bb.s.s.00111.00271

SHEAR PLATE CONNECTION SUMMARY

Filler Beam profile: W10X12
Support Girder profile: W18X35
Slope: 0 deg.
Skew: 88.6
Vertical Offset: -7.88
Horizontal Offset: 0
Span: 2.78 ft.
Reaction, V: 20 kips
Shear Capacity, Rn: 24.5 kips
Design/Reference according to AISC 14th Ed. - ASD
Shear Plate: Extended Configuration
Beam material grade: A992
Support material grade: A992
Plate material grade: A36
Weld grade: E70
Shear Plate Size: 10.500 in. x 5.500 in. x 0.875 in.
Configuration Geometry:
Welds at shear plate to support: 9/16 FILLET, 10/16 FILLET
Bolt: 2 rows x 3 columns 0.75 in. Diameter A325N_TC bolts
Vertical spacing: 3 in.
Horizontal spacing: 3 in.
Shear plate edge setback = 1 in.
Beam centerline setback = 1.02 in.
Edge distance at vertical edge of plate: 1.5 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: 2 in.
Edge distance at bottom edge of beam: 2.88 in.
Bottom cope depth: 1 in.
Bottom cope length: 2.5 in.
Horizontal distance to first hole: 3 in.
Down distance from top of filler beam flange: 3 in.
Holes in beam web: STD diameter = 0.812 in.
Holes in shear plate: SSL diameter = 0.812 in., slot width = 1 in.

BOLT STRENGTH BEAM SIDE:

Bolt Strength:
Using Instantaneous Center Of Rotation Method (AISC 7-1)
ex = 6.161 in.
Angle = 0.000 deg.
C = 2.165
Using Table 7-1 to determine (1/omega) * rn:
Rn = (1/omega) * rn * C = 11.93 * 2.16 = 25.82 kips

BOLT BEARING AT BEAM SIDE:
Vertical Shear Only Load Case:
ICR cordinate relative to CG = (1.79, -0.00)
At Row 1, At Column 1:
Ri1 = 11.71 kips
Ri vector at Beam   = <3.50, 11.17>
Lcsbm at Beam spacing  = 3.12 in.
Lcebm at Beam edge    = 2.74 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * 3.12 * (0.19/1) * 65.00 = 23.09 kips/bolt
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 2.74 * (0.19/1) * 65.00 = 20.29 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.19/1) * 65.00 = 11.11 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(23.09, 20.29, 11.11) = 11.11 kips/bolt
Ri vector at Shear Plate   = <-3.50, -11.17>
Lcsshpl at Shear Plate spacing  = 3.05 in.
Lceshpl at Shear Plate edge    = 4.03 in.
1/omegaRnsshpl at Shear Plate spacing = 1/omega * hf1 * Lcs * t * Fu = 0.50 * 1.20 * 3.05 * 0.88 * 58.00 = 92.86 kips/bolt
1/omegaRneshpl at Shear Plate edge = 1/omega * hf1 * Lce * t * Fu = 0.50 * 1.20 * 4.03 * 0.88 * 58.00 = 122.66 kips/bolt
1/omegaRndshpl on Shear Plate at Bolt Diameter   = 1/omega * hf2 * db * t * Fu = 0.50 * 2.40 * 0.75 * 0.88 * 58.00 = 45.67 kips/bolt
Shear Plate bearing capacity, 1/omegaRnshpl = min(1/omegaRnsshpl,1/omegaRneshpl,1/omegaRndshpl) = min(92.86, 122.66, 45.67) = 45.67 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(11.115, 45.675) = 11.11 kips/bolt
Bolt Shear Demand to Bearing ratio = 11.11 / 11.71 = 0.95

At Row 1, At Column 2:
Ri1 = 10.51 kips
Ri vector at Beam   = <6.76, 8.05>
Lcsbm at Beam spacing  = 3.12 in.
Lcebm at Beam edge    = 3.51 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * 3.12 * (0.19/1) * 65.00 = 23.09 kips/bolt
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 3.51 * (0.19/1) * 65.00 = 26.02 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.19/1) * 65.00 = 11.11 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(23.09, 26.02, 11.11) = 11.11 kips/bolt
Ri vector at Shear Plate   = <-6.76, -8.05>
Lcsshpl at Shear Plate spacing  = 3.05 in.
Lceshpl at Shear Plate edge    = 5.02 in.
1/omegaRnsshpl at Shear Plate spacing = 1/omega * hf1 * Lcs * t * Fu = 0.50 * 1.20 * 3.05 * 0.88 * 58.00 = 92.86 kips/bolt
1/omegaRneshpl at Shear Plate edge = 1/omega * hf1 * Lce * t * Fu = 0.50 * 1.20 * 5.02 * 0.88 * 58.00 = 152.85 kips/bolt
1/omegaRndshpl on Shear Plate at Bolt Diameter   = 1/omega * hf2 * db * t * Fu = 0.50 * 2.40 * 0.75 * 0.88 * 58.00 = 45.67 kips/bolt
Shear Plate bearing capacity, 1/omegaRnshpl = min(1/omegaRnsshpl,1/omegaRneshpl,1/omegaRndshpl) = min(92.86, 152.85, 45.67) = 45.67 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(11.115, 45.675) = 11.11 kips/bolt
Bolt Shear Demand to Bearing ratio = 11.11 / 10.51 = 1.06

At Row 1, At Column 3:
Ri1 = 10.03 kips
Ri vector at Beam   = <7.80, -6.31>
Lcsbm at Beam spacing  = 3.12 in.
Lcebm at Beam edge    = 10.52 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * 3.12 * (0.19/1) * 65.00 = 23.09 kips/bolt
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 10.52 * (0.19/1) * 65.00 = 77.93 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.19/1) * 65.00 = 11.11 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(23.09, 77.93, 11.11) = 11.11 kips/bolt
Ri vector at Shear Plate   = <-7.80, 6.31>
Lcsshpl at Shear Plate spacing  = 3.05 in.
Lceshpl at Shear Plate edge    = 1.34 in.
1/omegaRnsshpl at Shear Plate spacing = 1/omega * hf1 * Lcs * t * Fu = 0.50 * 1.20 * 3.05 * 0.88 * 58.00 = 92.86 kips/bolt
1/omegaRneshpl at Shear Plate edge = 1/omega * hf1 * Lce * t * Fu = 0.50 * 1.20 * 1.34 * 0.88 * 58.00 = 40.93 kips/bolt
1/omegaRndshpl on Shear Plate at Bolt Diameter   = 1/omega * hf2 * db * t * Fu = 0.50 * 2.40 * 0.75 * 0.88 * 58.00 = 45.67 kips/bolt
Shear Plate bearing capacity, 1/omegaRnshpl = min(1/omegaRnsshpl,1/omegaRneshpl,1/omegaRndshpl) = min(92.86, 40.93, 45.67) = 40.93 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(11.115, 40.932) = 11.11 kips/bolt
Bolt Shear Demand to Bearing ratio = 11.11 / 10.03 = 1.11

At Row 2, At Column 1:
Ri1 = 11.71 kips
Ri vector at Beam   = <-3.50, 11.17>
Lcsbm at Beam spacing  = 3.12 in.
Lcebm at Beam edge    = 5.88 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * 3.12 * (0.19/1) * 65.00 = 23.09 kips/bolt
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 5.88 * (0.19/1) * 65.00 = 43.58 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.19/1) * 65.00 = 11.11 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(23.09, 43.58, 11.11) = 11.11 kips/bolt
Ri vector at Shear Plate   = <3.50, -11.17>
Lcsshpl at Shear Plate spacing  = 3.05 in.
Lceshpl at Shear Plate edge    = 0.88 in.
1/omegaRnsshpl at Shear Plate spacing = 1/omega * hf1 * Lcs * t * Fu = 0.50 * 1.20 * 3.05 * 0.88 * 58.00 = 92.86 kips/bolt
1/omegaRneshpl at Shear Plate edge = 1/omega * hf1 * Lce * t * Fu = 0.50 * 1.20 * 0.88 * 0.88 * 58.00 = 26.92 kips/bolt
1/omegaRndshpl on Shear Plate at Bolt Diameter   = 1/omega * hf2 * db * t * Fu = 0.50 * 2.40 * 0.75 * 0.88 * 58.00 = 45.67 kips/bolt
Shear Plate bearing capacity, 1/omegaRnshpl = min(1/omegaRnsshpl,1/omegaRneshpl,1/omegaRndshpl) = min(92.86, 26.92, 45.67) = 26.92 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(11.115, 26.924) = 11.11 kips/bolt
Bolt Shear Demand to Bearing ratio = 11.11 / 11.71 = 0.95

At Row 2, At Column 2:
Ri1 = 10.51 kips
Ri vector at Beam   = <-6.76, 8.05>
Lcsbm at Beam spacing  = 3.12 in.
Lcebm at Beam edge    = 7.37 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * 3.12 * (0.19/1) * 65.00 = 23.09 kips/bolt
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 7.37 * (0.19/1) * 65.00 = 54.61 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.19/1) * 65.00 = 11.11 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(23.09, 54.61, 11.11) = 11.11 kips/bolt
Ri vector at Shear Plate   = <6.76, -8.05>
Lcsshpl at Shear Plate spacing  = 3.05 in.
Lceshpl at Shear Plate edge    = 1.10 in.
1/omegaRnsshpl at Shear Plate spacing = 1/omega * hf1 * Lcs * t * Fu = 0.50 * 1.20 * 3.05 * 0.88 * 58.00 = 92.86 kips/bolt
1/omegaRneshpl at Shear Plate edge = 1/omega * hf1 * Lce * t * Fu = 0.50 * 1.20 * 1.10 * 0.88 * 58.00 = 33.55 kips/bolt
1/omegaRndshpl on Shear Plate at Bolt Diameter   = 1/omega * hf2 * db * t * Fu = 0.50 * 2.40 * 0.75 * 0.88 * 58.00 = 45.67 kips/bolt
Shear Plate bearing capacity, 1/omegaRnshpl = min(1/omegaRnsshpl,1/omegaRneshpl,1/omegaRndshpl) = min(92.86, 33.55, 45.67) = 33.55 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(11.115, 33.547) = 11.11 kips/bolt
Bolt Shear Demand to Bearing ratio = 11.11 / 10.51 = 1.06

At Row 2, At Column 3:
Ri1 = 10.03 kips
Ri vector at Beam   = <-7.80, -6.31>
Lcsbm at Beam spacing  = 3.12 in.
Lcebm at Beam edge    = 5.75 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * 3.12 * (0.19/1) * 65.00 = 23.09 kips/bolt
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 5.75 * (0.19/1) * 65.00 = 42.57 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.19/1) * 65.00 = 11.11 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(23.09, 42.57, 11.11) = 11.11 kips/bolt
Ri vector at Shear Plate   = <7.80, 6.31>
Lcsshpl at Shear Plate spacing  = 3.05 in.
Lceshpl at Shear Plate edge    = 1.29 in.
1/omegaRnsshpl at Shear Plate spacing = 1/omega * hf1 * Lcs * t * Fu = 0.50 * 1.20 * 3.05 * 0.88 * 58.00 = 92.86 kips/bolt
1/omegaRneshpl at Shear Plate edge = 1/omega * hf1 * Lce * t * Fu = 0.50 * 1.20 * 1.29 * 0.88 * 58.00 = 39.17 kips/bolt
1/omegaRndshpl on Shear Plate at Bolt Diameter   = 1/omega * hf2 * db * t * Fu = 0.50 * 2.40 * 0.75 * 0.88 * 58.00 = 45.67 kips/bolt
Shear Plate bearing capacity, 1/omegaRnshpl = min(1/omegaRnsshpl,1/omegaRneshpl,1/omegaRndshpl) = min(92.86, 39.17, 45.67) = 39.17 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(11.115, 39.173) = 11.11 kips/bolt
Bolt Shear Demand to Bearing ratio = 11.11 / 10.03 = 1.11

Min Bolt Shear Demand to Bearing ratio for vertical shear only = min(1.0, 0.949382, 1.05767, 1.10819, 0.949384, 1.0577, 1.10825) = 0.95


Bearing Capacity at Beam and Shear Plate at Vertical Shear Load Only, Rbv1 = Min Bolt Shear Demand to Bearing Ratio * Bolt Shear = 0.95 * 25.82 = 24.51 kips

Web Depth = d - [Top Cope Depth] - [Bottom Cope Depth] = 9.87 - 0 - 1 = 8.87 in.
Gross Area (Shear) = [Web Depth] * tw = 8.87 * 0.19 = 1.69 in^2
Net Shear Area (Shear) = ([Web Depth] - ([# rows] * [Diameter + 0.0625])) * tw 
    = (8.87 - (2 * 0.88)) * 0.19 = 1.35 in^2

Using Eq.J4-3:
Shear Yielding = (1/omega) * 0.6 * Fybeam * [Gross Area] = 0.67 * 0.6 * 50.00 * 1.69 = 33.71 kips

Using Eq.J4-4:
Shear Rupture = (1/omega) * 0.6 * Fubeam * [Net Area] = 0.50 * 0.6 * 65.00 * 1.35 = 26.38 kips


Block Shear

Using Eq.J4-5:
Block Shear = {(1/omega) * ((0.6 * Fu * Anv) + (Ubs * Fu * Ant))} <= {(1/omega) * ((0.6 * Fy * Agv) + (Ubs * Fu * Ant))}

Block Shear not required.


Flexure at Longest Cope (Bottom Cope Only at Section)
Eccentricity at Section, e = 3.66 in.
Fy = 50.00 ksi
Snet1 (bolt holes not applicable) = 3.63 in^3
Snet2 (bolt holes applicable) = 3.63 in^3
Znet = 6.34 in^3

Using Eq. 9-19
Flexural Yielding = (1/omega) * Fy * Snet1 / e = 0.60 * 50.00 * 3.63 / 3.66 = 29.79 kips

Using Eq. 9-4
Flexural Rupture = (1/omega) * Fu * Znet / e = 0.50 * 65.00 * 6.34 / 3.66 = 56.29 kips


Flexure at Furthest Bolt Line within Cope (Bottom Cope Only at Section)
Eccentricity at Section, e = 3.16 in.
Fy = 50.00 ksi
Snet1 (bolt holes not applicable) = 3.63 in^3
Snet2 (bolt holes applicable) = 3.24 in^3
Znet = 5.48 in^3

Using Eq. 9-19
Flexural Yielding = (1/omega) * Fy * Snet1 / e = 0.60 * 50.00 * 3.63 / 3.16 = 34.50 kips

Using Eq. 9-4
Flexural Rupture = (1/omega) * Fu * Znet / e = 0.50 * 65.00 * 5.48 / 3.16 = 56.35 kips


Section Bending Strength Calculations Summary:

   Coped Beam Flexure at Longest Cope (Bottom Cope Only at Section)
   Flexural Yielding : 29.79 >= 20.00 kips (OK)
   Flexural Rupture : 56.29 >= 20.00 kips (OK)

   Coped Beam Flexure at Furthest Bolt Line within Cope (Bottom Cope Only at Section)
   Flexural Yielding : 34.50 >= 20.00 kips (OK)
   Flexural Rupture : 56.35 >= 20.00 kips (OK)

Gross Area = 0.88 * 5.50 = 4.81 in^2
Net Area = (5.50 - (2 *(0.81 + 1/16))) * 0.88 = 3.28 in^2

Using Eq.J4-3:
Shear Yielding = (1/omega) * 0.6 * Fypl * [Gross Area] = 0.67 * 0.6 * 36.00 * 4.81 = 69.30 kips

Using Eq.J4-4:
Shear Rupture = (1/omega) * 0.6 * Fupl * [Net Area] = 0.50 * 0.6 * 58.00 * 3.28 = 57.09 kips


Block Shear

Using Eq.J4-5:
Block Shear = {(1/omega) * ((0.6 * Fu * Anv) + (Ubs * Fu * Ant))} <= {(1/omega) * ((0.6 * Fy * Agv) + (Ubs * Fu * Ant))}
Block 1 (Shear): 
Gross Shear Length = (5.5 - 1.25) = 4.25 in.
Net Shear Length = 4.25 - (1.5 * (0.812 + 0.0625)) = 2.94 in.
Gross Tension Length = (6 + 1.5) = 7.50 in.
Net Tension Length = 7.5 - (2.5 * (1 + 0.0625)) = 4.84 in.
1. (1/omega) * [material thickness] * ((0.60 * Fupl* [net shear length]) + (Ubs * Fupl * [net tension length])) 
    = 0.50 * 0.88 * ((0.60 * 58.00 * 2.94) + (0.50 * 58.00 * 4.84)) = 106.18 kips
2. (1/omega) * [material thickness] * ((0.60 * Fypl * [gross shear length]) + (Ubs * Fupl * [net tension length])) 
    = 0.50 * 0.88 * ((0.60 * 36.00 * 4.25) + (0.50 * 58.00 * 4.84)) = 101.62 kips
Block Shear = 101.62 kips

Block 2 (Shear): 
Gross Shear Length = 2 * (5.5 - 1.25) = 8.50 in.
Net Shear Length = 2 * ( 4.25 - (1.5 * (0.812 + 0.0625)) ) = 5.88 in.
Gross Tension Length = (6 + 1.5) - 1.5 = 6.00 in.
Net Tension Length = 6 - 2 * (1 + 0.0625) = 3.88 in.
1. (1/omega) * [material thickness] * ((0.60 * Fupl* [net shear length]) + (Ubs * Fupl * [net tension length])) 
    = 0.50 * 0.88 * ((0.60 * 58.00 * 5.88) + (0.50 * 58.00 * 3.88)) = 138.61 kips
2. (1/omega) * [material thickness] * ((0.60 * Fypl * [gross shear length]) + (Ubs * Fupl * [net tension length])) 
    = 0.50 * 0.88 * ((0.60 * 36.00 * 8.50) + (0.50 * 58.00 * 3.88)) = 129.49 kips
Block Shear = 129.49 kips

Flexural and Buckling Strength:

Eccentricity at first line of bolts, e = 3.16 in.
Zgross = 6.62 in^3
Znet   = 4.32 in^3
Sgross = 4.41 in^3
Snet   = 3.16 in^3

Using Eq. 9-4
Flexural Rupture = (1/omega) * Fu * Znet / e = 0.50 * 58.00 * 4.32 / 3.16 = 39.64 kips


Using Eq. 9-14 through 9-18, Fcr = Fy * Q
tw = 0.88 in.
ho = 5.50 in.
c = 3.01 in.
lambda = (ho * Fy ^ 0.5) / ( 10 * tw * ( 475.00 + 280.00 * (ho / c)^2 ) ^0.5 ) = 
 = 5.50 * 36.00^0.5 / (10 * 0.88 * (475.00 + 280.00 * (5.50/3.01)^2 )^0.5) = 0.10
When lambda <= 0.70, Q=1
Q = 1.00
Fcrmin =1/omega * Fcr = 0.60 * 36.00 * 1.00 = 21.60 ksi

Using Eq. 9-6
Buckling = Fcr * Sgross / e = 21.60 * 4.41 / 3.16 = 30.15 kips

Interaction Check of Flexural Yielding, Per AISC 10-5: 
Eccentricity at CG of Bolt Group, e = 6.16 in.
Zgross = 6.62
Znet = 4.32
Mr = Vr * e = 20.00 * 6.16 = 123.21 kips-in
Mc = 1/omega * Mn = 1/omega * Fy * Zgross = 0.60 * 36.00 * 6.62 = 142.93 kips-in
Vr = 20.00 kips
Vc = 1/omega * Vn = 1/omega * 0.60 * Fy * Ag = 0.67 * 0.60 * 36.00 * 4.81 = 69.30 kips
Interaction due to moment and shear, (Vr/Vc)^2 + (Mr/Mc)^2 <= 1.0
(Vr/Vc)^2 + (Mr/Mc)^2 = (20.00 / 69.30)^2 + (123.21 / 142.93)^2 = 0.83 <= 1  (OK)

Note: Mn <= 1.6My by inspection

MAXIMUM PLATE THICKNESS:
tmax = 6 * Mmax / (Fypl * d^2) Eq. 10-3
Mmax = (1/0.9) * Fv * Ab * C' Eq. 10-4
Mmax = (1/0.9) * 54 * 0.441786 * 15.7877 = 418.487 kips-in
tmax = 6 * 418.487 / (36 * 5.5^2) = 2.31 in.
Maximum Plate Thickness is Not a Limiting Criteria.

WELD:

 Weld Requirements:

At shear only case: 
Weld Length for shear, Lv = 5.500 in.
Shear Load per inch per weld, fv = R/Lv/2 = 20.000 / 5.500 / 2 = 1.818 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/ (1/omega * coeff) = 1.818 / (0.500 * 1.856) = 1.959/16

Minimum fillet weld size : 
   At shear only load case = 0.12 in.
   per Table J2.4     = 0.19 in.
   5/8(tp)            = 0.55 in.
   user preference    = 0.25 in.

Dmax1 (using eqn 9-3)
 = tshpl * Fushpl / ( Fexx * C1 * 0.088)
 = 0.875 * 58.000 / ( 70.000 * 1.000 * 0.088 ) 
 = 8.202 
Dmax2 (using eqn 9-3)
 = twsupport * Fusupport / ( Fexx * C1 * 0.088 )
 = 0.300 * 65.000 / ( 70.000 * 1.000 * 0.088 ) 
 = 3.152 
Dmax3 = project max fillet weld = 12.000
Dmax=min(Dmax1, Dmax2, Dmax3) = min(8.202, 3.152, 12.000)
 = 3.152 

Dihedral Angle, DA       = 88.60 deg.
Gap on Obtuse Angle Side = 0.02 in.
Use weld size
Acute Side  D1 = 9.00
Obtuse Side D2 = 10.00

Weld Strength :
Vertical weld capacity during shear only load, 1/omega * Rnv1 = 0.50 * 1.86 * 5.50 * (3.15 + 3.15) = 32.18 kips
Check Effective Throat:
Acute Side Effect throat  = (D1/sin(DA)) * cos(DA/2) = (0.56/ sin( 88.60)) * cos( 44.30) = 0.40 in.
Obtuse Side Effect throat = ((D2/sin(DA)-tshpl/tan(DA))*sin((180-(180-DA))/2))= ((0.62 / sin(88.60) -0.88 / tan(88.60)) * sin((180 - (180 - 88.60)) / 2)) = 0.38 in.
Total Effective Throat    = 0.40 + 0.38 = 0.82 in.
Total Effective Throat of Square Case = D1 * 2^0.5 = 0.56 * 2^0.5 = 0.80 in.
0.80 in. <= 0.82 in. (OK)