moment connection: w beam (flange plate) with …

MOMENT CONNECTION: W BEAM (FLANGE PLATE) WITH SHEAR PLATE PERPENDICULARMOMENT CONNECTION TO W COLUMN FLANGE AND WEB TOP CONDITION

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

COLUMN PROPERTIES : W14X90 - A992

Depth,

Flange Width,

Distance k,

Area,

Minimum YieldStress,

Modulus ofElasticity,

Web Thickness,

Flange Thickness,

Distance k1,

Distance k (Design),

Minimum TensileStress,

d = 14 in

bf = 14.5 in

k = 2 in

Ag = 26.5 in²

Fy = 50 ksi

E = 29000 ksi

tw = 0.44 in

tf = 0.71 in

k1 = 1.438 in

kdes = 1.31 in

Fu = 65 ksi

BEAM 1 PROPERTIES : W16X57 - A992

Depth,

Flange Width,

Distance k,

Area,



Web Thickness,

Flange Thickness,

Distance k1,



d = 16.4 in

bf = 7.12 in

k = 1.375 in

Ag = 16.8 in²

Fy = 50 ksi

E = 29000 ksi

tw = 0.43 in

tf = 0.715 in

k1 = 0.875 in

kdes = 1.12 in

Fu = 65 ksi

Cut Distance fromWeb,

z = 0 in

Top of SteelElevation,

Gage, g = 3.5 inElev = 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,

BEAM 3 PROPERTIES : W16X57 - A992

Depth,

Flange Width,

Distance k,

Area,



Web Thickness,

Flange Thickness,

Distance k1,



d = 16.4 in

bf = 7.12 in

k = 1.375 in

Ag = 16.8 in²

Fy = 50 ksi

E = 29000 ksi

tw = 0.43 in

tf = 0.715 in

k1 = 0.875 in

kdes = 1.12 in

Fu = 65 ksi

Cut Distance fromWeb,

z = 0 in

Top of SteelElevation,

Gage, g = 3.5 inElev = 0 ft + 0 in

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

Skew, θsk = 0 degSlope, θsl = 0 degDescription: Created By: GIZA™ 19

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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,

SHEAR PLATE 1 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

SHEAR PLATE 3 PROPERTIES : A36


Fy = 36 ksi

E = 29000 ksi




Clip, c = 1.25 in

FLANGE PLATE 1 PROPERTIES : A572-50


Fy = 50 ksi

E = 29000 ksi




Clip, c = 0 in

FLANGE PLATE 3 PROPERTIES : A572-50


Fy = 50 ksi

E = 29000 ksi




Clip, c = 1.25 in

STIFFENER PLATE PROPERTIES : A36


Width, b = 7.03 in Length, L = 12.5 in

Fy = 36 ksi

E = 29000 ksi




Clip, c = 1.25 in


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DOUBLER PLATE PROPERTIES : A36


Fy = 36 ksi

E = 29000 ksi




Extension, x = 0 in

CAP PLATE PROPERTIES : A572-50


Fy = 50 ksi

E = 29000 ksi




Clear Distance fromColumn Edges,

clear = 0.75 in

BOLTS PROPERTIES : 3/4" - ø - A325-N

For Shear Plate 1 to Beam 1 Web Connection:

Bolt Diameter,

Bolt Shear Strength,

Bolt Type,

Number of Bolt Rows,

Bolt TensileStrength,

Connection Type,

Bolt VerticalSpacing,

db = 0.75 in

Λrv = 17.892 kips

Bolt_Type = A325-N

nr = 4

Λrn = 29.821 kips

Conn_type = BearingType

s = 3 in

Number of BoltColumn Lines,

Total Number ofBolts (nr·nv),

Bolt HorizontalSpacing,

nv = 1 sv = 0 in

nb = 4

Holes at Beam Web, Holes at Shear Plate,

Vertical HoleDimension,

Horizontal HoleDimension,



hdv = 0.875 in

hdh = 0.875 in

hdv = 0.875 in

hdh = 1.063 in

Bolt First Down fromTop of Beam,

D = 3.75 in

Vertical EdgeDistance (D - dcT),

Vertical EdgeDistance min(Lev1,Lev2),

Lev = 3.75 in Lev = 1.5 in

Horizontal EdgeDistance,


Leh = 1.75 in Leh = 1.5 in

BOLTS PROPERTIES : 3/4" - ø - A325-N

For Shear Plate 3 to Beam 3 Web Connection:


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Bolt Diameter,


Bolt Type,



Connection Type,


db = 0.75 in

Λrv = 17.892 kips

Bolt_Type = A325-N

nr = 4

Λrn = 29.821 kips

Conn_type = BearingType

s = 3 in

Number of BoltColumn Lines,

Total Number ofBolts (nr·nv),


nv = 1 sv = 0 in

nb = 4

Holes at Beam Web, Holes at Shear Plate,





hdv = 0.875 in

hdh = 0.875 in

hdv = 0.875 in

hdh = 1.063 in


D = 3.75 in

Vertical EdgeDistance (D - dcT),

Vertical EdgeDistance min(Lev1,Lev2),

Lev = 3.75 in Lev = 1.5 in



Leh = 1.75 in Leh = 1.5 in

BOLTS PROPERTIES : 1" - ø - A490-SC-OVS-CLASS A

For Flange Plate 1 to Beam 1 Flange Connection:

Bolt Diameter,


Bolt Type,



Connection Type,


db = 1 in

Λrv = 18.442 kips

Bolt_Type = A490-SC-OVS-CLASS A

nr = 6

Λrn = 66.562 kips

Conn_type = SlipCritical Type

s = 3 in

Number of BoltColumn Lines(Considering Half ofFlange Plate Width),

Total Number ofBolts 2·(nr·nv),


nv = 1 sv = 0 in

nb = 12

Holes at Beam Flange, Holes at Flange Plate,





hdv = 1.125 in

hdh = 1.125 in

hdv = 1.312 in

hdh = 1.312 in


D = 3.75 in


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Vertical EdgeDistance,


Lev = 1.5 in Lev = 1.5 in



Leh = 1.81 in Leh = 2 in

BOLTS PROPERTIES : 1" - ø - A490-SC-OVS-CLASS A

For Flange Plate 3 to Beam 3 Flange Connection:

Bolt Diameter,


Bolt Type,



Connection Type,


db = 1 in

Λrv = 18.442 kips

Bolt_Type = A490-SC-OVS-CLASS A

nr = 6

Λrn = 66.562 kips

Conn_type = SlipCritical Type

s = 3 in

Number of BoltColumn Lines(Considering Half ofFlange Plate Width),

Total Number ofBolts 2·(nr·nv),


nv = 1 sv = 0 in

nb = 12

Holes at Beam Flange, Holes at Flange Plate,





hdv = 1.125 in

hdh = 1.125 in

hdv = 1.312 in

hdh = 1.312 in


D = 3.75 in



Lev = 1.5 in Lev = 1.5 in



Leh = 1.81 in Leh = 1.75 in

WELDS PROPERTIES : E70xx LH

Minimum Tensile Stress, Fu = 70 ksi

For Flange Plate 1 to Column Flange Connection:

w = CJPPreferred Weld Size (w2),

For Flange Plate 3 to Column Flange Connection:

w = 0.25 inPreferred Weld Size (w10),

For Flange Plate 3 to Column Web Connection:



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For Shear Plate 1 to Column Flange Connection:


For Shear Plate 3 to Column Web Connection:


For Doubler Plate to Column Flange:

w = CJPPreferred Weld Size (w11),

For Doubler Plate to Column Web:


For Shear Plate 3 to Flange Plate Connection:



For Stiffener Plate to Column Flange Connection:


For Stiffener Plate to Column Web Connection:

For Cap Plate to Column Connection:

Preferred Weld Size (w14), w = 0.5 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),

Λbrg = 2.00 Λbrg = 0.75 Λbrg = 0.75

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

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

For Fillet WeldShear (vw),

Λvw = 2.00 Λvw = 0.75 Λvw = 0.75

For Flange LocalBending (fb),

Λfb = 1.67 Λfb = 0.90 Λfb = 0.90

For Flexural LocalBuckling/FlexuralStrength (b),

Λb = 1.67 Λb = 0.90 Λb = 0.90

For Partial Pen Weld- Tension (twp),

Λtwp = 1.88 Λtwp = 0.80 Λtwp = 0.80


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For Member Shear forC, WT, L(v),

Λv = 1.67 Λv = 0.90 Λv = 0.90

For Shear Rupture(vr),

Λvr = 2.00 Λvr = 0.75 Λvr = 0.75

For Shear Yielding(vy),

Λvy = 1.50 Λvy = 1.00 Λvy = 1.00

For Tension onBolts/CombinesTension & Shear inN-type Bolts(t),

Λt = 2.00 Λt = 0.75 Λt = 0.75

For Tension Rupture(tr),

Λtr = 2.00 Λtr = 0.75 Λtr = 0.75

For TensionYielding(ty),

Λty = 1.67 Λty = 0.90 Λty = 0.90

For Web CompressionBuckling (cb),

Λcb = 1.67 Λcb = 0.90 Λcb = 0.90

For WebCrippling(cr),

Λcr = 2.00 Λcr = 0.75 Λcr = 0.75

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

Λwy = 1.50 Λwy = 1.00 Λwy = 1.00

APPLIED LOADS:

Beam 1:

Given End Reaction

Shear Load, V = 50 kips

Axial Load, P = 20 kips

Moment Load, M = 230 kips·ft

Beam 3:

Given End Reaction

Shear Load, V = 40 kips

Adjacent Shear Load(if any),

V2 = 0 kips


Moment Load, M = 200 kips·ft

Column:


Story Shear, Vs = 0 kips Vs2 = 0 kipsat Strong Axis at Weak Axis


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II. CALCULATIONS

A. BEAM 1 FLANGE CHECK

1. Forces Acting on the Connection

At Beam Flange,

Ffbm = +P2

Md - tf

Ffbm = 185.964 kips

At Interface of Beam Flange & Flange Plate,

Ffbs = +P2

Md

Ffbs = 178.293 kips

At Flange Plate,

Ff = Ff = 170.933 kipsP2

Md + tfp

+

2. Bolt Capacity

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

Bearing Area,

Abrg = db·tf Abrg = 0.715 in²

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

hdh < hdls(db)

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

Fbe = 83.655 kips

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

hdh < hdls(db)

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

Fbs = 78.427 kips

Number of Areas in Consideration,

n1 = 1

Number of Flange Plate,

n2 = 1

Bearing Force,

min(Fbe, Fbs) > Λrv

Ffbrg = Ffbs

Ffbrg = 178.293 kips

Bolt Capacity,

Rbrg = 2·nv·[min(n1·Fbe, n2·Λrv) + min(n1·Fbs, n2·Λrv)·(nr - 1)]

Rbrg = 221.299 kips Ffbrg = 178.293 kips

Bolt Capacity > Applied Force, UCV = 0.806, OK


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3. Block Shear Capacity

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

Gross Shear Area,

Agv = 2·[(nr - 1)·s + Lev]·tf Agv = 26.097 in²

Net Shear Area,

Anv = 2·[(nr - 1)·s + Lev - (nr - 0.5)·hdv]·tf

Anv = 17.249 in²

Net Tension Area,

Ant = [2·Leh - (2·nv - 1)·hdh]·tf Ant = 1.784 in²


n1 = n

Reduction Factor,

Ubs = 1.0 (tension stress is uniform)

Block Shear Capacity,(J4-5)

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

Ffbm = 185.964 kips

Block Shear Capacity > Applied Force, UCV = 0.314, OK

Rbs = 591.511 kips

4. Beam Flexural Strength on Reduced Area without Reinforcement

(AISC 14th Ed. Specifications Chapter F, Section F13, page 16.1-64)

a. Gross Tension Flange Area

Afg = bf·tf Afg = 5.091 in²

b. Net Tension Area

Afn = Afg - (2·nv·hdh·tf) Afn = 3.482 in²

c. Value of Yt

Yt = 1.0Fy

Fu ≤ 0.8

Ix = 2

d. Section Modulus of Section

bf·tf

12

3+ bf·tf· d -tf

2

2+ tw·(d - 2tf)

12

3

Ix = 746.864 in⁴

Sx =Ix

0.5(d)

Sx = 92.2 in³

e. Revised Flexural Requirement Due to Axial Load

Mrev = M + 0.5·P·(d - tf) Mrev = 243.071 kips·ft


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Afg

Net Moment Capacity, (F13-1)

Λb·Fu·Afn·SxMn =

Mn = 307.436 kips·ft Mrev = 243.071 kips·ft

Net Moment Capacity > Applied Force, UCV = 0.791, OK

f. Tensile Rupture Capacity

B. BEAM 1 FLANGE TO FLANGE PLATE 1 CHECK

1. Bolt Shear Capacity


Shear Capacity Per Bolt,

Λrv = 18.442 kips

Bolt Shear Capacity,

Rb = n·nb·Λrv

Bolt Shear Capacity > Applied Force, UCV = 0.806, OK

Rb = 221.299 kips Ffbs = 178.293 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)

Flange Plate Thickness,

t1 = 0.75 in

Beam Flange Thickness,

t2 = 0.715 in

a. Vertical Spacing,

Minimum Bolt Spacing,

s = 3 in

smin = 2 3

2·db smin = 2.667 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


Flange Plate Edge Distances,

Lev1 = 1.5 in

Leh1 = 2 in

Beam Flange Edge Distances,


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Lev2 = 3.25 in

Leh2 = 1.81 in

i) Minimum Vertical Edge Distance,

Connection Edge Distance,

3.25Lev2

Lev1Levcon =

1.5Levcon = in

1.375Levmin1

Levmin2 Levmin = 1.25Levmin =

Minimum Edge Distance,

in

Specified Edge Distance is Acceptable, OK

1.375Lehmin1

2

Leh2

ii) Minimum Horizontal Edge Distance,


Lehcon =Leh1

Lehcon = 1.81


Lehmin = Lehmin2 Lehmin = 1.25

in

in


iii) Maximum Edge Distance,


t1 = 0.75 in


t2 = 0.715 in

Nearest Connection Edge Distance,

Lemin = min(Lehcon, Levcon)

Lemin = 1.5 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

C. FLANGE PLATE 1 CHECK

1. Bolt Capacity


Bearing Area,

Abrg = db·t Abrg = 0.75 in²Description: Created By: GIZA™ 19

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Abrg = db·t Abrg = 0.75 in²


hdh < hdls(db)

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

Fbe = 37.02 kips


hdh < hdls(db)

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

Fbs = 74.039 kips


n1 = 1


n2 = 1

Bolt Capacity,


Rbrg = 221.299 kips Ff = 170.933 kips




Flange Plate Width,

b = g + 2·(nv - 1)·sv + 2·Leh b = 7.5 in

Vertical Bolt Lines Check,

Number of vertical bolt lines is OK

Pattern 1

Reduction Factor,

Ubs = 1.0

Gross Shear Area,

Agv = 2·[(nr - 1)·s + Lev]·t Agv = 24.75 in²

Net Shear Area,

Anv = 2·[(nr - 1)·s + Lev - (nr - 0.5)·hdv]·t

Anv = 13.922 in²

Net Tension Area,

Ant = [(b - 2·Leh) - (2·nv - 1)·hdh]·t Ant = 1.641 in²


n1 = n


(tension stress is uniform)


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Rbs1 = Λbs·n1·min(0.6·Fu·Anv + Ubs·Fu·Ant, 0.6·Fy·Agv + Ubs·Fu·Ant)

Rbs1 = 487.195 kips Ff = 170.933 kips


Pattern 2

Gross Shear Area,


Net Shear Area,


Anv = 13.922 in²

Net Tension Area,

Ant = [2·Leh - (2·nv - 1)·hdh]·t Ant = 2.016 in²


n1 = n

Reduction Factor,




Ff = 170.933 kips


Rbs2 = 505.477 kips

Governing Block Shear Capacity,

Rbs = min(Rbs1, Rbs2)

Rbs = 487.195 kips Ff = 170.933 kips


3. Yielding Capacity


Width,

b = g + 2·(nv - 1)·sv + 2·Leh b = 7.5 in

Gross Tension Area,

Ag = b·t


n1 = n

Tensile Yielding Capacity, (J4-1)

Rty = Λty·n1·Fy·Ag

Rty = 253.125 kips Ff = 170.933 kips

Tensile Yielding Capacity > Applied Force, UCV = 0.675, OK


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4. Rupture Capacity


Effective Net Area,

Ae = min[(b - nv·hdh)·t, 0.85·b·t] Ae = 3.656 in²


n1 = n

Tensile Rupture Capacity, (J4-2)

Rtr = Λtr·n1·Fu·Ae

Rtr = 178.242 kips Ff = 170.933 kips

Tensile Rupture Capacity > Applied Force, UCV = 0.959, OK

5. 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

Beam Flange Vertical Edge Distance,

Le1 = 3.25 in

Laterally Unbraced Length,

Lu = gap + D Lu = 3.75 in

Column Flange Width,

b1 = bf

Gross Area,

Ag = min(b1, b)·t Ag = 5.625 in²

t

0.5

Radius of Gyration,

r = r = 0.217 in(12)

Slenderness Ratio,

KLr =K·Lur

KLr = 11.258

π ·E2

2

Elastic Critical Buckling Stress,

Fe =KLr

Fe = 2258.134 ksi

Flexural Buckling Stress,

Fcr = Fy

KLr ≤ 25

Fcr = 50 ksi


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n1 = n

Compression Capacity,

Rcb = Λc·n1·Fcr·Ag

Rcb = 253.125 kips Ff = 170.933 kips

Compression Capacity > Applied Force, UCV = 0.675, OK

D. FLANGE PLATE 1 TO COLUMN FLANGE CHECK

1. Weld Capacity

a. Using Complete-Joint-Penetration Groove Weld (TC-U4b-GF)

Minimum Thickness,

tmin = t wmin = 0.75 in

Column Minimum Tensile Stress,

Fy1 = 50 ksi

Flange Plate Minimum Tensile Stress,

Fy2 = 65 ksi

Length of Weld,

Lw = min(bf, bf1) Lw = 7.5 in

Weld Capacity,

Rw = ·Λty·min(Fy1, Fy2)·n1·Lw·min

Rw = 253.125 kips

CJP Weld Capacity > Applied Force, UCV = 0.675, OK

Ff = 170.933 kips


n1 = 1

E. BEAM 1 WEB CHECK

1. Bolt Capacity


Bearing Area,

Abrg = db·tw Abrg = 0.322 in²


hdh < hdls(db)

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

Fbe = 37.732 kips


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hdh < hdls(db)

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

Fbs = 37.732 kips


n1 = 1

Number of Shear Plate,

n2 = 1

Bolt Capacity,

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

Rbrg = 71.569 kips V = 50 kips


2. 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 = 14.16 in

Limiting Depth-Thickness Ratio,

htw = htw = 32.93

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 = 211.56 kips V = 50 kips

Shear Capacity of Section > Applied Force, UCV = 0.236, OK

F. BEAM 1 WEB TO SHEAR PLATE 1 CHECK




Λrv = 17.892 kips


Rb = n·nb·Λrv


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Rb = 71.569 kips V = 50 kips



Shear Plate Thickness,

t1 = 0.375 in

Beam Web Thickness,

t2 = 0.43 in



s = 3 in

smin = 2 3

2·db smin = 2 in



smax = 9 in




Shear Plate Edge Distances,

Lev1 = 1.5 in

Leh1 = 1.5 in

Beam Web Edge Distances,

Lev2 = NA

Leh2 = 1.75 in



Lev1Levcon = Levcon = 1.5 in

Levmin1 Levmin = 1Levmin =


in



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1.125Lehmin1

1.5

Leh2



Lehcon =Leh1

Lehcon = 1.75


Lehmin = Lehmin2 Lehmin = 1

in

in




t1 = 0.375 in

Beam Web Thickness,

t2 = 0.43 in



Lemin = 1.5 in




0 0

Lemax = 4.5 in


G. SHEAR PLATE 1 CHECK

1. Bolt Capacity


Bearing Area,



hdh < hdls(db)


Fbe = 20.798 kips



Fbs = 29.362 kips


n1 = n

hdh < hdls(db)


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n1 = n

Bolt Capacity,

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





Length,

L = (nr - 1)·s + 2·Lev L = 12 in


n1 = n

Shear Yielding Capacity, (J4-3)

Rvy = Λvy·n1·0.6·Fy·L·t

Rvy = 97.2 kips V = 50 kips

Shear Yielding Capacity > Applied Force, UCV = 0.514, OK

3. Rupture Capacity


a. Shear Rupture Capacity due to Shear Load

Anv = (L - nr·hdv)·t

Anv = 3.187 in²

Net Shear Area,


n1 = n

Shear Rupture Capacity, (J4-4)

Rvr = Λvr·n1·0.6·Fu·Anv

Rvr = 83.194 kips V = 50 kips

Shear Rupture Capacity > Applied Force, UCV = 0.601, OK



Reduction Factor,


Gross Shear Area,

Agv = [(nr - 1)·s + Lev]·t Agv = 3.938 in²

Net Tension Area,

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

Ant = 0.363 in²


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Net Shear Area,

Anv = Agv - [(nr - 0.5)·hdv]·t Anv = 2.789 in²


n1 = n

Block Shear Capacity, (J4-5)


Rbs = 79.59 kips V = 50 kips


H. SHEAR PLATE 1 TO COLUMN FLANGE 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)

Number of Weld Sides,

nws = 2

Minimum Weld Size,

wmin = 0.187 in w = 0.25 in

Preferred Weld Size > Minimum Weld Size, OK

a. Using Fillet Weld

Shear Strength,

For Column,

Rv1 = Λvr·0.6.Fu·tf·nws Rv1 = 25.74 kips/in

For Shear Plate,

Number of Plates,

n1 = n

Rv2 = Λvr·Fu·t·n1 Rv2 = 9.787 kips/in

Rv3 = Λvw·0.6·Fu·sin(45deg)·nws

For Weld,

Rv3 = 44.548 ksi

Maximum Effective Weld Size,

weff =min(Rv1, Rv2)

Rv3 weff = 0.22 in

Length of Weld,

Lw = (nr - 1)·s + 2·Lev Lw = 12 in

Weld Capacity,

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

Rw = 117.45 kips V = 50 kips

Weld Capacity > Applied Force, UCV = 0.426, OK


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I. FLANGE PLATE 1 TO COLUMN CHECK

1. Weld Capacity

a. Flange Plate to Column Flange Using Complete-Joint-Penetration Groove Weld

Flange Plate,

Fy1 = 65 ksi

Column,

Fy2 = 65 ksi

Doubler Plate,

Fy3 = 58 ksi

Length of Weld,

Lw = 7.5 in

Complete Penetration Groove Weld Tension Capacity,

Rwcpt = min(Λtr·Fu1,,0.6·Λvwp·Fu)Lw·tE

Rwcpt = 253.125 kips Ffy = 170.933 kips

Complete Penetration Groove Weld Shear Capacity,

Rwcps = Λvy·0.6·min(Fy1, Fy2)·Lw·t)

Rwcps = 168.75 kips Ffx = 170.933 kips

Ffy

Interaction Equation For Complete Penetration Weld Capacity,

+ ≤ 1.0Rwcpt

Ffx

Rwcps

22

IQcpf = +Ffy

Rwcpt

Ffx

Rwcps

22


IQcpf = 0.675


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A. BEAM 3 FLANGE CHECK


At Beam Flange,

Ffbm = +P2

Md - tf

Ffbm = 163.012 kips

At Interface of Beam Flange & Flange Plate,

Ffbs = +P2

Md

Ffbs = 156.341 kips

At Flange Plate,

Ff = Ff = 149.942 kipsP2

Md + tfp

+

2. Bolt Capacity


Bearing Area,

Abrg = db·tf Abrg = 0.715 in²


hdh < hdls(db)

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

Fbe = 83.655 kips


hdh < hdls(db)

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

Fbs = 78.427 kips


n1 = 1


n2 = 1

Bearing Force,

min(Fbe, Fbs) > Λrv

Ffbrg = Ffbs

Ffbrg = 156.341 kips

Bolt Capacity,


Rbrg = 221.299 kips Ffbrg = 156.341 kips





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Gross Shear Area,

Agv = 2·[(nr - 1)·s + Lev]·tf Agv = 26.097 in²

Net Shear Area,

Anv = 2·[(nr - 1)·s + Lev - (nr - 0.5)·hdv]·tf

Anv = 17.249 in²

Net Tension Area,

Ant = [2·Leh - (2·nv - 1)·hdh]·tf Ant = 1.784 in²


n1 = n

Reduction Factor,




Ffbm = 163.012 kips


Rbs = 591.511 kips

4. Beam Flexural Strength on Reduced Area without Reinforcement

(AISC 14th Ed. Specifications Chapter F, Section F13, page 16.1-64)

a. Gross Tension Flange Area

Afg = bf·tf Afg = 5.091 in²

b. Net Tension Area

Afn = Afg - (2·nv·hdh·tf) Afn = 3.482 in²

c. Value of Yt

Yt = 1.0Fy

Fu ≤ 0.8

Ix = 2

d. Section Modulus of Section

bf·tf

12

3+ bf·tf· d -tf

2

2+ tw·(d - 2tf)

12

3

Ix = 746.864 in⁴

Sx =Ix

0.5(d)

Sx = 92.2 in³

e. Revised Flexural Requirement Due to Axial Load

Mrev = M + 0.5·P·(d - tf) Mrev = 213.071 kips·ft


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Afg

Net Moment Capacity, (F13-1)

Λb·Fu·Afn·SxMn =

Mn = 307.436 kips·ft Mrev = 213.071 kips·ft

Net Moment Capacity > Applied Force, UCV = 0.693, OK

f. Tensile Rupture Capacity

B. BEAM 3 FLANGE TO FLANGE PLATE 3 CHECK




Λrv = 18.442 kips


Rb = n·nb·Λrv


Rb = 221.299 kips Ffbs = 156.341 kips




t1 = 0.75 in


t2 = 0.715 in



s = 3 in

smin = 2 3

2·db smin = 2.667 in



smax = 12 in




Flange Plate Edge Distances,

Lev1 = 1.5 in

Leh1 = 1.75 in

Beam Flange Edge Distances,


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Lev2 = 3.25 in

Leh2 = 1.81 in



3.25Lev2

Lev1Levcon =

1.5Levcon = in

1.375Levmin1

Levmin2 Levmin = 1.25Levmin =


in


1.375Lehmin1

1.75

Leh2



Lehcon =Leh1

Lehcon = 1.81


Lehmin = Lehmin2 Lehmin = 1.25

in

in




t1 = 0.75 in


t2 = 0.715 in



Lemin = 1.5 in




0 0

Lemax = 6 in


C. FLANGE PLATE 3 CHECK

1. Bolt Capacity


Bearing Area,

Abrg = db·t Abrg = 0.75 in²Description: Created By: GIZA™ 19

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hdh < hdls(db)


Fbe = 37.02 kips


hdh < hdls(db)


Fbs = 74.039 kips


n1 = 1


n2 = 1

Bolt Capacity,


Rbrg = 221.299 kips Ff = 149.942 kips




Flange Plate Width,

b = g + 2·(nv - 1)·sv + 2·Leh b = 7 in

Vertical Bolt Lines Check,

Number of vertical bolt lines is OK

Pattern 1

Reduction Factor,

Ubs = 1.0

Gross Shear Area,


Net Shear Area,


Anv = 13.922 in²

Net Tension Area,

Ant = [(b - 2·Leh) - (2·nv - 1)·hdh]·t Ant = 1.641 in²


n1 = n


(tension stress is uniform)


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Rbs1 = 487.195 kips Ff = 149.942 kips


Pattern 2

Gross Shear Area,


Net Shear Area,


Anv = 13.922 in²

Net Tension Area,

Ant = [2·Leh - (2·nv - 1)·hdh]·t Ant = 1.641 in²


n1 = n

Reduction Factor,




Ff = 149.942 kips


Rbs2 = 487.195 kips

Governing Block Shear Capacity,

Rbs = min(Rbs1, Rbs2)

Rbs = 487.195 kips Ff = 149.942 kips




Width,

b = g + 2·(nv - 1)·sv + 2·Leh b = 7 in

Gross Tension Area,

Ag = b·t


n1 = n

Tensile Yielding Capacity, (J4-1)

Rty = Λty·n1·Fy·Ag

Rty = 236.25 kips Ff = 149.942 kips

Tensile Yielding Capacity > Applied Force, UCV = 0.635, OK


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4. Rupture Capacity


Effective Net Area,

Ae = min[(b - nv·hdh)·t, 0.85·b·t] Ae = 3.281 in²


n1 = n

Tensile Rupture Capacity, (J4-2)

Rtr = Λtr·n1·Fu·Ae

Rtr = 159.961 kips Ff = 149.942 kips

Tensile Rupture Capacity > Applied Force, UCV = 0.937, OK

5. 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

Beam Flange Vertical Edge Distance,

Le1 = 3.25 in

Laterally Unbraced Length,

Lu = gap + D Lu = 3.75 in

Column Flange Width,

b1 = bf

Gross Area,

Ag = min(b1, b)·t Ag = 5.25 in²

t

0.5

Radius of Gyration,

r = r = 0.217 in(12)

Slenderness Ratio,

KLr =K·Lur

KLr = 11.258

π ·E2

2

Elastic Critical Buckling Stress,

Fe =KLr

Fe = 2258.134 ksi

Flexural Buckling Stress,

Fcr = Fy

KLr ≤ 25

Fcr = 50 ksi


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n1 = n

Compression Capacity,

Rcb = Λc·n1·Fcr·Ag

Rcb = 236.25 kips Ff = 149.942 kips

Compression Capacity > Applied Force, UCV = 0.635, OK

D. BEAM 3 WEB CHECK

1. Bolt Capacity


Bearing Area,

Abrg = db·tw Abrg = 0.322 in²


hdh < hdls(db)

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

Fbe = 37.732 kips


hdh < hdls(db)

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

Fbs = 37.732 kips


n1 = 1

Number of Shear Plate,

n2 = 1

Bolt Capacity,

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



2. Shear Capacity


tw

h

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

h = d - 2·kdes h = 14.16 in

Limiting Depth-Thickness Ratio,

htw = htw = 32.93

Clear Distance Between Transverse Stiffeners,

htw < 260 a = 0 in


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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 = 211.56 kips V = 40 kips

Shear Capacity of Section > Applied Force, UCV = 0.189, OK

E. BEAM 3 WEB TO SHEAR PLATE 3 CHECK




Λrv = 17.892 kips


Rb = n·nb·Λrv


Rb = 71.569 kips V = 40 kips




t1 = 0.375 in

Beam Web Thickness,

t2 = 0.43 in



s = 3 in

smin = 2 3

2·db smin = 2 in



smax = 9 in




Shear Plate Edge Distances,

Lev1 = 1.5 inDescription: Created By: GIZA™ 19

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Lev1 = 1.5 in

Leh1 = 1.5 in

Beam Web Edge Distances,

Lev2 = NA

Leh2 = 1.75 in



Lev1Levcon = Levcon = 1.5 in

Levmin1 Levmin = 1Levmin =


in


1.125Lehmin1

1.5

Leh2



Lehcon =Leh1

Lehcon = 1.75


Lehmin = Lehmin2 Lehmin = 1

in

in




t1 = 0.375 in

Beam Web Thickness,

t2 = 0.43 in



Lemin = 1.5 in




0 0

Lemax = 4.5 in


F. SHEAR PLATE 3 CHECK

1. Bolt Capacity



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Bearing Area,



hdh < hdls(db)


Fbe = 20.798 kips



Fbs = 29.362 kips


n1 = n

hdh < hdls(db)

Bolt Capacity,

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





Length,

L = (nr - 1)·s + 2·Lev L = 12 in


n1 = n

Shear Yielding Capacity, (J4-3)

Rvy = Λvy·n1·0.6·Fy·L·t

Rvy = 97.2 kips V = 40 kips

Shear Yielding Capacity > Applied Force, UCV = 0.412, OK

3. Rupture Capacity


a. Shear Rupture Capacity due to Shear Load

Anv = (L - nr·hdv)·t

Anv = 3.187 in²

Net Shear Area,


n1 = n

Shear Rupture Capacity, (J4-4)


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Rvr = Λvr·n1·0.6·Fu·Anv

Rvr = 83.194 kips V = 40 kips

Shear Rupture Capacity > Applied Force, UCV = 0.481, OK



Reduction Factor,


Gross Shear Area,

Agv = [(nr - 1)·s + Lev]·t Agv = 3.938 in²

Net Tension Area,

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

Ant = 0.363 in²

Net Shear Area,

Anv = Agv - [(nr - 0.5)·hdv]·t Anv = 2.789 in²


n1 = n

Block Shear Capacity, (J4-5)


Rbs = 79.59 kips V = 40 kips


G. SHEAR PLATE 3 TO COLUMN WEB CHECK

1. Weld Capacity


(AISC 14th Ed. Manual, Part 10, page 10-102)



nws = 2

Minimum Weld Size,

wmin = 0.125 in w = 0.25 in


H. SHEAR PLATE 3 TO FLANGE/CAP PLATE 3 CHECK


Eccentricity,

e = 0.5·(bf - tw) + gap + Leh + 0.5·(nv - 1)·sv

e = 9.28 in


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Shear Force,

Vpl =d

V·eVpl = 22.634 kips

2. Weld Capacity


(AISC 14th Ed. Manual, Part 10, page 10-102)



nws = 2

Minimum Weld Size,

wmin = 0.187 in w = 0.25 in


Shear Strength,

For Flange Plate,

Rv1 = Λvr·0.6·Fu·t·nws Rv1 = 43.875 kips/in

For Shear Plate,

Number of Plates,

Rv2 = Λvr·0.6·Fu·t·n1

n1 = n

Rv2 = 9.787 kips/in

Rv3 = 44.548 ksi

For Weld,

Rv3 = Λvw·0.6·Fu·sin(45deg)·nws


weff = weff = 0.22 inmin(Rv1, Rv2)

Rv3

Length of Weld,

Lw = 0.5·(bf - tw) - c Lw = 5.78 in

Weld Capacity,

Rw = Λvw·0.6·Fu·sin(45deg)·nws·n1·Lw·min(w, weff)

Rw = 56.572 kips Vpl = 22.634 kips



n1 = n

I. CAP PLATE TO COLUMN CHECK


Flange Force of Beam 3,

Ff1 = 170.933 kips

Flange Force of Beam 1,Description: Created By: GIZA™ 19

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Ffw = Ff1

Fff = Ff2

Flange Force of Beam 1,

Ff2 = 149.942 kips

Shear Force onColumn Flange,

Fff = 149.942 kips

Shear Force onColumn Web,

Ffw = 170.933 kips

2. Weld Capacity


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

Flange Plate 1 Minimum Tensile Stress,

Fu1 = 65 ksi

Flange Plate 3 Minimum Tensile Stress,

Fu2 = 65 ksi

Minimum Tensile Stress,

Fu = min(Fu1, Fu2)

a. Top Cap Plate to Column Flange Connection Using Fillet Weld

Minimum Weld Size,

wmin = 0.187 in w = 0.5 in


No. of Weld side,

nws = 2

Shear Strength,

For Column:

Rv1 = Λvr·0.6·Fu·tf Rv1 = 20.767 kips/in

For Cap Plate:

Rv2 = Λvr·0.6·Fu·t·nws Rv2 = 43.875 kips/in

For Weld:

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

Maximum effective weld size,

weffL = min(Rv1, Rv2)Rv3

WeffL = 0.466 in

Length of Weld,

LwL = bf + (bf - 2·k1) LwL = 26.125 in

Weld Capacity,

Rwcpl = Λvw·0.6·Fu3·sin(45deg)·nws·min(w, weff)·LwL

Rwcpl = 542.551 kips Fff = 149.942 kips


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b. Top Cap Plate to Column Web Connection Using Fillet Weld

No. of Weld side,

nws = 2

Minimum Weld Size,

wmin = 0.187 in w = 0.5 in


Shear Strength,

For Column:

Rv1 = Λvr·0.6·Fu·tw Rv1 = 12.87 kips/in

For Cap Plate:

Rv2 = Λtr·Fu·t·nws Rv2 = 43.875 kips/in

For Weld:

Rv3 = Λvw·1.5·0.6·Fu·sin(45deg)·nws Rv3 = 44.548 ksi

Maximum effective weld size,

weffT =min(Rv1, Rv2)

Rv3weffT = 0.289 in

Length of Weld,

LwT = d - 2·k LwT = 17.89 in

Weld Capacity,

Rwcpt = Λvw·1.5·0.6·Fu·sin(45deg)·nws·min(w, weff)·LwT

Rwcpt = 230.244 kips Ffw = 170.933 kips


J. COLUMN FLANGE CHECK

1. Flange Local Bending

(AISC 14th Ed. Specifications Chapter J, Section J10.1, page 16.1-133)

Local Bending Capacity (J10-1),

Rfb = Λfb·6.25·tf²·Fy

Please refer to Design of Stiffener/Flange Plate, OK

Rfb = 141.778 kips Ff = 170.933 kips

2. Flange Panel Zone Shear

(AISC 14th Ed. Chapter J, Specifications Section J10.6, page 16.1-136 to 137)

Force Acting on the Flange Panel Zone,

Vpz = minΛb·Fy·Zy

d + t- Vs2

M

d + t,


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Vpz = 139.942 kips

Column Strength,

Pc = 1325 kips

Pc = Fy·Ag

Code = "LRFD"

Flange Panel Zone Shear Capacity (J10-9,J10-10),

P > 0.40·Pc

Rvz = 1.4P

Pc-Λv·0.6·Fy·bf·tf·2·

Rvz = 526.56 kips Vpz = 139.942 kips

Column Flange Panel Zone Shear Capacity > Applied Force, UCV = 0.266, OK

K. COLUMN WEB CHECK

1. Web Local Yielding Capacity


Bearing Length,

N = t N = 0.75 in

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

Rwy = Λwy·Fy·tw·(N + 5·kdes)

Rwy = 160.6 kips Ff = 170.933 kips


2. Web Local Crippling Capacity


Bearing Length,

N = 0.75 inN = L

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

Esq =E·Fy·tf

tw

0.5

Esq = 1529.632 ksi

N1 = 1 + 3N

d·

tw

tf

1.5

N1 = 1.078·

De ≥d

2

Rwc = Λcr·0.8·tw²·N1·Esq

Rwc = 191.613 kips Ff = 170.933 kips


3. Web Panel Zone Shear

(AISC 14th Ed, Chapter J, Specifications Section J10.6, pages 16.1-136 to 137)Description: Created By: GIZA™ 19

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(AISC 14th Ed, Chapter J, Specifications Section J10.6, pages 16.1-136 to 137)

Force Acting on the Web Panel Zone,

Vpz = min M

d + t d + t

2·Λb·Fy·Zx, - Vs

Vpz = 160.933 kips

Pc = Fy·Ag

Code = LRFD

Pc = 1325 kips

Column Strength,

Web Panel Zone Shear Capacity (J10-9,J10-10),

Rvz = Λv·0.6·Fy·d·tw· 1.4 -P

Pc

P > 0.40·Pc

Please refer to Design of Doubler Plate, OK

Rvz = 157.533 kips Vpz = 160.933 kips

4. Shear Buckling of Column Web

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

Minimum Thickness of Column Web based on shear buckling (G2-1),

d - 2·kdes2.24twm =

0.5FyE

twm = 0.211 in tw = 0.44 in

·

Shear Buckling will not control, OK

Clear distance between flanges of column, less the fillet or corner radii,

h = d - 2·kdes h = 11.38 in

Limiting depth-thickness ratio,

htw = htw = 25.864htw

Clear distance between transverse stiffeners,

a = 0 in

htw < 260

Web plate buckling coefficient,

kv = 5

htw ≤ 260


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Web shear coefficient,

≤ 1.1·

0.5kv·EFy

Cv = 1

htw

Λvcol = Λvy

≤ 2.24·

0.5EFy

htw

Λvcol = 1

Shear Buckling Capacity,

Rvcol = Λvcol·0.6·Fy·Cv·tw·d

Rvcol = 184.8 kips Vpz = 160.933 kips

Shear Buckling Capacity need not be checked

L. REINFORCEMENT DESIGN FORCES

1. Flange Plate Design Force

Due to Tensile Actiona)

Fstt = max(Ff1 - min(Rwy, Rfb), 0kips)

Lwf ≥ 0.15· bf

Fstt = 29.155 kips

Fstc = max(Ff1 - min(Rwy, Rwc) , 0kips) Fstc = 10.333 kips

Flange Plate Design Force at Column Flange,

Fst = max(Fstt, Fstc) Fst = 29.155 kips

Flange Plate Design Force at Column Web,

Fstw = Fst Fstw = 29.155 kips

Due to Compressive Actionb)

Force Distribution at Column Flange

Due to Strong Axis Connection,

Ffy = Fst2

Ffy = 14.577 kips

Due to Weak Axis Connection,

c)

4Ffx =

Ff2

Resultant Force,

Ffx = 37.485 kips

Ffx + FfyFffp = Fffp = 40.22 kips2 2


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Force Distribution at Column Web


Fwy = Fstw2

Fwy = 14.577 kips


d)

2

Ff2Fwx = Fwx = 74.971 kips

Resultant Force,

Fwfp = Fwfp = 76.375 kipsFwx + Fwy2 2

2. Doubler Plate Design Force

Required Strength for Doubler Plate,

tw ≥ twm

Vudp = max(Vpz - Rvz, 0kips) Vudp = 3.4 kips

Total Panel Zone Thickness,

tpz = tw tpz = 0.44 in

M. FLANGE PLATE 3 CHECK DUE TO COMBINED FORCES

1. Width of Stiffeners

(AISC 14th Ed, Specifications Chapter J, Section J10.8, page 16.1-138)

(Steel Design Guide Series 13, Chapter 4, Section 4.3.1, page 22)

Thickness of Doubler Plate,

t = 0.375 in

Width of Primary Flange,

bf = 14.5 in

tpz2

bmin = -Lwf3

Minimum Width of Stiffener Plates

bmin = 2.28 in

a.

Maximum Width of Stiffener Plates

bmax = 0.5·(bf - tw) - t bmax = 7.03 in

b.

Width of Stiffener Plates

b = 7 in

b = Floor min(max(bmin, bgiv), bmax),18

in

2. Length of Stiffeners




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2

d

a. Minimum Length of Stiffener Plates

Lmin = Lmin = 7 in

b. Maximum Length of Stiffener Plates

Lmax = d - 2·tf Lmax = 12.58 in

Length of Stiffener Plates

Lst = Floor1

8min(max(Lmin, Lgiv), Lmax), in

Lst = 12.5 in

3. Thickness of Stiffeners

Minimum Thickness of Stiffener Plate,

(AISC Specifications 14th Ed, Chapter J, Section J10.8, page 16.1-138)


16

btf

2tmin = max ,

tmin = 0.438 in t = 0.75 in

Provided Thickness > Minimum Thickness, OK


(AISC 14th Ed. Specifications, Chapter J, Section J4.1&2, page 16.1-128&129)

a)

Tension Capacity,

Rtyfpf = Λty·Fy·t·(b - c)

Rtyfpf = 195.075 kips Ffy = 14.577 kips

Shear Yielding,

Rvyfpf = Λvy·0.6·Fy·t·(b - c)

Rvyfpf = 130.05 kips Ffx = 37.485 kips

At Column Flange

Interaction at Column Flange,

Iycf = 0.089

Ffy

Rtyfpf+

2

Iycf =

≤ 1.0

Yielding Capacity > Applied Force, UCV = 0.089, OK

Ffx

Rvyfpf

2

Ffy

Rtyfpf+

2Ffx

Rvyfpf

2

b)

Tension Capacity,

At Column Web

Rtyfpw = Λty·Fy·t·(L - 2·c)Description: Created By: GIZA™ 19

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Rtyfpw = Λty·Fy·t·(L - 2·c)

Rtyfpw = 340.2 kips Fwx = 74.971 kips

Shear Yielding,

Rvyfpw = 225 kips Fwy = 14.577 kips

Rvyfpw = Λvy·0.6·Fy·t·(L - 2·c)

Interaction at Column Web,

Iycw = 0.053


Fwx

Rtyfpw+

2

Iycw =

≤ 1.0

Fwy

Rvyfpw

2

Fwx

Rtyfpw+

2Fwy

Rvyfpw

2

5. Bearing Capacity

(AISC 14th Ed. Specifications, Chapter J, Section J7, pages 16.1-131)

a. At Column Flange

Bearing Capacity, (J7-1)

Rcb = 1.8·Λbrg·Fy·t·2·(b - c)

Rcb = 582.187 kips Fstc = 10.333 kips

Bearing Capacity > Applied Force, UCV = 0.018, OK

b. At Column Web


Rcb = 1.8·Λbrg·Fy·t·(L - 2·c)

Rcb = 506.25 kips Fwx = 74.971 kips


N. FLANGE PLATE 3 TO COLUMN CHECK

1. Weld Capacity

a. Flange Plate to Column Flange Connection Using Fillet Weld


Minimum Weld Size,

wmin = 0.25 in w = 0.25 in

Preferred Weld Size = Minimum Weld Size, OK


nws = 2

Shear Strength,

For Column Flange,

Rv1 = Λvr·0.6·Fu·tf·nws Rv1 = 41.535 kips/inDescription: Created By: GIZA™ 19

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Rv1 = Λvr·0.6·Fu·tf·nws Rv1 = 41.535 kips/in

For Flange Plate,

Rv2 = Λvr·0.60·Fu·t Rv2 = 21.937 kips/in

Effective Load Angle Factor,

θf = atanFfx

Ffyθf = 21.25 deg

μf = 1.0 + 0.50·sin(θ)1.5

μf = 1.109

For Weld,

Rv3 = μf·Λvw·0.6·Fu·sin(45deg)·nws Rv3 = 49.408 ksi

Rv3

min(Rv1, Rv2)


weff = weff = 0.444 in

Length of Weld,

Lw = b - c Lw = 5.78 in

Weld Capacity,

Rw = μf·Λvw·0.6·Fu·sin(45deg)·nws·n1·Lw·min(w, weff)

Rw = 71.394 kips Fffp = 40.22 kips


b. Flange Plate to Column Web Connection Using Fillet Weld


Minimum Weld Size,

wmin = 0.187 in w = 0.25 in



nws = 2

Shear Strength,

For Column Web,

Rv4 = Λvr·0.6·Fu·tw·nws Rv4 = 25.74 kips/in

Doubler Plate Thickness,

t1 = 0.375 in


t = 0.75 in

For Doubler Plate,

Rv8 = Λvr·0.6·Fu·t1·nws Rv8 = 0 kips/in

For Flange Plate,



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1.5


θw = atanFwy

Fwxθw = 78.997 deg

μw = 1.0 + 0.50·sin(θ) μw = 1.486

Fwy > 0kips

For Weld,

Rv6 = μw·Λvw·0.6·Fu·sin(45deg)·nws·1.5 Rv6 = 66.21 ksi

Rv6

min(0.5·Rv4, Rv5)



Fwy > 0kips

Length of Weld,

Lw = L - 2c Lw = 10 in

Weld Capacity,

Rw = μw·Λvw·0.6·Fu·sin(45deg)·nws·n1·Lw·min(w, weff)·1.5

Rw = 128.7 kips Fwfp = 76.375 kips


O. STIFFENER PLATE CHECK

1. Stiffener Plate Design Force

Due to Tensile Actiona)

Fstt = max(Ff1 - min(Rwy, Rfb), 0kips)

Lwf ≥ 0.15· bf

Fstt = 29.155 kips

Fstc = max(Ff1 - min(Rwy, Rwc) , 0kips) Fstc = 10.333 kips

Stiffener Plate Design Force at Column Flange,

Fst = max(Fstt, Fstc) Fst = 29.155 kips

Stiffener Plate Design Force at Column Web,

Fstw = Fst Fstw = 29.155 kips

Due to Compressive Actionb)

Force Distribution at Column Flange


Ffy = Fst2

Ffy = 14.577 kips


c)


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4Ffx =

Ff2

Resultant Force,

Ffx = 37.485 kips

Ffx + FfyFfst = Ffst = 40.22 kips2 2

Force Distribution at Column Web


Fwy = Fstw2

Fwy = 14.577 kips


d)

2

Ff2Fwx = Fwx = 74.971 kips

Resultant Force,

Fwst = Fwst = 76.375 kipsFwx + Fwy2 2

2. Width of Stiffeners



Thickness of Doubler Plate,

t = 0.375 in

Width of Primary Flange,

bf = 14.5 in

tpz2

bmin = -Lwf3

Minimum Width of Stiffener Plates

bmin = 2.28 in

a.

Maximum Width of Stiffener Plates

bmax = 0.5·(bf - tw) - t bmax = 7.03 in

b.

Width of Stiffener Plates

b = 7 in

b = Floor min(max(bmin, bgiv), bmax),18

in

3. Length of Stiffeners



2

d

a. Minimum Length of Stiffener Plates

Lmin = Lmin = 7 in

b. Maximum Length of Stiffener Plates

Lmax = d - 2·tf Lmax = 12.58 inDescription: Created By: GIZA™ 19

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Lmax = d - 2·tf Lmax = 12.58 in

Length of Stiffener Plates

Lst = Floor1

8min(max(Lmin, Lgiv), Lmax), in

Lst = 12.5 in

4. Thickness of Stiffeners

Minimum Thickness of Stiffener Plate,

(AISC Specifications 14th Ed, Chapter J, Section J10.8, page 16.1-138)


16

btf

2tmin = max ,

tmin = 0.438 in t = 0.5 in

Provided Thickness > Minimum Thickness, OK


(AISC 14th Ed. Specifications, Chapter J, Section J4.1&2, page 16.1-128&129)

a)

Tension Capacity,

Rtystf = Λty·Fy·t·(b - c)

Rtystf = 93.15 kips Ffy = 14.577 kips

Shear Yielding,

Rvystf = Λvy·0.6·Fy·t·(b - c)

Rvystf = 62.1 kips Ffx = 37.485 kips

At Column Flange

Interaction at Column Flange,

Iycf = 0.389

Ffy

Rtystf+

2

Iycf =

≤ 1.0


Ffx

Rvystf

2

Ffy

Rtystf+

2Ffx

Rvystf

2

b)

Tension Capacity,

At Column Web

Rtystw = Λty·Fy·t·(L - 2·c)

Rtystw = 163.296 kips Fwx = 74.971 kips

Shear Yielding,

Rvystw = Λvy·0.6·Fy·t·(L - 2·c)


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Rvystw = 108 kips Fwy = 14.577 kips

Interaction at Column Web,

Iycw = 0.229


Fwx

Rtystw+

2

Iycw =

≤ 1.0

Fwy

Rvystw

2

Fwx

Rtystw+

2Fwy

Rvystw

2

6. Bearing Capacity

(AISC 14th Ed. Specifications, Chapter J, Section J7, pages 16.1-131)

a. At Column Flange


Rcb = 1.8·Λbrg·n·Fy·(b - c)·t

Rcb = 279.45 kips Fstc = 10.333 kips


b. At Column Web


Rcb = 1.8·Λbrg·n·Fy·(L - 2·c)·t

Rcb = 243 kips Fwx = 74.971 kips


P. STIFFENER PLATE TO COLUMN CHECK

1. Weld Capacity

a. Stiffener Plate to Column Flange Connection Using Fillet Weld


Minimum Weld Size,

wmin = 0.187 in w = 0.25 in



nws = 2

Shear Strength,

For Column Flange,

Rv1 = Λvr·0.6·Fu·tf·nws Rv1 = 41.535 kips/in

For Stiffener Plate,



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θf = atanFfx

Ffyθf = 21.25 deg

μf = 1.0 + 0.50·sin(θ)1.5

μf = 1.109

For Weld,

Rv3 = μf·Λvw·0.6·Fu·sin(45deg)·nws Rv3 = 49.408 ksi

Rv3

min(Rv1, Rv2)



Length of Weld,

Lw = b - c Lw = 5.78 in

Weld Capacity,

Rw = μf·Λvw·0.6·Fu·sin(45deg)·nws·n1·Lw·min(w, weff)

Rw = 71.394 kips Ffst = 40.22 kips


b. Stiffener Plate to Column Web Connection Using Fillet Weld


Minimum Weld Size,

wmin = 0.187 in w = 0.25 in



nws = 2

Shear Strength,

For Column Web,

Rv4 = Λvr·0.6·Fu·tw·nws Rv4 = 25.74 kips/in

Doubler Plate Thickness,

t1 = 0.375 in

Stiffener Plate Thickness,

t = 0.5 in

For Doubler Plate,

Rv8 = Λvr·0.6·Fu·t1·nws Rv8 = 9.787 kips/in

For Stiffener Plate,



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1.5


θw = atanFwy

Fwxθw = 0 deg

μw = 1.0 + 0.50·sin(θ) μw = 1

Fwy > 0kips

For Weld,

Rv6 = μw·Λvw·0.6·Fu·sin(45deg)·nws·1.5 Rv6 = 44.548 ksi

Rv6

min(0.5·Rv4, Rv5)



Fwy > 0kips

Length of Weld,

Lw = L - 2c Lw = 10 in

Weld Capacity,

Rw = μw·Λvw·0.6·Fu·sin(45deg)·nws·n1·Lw·min(w, weff)·1.5

Rw = 111.369 kips Fwst = 74.971 kips


Q. DOUBLER PLATE CHECK

UNEXTENDED Configuration with Stiffeners

1. Doubler Plate Length

L = 15.75 in

Length of Doubler Plate,

2. Required Doubler Plate Thickness

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

a) Minimum Thickness based on Shear Buckling of Column Web,

treq1 = max , 0intwcolm - twndp

treq1 = 0 in

·

b) Minimum Thickness based on Shear Buckling of Doubler Plate,

treq2 = in418

(d - 2·kdes)in

Fyksi

0.5

treq2 = 0.163 in

c) Minimum Thickness of Doubler Plate for Fillet Welding, (clear k-area)

treq3 = 0 in

treq = max(treq1, treq2, treq3)

Minimum Doubler Plate Thickness,


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treq = max(treq1, treq2, treq3)

treq = 0.163 in t = 0.375 in

Doubler Thickness > Required Thickness, OK

3. Shear Buckling Capacity of Doubler Plate


Governing Shear Force on Doubler Plate,

VuG = max Vudp

n

, Fstw

2

VuG = 14.577 kips


Rvb = Λvy·0.6·Fy·d·t

Rvb = 113.4 kips VuG = 14.577 kips

Shear Capacity of Doubler Plate > Applied Force, UCV = 0.129, OK

4. Shear Buckling Capacity of Doubler Plate due to Weak Axis Shear Load


Force Acting on the Connection,

VuG = V2

n = 1

VuG = 0 kips


Rvb = Λvy·0.6·Fy·Ldp·t

Rvb = 127.575 kips VuG = 0 kips

Shear Capacity of Doubler Plate > Applied Force, UCV = 0, OK

R. DOUBLER PLATE TO COLUMN FLANGE 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 Full Penetration Groove Weld

Yield Stress of Column,

Fy1 = 50 ksi

Yield Stress of Doubler Plate,

Fy2 = 36 ksi

Complete Penetration Groove Weld Capacity,

Rwcp = Λvy·min(Fy1, Fy2)0.60·L·t·n


Rwcp = 127.575 kips Vudp = 3.4 kips


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S. DOUBLER PLATE TO COLUMN WEB CHECK

1. Weld Check

(AISC 14th Ed, Chapter J, Specifications Section J2.2b, Table J2.4)

Minimum Weld Size,

wmin = 0.187 in w = 0.25 in

Weld size need not be checked; Remaining gaps filled, OK

Maximum Weld Size,

wmax =

wmax = 0.312 in w = 0.25 in

Weld size need not be checked; Remaining gaps filled, OK

t ≥ in1

4

t - in1

16


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III. DETAILS

A. SKETCH

MOMENT CONNECTION: W BEAM (FLANGE PLATE) WITH SHEAR PLATE PERPENDICULARMOMENT CONNECTION TO W COLUMN FLANGE AND WEB TOP CONDITION


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B. CONNECTION SCHEDULE

Column

A992W14X90

Mark Size Grade

Beam 1

Mark

Web

Size Grade gap D Lehθskθsl

W16X57 A992 1/2" 0° 0° 3 3/4" 1 3/4"

Lev g

3 1/4" 3 1/2"

Flange

Beam 3

Mark

Web

Size Grade gap D Lehθskθsl

W16X57 A992 1/2" 0° 0° 3 3/4" 1 3/4"

Lev g

3 1/4" 3 1/2"

Flange

Bolts 1 at Beam Web

0"13"

Remarks svnvsnrBolt Typedb

Short-Slotted Holesin Shear Plate Only

4A325-N3/4"

Bolts 3 at Beam Web

0"13"


Short-Slotted Holesin Shear Plate Only

4A325-N3/4"

Bolts 1 at Beam Flange

NA23"


Oversized Holes inFlange Plate Only

6A490-SC-OVS-

CLASS A1"

Bolts 3 at Beam Flange

NA23"


Oversized Holes inFlange Plate Only

6A490-SC-OVS-

CLASS A1"


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Shear Plate 1 Weld

3/8" 1/4"

Lev w1LehGradet

1 1/2" 1 1/2"A36

Shear Plate 3

1/4" 1/4"

w13

Weld

3/8"

Lev w8LehGradet

1 1/2" 1 1/2"A36

Flange Plate 1 Weld

w2

3/4" 0"

Grade ClipLeht

A572-50 2" CJP

Flange Plate 3 Weld

t

3/4" 1/4"1 1/4"

Grade w10w9ClipLeh

A572-50 1 3/4" 1/4"

Gradet n Clip

1/4"1/4"1 1/4"A3611/2"

WeldStiffener Plate

w7w6

Doubler Plate

Fill Gap

w12 Remarks

ConnectionWeld

3/8" CJP

Grade w11Xnt

A361 NAUNEXTENDED

Configuration withStiffeners

Cap Plate Weld

1/2"A572-50 3/4"3/4"

t Grade Clear w14


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Beam Loads

(Beam 3 Moment)M

(Beam 3 Shear)V

50 kips 230 kips·ft

(Beam 1 Axial)P

(Beam 1 Moment)M

(Beam 3 Axial)P

(Beam 1 Shear)V

20 kips 20 kips 200 kips·ft40 kips

Column Loads

(Story Shear) Vs

0 kips

(Column Axial) P

600 kips

(Story Shear) Vs2

0 kips


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IV. REFERENCES

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

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RCM

00

LM2-CTB

57 of 57

NASCC 2019

Date: 03/29/2019


moment connection: w beam (flange plate) with …

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