Limit State Definitions of the Connection Design Calculations SDS2 V7331

8/18/2019 Limit State Definitions of the Connection Design Calculations SDS2 V7331

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*** CONNECTION CALCULATION COVER SHEET ***Page 1

SDS/2 v 7.331

SYMBOLS

A Section gross area orDimension from weld line to C/L boltsfor a single-plate shear connection

Ab Bolt area based on nominal diameterAe Effective net areaAfg Gross beam flange area

Afn Net beam flange areaAg Gross areaAgt Gross tension areaAgv Gross shear areaAn Net areaAnt Net tension areaAnv Net shear areaAst Cross sectional area of a pair of stiffenersAt Net tension areaAv Net shear areaB Allowable tension per bolt, AISC manual Page 9-12Bc Bolt tension including prying actionBf Section flange widthC Fastener/ weld group coefficient ( AISC manual TABLE 7-6, 8-4)

ultimate strength method unless noted.

Ca Coefficient used in moment end PL designCc Slenderness ratio separating elastic & inelastic bucklingCdb Bottom cope depthCdt Top cope depthCJP Complete joint penetration -- weldClb Bottom cope lengthClip_stbk Dim. from face of clip angle to end of beamClt Top cope lengthCol_spa Spacing between bolt columnsColumn Number of fasteners perpendicular to the line of forceCn_depth Connection element depthCn_thick Connection element thicknessCn_width Connection element widthCv Ratio of critical web stress to the shear yield stress

of the web materialD Section depthDb Nominal bolt diameterDc Depth of column web clear of filletsDh Hole dimension:

Nominal dim of bolt hole + 1/16, (2 mm)


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Page 2E Modulus of elasticity of steel

29,000 KSI (200,000 MPa)Eff_weld Max. effective weld size based on mtrl thickness,


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Page 3OMEGA AISC 2005 specification ASD safety factorOsl Outstanding angle leg sizePair Pairs of transverse beam stiffeners, 1 or 2Pbf Factored flange or connection plate force;

computed flange force multiplied by a load factorPHI AISC 2005/2010 specification LRFD resistance factorPI 3.14159.....Pn Nominal axial strengthPu Required tensile or compressive strengthQs Stress reduction factor, Appendix BRbs Resistance to block shearRn Nominal strengthRo Shear tab or tee strength at yield

Row Number of fasteners in the line of forceRstr Bolt slip resistance, (A-J3-1)Rv Force transmitted by one fastenerSetback Distance from face of support to end of beamShear Number of shear planes:

(1 = single shear; 2 = double shear)Sn Section modulus of the coped portion of a beamSpa or S Bolt spacingSQR[ ] Square of expression in bracketsSQRT[ ] Square root of expression in bracketsSx Section modulusSx_net Net section modulusS_g S^2/4g, AISC chapter B3.13T_allow Allowable tension per boltTb Bolt pre-tension: Table J3.1

Tc HSS brace welded pl end fitting, cap plate thicknessTf Flange or angle leg thicknessTw Web or tube wall thicknessTs HSS brace welded pl end fitting, tee stem thicknessT_slab Concrete slab thickness, composite designT_sup Thickness of supporting memberU Shear lag reduction coefficient, Chapter D3Vb Vert. force at gusset-beam interfaceVc Vert. force at gusset-column interfaceVn Nominal shear strengthWeld_size Fillet weld leg size or groove weld throatWeld_len Length of weldWeld_spa Spacing between two parallel weld segmentsWg Element gross widthWn Element net widthWs 'Whitmore' section width, gusset Pl designZx Plastic section modulusZe Effective plastic section modulus


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Page 4a Clear dist. between transverse stiffenersb Width of compression element, or other partc Cope length from end of beam webd Depth of connected elementdc Beam cope depthe Cope length from face of conn. or weld lineeb Shear tab bolt design eccentricityew Shear tab weld design eccentricityfa Calculated axial stressfb Calculated bending stressfp Calculated bearing stressfr Calculated force on a weldft Calculated tension stress

fv Calculated shear stressf'c Compression strength of concreteg Angle leg gageg1,g2 Angle leg gages, 5 in or larger leg sizeh Clear dist. between flanges of a beam or girder.ho Depth of the remaining web at a coped beam sectionkl Horiz. weld segment length, AISC manual Table 8-8kv Shear buckling coefficient for girder websl Lengthlb Length of bearingn Modular ratio Es/Ec, 9r Radius of gyrationt Thickness of connected elementtc Thickness of connected element required to develop

'B' in bolts with no prying action, AISC manual pg 9-13

q Prying force per bolt at design load, AISC manual pg 9-12


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Page 5SDS/2 referneces to the AISC 2010 Specification for StructuralSteel Buildings, June 22, 2010

CHAPTER B DESIGN REQUIREMENTSB3 Design BasisB4 Classification of sections for local buckling

CHAPTER D DESIGN OF MEMBERS FOR TENSIONGross area yielding: Pn = Fy * Ag (D2-1)

PHI = .9 (LRFD) , OMEGA = 1.67 (ASD)

Tension rupture net area: Pn = Fu * Ae (D2-2)PHI = .75(LRFD) , OMEGA = 2.0 (ASD)

Design strength = PHI*Pn (LRFD), Allowable strength = Pn/OMEGA (ASD)

Pin-connected members:Tension rupture on net area: Pn = Fu * (2t*be) (D5-1)Shear rupture: Pn = .6Fu * Asf

PHI = .75 (LRFD) , OMEGA = 2.0 (ASD)

Design strength = PHI*Pn (LRFD), Allowable strength = Pn/OMEGA (ASD)

CHAPTER E DESIGN OF MEMBERS FOR COMPRESSIONPHI = .9 (LRFD) , OMEGA = 1.67 (ASD)

Design strength = PHI*Pn (LRFD) , Allowable strength = Pn/OMEGA (ASD)

Pn from: E3 -- flexural buckling, members without slender elements

E4 -- Torsion/buckling, members without slender elements

E5 -- Single angle compression members

E6 -- Built up members

E7 -- Members with slender elements


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Page 6CHAPTER F DESIGN OF MEMBERS FOR FLEXURE

PHI = .9 (LRFD) , OMEGA = 1.67 (ASD)Design strength = PHI*Mn (LRFD), Allowable strength = Mn/OMEGA (ASD)

Mn from: F2 -- Double symmetric compact I-shaped member andchannels bent about their major axis

F3 -- Doubly symmetric I-shaped members with compact

webs and noncompact or slender flanges bent about

their major axis

F4 -- Other I-shaped members with compact or noncompact

webs bent about their major axis

F5 -- Doubly symmetric and singly symmetric I-shaped

members with slender webs bent about their major axis

F6 -- I-shaped members and channels bent about theirminor axis

F7 -- Square and rect. HSS and box-shaped members

F8 -- Round HSS

F9 -- Tees and double angles loaded in the plane of symmetry

F10 -- Single angles

F11 -- Rectangular bars and rounds

F12 -- Unsymmetrical shapes


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Page 7

CHAPTER G DESIGN OF MEMBERS FOR SHEARPHI = .9 (LRFD) , OMEGA = 1.67 (ASD)

all provisions except G2

Design strength = PHI*Vn (LRFD), Allowable strength = Vn/OMEGA (ASD)

Vn from: G2 -- Members with unstiffened or stiffened websPHI = 1.0 (LRFD) , OMEGA = 1.5 (ASD)

G4 -- Single angles

G5 -- Rectangular and box members

G6 -- Round HSS

G7 -- Weak axis shear in singly and doubly symmetric shapes


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Page 8

CHAPTER H DESIGN OF MEMBERS FOR COMBINED FORCES AND TORSIONH1.1 -- For design according to sect B3.3 (LRFD)

Pc = PHI c * PnMc = PHI b * MnPHI c = .9, PHI b = .9

-- For design according to sect B3.4 (ASD)Pc = Pn / OMEGA cMc = Mn / OMEGA bOMEGA c = 1.67, OMEGA b = 1.67

H1.2 -- Doubly and singly symmetric members flexure and tension

For design according to sect B3.3 (LRFD)Pc = PHI t * PnMc = PHI b * PnPHI t tension resistance factor sec D2PHI b = .9

For design according to sect B3.4 (ASD)Pc = Pn / OMEGA tMc = Mn / OMEGA bOMEGA t = safety factor for tension from D2OMEGA b = 1.67

H2 -- Unsymmetric and other members subject to flexureand axial force

For design according to sec B3.3 (LRFD)

Fa = PHI c * FcrFbw, Fbz = PHI b * Mn / SPHI c = .9, PHI t = resistance factor from D2PHI b = .9

For design according to sed B3.4 (ASD)Fa = Fcr / OMEGA cFbw, Fbz = Mn / (OMEGA b * S )OMEGA c = 1.67, OMEGA t = safety factor from D2OMEGA b = 1.67

H3 -- Members under torsion and combined torsion, flexureand/or axial force

1. Torsional Strength of round and rect HSSPHI t = .9 (LRFD), OMEGA t = 1.67 (ASD)

3. Strength of non-HSS members under torsion andcombined stress

PHI t = .9 (LRFD), OMEGA t = 1.67 (ASD)


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Page 9

CHAPTER I DESIGN OF COMPOSITE MEMBERSI2.1b Compressive strength

PHI = .75, OMEGA = 2Design strength = PHI*Pn (LRFD), Allowable strengthPn/OMEGA (ASD)

I2.1c Tensile strengthPHI = .9 OMEGA = 1.67Design strength = PHI*Pn (LRFD), Allowable strength Pn/OMEGA (ASD)

I2.1d Load transfer

I2.2b Compressive strength

I2.2c Tensile strength

I2.2d Load transfer

I3.2a Positive flexural strength

I3.2b Negative flexural strength


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Page 10CHAPTER J DESIGN OF CONNECTIONS

Design strength = PHI * Rn (LRFD), Allowable strength Rn/OMEGA (ASD)Rn from: J2 -- Welds and base metal

PHI and OMEGA from table J2.5

J3 -- Bolts and threaded partsJ3.7 PHI = .75, OMEGA = 2.0J3.8 PHI = 1.0, OMEGA = 1.5 or

PHI = .85, OMEGA = 1.76 orPHI = .70, OMEGA = 2.14

J3.10 PHI = .75 OMEGA = 2.0

J4 -- Affected elements of members and connecting elements

J4.1 Strength of elements in tension:Tension yield, PHI = .9, OMEGA = 1.67 (J4-1)Tension rupture, PHI = .75, OMEGA = 2.0 (J4-2)

J4.2 Strength of elements in shearShear yielding, PHI = 1.0, OMEGA = 1.5 (J4-3)Shear rupture, PHI = .75, OMEGA = 2.0 (J4-4)

J4.3 Block shear strength (J4-5)PHI = .75, OMEGA = 2.0

J4.4 Strength of elements in compression (J4-6)PHI = .9, OMEGA = 1.67

J7 -- Bearing strengthPHI = .75, OMEGA = 2.0

J8 -- Column bases and bearing on concrete

PHI = .65, OMEGA = 2.31

J10 -- Flanges and webs with concentrated forcesJ10.1 Flange local bending (J10-1)

PHI = .9, OMEGA = 1.67J10.2 Web local yielding (J10-2, -3

PHI = 1.0, OMEGA = 1.5J10.3 Web crippling (J10-4, -5a -5b

PHI = .75, OMEGA = 2.0J10.4 Web sidesway buckling

PHI = .85, OMEGA = 1.76J10.5 Web compression buckling (J10-8)

PHI = .9, OMEGA = 1.67J10.6 Web panel zone shear (J10-9,-10,-11,-12)

PHI = .9, OMEGA = 1.67


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Page 11CHAPTER K DESIGN OF HSS AND BOX MEMBER CONNECTIONS

Design strength PHI*Rn (LRFD), Allowable strength Rn/OMEGA (ASD)

Rn from

K1 -- Concentrated Forces on HSSK1.2 Round HSSK1.3 Rectangular HSS

K2 -- HSS-to-HSS Truss ConnectionsK2.2 Round HSSK2.3 Rectangular HSS

K3 -- HSS-to-HSS Moment ConnectionsK3.2 Round HSSK3.3 Rectangular HSS

K4 -- Welds of Plates and Branches To Rectangualr HSS


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Page 12

SUMMARY OF AISC 2010 SPECIFICATION LRFD RESISTANCE FACTORS:

CHAPTER PHID Gross tension yielding (D2-1) 0.90

Net fracture (D2-2) 0.75Pin conn, eff area tension (D5-1) 0.75Pin conn, eff area shear (D5-2) 0.75

E Compression 0.90

F Flexure 0.90

G1 General Shear 0.90G2 Web Shear 1.00

H Combined forces H1.1 compression 0.90H1.1 flexure 0.90H1.2 flexure 0.90H2.1 compression 0.90H2.1 flexure 0.90H2.2 flexure 0.90H3.1 HSS 0.90H3.3 non-HSS 0.90

I Composite I2.1b 0.75I2.1c 0.90I2.1e 0.90

I2.2c 0.90I3.2a 0.90I3.2b 0.90I3.3 flexure encased 0.90I3.4 flexure filled 0.90I4.1b shear concrete 0.75I4.1c shear steel 0.75I6.3a direct bearing 0.65I6.3c shear connection 0.45I8.3a shear, anchor 0.65I8.3b tension, anchor 0.75I8.3d shear, steel channel 0.75

J ConnectionsPJP weld tension base 0.75PJP weld tension weld 0.80PJP weld compression base 0.90PJP weld compression weld 0.80PJP weld comp, not fin to bear, base 0.90PJP weld comp, not fin to bear, weld 0.80PJP weld shear 0.75Fillet weld shear 0.75Plug & slot weld shear 0.75Fillet weld alt (J2-4) 0.75Ten/Shr bolts & threaded parts J3.6 0.75Comb Ten/Shr brg conns J3.7 0.75SC bolts J3.8a 1.00SC bolts J3.8b 0.85SC bolts J3.8c 0.70Bearing strength J3.10 0.75Tension yielding J4.1 0.90

Tension rupture J4.1 0.75Shear yielding J4.2 1.00Shear rupture J4.2 0.75


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Page 13

J - continued

Block shear rupture strength J4.3 0.75Compression element J4.4 0.90Bearing J7 0.75Bearing on concrete J8 0.65Col base brg on concrete J9 0.60Local flange bending J10.1 0.90Local web yielding J10.2 1.00Local web crippling J10.3 0.75Web sidesway buckling J10.4 0.85Web compression buckling J10.5 0.90

Web panel zone shear J10.6 0.90

K HSS & Box member Connectionsformula (K1-1) 0.90

(K1-2) 0.90(K1-4) 1.00(K1-7) 0.95(K1-8) 0.95(K1-9) 1.00(K1-10) 0.75(K1-11) 0.90(K1-12) 1.00

(K1-13) 1.00(K1-14) 1.00

(K1-15) 0.75(K2-1) 0.95(K2-2) 0.90(K2-3) 0.90(K2-4) 0.90(K2-5) 0.90(K2-7) 1.00(K2-8) 0.95(K2-9) 1.00(K2-10) 0.75(K2-11) 0.90(K2-12) 0.95(K2-14) 0.90(K2-15) 0.95(K2-16) 0.95(K2-17 -- 22) 0.95

(K3-1) 0.90(K3-2) 0.95(K3-3) 0.90(K3-4) 0.95(K3-6) 1.00(K3-7) 1.00(K3-8) 0.95(K3-9) 1.00(K3-10) 1.00(K3-11) 0.95(K3-12) 1.00(K4.a) 0.75(K4.b) 0.80


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Page 14CONNECTION STRENGTH CALCULATIONS, AISC 2010 SPECIFICATION

Load = Allowable connection shear reaction forthe limit state being checked.

Moment = Allow. conn. moment for the limit state being checked.Tension = Allow. conn. tension for the limit state being checked.Axial load = Allow. brace tension or compression for the

limit state being checked.(Load and Tension are calculated from combined shearand axial loads where applicable)Formulas are based on U.S. Customary (USC) units.

***************************************************

* Formulas not shown are not yet updated for the ** AISC 2010 Specification format. ****************************************************

Calculation LRFD design strength / ASD allowable strengthnumber

(1) Bolt shear, eccentricity not considered:Rn = Fn * Ab Sect. J3.6, .8

(LRFD) Load = PHI*Rn * Row * Column * Shear(ASD) Load = (Rn/OMEGA) * Row * Column * Shear

(2) Beam web shear:Rn = .6 * Fy * D * Tw Shear yielding Sect. J4.2

(LRFD) Load = PHI*Rn

(ASD) Load = Rn/OMEGA

(3) Bolt shear, eccentricity considered:Rn = Fn * Ab Sect. J3.6, .8

(LRFD) Load = (PHI*Rn) * C * Rn * Shear(ASD) Load = (Rn/OMEGA) * C * Rn * Shear

(4) Beam web net shear, coped bolted connection:Anv = Tw * (D - Row * Dh - Cdt - Cdb)Rn = .6 * Fu * Anv Shear rupture Sect. J4.2

(LRFD) Load = PHI * Rn(ASD) Load = Rn/OMEGA

(5) Beam web shear, coped welded connection:Rn from Sect. J4.2(a) Shear yieldingAgv = Tw * (D - Cdt - Cdb)

(LRFD) Load = PHI*Rn(ASD) Load = Rn/OMEGA

(6) Coped beam, PL, resistance to block shear, bolted:Rn from Sect. J4.3 Block Shear strengthN = number of bolt rows, Col = number of bolt columnsAgv =Tw(Lv+Spa(N-1)Anv = Tw( (Spa(N-1) + Lv - (N-.5)Dh ))Ant = Tw( (Spa*(Col-1)+Lh -.5Dh )Ubs = 1 for one column, Ubs = .5 for two columns



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Page 15(7) Coped beam resistance to block shear, welded clip:

Rn from Sect. J4.3 Block Shear strengthCoped top and bottom:

Agv = Tw * Cn_depthUbs = 1.0

Coped top or bottom only:Agv = Tw * Cn_depthAgt = (Clip_leg - Setback) * TwUbs = 1.0


(8) Beam web shear, welded end PL shear connection:

Eff_depth = MIN[Cn_depth - 2*Weld_size, Depth - 2*K_dist]Anv = Tw * Eff_depthRn = .6 * Fu * Anv, Shear rupture Sect. J4.2


(9) Bolt bearing, angle brace to gusset connection.:Bolt nearest the edge: Rn_edge from sect J3.10Interior bolt: Rn_int from sect. J3.10N_e = number of edge boltsN_i = number of interior bolts

(LRFD) Axial load = PHI(Rn_edge*N_e + Rn_int*N_i)(ASD) Axial load = (Rn_edge*N_e + Rn_int*N_i)/OMEGA

(10) Bolt shear, angle brace to gusset connection.:n = number of bolts in connectionOne column -- n = RowTwo columns -- n = 2 * RowFour columns -- n = 4 * Row - 2Rn from Sect. J3.6, .8

(LRFD) Axial load = PHI*Rn * n(ASD) Axial load = (Rn/OMEGA) * n

(11) Brace block shear, angle brace to gusset connection.:n = number of anglesAnv = n*t((S - Dh)*(Row - 1) + Le - .5 * dh)Agv = n*t(S(Row -1) + Le)

One columns --Ant = n*t( Leg - g1 - .5 * Dh )Ubs = 1

Two columns -- single angle or double angle both sidesAnt = n*t( Leg - g1 - 1.5 * Dh )Ubs = 0.5

Two columns -- double angle both sides or star angleAnt = n*t( Leg - g1 - 0.5 * Dh )Ubs = 1

Four columns --Ant = n*t(Leg - g1 - 1.5 * Dh + SQR[.5 * S] / 4.0 / ga2)Ubs = 0.5

Rn from Sect. J4.3 Block Shear strength(LRFD) Axial load = PHI*Rn(ASD) Axial load = (Rn/OMEGA)


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Page 16(12) Gus block shear, double angle brace to gusset connection.:

Either double angle same side horizontal brace orStar angle vertical brace.Two columns -- One column per angle

Agv = 2t * ( S * ( Row - 1 ) + Le )Anv = 2t * ( S * ( Row - 1 ) + Le - dh * ( Row - .5 ) )Ant = (2 * g1 - Dh ) * t

Four columns -- staggeredAgv = 2t * ( S * ( Row - 1.5 ) + Le )Anv = 2t * ( S * ( Row - 1.5 ) + Le - dh * ( Row - 1.5 ) )Ant = ( g1 + g2 - 1.5 * Dh ) * 2 * t

Four columns -- nonstaggeredAgv = 2t * ( S * ( Row - 1 ) + Le )

Anv = 2t * ( S * ( Row - 1 ) + Le - dh * ( Row - .5 ) )Ant = ( g1 + g2 - 1.5 * Dh ) * 2 * tUbs = 1Rn from Sect. J4.3 Block Shear strengthFor perpendicular brace connections also check minimum of:'L' shaped failure pattern from Load Calc 11 andStraight line tension rupture

(LRFD) Axial load = PHI*Rn(ASD) Axial load = Rn/OMEGA

(13) Net brace tension, angle brace to gusset connection.:n = number of anglesS = longitudinal bolt spa.U = shear lag factor, from Table D3.1Wg = n*( Leg + Osl - Thickness )

Two columns -- Wn = Wg - 2 * Dh + n * S_gFour columns -- Wn = Wg - 4 * Dh + n * S_gAnt = Wn * tAe = Ant * U, effective net areaPn = Fu * Ae, Sect. D2, Tensile rupture

(LRFD) Axial tension = PHI * Pn(ASD) Axial tension = Pn/OMEGA


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Page 17(14) Intersection gusset tension, angle brace to

gusset connection:Non staggered bolt pattern

add = 0Staggered bolt pattern - Single Angle ordouble angle both sides of gusset

add = S_gStaggered bolt pattern - Double Angle same side orstar angle vertical braceTwo columns -- add = S_gFour columns -- add = 2 * S_g

Wn = (b - Column * Dh + add)Ae = t * MIN[ Wn, .85 * b]

Ag = b * tRn from Sect J4.1, elements in tension, minimumof yielding or rupture

(LRFD) Axial tension = PHI * Rn(ASD) Axial tension = Rn/OMEGA

(15) Connection gross shear:Two side gusset PL, End PL or two side clip L:

Ag = NS_depth * NS_thick + FS_depth * FS_thickRn from J4.2, shear yielding; .6Fy*Ag


(16) Connection net shear, bent pl, clip angle, splice pl:Wn = Cn_depth - Dh * Row, net width

Anv = 2 * Cn_thick * WnRn from J4.2, shear rupture; .6Fu*Anv(LRFD) Load = PHI * Rn(ASD) Load = Rn/OMEGA

(17) Conn. gross shear; single Pl conn., one side gussetor single clip angle:

Ag = Cn_depth * Cn_thickRn from J4.2, shear yielding; .6Fy * Ag


(18) OSL bending, one side clip angle:Rn_g = Fy * / Sx_gross Sect J4.1, gross flexure yieldRn_n = Fu * Sx_net Sect J4.1, net flexure rupture

(LRFD) Load = MIN[ PHI * Rn_g, PHI * R_n ] / La(ASD) Load = MIN[ Rn_g/OMEGA, R_n/OMEGA ] / La

(19) Bending, net section of gusset/shear plate:D = plate width, t = plate thickness, n = Row, b = SpacingSx_net = t*D^2/6-b^2*n(n^2-1)t(Dh)/6Deb = bolt eccentricity, unstiffened element Qs from sect E7

(LRFD) Load = PHI * Fu * Qs * Sx_net / eb(ASD) Load = (Fu/OMEGA) * Qs * Sx_net / eb


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Page 18(20) Bearing on connection, eccentricity considered:

Rn calculated from sect J3-10 for edge and interior boltsRn_ave = average strength of edge and interior bolts

(LRFD) Load = PHI*Rn_ave*C*Shear(ASD) Load = (Rn_ave/OMEGA)*C*Shear

(21) Connection net shear:k=1 for shear tab, shear tee & thru plk = 2 for end plate, dbl clip angle.Anv = Cn_thick*(Cn_depth-Dh*RowRn = k * .6 * Fu * Anv, shear rupture Sect J4.2

(LRFD) Load = PHI * Rn(ASD) Load = Rn / OMEGA

(22) Weld, shear plate to support eccentricity not considered:(For moment connection web plates to WF col webs, deducttwo .75 corner clips; Cn_depth = Pl depth - 1.5)Aw = 2 * .707 * Weld_size * Cn_depthRn = 2 * Fn * Aw, Sect J2.4


(23) Weld, two side clip angle to support:(Volume II page 2-37)La = Osl, L = Cn_depthFw = .6 * Fexx Table J2.5Rn = Fw * .707 * weld_size Spec J2.4(LRFD) Fr = PHI * Rn

(ASD) Fr = Rn / OMEGAK = (9*La/5/L/L)^2+(1/2/L)^2Load = SQRT[Fr^2/K]

(24) Fillet weld stress, shear end Pl to beam web:Fw = .6 * Fexx Table J2.5Rn = Fw * .707 * weld_size Spec J2.4(LRFD) Min_web = PHI*Rn*Side/(PHI*.6Fy_web), (J4-3)(ASD) Min_web = Rn/OMEGA*Side/(.6Fy_web/OMEGA), (J4-3)Web_factor = MIN[Tw/Min_web,1]Weld_len = Cn_depth-2*Weld_size(LRFD) Fr = PHI * Rn(ASD) Fr = Rn / OMEGA

Load = 2*Fr*Weld_len*Web_factor

(25) Column web crippling Sect. J10.3:lb = thick of flange or Pl connected to column

Load applied at a dist. >= d/2 from top of column,Rn =.8Tw^2[1+3(lb/d)*(Tw/Tf)^1.5]SQRT[E*Fy*Tf/TS] (J10-4)

Load applied at a dist. < d/2 from top of column,lb/d .2Rn =.40Tw^2[1+(4lb/d - .2)*(Tw/Tf)^1.5]SQRT[E*Fy*Tf/TS] (J10-5b)

(LRFD) Moment = PHI * Rn * .95 * D_beam(ASD) Moment = (Rn/OMEGA) * .95 * D_beam

For axial load reduce moment by: Ff * .95 * D_beamwhere Ff = the maximum flange force.


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Page 19(26) Clip angle to beam web weld, ecc. considered

[ shaped weld:Side = 1 or 2 (Connection on 1 or 2 sides of beam)La = Face of connection to C.G. weld groupkl = angle leg - clip_stbkFw = .6 * Fexx Table J2.5Rn = Fw * .707 * weld_size Spec J2.4(LRFD) Min_web = .PHI*Rn*Side/(PHI*.6Fy_web), (J4-3)(ASD) Min_web = Rn/OMEGA*Side/(.6Fy_web/OMEGA), (J4-3)Web_factor = MIN[Tw/Min_web,1]N = Weld_size*16

Load = C*N*Side*Web_factor*Cn_depth

(27) Allowable load for bolts with applied axial tension:For shear end plates and clip angles-- the bolt tension isincreased due to the effect of eccentricity from the bolt groupc.g. to the centerline of the beam, Vecc:

applied T / N + applied T * Vecc / bolt group sxwhere N = the number of bolts.(See J3.7, .8 & .9 for combined tension and shear)Rn = F'nt * Ab (J3-2)Rn = Mu*Du*hf*Tb*Ns slip critical (J3-4)

ksc from (J3-5a, 5b)(LRFD) Load = PHI * Rn * ( Row_ns + Row_fs ) * Column / 2(ASD) Load = (Rn/OMEGA) * ( Row_ns + Row_fs ) * Column / 2See connection design notes for 'heavy' clip angles.)

(28) Unstiffened seat angle, OSL bending:

For seats with 3.5


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Page 20(30) Plate or Tee seat weld:

(Reaction taken at .8 * the seat widthfrom the face of the column)La = .8*Cn_widthFw = .6 * Fexx Table J2.5Rn = Fw * .707 * eff_weld_size Spec J2.4(LRFD) Fr = PHI * Rn(ASD) Fr = Rn / OMEGAK = (1/2.4/Cn_depth)^2+(La/.6/Cn_depth^2)^2

Load = SQRT[Fr^2/K]

(31) W Column web strength, Pl or Tee seat:(Ellifritt & Sputo, AISC 'Engineering Journal)

fourth quarter 1999, page 160)k = yield line factorB = seat pl length, parallel to col webL = stiffener length, W = stiffener widthB' = MAX[ W/2, 2 5/8]e = B'/2 + .25, load eccentricityF_star = Fy + 2/3 * (Fu - Fy)m = Tw^2 * F_star / 4Pn = k * L * m / e

Load = .9 Pn

(32) Tee or Plate seat stiffener b/t ratio:Angle = ATN(Cn_width/Cn_depth)b/t = Cn_width*COS(Angle)/Cn_thickApb = Cn_width*Cn_thick

Rn = 1.8 * Fy * Apb Section J7(LRFD) Load = Qs*PHI*Rn(ASD) Load = Qs*Rn/OMEGA

(33) Stiffened angle seat-to-support weld;(Two vert. welds plus weld on heel of angle):

Ew = .8(Stiff width + L thick)b = horiz. weld lengthd = angle vert leg dimensionSx = (2bd + d^2) / 3, na to heel of angle.Fw = .6 * Fexx Table J2.5Rn = Fw * .707 * eff_weld_size Spec J2.4(LRFD) Fr = PHI * Rn(ASD) Fr = Rn / OMEGAA = b + d + d, total weld lengthK = (Ew/Sx)^2+(1/A)^2

Load = SQRT[Fr^2/K]


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Page 21(34) Stiffened seat angle, stiffener-to-angle weld:

pl_w = stiff width; pl_len = stiff lengthlw = pl_w - .5; lh = pl_len - .5, weld lengthsT = lw + lhx_bar = (lw * (.5 * lw + .5) ) / Ty_bar = (lw * pl_len + lh * .5 * lh) / Tix = lh^3/12 + lh(y_bar - .5*lh)^2 + lw(pl_len - y_bar)^2iy = lh * x_bar^2 + lw^3 /12. + lw(.5*lw + .5 - x_bar)^2ip = ix + iyEw = 2 * pl_w / 3 weld eccentricityFw = .6 * Fexx Table J2.5Rn = Fw * .707 * weld_size Spec J2.4(LRFD) Fr = PHI * Rn

(ASD) Fr = Rn / OMEGAR_unit = 1.0, unit load

point p1, bottom inside corner of stiffenerfv = R_unit / T + R_unit * (Ew - x_bar) * x_bar / ipfh = R_unit * (Ew - x_bar) * y_bar / ipfr1 = SQRT[ fv^2 + fh^2 ]

point p2, top outside corner of stiffenerfv = R_unit/T + R_unit*(Ew - x_bar) * (pl_w - x_bar)/ipfh = R_unit*(Ew - x_bar) * (pl_len - y_bar)/ipfr2 = SQRT[ fv^2 + fh^2 ]

Load = 2 * Fr / max( fr1, fr2)

(35) Stiffened seat angle, bearing on stiffener:Apb = t( b - corner_clip )Rn = 1.8 * Fy * Apb J7 Bearing strength


(36) Shear on support, shear connection:Conn. to a W or C web with a member opposite:

Ag = Cn_depth*T_supOther cases:

Ag = 2*Cn_depth*T_sup(For moment connections to WF col webs, deducttwo .75 corner clips, Cn_depth = Cn_depth - 1.5)

Rn = .6 * Fy * Ag Sect J4.2 shear yield(LRFD) Load = PHI * Rn(ASD) Load = Rn / OMEGA

(37) Not used

(38) Single Pl shear connection yield strength:No axial load and dim A 3.5 inches:Refer to misc design note 33;P = applied axial load, R = shear reactionsigma = P / Ag_web + R * ecc / Zxtau = R / Ag_webSee misc. design note 33

Load = maximum R to satisfy the yield criterion


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Page 22(39) Not used

(40) Clip angle connection with axial tension,bolt strength:(LRFD) B = PHI * Fnt * Ab(ASD) B = Ab * Fnt / OMEGATf = Cn_thickp = Cn_depth / Row d'= Db + 1/16 (Db + 2 mm)Delta = 1 - d' / p(LRFD) M = p * Tf^2 * PHI * Fu / 4(ASD) M = p * Tf^2 * Fu / (OMEGA * 4)T2 = (B * a' + M) / (a' + b')T3 = B

N = Row_ns + Row_fsVecc = vertical dim. from bolt group c.g. to the beam c/lHecc = horizontal dim. from bolt group c.g. to the beam c/lSx = section modulus of bolt group about x-axisSy = section modulus of bolt group about y-axisK = 1 / N + abs(Vecc) / Sx +/- Hecc / Sy(K should be determined for the top bolts on NS and FSif Vecc < 0 or the bottom bolts on NS and FS if Vecc > 0)

Tension = MIN[T2, T3] / maximum K(See connection design notes for 'heavy' clip angles.)

(41) Coped beam strength:('Coped beams' pages 9-6 thru 9-9)

Beam coped at top only, available buckling stress, fig 9-2:

ho = d - dctc


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Page 23(42) Stiffened beam web (transverse stiffener):

b = Stiff width, t = stiff thick, l = stiff lengthLeff = Effective beam web length

= 25*Tw, interior stiffeners= 12*Tw, near end of beam

Ag = 2b*t*Pair+Tw*Leff; (Gross effective area)K = Tw+2bOne pair: Ix = t*K^3/12 (in plane of web)

Iy = Tw*Leff^3/12 ( perp to web)Two pairs: Stif_spa=Spacing between stiff pairs

Ix = 2t*K^3/12Iy = Tw*Leff^3/12+2K*t(.5Stif_spa)^2

Rx = SQRT[Ix/Ag]; Ry = SQRT[Iy/Ag]

Kl/r = .75(l)/MIN[Rx,Ry]Pn = Fcr * Ag; Fcr from (E7-2, -3)Qs from (E7-4, -5, -6)

(LRFD) Load = PHI * Pn(ASD) Load = Pn/OMEGA

(43) Clip angle connection with axial tension,angle failure mode:Tf = Cn_thickp = Cn_depth / Row d'= Db + 1/16 (Db + 2 mm)Delta = 1 - d' / p(LRFD) M = p * Tf^2 * PHI * Fu / 4(ASD) M = p * Tf^2 * Fu / (OMEGA * 4)T = (1 + Delta) * M / b'N = Row_ns + Row_fs

Vecc = vertical dim. from bolt group c.g. to the beam c/lHecc = horizontal dim. from bolt group c.g. to the beam c/lSx = section modulus of bolt group about x-axisSy = section modulus of bolt group about y-axisK = 1 / N + abs(Vecc) / Sx +/- Hecc / Sy(K should be determined for the top bolts on NS and FSif Vecc < 0 or the bottom bolts on NS and FS if Vecc > 0)

Tension = T / maximum K(See connection design notes for 'heavy' clip angles.)

(44) Moment connection to col web, flange plate weld:Weld_f = Weld size to col flangeWeld_w = Weld size to col webFlg_l = .5(Bf_col-Tw_col)-Fil_rad-1/2; flg weld lengthWeb_l = D_col-2*Kdist_col; web weld lengthD_prime = D_beam - tf_beam for welded flg plD_prime = D_beam + Pl_thick for bolted flg plFw = .6 * Fexx Table J2.5Rn = Fw * .707 * eff_weld_size Spec J2.4(LRFD) Fr = PHI * Rn(ASD) Fr = Rn / OMEGAF_web = Fr_w * Web_l * 2F_web is reduced by 50 percent and may be limited by

web bending strength if there is no opposingif there is no opposing column stiffener.

F_flg = Fr_f * Flg_l * 4Moment = D_prime*(F_web + F_flg)

For axial load reduce moment by: Ff*D_primewhere Ff = the maximum flange force.


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Page 24(45) Not used

(46) Moment connection, flange PL tension & comp:Agt = Ag = b*t, Rn = Fy * Agt J4-1Ant = t*(b-2*Dh), Rn = Fu * Ant J4-1


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Page 25(51) Pl to Flange fillet weld, extended End-Plate:

(LRFD Vol II)Flg_perimeter = 2(Bf+Tf)-Tw

Fw = .6 * Fexx Table J2.5Fw = Fw * (1.0 + .5 Sin^1.5(Theta)) Formula (J2.5)

Theta = 90 degreesRn = Fw * .707 * Weld_size Spec J2.4(LRFD) Fr = PHI * Rn(ASD) Fr = Rn / OMEGAMoment = Fr*Flg_perimeter*(D-Tf)

For axial load reduce moment by: Ff*(D-Tf)where Ff = the maximum flange force.

(52) Pl to Web fillet weld shear strength, extended End-Plate:Fw = .6 * Fexx Table J2.5Rn = Fw * .707 * weld_size Spec J2.4(LRFD) Fr = PHI * Rn(ASD) Fr = Rn / OMEGA

Load = 2 * Fr * Eff_weld_len

(53) W Section col. butt plate, AISC CASE III:D = upper col depth D_l=Lower col depthBf = Upper col flg width, Bf_l=Lower col flg widthArea = Upper column areaP = Load from upper columnDelta = .5(T of lower col - D_u)

Delta >= t, check shear and bend stress

Delta < t, check shear stressPo = (P/Area)(D*Tw), direct brg.fv = .25(P-Po)/B*tA = D_l-2Tf_l, B = .5Bf_uQ = (Load-Po)/Bf*Dfb = Beta*Q*B^2/t^2('Formulas for Stress and Strain',

R.J.Roark 5th ed.Table 26; 7a)Load = largest value of P to satisfy:

Bending and shear yield ----(LRFD) fb


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Page 26(55) Beam web block shear strength, axially loaded, welded clip L conn:

(J4.3)Coped beam, tension yield:

Tension = (LRFD) PHI*Fy*Ag, Ag =Tw*Cn_depth= (ASD) Fy*Ag/OMEGA

Un-coped beam:Av = (Cn_width-Clip_stbk)*Tw*2At = Cn_depth*TwUbs = 1.Rn = Tension rupture + MIN( Shear yield, Shear rupture

(LRFD) Tension = PHI * Rn(ASD) Tension = Rn / OMEGA

(56) Beam web block shear strength, axially loaded, bolted clip L conn:(J4.3)

Sh = Horiz bolt spacingOne bolt column-

Anv = 2*Tw*(Lh-.5*Dh)Agv = 2*Tw*Lh

More than one bolt column-Anv = 2*Tw*[Lh-.5*Dh+(Column-1)*(Sh-Dh)]Agv = 2*Tw *(Column-1)Sh

Ant = (Spa-Dh)*(Row-1)*TwRn = Net rupture + MIN( Shear yield, Shear rupture)

(LRFD) Tension = PHI * Rn(ASD) Tension = Rn / OMEGA

(57) Tension stress on axially loaded clip angle connection:-the effect of vertical eccentricity is included-Vecc = vertical dim. from conn c/l to the beam c/lBolted to beam:

Area = ( Length_ns - Dh * Row_ns ) * Thick_ns+ ( Length_fs - Dh * Row_fs ) * Thick_fs

Sx = net section modulusWelded to beam:

Area = Length_ns * Thick_ns + Length_fs * Thick_fsSx = gross section modulus

V = applied shearBolted connection, tension and shear rupture J4:

(LRFD) Ft = PHI*Rn, Fv = PHI*Rn(ASD) Ft = PHI/OMEGA, Fv = PHI*Rn/OMEGA

Welded connection, tension and shear yield J4:(LRFD) Ft = PHI*Rn, Fv = PHI*Rn(ASD) Ft = Rn/OMEGA, Fv = PHI/OMEGA

Interaction equation: fv/Fv + ft/Ft


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Page 27(58) Combined weld stress, end plate, with axial load:

Elastic method.Lw = Cn_depth - 2 * Weld_size, (effective weld length)Extended end Pl: Lw = Beam T distanceFw = .6 * Fexx Table J2.5Rn = Fw * .707 * eff_weld_size Spec J2.4(LRFD) Fr = PHI * Rn(ASD) Fr = Rn / OMEGAFh = Applied axial tension / 2 / Lw

Load = 2 * Lw * SQRT[ Fr^2 - Fh^2 ]

(59) Beam flexural strength:Mn = Mp = Fy * Zx (F2-1)

(LRFD) Moment = PHI * Mp(ASD) Moment = Mp / OMEGAFor axial load reduce moment using interaction equationsfrom Chapter F

(60) Plate strength, end PL with axial tension load:(LRFD) M = p * Tf^2 * PHI * Fu / 4.(ASD) M = p * Tf^2 * Fu / (OMEGA * 4)Tf = Cn_thick p = Cn_depth/Row Delta = 1-d'/pd'= Db+1/16 T = (1+Delta)*M/b'b' = dim b - .5 * Db, a' = dim a + .5 * DbVecc = Dim from bolt group cg to beam centerlineVecc = 0.

Tension = 2 T * bolt rowsVecc > 0.

Tension = T/( 1/2*bolt rows + Vecc/bolt group Sx)

(61) Bolt strength, end PL with axial tension load:Tf = pl thickp = pl depth/Row d'= Db+1/16 (Db+2 mm)b' = dim b - .5 * Db, a' = dim a + .5 * Db(LRFD) B = PHI * Ft * Ab; M = p * Tf^2 * PHI * Fu / 4(ASD) B = Ab * Ft/ OMEGA; M = p * Tf^2 * Fu / (4 * OMEGA)Delta = 1-d'/pT2 = (B*a'+M)/(a'+ b') with prying actionT3 = B without prying actionVecc = Dim from bolt group cg to beam centerlineTension = MIN[T2,T3]/( 1/2*row + Vecc/bolt group Sx)

(62) Column bearing, AISC CASE II:Rn =1.8*Fy(Col_brg_Area+Fill_brg_area) Sect J7



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Page 28(63) Coped beam web reinforced with bolted doubler PLs:

(doubler plate stress)(LRFD) Fv = PHI * .6 * Fu, shear rupture

Fb = PHI*Fy, bending(ASD) Fv = .6Fu / OMEGA, shear rupture

Fb = Fy / OMEGA, bendingBm_load = unreinforced coped beam strength, see #(41)Tp = Doubler thicknessDp = Doubler depthSnet = Shear*Tp*Dp^2/6-Spa^2*Row*(Row^2-1)*Tp*Dh/6*DpAnet = Tp*(Dp-Row*Dh)*ShearShear_load = Fv*AnetCope length is measured from the face of the conn.

Moment_load = Qs*Fb*Snet/MAX[Clt+2.5,Clb+2.5]Load = MIN[Moment_load,Shear_load]+Bm_load

(64) Coped beam web reinforced with bolted doubler PLs:(doubler bolt shear)

Bm_load = Coped beam strength, see #(41)First bolt is 2 1/2 in. (64 mm) past cope.Cope length is measured from the face of the connection.La = MAX[Clt,Clb]+2.5+(Dblr_col-1)*Col_spa*.5

(LRFD) Load = PHI * Rnv * Shear * C + Bm_load(ASD) Load = ( Rnv/OMEGA) * Shear * C + Bm_load

(65) Coped beam web reinforced with bolted doubler PLs:(doubler bolt bearing)Bm_load = Coped beam strength, see #(41)

(First bolt is 2 1/2 in. (64 mm) past cope)Tp = Doubler thicknessCope length is measured from the face of the connection.La = MAX[Clt,Clb]+2.5+(Dblr_col-1)*Col_spa*.5Rn is calculated using J3-10

(LRFD) Load = PHI*Rn*C * MIN[Tp*Shear,Tw] + Bm_load(ASD) Load = (Rn/OMEGA) *C * MIN[Tp*Shear,Tw] + Bm_load

(66) Coped beam web reinforced with welded doubler PLs:(doubler plate stress)Bm_load = Coped beam strength, see #(41)Cope length is measured from the face of the conn.Tp = Doubler plate thicknessDp = Doubler plate depthSx = Cn_side*Tp*Dp^2/6Ag = Tp*Dp*Cn_sideShear yielding: (LRFD) PHI*.6Fy*Agv

(ASD) .6Fy/OMEGA * AgvFlexural yielding: (LRFD)= PHI*Fy*Sx/MAX[Clt,Clb]

(ASD)= (Fy/OMEGA) *Sx/MAX[Clt,Clb]Load = MIN[Shear yielding,Flexural yielding]+Bm_load

(67) Coped beam web reinforced with welded doubler PLs:(doubler to web weld stress, ']' shaped weld)

Bm_load = Coped beam strength, see #(41)Nws = INT[Weld_size/16], number off sixteenths in fillet weld sizeDp = Doubler plate depthC = weld coefficient, table 8-8

Load = C * Dp * Nws * Cn_side + Bm_load


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Page 29(68) Bolted moment connection, flange bolt shear:

(LRFD) Rv = PHI*Rn*Shear, Rn from J3-6(ASD) Rv = Rn/OMEGA *Shear

(Rn for bearing type bolts is reduced to 83.3 percent whenbolt pattern length > 38 in. Table J3.2)

Moment = Rv * 2 * Row * D(For axial load reduce moment by: Ff*Dwhere Ff = the maximum flange force)

(69) Bolted moment connection, bolt bearing on flg. conn Pl:Rn is calculated using J3.10)N_e = number of edge boltsN_i = number of interior bolts

(LRFD) Moment = PHI*(Rn_e*N_e + Rn_i*N_i) (D + Cn_thick)(ASD) Moment = (Rn_e*N_e + Rn_i*N_i)/OMEGA * (D + Cn_thick)( For axial load reduce moment by: Ff*(D + Cn_thick)

where Ff = the flange force)

(70) Extended end pl shear yielding:Bp = Eff pl width


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Page 30(73) Wf brace, bolt brg on brace:

Lc_edge = Le - .5DhLc_int = Spacing - DhN_e = number of edge boltsN_i = number of interior boltsRn_edge and Rn_int are calculated using formula (J3-6a)with the appropriate clear distance for Lc (Lc_edge orLc_int) and thickness for t (tf or tw).

(LRFD) F = PHI * Rn_edge * N_e + PHI * Rn_int * N_i(ASD) F = Rn_edge / OMEGA * N_e + Rn_int / OMEGA * N_iF_web = capacity of web connection

= F evaluated with a thickness of twF_flg = capacity of flange connections

= F evaluated with a thickness of tf

At = total cross-sectional areaAw = tw * (depth - 2 * tf)Af = bf * tfP_total,web = F_web * At / AwP_total,flg = F_flg * At / (2*Af)

Axial load = MIN[ P_total,web, P_total,flg ]

(74) Wf brace block shear:Web connection,

Rn from J4.3, '[' shaped failure pattern(LRFD) F_web = PHI * Rn(ASD) F_web = Rn/OMEGA

Flange connection,Rn from J4.3, 'L' shaped failure pattern(LRFD) F_flg = PHI * Rn(ASD) F_flg = Rn / OMEGA


Tension = MIN[ P_total,web, P_total,flg ]


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Page 31(75) Combined beam web stress, end PL with axial load:

Refer to misc design note 33;Ae_web = Tw*(Cn_depth-2*Weld_size), fillet weldsAe_web = Tw*(Cn_depth-Tw), CJP weldExtended end Pl: Ae_web = Tw * Bm T distanceT = applied tension, R = shear reactionsigma = T / Ae_webtau = R / Ae_web


(76) Moment, flange-angle connection,bolt failure mode:

a = Osl - Osl_ga b = Osl_ga - Cn_thick

Rn = Fnt * Ab(LRFD) B = PHI * Rn(ASD) B = Rn / OMEGAp = .5 conn lengthd = Db d'= Db + 1/16 (Db + 2 mm)Tf = Cn_thick b'= b - .5 * Da'= a + .5 * d Delta = 1 - d' / P(LRFD) M = p * Tf^2 * PHI * Fu / 4(ASD) M = p * Tf^2 * Fu / (OMEGA * 4)T2 = (B * a' + M) / (a' + b'); T3 = B

Moment = Row * 2 * MIN[T2, T3] * (D + 2 * Osl_ga)For axial load reduce moment by: Ff*(D + 2 * Osl_ga)where Ff = the maximum flange force.

(77) Moment flange angle conn., angle stress, tension

and compression:a = Osl - Osl_ga b = Osl_ga - Cn_thickp =.5 * Cn_lengthd = Db d'= Db + 1/16 (Db + 2 mm)f = Cn_thick b'= b - .5 * da' = a + .5 * d Delta = 1 - d' / pDm = bm depth + 2 * angle thickness(LRFD) M = p * Tf^2 * PHI * Fu / 4(ASD) M = p * Tf^2 * Fu / (OMEGA * 4)T1 = (1 + Delta) * M / b'OSL bending --(LRFD)

M1 = T1*2*DmAngle net tension rupture-- J4.1:

M2 = PHI*Ant*Fu* DmAngle gross tension yield -- J4.1:

M3 = PHI*Agt*Fy* DmAngle gross compression -- J4.1 & E3:

M4 = PHI*Ag*(Pu or Fcr)* Dm(ASD)

M1 = T1*2*DmAngle net tension rupture-- J4.1:

M2 = Ant*Fu/OMEGA * DmAngle gross tension yield -- J4.1:

M3 = Agt*Fy/OMEGA * DmAngle gross compression -- J4.1 & E3:

M4 = Ag*(Pu or Fcr)/OMEGA * DmMoment = MIN[M1, M2, M3, M4]

For axial load reduce moment by: Ff*Dmwhere Ff = the maximum flange force.

(78) & (79) Not used


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Page 32(80) Eight-bolt Stiffened extended End-Plate:

Bolt stress, Design guide 4 simplified approach, page 18.Only A325 or F1852 bolts allowedInteraction eqns apply to brg type boltsMoment = 6*Ab*Ft*(D-Tf)

For axial load reduce moment by: Ff*(D-Tf)where Ff = the maximum flange force.

(81) Eight-bolt Stiffened extended End-Plate:Plate strength, design guide 4 simplified approach, page 18.Only A325 or F1852 bolts allowedBp = eff. end pl width


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Page 33(86) Bearing on beam web, bolted clip angle conn. with axial load:

P_axial = Max. of applied tension or compression forcen = rows, m = columns, d = col spacing, b = vert spacingV = shearIp = bolt group polar moment of inertiamom = V * horiz ecc,

where horiz ecc = 0 for 1 column of bolts= la_x for 2 columns of bolts

f1 = V / ( m * n ), f2 = abs(mom) * .5 * d / Ipf3 = P_axial / ( m * n ), f4 = abs(mom) * (n - 1) * b * .5 / IpRv = SQRT[ (f1 + f2)^2 + (f3 + f4)^2 ]Rn is calculated using J3.10(LRFD) Load = maximum V so that Rv


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(LRFD) Load = maximum V so that Rv


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Page 34(90) Angle brace, net area tension:

S = longitudinal bolt spacingn = 1 for single angle brace, 2 for double angle braceWg = Leg+Osl-ThicknessWn = Wg-Dh, for one bolt columnWn = Wg-Column*Dh+S^2/4/g2, two bolt columnsAnt = Wn*tAe = Ant*U, J3.3Rn = Fu * Ae. tension rupture

(LRFD) Tension = PHI*Rn(ASD) Tension = Rn/OMEGA

(91) Brace gusset tension:

S = longitudinal bolt spacingWn = (b-Dh), for one bolt columnWn = (b-Column*Dh+S^2/4/g2), for two bolt columnsAnt = MIN[Wn, .85 * b] * tAgt = b*tRn_net = Fu * AntRn_gross = Fy * Agt

(LRFD) Tension = MIN[PHI*Rn_net, PHI*Rn_gross](ASD) Tension = MIN[Rn_net/OMEGA, Rn_gross/OMEGA]

(92) Angle brace block shear, (tension loaded brace):t = brace thickness, S = bolt spacingn = 1 for single angle, 2 for double angleAnv = ((S-Dh)*(Row-1)+Le-.5*Dh)*tAgv = (S*(Row-1)+Le)*t

One bolt column:Ant = (Leg-ga-.5*Dh)*tTwo bolt columns:

Ant = (Leg-g1 - 1.5 * Dh + S^2/4/g2)*tRn = Block shear from J4.3

(LRFD) Tension = PHI * Rn(ASD) Tension = Rn/OMEGA

(93) Angle brace gross area axial load:n = 1 for single L brace, 2 for dbl LAg = (Leg+Osl-t)*t*nRn = Fy * Ag

(LRFD) Tension or Compression = PHI*Rn(ASD) Tension or Compression = Rn/OMEGA

(94) Angle brace gusset block shear:Brace connected to one member:

L shaped failure patternRn = block shear strength, J4.3

Brace connected to two members with 2 columns of bolts:U shaped failure patternRn = block shear strength, J4.3

(LRFD) Axial load = PHI * Rn(ASD) Axial load = Rn/OMEGA

(95) Not used


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Page 35(96) Wf brace gusset plate block shear:

Under claw angles --Lhd = dim. between bolt cols in claw LsAnt = t * ( Lhd - dh )Anv = t * ( S * ( Row - 1 ) + edge_dist - ( Row - .5) * dh )Agv = t * S * ( Row - 1 ) + edge_distRn1 from J4.3

Under web splice --Ant = t * ( Col_spa - Dh )Anv = 2t * (S * ( Row - 1 ) + edge_dist - ( Row - .5) * Dh)Agv = 2t * (S * ( Row - 1 ) + edge_dist)K = ( Web_row + Flg_row )/ Web_row

Rn2 from J4.3 * K

Rn = MIN[Rn1, Rn2](LRFD) Tension = PHI * Rn(ASD) Tension = Rn /OMEGA

(97) Not used

(98) Beam web stress, axial & shear load:Refer to misc design note 33;Ag = depth * TwT = applied tension, R = shear reactionsigma = T / Agtau = R / Ag


(99) Horiz. brace interactive gusset stress:Refer to misc design note 33;theta = included angle between brace and supportT = applied brace tension, formula evaluated at each bmsigma = T * sin(theta) / Agtau = T * cos(theta) / Ag

Load = maximum T to satisfy the yield criterion

(100) Not used

(101) Angle brace intersection gusset compression:L = dim. from bolt to brace intersection pointSee misc note 36 for the effective length factor KAg = b * t

Pn = Fy * Ag J4.4(LRFD) Axial load = PHI * Pn(ASD) Axial load = Pn / OMEGA

For Kl/r > 25, chapter E provisions apply(LRFD) Axial load = PHI * Fcr(ASD) Axial load = Fcr / OMEGA


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Page 36(102) 'K' brace connection interactive gusset stress:

See design note #21.Pp = brace force component parallel to supportPn = brace force component normal to supportEo = ecc. from C/L gusset to normal componentAg = Thickness*LengthSx = Thickness*Length^2/6fv = SUM[Pp]/Agft = SUM[Pn]/Ag+SUM[Pn*Eo]/Sx(LRFD) Fv = PHI *.6 Fy, Ft = PHI * Fy; shear and tension yield(ASD) Fv = .6 Fy/OMEGA, Ft = Fy/OMEGA; shear and tension yield

Axial load = largest force to satisfy: fv/Fv+ft/Ft


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Page 37(107) Gusset plate weld, eccentrically loaded fillets:

(Elastic method)L = weld lengthP = brace axial loadEcc = eccentricity measured from C/L of weldtheta = angle between the weld axis and line of forceRn = Fw * .707 * Eff_weld / Richard_factor(LRFD) Fr = PHI * Rn * / Richard_factor(ASD) Fr = Rn/OMEGA / Richard_factor

(if the eccentricity < .5, Richard_factor = 1.25otherwise Richard_factor = 1.0)

Sx = 2 * L^2 / 6f1 = P * COS(theta) / 2 / L, parallel to weld axis

f2 = P * SIN(theta) / 2 / L, perp. to weld axisf3 = P * SIN(theta) * Ecc / Sx, perp. to weld axisAxial load = largest value of P to satisfy:

f1^2 + (f2 + f3)^2 = Yt * Fy * Afg

Mn = Fy * Zx

Fu * Afn < Yt * Fy * AfgMn = Fu * Afn * Sx / AfgYt = 1.0 for Fy/Fu

= .8 otherwise(LRFD) Moment = PHI * Mn(ASD) Moment = Mn / OMEGA

(110) Bearing strength at bolt holes, without eccentricity:N_e = number of edge boltsLc = Le - .5DhRn_e from section J3.10

N_i = number of interior boltsLc = Spacing - DhRn_i from section J3.10

(LRFD) Load = PHI(Rn_e * N_e + Rn_i * N_i) * Shear(ASD) Load = (Rn_e * N_e + Rn_i * N_i) / OMEGA * Shear

(111) 'One side' clip angle weld design, L shaped weld:C = weld group coefficient Table 8-10D = number of sixteenths of an inch in weld sizeMinimum support thickness:(LRFD) Min_t = .707* PHI*Fw * Weld_size /(PHI*.6*Fy)(ASD) Min_t = .707* Fw/OMEGA * Weld_size /(.6*Fy/OMEGA)Factor = Support thickness / Min_t


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Page 38(112) Shear tab weld strength:

C = coefficient from Table 8-4, k = 0Weld size = fillet leg for perp fillets

= eff weld throat / .707, for skew filletsD = number of sixteenths in weld sizeFillet weld ---

Load = C * Cn_depth * D

(113) Column moment strength, 4- or 8-tension-boltextended end plate moment connection:

(LRFD Vol II AISC Pages 10-36 to 10-39)Tw_c = Column web thicknessFy_c = Column yield strength

Tf_c = Column flange thicknessk = Column 'k' distanceDepth_b = Beam depthTf_b = Beam flange thicknessFy_b = Beam yield strengthPf = Distance from top of beam flange to 1st boltTp = End plate thicknessPb = Bolt spacing (8-bolt end plate only)

Col web yielding opposite bm comp flg ---Intermediate column locations,Rn = (6k + N + 2Tp) Fy Tw

Column-end locations,Rn1 = (3k + N + 2Tp) Fy Tw

Column web buckling ---Intermediate column locations,Rn = 4100 Tw^3 * SQRT[Fy] / Dc

Column-end locations,Rn2 = 4100 Tw^3 * SQRT[Fy] / (2 Dc)

Column flange bending at beam tension flg ---Four bolt, Alpha_m = 1.36(Pe/Db)^.25

Bs = 2.5 (2 * Pf + Tf_b)Eight bolt, Alpha_m = 1.13 *(Pe/Db)^.25

Bs = 2.5Pf + Tf_b + 3.5PbRn3 = Bs/(Alpha_m * Pe) Tf_c^2*Fy_c

(LRFD) Rn = PHI * MIN[Rn1, Rn2, Rn3](ASD) Rn = MIN[Rn1, Rn2, Rn3] / OMEGAMoment = Rn * (Depth_b - Tf_b)

For axial load reduce moment by: Ff * (Depth_b - Tf_b)where Ff = the maximum flange force.

(114) Not used

(115) Angle brace and gusset bearing strength:N_e = number of edge boltsLc = Le - .5DhRn_e from section J3.10

N_i = number of interior boltsLc = Spacing - DhRn_i from section J3.10

(LRFD) Load = PHI(Rn_e * N_e + Rn_i * N_i) * Shear

(ASD) Load = (Rn_e * N_e + Rn_i * N_i) / OMEGA * Shear


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Page 39(116)'L' Shaped weld connecting a gusset to a

column and a base or cap plate:(Elastic method)Wx = Horiz. weld length, Wy = vert. weld lengthLw = Wx + Wy, total weld lengththeta = Angle between brace and verticalC_h, C_v = Horiz. or vert. dist from the C.G. of weld group

to the point of weld being checkedEcc = Perp dist. from C.G. of weld group to line of forceIp = polar moment inertia of the weld groupFw = .6 * Fexx Table J2.5Rn = Fw * .707 * weld_size Spec J2.4(LRFD) Fr = PHI * 2 * Rn

(ASD) Fr = 2 * Rn / OMEGATop end of the vert weld:f1 = P(COS(theta)/Lw + ECc*C_h/Ip)f2 = P(SIN(theta)/Lw + Ecc*C_v/Ip)

P1 = largest P to satisfy f1^2 + f2^2


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Page 40(122) Tee or channel brace gross area axial stress:

Pn = Fy * Ag, sect D2(LRFD) Axial load = PHI * Pn(ASD) Axial load = Pn / OMEGA

(123) Tee or channel brace net section axial tension:Deduct = 2 * Tf * Dh (Tee)Deduct = Column * Tw * Dh (Channel)Ant = Agt - DeductAe = Ant * U; U from table D3.1

Pn = Fu * Ae Section D2(LRFD) Axial load = PHI * Pn(ASD) Axial load = Pn / OMEGA

(124) Connection plate tension strength:Pn_n = Fu * An, Pn_g = Fy * Ag, D2

Wg = bWn = b - (Column * Dh)


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Page 41(129) Skew fillet welds, end plate shear connection:

Fw = .6 * Fexx Table J2.5Rn = Fw * eff_throat Spec J2.4(LRFD) Fr = PHI * Rn(ASD) Fr = Rn / OMEGAMin_web = Fr * Eff_throat /( PHI*.6*Fy) LRFD shear yieldMin_web = Fr * Eff_throat /( .6*Fy/OMEGA) ASD shear yieldWeb_factor = MIN[Tw / Min_web,1]Weld_len = Cn_depth - 2 * Weld_size

Load = Fr * Weld_len * Web_factor

(130 thru 137) Not used

(138) Threaded round bar tension stress:Rn = Fnt * Ab, Fnt = .75*Fu, from table J3.2(LRFD) Axial load = PHI * Rn(ASD) Axial load = Rn/OMEGA

(139) Not used(140) Not used

(141) Turnbuckle strength:AISC Manual table 15-5

(142) Clevis strength:AISC Manual table 15-4

(143) Not used

(144) Brace gusset weld to beam flange:(brace gusset lap welded to a beam flange)theta = angle between brace and beamEcc = eccentricity from weld C.G. to line of brace forceFw = .6 * Fexx Table J2.5Rn = Fw * .707 * weld_size Spec J2.4Fv = (LRFD) PHI * .6Fy, (ASD) .6Fy/OMEGA, shear yield,J4.2Min_t = Fw * .707 * Weld_size /FvPl_factor = MIN[ t / Min_t, 1 ](LRFD) Fr = PHI * Rn * Pl_factor(ASD) Fr = (Rn / OMEGA) * Pl_factor

Ecc = 0:Axial load = 2. * Fr * Weld_len

Ecc > 0:Ix = Weld_len * SQR[.5 * Weld_spa] * 2.Iy = Weld_len^3 / 6.Ip = Ix + Iyk = COS(theta) / 2. / Weld_len + Ecc * .5 * weld_spa / Ipm = Ecc * .5 * Weld_len / Ip + SIN(theta) / 2. / Weld_len

Axial load = Fr / SQRT[ SQR[k] + SQR[m] ]

(145) Not used

(146) Weld stress - two parallel fillet welds,load not in plane of weld group:C = coefficient from Table 8-5, angle = 0, k = 0;D = number of sixteenths in weld size

Load = C * Cn_depth * D


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Page 42(147) Vert Brace gusset to beam weld strength:

(See connection design notes for interface forces)Elastic methods_weld = SQR[ weld_length] / 3(LRFD) Fr = .707 * PHI * Fw * Weld_size(ASD) Fr = .707 * Fw/OMEGA * Weld_sizeFr = Fr / 1.25, 'Richard factor' page 7-122min_pl = Fr * 2 * weld size / Fv, (Fv = pl shear yield J4.2)when t < min_pl, Fr = Fr * t / min_plf1 = Hb / ( 2 * weld_length )f2 = Vb / ( 2 * weld_length ) + Mb / s_weldfr = SQRT[ f1^2 + f2^2 ]

Axial load = Maximum value of P to satisfy fr


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Page 43(152) VB Gusset clip L OSL stress, with prying:

(See connection design notes for interface forces)a = osl - osl_ga, b = osl_ga - Tfp = Cn_depth / Row, d' = Db + 1/8 inmax a = 1.25 * bb' = b - .5 * Dba' = a + .5 * Dbdelta = 1 - d' / p(LRFD) M = p * Tf^2 * PHI * Fu / 4(ASD) M = p * Tf^2 * Fu / (OMEGA * 4)t = (1 + delta) * m / b'

Axial load = Max value of P to satisfy Hc


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Page 44(157) VB Gusset clip L OSL bolt bearing:

(See connection design notes for interface forces)LRFD:

P_allow_top = PHI*Rn*ColumnP_allow_lower = PHI*Rn*(Row - 1)Column

ASD:P_allow_top = Rn/OMEGA * ColumnP_allow_lower = Rn/OMEGA * (Row - 1)Column

Rn is calculated using J4-10Pallow = P_allow_top + P_allow_lower

Axial load = Max value of P so that Vc


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Page 45(161) Wf brace, bolt bearing strength at gusset:

Lc_e = Le - .5DhLc_i = Spacing - DhN_e = number of edge boltsN_i = number of interior boltsRn_edge and Rn_int are calculated using formula (J3-6a)with the appropriate clear distance for Lc (Lc_edge orLc_int) and t equals the gusset thickness.

(LRFD) F = PHI * ( Rn_e * N_e + Rn_i * N_i )(ASD) F = ( Rn_e * N_e + Rn_i * N_i ) / OMEGAF_web = capacity of web connection

= F evaluated using the edge distance of the web boltsF_flg = capacity of flange connections

= F evaluated using the edge distance of the flange bolts


Axial load = MIN[ P_total,web, P_total,flg ]

(162) Wf brace, tension on net brace area:Flange connection: Flg_deduct = Dh * Tf * 4Web connection: Web_deduct = Dh * Tw * 2U from Table D3.1An = Ag - Flg_deduct - Web_deduct

(LRFD) Tension = PHI * U * An * Fu

(ASD) Tension = U * An * Fu / OMEGA

(163) Intersecting gusset gross area:(WF brace, web horiz. both flgs bolted to gusset)

Ag = 2 * Width * ThickTension yield Ru = Fy * Ag, J4.1(LRFD) Axial tension = PHI * Ru(ASD) Axial tension = Ru/OMEGA

(164) Wf brace, tension on net conn. area:(Web Channel, no flange connection)An = Ag_c - ( Dh * Tw_c * Web_col )Ae = U * An * 2Pn = Fu * Ae tension rupture (D2-2)

(LRFD) Tension = PHI * Pn(ASD) Tension = Pn / OMEGA


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Page 46(165)'L' Shaped weld, brace gusset to a

column and base (or cap) Pl:(Uniform force method, with bothinterfaces equally stiff, Vol II pg 7-109)Brace W.P. at bottom of base plate.v = weld length to col, h = weld length to Pltheta = angle between brace and colec = ecc. at col, eb = ecc. at base PlAlpha_bar = .5 * h, Beta_bar = .5 * vK = eb * TAN(theta) - ecK_prime = Alpha_bar * ( TAN(theta) + Alpha_bar / beta_bar )D = SQR[TAN(theta)] + SQR[Alpha_bar / Beta_bar ]term1 = SQR[ Alpha_bar / Beta_bar ]

Alpha = ( K_prime * TAN(theta) + K * term1 ) / DBeta = ( K_prime - K * TAN(theta) ) / Ddelta_alpha = Alpha_bar - Alphadelta_beta = beta_bar - Betar = SQRT[ ( Alpha + ec )^2 + ( Beta + eb )^2]Hb = Alpha*P/r, Vb = eb*P/r, Mb = Vb*delta_alphaVc = Beta*P/r, Hc = ec*P/r, Mc = Hc*delta_betatop end of vert weld:

f1 = Vc / vf2 = Hc / v + Mc / Sx_v

toe end of horiz weld:f1 = Vb / h + Mb / Sx_hf2 = Hb / h

fr = SQRT[ f1^2 + f2^2 ]

(LRFD) Fr = PHI*.707 * Fw * weld size(ASD) Fr = .707 * Fw/OMEGA * weld sizeAxial load = largest value of P so that fr


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Page 47(168) Bolt shear strength at beam connections, horizontal:

brace gusset connected to two beams:See formula (3) for Rv

Gusset PL to beam flange bolts --p1 = Rv * Row1, at beam 1p1 = Rv * Row2, at beam 2

Gusset PL to clip angle bolts --eccentricity = dist from bolt line to face of bm web

p1 = Rv * C at beam 1p2 = Rv * C at beam 2

theta = plane angle between the brace and beam 2Axial load = MIN[ p2/cos(theta), p1/sin(theta)

(169) Interactive beam web strength, clip L with applied tension load:Coped top and bottom, N = 0Coped top or bottom, N = 1Un-coped, N = 2

Vertical load capacity:If welded: Agt = Ant = N * tw * conn_width

Agv = Anv = tw * conn_depthUbs = 1.0

If bolted: Agt = N * tw * (end_dist + col_spa * (column - 1))Ant = Agt - N * tw * (column - 0.5) * DhAgv = tw * (row - 1) * spacing

Anv = tw * (row - 1) * (spacing - Dh)Ubs = 0.5 if column > 1= 1.0 if column = 1

Calculate Rbs_v using (J4-5)

Horizontal load capacity:If welded: Agt = Ant = tw * conn_depth

Agv = Anv = N * tw * conn_widthUbs = 1.0

If bolted: Agt = tw * (row - 1) * spacingAnt = tw * (row - 1) * (spacing - Dh)Agv = N * tw * (end_dist + col_spa * (column - 1))Anv = Agt - N * tw * (column - 0.5) * DhUbs = 1.0

Calculate Rbs_h using (J4-5)

Elliptical interaction: (V/Rbs_v)^2 + (T/Rbs_h)^2


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Page 48(172) Tension loaded end pl or clip L OSL -- gross shear:

(LRFD) Fv_allow = PHI*Rn, Rn = shear yielding from J4.2(ASD) Fv_allow = Rn/OMEGAFv_allow^2 = fv_shear^2 + fv_tension^2 )Ag = Conn_depth * t * 2K = SQR[ Fv ] - SQR[ ten_load / Ag ]

Load = SQRT[ K ] * Ag

(173) Tension loaded end pl or clip L OSL -- net shear:(LRFD) Fv_allow = PHI*Rn, Rn = shear rupture from J4.2(ASD) Fv_allow = Rn/OMEGAFv_allow^2 = fv_shear^2 + fv_tension^2 )An = (Conn_depth - Row * Dh) * t * 2

K = SQR[ Fv ] - SQR[ ten_load / An ]Load = SQRT[ K ] * An

(174) Col. web local bending stress (axially loaded end pl or clip L):(Tw, Depth & K_dist are column dimensions)Moment at point of loads and ends, Table 3-23, case 16

c = Distance between the top & bot boltsl = c + 12 * Tw; effective web lengthFor a 1 inch wide strip of web, with fixed ends:

Zx = SQR[Tw] / 4L = Depth - 2*K_dist, a = .5(L - Gage)Mp from section F2, Flexure(LRFD) P = PHI*Mp * /Zx * L / a(L-a)(ASD) P = Mp/OMEGA * /Zx * L / a(L-a)

Axial load = 2 * P * l

(175) Col/Bm web local bending stress, single brace gussetwelded to web with no member framing opposite:

Design of Welded Structures - Blodgett, pg 6.6-7d = gusset_length, e = 12tw, Zx = SQR[Tw]/4.L = depth - 2 * k_distMp from section F2, Flexure(LRFD) K = 8*Mp/OMEGA * Zx (d+e)/[L(1 + 6Ecc/(d+2e)](ASD) K = 8*PHI*Mp * Zx (d+e)/[L(1 + 6Ecc/(d+2e)]theta = angle between brace and member

Axial load = K / SIN[theta]

(176) Supporting bm web local stress (axially loaded end pl or clip L:a = bottom conn hole to toe of filletb = dist between top & bot conn holesc = top conn hole to toe of fillerL = a + b + cl = conn gage + 12 * tw, effective web widthM = moment on a 1 in. wide strip of web, length Lfixed ends, with a uniform load located over bw = load, kips per inch, on length bZx = l * Tw^2 / 6Mp = Fy*Zx Section F2, flexure(LRFD) w = largest load to satisfy M/Zx


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Page 49(178) HSS brace to gusset weld:

(Brace notched to fit over gusset)AISC Manual J2.4Ww = fillet weld size, We = Ww - 1/16Aw =4(.707) We * LwRn = Fw*Aw, Fw = .6 * Fexx

t1 = 1.06 * Fexx*Ww / Fy_plate, HSS Manual pg 6-28when gusset pl thick < t1: Rn = Rn *t/t1

(LRFD) Axial load = PHI * Rn(ASD) Axial load = Rn / OMEGA

(179) HSS brace net area tension:An = Ag - 2Tw * (Guss_thick + 1/8)

Ae = An * UU = 1 - x_bar / LRound HSS, x_bar = D / PIRect. HSS, x_bar = (B^2 + 2BH)/4(B+H)where: H = tube dim parallel to gusset

B = tube dim perp to gussetPn = Fu * Ae, D3

(LRFD) Axial load = PHI * Pn(ASD) Axial load = Pn/OMEGA

(180) HSS brace gross area:Pn = Fy * Ag, D2

(LRFD) Axial load = PHI * Pn(ASD) Axial load = Pn/OMEGA

(181) HSS brace gusset block shear (brace welded to gusset):Agv = 2. * weld length * tAgt = brace width * tRn = block shear strength, J4.3

(LRFD) Axial load = PHI * Rn(ASD) Axial load = Rn/OMEA

(182) HSS brace tearout (brace welded to gusset):Ag = 4 * weld_len * TwShear yield Rn = .6 * Fy * Ag, J4.2


(183) Perp. to bm. horiz. L brace gusset block shear:One column:

L shaped failure patternRn = block shear strength, J4.3

Two columns:Minimum of L shaped and [ shaped failure patternRn = block shear strength, J4.3



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Page 50(184) Perp. to bm. horiz. Tee brace gusset block shear:

Minimum of Straight line net areaL shaped failure pattern[ shaped failure pattern

Rn = block shear strength, J4.3(LRFD) Axial load = PHI * Rn(ASD) Axial load = Rn/OMEGA

(185) Beam web local bending stress, single brace gusset:welded to web with no member framing opposite:

d = gusset_length, e = 12 * tw, Zx = SQR[tw]/4a = dim from edge of web to c/l of gussetb = dim c/l of gusset to opposite edge of web

l = a + b, beam 'T' dimensiontheta = angle between brace and beamK = 1/(d + e) * (1 + 6*ecc/( d + 2*e))(LRFD) Fb = PHI * Fy * Zx, F2(LRFD) Fb = Fy * Zx / OMEGA, F2Moment at point of loads and ends, Table 3-23, case 16

p1 = l^3 * Fb * Zx / ( 2. * sqr(a) * sqr(b)) / Kp2 = l^2 * Fb * Zx / (a * b^2) / Kp3 = l^2 * Fb * Zx / (b * a^2) / K

Axial load = MIN[p1,p2,p2]/SIN[theta]

(186) Clip L to gusset weld stress:(See connection design notes for UFM interface forces)ecc = dist from heel of angle to bolt line

f_pa = force parallel to angle's longitudinal axisf_pr = force perpendicular to angle's longitudinal axislen = weld length, b = clip length, d = clip leg - setbackIp = polar moment of inertia of the weld

= 2 * [ len^3 / 12 - d^2 * (b + d)^2 / len ]ybar = d^2 / lenecc = clip leg - ybarBrace connecting to a col & beam:

At beam: f_pa = Hb, f_pr = Vb, Mom = MbAt column: f_pa = Vc, f_pr = Hc, Mom = Mc

total_m = Mom + f_pa*eccf1 = f_pa / (2 * len) + total_m * (d - ybar) / Ipf2 = f_pr / (2 * len) + total_m * (.5 * b) / IpRv = SQRT( f1^2 + f2^2 )Rn of effective weld from Table J2.5

(LRFD) Axial load = maximum P to satisfy Rv


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Page 51(188) Clip L to gusset bolt bearing:

(See connection design notes for UFM interface forces)ecc = dist from heel of angle to bolt linef_pa = force parallel to angle's longitudinal axisf_pr = force perpendicular to angle's longitudinal axisnb = number of boltsIp = polar moment of inertia of bolt groupBrace connecting to a col & beam:

At beam: f_pa = Hb, f_pr = Vb, Mom = MbAt column: f_pa = Vc, f_pr = Hc, Mom = Mc

total_m = Mom + f_pa*eccf1 = f_pa/nb + total_m * (column - 1)*col_spa * .5/Ipf2 = f_pr/nb + total_m * (row - 1)*spacing * .5/ Ip

Rv = SQRT( f1^2 + f2^2 )Rn from Spec J3.10)(LRFD) Axial load = maximum P to satisfy Rv


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Page 52(190) Clip L to support bolt shear and tension:

(If there are 4 columns of bolts, only the 2 inside columnsare effective for tension.)

(See connection design notes for UFM interface forces)Q = prying forceAb = bolt cross-sectional areaf_pa = force parallel to angle's longitudinal axisf_pr = force perpendicular to angle's longitudinal axisIx = moment of inertia of the inside bolt columns

= (Row * Spa^2 * (Row^2 - 1) / 12) * 2Sx = 2 * Ix / (Spa * (Row - 1))Brace connecting to a col & beam:

At beam: f_pa = Hb, f_pr = Vb, Mom = Mb

At column: f_pa = Vc, f_pr = Hc, Mom = Mcft = applied tensile stress= (f_pr / Row / 2 + Q) / Ab + Mom / Sx / Ab

fv = applied shear stress= f_pa / (Row * Column * Ab)

Calculate the allowable tensile stress, F'nt, given fv andthe allowable shear stress, F'nv, given ft using formula(J3-3a) for LRFD or (J3-3b) for ASD.Axial load = maximum P to satisfy ft


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Page 53(193) Wf brace net or gross area stress:

(Both flanges bolted to gusset)Ag = Bf * Tf * 2 + (Depth - 2 Tf)*TwAn = Ag - Tf * Dh * 2 * ColumnRn = Fu * U * An, tension rupture J4.1


(194) Wf brace net brace block shear:(Both flanges bolted to gusset)Ant = 2Tf * (Bf - Gage - 2 * Sec_gage - Dh )Anv = 4*Tf*(S(Row - 1) + End_edge - Dh(Row - .5))Agv = 4*Tf*(S(Row-1) + End_edge)

Rn = block shear strength, J4.3(LRFD) Axial load = PHI * Rn(ASD) Axial load = Rn / OMEGA

(195) Guss plate block shear:(WF brace, both flanges bolted to gusset)

Ant = (Gage + 2 * Sec_gage) - Dh * (Column -1)Ant = t * Ant * 2Anv = S * (Row - 1) + End_edge - Dh * (Row - .5)Anv = Anv * t * 4Agv = t * 4 *(Spacing*(Row-1) + End_edge)Rn = block shear strength, J4.3


(196) Intersecting gusset net area:(WF brace, web horiz. both flgs bolted to gusset)Ag = 2 * Width * ThickAn = 2(Width - Column * Dh) * Thick


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Page 54(199) Gusset to clip L weld stress:

(WF brace, both flgs bolted to gusset)theta = angle between brace and memberTl = 2. * angle_lengthFw = .6 * Fexx Table J2.5Rn = Fw * .707 * Weld_size Spec J2.4(LRFD) Fr = PHI * Rn(ASD) Fr = Rn / OMEGAk = SQR[ COS[theta] / Tl] + SQR[SIN[theta] / Tl]p = SQRT[ SQR[Fr] / k ]

Axial load = 2 p

(200) WF brace, web horiz, weld stress, angle

connection to supporting member:theta = angle between brace and supportFw = .6 * Fexx Table J2.5Rn = Fw * .707 * Weld_size Spec J2.4(LRFD) Fr = PHI * Rn(ASD) Fr = Rn / OMEGAL = weld length, Sx = 2 * L^2 / 6K = ecc * SIN(theta) / Sx + SIN(theta) / 2L

Axial load = 2SQRT[Fr^2 /(COS(Theta)/2L)^2 + K^2]

(201) Shear tee shop bolts, with eccentricity:J3.7 & J3.9 interaction formulas applyApplied tension = P * Ecc / Sx of bolt groupEcc = Dist. from flg of tee to C.G. of bolt group in stemft = (Applied tension + Q) / Ab

fv = P / (Row*Column*Ab)(LRFD) Fv = PHI*Rn; Rn from J3.6 or J3.8(ASD) Fv = Rn/OMEGA; Rn from J3.6 or J3.8

Load = max value of P for ft


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Page 55(204) Bolt shear, shr tab with axial load:

Nb = number of bolts, row * columnc = .5 * Spacing * (Row - 1)P = vertical reactionr1 = Axial load / Nb + P * eb * c / Ip bolt groupr2 = P / Nb + P * eb * .5 * col_spa / Ip bolt group(LRFD) Rv_allow = PHI*Rn; Rn from J3.6, J3.8(ASD) Rv_allow = Rn/OMEGA; Rn from J3.6, J3.8

Load = largest P to satisfy:SQRT[ SQR[r1] + SQR[r2] ]


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Page 56(208) W Column splice, flange Pl net/gross area:

net_w = Pl_w - 2 * dh


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Page 58(217) HSS brace gusset gross area ten. stress:

delta = Weld_len * TAN(30)Ws = H + 2*deltaH = HSS dim parallel to the gussetAg = t * WsRn = Fy*Ag, tension yhield, J4.1


(218) HSS brace intersection gusset gross area compr. stress:delta = Weld_len * TAN(30)Ws = H + 2*delta


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Page 59(226) Wide flange vert. brace web channel block shear:

Ant = (Col_spa - Dh) * Tw * 2Anv = 4*Tw(Spa * (Row-1) + Le - (Row - .5) * Dh )Agv = 4*Tw(Spa * (Row-1) + Le )Rn = block shear strength, J4.3


(227) HSS brace, welded Pl Tee ftg., tee stem to cap Pl weld:Fw = .6Fexx*(1 + .5 SIN(90)^1.5)Eff throat = PHI * Fy * t / (2 * Fw)


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Page 60(233) VB Gusset - column flange stress, with prying:

(See connection design notes for interface forces)a = .5*(Col flg ga - tw), b = clip gage - clip thickp = Cn_depth / Row, d' = Db + 1/8 inmax a = 1.25 * bb' = b - .5 * Dba' = a + .5 * Dbdelta = 1 - d' / p(LRFD) m = p * Tf^2 * PHI * Fu / 4., section F flexure(ASD) m = p * Tf^2 * Fu / (OMEGA * 4)t = (1 + delta) * m / b'

Axial load = Max value of P to satisfy Hc


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Page 61(237) Beam splice with axial load, web plate net area stress:

Shear, axial interaction: fv/Fv + fa/Fa Tw_col, Ru = Ru * Tw_col/t1

Load = Ru( H + Ew ) / H

(239) HSS wall compression yielding under cap pl:(AISC specification formula (K1-14) )

If (5 * tp + lb) >= BRn = A * Fy

If (5 * tp + lb) < BRn = (5 * tp + lb) * Fy * t

lb = 2*k dist, for unstiffened W beams= 2*stiff width + tw, for stiffened W beams= 2 in., for joists

t = HSS wall thickness, tp = cap pl thickB = HSS dimension perp to beam


(240) HSS wall compression crippling under cap pl:(AISC specification formula (K1-15) )

Rn = .8 * t^2 (1 + 3(lb/.5B)(t/tp)^1.5 )sqrt(E*Fy (tp/t))t = HSS wall thickness, tp = cap pl thicknesslb = 2*k dist, for unstiffened W beams

= 2*stiff width + tw, for stiffened W beams= 2 in., for joists

B = HSS dimension perp to beamFy = yield strength of HSSE = modulus of elasticity of the HSS

(LRFD) Load = PHI * Rn, J10(ASD) Load = PHI * Rn, J10

(241) HSS cap PL flexural strength, compressive reaction:(AISC Manual page 14-18)

Rn = (B * t1^2 / 4(Nr/2 + a - H/2))Fy_plt1 = cap pl thicknessNr = bearing length of attached membera = dist from HSS centroid to end of beamB = HSS dimension perp to beamH = HSS dimension parallel to beam



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Page 62(242) W brace, web horiz, support flg local bending stress:

theta = acute angle between brace and support memberEcc = .5 * Brace depth - support mbr k1 dist.Eff flg length = guss length + 2Ecc*Tan(30)Zx = Eff flange length * Tf^2 / 4

(LRFD) Axial load = PHI*Mn * 2. / (Ecc * SIN(theta) ), F11/1(ASD) Axial load = Mn/OMEGA * 2. / (Ecc * SIN(theta) ), F11/1

(243) W brace, web horiz, to bm & col, beam flg local bending:(See connection design notes for interface forces)Ecc = .5 * Brace depth - bm k1 dist.Eff flg length = guss length + Ecc*Tan(30)Zx = Eff flg length * Tf_bm^2 / 4

Axial load = Max P so that(LRFD) .5 * Vb * Ecc


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Page 63(250) W brace, web horz, to bm & col, col/bm flg bending:

(See connection design notes for interface forces)T_allow from flange failure mode including pryingAISC manual page 9-10,analysis for prying action.N = number of bolts in connection

Column flange --T_applied = Hc / N + tension from moment

Beam flange --T_applied = Vb / N + tension from moment

Axial load = Max P so that T_applied


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Page 64(256) HSS column wall yield line, at stiffened

plate or tee seat:L = stiff. depth, W = Stiff. widthB = HSS widthPHI = .9, e = .8 * WOMEGA = 1.67, e = .8 * Wf = 1/(B - .2L), g = (1 + .661B/L)h = SQRT[ (B-.4L)(7B + .4L)]m = B(B -.4L)/(4L), n = 2L + 2.56Bk = f( gh + m + n )Rn = k * t^2 * Fy_col * L / (4e)


(257) & (258) Not used

(259) Beam bolted moment conn., flange block shear:Ga = Flg. gage; N = number of bolt rowsS = Bolt spacing; Ed = flg end edge dist.L shaped failure pattern,

Agv = 2*Tf((Row-1) * S + Ed)Anv = 2*Tf((Row-1) * S + Ed - Dh(Row-.5))Ant = Bf - (Ga - Dh )

Block shear J4.3Rn from formula (J4-5)(LRFD) Rbs = PHI*Rn(ASD) Rbs = Rn/OMEGA

Moment = Rbs*(Depth - Tf)For axial load reduce moment by: Ff*(Depth-Tf)where Ff = the maximum flange force.

(260) Col/Bm local web crippling under vert. brace gusset:N = gusset length, ecc = eccentricity from gusset c/ltheta = angle between the brace and supportA_web = N * TwSx_web = Tw * N * N / 6

Load applied at a distance >= d/2 from top of column,Rn = 135 * Tw^2 * [ 1 + 3 * (N/d) * (Tw/Tf)^1.5 ] * SQRT[ Fy * Tf / Tw ]

Load applied at a dist. < d/2 from top of column,N/d .2Rn = 68 * Tw^2 * [ 1 + ( 4 * N/d - .2 ) * (Tw/Tf)^1.5 ] * SQRT[ Fy * Tf / T

K = 1 / A_web + ecc / Sx_webRn' = ( Rn / A_web / K )

(LRFD) Axial load = PHI * Rn' / sin(theta)(ASD) Axial load = Rn' / sin(theta) / OMEGA


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Page 65(261) Beam local web crippling under vert. brace gusset:

(Brace gusset connecting to a col and beam.)Refer to misc connection design notes for interface forces.N = gusset lengthA_web = Tw * N, Sx_web = Tw * N * N / 6For N/d .2

Rn = 68 * Tw^2 * [ 1 + ( 4 * N/D - .2 ) * (Tw/Tf)^1.5 ] * SQRT[ Fy * Tf / Tw ](LRFD) Fp = PHI * Rn / A_web(ASD) Fp = Rn / A_web / OMEGAfp = Vb / A_web + Mb / Zx_webAxial load = maximum P to satisfy fp


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Page 66(264) Concentrated transverse force on an HSS face:

b1 = width of the loaded platet1 or N = thickness of the loaded platet = HSS design wall thicknessB = overall HSS widthk = HSS outside corner radiush = flat side of HSS wall, B - 2k

Round HSSD = HSS diameterRn = Qf * 5.5 * Fy * t^2 / ( 1 - .81 * b1 / D )

(LRFD) F1 = PHI * Rn; PHI = .9(ASD) F1 = Rn / OMEGA; OMEGA = 1.67

Rectangular HSSRn = 10 * Fy * t * b1 / ( B / t )

(LRFD) F1 = PHI * Rn; PHI = .95(ASD) F1 = Rn / Omega; OMEGA = 1.58

When b1 >= B - 2 * corner_radiusWeb yielding

Rn = 2 * Fy * t * ( 5 * k + lb ), or= 2 * Fy * t * ( 2.5 * k + lb ); at end of HSS

(LRFD) F2 = PHI * Rn; PHI = 1(ASD) F2 = Rn / OMEGA; OMEGA = 1.5

Web cripplingRn = 1.6 * t^2 * [ 1 + 3 * lb / h ] * SQRT[ E * Fy ]


When .85 * B < b1 < B - 2t:bep = 10 * b1 / ( B / t )


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Page 67(265) Concentrated longitudinal force on an HSS face:

tp = loaded plate thicknesslb = length of the loaded platet = HSS design wall thicknessB = overall HSS widthD = round HSS outside diameter

Round HSSRn = Qf * 5.5 * Fy * t^2 / ( 1 + .25 * lb / D )


Rectangular HSS

term1 = Fy * t^2 / ( 1 - tp / B )term2 = 2 * lb / B + 4 * SQRT[ 1 - tp / B ]Rn = term1 * term2 * Qf

(LRFD) F1 = PHI * Rn; PHI = 1(ASD) F1 = Rn / OMEGA; OMEGA = 1.5

Shear strength:Aw = 2 * lb * tRn = .6 * Fy * Aw


Load = MIN[ F1, F2 ]

(266) Plate pull-through along bolt line:

For each line of bolts:N = number of boltsAg = 2 * T * (end dist + (N-1) * spacingAn = Ag - 2( N- .5) * DhRn = block shear strength, J4.3

(LRFD) Axial load = PHI * Rn * number of bolt columns(ASD) Axial load = Rn/OMEGA * number of bolt columns

(267) Claw angle net/gross area:(W brace, web horiz, web claw L conn)Gross width = Leg + Osl - tAg = Gross width * tAn = (Gross width - Dh) * t(LRFD)

Rn_g = PHI * Rn, tension yleld J4Rn_n = PHI * Rn, tension rupture J4

(ASD)Rn_g = Rn/OMEGA, tension yleld J4Rn_n = Rn/OMEGA, tension rupture J4

Axial load = 4 * MIN[Rn_g, Rn_n]

(268) Claw angle block shear:(W brace, web horiz, web claw L conn)

Ant = (angle_toe_edge - .5Dh) * tAnv = t* S * (Row - 1 ) + Le - (Row - .5) * dhAgv = t * S * (Row - 1 ) + LeRn = block shear strength, J4.3

(LRFD) Axial load = 4 * PHI * Rn(ASD) Axial load = 4 * Rn/OMEGA


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Page 68(269) W brace net area:

(W brace, web horiz, web claw L conn)Ag = (D - 2Tf)Tw + 2Bf*Tf + Fillet AreaAn = Ag - (Dh * Tw * 2)

(LRFD)Rn_n = PHI * Pn, (Pn = Fu * Ae, tension rupture

(ASD)Rn_n = PHI * Pn/OMEGA, (Pn = Fu * Ae, tension rupture

Axial load = Rn_n

(270) V brace, guss shr tab weld to col:(guss to col and beam)

ew = eccentricity of loadmom = vc * eccf1 = vc / weld_lenf2 = 0f3 = mom * (weld_len / 2) / Ixf4 = hc / weld_lenfr = SQRT[ (f1 + f2)^2 + (f3 + f4)^2 ]Fw = .6 * Fexx Table J2.5Rn = Fw * .707 * Eff_weld Spec J2.4(LRFD) Fr = PHI * Rn(ASD) Fr = Rn / OMEGA

Load = 2 * Fr / fr

(271) H brace guss to L bolt shr(guss clip L to bm web conn)

ex = eccentricity in the x directioney = eccentricity in the y direction(LRFD) Rv = PHI * Rn, J3.6,8(ASD) Rv = Rn/OMEGA,num = Row * Columndx = Spa * (Row - 1) / 2dy = Col_spa * (Column - 1) / 2px = P * cos(Phi)py = P * sin(Phi)mom = abs( px * ey - py * ex )fx = px / num + mom * dy / Ipfy = py / num + mom * dx / Ipfv = SQRT( fx^2 + fy^2 )Axial load = maximum P to satisfy fv


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Page 69(272) H brace guss to L bolt brg:

(guss clip L to bm web conn)ex = eccentricity in the x directioney = eccentricity in the y direction(LRFD) Rv = PHI * Rn, J3.10(ASD) Rv = Rn/OMEGAnum = Row * Columndx = Spa * (Row - 1) / 2dy = Col_spa * (Column - 1) / 2px = P * cos(Phi)py = P * sin(Phi)mom = abs( px * ey - py * ex )rx = px / num + mom * dy / Ip

ry = py / num + mom * dx / Iprv = SQRT( rx^2 + ry^2 )Axial load = maximum P to satisfy rv


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Page 70(275) H brace guss to L weld:

(guss clip L to bm web conn)x0 = angle leg + bm tw / 2y0 = brace wp to centerline of anglelength = angle lengthside = 1 for a one side clip

= 2 for a two sided clipwx = Leg - Setbackwy = lengthx bar = (wx)^2 / Weld_leny bar = wy / 2Ix = (wy)^3 / 12 + 2 * wx * (y bar)^2Iy = (wx)^3/6 + 2*wx*(.5*wx-x bar)^2 + wy*(x bar)^2

Ip = Ix + Iym = ( 1/Weld_len + y0 * wy / (2 * Ip) )^2k = ( 1/Weld_len + x0 * (wx - x bar)/(2 * Ip) )^2denom = sin(phi)^2 * m + cos(phi)^2 * kRn = 0.707 * Fw * min(Eff_weld, Weld_size)Fw = .6 * Fexx(LRFD) Fr = PHI * Rn(ASD) Fr = PHI * RnAxial load = side * SQRT( (Fr)^2 / denom )

(276) H brace guss gross area interactive stress:(guss clip L to bm web conn)Refer to misc design note 33;x0 = angle leg + bm tw / 2length = angle length

Ag = length * TfSx = Tf * (length)^2 / 6tau = cos(Phi) / Agsigma = sin(Phi) / Ag+ cos(Phi) * x0 / SxAxial load = maximum to satisfy the yield criterion

(277) H brace guss net area interactive stress:(guss clip L to bm web conn)x0 = angle leg + bm tw / 2length = angle lengthnet length = length - (row - 1) * dhAn = net length * thick(LRFD) Fv = PHI * Rn, shear yield J4.2

Ft = PHI * Rn, tension yield J4.1(ASD) Fv = Rn/OMEGA, shear yield J4.2

Ft = Rn/OMEGA, tension yield J4.1t1 = cos(Phi) / (An * Fv)t2 = sin(Phi) / (An * Ft)t3 = cos(Phi) * x0 / (Sx_net * Ft)Axial load = shear / ( t1 + t2 + t3 )


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Page 71(278) H brace guss L to bm bolts, shr/ten:

(guss clip L to bm web conn)num = Row * Columnb = gage - Tfif Column = 2

fv = P * cos(Phi) / (num * Ab)ft = tension per bolt with prying

if column = 1f1 = P * cos(Phi) / Rowmom = P * cos(Phi) * gagef2 = mom * .5 * Spa * (Row - 1)/IpRv = SQRT( f1 * f1 + f2 * f2 )fv = Rv / Ab

ft = tension per bolt with prying(LRFD)Fv = PHI * Rn, shear J3Ft = PHI * Rn, tension J3

(ASD)Fv = Rn/OMEGA, shear J3Ft = Rn/OMEGA, tension J3

Axial load = max P to satisfy fv 0)

Tension = T / maximum K / sin(Phi)

(280) Bolted moment connection with HSS column:(Flange plate Weld to Column)

Con_depth = Length of side projection - Corner RadiusTpl = Thickness of the flange plate(LRFD)

Fw = .6 * PHI * FexxEff_weld_plate = PHI * .6 * Fy_pl * Tpl / ( Fw * .707 * 2 )Eff_weld_column = PHI * .6 * Fy_col * Tw / ( Fw * .707 )

(ASD)Fw = .6 * Fexx / OMEGAEff_weld_plate = .6 * Fy_pl * Tpl / OMEGA / ( Fw * .707 * 2 )Eff_weld_column = .6 * Fy_col * Tw / OMEGA / ( Fw * .707 )

Eff_weld = MIN[ Eff_weld_plate, Eff_weld_column, weld ]Fr = 2 * .707 * Eff_weld * FwRv = 2 * Fr * Con_depthMoment = Rv * ( D + Tpl )

For axial load reduce moment by: Ff * ( D + Tpl )where Ff = the maximum flange force.


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Page 72(281) Bolted moment connection with HSS column:

(Flange plate Tension / Compression)Capacity at last bolt row:

Eff_width = MIN[ whitmore width, overall plate width ]t = Thickness of the flange plateAg = t * Eff_widthAn = t * ( Eff_width - 2 * Dh )

(LRFD) F1 = PHI * Ag * Fy (compression)F2 = PHI * Ag * Fy (gross tension)F3 = PHI * An * Fu (net tension)

(ASD) F1 = Ag * Fy / OMEGA (compression)F2 = Ag * Fy / OMEGA (gross tension)F3 = An * Fu / OMEGA (net tension)

Ff,bolt = MIN[ F1, F2, F3 ]Capacity at notch:Ag = 2 * t * w_s

(LRFD) F1 = PHI * Ag * Fy (compression)F2 = PHI * Ag * Fy (gross tension)

(ASD) F1 = Ag * Fy / OMEGA (compression)F2 = Ag * Fy / OMEGA (gross tension)

Ff,notch = MIN[ F1, F2 ]

Moment = MIN[ Ff,bolt, Ff,notch ] * ( D + t )For axial load reduce moment by: Ff * (D + t)where Ff = the maximum flange force.

(282) Axially load shear tab fillet welds:ft1 = applied axial load / ( 2 * conn_depth)

ft2 = R * ew * .5 * conn_depth / Ix; twistingfv = R / (2 * conn_depth )fr = SQRT( fv^2 + (ft1 + ft2)^2 )Fw = .6 * Fexx Table J2.5Rn = Fw * .707 * Weld_size Spec J2.4(LRFD) Fr = PHI * Rn(ASD) Fr = Rn / OMEGA

Load = largest R to satisfy fr = 0.

Axial load = t1^2 * ( 1 + delta*alpha)n / K

(285) End pl weld strength, HSS beam with axial load:(Based on AISC Manual page 9-10 thru 13,but with modifications based on Packer and Henderson (1992) )

H = HSS section depthfh = applied ten / ( 2.* H )Fw = .6FexxWhen tension predominates, dsn shr/dsn ten


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Page 73(286) End plate bolt shear strength, HSS beam with axial load:

Tb = applied tension per bolt with prying from formula 284Slip-critical bolts:

Fv = allowable shear load per bolt calculated usinginteraction equation in Section J3.9

Bearing bolts:Fv = allowable shear load per bolt calculated using

interaction equations in Section J3.7Load = Fv * Ab * number of bolts

(287) Block shear rupture strength, with applied axial tension:AISC specification section J4.3

t1 = thickness required for axial tension, J4.3

t2 = thickness required for shear, J4.3Elliptical interaction.....Reqd T = SQRT( t1^2 + t2^2 )

Load = Applied shear * conn_thick / Reqd T

(288) Flush and Extended Moment End Plate connection strength:Refer to AISC design guide 16, analysis flow chart, for PHIfactors, definitions and calculation of variables.

Plate yielding:Mpl = PHIb * Fypl * tp^2 * Y

(LRFD) M1 = PHIb * Mpl; PHIb = .9(ASD) M1 = Mpl / OMEGAb; OMEGAb = 1.67

Bolt rupture, no prying:Mnp = 2Pt * SUM(dn)

(LRFD) M2 = PHIbr * Mnp; PHIbr = .75(ASD) M2 = Mnp / OMEGAbr; OMEGAbr = 2

(LRFD) M3 = PHI * Mq; PHI = .75(ASD) M3 = Mq / OMEGA; OMEGA = 2

M2 < M1 / 1.11Moment = MIN[ M2, M1 / gamma r ]Thick PL behavior controlled by bolt rupture

M2 >= M1 / 1.11M1 / gamma r < M3

Moment = M3; Thin PL behavior controlled by bolt ruptureM1 / gamma r > M3

Moment = M1 / gamma r; Thin PL behavior controlled by PL yieldingFor axial load reduce moment by: Ff * (Depth - Tf)where Ff = the maximum flange force.

(289) Shear tee flange bolts, shear/tension interaction:rigid support

n = number of boltsn_prime = num of bolts above the NAd_m = moment arm between the resultant ten and comp forcePu = connection shear forcee = eccentricity of Vf from the tee flanger_uv = applied shear load per bolt

= Pu / nr_ut = applied tension load per bolt

= Pu * e / ( 2 * n_prime * d_m )Load = maximum Pu so that the interaction equation of

Section J3.7 or J3.9 is satisfied


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Page 74(290) Shear tee flange strength, bending with prying:

rigid supportAISC manual page 7-12n = number of boltsn_prime = num of bolts above the NAd_m = moment arm between the resultant ten and comp forcePu = connection shear forcee = eccentricity of Pu from the tee flanger_ut = Pu * e / ( 2 * n_prime * d_m )p = conn length / number of bolt rowsb = 0.5 * ( gage - Tw_tee ) a = 0.5 * ( Bf_tee - gage )b' = b - 0.5 * Db a' = a + 0.5 * Dbd' = Db + 2 mm delta = 1 - d' / p

rho = b' / a' beta = ( 1 / rho ) * ( Tr / Pf - 1 )if beta

8/18/2019 Limit State Defini

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Limit State Definitions of the Connection Design Calculations SDS2 V7331