists

M �nxo nominal flexural strength about the centroidal x-axis determined in accordancewith AISI, excluding lateral buckling

Vn � nominal shear force when shear alone exists

LRFD Method. For beams with unreinforced webs, the required flexural strength, Mu, andrequired shear strength, Vu, must satisfy the following:

2 2M Vu u� � 1.0 (10.48)� � � �� M � Vb nxo v n

For beams with transverse web stiffeners the required flexural strength, Mu, and therequired shear strength, Vu, shall not exceed �bMn and �vVn, respectively. WhenMu / (�bM ) � 0.5 and Vu / (�vVn) � 0.7, then Mu and Vu must satisfy the following interac-nxo

tion equation:

M Vu u0.6 � � 1.3 (10.49)� � � �� M � Vb nxo v n

where �b � resistance factor for bending (Table 10.1)�v � resistance factor for shear (Table 10.1)Mn � nominal flexural strength when bending alone exists

10.12.7 Web Crippling

At points of concentrated loads or reactions, the webs of cold-formed members are suscep-tible to web crippling. If the web depth-to-thickness ratio, h / t, is greater than 200, stiffeners

10.22 SECTION TEN

TABLE 10.4 Equation Numbers for Nominal Strength of Webs at Concentrated Load or Reaction*

Load spacingLoad

location**

Single web shapes

Stiffened orpartially stiffened

flangesUnstiffened

flanges

Double web shapes(back-to-back C’s

or similar)

All types of flanges

Load on either flange or opposing loads,bearing edges spaced �1.5h

Beam endsBeam interiors

Eq. 10.50a†Eq. 10.50d

Eq. 10.50bEq. 10.50d

Eq. 10.50cEq. 10.50e

Opposing loads, bearing edges spaced�1.5h

Beam endsBeam interiors

Eq. 10.50fEq. 10.50h

Eq. 10.50ƒEq. 10.50h

Eq. 10.50gEq. 10.50i

* When Fy � 66.5 ksi (459 MPa), the value of kC3 should be taken as 1.34 in Eq. 10.50a, 10.50b, and 10.50f** Beam ends condition applies when distance from edge of bearing to end of beam is �1.5h; otherwise, beam interiors condition

applies.† For a Z-section with flange bolted to end support member, Eq. 10.50a may be multiplied by 1.3 for sections meeting the following

conditions: h / t � 150, R / t � 4, t � 0.060 in (1.52 mm), support member thickness �3⁄16 in (4.76 mm).

must be used to transmit the loads directly into the webs. For unstiffened webs, the AISISpecification gives equations to calculate the nominal bearing strength to resist the concen-trated load. The equations, which are based on the results of numerous tests, provide forseveral different conditions for load placement and type of section. They apply for beamswith R / t � 6, R is the radius between the flange and the web. They also apply to deck whenR / t � 7, N / t � 210, N /h � 3.5, where N is the bearing length.

Table 10.4 indicates the equation to be used for the various conditions. The nominalstrength to resist a concentrated load or reaction, per web, Pn (kips or N ), is calculated fromthe following equations:

2P � t kC C C C [331 � 0.61(h / t)][1 � 0.01(N / t)] (10.50a)n 3 4 9

2P � t kC C C C [217 � 0.28(h / t)][1 � 0.01(N / t)] (10.50b)n 3 4 9

When N / t � 60, the factor [1 � 0.01(N / t)] may be increased to [0.71 � 0.015(N / t)]

2P � t F C (10.0 � 1.25 �N / t) (10.50c)n y 6

2P � t kC C C C [538 � 0.74(h / t)][1 � 0.007(N / t)] (10.50d )n 1 2 9

When N / t � 60, the factor [1 � 0.007(N / t)] may be increased to [0.75 � 0.011(N / t)]

2P � t F C (0.88 � 0.12m)(15.0 � 3.25 �N / t) (10.50e)n y 5

2P � t kC C C C [244 � 0.57(h / t)][1 � 0.01(N / t)] (10.50f )n 3 4 9

2P � t F C (0.64 � 0.31 m)(10.0 � 1.25 �N / t) (10.50g)n y 8

2P � t kC C C C [771 � 2.26(h / t)][1 � 0.0013(N / t)] (10.50h)n 1 2 9

2P � t F C (0.82 � 0.15m)(15.0 � 3.25 �N / t) (10.50i)n y 7

In Eqs. 10.50a through 10.50i, the following definitions apply:


C � 1.22 � 0.22k (10.51a)1

C � 1.06 � 0.06R / t � 1.0 (10.51b)2

C � 1.33 � 0.33k (10.51c)3

C � 1.15 � 0.15R / t � 1.0 but not less than 0.50 (10.51d )4

C � 1.49 � 0.53k � 0.6 (10.51e)5

h / tC � 1 � when h / t � 150 (10.51f )� �6 750

� 1.20, when h / t � 150 (10.51g)

C � 1/k, when h / t � 66.5 (10.51h)7

h / t 1� 1.10 � , when h / t � 66.5 (10.51i)� �665 k

h / t 1C � 0.98 � (10.51j )� �8 865 k

C � 1.0 for U.S. customary units, kips and in9

� 6.9 for metric units, N and mm

C � 0.7 � 0.3( /90)2 (10.51k)

Fy � design yield stress of the web, ksi (MPa)

h � depth of the flat portion of the web measuredalong the plane of the web, in (mm)

k � 894 Fy /E (10.51l )

m � t /0.075, when t is in inches (10.51m)

m � t /1.91, when t is in mm (10.51n)

t � web thickness, in (mm)

N � actual length of bearing, in (mm). For the case oftwo equal and opposite concentratedloads distributed over unequal bearing lengths,the smaller value of N applies

R � inside bend radius

� angle between the plane of the web and theplane of the bearing surface �45, but notmore than 90

10.12.8 Combined Bending and Web Crippling Strength

For beams with unreinforced flat webs, combinations of bending and web crippling nearconcentrated loads or reactions must satisfy interaction equations given in the AISI Specifi-

10.24 SECTION TEN

cation. Equations are given for two types of webs and for nested Z-sections, with separateequations for ASD and LRFD. See the AISI Specification for various exceptions and limi-tations that may apply. Symbols have common definitions except as noted.

ASD Method

(a) For shapes having single unreinforced webs:

� P � Mw b1.2 � � 1.5 (10.52)� � � �P Mn nxo

(b) For shapes having multiple unreinforced webs such as I-sections made of two C-sectionsconnected back-to-back, or similar sections which provide a high degree of restraintagainst rotation of the web (such as I-sections made by welding two angles to a C-section):

� P � Mw b1.1 � � 1.5 (10.53)� � � �P Mn nxo

In Eqs. 10.52 and 10.53:

P � required strength for the concentrated load or reaction in the presence of bendingmoment

Pn � nominal strength for concentrated load or reaction in the absence of bending momentdetermined in accordance with Art. 10.12.6

M � required flexural strength at, or immediately adjacent to, the point of application ofthe concentrated load or reaction, P

Mnxo � nominal flexural strength about the centroidal x-axis determined in accordance withArt. 10.12.1

w � flat width of the beam flange which contacts the bearing platet � thickness of the web or flange

�w � safety factor for web crippling, Table 10.1�b � safety factor for bending, Table 10.1

(c) For the support point of two nested Z-sections:

M P� � 1.00 (10.54)

M Pno n

where M � required flexural strength at the section under considerationMno � nominal flexural strength for the nested Z-sections, i.e. sum of the two sections

evaluated individually, determined in accordance with Art. 10.12.1P � required strength for the concentrated load or reaction in the presence of bending

momentPn � nominal web crippling strength assuming single web interior one-flange loading

for the nested Z-sections, i.e., sum of the two webs evaluated individually

LRFD Method

(a) For shapes having single unreinforced webs:

P Mu u1.07 � � 1.42 (10.55)� � � �� P � Mw n b nxo

(b) For shapes having multiple unreinforced webs such as I-sections made of two C-sections


connected back-to-back, or similar sections which provide a high degree of restraintagainst rotation of the web (such as I-sections made by welding two angles to a C-section):

P Mu u0.82 � � 1.32 (10.56)� � � �� P � Mw n b nxo

In Eqs. 10.55 and 10.56:

�b � resistance factor for bending, Table 10.1�w � resistance factor for web crippling, Table 10.1Pu � required strength for the concentrated load or reaction in the presence of bending

momentMu � required flexural strength at, or immediately adjacent to, the point of application

of the concentrated load or reaction Pu

(c) For two nested Z-sections:

M Pu u� � 1.68� (10.57)M Pno n

Mu � required flexural strength at the section under considerationPu � required strength for the concentrated load or reaction in the presence of bending

moment� � 0.9

10.13 CONCENTRICALLY LOADED COMPRESSION MEMBERS

These provisions are for members in which the resultant of all loads is an axial load passingthrough the effective section calculated at the stress Fn as subsequently defined. Concentri-cally loaded angle sections should be designed for an additional moment according to theAISI Specification. The slenderness ratio, KL /r, of all compression members should prefer-ably be limited to 200 (300 during construction).

The nominal axial strength, Pn, is

P � A F (10.58)n e n

where Ae is the effective area at the stress Fn, which is determined as follows.2�For � � �1.5 F � (0.658 )F (10.59a)cc n y

0.877For � � �1.5 F � F (10.59b)� �c n y2�c

where

Fy� � (10.60)c �Fe

Fe is the least of the elastic flexural, torsional and torsional-flexural buckling stresses (Arts.10.14.1–10.14.3). Equation 10.59a is based on elastic buckling while Eq. 10.59b representsinelastic buckling, providing a transition to the yield point stress as the column length de-creases.

10.26 SECTION TEN

10.13.1 Elastic Flexural Buckling

For doubly-symmetric, closed, or any other sections that are not subject to torsional ortorsional-flexural buckling, the elastic buckling stress is

2�F � (10.61)e 2(KL /r)

where E � modulus of elasticity (29,500 ksi or 203 000 MPa)K � effective length factor (see Fig. 6.3)L � unbraced length of memberr � radius of gyration of full, unreduced cross section

10.13.2 Symmetric Sections Subject to Torsional orTorsional-Flexural Buckling

Singly-Symmetric Sections. For singly-symmetric sections, such as C-sections, subject totorsional-flexural buckling, Fe is the smaller of Eq. 10.61 and that given by Eq. 10.62 or10.63.

1 2F � [(� � � ) � �(� � � ) � 2�� ] (10.62)e ex t ex t ex t2�

As an alternative to Eq. 10.62, a conservative estimate can be calculated from the following:

� �ex tF � (10.63)e � � �ex t

In the above, �ex and �t are given by Eqs. 10.31 and 10.33, and

2� � 1 � (x /r ) (10.64)o o

where ro is given by Eq. 10.36 and xo � distance from shear center to centroid along principalx-axis taken as negative. For singly-symmetric sections, the x-axis is assumed to be the axisof symmetry.

Doubly-Symmetric Sections. For doubly-symmetric sections, such as back-to-back C-sections, subject to torsional buckling, Fe is taken as the smaller of Eq. 10.61 and thetorsional buckling stress, �t, given by Eq. 10.33.

10.13.3 Non-symmetric Sections

For shapes with cross sections that do not have any symmetry, either about an axis or abouta point, Fe should be determined by rational analysis or by tests.

10.13.4 Beams (C- or Z-Section) Having One Flange Through-Fastened toDeck or Sheathing

For such sections axially loaded in compression, refer to the AISI Specifications which givea special set of provisions. Based on the results of structural tests, they account for the partial


restraint to weak axis buckling provided by the deck or sheathing. Strong axis bucklingshould be considered using the same equations as for members not attached to sheathing.

10.14 COMBINED TENSILE AXIAL LOAD AND BENDING

Members under combined axial tensile load and bending must satisfy the interaction equa-tions given by the AISI Specification to prevent yielding. Separate equations are given forASD and LRFD but symbols have common definitions except as noted.

ASD Method. To check the tension flange

� M� M � Tb yb x t� � � 1.0 (10.65)M M Tnxt nyt n

To check the compression flange

� M� M � Tb yb x t� � � 1.0 (10.66)M M Tnx ny n

where T � required tensile axial strengthMx , My � required flexural strengths with respect to the centroidal axes of the section

Tn � nominal tensile axial strength determined in accordance with Art. 10.11Mnx , Mny � nominal flexural strengths about the centroidal axes determined in accordance

with Art. 10.12Mnxt , Mnyt � SƒtFy

Sft � section modulus of the full section for the extreme tension fiber about theappropriate axis

�b � safety factor for bending, Table 10.1�t � safety factor for tension member, Table 10.1

LRFD Method. To check the tension flange

MM Tuyux u� � � 1.0 (10.67)� M � M � Tb nxt b nyt t n

To check the compression flange

MM Tuyux u� � � 1.0 (10.68)� M � M � Tb nx b ny t n

where Tu � required tensile axial strengthMux , Muy � required flexural strengths with respect to the centroidal axes

�b � 0.90 or 0.95 for bending strength, or 0.90 for laterally unbraced beams�t � 0.95

10.15 COMBINED COMPRESSIVE AXIAL LOAD AND BENDING

Members under combined compression axial load and bending are generally referred to asbeam-columns. Bending in such members may be caused by eccentric loading, lateral loads,

10.28 SECTION TEN

or end moments, and the compression load can amplify the bending. These members mustsatisfy the interaction equations given by the AISI Specification to prevent both bucklingand yielding. Separate equations are given for ASD and LRFD but symbols have commondefinitions except as noted.

ASD Method

� C M� P � C M b my yc b mx x� � � 1.0 (10.69)P M � M �n nx x ny y

� M� P � M b yc b x� � � 1.0 (10.70)P M Mno nx ny

When �c P /Pn � 0.15, the following equation may be used in lieu of the above two equa-tions:

� M� P � M b yc b x� � � 1.0 (10.71)P M Mn nx ny

where P � required compressive axial strengthMx , My � required flexural strengths with respect to the centroidal axes of the effective

section determined for the required compressive axial strength alone. For anglesections, My should be taken either as the required flexural strength or the re-quired flexural strength plus PL /1000, whichever results in a lower permissiblevalue of P

Pn � nominal axial strength determined in accordance with Art. 10.14Pno � nominal axis strength determined in accordance with Art. 10.14, with Fn � Fy

Mnx , Mny � nominal flexural strengths about the centroidal axes determined in accordancewith Art. 10.12

� Pc� � 1 � (10.72)x PEx

� Pc� � 1 � (10.73)y PEy

2� EIxP � (10.74)Ex 2(K L )x x

2� EIyP � (10.75)Ey 2(K L )y y

�b � safety factor for bending, Table 10.1�c � safety factor for compression, Table 10.1Ix � moment of inertia of the full, unreduced cross section about the x-axisIy � moment of inertia of the full, unreduced cross section about the y-axisLx � actual unbraced length for bending about the x-axisLy � actual unbraced length for bending about the y-axisKx � effective length factor for buckling about the x-axisKy � effective length factor for buckling about the y-axis


Cmx, Cmy � coefficients whose value is as follows:1. For compression members in frames subject to joint translation (sidesway)

C � 0.85m

2. For restrained compression members in frames braced against joint transla-tion and not subject to transverse loading between their supports in the planeof bending

C � 0.6 � 0.4(M /M ) (10.76)m 1 2

where M1 /M2 is the ratio of the smaller to the larger moment at the ends ofthat portion of the member under consideration which is unbraced in theplane of bending. M1 /M2 is positive when the member is bent in reversecurvature and negative when it is bent in single curvature

3. For compression members in frames braced against joint translation in theplane of loading and subject to transverse loading between their supports, thevalue of Cm may be determined by rational analysis. However, in lieu of suchanalysis, the following values may be used:(a) for members whose ends are restrained, Cm � 0.85(b) for members whose ends are unrestrained, Cm � 1.0

LRFD Method

C MP C M my uyu mx ux� � � 1.0 (10.77)� P � M � � M �c n b nx x b ny y

MP M uyu ux� � � 1.0 (10.78)� P � M � Mc no b nx b ny

When Pu /�c Pn � 0.15, the following equation may be used in lieu of the above two equa-tions:

MP M uyu ux� � � 1.0 (10.79)� P � M � Mc n b nx b ny

where Pu � required compressive axial strengthMux , Muy � required flexural strengths with respect to the centroidal axes of the effective

section determined for the required compressive axial strength alone. For anglesections, Muy, shall be taken either as the required flexural strength or the re-quired flexural strength plus Pu L /1000, whichever results in a lower permissiblevalue of Pu.

Pu� � 1 � (10.80)x PEx

Pu� � 1 � (10.81)y PEy

�b � 0.90 or 0.95 for bending strength, or 0.90 for laterally unbraced beams�c � 0.85

10.30 SECTION TEN

10.16 CYLINDRICAL TUBULAR MEMBERS

The AISI Specification gives separate provisions for cylindrical members, but they apply onlyif the ratio of outside diameter-to-wall thickness, D / t is not greater than 0.441 E /Fy.

10.16.1 Flexure

Cylinders with small D / t ratios can develop their plastic moment strength while those withgreater D / t ratios will develop smaller capacities. The nominal flexural strength, Mn, iscalculated from the following equations, the selection of which depends on the D / t ratio:

For D / t � 0.0714E /Fy ,

M � 1.25F S (10.82)n y ƒ

For 0.0714E /Fy � D / t � 0.318E /Fy ,

E /FyM � 0.970 � 0.020 F S (10.83)� � ��n y ƒD / t

For 0.318E /Fy � D / t � 0.441E /Fy ,

M � [0.328E / (D / t)]S (10.84)n ƒ

In the above, Sƒ � elastic section modulus of the full, unreduced cross section.

10.16.2 Axial Compression

The nominal axial strength of round tubes is calculated from the same column equations asfor other members, Eqs. 10.58–10.60 of Art. 10.14, with the following exception. The ef-fective area, Ae, is

A � A � R(A � A ) (10.85)e o o

where

R � F /2F � 1.0 (10.86)y e

0.037A � � 0.667 A � A� �o (DF ) / (tE )y

(10.87)

A � Area of the unreduced cross section

Torsional or flexural-torsional buckling need not be checked for cylindrical members. How-ever, combined axial load and bending must be checked as for other members (Art. 10.15).

10.17 WELDED CONNECTIONS

Various types of welds may be used to joint cold-formed steel members such as groovewelds in butt joints, fillet welds, flare groove welds, arc spot welds, arc seam welds, and


resistance welds. The nominal strength, Pn, for several of these weld types is given in thisarticle. More complete information may be found in the AISI Specification. The provisionsgiven are applicable where the thickness of the thinnest part connected is 0.18 in (4.57 mm)or less. For thicker parts, refer to the AISC Specification. Welders and welding proceduresshould be qualified in accordance with specifications of the American Welding Society(AWS)

10.17.1 Groove Welds in Butt Joints

For tension or compression, the nominal strength is

P � Lt F (10.88)n e y

For shear, the nominal strength is the smaller of the limit based on shear in the weld andthat based on shear in the base metal.

For shear in welds,

P � Lt 0.6F (10.89)n e xx

For shear in base metal,

P � Lt F /�3 (10.90)n e y

where Fxx � filler metal strength designation for AWS electrode classificationFy � yield stressL � length of weldte � effective throat dimension

10.17.2 Fillet Welds

Fillet welds are considered to transmit longitudinal and transverse loads with shear stresses.For these welds, the nominal strength is the smaller of the limit based on weld strength andthat based on the strength of the connected part.

For weld strength (consider only if t � 0.15 in or 3.8 mm),

P � 0.75t LF (10.91)n w xx

For strength of connected part, welds longitudinal to the loading,

0.01Lwhen L / t � 25 P � 1 � tLF (10.92)� �n ut

when L / t � 25 P � 0.75tLF (10.93)n u

For strength of connected part, welds transverse to the loading,

P � tLF (10.94)n u

where t � least of t1 and t2 (see Fig. 10.8)tw � effective throat of weld

� 0.707w1 or 0.707w2, whichever is smaller (see Fig. 10.8)Fu � tensile strength

10.32 SECTION TEN

FIGURE 10.8 Cross section of fillet welds. (a) At lap joint; (b) at T joint. (Source: Specification forthe Design of Cold-Formed Steel Structural Members, American Iron and Steel Institute, Washington, DC,1996, with permission.)

10.17.3 Arc Spot Welds

Arc spot welds, also know as puddle welds, are made in the flat welding position to joinsheets to thicker members. They are made by using the arc to burn a hole in the top sheet(or sheets), then depositing weld metal to fill the hole and fuse it to the underlying member.Thus, no hole need be punched in the sheet. Such welds should not be made where the topsheet (or sheets) is over 0.15 in (3.81 mm) thick. Where the thickness of the sheet is lessthan 0.028 in (0.711 mm), a washer should be used on top of the sheet and the weld madeinside this washer. The washer should have a thickness of 0.05 to 0.08 in (1.27 to 2.03 mm),with a prepunched hole of 0.375 in (9.53 mm) diameter. Arc spot welds are specified byminimum effective diameter of fused area, de , and the minimum is 0.375 in (9.53 mm). TheAISI Specification gives provisions for both shear and tension (uplift) loadings.

For shear, the nominal strength is the smaller of the limit based on the strength of theweld and that based on the strength of the connected part.

For weld strength (use � � 0.60),

2�d eP � 0.75F (10.95)n xx4

For strength of connected part,

when (da / t) � 0.815 (use � � 0.60),�E /Fu

P � 2.20td F (10.96)n a u

when 0.815 � (da / t) � 1.397 (use � � 0.50),�E /F �E /Fu u

�E /FuP � 0.280 1 � 5.59 td F (10.97)� �n a ud / ta

when (da / t) � 1.397 (use � � 0.50),�E /Fu

P � 1.40td F (10.98)n a u

where d � visible diameter of outer surface of arc spot weldda � average diameter of the arc spot weld at mid-thickness of t; use da � (d � t) for

a single sheet, da � (d � 2t) for multiple sheets (four sheet maximum)de � effective diameter of fused area at plane of maximum shear transfer � 0.7d �

1.5t but � 0.55dt � total base steel thickness of sheets involved in shear transfer

See Fig. 10.9 for illustration of diameters d, da, and de.


FIGURE 10.9 Cross section of arc spot weld connecting sheets to underlying member. (a) With one sheetconnected; (b) with two sheets connected. (Source: Specification for the Design of Cold-Formed SteelStructural Members, American Iron and Steel Institute, Washington, DC, 1996, with permission.)

Also for arc spot welds in shear, the edge distance must be sufficient. AISI requires thatthe clear distance from the edge of a weld to the end of a member be not less than 1.0d.Furthermore, the distance measured in the line of force from the centerline of a weld to thenearest edge of an adjacent weld, or to the end of the connected part toward which the forceis directed, be not less than 1.5d and also not less than the following:

For ASD

P�e � (10.100)min F tu

For LRFD

Pue � (10.101)min �F tu

For Fu /Fsy � 1.08, use � � 2.0 (ASD) and � � 0.70 (LRFD). For Fu /Fsy � 1.08, use � �2.22 (ASD) and � � 0.60 (LRFD). In the above, P � required strength per weld (nominal

10.34 SECTION TEN

force), Pu � required strength per weld (factored force), t � thickness of thinnest connectedsheet, and Fsy � specified yield stress.

For tension, such as caused by uplift, the nominal strength is the smaller of the limitbased on the strength of the weld and that based on the strength of the connected part.

For weld strength,

2�d eP � F (10.102)n xx4

For strength of connected part,

when Fu /E � 0.00187

P � [6.59 � 3150(F /E )]td F � 1.46td F (10.103)n u a u a u

when Fu /E � 0.00187

P � 0.70td F (10.104)n a u

In the above, Fxx � 60 ksi (414 MPa), Fu � 82 ksi (565 MPa) for the connecting sheets,Fxx � Fu, and emin � d. If loading is eccentric, strength is 50% of that calculated. At deckside laps, strength is 70% of that calculated. If connecting multiple sheets, t is sum ofthicknesses.

10.17.4 Resistance Welds

Resistance welds, often referred to as spot welds, are made by placing two lapped sheetsbetween opposing electrodes that press the sheets together. The weld is created by the heatgenerated by resistance to current flow. The nominal shear strength is determined as follows,based on the thickness of the thinnest sheet joined, t.

In traditional units:

For 0.01 � t � 0.14 in,

1.47P (kips) � 144t (10.105)n

For 0.14 � t � 0.18 in,

P (kips) � 43.4t � 1.93 (10.106)n

In SI units:For 0.25 � t � 3.56 mm,

1.47P (kips) � 5.51t (10.107)n

For 3.56 � t � 4.57 mm,

P (kips) � 7.6t � 8.57 (10.108)n

10.18 BOLTED CONNECTIONS

Bolted connections of cold-formed steel members are designed as bearing type connections.Bolt pretensioning is not required and installation should be to the snug-tight condition. TheAISI Specification gives applicable provisions when the thickness, t, of the thinnest connectedpart is less than 3⁄16 in (4.76 mm). For thicker members, the AISC Specification applies. The


most commonly used grades are A307 carbon steel bolts and A325 high strength bolts, butother types can also be used. Standard hole diameter is d � 1⁄32 in for d � 1⁄2 in (d � 0.8mm for d � 12.7 mm) where d is bolt diameter. Standard hole diameter is d � 1⁄16 in ford � 1⁄2 in (d � 1.6 mm for d � 12.7 mm). See the AISI Specification for information onslotted holes.

Several conditions must be checked for a bolted connection, including shearing strengthof sheet (edge distance and spacing effects), tension strength in each connected part, bearingstrength, bolt shear strength, and bolt tension strength. Each of these is treated in the fol-lowing articles.

10.8.1 Sheet Shearing (Spacing and Edge Distance)

If bolts are too close to the ends of members, or if the bolts are spaced too closely, theconnection may be limited in strength by the shear strength along a line parallel to themember force. Minimum center-to-center spacing of bolts is 3d and minimum center-to-edgedistance is 1.5d. Additionally, the nominal strength, Pn, is limited to

P � teF (10.109)n u

where t � thickness of thinnest part and e � distance in line of force from center of holeto nearest edge of adjacent hole or end of connected part.

10.18.2 Tension in Connected Part

For components in tension, limit states of both yielding and fracture must be considered,with the smaller value controlling. The nominal tension strength, Pn, on the net section, An,of each connected part must not exceed

P � F A (10.110)n y n

Also, where washers are provided under both the bolt head and the nut,

P � (1.0 � 0.9r � 3rd /s)F A (10.111)n u n

And where only one washer or no washers are provided,

P � (1.0 � r � 2.5rd /s)F A (10.112)n u n

In the above, r � force transmitted by the bolts divided by the tension force in the member(take r as zero if �0.2), and s � spacing of bolts perpendicular to line of force (take s asgross width if only one bolt).

10.18.3 Bearing

The bearing strength varies from to Pn � 2.22Fudt to Pn � 3.33fudt depending on whetherwashers are used, the type of joint, and the Fu /Fsy ratio of the connected part. The AISIprovisions are summarized in Tables 10.5 and 10.6.

10.18.4 Shear and Tension in Bolts

The nominal bolt strength resulting from shear, tension, or a combination thereof is calculatedas follows:

10.36 SECTION TEN

TABLE 10.5 Nominal Bearing Strength for Bolted Connections with Washers under Both Bolt Head and Nut

Thickness ofconnected part, t

in (mm) Type of joint

Fu /Fsy ratioof connected

part�

ASD�

LRFD

Nominalresistance

Pn

0.024 � t � 0.1875

(0.61) � t � (4.76)

Inside sheet ofdouble shearconnection

Single shearand outsidesheets ofdouble shearconnection

�1.08

�1.08

No limit

2.22

2.22

2.22

0.55

0.65

0.60

3.33Fudt

3.00Fudt

3.00 Fudt

t � 3⁄16

t � (4.76) See AISC, ASD, or LRFD Specifications

Source: Specification for the Design of Cold-Formed Steel Structural Members, American Iron and Steel Institute, Washington, DC,1996, with permission.

TABLE 10.6 Nominal Bearing Strength for Bolted Connections Without Washers Under Both Bolt Head and Nut orwith Only One Washer

Thickness ofconnected part, t

in (mm) Type of joint

Fu /Fsy ratioof connected

part�

ASD�

LRFD

Nominalresistance

Pn

0.024 � t � 0.1875

(0.61) � t � (4.76)

Inside sheet ofdoubleshear con-nection

Single shearand outsidesheets ofdoubleshear con-nection

�1.08

�1.08

2.22

2.22

0.65

0.70

3.00Fudt

2.22Fudt

t � 3⁄16

t � (4.76) See AISC, ASD, or LRFD Specifications

Source: Specification for the Design of Cold-Formed Steel Structural Members, American Iron and Steel Institute, Washington, DC,1996, with permission.

P � A F (10.113)n b

where Ab � gross cross-sectional area of bolt. For bolts in shear, F � Fnv from Table 10.7.For bolts in tension, F � Fnt from Table 10.7. For bolts subject to a combination of shearand tension, F � from Tables 10.8–10.11, depending upon the design method (ASD orF�nt

LRFD) and the system of units.


TABLE 10.7 Nominal Tensile and Shear Strength for Bolts

Description of bolts

Tensile strength

Factor ofsafety

�(ASD)

Resistancefactor

�(LRFD)

Nominalstress

Fnt , ksi(MPa)

Shear strength

Factor ofsafety

�(ASD)

Resistancefactor

�(LRFD)

Nominalstress

Fnv, ksi(MPa)

A307 Bolts, Grade A1⁄4 in (6.4 mm) � d� 1⁄2 in (12.7 mm)

2.25 0.75 40.5(279)

2.4 0.65 24.0(165)

A307 Bolts, Grade Ad � 1⁄2 in

2.25 0.75 45.0(310)

2.4 0.65 27.0(186)

A325 bolts, when threads arenot excluded from shearplanes

2.0 0.75 90.0(621)

2.4 0.65 54.0(372)

A325 bolts, when threads areexcluded from shearplanes

2.0 0.75 90.0(621)

2.4 0.65 72.0(496)

Source: Specification for the Design of Cold-Formed Steel Structural Members, American Iron and Steel Institute,Washington, DC, 1996, with permission.

TABLE 10.8 Nominal Tension Stress, F (ksi), for Bolts Subject to Combination of Shear and�nt

Tension—ASD Method*

Description of boltsThreads not excluded

from shear planesThreads excluded from

shear planesFactor ofsafety �

A325 Bolts

A354 Grade BD Bolts

A449 Bolts

A490 Bolts

110 � 3.6ƒv � 90

122 � 3.6ƒv � 101

100 � 3.6ƒv � 81

136 � 3.6ƒv � 112.5

110 � 2.8ƒv � 90

122 � 2.8ƒv � 101

100 � 2.8ƒv � 81

136 � 2.8ƒv � 112.5

2.0

2.0

2.0

2.0

A307 Bolts, Grade A 2.25When 1⁄4 in � d � 1⁄2 inWhen d � 1⁄2 in

52 � 4ƒv � 40.558.5 � 4ƒv � 45

* The shear stress ƒv , must also satisfy Table 10.7.Source: Specification for the Design of Cold-Formed Steel Structural Members, American Iron and Steel Institute, Washington, DC,

1996, with permission.

10.19 SCREW CONNECTIONS

Screws are frequently used for connections in cold-formed steel because they can be drivenwith a hand-held drill, usually without punching a hole. The AISI Specification gives pro-visions for calculating nominal strength for self-tapping screws with 0.08 � d � 0.25 in(2.03 � d � 6.35 mm) where d is the nominal screw diameter. The screws can be of thethread-forming or thread-cutting type, with or without a self-drilling point.

10.38 SECTION TEN

TABLE 10.9 Nominal Tension Stress, F (ksi), for Bolts Subject to Combination of Shear and Tension—LRFD�nt

Method*



shear planesResistanceFactor �

A325 Bolts

A354 Grade BD Bolts

A449 Bolts

A490 Bolts

113 � 2.4ƒv � 90

127 � 2.4ƒv � 101

101 � 2.4ƒv � 81

141 � 2.4ƒv � 112.5

113 � 1.9ƒv � 90

127 � 1.9ƒv � 101

101 � 1.9ƒv � 81

141 � 1.9ƒv � 112.5

0.75

0.75

0.75

0.75

A307 Bolts, Grade A 0.75When 1⁄4 in � d � 1⁄2 inWhen d � 1⁄2 in

47 � 2.4ƒv � 40.552 � 2.4ƒv � 45



TABLE 10.10 Nominal Tension Stress, F (MPa), for Bolts Subject to Combination of Shear and Tension—ASD�nt

Method*



shear planes

Factorof safety

�

A325 BoltsA354 Grade BD BoltsA449 BoltsA490 Bolts

758 � 25ƒv � 607841 � 25ƒv � 676690 � 25ƒv � 552938 � 25ƒv � 745

758 � 19ƒv � 607841 � 19ƒv � 676690 � 19ƒv � 552938 � 19ƒv � 745

2.02.02.02.0

A307 Bolts, Grade A 2.25When 6.4 mm � d � 12.7 mmWhen d � 12.7 mm

359 � 28ƒv � 276403 � 28ƒv � 310



The distance between the centers of fasteners, and the distance from the center of afastener to the edge of any part, must not be less than 3d. However, if the connection issubjected to shear force in one direction only, the minimum edge distance in the directionperpendicular to the force is 1.5d.

Nominal strength equations are given for shear and for tension using the following no-tation:

Pns � nominal shear strength per screw

Pnt � nominal tension strength per screw

Pnot � nominal pull-out strength per screw

Pnov � nominal pull-over strength per screw

t1 � thickness of member in contact with the screw head


TABLE 10.11 Nominal Tension Stress, F (MPa), for Bolts Subject to Combination of Shear and Tension—LRFD�nt

Method*



shear planesResistancefactor �

A325 BoltsA354 Grade BD BoltsA449 BoltsA490 Bolts

779 � 17ƒv � 621876 � 17ƒv � 696696 � 17ƒv � 558972 � 17ƒv � 776

779 � 13ƒv � 621876 � 13ƒv � 696696 � 13ƒv � 558972 � 13ƒv � 776

0.750.750.750.75

A307 Bolts, Grade A 0.75When 6.4 mm � d � 12.7 mmWhen d � 12.7 mm

324 � 25ƒv � 279359 � 25ƒv � 310



t2 � thickness of member not in contact with the screw head

Fu1 � tensile strength of member in contact with the screw head

Fu2 � tensile strength of member not in contact with the screw head

10.19.1 Shear

The nominal shear strength per screw, Pns, should be determined as follows:For t2 / t1 � 1.0, Pns shall be taken as the smallest of

3 1 / 2P � 4.2(t d ) F (10.114)ns 2 u2

P � 2.7t dF (10.115)ns 1 u1

P � 2.7t dF (10.116)ns 2 u2

For t2 / t1 � 2.5, Pns shall be taken as the smaller of

P � 2.7t dF (10.117)ns 1 u1

P � 2.7t dF (10.118)ns 2 u2

For 1.0 � t2 / t1 � 2.5, Pns should be determined by linear interpolation between the abovetwo cases.

The nominal shear strength of the screw itself should be at least 1.25Pns. Table 10.12gives values of Pns for #8, #10, and #12 screws.

10.19.2 Tension

For screws that carry tension the diameter of the head of the screw, or of the washer if oneis used, must be at least 5⁄16 in (7.94 mm). Washers must be at least 0.05 in (1.27 mm) thick.Two conditions must be checked: (1) pull-out of the screw and (2) pull-over of the sheet. In

10.40 SECTION TEN

TABLE 10.12 Nominal Shear Strength of Screws, Pns, kips (kips � 4.448 � kN)

Screwdesignation

Diameter,in

Thickness ofmember in

contact withscrew head,

in

Thickness of member not in contact with the screw head,in

0.036 0.048 0.060 0.075 0.090 0.105 0.135

(a) Screws in sheet with Fu � 45 ksi

#8 0.1640

0.0360.0480.0600.0750.0900.1050.135

0.520.520.520.520.520.520.52

0.720.800.800.800.800.800.80

0.720.961.121.121.121.121.12

0.720.961.201.491.491.491.49

0.720.961.201.491.791.791.79

0.720.961.201.491.792.092.09

0.720.961.201.491.792.092.69

#10 0.1900

0.0360.0480.0600.0750.0900.1050.135

0.560.560.560.560.560.560.56

0.830.870.870.870.870.870.87

0.831.111.211.211.211.211.21

0.831.111.391.691.691.691.69

0.831.111.391.732.082.082.08

0.831.111.391.732.082.422.42

0.831.111.391.732.082.423.12

#12 0.2160

0.0360.0480.0600.0750.0900.1050.135

0.600.600.600.600.600.600.60

0.930.920.920.920.920.920.92

0.941.261.291.291.291.291.29

0.941.261.571.801.801.801.80

0.941.261.571.972.362.362.36

0.941.261.571.972.362.762.76

0.941.261.571.972.362.763.54

(b) Screws in sheet with Fu � 65 ksi

#8 0.1640

0.0360.0480.0600.0750.0900.1050.135

0.760.760.760.760.760.760.76

1.041.161.161.161.161.161.16

1.041.381.621.621.621.621.62

1.041.381.732.162.162.162.16

1.041.381.732.162.592.592.59

1.041.381.732.162.593.023.02

1.041.381.732.162.593.023.89

#10 0.1900

0.0360.0480.0600.0750.0900.1050.135

0.810.810.810.810.810.810.81

1.201.251.251.251.251.251.25

1.201.601.751.751.751.751.75

1.201.602.002.442.442.442.44

1.201.602.002.503.003.003.00

1.201.602.002.503.003.503.50

1.201.602.002.503.003.504.50

#12 0.2160

0.0360.0480.0600.0750.0900.1050.135

0.870.870.870.870.870.870.87

1.341.331.331.331.331.331.33

1.361.821.861.861.861.861.86

1.361.822.272.612.612.612.61

1.361.822.272.843.413.413.41

1.361.822.272.843.413.983.98

1.361.822.272.843.413.985.12

Source: Adapted from Cold-Formed Steel Design Manual, American Iron and Steel Institute, 1996, Washington,DC.


addition, the nominal tensile strength of the screw itself should be at least 1.25Pnot or1.25Pnov, whichever is less.

Pull-Out. The nominal pull-out strength, Pnot , is calculated as

P � 0.85t dF (10.119)not c u2

where tc is the lesser of the depth of screw penetration and the thickness t2.

Pull-Over. The nominal pull-over strength, Pnov, is calculated as

P � 1.5t d F (10.120)nov 1 w u1

where dw is the larger of the screw head diameter or the washer diameter, and must be takenno larger than 1⁄2 in (12.7 mm).

10.20 OTHER LIMIT STATES AT CONNECTIONS

The AISI Specification gives procedures for checking certain other important limit states atmember end connections. Included are shear-lag effects in bolted and welded connectionswhere not all elements of the cross section are connected, shear strength along a planethrough fasteners in beam webs where one or both flanges are coped, and block shear rupturewhere a connecting element can fail through a combination of shear on one plane and tensionon a perpendicular plane. Many of these requirements are similar to those of AISC.

10.21 WALL STUD ASSEMBLIES

Steel studs are being increasingly used for the construction of interior and exterior walls inresidential and light commercial applications. Typical studs for load bearing walls are C-sections of 33 ksi yield point steel, 3.5 deep by 1.625 in wide, 0.033 or 0.043 in thick, witha 1⁄2 in stiffener lip on the edge of the flange. The stud depth is sometimes increased to 5.5in so that thicker insulation can be used in the cavity, or for high walls or severe loadings.A steel bracing member (blocking) usually runs between the studs at midheight. Often theexterior surface of the wall is sheathed with CDX or plywood, and the interior with gypsumboard. In some cases, both surfaces may be sheathed with gypsum. Similar C-sections, 5.5to 12 in deep, are used for floor joists. Roof construction may be with steel rafters or withsteel trusses, available fabricated from C-sections or from proprietary shapes. Figure 10.10depicts the various components in a typical steel framed dwelling.

The AISI Specification provides design methods for wall stud assemblies. For compressionloads, the studs can be designed as a stand-alone system or with the effect of sheathingconsidered. However, the latter provisions only apply where the same sheathing is attachedto both flanges. Design for bending, or compression combined with bending, is the same asthat for other sections except that lateral buckling need not be considered because of thebracing provided by the sheathing. Testing can also be used to establish the strength ofassemblies.

Steel stud wall assemblies with sheathing also serve as in-plane shear diaphragms to bracethe structure and resist racking from wind or seismic loads. The shear strength can beestablished by calculations or tests, but tests are preferable. A comprehensive set of testresults, including both static and cyclic loadings, has been compiled by AISI and serves asthe basis for values in most building codes. The cyclic data are important in designing forseismic loads.

10.42 SECTION TEN

FIGURE 10.10 Steel framing in residential construction. (Source: Prescriptive Method for ResidentialCold-Formed Steel Framing, 2nd Ed., NAHB Research Center, Upper Marlboro, MD, 1997, with permission.)

(Prescriptive Method for Residential Cold-Formed Steel Framing, Second Ed., and Com-mentary, NAHB Research Center, Upper Marlboro, MD, 1997; Shear Wall Design Guide,RG9804, American Iron and Steel Institute, Washington, DC, 1998; Technical Notes, LightGauge Steel Engineers Association, Nashville, TN, 1998.)

10.22 EXAMPLE OF EFFECTIVE SECTION CALCULATION

A 5.5 in deep by 1.25 in wide by 0.057 in thick C-section without lips is shown in Fig.10.11a. The specified yield stress for the material is 33 ksi. It is required to determine theeffective section modulus, Se, for a maximum bending stress equal to the yield stress.

First, determine the effective width of the compression (top) flange (Art. 10.8.1 and10.9.2). The radius to midthickness of the bend is


FIGURE 10.11 Unstiffened C-section for example problem (Art. 10.22). (a) Cross section; (b) stressdistribution on effective section. (Source: Cold-Formed Steel Design Manual, American Iron and SteelInstitute, Washington, DC, 1996, with permission.)

r � R � t /2

� 0.1875 � 0.057/2

� 0.216 in

The flat width of the flange is

w � 1.25 � 0.216 � 0.057/2

� 1.006 in

w / t � 1.006/0.057 � 17.65

The plate buckling coefficient (Art. 10.9.2) is k � 0.43.

1.052 w ƒ� � � ��t E�k

1.052 33� � (17.65) (Eq. 10.4)�29500�0.43

� 0.947 � 0.673

� � (1 � 0.22/�) /�

� � (1 � 0.22/0.947) /0.947 (Eq. 10.7)

� � 0.811

The effective width of the top flange is

10.44 SECTION TEN

b � �w

� (0.811)(1.006) (Eq. 10.6)

� 0.816 in

The next step is to determine whether the web is fully effective. To do this, first determinethe location of the neutral axis. Because the top flange is not fully effective, the neutral axiswill be located below the centroidal axis of the gross cross section. Table 10.13 shows thecalculations to determine the distance of the neutral axis from the top fiber, , and theymoment of inertia of the effective section, Ix. The web is treated as a stiffened element witha stress gradient (Art. 10.8.2). With a stress of 33 ksi in the top flange, the stresses at theedges of the flat web, ƒ1 and ƒ2 (Fig 10.1b) can be readily determined from similar triangles.The other calculations follow from Art. 10.8.2.

2.819 � 0.216 � 0.057/2ƒ � (33) � 30.14 ksi1 2.819

5.500 � 2.819 � 0.216 � 0.057/2ƒ � � (33) � �28.52 ksi2 2.819

� � ƒ /ƒ � �28.52/30.14 � �0.946 (Eq. 10.8)2 1

3k � 4 � 2 (1 � �) � 2(1 � �) (Eq. 10.9)3� 4 � 2[1 � (�0.946)] � 2[1 � (�0.946)]

� 22.63

w � 5.500 � 2(0.216) � 0.057 � 5.011 in

w / t � 5.011/0.057 � 87.91

1.052 w ƒ� � (Eq. 10.4)� ��t E�k

1.052 30.14� (87.91) �29500�22.63

� 0.621 � 0.673, therefore, b � w � 5.011 in

b � b / (3 � �) (Eq. 10.10)1

� 5.011/(3 � (�0.946)) � 1.270 in

For � � �0.236

b � b /2 (Eq. 10.11)2 e

� 5.011/2 � 2.506 in

b � b � 1.270 � 2.506 � 3.776 in1 2

Based on the assumption of a fully effective web, the width that is in compression, Fig.10.11b, is 2.819 � 0.057/2 � 0.216 � 2.575 in. Because this is less than 3.776 in, the webis fully effective and no further iteration is required. If the web had not been fully effective,


TABLE 10.13 Example of Effective Section Property Calculations

ElementL

(in)

y from topfiber(in)

Ly(in2)

Ly 2

(in3)

Ix aboutown axis

(in3)

Top flange 0.816 0.0285 0.023 0.001 —

Top radius 0.339 0.1069 0.036 0.004 0.002

Web 5.011 2.7500 13.780 37.896 10.486

Bottom radius 0.339 5.3931 1.828 9.860 0.002

Bottom flange 1.006 5.4715 5.504 30.117 —

Sum � 7.511 21.171 77.878 10.490

y � �Ly / �L

� 21.171 / 7.511 � 2.819 in below top fiber

2 2I � [�I � � �Ly � y �L]tx x

2� [10.490 � 77.878 � (2.819) (7.511)](0.057)

4� 1.635 in

Source: Adapted from Cold-Formed Steel Design Manual, American Iron and Steel Institute, 1996, Washington,DC.

additional iterations in section property calculations would be required until the final effectivesection was determined for the stresses acting on that effective section. In the present case,the effective section modulus is Se � Ix / � 1.635/2.819 � 0.580 in3.y

10.23 EXAMPLE OF BENDING STRENGTH CALCULATION

For the unstiffened C-section in Art. 10.22, determine the moment strength based on initi-ation of yielding for a fully braced section. Then determine the allowable moment based onASD and the maximum factored moment based on LRFD.

From Art. 10.12.1, the nominal strength is

M � S Fn e y

� 0.580 � 33 (Eq. 10.24)

� 19.1 in-kip

From Table 1.1, � � 1.67 and � � 0.90. Therefore, for ASD, the allowable moment basedon nominal loads is

M � M /�

� 19.1/1.67

� 11.4 in-kip

10.46 SECTION TEN

For LRFD, the maximum moment based on factored loads is

M � �Mu

� 0.90 � 19.1

� 17.2 in-kip

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