Structural Steel Designers Handbook Part 6 pps

BUILDING DESIGN CRITERIA 6.35 TABLE 6.20 Design Shear Strength of Fasteners in Bearing-Type Connections Description of fasteners Shear strength, ksi LRFD Nominal strength* ASD Allowable shear F v A307 bolts 24 10.0 A325 bolts, when threads are not excluded from shear planes 48 21.0 A325 bolts, when threads are excluded from shear planes 60 30.0 A490 bolts, when threads are not excluded from shear planes 60 28.0 A490 bolts, when threads are excluded from the shear planes 75 40.0 Threaded parts, when threads are not excluded from the shear planes 0.40F u 0.17F u Threaded parts, when threads are excluded from the shear planes 0.50F u 0.22F u A502, grade 1, hot-driven rivets 25 17.5 A502, grades 2 and 3, hot-driven rivets 33 22.0 *Resistance factor ␾ ϭ 0.75. where C v ϭ when C v Ͻ 0.8 45,000k v 2 F (h/t) y ϭ when C v Ͼ 0.8 190 k v Ί h/tF y k v ϭ 4.00 ϩ when a /h Ͻ 1.00 5.34 2 (a/h) ϭ 5.34 ϩ when a /h Ͼ 1.0 4.00 2 (a/h) Alternative rules are given for design on the basis of tension field action. 6.14.2 Shear in Bolts For bolts and threaded parts, design shear strengths are specified in Tables 6.20 and 6.21. The design strengths permitted for high-strength bolts depend on whether a connection is slip-critical or bearing type. Bearing type connections should be used where possible because they are more economical. Bearing-type joints are connections in which load is resisted by shear in and bearing on the bolts. Design strength is influenced by the presence of threads; i.e., a bolt with threads excluded from the shear plane is assigned a higher design strength than a bolt with threads 6.36 SECTION SIX TABLE 6.21 Allowable Shear F v (ksi) for Slip-Critical Connections* Type of bolt Standard-size holes Oversized and short- slotted holes Long-slotted holes Transverse loading Parallel loading A325 17 15 12 10 A490 21 18 15 13 *Applies to both ASD and LRFD, LRFD design for slip-critical connections is made for service loads. For LRFD, ␾ ϭ 1.0. For LRFD, when the loading combination includes wind or seismic loads, the combined load effects at service loads may be multiplied by 0.75. included in the shear plane (see Table 6.20). Design stresses are assumed to act on the nominal body area of bolts in both ASD and LRFD. For LRFD, bearing-type joints are designed for factored loads. The design shear strength of a high-strength bolt or threaded part, ␾ F v A b (kips), multiplied by the number of shear planes, must equal or exceed the required force per bolt due to factored loads, where ␾ ϭ resistance factor ϭ 0.75 F v ϭ nominal shear strength in Table 6.19, ksi A b ϭ nominal unthreaded body area of bolt, in 2 For ASD, bearing-type joints are designed for service loads using the same procedure as above, except that there is no resistance factor so the design shear strength is simply F v A b (kips). Bolts in both bearing-type and slip critical-joints must also be checked for bearing strength. For LRFD, the check is made for factored loads. The design bearing strength per bolt is ␾ R n (kips) where ␾ ϭ 0.75 and R n is determined as follows. For standard holes, oversized, and short-slotted holes, or for long-slotted holes with the slot parallel to the direction of the bearing force, when deformation at the bolt hole at service load is a design consideration, R n ϭ 1.2L c tF u Յ 1.2dtF u . In the foregoing, L c (in) is the clear distance in direction of force between edge of hole and edge of adjacent hole or edge of material, d (in) is the nominal bolt diameter, t (in) is the thickness of the connected material, and F u (ksi) is the tensile strength of the material. The bearing strength differs for other conditions. For ASD, the check is made for service loads. The allowable bearing load per bolt is 1.2dtF u (kips) for standard holes or short-slotted holes with two or more bolts in the line of force, when deformation at the bolt hole at service load is a design consideration. The allowable bearing load differs for other conditions. Bearing-type connections are assigned higher design strengths than slip-critical joints and hence are more economical. Also, erection is faster with bearing-type joints because the bolts need not be highly tensioned. In connections where slip can be tolerated, bolts not subject to tension loads nor loosening or fatigue due to vibration or load fluctuations need only be made snug-tight. This can be accomplished with a few impacts of an impact wrench or by full manual effort with a spud wrench sufficient to bring connected plies into firm contact. Slip-critical joints and connec- tions subject to direct tension should be indicated on construction drawings. Where permitted by building codes, ASTM A307 bolts or snug-tight high-strength bolts may be used for connections that are not slip critical. The AISC specifications for structural steel for buildings require that fully tensioned, high-strength bolts (Table 6.22) or welds be used for the following joints: Column splices in multistory framing, if it is more than 200 ft high, or when it is between 100 and 200 ft high and the smaller horizontal dimension of the framing is less than 40% BUILDING DESIGN CRITERIA 6.37 TABLE 6.22 Minimum Pretension (kips) for Bolts* Bolt size, in A325 bolts A490 bolts 1 ⁄ 2 12 15 5 ⁄ 8 19 24 3 ⁄ 4 28 35 7 ⁄ 8 39 49 15164 1 1 ⁄ 8 56 80 1 1 ⁄ 4 71 102 1 3 ⁄ 8 85 121 1 1 ⁄ 2 103 148 Over 1 1 ⁄ 2 — 0.7 T.S. Equal to 70% of minimum tensile strengths (T.S.) of bolts, rounded off to the nearest kip. of the height, or when it is less than 100 ft high and the smaller horizontal dimension is less than 25% of the height. Connections, in framing more than 125 ft high, on which column bracing is dependent and connections of all beams or girders to columns. Crane supports, as well as roof-truss splices, truss-to-column joints, column splices and bracing, and crane supports, in framing supporting cranes with capacity exceeding 5 tons. Connections for supports for impact loads, loads causing stress reversal, or running ma- chinery. The height of framing should be measured from curb level (or mean level of adjoining land when there is no curb) to the highest point of roof beams for flat roofs or to mean height of gable for roofs with a rise of more than 2 2 ⁄ 3 in 12. Penthouses may be excluded. Slip-critical joints are connections in which slip would be detrimental to the servicea- bility of the structure in which the joints are components. These include connections subject to fatigue loading or significant load reversal or in which bolts are installed in oversized holes or share loads with welds at a common faying surface. In slip-critical joints, the fasteners must be high-strength bolts tightened to the specified minimum pretension listed in Table 6.22. The clamping force generated develops the frictional resistance on the slip planes between the connected piles. For LRFD, slip-critical bolts can be designed for either factored loads or service loads. In the first case, the design slip resistance per bolt, ␾ R str (kips), for use at factored loads must equal or exceed the required force per bolt due to factored loads, where: R ϭ 1.13 ␮ TN (6.36) str b s where T b ϭ minimum fastener tension, kips (Table 6.21) N s ϭ number of slip planes ␮ ϭ mean slip coefficient for Class A, B, or C surfaces, as applicable, or as estab- lished by tests For Class A surfaces (unpainted clean mill scale steel surfaces or surfaces with Class A coatings on blast-cleaned steel), ␮ ϭ 0.33 For Class B surfaces (unpainted blast-cleaned steel surfaces or surface with Class B coatings on blast-cleaned steel), ␮ ϭ 0.50 6.38 SECTION SIX For Class C surfaces (hot-dip galvanized and roughened surfaces), ␮ ϭ 0.40 ␾ ϭ resistance factor For standard holes, ␾ ϭ 1.0 For oversized and short-slotted holes, ␾ ϭ 0.85 For long-slotted holes transverse to the direction of load, ␾ ϭ 0.70 For long-slotted holes parallel to the direction of load, ␾ ϭ 0.60 Finger shims up to 1 ⁄ 4 in are permitted to be introduced into slip-critical connections designed on the basis of standard holes without reducing the design shear stress of the fastener to that specified for slotted holes. For LRFD design of slip-critical bolts at service loads, the design slip resistance per bolt, ␾ F v A b N s (kips), must equal or exceed the shear per bolt due to service loads, where: ␾ ϭ 1.0 for standard, oversized, and short-slotted holes and long-slotted holes when the long slot is perpendicular to the line of force ϭ 0.85 for long-slotted holes when the long slot is parallel to the line of force F v ϭ nominal slip-critical shear resistance, ksi (Table 6.21) A b ϭ nominal unthreaded body area of bolt, in 2 For ASD design of slip-critical bolts, the design slip resistance per bolt is simply F v A b N s (kips) where F v is as given in Table 6.21. Note that all of the values in Table 6.21 are for Class A surfaces with a slip coefficient ␮ ϭ 0.33. These values may be adjusted for other surfaces when specified as prescribed in the AISC specifications. As noted previously, bolts in slip critical-joints must also be checked for bearing strength. 6.14.3 Shear in Welds Welds subject to static loads should be proportioned for the design strengths in Table 6.23. The effective area of groove and fillet welds for computation of design strength is the effective length times the effective throat thickness. The effective area for a plug or slot weld is taken as the nominal cross-sectional area of the hole or slot in the plane of the faying surface. Effective length of fillet welds, except fillet welds in holes or slots, is the overall length of the weld, including returns. For a groove weld, the effective length is taken as the width of the part joined. The effective throat thickness of a fillet weld is the shortest distance from the root of the joint to the nominal face of the weld. However, for fillet welds made by the submerged-arc process, the effective throat thickness is taken as the leg size for 3 ⁄ 8 -in and smaller welds and equal to the theoretical throat plus 0.11 in for fillet welds larger than 3 ⁄ 8 in. The effective throat thickness of a complete-penetration groove weld equals the thickness of the thinner part joined. Table 6.24 shows the effective throat thickness for partial- penetration groove welds. Flare bevel and flare V-groove welds when flush to the surface of a bar or 90 Њ bend in a formed section should have effective throat thicknesses of 5 ⁄ 16 and 1 ⁄ 2 times the radius of the bar or bend, respectively, and when the radius is 1 in or more, for gas-metal arc welding, 3 ⁄ 4 of the radius. To provide adequate resistance to fatigue, design stresses should be reduced for welds and base metal adjacent to welds in connections subject to stress fluctuations (see Art. 6.22). To ensure adequate placement of the welds to avoid stress concentrations and cold joints, the AISC specifications set maximum and minimum limits on the size and spacing of the welds. These are discussed in Art. 5.19. BUILDING DESIGN CRITERIA 6.39 TABLE 6.23 Design Strength for Welds, ksi Types of weld and stress Material LRFD Resistance factor ␾ Nominal strength* F BM or F w ASD Allowable stress Complete penetration groove weld Tension normal to effective area Base 0.90 F y Compression normal to effective area Base 0.90 F y Same as base metal Tension or compression parallel to axis of weld Shear on effective area Base Weld electrode 0.90 0.80 0.60F y 0.60F EXX 0.30 ϫ nominal tensile strength of weld metal Partial penetration groove welds Compression normal to effective area Base 0.90 F y Same as base metal Tension or compression parallel to axis of weld Shear parallel to axis of weld Base Weld electrode 0.75 0.60F EXX 0.30 ϫ nominal tensile strength of weld metal Tension normal to effective area Base Weld electrode 0.90 0.80 F y 0.60F EXX 0.30 ϫ nominal tensile strength of weld metal Fillet welds Shear on effective area Base Weld electrode 0.75 0.60F EXX 0.30 ϫ nominal tensile strength of weld metal Tension or compression parallel to axis of weld Base 0.90 F y Same as base metal Plug or slot welds Shear parallel to faying surfaces (on effective area) Base Weld electrode 0.75 0.60F EXX 0.30 ϫ nominal tensile strength of weld metal *Design strength is the smaller of F BM and F w : F ϭ nominal strength of base metal to be welded, ksi BM F ϭ nominal strength of weld electrode material, ksi w F ϭ specified minimum yield stress of base metal, ksi y F ϭ classification strength of weld metal, as specified in appropriate AWS specifications, ksi EXX 6.40 SECTION SIX TABLE 6.24 Effective Throat Thickness of Partial-Penetration Groove Welds Welding process Welding position Included angle at root of groove Effective throat thickness Shielded metal arc Submerged arc Gas metal arc Flux-cored arc All J or U joint Bevel or V joint · Ն60Њ Depth of chamfer Bevel or V joint Ͻ60Њ but Ն45Њ Depth of chamfer minus 1 ⁄ 8 -in 6.15 COMBINED TENSION AND SHEAR Combined tension and shear stresses are of concern principally for fasteners, plate-girder webs, and ends of coped beams, gusset plates, and similar locations. 6.15.1 Tension and Shear in Bolts The AISC ‘‘Load and Resistance Factor Design (LRFD) Specification for Structural Steel Buildings’’ contains interaction formulas for design of bolts subject to combined tension and shear in bearing-type connections. The specification stipulates that the tension stress applied by factored loads must not exceed the design tension stress F t (ksi) computed from the appropriate formula (Table 6.24) when the applied shear stress ƒ v (ksi) is caused by the same factored loads. This shear stress must not exceed the design shear strength. For bolts in slip-critical connections designed by LRFD for factored loads, the design slip resistance ␾ R str (kips) for shear alone given in Art. 6.14.2 must be multiplied by the factor T u 1 Ϫ (6.37) 1.13TN bb where T u (kips) is the applied factored-load tension on the connection, N b is the number of bolts carrying T u , and T b (kips) is the minimum fastener tension. For bolts in slip-critical connections designed by LRFD for service loads, the design slip resistance ␾ F v A b (kips) for shear alone given in Art. 6.14.2 must be multiplied by the factor T 1 Ϫ (6.38) 0.8TN bb where T (kips) is the applied service-load tension on the connection and N b is the number of bolts carrying T. According to the AISC ‘‘Specification for Structural Steel Buildings—Allowable Stress Design,’’ for bearing-type connections the applied tension stress must not exceed the allow- able tension stress F t as given by Table 6.25. The applied shear stress must not exceed the allowable shear stress. When the allowable stresses are increased for wind or seismic loads, the constants, except for the coefficients of ƒ v , in the equations may be increased one-third. To account for combined loading for a slip-critical connection allowable shear stress is to be reduced by the factor (1 Ϫ ƒ t A b /T b ), where T b is the minimum pretension force (kips; see Table 6.22), and ƒ t is the average tensile stress (ksi) applied to the bolts. BUILDING DESIGN CRITERIA 6.41 TABLE 6.25 Tension Stress Limit F t (ksi) for Fasteners in Bearing-Type Connections Type of bolt Type of design Threads in the shear plane Included Excluded A307 LRFD* ASD 59 Ϫ 1.9ƒ v Յ 45 26 Ϫ 1.8ƒ v Յ 20 A325 LRFD* ASD 117 Ϫ 2.5ƒ v Յ 90 22 ͙44 Ϫ 4.39ƒ v 117 Ϫ 2.0ƒ v Յ 90 22 ͙44 Ϫ 2.15ƒ v A490 LRFD* ASD 147 Ϫ 2.5ƒ v Յ 113 22 ͙54 Ϫ 3.75ƒ v 147 Ϫ 2.0ƒ v Յ 113 22 ͙54 Ϫ 1.82ƒ v *Resistance factor ␾ ϭ 0.75. 6.15.2 Tension and Shear in Girder Webs In plate girders designed for tension-field action, the interaction of bending and shear must be considered. Rules for considering this effect are given in the AISC LRFD and ASD Specifications. 6.15.3 Block Shear This is a failure mode that may occur at the ends of coped beams, in gusset plates, and in similar locations. It is a tearing failure mode involving shear rupture along one path, such as through a line of bolt holes, and tensile rupture along a perpendicular line. The AISC LRFD specification requires that the block shear rupture design strength, ␾ R n (kips), be determined as follows. When F u A nt Ն 0.6F u A n v , then ␾ R n ϭ ␾ (0.6F y A g v ϩ F u A nt ) and when 0.6F u A n v Ն F u A nt , then ␾ R n ϭ ␾ (0.6F u A n v ϩ F y A gt ). In addition, for all cases ␾ R n Յ ␾ [0.6F u A n v ϩ F u A nt ]. In the foregoing, the resistance factor ␾ ϭ 0.75, F u (ksi) is the tensile strength of the material, F y (ksi) is the yield stress of the material, A g v (in 2 ) is the gross area subject to shear, A gt (in 2 ) is the gross area subject to tension, A n v (in 2 ) is the net area subject to shear, and A nt (in 2 ) is the net area subject to tension. The AISC ASD specification specifies allowable shear and tensile stresses for the end connections of beams where the top flange is coped and in similar situations where failure might occur by shear along a plane through fasteners or by a combination of shear along a plane through fasteners and tension along a perpendicular plane. The shear stress F v should not exceed 0.30F u acting on the net shear area. Also, the tensile stress F t should not exceed 0.50F u acting on the net tension area (Art. 6.25). 6.16 COMPRESSION Compressive forces can produce local or overall buckling failures in a steel member. Overall buckling is the out-of-plane bending exhibited by an axially loaded column or beam (Art. 6.17). Local buckling may manifest itself as a web failure beneath a concentrated load or over a reaction or as buckling of a flange or web along the length of a beam or column. 6.42 SECTION SIX FIGURE 6.4 Effective length factor K for columns. 6.16.1 Local Buckling Local buckling characteristics of the cross section of a member subjected to compression may affect its strength. With respect to potential for local buckling, sections may be classified as compact, noncompact, or slender-element (Art. 6.23). 6.16.2 Axial Compression Design of members that are subjected to compression applied through the centroidal axis (axial compression) is based on the assumption of uniform stress over the gross area. This concept is applicable to both load and resistance factor design (LRFD) and allowable stress design (ASD). Design of an axially loaded compression member or column for both LRFD and ASD utilizes the concept of effective column length KL. The buckling coefficient K is the ratio of the effective column length to the unbraced length L. Values of K depend on the support conditions of the column to be designed. The AISC specifications for LRFD and ASD indicate that K should be taken as unity for columns in braced frames unless analysis indi- cates that a smaller value is justified. Analysis is required for determination of K for unbraced frames, but K should not be less than unity. Design values for K recommended by the Structural Stability Research Council for use with six idealized conditions of rotation and translation at column supports are illustrated in Fig. 6.4 (see also Arts. 7.4 and 7.9). The axially compression strength of a column depends on its stiffness measured by the slenderness ratio KL /r, where r is the radius of gyration about the plane of buckling. For serviceability considerations, AISC recommends that KL/r not exceed 200. LRFD strength for a compression member wf;P n (kips) is given by ␾ P ϭ 0.85AF (6.39) ngcr with ␾ ϭ 0.85. For ␭ c Յ 1.5, BUILDING DESIGN CRITERIA 6.43 2 ␭ c F ϭ 0.658 F (6.40a) cr y for ␭ c Ͼ 1.5, 0.877 F ϭ F (6.40b) cr y 2 ␭ c where ␭ c ϭ (KL/r ␲ ) ͙F /E y F y ϭ minimum specified yield stress of steel, ksi A g ϭ gross area of member, in 2 E ϭ elastic modulus of the steel ϭ 29,000 ksi For the strength of composite columns, see Art. 6.26.4; for built-up columns, see Art. 6.28. For ASD, the allowable compression stress depends on whether buckling will be elastic or inelastic, as indicated by the slenderness ratio 2 C ϭ ͙2 ␲ E/F (6.41) cy When KL/r Ͻ C c , the allowable compression stress F a (kips) on the gross section should be computed from 22 1 Ϫ (KL/r)/2C c F ϭ F (6.42) ay 33 5 ⁄ 3 ϩ 3(KL /r)/8C Ϫ (KL/r)/8C cc When KL /r Ͼ C c , the allowable compression stress is 2 12 ␲ E F ϭ (6.43) a 2 23(KL/r) Tables of allowable loads for columns are contained in the AISC ‘‘Manual of Steel Con- struction’’ for ASD and for LRFD. For composite compression members, see Art. 6.26.4; for built-up compression members, see Art. 6.28. (T.V. Galambos, Guide to Stability Design Criteria for Metal Structures, John Wiley & Sons, Inc., New York.) 6.16.3 Concentrated Loads on Beams Large concentrated loads or reactions on flexural members may cause their webs to fail by yielding or crippling unless the webs are made sufficiently thick to preclude this or are assisted by bearing stiffeners. Also, adequate bearing length should be provided on the flange of the member. Web yielding manifests as a stress concentration in a web beneath a concentrated load. The AISC LRFD specification for structural steel buildings limits the design strength of the web at the toe of the fillet under a concentrated load to ␾ R n (kips), where ␾ ϭ 1.0 and R n is determined from Eq. (6.44) or (6.45). When the concentrated loads is applied at a distance from the end of the member greater than the member depth, R ϭ (5k ϩ N)Ft (6.44) nyw When the load acts at or near the end of the member, R ϭ (2.5k ϩ N )Ft (6.45) nyw [...]... TABLE 6. 30 Nominal Bolt Hole Dimensions, in Slotted holes—width ϫ length Round-hole diameter Bolt diameter 1 ⁄2 ⁄8 3 ⁄4 7 ⁄8 1 Ն11⁄8 5 Standard Oversize 9 16 11 16 13 16 15 16 1 16 1 ⁄8 ⁄ 16 15 ⁄ 16 11⁄ 16 11⁄4 d ϩ 5⁄ 16 ⁄ ⁄ ⁄ ⁄ 1⁄ d ϩ ⁄ 16 5 13 Short-slot Long-slot 11 16 ϫ 16 7 11 16 ϫ 8 13 16 ϫ 1 15 16 ϫ 8 1 5 16 ϫ 16 1 16 ϫ ϩ 38 9 ⁄ ⁄ ⁄ ⁄ ⁄ 1⁄ (d ϩ ⁄ ) ⁄ 1 1⁄ 1⁄ (d ⁄) ⁄ 16 ϫ 11⁄4 ⁄ 16 ϫ 19⁄ 16 13 ⁄ 16 ϫ 17⁄8... Art 6. 16. 2 e with K Ն 1.0 in the plane of bending 6. 19.2 ASD for Bending and Compression In ASD, the interaction of bending and axial compression is governed by Eqs (6. 68) and (6. 69) or (6. 70): 6. 50 SECTION SIX ƒa ϩ Fa Cmxƒbx Cmyƒby ϩ Յ 1.0 ƒa ƒa 1Ϫ Fbx 1Ϫ Fby FЈ FЈ ex ey ͩ ͪ ͩ ͪ ƒa ƒbx ƒby ϩ ϩ Յ 1.0 0 .60 Fy Fbx Fby (6. 68) (6. 69) When ƒa / Fa Յ 0.15, Eq. (6. 70) is permitted in lieu of Eqs (6. 68) and (6. 69):... computed from Eqs (6. 56) and (6. 57): Lc ϭ 76bƒ / ͙Fy Lc ϭ where bƒ d Aƒ Fy ϭ ϭ ϭ ϭ 20,000 (d / Aƒ)Fy (6. 56) (6. 57) width of flange, in nominal depth of the beam, in area of the compression flange, in minimum specified yield stress, ksi When L Ͼ Lc , the allowable bending stress for compact or noncompact sections is the larger of Fb (ksi) computed from Eq (6. 58) and Eq (6. 59), (6. 60), or (6. 61): Fb ϭ 12,000Cb... Fb ϭ 12,000Cb / (Ld / Aƒ) Յ 0 .60 Fy (6. 58) where Cb is the bending coefficient defined in Sec 6. 17.2 When L / rT Յ ͙102,000Cb / Fy , Fb ϭ 0 .60 Fy (6. 59) When ͙102,000Cb / Fy Յ L / rT Յ ͙510,000Cb / Fy , Fb ϭ ͫ ͬ Fy(L / rT)2 2 Ϫ Fy Յ 0 .60 Fy 3 1,530,000Cb (6. 60) When L / rT Յ ͙510,000Cb / Fy , Fb ϭ 170,000Cb / (L / rT)2 Յ 0 .60 Fy (6. 61) The AISC specifications for structural steel buildings do not require... fillet weld or automatic end weld E E EЈ 17,18 17,18 C 20,21 D E 19 19 C D E EЈ 15,23,24,25, 26 15,23,24, 26 15,23,24, 26 15,23,24, 26 D E C 19 19 22 6. 61 6. 62 SECTION SIX TABLE 6. 28 Stress Categories for Determination of Allowable Stress Ranges* (for tensile stresses or for stress reversal, except as noted) (Continued ) Structural detail Stress category Diagram number Fillet-welds connections (Continued ) Shear... is determined by Eq 6. 72b FSR ϭ (Cƒ / N )0. 167 (6. 72b) For stress category CЈ, use Eq 6. 72c or Eq 6. 72d as indicated in Table 6. 26 FSR ϭ ͩ ͪ ͩ 44 ϫ 108 N FSR ϭ ͩ 0.333 ͪ ͩ ͪ ͪ ͩ ͪ 0.71 Ϫ 0 .65 (2a / t) ϩ 0.79W/ t 44 ϫ 108 Յ 0. 167 1.1t N 44 ϫ 108 N ͪ ͩ 0.333 0. 06 ϩ 0.79W/ t 44 ϫ 108 Յ 0. 167 1.1t N 0.333 (6. 72c) 0.333 (6. 72d ) where 2a ϭ the length of the unwelded root face in the direction of the thickness... from Eq (6. 46) or (6. 47) When the concentrated load is applied at a distance of at least d / 2 from the member end, Rn ϭ 135tw2[1 ϩ 3(N / d )(tw / tƒ)1.5͉ ͙Fytƒ / tw (6. 46) When the concentrated load is applied less than d / 2 from the member end, for N / d Յ 0.2 Rn ϭ 68 tw2[1 ϩ 3(N / d )(tw / tƒ)1.5] ͙Fytƒ / tw For N / d Ͼ 0.2, ͫ ͩ 2 Rn ϭ 68 t w 1 ϩ 4N Ϫ 0.2 d ͪͩ ͪ ͬ Ί tw tƒ 1.5 Fytƒ tw (6. 47a) (6. 57b)... in 24 in Ͼ R Ͼ 6 in 6 in Ͼ R Ͼ 2 in 2 in Ͼ R 6. 59 6. 60 SECTION SIX TABLE 6. 28 Stress Categories for Determination of Allowable Stress Ranges* (for tensile stresses or for stress reversal, except as noted) (Continued ) Structural detail Stress category Diagram number Groove welds Detail base metal for transverse loading: equal thickness; reinforcement removed R Ͼ 14 in 24 in Ͼ R Ͼ 6 in 6 in Ͼ R Ͼ 2 in... ͙Fy(Fy ϩ 16. 5) (6. 75a) where h is the distance between adjacent lines of fasteners or clear distance between flanges for welded flange-to-web connections However, when transverse stiffeners are utilized and they are spaced not more than 1.5h apart, the maximum depth / thickness ratio is 6. 66 SECTION SIX h / tw ϭ 2000 / ͙Fy (6. 75b) In these equations, Fy is the yield stress of the flange steel, ksi 6. 25.3... Specification for Structural Steel Buildings, American Institute of Steel Construction, 1999 BUILDING DESIGN CRITERIA 6. 57 fluctuations per day ϫ 365 ϫ years of design life For stress category F, the allowable stress range for shear on the throat of continuous and intermittent fillet welds, and on the shear area of plug and slot welds, is determined by Eq 6. 72b FSR ϭ (Cƒ / N )0. 167 (6. 72b) For stress . Eq. (6. 58) and Eq. (6. 59), (6. 60), or (6. 61): F ϭ 12,000C /(Ld /A ) Յ 0 .60 F (6. 58) bbƒ y where C b is the bending coefficient defined in Sec. 6. 17.2. When L /r T Յ ͙102,000C /F , by F ϭ 0 .60 F (6. 59) by When. is F ϭ 0 .66 F (6. 55) by This stress can be used, however, only if L does not exceed the smaller of the values of L c computed from Eqs. (6. 56) and (6. 57): L ϭ 76b /͙F (6. 56) c ƒ y 20,000 L ϭ (6. 57) c (d/A. myby ϩϩՅ 1.0 (6. 68) F ƒƒ aa a 1 Ϫ F 1 Ϫ F ͩͪͩͪ bx by FЈ FЈ ex ey ƒƒƒ abxby ϩϩՅ 1.0 (6. 69) 0 .60 FF F ybxby When ƒ a /F a Յ 0.15, Eq. (6. 70) is permitted in lieu of Eqs. (6. 68) and (6. 69): ƒƒ ƒ abxby ϩϩՅ