VERTICAL BRACE CONNECTION: WT BRACE (DIRECTLY BOLTED … · 2019. 6. 10. · VERTICAL BRACE CONNECTION: WT BRACE (DIRECTLY BOLTED STEM TO GUSSET PLATE) WITH DOUBLE ANGLE (WELDED/BOLTED)

VERTICAL BRACE CONNECTION: WT BRACE (DIRECTLY BOLTED STEM TO GUSSET PLATE)WITH DOUBLE ANGLE (WELDED/BOLTED) TWO-WAY GUSSET PLATE CONNECTION TO W

BEAM AND W COLUMN WEB

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I. DESIGN DATA AND LOADS (LRFD-14th Edition)

COLUMN PROPERTIES : W12X96 - A992

Depth,

Flange Width,

Distance k,

Area,

Minimum YieldStress,

Modulus ofElasticity,

Web Thickness,

Flange Thickness,

Distance k1,

Distance k (Design),

Minimum TensileStress,

d = 12.7 in

bf = 12.2 in

k = 1.812 in

Ag = 28.2 in²

Fy = 50 ksi

E = 29000 ksi

tw = 0.55 in

tf = 0.9 in

k1 = 1.125 in

kdes = 1.5 in

Fu = 65 ksi

Gage, g = 5.5 in

BEAM PROPERTIES : W16X50 - A992

Depth,

Flange Width,

Distance k,

Area,



Web Thickness,

Flange Thickness,

Distance k1,



d = 16.3 in

bf = 7.07 in

k = 1.312 in

Ag = 14.7 in²

Fy = 50 ksi

E = 29000 ksi

tw = 0.38 in

tf = 0.63 in

k1 = 0.812 in

kdes = 1.03 in

Fu = 65 ksi

Cut Distance fromWeb,

z = 0 in

Top of SteelElevation,

Elev = 0 ft + 0 in

Span Length, L = 30 ft Erection Clearance, gap = 0.5 in

Skew, θsk = 0 degSlope, θsl = 0 deg

Depth of BottomCope,

dcB = 0 in

cB = 0 inLength of BottomCope,

Depth of Top Cope, dcT = 0 in

cT = 0 inLength of Top Cope,

BRACE PROPERTIES : WT6X9.5 - A992

Depth,

Flange Width,

Distance k,

Area,



Web Thickness,

Flange Thickness,



d = 6.08 in

bf = 4.01 in

k = 0.875 in

Ag = 2.79 in²

Fy = 50 ksi

E = 29000 ksi

tw = 0.235 in

tf = 0.35 in

kdes = 0.65 in

Fu = 65 ksi

Unbraced Length, Lu = 12 ft + 11.312 in

Angle from VerticalMember,

θ = 59.32 deg


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Angle from VerticalMember,

θ = 59.32 deg

Vertical Distance toCentroidal Axis,

ȳ = 1.65 in

GUSSET PLATE PROPERTIES : A36

Thickness, t = 0.375 in Number of Plates, n = 1

Fy = 36 ksi

E = 29000 ksi


Fu = 58 ksiMinimum YieldStress,


Clip, c = 0 in

GUSSET CONNECTION ANGLE PROPERTIES : 2L4X4X1/2 - A36

Column Side LegSize,

Gusset Side LegSize,

Thickness,

Number of ConnectionAngles,

leg1 = 4 in

leg2 = 4 in

t = 0.5 in

n = 2



Fy = 36 ksi

Fu = 58 ksi

E = 29000 ksi


g1 = 2.5 inColumn Side BoltGage,

g2 = 0 inGusset Side BoltGage,

BEAM CONNECTION ANGLE PROPERTIES : 2L4X4X1/2 - A36

Column Side LegSize,

Beam Side Leg Size,

Thickness,

Number of ConnectionAngles,

leg1 = 4 in

leg2 = 4 in

t = 0.5 in

n = 2



Fy = 36 ksi

Fu = 58 ksi

E = 29000 ksi


g1 = 2.5 inColumn Side BoltGage,

g2 = 0 inBeam Side Bolt Gage,

BOLTS PROPERTIES : 3/4" - ø - A325-SC-OVS-CLASS A

For Gusset Plate to WT Brace Connection:

db = 0.75 inBolt Diameter,

Bolt Shear Strength, Λrv = 8.068 kips Bolt TensileStrength,

Λrn = 29.821 kips

Connection Type, Conn_type = SlipCritical

Bolt Type, Bolt_Type = A325-SC-OVS-CLASS A

Number of Bolt Rows, Bolt VerticalSpacing,

s = 3 innr = 6


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Bolt HorizontalSpacing,

sv = 3 inNumber of BoltColumn Lines,

nv = 2

Total Number ofBolts (nr·nv),

nb = 12

Holes at GussetPlate,

Holes at WT Brace,

Vertical HoleDimension,


Horizontal HoleDimension,


Vertical EdgeDistance,


hdv = 1 in

hdh = 1 in

Lev = 1.5 in

hdv = 0.875 in

hdh = 0.875 in

Lev = 1.5 in

Bolt First Down fromBrace Flange,

D = 2 in

BOLTS PROPERTIES : 3/4" - ø - A325-SC-SSLT-CLASS A

For Gusset Connection Angle to Column Web Connection:

Bolt Diameter,

Bolt Shear Strength,

Bolt Type,

Number of Bolt Rows,

Number of BoltColumn Lines,


db = 0.75 in

Λrv = 9.492 kips

Bolt_Type = A325-SC-SSLT-CLASS A

nr = 4

nv = 1

nb = 4

Holes at Column Web,


hdv = 0.875 in


hdh = 0.875 in

Bolt TensileStrength,

Connection Type,


Holes at Connection Angle,

Λrn = 29.821 kips

Conn_type = SlipCritical

s = 3 in

sv = 0 in

Bolt VerticalSpacing,


hdv = 0.875 in


hdh = 1.063 in

Adjacent Number ofBolt Rows (if any),

nr2 = 3

Vertical EdgeDistance (Lev2),

Lev = 2.25 in Distance of FirstBolt at Gusset Plateto Beam,

y = 3 in


Lev = 1.25 in

Horizontal EdgeDistance(leg1 - g1 - (nv -1)·(sv)),

Leh = 1.5 in

BOLTS PROPERTIES : 3/4" - ø - A325-SC-SSLT-CLASS A

For Beam Connection Angle to Column Web Connection:


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Bolt Diameter,

Bolt Shear Strength,

Bolt Type,

Number of Bolt Rows,

Number of BoltColumn Lines,


db = 0.75 in

Λrv = 9.492 kips

Bolt_Type = A325-SC-SSLT-CLASS A

nr = 4

nv = 1

nb = 4

Holes at Column Web,


hdv = 0.875 in


hdh = 0.875 in

Bolt TensileStrength,

Connection Type,


Holes at Connection Angle,

Λrn = 29.821 kips

Conn_type = SlipCritical

s = 3 in

sv = 0 in

Bolt VerticalSpacing,


hdv = 0.875 in


hdh = 1.063 in

Adjacent Number ofBolt Rows (if any),

nr2 = 4

Bolt First Down fromTop of Beam,

D = 3 in Vertical EdgeDistance,

Lev = 1.25 in

Horizontal EdgeDistance(leg1 - g1 - (nv -1)·(sv)),

Leh = 1.5 in

WELDS PROPERTIES : E70xx LH

Minimum Tensile Stress, Fu = 70 ksi

For Gusset Connection Angle to Gusset Plate Connection:

w = 0.187 inPreferred Weld Size (w2),

For Gusset Plate to Beam Flange Connection:

Preferred Weld Size(w3),

w = 0.25 in Length of Weld, Lw = 34.187 in

For Beam Connection Angle to Beam Web Connection:

Preferred Weld Size (w1), w = 0.187 in

SAFETY AND RESISTANCE FACTORS:

Safety Factor, Ω(ASD) Resistance Factor, ϕ(LRFD)

Modification Factor,

Ω

1Λ = (if ASD) (if LRFD)Λ = ϕ

safety factor resistance factor modification factor

For Member inBearing/ BoltBearing (brg),

Ωbrg = 2.00 ϕbrg = 0.75 Λbrg = 0.75


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For Block Shear (bs), Ωbs = 2.00 ϕbs = 0.75 Λbs = 0.75

For Compression (c), Ωc = 1.67 ϕc = 0.90 Λc = 0.90

For Fillet WeldShear (vw),

Ωvw = 2.00 ϕvw = 0.75 Λvw = 0.75

For Flexural LocalBuckling/FlexuralStrength (b),

Ωb = 1.67 ϕb = 0.90 Λb = 0.90

For Shear Rupture(vr),

Ωvr = 2.00 ϕvr = 0.75 Λvr = 0.75

For Shear Yielding(vy),

Ωvy = 1.50 ϕvy = 1.00 Λvy = 1.00

For Tension Rupture(tr),

Ωtr = 2.00 ϕtr = 0.75 Λtr = 0.75

For TensionYielding(ty),

Ωty = 1.67 ϕty = 0.90 Λty = 0.90

For WebCrippling(cr),

Ωcr = 2.00 ϕcr = 0.75 Λcr = 0.75

For Member ShearYielding for S, M,W, HSS (wy),

Ωwy = 1.50 ϕwy = 1.00 Λwy = 1.00

For Eccentric Weld(ew),

Ωew = 2.00 ϕew = 0.75 Λew = 0.75

APPLIED LOADS:

Given Tension Load, Given CompressionLoad,

Pt1 = 50 kips Pc1 = 50 kips

Governing TensionLoad,

Governing CompressionLoad,

Pt = 50 kips Pc = 50 kips

Maximum Axial Load, P = max(Pt,Pc) P = 50 kips

Brace:

Given Load

Beam:

Given End Reaction

Shear Load, V = 15 kips

Adjacent Shear Load(if any),

V2 = 0 kips

Transfer Force, TF = 0 kips


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II. CALCULATIONS

A. BRACE CHECK

1. Rupture Capacity

(AISC 14th Ed. Specifications, Chapter D, Section D2, pages 16.1-26 to 16.1-27)

(0.5bf + 0.5tw)·tf - nv·hd·tw

Gross Area of Connected Element,

Agce = ·t Agce = 1.429 in²

Length of the Connection,

Lcon = (nr - 1)·s Lcon = 15 in

Net Tension Area,

Ant = Ag - Ant = 1.636 in²

d

Eccentricity of the Connection,

econ =

econ = 0.453 in

(0.5·bf + 0.5·tw)·0.5·tf + (d - tf)· 0.5·(tw)

(0.5·bf + 0.5·tw)·tf + (d - tf)·tw

0.52

Reduction Coefficient,

(AISC 14th Ed. Specifications, Chapter D, Table D3.1, page 16.1-28)

Ua = max -1Lcon

econ, 0.8

nr ≥ 4

U = maxAg

Agce,Ua U = 0.97

Effective Net Tension Area,

Ae = U·Ant Ae = 1.586 in²

Tensile Rupture Capacity, (D2-2)

Rtr = Λtr·Fu·Ae

Pt = 50 kipsRtr = 77.34 kips

Tensile Rupture Capacity > Applied Force, UCV = 0.646, OK

2. Bolt Capacity

(AISC 14th Ed. Specifications, Chapter J, Section J3.10, pages 16.1-127 to 16.1-128)

Bearing Area,

Bolt Vertical Centerline Distance from Beam Centerline,

Abrg = db·tw Abrg = 0.176 in²

ah = |D + 0.5(nv - 1)·s - y| ah = 1.85 in

Eccentricity distance of Axial Load from Bolt Group Centerline,

Yo = ah Yo = 1.85 in


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Load Inclination from Vertical,

θ = 90 deg

Eccentric Load Coefficient,

(AISC 14th Ed. Manual Part 7, Instantaneous Center of Rotation Method, pages 7-6to 7-8)

C = 10.941

Available Bearing Strength Using Edge Distance, (J3-6a, J3-6c)

Fbe = Λbrg·Fu·

hdv < hdls(db)

1.2·(Lev - 0.5·hdv)·tw

1.2·(Leh - 0.5·hdh)·tw

2.4·Abrg

Fbe = 8.833 kips

Available Bearing Strength Using Bolt Spacing, (J3-6a, J3-6c)

Fbe = min(Fbe)

hdv < hdls(db)

Fbs = Λbrg·Fu·

1.2·(s - hdv)·tw

1.2·(s - hdh)·tw

2.4·Abrg

nv > 1

Fbs = min(Fbs)

Fbs = 20.621 kips

Number of Areas in Consideration,

n1 = 1

Bolt Capacity,

nv > 1

Rbrg = C·min(n1·Fbe, n1·Fbs, n·Λrv)

Rbrg = 88.277 kips P = 50 kips

Bolt Capacity > Applied Force, UCV = 0.566, OK

3. Block Shear Capacity

(AISC 14th Ed. Specifications Chapter J, Section J4.3, page 16.1-129)

Pattern 1

Reduction Factor,

U = 0.5 (Tension Stress is Non-Uniform)bs

Gross Shear Area

Agv = [(nr - 1)·s + Lev]·

Net Tension Area

Ant = [(d - D) - (nv - 0.5)·hd]·tw

Agv = 3.877 in²

Ant = 0.65 in²

tw


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tw

Net Shear Area

Anv = [(nr - 1)·s + Lev - (nr - 0.5)·hd]·

Ant = 0.65 in²

Anv = 2.747 in²

bs bsRbs = Λ min(0.6·Fu·Anv + U ·Fu·Ant, 0.6·Fy·Agv + U ·Fu·Ant)

Block Shear Capacity, (J4-5)

Rbs = 96.19 kips

1

1

bs

Pattern 2

bs

Reduction Factor,

(Tension Stress is Uniform)U = 1.0

Gross Shear Area

Agv = [(nr - 1)·s + Lev]·2·tw

Net Tension Area

Ant = [(nv - 1)·sv - (nv - 1)·hd]·tw

Net Shear Area

Agv = 7.755 in²

Anv = Agv - (nr - 0.5)·2hd· Anv = 5.493 in²

Ant = 0.499 in²

tw

bs

Rbs = 185.018 kips

bs2

2

Rbs = Λ min(0.6·Fu·Anv + U ·Fu·Ant, 0.6·Fy·Agv + U ·Fu·Ant)


bs

Rbs = min(Rbs ,Rbs )21

Governing Block Shear Capacity, (J4-5)

Rbs = 96.19 kips Pt = 50 kips

Block Shear Capacity > Applied Force, UCV = 0.52, OK

B. BRACE TO GUSSET PLATE CHECK

1. Bolt Shear Capacity

(AISC 14th Ed. Specifications, Chapter J, Section J3.6, page 16.1-125)

Shear Capacity Per Bolt,

Λrv = 8.068 kips

Bolt Shear Capacity,

Rb = n·C·Λrv

Bolt Shear Capacity > Applied Force, UCV = 0.566, OK

Rb = 88.277 kips P = 50 kips

2. Check for Spacing

(AISC 14th Ed. Specifications, Chapter J, Section J3.3 and J3.5, pages 16.1-122 to 16.1-124)Description: Created By: GIZA™ 19

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(AISC 14th Ed. Specifications, Chapter J, Section J3.3 and J3.5, pages 16.1-122 to 16.1-124)

WT Brace Thickness,

t1 = 0.235 in

Gusset Plate Thickness,

t2 = 0.375 in

a. Vertical Spacing,

Minimum Bolt Spacing,

s = 3 in

smin = 2 3

2·db smin = 2 in

smax = min(12·in, 24·min(t1, t2))

Specified Bolt Spacing is acceptable, OK

smax = 5.64 in

Maximum Bolt Spacing,

b. Horizontal Spacing,


sv = 3 in

svmin = 2 3

2·db svmin = 2 in

svmax = min(12·in, 24·min(t1, t2))


svmax = 5.64 in


3. Check for Edge Distance


Brace Edge Distances,

Lev1 = 1.5 in

Leh1 = 1.08 in

Gusset Plate Edge Distances,

Lev2 = 1.5 in

i) Minimum Vertical Edge Distance,

Connection Edge Distance,

1.5Lev2

Lev1Levcon =

1.5Levcon = in

1Levmin1

Levmin2 Levmin = 1.063Levmin =

Minimum Edge Distance,

in


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Specified Edge Distance is Acceptable, OK

1Lehmin1

1.08

Leh2

ii) Minimum Horizontal Edge Distance,


Lehcon =Leh1

Lehcon = NA


Lehmin = Lehmin2 Lehmin = NA

in

in


iii) Maximum Edge Distance,

Brace Thickness,

t1 = 0.235 in

Gusset Plate Thickness,

t2 = 0.375 in

Nearest Connection Edge Distance,

Lemin = min(Lehcon, Levcon)

Lemin = 1.08 in

Maximum Edge Distance,

Lemin = Levcon ˅ Lemin = Lehcon

Lemax = min(6in, 12·t1)

0 0

Lemax = 2.82 in

Maximum Edge Distance Requirement is Satisfied, OK

C. GUSSET PLATE CHECK

1. Bolt Capacity


Bearing Area,

Abrg = db·t Abrg = 0.281 in²

Bolt Vertical Centerline Distance from Beam Centerline,

ah = |D + 0.5·nv - 1)·s - y| ah = 1.85 in

Eccentricity distance of Axial Load from Bolt Group Centerline,

Yo = ah Yo = 1.85 in

θ = 90 deg


(AISC 14th Ed. Manual Part 7, Instantaneous Center of Rotation Method, pages 7-6to 7-8)

C = 10.941



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C = 10.941


Fbe = Λbrg·Fu·

hdv < hdls(db)

1.2·(Lev - 0.5·hdv)·t

2.4·Abrg

Fbe = 19.575 kips


Fbe = min(Fbe)

Fbs = Λbrg·Fu·

hdv < hdls(db)

1.2·(s - hdv)·t

1.2·(s - hdh)·t

2.4·Abrg

nv > 1

Fbs = min(Fbs) Fbs = 29.362 kips

Bolt Capacity,

Rbrg = Cmin(Fbe,Fbs,Λrv)

Rbrg = 88.277 kips P = 50 kips


2. Whitmore Section

Width of Whitmore Section,

bwh1 = 2·(nr - 1)·s·tan(30deg) + (nv - 1)·sv

bwh1 = 20.321 in

Width of Whitmore Section Outside Gusset Plate,

bwhog = 0.063 in

Available Width of Whitmore Section in Gusset Plate,

bwh = bwh1 - 2·bwhog bwh = 20.196 in

Effective Length of Whitmore Section,

Lwh = 5.5 in

3. Yielding Capacity


Width,

b = bwh b = 20.196 in

Gross Tension Area,

Ag = b·t


n1 = n

Tensile Yielding Capacity, (J4-1)Description: Created By: GIZA™ 19

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Tensile Yielding Capacity, (J4-1)

Rty = Λty·n1·Fy·Ag

Rty = 245.375 kips Pt = 50 kips

Tensile Yielding Capacity > Applied Force, UCV = 0.204, OK

4. Compression Capacity

(AISC 14th Ed. Specifications, Chapter J, Section J4.4, page 16.1-129 to 16.1-130)

(Commentary on the Specification for Structural Steel Building Table C-A-7.1)

Effective Length Factor,

K = 0.65

Laterally Unbraced Length,

Lu = Lwh Lu = 5.5 in

Gross Area,

Ag = bwh·t Ag = 7.573 in²

t

0.5

Radius of Gyration,

r = r = 0.108 in(12)

Slenderness Ratio,

KLr =K·Lur

KLr = 33.024

π ·E2

2

Elastic Critical Buckling Stress,

Fe =KLr

Fe = 262.438 ksi

Flexural Buckling Stress,

EFy

KLr > 25

KLr ≤ 4.71·

0.5

Fe

Fy

Fcr = 0.658 ·Fy Fcr = 33.991 ksi


n1 = n

Compression Capacity,

Rcb = Λc·n1·Fcr·Ag

Rcb = 231.684 kips Pc = 50 kips

Compression Capacity > Applied Force, UCV = 0.216, OK



Reduction Factor,

Ubs = 1.0 (tension stress is uniform)


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Gross Shear Area,

Agv = 2·[Lev + (nr - 1)·s]·t Agv = 12.375 in²

Net Tension Area,

Ant = [(nv - 1)·sv - (nv - 1)·hdh]·t

Ant = 0.75 in²

Net Shear Area,

Anv = Agv - 2·[(nr - 0.5)·hdv]·t Anv = 8.25 in²


n1 = n


Rbs = Λbs·n1·min(0.6·Fu·Anv + Ubs·Fu·Ant, 0.6·Fy·Agv + Ubs·Fu·Ant)

Rbs = 233.1 kips Pt = 50 kips


D. GUSSET PLATE FORCE DISTRIBUTION

1. Gusset Plate Edge Forces

(AISC 14th Ed. Manual Part 13, pages 13-3 to 13-11)

Uniform Force Method

Beam,

eb = 0.5·d

Column,

ec = 0in

Horizontal Side, Vertical Side,

αbar = 0.5·Lw + gap βbar = 0.5·(nr - 1)·s + y

αbar = 17.594 in βbar = 7.5 in

tan(θ)

αbar + ecα = αbar β = - eb

α = 17.594 in β = 2.288 in


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r =P

0.5

(α + ec) + (β + eb)2 2

r = 2.444 kips/in

Horizontal Side, Vertical Side,

Hb = α·r Hc = ec·r

Hb = 43.002 kips Hc = 0 kips

Vb = eb·r Vc = β·r

Vb = 19.92 kips Vc = 5.592 kips

Mb = |Vb·(α - αbar)| Mc = |Hc·(β - βbar)|

Mb = 0 kips·in Mc = 0 kips·in

Redistribution of Forces,

Shear Transfer,

ΔV = 0 kips

Gusset-to-Beam Connection,

Vb = Vb - ΔV Hb = Hb Mb = |ΔV·αbar + Mb|

Vb = 19.92 kips Hb = 43.002 kips Mb = 0 kips·in

Gusset-to-Column Connection,

Vc = |Vc + ΔV| Hc = |Hc| Mc = |Hc·(β - βbar)|

Vc = 5.592 kips Hc = 0 kips Mc = 0 kips·in

E. GUSSET PLATE TO COLUMN WEB CHECK

Note: Since Hc and Mc are both equal to 0 kips, limit states will only be checked dueto force Vc

1. Forces Acting on Connection

Vertical Force,

Vc = 5.592 kips


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Horizontal Force,

Hc = 0 kips

Moment Force,

Mc = 0 kips·in

Resultant Force,

Vc + Hc

0.522

Rc = Rc = 5.592 kips

E.A. GUSSET PLATE CHECK



a. Block Shear Capacity due to Shear Load

Reduction Factor,


Connection Angle,

Lev1 = Lev

Gross Shear Area,

Agv = [Lev + (nr - 1)·s + Lev1]·t Agv = 4.687 in²

Net Tension Area,

Ant = (leg2 - gap)·t Ant = 1.312 in²

Net Shear Area,

Anv = Agv Anv = 4.687 in²


n1 = 1


Rbs = Λbs·n1min(0.6·Fu·Anv + Ubs·Fu·Ant, 0.6·Fy·Agv + Ubs·Fu·Ant)

Rbs = 133.031 kips Vc = 5.592 kips


E.B. GUSSET CONNECTION ANGLE TO GUSSET PLATE CHECK

1. Weld Capacity

(AISC 14th Ed. Specifications, Chapter J, pages 16.1-110 to 16.1-117)(AISC 14th Ed. Manual, Part 8, pages 8-9 to 8-15)

a. Using Fillet Weld

Number of Weld Sides,

nws = 2

Minimum Weld Size,

wmin = 0.187 in w = 0.187 in


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wmin = 0.187 in

Preferred Weld Size = Minimum Weld Size, OK

w = 0.187 in

Maximum Weld Size,

wmax = t - in

t ≥ in1

4

1

16

wmax = 0.438 in

Preferred Weld Size < Maximum Weld Size, OK

w = 0.187 in

Shear Strength,

For Gusset Plate,

Rv1 = Λvr·0.6·Fu·t Rv1 = 9.787 kips/in

For Connection Angle,

Rv2 = Λvr·0.6·Fu·tn Rv2 = 26.1 kips/in

For Weld,

Rv3 = Λvw·0.6·Fu·sin(45deg)·nws Rv3 = 44.548 ksi

Maximum Effective Weld Size,

weff =min(Rv1, Rv2)

Rv3weff = 0.22 in

Length of Weld,

Lw = (nr - 1)·s + 2·Lev Lw = 11.5 in


kl = leg2 - gap kl = 3.5 in

xl =kl

2kl + Lwxl = 0.662 in

2

al = leg2 - xl +Mc

Vcal = 3.338 in

k =kl

Lwk = 0.304

a =al

Lwa = 0.29

θw = atanHc

Vcθw = 0 deg


Electrode Strength Coefficient,

(AISC 14th Ed. Manual Part 8, Table 8-3, pages 8-65)

C1 = 1 ksi

(AISC 14th Ed. Manual Part 8, Table 8-8, pages 8-90 to 8-95)Description: Created By: GIZA™ 19

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(AISC 14th Ed. Manual Part 8, Table 8-8, pages 8-90 to 8-95)

Co = 2.821

Weld Capacity,

Rw = Λew·nws·Co·C1·16·Lw·min(w, weff)

Rw = 145.978 kips Rc = 5.592 kips

Weld Capacity > Applied Force, UCV = 0.038, OK

E.C. GUSSET CONNECTION ANGLE CHECK

1. Bolt Capacity


a. Bolt Capacity due to Shear Load (Primary Side)

Bearing Area,



hdh < hdls(db)

Fbe = Λbrg·Fu·min[1.2·(Lev - 0.5·hdv)·t, 2.4·Abrg]

Fbe = 21.206 kips


hdh < hdls(db)

Fbs = Λbrg·Fu·min[1.2·(s - hdv)·t, 2.4·Abrg]

Fbs = 39.15 kips


n1 = n

Connection Angle,

n2 = n

Bolt Capacity,

Rbrg = nv·[min(n1·Fbe, n2·Λrv) + min(n1·Fbs, n2·Λrv)·(nr - 1)]

Rbrg = 75.936 kips Vc = 5.592 kips




a. Shear Yielding Capacity due to Shear Load

Length,

L = (nr - 1)·s + 2·Lev L = 11.5 in


n1 = n


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Shear Yielding Capacity, (J4-3)

Rvy = Λvy·n1·0.6·Fy·L·t

Rvy = 248.4 kips Vc = 5.592 kips

Shear Yielding Capacity > Applied Force, UCV = 0.023, OK

3. Rupture Capacity


a. Shear Rupture Capacity due to Shear Load (Primary Side)

Net Shear Area,

Anv = (L - nr·hdv)·t

Anv = 4 in²


n1 = n

Shear Rupture Capacity, (J4-4)

Rvr = Λvr·n1·0.6·Fu·Anv

Rvr = 208.8 kips Vc = 5.592 kips

Shear Rupture Capacity > Applied Force, UCV = 0.027, OK



a. Block Shear Capacity due to Shear Load (Primary Side)

Reduction Factor,


Gross Shear Area,

Agv = [(nr - 1)·s + Lev]·t Agv = 5.125 in²

Net Tension Area,

Ant = [Leh + (nv - 1)·sv - (nv - 0.5)·hdh]·t

Ant = 0.484 in²

Net Shear Area,

Anv = Agv - [(nr - 0.5)·hdv]·t Anv = 3.594 in²


n1 = n



Rbs = 208.191 kips Vc = 5.592 kips


E.D. GUSSET CONNECTION ANGLE TO COLUMN WEB CHECK



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Shear Capacity Per Bolt,

Λrv = 9.492 kips


Rb = n·nb·Λrv


Rb = 75.936 kips Vc = 5.592 kips



Connection Angle Thickness,

t1 = 0.5 in

Column Web Thickness,

t2 = 0.55 in



s = 3 in

smin = 2 3

2·db smin = 2 in



smax = 12 in




Connection Angle Edge Distances,

Lev1 = 1.25 in

Leh1 = 1.5 in



Lev1Levcon = Levcon = 1.25 in

Levmin1 Levmin = 1Levmin =


in



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1.125Lehmin1

1.5

Leh2



Lehcon =Leh1

Lehcon = NA



in

in




t1 = 0.5 in



Lemin = 1.25 in




0 0

Lemax = 6 in


F. COLUMN WEB CHECK DUE TO GUSSET PLATE STRESSES

1. Bolt Capacity


Bearing Area,

Abrg = db Abrg = 0.413 in²


Fbe = Λbrg·Fu·2.4·Abrg

Fbe = 48.263 kips

hdh < hdls(db)


hdh < hdls(db)

Fbs = 48.263 kips

Fbs = Λbrg·Fu·

1.2·(s - hdv)

1.2·(sv - hdh)

2.4·Abrg

Fbs = min(Fbs , Fbs )0 2


n1 = nDescription: Created By: GIZA™ 19

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n1 = n

Connection Angle,

n2 = n

Bolt Capacity,

Rbrg = nv·[min(n1·Fbe, n2·ΛRv) + min(n1·Fbs, n2·ΛRv)·(nr - 1)]

Rbrg = 75.936 kips Vc = 5.592 kips


G. GUSSET PLATE TO BEAM FLANGE CHECK


Vertical Force,

Vb = 19.92 kips

Horizontal Force,

Hb = 43.002 kips

Moment Force,

Mb = 0 kips·in

2Vb + HbRb =

Resultant Force,

0.52

Rb = 47.391 kips

2. Weld Capacity

(AISC 14th Ed. Specifications, Chapter J, pages 16.1-110 to 16.1-117)

(AISC 14th Ed. Manual, Part 8, pages 8-9 to 8-15)



nws = 2

Minimum Weld Size,

wmin = 0.187 in w = 0.25 in

Preferred Weld Size > Minimum Weld Size, OK

2

Maximum Force on Welds Per Unit Length,

fmax =Hb

Lw

2

+Vb

Lw +4·Mb

Lw

2 0.5

fmax = 1.386 kips/in

·fave =1

2 2Hb

Lw

2

+Vb

Lw +4·Mb

Lw

2 0.5

+ 2Hb

Lw

2

+Vb

Lw -4·Mb

Lw

2 0.5

fave = 1.386 kips/in

Average Force on Welds Per Unit Length,

Total Force Per Unit Length on Welds of Gusset Plate to Beam Connection,

Ruw = max(fmax, 1.25·fave) Ruw = 1.733 kips/inDescription: Created By: GIZA™ 19

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Ruw = max(fmax, 1.25·fave) Ruw = 1.733 kips/in

Shear Strength,

For Beam,

Rv1 = Λvr·0.6·Fu·tf·nws Rv1 = 36.855 kips/in

For Gusset Plate,

Rv2 = Λvr·0.6·Fu·t Rv2 = 9.787 kips/in

Hb

Effective Load Angle Factor,

θ = atanVb +

4·Mb

Lwθ = 24.855 deg

μ = 1.0 + 0.50·sin(θ)1.5 μ = 1.136

For Weld,

Rv3 = Λvw·μ·0.6·Fu·sin(45deg)·nws

Rv3 = 50.618 ksi

Maximum effective weld size,

weff =min(Rv1, Rv2)

Rv3weff = 0.193 in

Weld Capacity,

Rw = Λvw·μ·0.6·Fu·sin(45deg)·nws·min(weff, w)

Rw = 9.787 kips/in Ruw = 1.733 kips/in


G.A. GUSSET PLATE CHECK




Length,

L = Lw L = 34.187 in


n1 = n



Rvy = 276.919 kips Hb = 43.002 kips


b. Tensile Yielding Capacity due to Axial Load


Length,

L = Lw L = 34.187 inDescription: Created By: GIZA™ 19

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L = Lw L = 34.187 in

4·Mb

Equivalent Normal Force,

Nb = Vb +L Nb = 19.92 kips

Gross Tension Area,

Ag = L·t


Rty = Λty·n·Fy·Ag

Rty = 415.378 kips Nb = 19.92 kips

Tensile Yielding Capacity > Applied Force, UCV = 0.048, OK

Interaction of Yielding Capacities,

≤ 1.0Hb

Rvy+

2Nb

Rty

2

UCV = UCV = 0.026

Yielding Capacity > Applied Force, UCV = 0.026, OK

Hb

Rvy+

2Nb

Rty

2

H. BEAM WEB CHECK DUE TO GUSSET PLATE STRESSES

1. Force Acting on Connection

Equivalent Normal Force Acting on the Connection,

Nb = 19.92 kips

2. Web Local Yielding Capacity


Distance of Force to Beam End,

De = 0.5·Lw De = 17.094 in

Bearing Length,

N = Lw N = 34.187 in

Web Local Yielding Capacity, (J10-2, J10-3)

De > d

Rwy = Λwy·Fy·tw·(N + 5·kdes)

Rwy = 747.412 kips Nb = 19.92 kips

Web Local Yielding Capacity > Applied Force, UCV = 0.027, OK

3. Web Local Crippling Capacity


Bearing Length,

N = 34.187 inN = L


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Web Crippling Capacity, (J10-4, J10-5a, J10-5b)

Esq =E·Fy·tf

tw

0.5

Esq = 1550.467 ksi

N1 = 1 + 3N

d·

tw

tf

1.5

N1 = 3.948·

De ≥d

2

Rwc = Λcr·0.8·tw²·N1·Esq

Rwc = 530.288 kips Nb = 19.92 kips

Web Local Crippling Capacity > Applied Force, UCV = 0.038, OK

4. Web Horizontal Shear Capacity

Force Acting on the Beam,

Horizontal Shear Force,

Vw =tf·bf

Ag1 -Hb· Vw = 29.972 kips

Web Horizontal Shear Capacity,

Rv = Λvy·0.6·Fy·Lw·tw

Rv = 389.738 kips Vw = 29.972 kips

Web Horizontal Shear Capacity > Applied Force, UCV = 0.077, OK

I. BEAM WEB TO COLUMN WEB CHECK


Vertical Force,

Vbm = V + Vb Vbm = 34.92 kips

Horizontal Force,

Hbm = TF + |(P·sin(θ) - Hb)| Hbm = 0 kips

Resultant Force,

Vbm + Hbm0.5

22Rbm = Rbm = 34.92 kips

I.A. BEAM WEB CHECK

1. Shear Capacity

(AISC 14th Ed. Specifications, Chapter G, Section G2.1, pages 16.1-67 to 16.1-69)

tw

h

Clear Distance Between Flanges of Beam Less the Fillet or Corner Radii,

h = d - 2·kdes h = 14.24 in

Limiting Depth-Thickness Ratio,

htw = htw = 37.474


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Clear Distance Between Transverse Stiffeners,

htw < 260 a = 0 in

Web Plate Buckling Coefficient, (G2-6)

htw < 260 kv = 5

Web Shear Coefficient, (G2-3, G2-4, G2-5)

kv·Ehtw ≤ 1.1·

FyCv = 1

0.5

Shear Capacity, (G2-1)

Rv = Λvbm·0.6·Fy·d·tw·Cv

Rv = 185.82 kips Vbm = 34.92 kips

Shear Capacity of Section > Applied Force, UCV = 0.188, OK



Reduction Factor,


Gross Shear Area,

Agv = 2·[(leg2 - gap)·tw] Agv = 2.66 in²

Connection Angle,

Lev1 = Lev

Net Tension Area,

Ant = [(nr - 1)·s + 2·Lev1]·tw Ant = 4.37 in²

Net Shear Area,

Anv = Agv Anv = 2.66 in²


n1 = 1



Rbs = 272.888 kips Hbm = 0 kips

Block Shear Capacity > Applied Force, UCV = 0, OK

I.B. BEAM CONNECTION ANGLE TO BEAM WEB CHECK

1. Weld Capacity

(AISC 14th Ed. Specifications, Chapter J, pages 16.1-110 to 16.1-117)(AISC 14th Ed. Manual, Part 8, pages 8-9 to 8-15)



nws = 2


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nws = 2

Minimum Weld Size,

wmin = 0.187 in

Preferred Weld Size = Minimum Weld Size, OK

w = 0.187 in

Maximum Weld Size,

wmax = t - in

t ≥ in1

4

1

16

wmax = 0.438 in

Preferred Weld Size < Maximum Weld Size, OK

w = 0.187 in

Shear Strength,

For Beam Web,

Rv1 = Λvr·0.6·Fu·tw Rv1 = 11.115 kips/in

For Connection Angle,

Rv2 = Λvr·0.6·Fu·tn Rv2 = 26.1 kips/in

For Weld,

Rv3 = Λvw·0.6·Fu·sin(45deg)·nws Rv3 = 44.548 ksi

Maximum Effective Weld Size,

weff =min(Rv1, Rv2)

Rv3weff = 0.25 in

Eccentric Distance of Axial Load from Weld Group Centerline,

ah = |(0.5·d) - [D + 0.5(nr - 1)·s]| ah = 0.65 in

Length of Weld,

Lw = (nr - 1)·s + 2·Lev Lw = 11.5 in


kl = leg2 - gap kl = 3.5 in

xl =kl

2kl + Lwxl = 0.662 in

2

al = leg2 - xl +Hbm·ah

Vbmal = 3.338 in

k =kl

Lwk = 0.304

a =al

Lwa = 0.29


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θw = atanHbm

Vbmθw = 0 deg


Electrode Strength Coefficient,

(AISC 14th Ed. Manual Part 8, Table 8-3, pages 8-65)

C1 = 1 ksi

(AISC 14th Ed. Manual Part 8, Table 8-8, pages 8-90 to 8-95)

Co = 2.821

Weld Capacity,

Rw = Λew·nws·Co·C1·16·Lw·min(w, weff)

Rw = 145.978 kips Rbm = 34.92 kips


I.C. BEAM CONNECTION ANGLE CHECK

1. Bolt Capacity


a. Bolt Capacity due to Shear Load (Primary Side)

Bearing Area,



hdh < hdls(db)

Fbe = Λbrg·Fu·min[1.2·(Lev - 0.5·hdv)·t, 2.4·Abrg]

Fbe = 21.206 kips


hdh < hdls(db)

Fbs = Λbrg·Fu·min[1.2·(s - hdv)·t, 2.4·Abrg]

Fbs = 39.15 kips


n1 = n

Connection Angle,

n2 = n

Bolt Capacity,

Rbrg = nv·[min(n1·Fbe, n2·Λrv) + min(n1·Fbs, n2·Λrv)·(nr - 1)]

Rbrg = 75.936 kips Vbm = 34.92 kips



(AISC 14th Ed. Specifications, Chapter J, Section J4.2, page 16.1-129)Description: Created By: GIZA™ 19

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Length,

L = (nr - 1)·s + 2·Lev L = 11.5 in


n1 = n



Rvy = 248.4 kips Vbm = 34.92 kips



b. Tensile Yielding Capacity due to Axial Load

Length,

L = (nr - 1)·s + 2·Lev L = 11.5 in

Gross Tension Area,

Ag = L·t


n1 = n


Rty = Λty·n1·Fy·Ag

Rty = 372.6 kips Hbm = 0 kips

Tensile Yielding Capacity > Applied Force, UCV = 0, OK

UCV = +

Interaction of Yielding Capacities,

+ ≤ 1.0VbmRvy

HbmRty

VbmRvy

Yielding Capacity > Applied Force, UCV = 0.02, OK

UCV = 0.02

2

22

HbmRty

2

3. Rupture Capacity


a. Shear Rupture Capacity due to Shear Load (Primary Side)

Net Shear Area,

Anv = (L - nr·hdv)·t

Anv = 4 in²


n1 = n


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Shear Rupture Capacity, (J4-4)

Rvr = Λvr·n1·0.6·Fu·Anv

Rvr = 208.8 kips Vbm = 34.92 kips

Shear Rupture Capacity > Applied Force, UCV = 0.167, OK



a. Block Shear Capacity due to Shear Load (Primary Side)

Reduction Factor,


Gross Shear Area,

Agv = [(nr - 1)·s + Lev]·t Agv = 5.125 in²

Net Tension Area,

Ant = [Leh + (nv - 1)·sv - (nv - 0.5)·hdh]·t

Ant = 0.484 in²

Net Shear Area,

Anv = Agv - [(nr - 0.5)·hdv]·t Anv = 3.594 in²


n1 = n



Rbs = 208.191 kips Vbm = 34.92 kips


I.D. BEAM CONNECTION ANGLE TO COLUMN WEB CHECK

1. Equivalent Tensile Force due to Moment Load in the Bolt Group

(AISC Eccentrically Loaded Bolt Groups, Eccentricity Normal to the Plane of theFaying Surface Case 1, pages 7-10 to 7-12)

Length of Connection Angle,

L = 11.5 in

4

Bolt Area,

Ab = 0.442 in²Ab =π·db2

Effective Width,

Weff = 8·t - tw Weff = 3.62 in

Actual Number of Bolts Under Tension,

nrt = 3

Location of Neutral Axis from the Bottom of Connection Angle,

ycg = 2.607 inDescription: Created By: GIZA™ 19

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ycg = 2.607 in

Distances of Bolts from the Centroid,

y1 = 7.643 in

y2 = 4.643 in

y3 = 1.643 in

y4 = -1.357 in

Moment of Inertia of Bolt Group in Tension,

Ixten = n·Ab·

nrt

i = 1

(y )2 73.037 in⁴Ixten =i

Outermost Bolt Location in Tension,

ymax = 7.643 in

3

Moment of Inertia of Compression Area,

Ixcomp =Weff·ycg3

21.39 in⁴Ixcomp =

Elastic Section Modulus at Bolt Group in Tension,

ymaxSxten =

Ixten + IxcompSxten = 12.355 in³

Elastic Section Modulus at Compression Area,

ycgSxcomp =

Ixten + IxcompSxcomp = 36.215 in³

Eccentricity Distance of Axial Load from Bolt Group Centerline,

Yo = 0.65 in

Equivalent Tensile Force Due to Moment Load,

SxtenTM =

Hbm·Yo·Ab TM = 0 kips



Shear Force per Bolt,

n·nb

VbmVB =

VB = 4.365 kips

Tension Force on Farthest Bolt,

n·nr

HbmTB = max , 0.001kip

TB = 0.001 kips

Combined Shear & Tension Capacity per Bolt (J3-3a, J3-3b),


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VB ≤ 0.3·Λrv ˅ TB ≤ 0.3·Λrn

ΛBv = Λrv ΛBv = 9.492 kips

Shear Capacity per Bolt (J3-5b, J3-5a),

Conn_type = Slip Critical-type

Code = LRFD

ΛRv = 1 -1.13·Tb

TBΛrv· ΛRv = 9.492 kips


Rb = ΛRv

Rb = 9.492 kips VB = 4.365 kips


3. Bolt Tensile Capacity with Prying of Angle


Combined Shear & Tension Capacity Per Bolt (J3-3a, J3-3b),

ΛB = Λrn

TB ≤ 0.3·Λrn ˅ VB ≤ 0.3·Λrv

ΛB = 29.821 kips

Conn_type = Slip Critical-Type

ΛRn = Λrn

ΛRn = 29.821 kips

Distance from First Bolt Centerline to the Centerline of Angle Leg,

b = g1 - 0.5·t b = 2.25 in

Distance of First Bolt Centerline to Edge of Angle Leg,

a1 = min[leg1 - (b + 0.5·t),1.25·b] a1 = 1.5 in

2

2

Tributary Length of Angle,

p = min(s, 2·b) p = 3 in

b' = b -db

b' = 1.875 in

a' = a +db

a' = 1.875 in

ρ =b'

a' ρ = 1

16δ = 1 -

db +1

in

pδ = 0.729


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4·ΛRn·b'

Λb·p·Futc =

0.5tc = 1.195 in

Required Thickness to Develop Bolt Strength,

α' =1

δ·(1 + ρ)·

tc

t

2

- 1 α' = 3.232

Allowable Tensile Force Per Bolt Considering Prying Action,

Nb1 = ΛRn· t

tc

2

· (1 + δ)

α' > 1.0

Nb1 = 9.026 kips

Minimum Thickness to Eliminate Prying Action,

t =4·TB·b'

Λb·p·Fu

t = 0.007 in t = 0.5 in

Consider Thick Connector Design

min

min

Allowable Tensile Force per Bolt without Prying Action,

Λb·p·Fu·t

4·b'Nb2 = min , ΛRn

2

Nb2 = 5.22 kips

Applicability of Prying,

t ≥ tmin ˅ Rwb < 10·Hbm

Prying = Not Applicable

Tensile Capacity Per Bolt,

Prying = Not Applicable

Nb = Nb2

Nb = 5.22 kips T = 0.001 kips

Bolt Tensile Capacity with Prying Action > Applied Force, UCV = 0, OK

B




t1 = 0.5 in

Column Web Thickness,

t2 = 0.55 in



s = 3 in

2Description: Created By: GIZA™ 19

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smin = 2 3

2·db smin = 2 in



smax = 12 in




Connection Angle Edge Distances,

Lev1 = 1.25 in

Leh1 = 1.5 in



Lev1Levcon = Levcon = 1.25 in

Levmin1 Levmin = 1Levmin =


in


1.125Lehmin1

1.5

Leh2



Lehcon =Leh1

Lehcon = NA



in

in




t1 = 0.5 in



Lemin = 1.25 in




0 0

Lemax = 6 in


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J. COLUMN WEB CHECK

1. Bolt Capacity


Bearing Area,

Abrg = db Abrg = 0.413 in²


Fbe = Λbrg·Fu·2.4·Abrg

Fbe = 48.263 kips

hdh < hdls(db)


hdh < hdls(db)

Fbs = 48.263 kips

Fbs = Λbrg·Fu·

1.2·(s - hdv)

1.2·(sv - hdh)

2.4·Abrg

Fbs = min(Fbs , Fbs )0 2


n1 = n

Connection Angle,

n2 = n

Bolt Capacity,

Rbrg = nv·[min(n1·Fbe, n2·ΛRv) + min(n1·Fbs, n2·ΛRv)·(nr - 1)]

Rbrg = 75.934 kips Vbm = 34.92 kips



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III. DETAILS

A. SKETCH

VERTICAL BRACE CONNECTION: WT BRACE (DIRECTLY BOLTED STEM TO GUSSET PLATE)WITH DOUBLE ANGLE (WELDED/BOLTED) TWO-WAY GUSSET PLATE CONNECTION TO W

BEAM AND W COLUMN WEB


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B. CONNECTION SCHEDULE

Column

A992W12X96

Mark Size Grade g

5 1/2"

Beam

gap

Web

Mark Size Grade Dθskθsl

W16X50 A992 1/2" 0° 0° 3"

Beam Connection Angle

2L4X4X1/2 4"2 1/2"

Lev leg1leg2g1GradeSize

1 1/4" 4"A36

Weld

3/16"

w1

Beam Loads

(Transfer Force) TF

0 kips15 kips

(Shear Load) V

StemBrace

WT6X9.5 59.32°

gap Levθ

(±2°)SizeMark Grade Dȳ

A992 1 5/8" NA 2" 1 1/2"

Bolts at WT Brace

3"23"

Remarks svnvsnrBolt Typedb

Oversized Holes inGusset Plate Only

6A325-SC-OVS-

CLASS A3/4"

Gusset Plate

w3

3/8" 2'-10 3/16"

Weld

2 1/4"

Grade

1 1/4"

y LwLev2 Lev1t

3"A36 1/4"


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Brace Loads

50 kips

(Tension Load) Pt

50 kips50 kips

(Compression Load) Pc (Maximum Axial Load) P

Gusset Connection Angle

2L4X4X1/2 4"2 1/2"

Lev leg1leg2g1GradeSize

1 1/4" 4"A36

Weld

3/16"

w2

Width of Whitmore Section Outside Gusset Plate

1/16"

Column Loads

0 kips0 kips

Uplift Force (PUplift)Moment(M)Axial(P)

0 kips·ft


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IV. REFERENCES

Steel Construction Manual (14th Ed.) - LRFD American Institute of Steel Construction,Inc. 2011

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Documents

VERTICAL BRACE CONNECTION: WT BRACE (DIRECTLY BOLTED … · 2019. 6. 10. · VERTICAL BRACE CONNECTION: WT BRACE (DIRECTLY BOLTED STEM TO GUSSET PLATE) WITH DOUBLE ANGLE (WELDED/BOLTED)