The cracked kettle: The bad reputation of realism

For the limit state of local buckling, the nominal flexural strength Mn = Fb S where the local buckling stress Fb is: deter-mined for the limit states of yielding and tensile rupture.

For the limit state of yielding, the nominal flexural strength Mn is the lesser of 1.3Fty S and 1.3Fcy S.

For the limit state of tensile rupture, the nominal flexural strength Mn = 1.42Ftu S /kt.

Fb = local buckling stress of the flat elements in flexure determined using Section F.8.2.2 or F.8.2.3.

ccf = distance from the centerline of the compression flange to the cross section’s neutral axis

ccw = distance from the web group’s extreme compression fiber to the cross section’s neutral axis

If = moment of inertia of the flange group about the cross section’s neutral axis. The flange group consists of the flat elements in uniform compression and the flat elements in uniform tension and their edge or intermediate stiffeners.

Iw = moment of inertia of the web group about the cross section’s neutral axis. The web group consists of the flat elements in flexure and their intermediate stiffeners.

If there are stiffeners located farther than the compression flange from the cross section’s neutral axis, the compressive flexural strength shall not exceed

Fcy If/ccs + Fb Iw/ccw

where

ccs = distance from the cross section’s neutral axis to the extreme fiber of compression flange stiffeners and

b) the tensile flexural strength

M nt = F t I f / c tf + F b Iw / c tw (F.8-2) where (see Figure F.8.1)

Ft = tensile stress for the flat elements in uniform tension determined using Section F.8.1.1

Fb = tensile stress for the flat elements in flexure deter-mined using Section F.8.1.2

F.8.2.1 Elements in Uniform Compression

For beam elements in uniform compression, the flexural compressive strength is given in Section B.5.4.

F.8.2.2 Elements in Flexure

For beam elements in flexure, the flexural compressive strength is given in Section B.5.5.

F.8.2.3 Alternate Compressive Flexural Strength As an alternate to Sections F.8.2.1 and F.8.2.2, the com-pressive strength of elements of beams composed of flat elements without welds may be determined as follows:

The flexural compressive stress Fc corresponding to the nominal flexural strength for the shape’s flat elements in uniform compression shall be determined in accordance with Section B.5.4.6.

The flexural compressive stress Fb corresponding to the nominal flexural strength for the shape’s flat elements in flex-ure shall be determined in accordance with Section B.5.5.4.

F.8.3 Weighted Average Flexural Strength

The weighted average nominal flexural strength Mn is the lesser of

a) the compressive flexural strength

M _nc = F c I _f / c _cf + F b I _w / c _cw (F.8-1) where (see Figure F.8.1)

Fc = local buckling stress of the flat elements in uniform compression determined using Section F.8.2.1 or F.8.2.3. The strength of stiffened elements shall not exceed the strength of an intermediate stiffener or an edge stiffener.

Figure F .8 .1

F.9.2 Flexural Members with Longitudinal Welds The lateral-torsional buckling strength Mn of members with longitudinal welds is

Mn = Mno(1 - Awz/Af) + Mnw(Awz/Af) (F.9-1) where

Mno = lateral-torsional buckling strength if no part of the cross section were weld-affected. Use buck-ling constants for unwelded metal (Table B.4.1 or Table B.4.2) and mechanical properties from Table A.3.4 or Table A.3.4M.

Mnw = lateral-torsional buckling strength if the entire cross section were weld-affected. Use buckling constants for weld-affected zones (Table B.4.1) and mechanical properties from Table A.3.5 or Table A.3.5M.

Af = area of the member farther than 2c/3 from the neutral axis, where c is the distance from the neu-tral axis to the extreme compression fiber.

ctf = distance from the extreme tension fiber to the cross section’s neutral axis

ctw = distance from the web group’s extreme tension fiber to the cross section’s neutral axis

F .9 Welded Flexural Members

F.9.1 Flexural Members with Transverse Welds The lateral-torsional buckling strength of members sup-ported at both ends with no transverse weld farther than 0.05L from the member ends shall be calculated as if there were no welds.

The lateral-torsional buckling strength of members sup-ported at both ends with a transverse weld farther than 0.05L from the member ends and members supported at only one end with a transverse weld at any location shall be calculated as if the entire cross-sectional area were weld-affected.

For tubes with circumferential welds, Section B.5.4.5 only applies if Rb /t ≤ 20.

Chapter G Design of Members for Shear

The shear stress Fs corresponding to the shear strength is

Limit State Fs b/t

Slenderness Limits yielding Fsy b/t ≤ S1 S1 = _______Bs- Fsy

1.25Ds

inelastic

buckling Bs- 1.25Ds b/t S1 < b/t < S2

elastic buckling

π²E ________

(1.25b/t)² b/t ≥ S2 S2 = C____s

1.25 where

b = clear height of the web (see Figure G.2.1) for un-stiffened webs and

b = ____________ a1 for webs with transverse stiffeners

√

^{____1 +__ 0.7____}

(

^a1__

)

²

a2

a1 = the lesser of the clear height of the web and the distance between stiffeners

a2 = the greater of the clear height of the web and the distance between stiffeners

t = web thickness Aw = dt

d = full depth of the section

Transverse stiffeners shall have a moment of inertia Is

not less than the following:

s ≤ 0.4, Is = 0.55Vb²

(

^s

)

^(G.2-2)

__ _______ __

b E b

s > 0.4, Is = 0.088Vb²

(

^b

)

^(G.2-3)

__ ________ __

b E s

This chapter addresses flat webs of members subjected to shear in the plane of the web and shear in round and oval tubes.

G .1 General Provisions

The design shear strength fvVn and the allowable shear strength Vn /Wv shall be determined from Section G.2 or G.3, where

fv = 0.90 (LRFD)

Wv = 1.65 (ASD building-type structures) Wv = 1.85 (ASD bridge-type structures)

The shear stress corresponding to the shear strength is For unwelded members:

Fs = Fso (G.1-1)

For welded members:

Fs = Fso(1 - Awz/Ag) + Fsw Awz/Ag (G.1-2) where

Fso = shear stress corresponding to the shear strength for an element if no part of the cross section were weld-affected. Use buckling constants for unwelded metal (Table B.4.1 or Table B.4.2) and mechanical properties from Table A.3.4 or Table A.3.4M.

Fsw = shear stress corresponding to the shear strength for an element if the entire cross section were affected. Use buckling constants for weld-affected zones (Table B.4.1) and mechanical properties from Table A.3.5 or Table A.3.5M.

For transversely welded elements with b/t ≤ S1, Fs = Fso.

Awz = cross sectional area of the weld-affected zone Ag = gross cross sectional area of the element.

The shear stress Fs corresponding to the nominal shear strength in weld-affected zones shall not exceed Fsuw/1.2.

G .2 Members with Flat Webs Supported on Both Edges

The nominal shear strength Vn of flat webs supported on both edges is

Vn = Fs Aw (G.2-1)

Figure G .2 .1

FLAT WEBS IN SHEAR

where

b = clear height of the web regardless of whether or not a longitudinal stiffener is present

Is = moment of inertia of the transverse stiffener. For a stiffener composed of members of equal size on each side of the web, the moment of inertia of the stiffener shall be computed about the centerline of the web. For a stiffener composed of a member on only one side of the web, the moment of inertia of the stiffener shall be computed about the face of the web in contact with the stiffener.

s = transverse stiffener spacing. For a stiffener com-posed of a pair of members, one on each side of the web, the stiffener spacing s is the clear distance between the pairs of stiffeners. For a stiffener com-posed of a member on only one side of the web, the stiffener spacing s is the distance between fastener lines or other connecting lines.

V = shear force on the web at the transverse stiffener Stiffeners shall extend from flange to flange but need not be connected to either flange. Unless the outer edge of a stiffener is continuously stiffened, its thickness shall not be less than ¹⁄12th the clear width of the outstanding leg.

G .3 Round or Oval Tubes

The nominal shear strength Vn of round or oval tubes is

Vn = Fs Ag/2 (G.3-1)

where:

Limit State Fs lt

Slenderness Limits yielding Fsy lt ≤ S1 S1 = _________1.3Bs- Fsy

1.63Ds

inelastic

buckling 1.3Bs- 1.63Dslt S1 < lt < S2

elastic

buckling _________1.3π²E

(1.25 lt)² lt ≥ S2 S2 = C____s

1.25

lt = 2.9

(

^{__ R}t ^b

)

^5/8

(

^___LR^v b

)

^{1/4 (G.3-2)}

Rb= mid-thickness radius of a round tube or maximum mid-thickness radius of an oval tube

t = thickness of tube

Lv= length of tube from maximum to zero shear force.

Chapter H Design of Members for Combined Forces and Torsion

maxi-mum mid-thickness radius of an oval tube

t = tube thickness

Ls = length of tube between circumferential stiffeners, or overall length if no circumferential stiffeners are present

R = outside radius of the tube J = torsion constant of the tube H.2.2 Rectangular Tubes

The nominal torsional strength Tn for rectangular tubes for the limit state of torsional yielding and torsional buckling is

Tn = FsC (H.2-3)

where Fs is determined in accordance with Section G.2 for the side with the larger slenderness and C is the torsional shear constant.

H.2.3 Rods

The nominal torsional strength Tn for rods for the limit state of torsional yielding is

Tn = 0.196FsyD³ (H.2-4)

where

D = diameter of the rod

H .3 Members Subject to Torsion, Flexure, Shear, and/or Axial Compression H.3.1 Flat Elements

Stresses in flat elements subject to torsion, flexure, shear, and/or axial compression shall satisfy the following:

For LRFD:

fc/(fFc) + [ fb/(fFb)]² + [ fs/(fFs)]² ≤ 1.0 (H.3-1) This chapter addresses members subject to axial force

and flexure about one or both axes, with or without torsion, and to members subject to torsion only.

H .1 Members Subject to Flexure and Axial Force

For members subject to flexure and axial force,



^{Pr Mrx Mry}



^{≤ 1.0 (H.1-1)}

x = subscript for major principal axis bending y = subscript for minor principal axis bending For LRFD:

Pr = required axial force using LRFD load combinations For axial tension:

Pc = design axial tensile strength determined in accor-dance with Chapter D

For axial compression:

Pc = design axial compressive strength determined in accordance with Chapter E

Mr = required flexural strength using LRFD load com-binations

Mc = design flexural strength determined in accordance with Chapter F

For ASD:

Pr = required axial force using ASD load combinations For axial tension:

Pc = allowable axial tensile strength determined in accor-dance with Chapter D

For axial compression:

Pc = allowable axial compressive strength determined in accordance with Chapter E

Mr= required flexural strength using ASD load combi-nations

Mc = allowable flexural strength determined in accor-dance with Chapter F

H .2 Members Subject to Torsion

The design torsional strength fTTn and the allowable torsional strength Tn/WT shall be determined in accordance with Section H.2, where

fT = 0.90 (LRFD)

WT = 1.65 (ASD building-type structures) WT = 1.85 (ASD bridge-type structures) H.2.1 Round or Oval Tubes

The nominal torsional strength Tn for round or oval tubes for the limit state of torsional yielding and torsional buckling is

For ASD:

fc/(Fc/W) + [ fb/(Fb/W)]² + [ fs/(Fs/W)]² ≤ 1.0 (H.3-2) where

fc = uniform compressive stress due to axial compres-sion and bending

fb= compressive stress due to flexure fs = shear stress due to shear and torsion

Fc = axial compression stress corresponding to the nomi-nal axial compression strength

Fb = bending stress corresponding to the nominal flexural compression strength

Fs = shear stress corresponding to the nominal shear strength

H.3.2 Curved Elements

Stresses in curved elements subject to torsion, flexure, shear, and/or axial compression shall satisfy the following:

For LRFD:

fc/(fFc) + fb/(fFb) + [ fs/(fFs)]² ≤ 1.0 (H.3-3) For ASD:

fc/(Fc/W) + fb/(Fb/W) + [ fs/(Fs/W)]² ≤ 1.0 (H.3-4) where

fc = compressive stress due to axial compression fb = compressive stress due to flexure

fs= shear stress due to shear and torsion

Fc = axial compression stress corresponding to the nomi-nal axial compression strength

Fb = bending stress corresponding to the nominal flexural compression strength

Fs= shear stress corresponding to the nominal shear strength

This chapter addresses connecting elements and con-nectors.

J .1 General Provisions J.1.1 Design Basis

The design strength and the allowable strength of con-nections shall be determined in accordance with the provi-sions of this chapter and Chapter B.

If the longitudinal centroidal axes of connected axially loaded members do not intersect at one point, the connection and members shall be designed for the effects of eccentricity.

J.1.2 Fasteners in Combination with Welds Fasteners shall not be considered to share load in com-bination with welds.

J.1.3 Maximum Spacing of Fasteners

The pitch and gage of fasteners joining components of tension members shall not exceed (3 + 20t) in. [(75 + 20t) mm] where t is the thickness of the outside component.

In outside components of compression members:

a) The component’s strength shall satisfy the requirements of Section E.3 with an effective length kL = s/2, where s is the pitch, and

b) If multiple rows of fasteners are used, the component’s strength shall satisfy the requirements of Section B.5.4.2 with a width b = 0.8g where g is the gage. If only one line of fasteners is used, the component’s strength shall satisfy the requirements of Section B.5.4.1 with a width b = the edge distance of the fastener.

J .2 Welds

The design strength fRn and allowable strength Rn/W of welds shall be determined from Sections J.2.1 through J.2.4 where

f = 0.75 (LRFD)

W = 1.95 (ASD building-type structures) W = 2.20 (ASD bridge-type structures) J.2.1 Groove Welds

J.2.1.1 Complete Penetration and Partial Penetration Groove Welds

The following types of groove welds are complete pen-etration welds:

a) Welds welded from both sides with the root of the first weld backgouged to sound metal before welding the second side.

b) Welds welded from one side using permanent or tempo-rary backing.

c) Welds welded from one side using AC-GTAW root pass without backing

d) Welds welded from one side using PAW-VP in the key-hole mode.

All other groove welds are partial penetration welds.

J.2.1.2 Effective Area

a) Size: The size Sw of a complete joint penetration groove weld is the thickness of the thinner part joined. The size Sw of a partial joint penetration groove weld is the depth of preparation (see Figure J.2.1) for all V and bevel groove welds with an included angle greater than 45°, and the depth of preparation of all J and U groove welds.

b) Length: The effective weld length Lwe for tension and compression is the length of the weld perpendicular to the direction of tensile or compressive stress. The effec-tive weld length for shear is the length of the weld paral-lel to the direction of shear stress.

c) Area: The effective area Awe of a groove weld is the effective weld length times the weld size.

Chapter J Design of Connections

Figure J .2 .1

PARTIAL JOINT PENETRATION GROOVE WELD

J.2.1.3 Strength

The nominal tensile or compressive strength Rn of a groove weld is:

Rn= Ftuw Awe (J.2-1)

where

Ftuw= least of the welded tensile ultimate strengths of the base metals and the filler. Welded tensile ultimate strengths of base metals shall be taken from Table A.3.5 or Table A.3.5M and tensile ultimate strengths of fillers from Table J.2.1 or Table J.2.1M.

Awe = weld effective area

The nominal shear strength Rn of a groove weld is:

Rn = Fsuw Awe (J.2-2)

where

Fsuw = least of the welded shear ultimate strengths of the base metals and the filler. Welded shear ultimate strengths of base metals shall be taken from Table A.3.5 or Table A.3.5M and shear ultimate strengths of fillers from Table J.2.1 or Table J.2.1M

Awe = weld effective area.

J.2.2 Fillet Welds

J.2.2.1 Effective Throat and Effective Length

a) The effective throat is the shortest distance from the joint root to the face of the diagrammatic weld (see Figure J.2.2).

Rn = Fsw Lwe (J.2-3)

where

Fsw = least of:

a) the product of the weld filler’s shear ultimate strength and the effective throat.

b) for base metal in shear at the weld-base metal joint, the product of the base metal’s welded shear ultimate strength and the fillet size Sw at the joint;

c) for base metal in tension at the weld-base metal joint, the product of the base metal’s welded tensile ultimate strength and the fillet size Sw

at the joint.

Welded shear and tensile ultimate strengths of base metals shall be taken from Table A.3.5 or Table A.3.5M and shear ultimate strengths of weld fillers from Table J.2.1 or Table J.2.1M.

Lwe = weld effective length J.2.3 Plug and Slot Welds J.2.3.1 Effective Area

The effective area Awe of plug or slot welds is the nomi-nal area of the hole or slot in the plane of the faying surface (see Figure J.2.3). Slot lengths shall not exceed 10 times the slotted material’s thickness.

Figure J .2 .2

EFFECTIVE THROAT OF A FILLET WELD

b) The weld effective length Lwe is the overall length of the weld, including boxing. If the effective length of a fillet weld is less than 4 times its nominal size Sw (see Figure J.2.2), the effective weld size shall be considered to be 25% of its effective length.

The minimum length of segments of an intermittent fillet weld shall be 1½ in. (40 mm). The maximum effective length of an end-loaded fillet weld is 100Sw.

J.2.2.2 Strength

Stress on a fillet weld shall be considered to be shear for any direction of applied load. The nominal shear strength Rn of a fillet weld is:

Figure J .2 .3

SLOT WELD PLAN VIEW

J.2.3.2 Strength

The nominal shear strength Rn of a plug or slot weld is:

Rn= Fsw Awe (J.2-4)

where

Fsw = lesser of the welded shear ultimate strengths of the filler and the base metal under the weld. Welded shear ultimate strengths of base metals shall be taken from Table A.3.5 or Table A.3.5M and shear ultimate strengths of fillers from Table J.2.1 or Table J.2.1M.

Awe= weld effective area

J.2.4 Stud Welds

The nominal tensile strength Rn of a stud weld is:

Rn = Tuw (J.2-5)

where

Tuw = tensile strength of the stud in Table J.2.2 or Table J.2.2M

The base metal thickness for arc stud welding shall not be less than 50% of the stud diameter. The base metal thickness for capacitor discharge stud welding shall not be less than 25% of the stud diameter.

J.2.5 Post-Weld Heat Treating

For 6005 lighting poles through 0.250 in. (6 mm) thick welded in the T1 temper with 4043 filler and artificially aged to the T5 temper after welding, design and allowable

stresses of the base metal within 1.0 in. (25 mm) of the weld shall be 85% of the values for unwelded 6005-T5.

For 6063 lighting poles through 0.375 in. (10 mm) thick welded in the T4 temper with 4043 filler and artificially aged to the T6 temper after welding:

a) The design and allowable stresses of the base metal within 1.0 in. (25 mm) of the weld shall be 85% of the values for unwelded 6063-T6.

b) The design stress is 12.5 ksi (85 MPa) and the allowable stress is 8 ksi (55 MPa) for welds in socket type bases.

c) The design stress is 9 ksi (60 MPa) and the allowable stress is 5.9 ksi (41 MPa) for welds in other than socket type bases.

J .3 Bolts

J.3.1 Bolt Material Bolt material shall be:

a) Aluminum: Bolts shall meet ASTM F 468 and be 2024-T4, 6061-T6, or 7075-T73. When 2024 bolts will be exposed to contact with liquid water or humidity near

Table J .2 .1

TENSILE STRENGTHS FOR 5183, 5356, AND 5556 STUDS

TENSILE STRENGTHS FOR 5183, 5356,

AND 5556 STUDS

the dew point in the intended service, they shall have a minimum 0.0002 in. (0.005 mm) thick anodic coating.

Nuts shall meet ASTM F 467. Nuts for ¼ in. (M6) bolts and smaller shall be 2024-T4; larger nuts shall be 6061-T6 or 6262-T9. Flat washers shall be Alclad 2024-T4.

Spring lock washers shall be 7075-T6.

b) Carbon steel: Carbon steel bolts, nuts, and washers shall have a hot-dip zinc coating meeting ASTM A 153 or a mechanically deposited zinc coating meeting ASTM B 695 and shall be lubricated in accordance with ASTM A 563. The zinc coating thickness shall be adequate to provide corrosion protection for the anticipated service.

If other coatings are used, their thickness shall be suf-ficient to provide corrosion protection for the intended service. Bolt hardness shall be less than Rockwell C35.

A 490 bolts shall not be used.

c) Stainless steel: Stainless steel bolts, nuts and washers shall be 300 series. Bolts shall meet ASTM F 593, A 193, or A 320. Nuts shall meet ASTM F 594 or A 194.

J.3.2 Holes and Slots for Bolts

The nominal diameter of holes for bolts shall not be more than ¹⁄16 in. (2 mm) greater than the nominal diameter of the bolt unless slip-critical connections are used.

The nominal width of slots for bolts shall not be more than ¹⁄16 in. (2 mm) greater than the nominal diameter of the bolt. If the nominal length of the slot exceeds 2.5D or the edge distance is less than 2D, where D is the nomi-nal bolt diameter, the edge distance perpendicular to the slot length and slot length shall be sized to avoid over-stressing the material along the slot. Unless slip-critical connections are used, the length shall be perpendicular to the direction of force.

J.3.3 Minimum Spacing of Bolts

The distance between bolt centers shall not be less than 2.5 times the nominal diameter of the bolt.

J.3.4 Minimum Edge Distance of Bolts

The distance from the center of a bolt to an edge of a part shall not be less than 1.5 times the nominal diameter of the bolt. See Section J.3.7 for the effect of edge distance

The distance from the center of a bolt to an edge of a part shall not be less than 1.5 times the nominal diameter of the bolt. See Section J.3.7 for the effect of edge distance

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