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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,
Minimum YieldStress,
Modulus ofElasticity,
Web Thickness,
Flange Thickness,
Distance k1,
Distance k (Design),
Minimum TensileStress,
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,
Minimum YieldStress,
Modulus ofElasticity,
Web Thickness,
Flange Thickness,
Distance k (Design),
Minimum TensileStress,
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
Minimum TensileStress,
Fu = 58 ksiMinimum YieldStress,
Modulus ofElasticity,
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
Minimum YieldStress,
Modulus ofElasticity,
Fy = 36 ksi
Fu = 58 ksi
E = 29000 ksi
Minimum TensileStress,
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
Minimum YieldStress,
Modulus ofElasticity,
Fy = 36 ksi
Fu = 58 ksi
E = 29000 ksi
Minimum TensileStress,
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,
Vertical HoleDimension,
Horizontal HoleDimension,
Horizontal HoleDimension,
Vertical EdgeDistance,
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,
Total Number ofBolts (nr·nv),
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,
Vertical HoleDimension,
hdv = 0.875 in
Horizontal HoleDimension,
hdh = 0.875 in
Bolt TensileStrength,
Connection Type,
Bolt HorizontalSpacing,
Holes at Connection Angle,
Λrn = 29.821 kips
Conn_type = SlipCritical
s = 3 in
sv = 0 in
Bolt VerticalSpacing,
Vertical HoleDimension,
hdv = 0.875 in
Horizontal HoleDimension,
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
Vertical EdgeDistance,
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,
Total Number ofBolts (nr·nv),
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,
Vertical HoleDimension,
hdv = 0.875 in
Horizontal HoleDimension,
hdh = 0.875 in
Bolt TensileStrength,
Connection Type,
Bolt HorizontalSpacing,
Holes at Connection Angle,
Λrn = 29.821 kips
Conn_type = SlipCritical
s = 3 in
sv = 0 in
Bolt VerticalSpacing,
Vertical HoleDimension,
hdv = 0.875 in
Horizontal HoleDimension,
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)
Block Shear Capacity, (J4-5)
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,
Minimum Bolt Spacing,
sv = 3 in
svmin = 2 3
2·db svmin = 2 in
svmax = min(12·in, 24·min(t1, t2))
Specified Bolt Spacing is acceptable, OK
svmax = 5.64 in
Maximum Bolt Spacing,
3. Check for Edge Distance
(AISC 14th Ed. Specifications, Chapter J, Section J3.4 and J3.5, pages 16.1-122 to 16.1-124)
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,
Connection Edge Distance,
Lehcon =Leh1
Lehcon = NA
Minimum Edge Distance,
Lehmin = Lehmin2 Lehmin = NA
in
in
Specified Edge Distance is Acceptable, OK
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
(AISC 14th Ed. Specifications, Chapter J, Section J3.10, pages 16.1-127 to 16.1-128)
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
Eccentric Load Coefficient,
(AISC 14th Ed. Manual Part 7, Instantaneous Center of Rotation Method, pages 7-6to 7-8)
C = 10.941
Load Inclination from Vertical,
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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)·t
2.4·Abrg
Fbe = 19.575 kips
Available Bearing Strength Using Bolt Spacing, (J3-6a, J3-6c)
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
Bolt Capacity > Applied Force, UCV = 0.566, OK
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
(AISC 14th Ed. Specifications, Chapter J, Section J4.1, page 16.1-128)
Width,
b = bwh b = 20.196 in
Gross Tension Area,
Ag = b·t
Number of Areas in Consideration,
n1 = n
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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
Number of Areas in Consideration,
n1 = n
Compression Capacity,
Rcb = Λc·n1·Fcr·Ag
Rcb = 231.684 kips Pc = 50 kips
Compression Capacity > Applied Force, UCV = 0.216, OK
5. Block Shear Capacity
(AISC 14th Ed. Specifications, Chapter J, Section J4.3, page 16.1-129)
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
Number of Areas in Consideration,
n1 = n
Block Shear Capacity, (J4-5)
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
Block Shear Capacity > Applied Force, UCV = 0.215, OK
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
1. Block Shear Capacity
(AISC 14th Ed. Specifications, Chapter J, Section J4.3, page 16.1-129)
a. Block Shear Capacity due to Shear Load
Reduction Factor,
Ubs = 1.0 (tension stress is uniform)
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
Number of Areas in Consideration,
n1 = 1
Block Shear Capacity, (J4-5)
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
Block Shear Capacity > Applied Force, UCV = 0.042, OK
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
Eccentric Load Coefficient,
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
Load Inclination from Vertical,
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
(AISC 14th Ed. Specifications, Chapter J, Section J3.10, pages 16.1-127 to 16.1-128)
a. Bolt Capacity due to Shear Load (Primary Side)
Bearing Area,
Abrg = db·t Abrg = 0.375 in²
Available Bearing Strength Using Edge Distance, (J3-6a, J3-6c)
hdh < hdls(db)
Fbe = Λbrg·Fu·min[1.2·(Lev - 0.5·hdv)·t, 2.4·Abrg]
Fbe = 21.206 kips
Available Bearing Strength Using Bolt Spacing, (J3-6a, J3-6c)
hdh < hdls(db)
Fbs = Λbrg·Fu·min[1.2·(s - hdv)·t, 2.4·Abrg]
Fbs = 39.15 kips
Number of Areas in Consideration,
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
Bolt Capacity > Applied Force, UCV = 0.074, OK
2. Yielding Capacity
(AISC 14th Ed. Specifications, Chapter J, Section J4.2, page 16.1-129)
a. Shear Yielding Capacity due to Shear Load
Length,
L = (nr - 1)·s + 2·Lev L = 11.5 in
Number of Areas in Consideration,
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
(AISC 14th Ed. Specifications, Chapter J, Section J4.2, page 16.1-129)
a. Shear Rupture Capacity due to Shear Load (Primary Side)
Net Shear Area,
Anv = (L - nr·hdv)·t
Anv = 4 in²
Number of Areas in Consideration,
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
4. Block Shear Capacity
(AISC 14th Ed. Specifications, Chapter J, Section J4.3, page 16.1-129)
a. Block Shear Capacity due to Shear Load (Primary Side)
Reduction Factor,
Ubs = 1.0 (tension stress is uniform)
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
Number of Areas in Consideration,
n1 = n
Block Shear Capacity, (J4-5)
Rbs = Λbs·n1·min(0.6·Fu·Anv + Ubs·Fu·Ant, 0.6·Fy·Agv + Ubs·Fu·Ant)
Rbs = 208.191 kips Vc = 5.592 kips
Block Shear Capacity > Applied Force, UCV = 0.027, OK
E.D. GUSSET CONNECTION ANGLE TO COLUMN WEB CHECK
1. Bolt Shear Capacity
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(AISC 14th Ed. Specifications, Chapter J, Section J3.6, page 16.1-125)
Shear Capacity Per Bolt,
Λrv = 9.492 kips
Bolt Shear Capacity,
Rb = n·nb·Λrv
Bolt Shear Capacity > Applied Force, UCV = 0.074, OK
Rb = 75.936 kips Vc = 5.592 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)
Connection Angle Thickness,
t1 = 0.5 in
Column Web Thickness,
t2 = 0.55 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 = 12 in
Maximum Bolt Spacing,
3. Check for Edge Distance
(AISC 14th Ed. Specifications, Chapter J, Section J3.4 and J3.5, pages 16.1-122 to 16.1-124)
Connection Angle Edge Distances,
Lev1 = 1.25 in
Leh1 = 1.5 in
i) Minimum Vertical Edge Distance,
Connection Edge Distance,
Lev1Levcon = Levcon = 1.25 in
Levmin1 Levmin = 1Levmin =
Minimum Edge Distance,
in
Specified Edge Distance is Acceptable, OK
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1.125Lehmin1
1.5
Leh2
ii) Minimum Horizontal Edge Distance,
Connection Edge Distance,
Lehcon =Leh1
Lehcon = NA
Minimum Edge Distance,
Lehmin = Lehmin2 Lehmin = NA
in
in
Specified Edge Distance is Acceptable, OK
iii) Maximum Edge Distance,
Connection Angle Thickness,
t1 = 0.5 in
Nearest Connection Edge Distance,
Lemin = min(Lehcon, Levcon)
Lemin = 1.25 in
Maximum Edge Distance,
Lemin = Levcon ˅ Lemin = Lehcon
Lemax = min(6in, 12·t1)
0 0
Lemax = 6 in
Maximum Edge Distance Requirement is Satisfied, OK
F. COLUMN WEB CHECK DUE TO GUSSET PLATE STRESSES
1. Bolt Capacity
(AISC 14th Ed. Specifications, Chapter J, Section J3.10, pages 16.1-127 to 16.1-128)
Bearing Area,
Abrg = db Abrg = 0.413 in²
Available Bearing Strength Using Edge Distance, (J3-6a, J3-6c)
Fbe = Λbrg·Fu·2.4·Abrg
Fbe = 48.263 kips
hdh < hdls(db)
Available Bearing Strength Using Bolt Spacing, (J3-6a, J3-6c)
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
Number of Areas in Consideration,
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
Bolt Capacity > Applied Force, UCV = 0.074, OK
G. GUSSET PLATE TO BEAM FLANGE CHECK
1. Forces Acting on Connection
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)
a. Using Fillet Weld
Number of Weld Sides,
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
Weld Capacity > Applied Force, UCV = 0.177, OK
G.A. GUSSET PLATE CHECK
1. Yielding Capacity
(AISC 14th Ed. Specifications, Chapter J, Section J4.2, page 16.1-129)
a. Shear Yielding Capacity due to Shear Load
Length,
L = Lw L = 34.187 in
Number of Areas in Consideration,
n1 = n
Shear Yielding Capacity, (J4-3)
Rvy = Λvy·n1·0.6·Fy·L·t
Rvy = 276.919 kips Hb = 43.002 kips
Shear Yielding Capacity > Applied Force, UCV = 0.155, OK
b. Tensile Yielding Capacity due to Axial Load
(AISC 14th Ed. Specifications, Chapter J, Section J4.1, page 16.1-128)
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
Tensile Yielding Capacity, (J4-1)
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
(AISC 14th Ed. Specifications, Chapter J, Section J10.2, page 16.1-134)
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
(AISC 14th Ed. Specifications, Chapter J, Section J10.3, pages 16.1-134 to 16.1-135)
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
1. Forces Acting on Connection
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
2. Block Shear Capacity
(AISC 14th Ed. Specifications, Chapter J, Section J4.3, page 16.1-129)
Reduction Factor,
Ubs = 1.0 (tension stress is uniform)
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
Number of Areas in Consideration,
n1 = 1
Block Shear Capacity, (J4-5)
Rbs = Λbs·n1·min(0.6·Fu·Anv + Ubs·Fu·Ant, 0.6·Fy·Agv + Ubs·Fu·Ant)
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)
a. Using Fillet Weld
Number of Weld Sides,
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
Eccentric Load Coefficient,
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
Load Inclination from Vertical,
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
Weld Capacity > Applied Force, UCV = 0.239, OK
I.C. BEAM CONNECTION ANGLE CHECK
1. Bolt Capacity
(AISC 14th Ed. Specifications, Chapter J, Section J3.10, pages 16.1-127 to 16.1-128)
a. Bolt Capacity due to Shear Load (Primary Side)
Bearing Area,
Abrg = db·t Abrg = 0.375 in²
Available Bearing Strength Using Edge Distance, (J3-6a, J3-6c)
hdh < hdls(db)
Fbe = Λbrg·Fu·min[1.2·(Lev - 0.5·hdv)·t, 2.4·Abrg]
Fbe = 21.206 kips
Available Bearing Strength Using Bolt Spacing, (J3-6a, J3-6c)
hdh < hdls(db)
Fbs = Λbrg·Fu·min[1.2·(s - hdv)·t, 2.4·Abrg]
Fbs = 39.15 kips
Number of Areas in Consideration,
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
Bolt Capacity > Applied Force, UCV = 0.46, OK
2. Yielding Capacity
(AISC 14th Ed. Specifications, Chapter J, Section J4.2, page 16.1-129)Description: Created By: GIZA™ 19
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(AISC 14th Ed. Specifications, Chapter J, Section J4.2, page 16.1-129)
a. Shear Yielding Capacity due to Shear Load
Length,
L = (nr - 1)·s + 2·Lev L = 11.5 in
Number of Areas in Consideration,
n1 = n
Shear Yielding Capacity, (J4-3)
Rvy = Λvy·n1·0.6·Fy·L·t
Rvy = 248.4 kips Vbm = 34.92 kips
Shear Yielding Capacity > Applied Force, UCV = 0.141, OK
(AISC 14th Ed. Specifications, Chapter J, Section J4.1, page 16.1-128)
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
Number of Areas in Consideration,
n1 = n
Tensile Yielding Capacity, (J4-1)
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
(AISC 14th Ed. Specifications, Chapter J, Section J4.2, page 16.1-129)
a. Shear Rupture Capacity due to Shear Load (Primary Side)
Net Shear Area,
Anv = (L - nr·hdv)·t
Anv = 4 in²
Number of Areas in Consideration,
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
4. Block Shear Capacity
(AISC 14th Ed. Specifications, Chapter J, Section J4.3, page 16.1-129)
a. Block Shear Capacity due to Shear Load (Primary Side)
Reduction Factor,
Ubs = 1.0 (tension stress is uniform)
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
Number of Areas in Consideration,
n1 = n
Block Shear Capacity, (J4-5)
Rbs = Λbs·n1·min(0.6·Fu·Anv + Ubs·Fu·Ant, 0.6·Fy·Agv + Ubs·Fu·Ant)
Rbs = 208.191 kips Vbm = 34.92 kips
Block Shear Capacity > Applied Force, UCV = 0.168, OK
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
2. Bolt Shear Capacity
(AISC 14th Ed. Specifications, Chapter J, Section J3.6, page 16.1-125)
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
Bolt Shear Capacity,
Rb = ΛRv
Rb = 9.492 kips VB = 4.365 kips
Bolt Shear Capacity > Applied Force, UCV = 0.46, OK
3. Bolt Tensile Capacity with Prying of Angle
(AISC 14th Ed. Specifications, Chapter J, Section J3.6, pages 16.1-125 to 16.1-126)
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
4. Check for Spacing
(AISC 14th Ed. Specifications, Chapter J, Section J3.3 and J3.5, pages 16.1-122 to 16.1-124)
Connection Angle Thickness,
t1 = 0.5 in
Column Web Thickness,
t2 = 0.55 in
a. Vertical Spacing,
Minimum Bolt Spacing,
s = 3 in
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smin = 2 3
2·db smin = 2 in
smax = min(12·in, 24·min(t1, t2))
Specified Bolt Spacing is acceptable, OK
smax = 12 in
Maximum Bolt Spacing,
5. Check for Edge Distance
(AISC 14th Ed. Specifications, Chapter J, Section J3.4 and J3.5, pages 16.1-122 to 16.1-124)
Connection Angle Edge Distances,
Lev1 = 1.25 in
Leh1 = 1.5 in
i) Minimum Vertical Edge Distance,
Connection Edge Distance,
Lev1Levcon = Levcon = 1.25 in
Levmin1 Levmin = 1Levmin =
Minimum Edge Distance,
in
Specified Edge Distance is Acceptable, OK
1.125Lehmin1
1.5
Leh2
ii) Minimum Horizontal Edge Distance,
Connection Edge Distance,
Lehcon =Leh1
Lehcon = NA
Minimum Edge Distance,
Lehmin = Lehmin2 Lehmin = NA
in
in
Specified Edge Distance is Acceptable, OK
iii) Maximum Edge Distance,
Connection Angle Thickness,
t1 = 0.5 in
Nearest Connection Edge Distance,
Lemin = min(Lehcon, Levcon)
Lemin = 1.25 in
Maximum Edge Distance,
Lemin = Levcon ˅ Lemin = Lehcon
Lemax = min(6in, 12·t1)
0 0
Lemax = 6 in
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Maximum Edge Distance Requirement is Satisfied, OK
J. COLUMN WEB CHECK
1. Bolt Capacity
(AISC 14th Ed. Specifications, Chapter J, Section J3.10, pages 16.1-127 to 16.1-128)
Bearing Area,
Abrg = db Abrg = 0.413 in²
Available Bearing Strength Using Edge Distance, (J3-6a, J3-6c)
Fbe = Λbrg·Fu·2.4·Abrg
Fbe = 48.263 kips
hdh < hdls(db)
Available Bearing Strength Using Bolt Spacing, (J3-6a, J3-6c)
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
Number of Areas in Consideration,
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
Bolt Capacity > Applied Force, UCV = 0.46, OK
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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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