moment connection: w beam (directly welded) with …

MOMENT CONNECTION: W BEAM (DIRECTLY WELDED) WITH END PLATE (4 BOLTS) ONE-WAY MOMENT CONNECTION TO W COLUMN FLANGE

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

COLUMN PROPERTIES : W21X73 - A992

Depth,

Flange Width,

Distance k,

Area,

Minimum YieldStress,

Modulus ofElasticity,

Web Thickness,

Flange Thickness,

Distance k1,

Distance k (Design),

Minimum TensileStress,

d = 21.2 in

bf = 8.3 in

k = 1.438 in

Ag = 21.5 in²

Fy = 50 ksi

E = 29000 ksi

tw = 0.455 in

tf = 0.74 in

k1 = 0.875 in

kdes = 1.24 in

Fu = 65 ksi

Gage, g = 5.438 in

BEAM PROPERTIES : W14X53 - A992

Depth,

Flange Width,

Distance k,

Area,

Minimum YieldStress,


Web Thickness,

Flange Thickness,

Distance k1,

Distance k (Design),


d = 13.9 in

bf = 8.06 in

k = 1.5 in

Ag = 15.6 in²

Fy = 50 ksi

E = 29000 ksi

tw = 0.37 in

tf = 0.66 in

k1 = 1 in

kdes = 1.25 in

Fu = 65 ksi

Cut Distance fromWeb,

z = 0 in

Top of SteelElevation,

Elev = 0 ft + 0 in

Span Length, L = 30 ft

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,

STIFFENER PLATE PROPERTIES : A36

Thickness, t = 0.375 in Number of Plates, n = 4

Width, b = 3.923 in Length, L = 19.5 in

Fy = 36 ksi

E = 29000 ksi


Fu = 58 ksiMinimum YieldStress,


Clip, c = 0.75 in

END PLATE STIFFENER PROPERTIES : A572-50

Thickness, t = 0.375 in Number of Plates, n = 2

Fy = 50 ksi

E = 29000 ksi



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E = 29000 ksiModulus ofElasticity,

Clip, c = 1 in

END PLATE PROPERTIES : A36

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

Fy = 36 ksi

E = 29000 ksi




BOLTS PROPERTIES : 1" - ø - A36

For End Plate to Column Flange Connection:

db = 1 inBolt Diameter,

Bolt Shear Strength, Λrv = 40.055 kips Bolt TensileStrength,

Λrn = 66.562 kips

Connection Type, Conn_Type = BearingType

Bolt Type, Bolt_Type = A490-N

Number of TensionBolts,

Bolt Outer Pitch, pfo = 1 inntb = 4

Bolt Inner Pitch, pfi = 1 inNumber ofCompression Bolts,

ncb = 4

Holes at ColumnFlange,

Holes at End Plate,

Vertical HoleDimension,

Vertical HoleDimension,

Horizontal HoleDimension,

Horizontal HoleDimension,

Vertical EdgeDistance,

hdv = 1.125 in

hdh = 1.125 in

hdv = 1.125 in

hdh = 1.125 in

Lev = 1.5 in

WELDS PROPERTIES : E70xx LH

Minimum Tensile Stress, Fu = 70 ksi

For Beam Web to End Plate Connection:

Preferred Weld Size (w1), w = 0.312 in

w = 0.25 inPreferred Weld Size (w15),

For End Plate Stiffener to Beam Flange Connection:

w = 0.312 inPreferred Weld Size (w16),

For End Plate Stiffener to End Plate Connection:

w = 0.25 inPreferred Weld Size (min(w7, w10)),

For Stiffener Plate to Column Flange Connection:


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w = 0.25 inPreferred Weld Size (min(w6, w9)),

For Stiffener Plate to Column Web Connection:

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 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 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 Rupture(tr),

Λtr = 2.00 Λtr = 0.75 Λtr = 0.75

For TensionYielding(ty),

Λty = 1.67 Λty = 0.90 Λty = 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

For Eccentric Weld(ew),

Λew = 2.00 Λew = 0.75 Λew = 0.75

APPLIED LOADS:

Beam:

Given End Reaction

Shear Load, V = 20 kips

Axial Load, P = 20 kips

Moment Load, M = 100 kips·ft


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Column:

Axial Load, P = 0 kips

Story Shear, Vs = 0 kips


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II. CALCULATIONS

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 = 11.4 in

Limiting Depth-Thickness Ratio,

htw = htw = 30.811

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 = 154.29 kips V = 20 kips

Shear Capacity of Section > Applied Force, UCV = 0.13, OK

B. BEAM FLANGE TO END PLATE CHECK

1. Forces Acting on the Connection

At Beam Flange,

Ffbm = +P2

Md - tf

Ffbm = 100.634 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)

Length,

Lwf = bf Lwf = 8.06 in

Yield Capacity of Beam,

Fy = 50 ksi

Yield Capacity of End Plate,

Fy1 = 50 ksi

Complete Penetration Groove Weld Capacity,

Rwcpb = Λty·min(Fy, Fy1)·tf·Lwf


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Rwcpb = 172.355 kips Ffbm = 100.634 kips

Weld Capacity > Applied Force, UCV = 0.584, OK

C. BEAM WEB TO END PLATE CHECK

1. Weld Capacity

a. Due to Tension Area

(AISC Steel Design Guide 4, Extended End Plate Moment Connections,Chapter 2, Section2.1.7, page 9)

Design Force to Develop Yield Stress of the Beam Web,

Ruw = Λty·Fy·tw Ruw = 16.65 kips/in

Using Fillet Weld,

Number of Weld Sides,

nws = 2

Minimum Weld Size,

wmin = 0.187 in w = 0.312 in

Preferred Weld Size > Minimum Weld Size, OK

Weld Capacity,

RwT = Λvw·0.6·Fuw·sin(45deg)·nws·w·1.5

Ruw = 16.65 kips/inRwT = 20.882 kips/in


b. Due to Compression Area

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

Using Fillet Weld,


nws = 2

Minimum Weld Size,

wmin = 0.187 in w = 0.312 in


Shear Strength,

For Beam,

Rv1 = Λvr·0.6·Fu·tw Rv1 = 52.2 kips/in

For End Plate,

Rv2 = Λvr·0.6·Fu·t·nws Rv2 = 10.822 kips/in

For Weld,

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

Maximum Effective Weld Size,

min(Rv1, Rv2)Rv3


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weff =min(Rv1, Rv2)

Rv3weff = 0.243 in

Length of Weld,

Lw = 0.5·d - k Lw = 5.45 in

Weld Capacity,

RwC = Λvw·0.6·Fuw·sin(45deg)·min(weff,w1)·nws·Lw

RwC = 58.983 kips V = 20 kips


D. END PLATE CHECK

1. Required Bolt Diameter

(AISC Steel Design Guide 4, Extended End Plate Moment Connections, Chapter 3 DesignProcedure, page 20)

Total Factored Moment Load,

Mu = M + 0.5P·(d - tf) Mu = 111.033 kips·ft

Geometric Design Data:

h = d

Depth of Beam:

h = 13.9 in

b = Floor

Width of Plate:

b = 9 inp bf + 1in,8

1in p

Pitch:

P = 1 infi P = 1 info

d = 1.5 ine

s = 0.5 b ·gp s = 3.498 in

Distance of Bolts to the Bottom of Beam:

h = h + P - 0.5·tf2 h = 14.57 in2

h = h - P - 1.5·tf3 h = 11.91 in3

fo

fi

F = Ft

Nominal Tensile Stress of Bolts:

nt1 F = 113 ksit

db = 0.615 in

π·Λ ·F ·(h + h )

Required Bolt Diameter,

db =reqd2·Mu

t t

reqd db = 1 in

2 3

Bolt Diameter > Bolt Diameter Required, OK

2. Bolt Moment Strength



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Bolt Tensile Strength,

Λrn = 66.562 kips

Bolt Moment Strength,

MSnp = 2·Λrn·(h2 + h3)

MSnp = 293.762 kips·ft Mu = 111.033 kips·ft

Bolt Moment Capacity > Applied Force, UCV = 0.378, OK

3. Required End Plate Thickness


End Plate Yield Line Mechanism Parameter,

P = min P = 1 inP ,sfi fifi

Y = h

2·s· b

2Y = 21.855 in

de ≤ s

11p2

fo2Y =

de ≤ s

g

2+h · de P Y = 13.398 in2 2

233h h h

foP2Y1fi3

ssi

Y =2

b· +

P++

g

2Yp + h · P + s +

Y = 189.439 in

Required End Plate Thickness,

t =reqd

t = 0.875 in

Λ ·Fy·Y

1.11·MS

b

np

t = 1 in

Ceil8

1, in

reqd

End Plate Thickness > Thickness Required, OK

4. Yielding Capacity


Shear Yielding Capacity,

Rvy = 2·λvy·0.6·Fy·t·bp

Rvy = 648 kips Ff = 100.634 kips

Shear Yielding Capacity > Applied Force, UCV = 0.155, OK

5. Rupture Capacity


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a. Due to Extended Portion

Anv = (bp - 2·hdh)·t

Anv = 6.75 in²

Net Shear Area,

Number of Areas in Consideration,

n1 = 2

Shear Rupture Capacity, (J4-4)

Rvr = Λvr·n1·0.6·Fu·Anv

Rvr = 352.35 kips Ff = 100.634 kips

Shear Rupture Capacity > Applied Force, UCV = 0.286, OK

E. END PLATE STIFFENER CHECK

1. Required End Plate Stiffener Thickness


Beam Minimum Yield Stress,

Fy1 = 50 ksi

Required End Plate Stiffener Thickness,

t = Ceilreqd tw· inFy

Fy1 ,8

1

t =reqd 0.375 in t = 0.375 in

End Plate Stiffener Thickness = Thickness Required, OK

2. Local Buckling Capacity


Height of End Plate Stiffener,

h = pfo + de h = 2.5 in

Length of End Plate Stiffener,

L = Ceil h

tan(30deg),1

8in L = 4.375 in

Width-to-Thickness Ratio,

0.5E

Fy ≤ 0.56h

t

h

t = 6.667 0.56

0.5

E

Fy = 13.487


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Section is Non-Slender, OK

F. END PLATE STIFFENER TO BEAM FLANGE CHECK

1. Weld Capacity


Design Force to Develop Yield Stress of the End Plate Stiffener,

Ruw = Λvy·0.6·Fy·tw Ruw = 11.25 kips/in

Using Fillet Weld,


nws = 2

Minimum Weld Size,

wmin = 0.25 in w = 0.312 in


Weld Capacity,

Rw = Λvw·0.6·Fuw·sin(45deg)·nws·w

Ruw = 11.25 kips/inRw = 13.921 kips/in


G. END PLATE STIFFENER TO END PLATE CHECK

1. Weld Capacity


Design Force to Develop Yield Stress of the End Plate Stiffener,

Ruw = Λty·Fy·tw Ruw = 16.875 kips/in

Using Fillet Weld,


nws = 2

Minimum Weld Size,

wmin = 0.312 in w = 0.312 in

Preferred Weld Size = Minimum Weld Size, OK

Weld Capacity,

Rw = Λvw·0.6·Fuw·sin(45deg)·nws·w·1.5

Ruw = 16.875 kips/inRw = 20.882 kips/in


H. END PLATE TO COLUMN FLANGE 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 = 40.055 kips

Bolt Shear Capacity,

Rb = n·ncb·Λrv

Bolt Shear Capacity > Applied Force, UCV = 0.125, OK

Rb = 160.221 kips V = 20 kips

I. COLUMN FLANGE CHECK

1. Column Flange Flexural Yielding at End Plate (Unstiffened)


Geometric Design Data:

P = 1 in P = 1 infi fo

h = 14.57 in2 h = 11.91 in3

bf·g


s = 0.5 s = 3.359 in

c = P + tf + P c = 2.66 in

c c

fi fo

Y = 2

bf

s

h3

c+s

h2

c+

g

2h3 · sc +

4

3·c+ h2 · sc +

4

c+

2

c 2+

2

g

Y = 81.755 in

c

c

b

Required Unstiffened Column Flange Thickness,

t =reqdΛ ·Fy·Y

1.11·MSnp

c

1.031 int =reqd tf = 0.74 in

Please refer to Design of Stiffener Plate, OK

2. Column Flange Flexural Yielding (Stiffened)


Geometric Design Data,

P = P + 0.5·(tf - t)so fo P =so

P = P + 0.5·(tf - t)si fi P =si

1.142 in

1.142 in

Thickness of Stiffener Plate,

t = 0.375 in


s = 3.359 inDescription: Created By: GIZA™ 19

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s =c 3.359 in

soc2sisi

Y =cs

Y =cs 172.745 in

2

bf·

s

h3

c+

P

h3s

h2

c+P

h2

so+

g

2· h3 · sc P h · s P+ + + +

Required Stiffened Column Flange Thickness,

t =reqd

0.709 in

Λ ·Fy·Y

1.11·MS

b

np

cs

t =reqd tf = 0.74 in

Column Flange Thickness > Thickness Required, OK

J. COLUMN WEB CHECK

1. Web Local Yielding Capacity


Distance of Force to Column End,

De = 100 in

Bearing Length,

N = tf N = 0.66 in

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

De > d

Rwy = Λwy·Fy·tw·(N + 6·kdes + 2·t)

Rwy = 229.775 kips Ff = 100.634 kips


2. Web Local Crippling Capacity


Bearing Length,

N = 0.66 inN = L

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

Esq =E·Fy·tf

tw

0.5

Esq = 1535.657 ksi

N1 = 1 + 3N

d·

tw

tf

1.5

N1 = 1.045·

De ≥d

2

Rwc = Λcr·0.8·tw²·N1·Esq

Rwc = 199.341 kips Ff = 100.634 kips


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3. Web Panel Zone Shear

(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 - tf d - tf

2·Λb·Fy·Zx, - Vs

Vpz = 90.634 kips

Pc = Fy·Ag

Code = LRFD

Pc = 1075 kips

Column Strength,

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

Rvz = Λv·0.6·Fy·d·tw

P ≤ 0.40·Pc

Web Panel Zone Shear Capacity > Applied Force, UCV = 0.348, OK

Rvz = 260.442 kips Vpz = 90.634 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 = 0.347 in tw = 0.455 in

·

Shear Buckling will not control, OK

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

h = d - 2·kdes h = 18.72 in

Limiting depth-thickness ratio,

htw = htw = 41.143htw

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 = 289.38 kips Vpz = 90.634 kips

Shear Buckling Capacity need not be checked

K. REINFORCEMENT DESIGN FORCES

1. Stiffener Plate Design Force

a. Due to Tensile Action

Rfb =Λb·Fy·Yc·tfcol

dbm - tfbm

2

Unstiffened Column Flange Bending Capacity,

Rfb = 152.16 kips

Lwf ≥ 0.15·bf

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

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

Stiffener Plate Design Force at Column Flange,

Fst = max(Fstt, Fstc) Fst = 0 kips

Stiffener Plate Design Force at Column Web,

Fstw = Fst Fstw = 0 kips

b. Due to Compressive Action

L. STIFFENER PLATE CHECK

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 in

Width of Primary Flange,

bf = 8.3 in


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tpz2

bmin = -Lwf3

Minimum Width of Stiffener Plates

bmin = 2.459 in

a.

Maximum Width of Stiffener Plates

bmax = 0.5·(bf - tw) - t bmax = 3.923 in

b.

Width of Stiffener Plates

b = 3.75 in

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

in

2. Length of Stiffeners

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


2

d

a. Minimum Length of Stiffener Plates

Lmin = Lmin = 10.6 in

b. Maximum Length of Stiffener Plates

Lmax = d - 2·tf Lmax = 19.72 in

Length of Stiffener Plates

Lst = Floor1

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

Lst = 19.5 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 = 0.33 in t = 0.375 in

Provided Thickness > Minimum Thickness, OK


(AISC 14th Ed. Specifications, Chapter J, Section J4.1, pages 16.1-128 to 16.1-129)

Length of Stiffeners,

L = b - c L = 3 in

Tensile Yielding Capacity,

Rty = Λty·Fy·t·2·L

Rty = 72.9 kips Fstt = 0 kips


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



Length,

L = Lw L = 18 in

Number of Areas in Consideration,

n1 = 2

Shear Yielding Capacity, (J4-3)

Rvy = Λvy·n1·0.6·Fy·L·t

Rvy = 291.6 kips Fstw = 0 kips

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

M. STIFFENER PLATE TO COLUMN FLANGE CHECK

1. Weld Capacity

a. Using Fillet Weld



No. of Weld Side,

nws = 2

Minimum Weld Size,

wmin = 0.187 in w = 0.25 in


Shear Strength,

For Column:

Rv1 = Λvr·0.6·Fu·tf·nws Rv1 = 43.29 kips/in

For Stiffener Plate:

Rv2 = Λtr·Fu·t Rv2 = 16.312 kips/in

For Weld:

Rv3 = Λvw·1.5·0.6·Fu·sin(45deg)·nws Rv3 = 66.822 ksi

Rv3

min(Rv1, Rv2)


weff = weff = 0.244 in

Length of Weld,

Lw = 2·(bst - c) Lw = 6 in

Weld Capacity,

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

Rwpl = 97.875 kips Fst = 0 kips


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Weld Capacity > Applied Force, UCV = 0, OK

N. STIFFENER PLATE TO COLUMN WEB CHECK

1. Weld Capacity

a. Using Fillet Weld



No. of Weld Side,

nws = 2

Minimum Weld Size,

wmin = 0.187 in w = 0.25 in


Shear Strength,

For Column:

Rv1 = Λvr·0.6·Fu·tw/2·nws Rv1 = 26.617 kips/in

For Stiffener Plate:

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

For Weld:

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

min(Rv1, Rv2, Rv3)


weff = 0.22 in

Length of Weld,

Lw = 2(L - 2·c) Lw = 36 in

Weld Capacity,

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

Rwpl = 352.35 kips Fstw = 0 kips

Weld Capacity > Applied Force, UCV = 0, OK


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III. DETAILS

A. SKETCH

MOMENT CONNECTION: W BEAM (DIRECTLY WELDED) WITH END PLATE (4 BOLTS) ONE-WAY MOMENT CONNECTION TO W COLUMN FLANGE


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B. CONNECTION SCHEDULE

Column

A992W21X73

Mark Size Grade g

5 7/16"

Bolts at Column Flange

pfi

1"1" A490-NStandard Holes in

All Plies

RemarksBolt Typedb pfo

1"

Beam

gap

Web

Mark Size Grade Dθskθsl

W14X53 A992 NA 0° 0° 3"

WeldEnd Plate

t w1

1" 1 1/2"

bp LevGrade

9" A36 5/16"

End Plate Stiffener Weld

t

1" 5/16"2 1/2"

Grade w16w15hL

A36 4 3/8" 5/16"

Gradet n Clip

1/4"1/4"3/4"A3643/8"

WeldStiffener Plate

min(w7,w10)

min(w6,w9)

Doubler Plate

NR

w12 Remarks

ConnectionWeld

NR NR

Grade w11Xnt

NRNR NR NR


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Beam Loads

100 kips·ft20 kips

(Beam Moment) M(Beam Axial) P(Beam Shear) V

20 kips

Column Loads

(Column Axial) P

0 kips 0 kips

(Story Shear) Vs


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IV. REFERENCES

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

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moment connection: w beam (directly welded) with …

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