bcw.s.s.01981.01986

SHEAR PLATE CONNECTION SUMMARY

Filler Beam profile: W18X40
Column profile: W14X132
Slope: 0 deg.
Skew: 90
Vertical Offset: 0
Horizontal Offset: 0
Span: 19.9 ft.
Reaction, V: 30 kips
Shear Capacity, Rn: 43 kips
Design/Reference according to AISC 14th Ed. - LRFD
Shear Plate: Extended Configuration
Beam material grade: A992
Support material grade: A992
Plate material grade: A572-GR.50
Weld grade: E70
Stabilizer plate grade: A572-GR.50
Shear Plate Size: 11.125 in. x 14.500 in. x 0.375 in.
Shear Plate Detailing Height at Support: 14.500 in.
Shear Plate Detailing Width at Support: 7.062 in.
Stabilizer plate size: 12.500 in. x 7.062 in. x 0.500 in.
(Required due to user requirement)
Configuration Geometry:
Welds at shear plate to support: 4/16 FILLET, 4/16 FILLET
Welds at stabilizer plate :
at column flange: 4/16 FILLET, 4/16 FILLET
at column web: 4/16 FILLET, 4/16 FILLET
at shear plate: 4/16 FILLET, 4/16 FILLET
Bolt: 5 rows x 1 column 0.875 in. Diameter A325N_TC bolts
Vertical spacing: 3 in.
Horizontal spacing: 3 in.
Shear plate edge setback = 7.62 in.
Beam centerline setback = 7.62 in.
Edge distance at vertical edge of plate: 1.75 in.
Edge distance at top edge of plate: 1.25 in.
Edge distance at bottom edge of plate: 1.25 in.
Edge distance at vertical edge of beam: 1.75 in.
Horizontal distance to first hole: 9.38 in.
Down distance from top of filler beam flange: 3 in.
Holes in beam web: STD diameter = 0.938 in.
Holes in shear plate: SSL diameter = 0.938 in., slot width = 1.12 in.

BOLT SHEAR CAPACITY AT BEAM AND SHEAR PLATE SIDE:
Bolt Shear Capacity at Shear Load Only:
Using Instantaneous Center Of Rotation Method (AISC 7-1)
ex = 9.375 in.
Angle = 0.000 deg.
C = 1.767
Using Table 7-1 to determine (phi)rn:
(phi)Rn = (phi)rn * C = 24.35 * 1.77 = 43.03 kips


Total Vertical Bolt Shear Capacity = 43.03 kips
43.03 kips >= 30.00 kips (OK)

BOLT BEARING AT BEAM AND SHEAR PLATE SIDE
Vertical Shear Only Load Case:
ICR cordinate relative to CG = (1.24, -0.00)
At Row 1, At Column 1:
Ribolt = 23.90 kips
Ri vector at Beam   = <23.41, 4.82>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 14.40 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.75 * 1.20 * na * (0.32/1) * 65.00 = na
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 14.40 * (0.32/1) * 65.00 = 265.27 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.88 * (0.32/1) * 65.00 = 32.25 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(na, 265.27, 32.25) = 32.25 kips/bolt
Ri vector at Shear Plate   = <-23.41, -4.82>
Lcsshpl at Shear Plate spacing  = na
Lceshpl at Shear Plate edge    = 9.00 in.
(phi)Rnsshpl at Shear Plate spacing = (phi) * hf1 * Lcs * t * Fu = 0.75 * 1.20 * na * 0.38 * 65.00 = na
(phi)Rneshpl at Shear Plate edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 9.00 * 0.38 * 65.00 = 197.39 kips/bolt
(phi)Rndshpl on Shear Plate at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.88 * 0.38 * 65.00 = 38.39 kips/bolt
Shear Plate bearing capacity, (phi)Rnshpl = min((phi)Rnsshpl,(phi)Rneshpl,(phi)Rndshpl) = min(na, 197.39, 38.39) = 38.39 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(32.249, 38.392) = 32.25 kips/bolt
Bolt Shear Demand to Bearing ratio = 32.25 / 23.90 = 1.35

At Row 2, At Column 1:
Ribolt = 22.05 kips
Ri vector at Beam   = <20.39, 8.40>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 15.28 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.75 * 1.20 * na * (0.32/1) * 65.00 = na
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 15.28 * (0.32/1) * 65.00 = 281.53 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.88 * (0.32/1) * 65.00 = 32.25 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(na, 281.53, 32.25) = 32.25 kips/bolt
Ri vector at Shear Plate   = <-20.39, -8.40>
Lcsshpl at Shear Plate spacing  = na
Lceshpl at Shear Plate edge    = 9.53 in.
(phi)Rnsshpl at Shear Plate spacing = (phi) * hf1 * Lcs * t * Fu = 0.75 * 1.20 * na * 0.38 * 65.00 = na
(phi)Rneshpl at Shear Plate edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 9.53 * 0.38 * 65.00 = 209.11 kips/bolt
(phi)Rndshpl on Shear Plate at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.88 * 0.38 * 65.00 = 38.39 kips/bolt
Shear Plate bearing capacity, (phi)Rnshpl = min((phi)Rnsshpl,(phi)Rneshpl,(phi)Rndshpl) = min(na, 209.11, 38.39) = 38.39 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(32.249, 38.392) = 32.25 kips/bolt
Bolt Shear Demand to Bearing ratio = 32.25 / 22.05 = 1.46

At Row 3, At Column 1:
Ribolt = 16.57 kips
Ri vector at Beam   = <0.00, 16.57>
Lcsbm at Beam spacing  = 2.06 in.
Lcebm at Beam edge    = 8.53 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.75 * 1.20 * 2.06 * (0.32/1) * 65.00 = 38.01 kips/bolt
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 8.53 * (0.32/1) * 65.00 = 157.21 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.88 * (0.32/1) * 65.00 = 32.25 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(38.01, 157.21, 32.25) = 32.25 kips/bolt
Ri vector at Shear Plate   = <-0.00, -16.57>
Lcsshpl at Shear Plate spacing  = 2.06 in.
Lceshpl at Shear Plate edge    = 6.78 in.
(phi)Rnsshpl at Shear Plate spacing = (phi) * hf1 * Lcs * t * Fu = 0.75 * 1.20 * 2.06 * 0.38 * 65.00 = 45.25 kips/bolt
(phi)Rneshpl at Shear Plate edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 6.78 * 0.38 * 65.00 = 148.77 kips/bolt
(phi)Rndshpl on Shear Plate at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.88 * 0.38 * 65.00 = 38.39 kips/bolt
Shear Plate bearing capacity, (phi)Rnshpl = min((phi)Rnsshpl,(phi)Rneshpl,(phi)Rndshpl) = min(45.25, 148.77, 38.39) = 38.39 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(32.249, 38.392) = 32.25 kips/bolt
Bolt Shear Demand to Bearing ratio = 32.25 / 16.57 = 1.95

At Row 4, At Column 1:
Ribolt = 22.05 kips
Ri vector at Beam   = <-20.39, 8.40>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 1.42 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.75 * 1.20 * na * (0.32/1) * 65.00 = na
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 1.42 * (0.32/1) * 65.00 = 26.24 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.88 * (0.32/1) * 65.00 = 32.25 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(na, 26.24, 32.25) = 26.24 kips/bolt
Ri vector at Shear Plate   = <20.39, -8.40>
Lcsshpl at Shear Plate spacing  = na
Lceshpl at Shear Plate edge    = 1.28 in.
(phi)Rnsshpl at Shear Plate spacing = (phi) * hf1 * Lcs * t * Fu = 0.75 * 1.20 * na * 0.38 * 65.00 = na
(phi)Rneshpl at Shear Plate edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 1.28 * 0.38 * 65.00 = 28.18 kips/bolt
(phi)Rndshpl on Shear Plate at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.88 * 0.38 * 65.00 = 38.39 kips/bolt
Shear Plate bearing capacity, (phi)Rnshpl = min((phi)Rnsshpl,(phi)Rneshpl,(phi)Rndshpl) = min(na, 28.18, 38.39) = 28.18 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(26.242, 28.177) = 26.24 kips/bolt
Bolt Shear Demand to Bearing ratio = 26.24 / 22.05 = 1.19

At Row 5, At Column 1:
Ribolt = 23.90 kips
Ri vector at Beam   = <-23.41, 4.82>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 1.32 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.75 * 1.20 * na * (0.32/1) * 65.00 = na
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 1.32 * (0.32/1) * 65.00 = 24.29 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.88 * (0.32/1) * 65.00 = 32.25 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(na, 24.29, 32.25) = 24.29 kips/bolt
Ri vector at Shear Plate   = <23.41, -4.82>
Lcsshpl at Shear Plate spacing  = na
Lceshpl at Shear Plate edge    = 1.21 in.
(phi)Rnsshpl at Shear Plate spacing = (phi) * hf1 * Lcs * t * Fu = 0.75 * 1.20 * na * 0.38 * 65.00 = na
(phi)Rneshpl at Shear Plate edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 1.21 * 0.38 * 65.00 = 26.60 kips/bolt
(phi)Rndshpl on Shear Plate at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.88 * 0.38 * 65.00 = 38.39 kips/bolt
Shear Plate bearing capacity, (phi)Rnshpl = min((phi)Rnsshpl,(phi)Rneshpl,(phi)Rndshpl) = min(na, 26.60, 38.39) = 26.60 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(24.288, 26.599) = 24.29 kips/bolt
Bolt Shear Demand to Bearing ratio = 24.29 / 23.90 = 1.02

Min Bolt Shear Demand to Bearing ratio Beam and Shear Plate for vertical shear only
 = min(1.00, 1.35, 1.46, 1.95, 1.19, 1.02) = 1.00

BEARING AT BEAM AND SHEAR PLATE SIDE SUMMARY:
Bearing Capacity at Vertical Shear Load Only, Rbv = Min Bolt Shear Demand to Bearing Ratio * Bolt Shear = 1.00 * 43.03 = 43.03 kips
Rbv = 43.03 kips >= Reaction V = 30.00 kips (OK)

Web Depth = d - [Top Cope Depth] - [Bottom Cope Depth] = 17.9 - 0 - 0 = 17.9 in.
Gross Area (Shear) = [Web Depth] * tw = 17.90 * 0.32 = 5.64 in^2
Net Shear Area (Shear) = ([Web Depth] - ([# rows] * [Diameter + 0.0625])) * tw 
    = (17.90 - (5 * 1.00)) * 0.32 = 4.06 in^2

Using Eq.J4-3:
Shear Yielding = (phi) * 0.6 * Fybeam * [Gross Area] = 1.00 * 0.6 * 50.00 * 5.64 = 169.16 kips

Using Eq.J4-4:
Shear Rupture = (phi) * 0.6 * Fubeam * [Net Area] = 0.75 * 0.6 * 65.00 * 4.06 = 118.86 kips


Block Shear

Using Eq.J4-5:
Block Shear = {(phi) * ((0.6 * Fu * Anv) + (Ubs * Fu * Ant))} <= {(phi) * ((0.6 * Fy * Agv) + (Ubs * Fu * Ant))}

Block Shear for Axial T/C is not required.

Gross Area = 0.38 * 14.50 = 5.44 in^2
Net Area = (14.50 - (5 *(0.94 + 1/16))) * 0.38 = 3.56 in^2

Using Eq.J4-3:
Shear Yielding = (phi) * 0.6 * Fypl * [Gross Area] = 1.00 * 0.6 * 50.00 * 5.44 = 163.12 kips

Using Eq.J4-4:
Shear Rupture = (phi) * 0.6 * Fupl * [Net Area] = 0.75 * 0.6 * 65.00 * 3.56 = 104.21 kips


Block Shear

Using Eq.J4-5:
Block Shear = {(phi) * ((0.6 * Fu * Anv) + (Ubs * Fu * Ant))} <= {(phi) * ((0.6 * Fy * Agv) + (Ubs * Fu * Ant))}

Block 1 (Shear): 
Gross Shear Length = (14.5 - 1.25) = 13.25 in.
Net Shear Length = 13.2 - (4.5 * (0.938 + 0.0625)) = 8.75 in.
Gross Tension Length = (0 + 1.75) = 1.75 in.
Net Tension Length = 1.75 - (0.5 * (1.12 + 0.0625)) = 1.16 in.
1. (phi) * [material thickness] * ((0.60 * Fupl* [net shear length]) + (Ubs * Fupl * [net tension length])) 
    = 0.75 * 0.38 * ((0.60 * 65.00 * 8.75) + (1.00 * 65.00 * 1.16)) = 117.12 kips
2. (phi) * [material thickness] * ((0.60 * Fypl * [gross shear length]) + (Ubs * Fupl * [net tension length])) 
    = 0.75 * 0.38 * ((0.60 * 50.00 * 13.25) + (1.00 * 65.00 * 1.16)) = 132.94 kips
Block Shear = 117.12 kips
117.12 kips >= Reaction V = 30.00 kips (OK)

Block Shear for Axial T/C is not required.

Flexural and Buckling Strength:

Eccentricity at first line of bolts, e = 9.38 in.
Zgross = 19.71 in^3
Znet   = 12.87 in^3
Sgross = 13.14 in^3
Snet   = 8.49 in^3

Using Eq. 9-4
Flexural Rupture = (phi) * Fu * Znet / e = 0.75 * 65.00 * 12.87 / 9.38 = 66.91 kips


Using Eq. 9-14 through 9-18, Fcr = Fy * Q
tw = 0.38 in.
ho = 14.50 in.
c = 9.38 in.
lambda = (ho * Fy ^ 0.5) / ( 10 * tw * ( 475.00 + 280.00 * (ho / c)^2 ) ^0.5 ) = 
 = 14.50 * 50.00^0.5 / (10 * 0.38 * (475.00 + 280.00 * (14.50/9.38)^2 )^0.5) = 0.81
When 0.70 < lambda <= 1.41, Q=1.34 - 0.49 * lambda
Q = 0.95
Fcrmin =phi * Fcr = 0.90 * 50.00 * 0.95 = 42.63 ksi

Using Eq. 9-6
Buckling = Fcr * Sgross / e = 42.63 * 13.14 / 9.38 = 59.75 kips

Interaction Check of Flexural Yielding, Per AISC 10-5: 
Eccentricity at CG of Bolt Group, e = 9.38 in.
Zgross = 19.71
Znet = 12.87
Mr = Vr * e = 30.00 * 9.38 = 281.25 kips-in
Mc = phi * Mn = phi * Fy * Zgross = 0.90 * 50.00 * 19.71 = 886.99 kips-in
Vr = 30.00 kips
Vc = phi * Vn = phi * 0.60 * Fy * Ag = 1.00 * 0.60 * 50.00 * 5.44 = 163.12 kips
Interaction due to moment and shear, (Vr/Vc)^2 + (Mr/Mc)^2 <= 1.0
(Vr/Vc)^2 + (Mr/Mc)^2 = (30.00 / 163.12)^2 + (281.25 / 886.99)^2 = 0.13 <= 1  (OK)

Note: Mn <= 1.6My by inspection

MAXIMUM PLATE THICKNESS:
No of bolt columns = 1
tp  < = db/2 + 1/16 = 0.375 <= 0.5 OK
tw  < = db/2 + 1/16 = 0.315 <= 0.5 OK
Leh(plate) >= 2 * db = 1.75 >= 1.75 OK
Leh(bm) >= 2 * db = 1.75 >= 1.75 OK
Maximum Plate Thickness is Not a Limiting Criteria.

STABILIZER PLATE:

Available Strength to Resist Lateral Displacement:
Using Eq. 10-6 (14th Ed.):
phiRn = 1500.00  * 3.14159 * L * tp^3 / a^2 = 0.90 * 1500.00 * 3.14159 * 14.50 * 0.38^3 / 9.38^2 = 36.90 kips
Stabilizer Plate Not Required for lateral displacement

Torsional Strength:
Using Eq. 10-8 and Eq. 10-7 (14th Ed.):
Required, Mta or Mtu = Ru * (tw + tp) /2 = 30.00 * ((0.31 + 0.38) / 2) = 10.31 kips-in
Lateral Shear Strength of Shear Plate, Mtn (no slab) = [phiv*(0.6*Fyp)-(Ru/(L*tp))] *L*tp^2/2 =  ((1.00 * 0.6 * 50.00) - (30.00 / (14.50 * 0.38))) * 0.5 * 14.50 * 0.38^2 = 24.96 kips-in
Stabilizer Plate Not Required for torsional strength

WELD:

 Weld Requirements:

At shear only case: 
Weld Length for shear, Lv = 13.000 in.
Shear Load per inch per weld, fv = R/Lv/2 = 30.000 / 13.000 / 2 = 1.154 kips/in/ weld 
theta = 0 deg.
cPhi  = 1.0 + 0.5 * sin(0)^1.5 = 1.000
Weld Coefficient = 0.6 * 70.000 * 1.000 * 1.000 * (2^0.5/2)*(1/16) = 1.856
Required weld size, Dv = fv/ (phi * coeff) = 1.154 / (0.750 * 1.856) = 0.829/16

Minimum fillet weld size : 
   At shear only load case = 0.05 in.
   per Table J2.4     = 0.19 in.
   5/8tp              = 0.23 in.
   user preference    = 0.25 in.

Dmax1 (using eqn 9-3)
 = tshpl * Fushpl / ( Fexx * C1 * 0.088)
 = 0.375 * 65.000 / ( 70.000 * 1.000 * 0.088 ) 
 = 3.940 
Dmax2 (using eqn 9-3)
 = twsupport * Fusupport / ( Fexx * C1 * 0.088 )
 = 0.645 * 65.000 / ( 70.000 * 1.000 * 0.088 ) 
 = 6.776 
Dmax3 = project max fillet weld = 12.000
Dmax=min(Dmax1, Dmax2, Dmax3) = min(3.940, 6.776, 12.000)
 = 3.940 

Use weld size
D1 = 4.00
D2 = 4.00

Weld Strength :

Vertical weld capacity during shear only load, phi * Rnv1 = 0.75 * 1.86 * 13.00 * (3.94 + 3.94) = 142.60 kips

142.60 kips >= Reaction V = 30.00 kips (OK)