SHEAR CONNECTION: W BEAM WITH SHEAR PLATE (PARTIAL …

SHEAR CONNECTION: W BEAM WITH SHEAR PLATE (PARTIAL DEPTH) ONE-WAY SHEARCONNECTION TO W GIRDER WEB

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

GIRDER PROPERTIES : W18X35 - A992

Depth,

Flange Width,

Distance k,

Area,

Minimum YieldStress,

Modulus ofElasticity,

Web Thickness,

Flange Thickness,

Distance k1,

Distance k (Design),

Minimum TensileStress,

d = 17.7 in

bf = 6 in

k = 1.125 in

Ag = 10.3 in²

Fy = 50 ksi

E = 29000 ksi

tw = 0.3 in

tf = 0.425 in

k1 = 0.75 in

kdes = 0.827 in

Fu = 65 ksi

Top of SteelElevation,

Elev = 0 ft + 0 in

BEAM PROPERTIES : W16X26 - A992

Depth,

Flange Width,

Distance k,

Area,

Minimum YieldStress,


Web Thickness,

Flange Thickness,

Distance k1,

Distance k (Design),


d = 15.7 in

bf = 5.5 in

k = 1.063 in

Ag = 7.68 in²

Fy = 50 ksi

E = 29000 ksi

tw = 0.25 in

tf = 0.345 in

k1 = 0.75 in

kdes = 0.747 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,

SHEAR PLATE PROPERTIES : A36

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

Fy = 36 ksi

E = 29000 ksi


Fu = 58 ksiMinimum YieldStress,


Clip, c = 0.75 in

BOLTS PROPERTIES : 3/4" - ø - A325-N

For Shear Plate to Beam Web Connection:

Bolt Diameter, db = 0.75 in

Λrv = 17.892 kipsDescription: Created By: GIZA™ 19

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Bolt Shear Strength,

Bolt Type,

Number of Bolt Rows,

Bolt TensileStrength,

Connection Type,

Bolt VerticalSpacing,

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,

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 in

Vertical EdgeDistance (D - dcT),

Vertical EdgeDistance min(Lev1,Lev2),

Lev = 3 in Lev = 1.5 in

Horizontal EdgeDistance,

Horizontal EdgeDistance,

Leh = 1.75 in Leh = 1.5 in

WELDS PROPERTIES : E70xx LH

Minimum Tensile Stress, Fu = 70 ksi

For Shear Plate to Girder Web Connection:

w = 0.25 inPreferred Weld Size (w1),

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

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

For Flexural LocalBuckling/FlexuralStrength (b),

Ωb = 1.67 ϕb = 0.90 Λb = 0.90

For Flexural Rupture(fr),

Ωfr = 2.00 ϕfr = 0.75 Λfr = 0.75

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

Ωv = 1.67 ϕv = 0.90 Λv = 0.90


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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

APPLIED LOADS:

Beam:

Given End Reaction

Shear Load, V = 20 kips

Adjacent Shear Load(if any),

V2 = 0 kips


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II. CALCULATIONS

A. BEAM WEB 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

Bearing Area,

Abrg = db·tw Abrg = 0.187 in²

Bolt Centerline Distance from Face of Support,

0.5·(bf - tw) + gap

cos(θsk)ab = + (z + 0.5·tw)·tan(θsk) + Leh + 0.5·(nv - 1)·sv

ab = 5.1 in

Eccentricity Distance of End Reaction from Bolt Group Centerline,

ebv = 5.1 in

Load Inclination from Vertical,

θ = 0 deg

Eccentric Load Coefficient,

(AISC 14th Ed. Manual Part 7, Instantaneous Center of Rotation Method, pages7-6 to 7-8)

C = 1.976

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

Fbe = Λbrg·Fu·

hdh < hdls(db)

1.2·(Lev - 0.5·hdv)·

1.2·(Leh - 0.5·hdh)·

2.4·Abrg

tw

tw

Fbe = min(Fbe , Fbe ) Fbe = 19.195 kips1 2

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

hdh < hdls(db)

1.2·(s - hdv)·tw

2.4·Abrg

Fbs = Λbrg·Fu· 1.2·(sv - hdh)·tw

Fbs = 21.937 kips

nv ≤ 1

Fbs = min(Fbs , Fbs )0 2

Number of Areas in Consideration,

n1 = 1


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Bolt Capacity,

ebv > 0 in

Rbrg = C·min(n1·Fbe, n1·Fbs, n·Λrv)

V = 20 kips

Bolt Capacity > Applied Force, UCV = 0.566, OK

Rbrg = 35.353 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 = 14.206 in

Limiting Depth-Thickness Ratio,

htw = htw = 56.824

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 = 105.975 kips V = 20 kips

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

B. BEAM WEB TO SHEAR PLATE CHECK

1. Bolt Shear Capacity

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

Shear Capacity Per Bolt,

Λrv = 17.892 kips

Bolt Shear Capacity,

Rb = n·C·Λrv

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

Rb = 35.353 kips V = 20 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)

Shear Plate Thickness,

t1 = 0.375 in

Beam Web Thickness,Description: Created By: GIZA™ 19

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Beam Web Thickness,

t2 = 0.25 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 = 6 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)

Shear Plate Edge Distances,

Lev1 = 1.5 in

Leh1 = 1.5 in

Beam Web Edge Distances,

Lev2 = NA

Leh2 = 1.75 in

i) Minimum Vertical Edge Distance,

Connection Edge Distance,

Lev1Levcon = Levcon = 1.5 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 = 1.75

Minimum Edge Distance,

Lehmin = Lehmin2 Lehmin = 1

in

in

Specified Edge Distance is Acceptable, OK

iii) Maximum Edge Distance,

Shear Plate Thickness,

t1 = 0.375 inDescription: Created By: GIZA™ 19

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t1 = 0.375 in

Beam Web Thickness,

t2 = 0.25 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 = 4.5 in

Maximum Edge Distance Requirement is Satisfied, OK

C. SHEAR PLATE CHECK

1. Check for Maximum Thickness

(AISC 14th Ed. Manual, Part 10, page 10-104)

Exceptions for nv = 1 and nv = 2 for Extended Configuration

Exception for 2 ≤ n ≤ 5 with SSLT Hole Type for Conventional Configuration

Shear Plate, Beam Web,

2t ≤

db

16

1+

2tw ≤

db

16

1+

Leh ≥ 2·db Leh ≥ 2·db

No Need to Check Maximum Thickness of Plate

Maximum Thickness Exceptions,

Coefficient for Eccentrically Loaded Bolts,

(AISC 14th Ed. Manual Part 7, page 7-19)

C' = 11.256 in

Area of Bolts,

Ab =π·db

4

2

Ab = 0.442 in²

Length of Plate,

L = (nr - 1)·s + 2·Lev L = 12 in

Maximum Thickness,

Case = 2

0.9

Fnv

tmax =

6· ·Ab·C'

Fy·L2

tmax = 0.345 in t = 0.375 in

Maximum plate thickness need not be checked, OK


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Governing Shear Plate Thickness,

Case = Maximum thickness need not be checked

tg = t

tg = 0.375 in

2. 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

Bearing Area,

Abrg = db·tg Abrg = 0.281 in²

Bolt Centerline Distance from Face of Support,

0.5·(bf - tw) + gap

cos(θsk)ab = + (z + 0.5·tw)·tan(θsk) + Leh + 0.5·(nv - 1)·sv

ab = 5.1 in

Eccentricity Distance of End Reaction from Bolt Group Centerline,

ebv = 5.1 in

Load Inclination from Vertical,

θ = 0 deg

Eccentric Load Coefficient,

(AISC 14th Ed. Manual Part 7, Instantaneous Center of Rotation Method, pages7-6 to 7-8)

C = 1.976

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

Fbe = Λbrg·Fu·

hdh < hdls(db)

1.2·(Lev - 0.5·hdv)·

1.2·(Leh - 0.5·hdh)·

2.4·Abrg

tg

tg

Fbe = min(Fbe) Fbe = 18.963 kips

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

hdh < hdls(db)

1.2·(s - hdv)·tg

2.4·Abrg

Fbs = Λbrg·Fu· 1.2·(sv - hdh)·tg

Fbs = 29.362 kips

nv ≤ 1

Fbs = min(Fbs , Fbs )0 2


n1 = n


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Bolt Capacity,

ebv > 0 in

Rbrg = C·min(n1·Fbe, n1·Fbs, n·Λrv)

V = 20 kips

Bolt Capacity > Applied Force, UCV = 0.566, OK

Rbrg = 35.353 kips

3. Yielding Capacity


a. Shear Yielding Capacity due to Shear Load

Length,

L = (nr - 1)·s + 2·Lev L = 12 in

Erection Stability,


Length of Connector > One-half of T-Dimension, OK


n1 = n

Shear Yielding Capacity, (J4-3)

Rvy = Λvy·n1·0.6·Fy·L·tg

Rvy = 97.2 kips V = 20 kips

Shear Yielding Capacity > Applied Force, UCV = 0.206, OK

4. Rupture Capacity


a. Shear Rupture Capacity due to Shear Load

Anv = (L - nr·hdv)·tg

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 = 20 kips

Shear Rupture Capacity > Applied Force, UCV = 0.24, OK

5. Block Shear Capacity


a. Block Shear Capacity due to Shear Load

Reduction Factor,

nv = 1

Ubs = 1.0

(tension stress is uniform)


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Ubs = 1.0

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

Rbs = 79.59 kips V = 20 kips

Block Shear Capacity > Applied Force, UCV = 0.251, OK

6. Local Buckling Capacity


cos(θsk)

Distance of Bolt Line to Support,

0.5·(bf - tw) + gap ab = 5.1 inab = + Leh

ab

L0.5ksi

1λ = ·0.5

10·tg·

L·Fy

Coefficient,

0.5

2

475 + 280·

λ = 0.427

Q = 1

λ ≤ 0.7

Allowable Flexural Local Buckling Stress or Yielding Stress,

Fcr = Q·Fy Fcr = 36 ksi

Gross Plastic Section Modulus,

Zx =tg ·L

4

2

Zx = 13.5 in³

Eccentricity,

e = ab e = 5.1 in


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Local Buckling Capacity,

Rbc = Λb·Fcr·Zx

e

Rbc = 85.765 kips V = 20 kips

Local Buckling Capacity will not control, OK

7. Shear and Flexural Yielding Capacity with Von-Mises Yield Criterion

(AISC 14th Ed., Manual Part 10, page 10-104)

(Muir, Larry and Hewitt,Christopher, "Design of Unstiffened Extended Single PlateShear Connections", Engineering Journal, 2nd Quarter 2009, page 69)

0.5

Λb·Fy·L·tg

L

e

Shear and Flexural Yielding Interaction Capacity,

Rfc =

2.25 + 16·2

Rfc = 64.31 kips V = 20 kips

Yielding Capacity > Applied Force, UCV = 0.311, OK

8. Flexural Rupture Capacity

(AISC 14th Ed. Manual Part 15, page 15-4)

(AISC 14th Ed. Steel Construction Manual Design Examples, page IIA-104)

Net Plastic Section Modulus,

Znet = -tg ·L

4

2tg ·hdv·nr·s

4

2

mod(nr, 2) = 0

Znet = 9.563 in³

Flexural Rupture Capacity,

Λfr·Fu·ZnetRfr = e

Rfr = 81.563 kips V = 20 kips

Flexural Rupture Capacity > Applied Force, UCV = 0.245, OK

D. SHEAR PLATE TO GIRDER WEB CHECK

1. Weld Check


a. Using Fillet Weld

Number of Weld Sides,

nws = 2

Minimum Weld Size,

wmin = 0.25 in w = 0.25 in


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wmin = 0.25 in w = 0.25 in

Preferred Weld Size = Minimum Weld Size, OK

E. GIRDER WEB CHECK

1. Rupture Strength at Weld

Length of Weld,

Lw = 12.312 in

Number of Weld Sides,

nws = 2

Rupture Strength at Weld,

Rv = Λvr·0.6·Fu·nws·Lw·tw

Rv = 216.084 kips V = 20 kips

Rupture Strength at Weld > Applied Force, UCV = 0.093, OK


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III. DETAILS

A. SKETCH

SHEAR CONNECTION: W BEAM WITH SHEAR PLATE (PARTIAL DEPTH) ONE-WAY SHEARCONNECTION TO W GIRDER WEB


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B. CONNECTION SCHEDULE

Girder

A992W18X35

Mark Size Grade

Beam

Mark

Web

Size Grade gap D Lehθskθsl

W16X26 A992 1/2" 0° 0° 3" 1 3/4"

Cope Dimensions

dcT cT dcB cB

0"0"0"0"

Bolts at Beam Web

0"13"

Remarks svnvsnrBolt Typedb

Short-Slotted Holesin Shear Plate Only

4A325-N3/4"

Shear Plate

1/4" 1/4"

w2

Weld

3/8"

Lev w1LehGradet

1 1/2" 1 1/2"A36

Governing Limit State of Shear Connection

0.56635.353 kips

Connection Capacity UCV Governing Check

Bolt Capacity at Shear Plate

Remarks on Connection / Connecting Elements

For Edge DistanceFor Bolt SpacingFor Connector

LengthFor Connector

ThicknessFor Bolts

OK OKOKOKOK


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Remarks on Connection / Connecting Elements

NOOK

For Weld on Shear Plate to Girder Web Conventional Shear Plate

Remarks on Beam Web / Girder Web

OKOK

For Beam Web For Girder Web


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IV. REFERENCES

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

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