bhss.s.s.00007.00007

SHEAR PLATE CONNECTION SUMMARY

Filler Beam profile: W24X55
Column profile: HSS12X12X1/2
Slope: 0 deg.
Skew: 90
Vertical Offset: -0.0901
Horizontal Offset: 0
Span: 19.6 ft.
Reaction, V: 103 kips
Shear Capacity, Rn: 125 kips
Design/Reference according to AISC 14th Ed. - ASD
Shear Plate: Extended Configuration
Beam material grade: A992
Support material grade: A500-GR.B
Plate material grade: A36
Weld grade: E70
Shear Plate Size: 7.500 in. x 20.500 in. x 0.500 in.
Configuration Geometry:
Welds at shear plate to support: 5/16 FILLET, 5/16 FILLET
Bolt: 7 rows x 2 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 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.
Horizontal distance to first hole: 3 in.
Down distance from top of filler beam flange: 2.75 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 = 4.500 in.
Angle = 0.000 deg.
C = 10.575
Using Table 7-1 to determine (1/omega) * rn:
Rn = (1/omega) * rn * C = 11.93 * 10.57 = 126.14 kips

BOLT BEARING AT BEAM SIDE:
Vertical Shear Only Load Case:
ICR cordinate relative to CG = (7.32, 0.00)
At Row 1, At Column 1:
Ri1 = 11.71 kips
Ri vector at Beam   = <8.36, 8.19>
Lcsbm at Beam spacing  = 3.12 in.
Lcebm at Beam edge    = 3.52 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * 3.12 * (0.40/1) * 65.00 = 48.00 kips/bolt
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 3.52 * (0.40/1) * 65.00 = 54.28 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.40/1) * 65.00 = 23.11 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(48.00, 54.28, 23.11) = 23.11 kips/bolt
Ri vector at Shear Plate   = <-8.36, -8.19>
Lcsshpl at Shear Plate spacing  = 3.05 in.
Lceshpl at Shear Plate edge    = 3.62 in.
1/omegaRnsshpl at Shear Plate spacing = 1/omega * hf1 * Lcs * t * Fu = 0.50 * 1.20 * 3.05 * 0.50 * 58.00 = 53.07 kips/bolt
1/omegaRneshpl at Shear Plate edge = 1/omega * hf1 * Lce * t * Fu = 0.50 * 1.20 * 3.62 * 0.50 * 58.00 = 62.97 kips/bolt
1/omegaRndshpl on Shear Plate at Bolt Diameter   = 1/omega * hf2 * db * t * Fu = 0.50 * 2.40 * 0.75 * 0.50 * 58.00 = 26.10 kips/bolt
Shear Plate bearing capacity, 1/omegaRnshpl = min(1/omegaRnsshpl,1/omegaRneshpl,1/omegaRndshpl) = min(53.07, 62.97, 26.10) = 26.10 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(23.107, 26.100) = 23.11 kips/bolt
Bolt Shear Demand to Bearing ratio = 23.11 / 11.71 = 1.97

At Row 1, At Column 2:
Ri1 = 11.56 kips
Ri vector at Beam   = <9.71, 6.27>
Lcsbm at Beam spacing  = 3.12 in.
Lcebm at Beam edge    = 4.66 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * 3.12 * (0.40/1) * 65.00 = 48.00 kips/bolt
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 4.66 * (0.40/1) * 65.00 = 71.80 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.40/1) * 65.00 = 23.11 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(48.00, 71.80, 23.11) = 23.11 kips/bolt
Ri vector at Shear Plate   = <-9.71, -6.27>
Lcsshpl at Shear Plate spacing  = 3.05 in.
Lceshpl at Shear Plate edge    = 6.55 in.
1/omegaRnsshpl at Shear Plate spacing = 1/omega * hf1 * Lcs * t * Fu = 0.50 * 1.20 * 3.05 * 0.50 * 58.00 = 53.07 kips/bolt
1/omegaRneshpl at Shear Plate edge = 1/omega * hf1 * Lce * t * Fu = 0.50 * 1.20 * 6.55 * 0.50 * 58.00 = 113.94 kips/bolt
1/omegaRndshpl on Shear Plate at Bolt Diameter   = 1/omega * hf2 * db * t * Fu = 0.50 * 2.40 * 0.75 * 0.50 * 58.00 = 26.10 kips/bolt
Shear Plate bearing capacity, 1/omegaRnshpl = min(1/omegaRnsshpl,1/omegaRneshpl,1/omegaRndshpl) = min(53.07, 113.94, 26.10) = 26.10 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(23.107, 26.100) = 23.11 kips/bolt
Bolt Shear Demand to Bearing ratio = 23.11 / 11.56 = 2.00

At Row 2, At Column 1:
Ri1 = 11.55 kips
Ri vector at Beam   = <6.50, 9.55>
Lcsbm at Beam spacing  = 3.12 in.
Lcebm at Beam edge    = 6.55 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * 3.12 * (0.40/1) * 65.00 = 48.00 kips/bolt
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 6.55 * (0.40/1) * 65.00 = 100.89 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.40/1) * 65.00 = 23.11 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(48.00, 100.89, 23.11) = 23.11 kips/bolt
Ri vector at Shear Plate   = <-6.50, -9.55>
Lcsshpl at Shear Plate spacing  = 3.05 in.
Lceshpl at Shear Plate edge    = 4.84 in.
1/omegaRnsshpl at Shear Plate spacing = 1/omega * hf1 * Lcs * t * Fu = 0.50 * 1.20 * 3.05 * 0.50 * 58.00 = 53.07 kips/bolt
1/omegaRneshpl at Shear Plate edge = 1/omega * hf1 * Lce * t * Fu = 0.50 * 1.20 * 4.84 * 0.50 * 58.00 = 84.22 kips/bolt
1/omegaRndshpl on Shear Plate at Bolt Diameter   = 1/omega * hf2 * db * t * Fu = 0.50 * 2.40 * 0.75 * 0.50 * 58.00 = 26.10 kips/bolt
Shear Plate bearing capacity, 1/omegaRnshpl = min(1/omegaRnsshpl,1/omegaRneshpl,1/omegaRndshpl) = min(53.07, 84.22, 26.10) = 26.10 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(23.107, 26.100) = 23.11 kips/bolt
Bolt Shear Demand to Bearing ratio = 23.11 / 11.55 = 2.00

At Row 2, At Column 2:
Ri1 = 11.22 kips
Ri vector at Beam   = <8.06, 7.81>
Lcsbm at Beam spacing  = 3.12 in.
Lcebm at Beam edge    = 7.86 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * 3.12 * (0.40/1) * 65.00 = 48.00 kips/bolt
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 7.86 * (0.40/1) * 65.00 = 121.02 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.40/1) * 65.00 = 23.11 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(48.00, 121.02, 23.11) = 23.11 kips/bolt
Ri vector at Shear Plate   = <-8.06, -7.81>
Lcsshpl at Shear Plate spacing  = 3.05 in.
Lceshpl at Shear Plate edge    = 7.77 in.
1/omegaRnsshpl at Shear Plate spacing = 1/omega * hf1 * Lcs * t * Fu = 0.50 * 1.20 * 3.05 * 0.50 * 58.00 = 53.07 kips/bolt
1/omegaRneshpl at Shear Plate edge = 1/omega * hf1 * Lce * t * Fu = 0.50 * 1.20 * 7.77 * 0.50 * 58.00 = 135.23 kips/bolt
1/omegaRndshpl on Shear Plate at Bolt Diameter   = 1/omega * hf2 * db * t * Fu = 0.50 * 2.40 * 0.75 * 0.50 * 58.00 = 26.10 kips/bolt
Shear Plate bearing capacity, 1/omegaRnshpl = min(1/omegaRnsshpl,1/omegaRneshpl,1/omegaRndshpl) = min(53.07, 135.23, 26.10) = 26.10 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(23.107, 26.100) = 23.11 kips/bolt
Bolt Shear Demand to Bearing ratio = 23.11 / 11.22 = 2.06

At Row 3, At Column 1:
Ri1 = 11.39 kips
Ri vector at Beam   = <3.67, 10.78>
Lcsbm at Beam spacing  = 3.12 in.
Lcebm at Beam edge    = 8.84 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * 3.12 * (0.40/1) * 65.00 = 48.00 kips/bolt
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 8.84 * (0.40/1) * 65.00 = 136.13 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.40/1) * 65.00 = 23.11 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(48.00, 136.13, 23.11) = 23.11 kips/bolt
Ri vector at Shear Plate   = <-3.67, -10.78>
Lcsshpl at Shear Plate spacing  = 3.05 in.
Lceshpl at Shear Plate edge    = 8.88 in.
1/omegaRnsshpl at Shear Plate spacing = 1/omega * hf1 * Lcs * t * Fu = 0.50 * 1.20 * 3.05 * 0.50 * 58.00 = 53.07 kips/bolt
1/omegaRneshpl at Shear Plate edge = 1/omega * hf1 * Lce * t * Fu = 0.50 * 1.20 * 8.88 * 0.50 * 58.00 = 154.57 kips/bolt
1/omegaRndshpl on Shear Plate at Bolt Diameter   = 1/omega * hf2 * db * t * Fu = 0.50 * 2.40 * 0.75 * 0.50 * 58.00 = 26.10 kips/bolt
Shear Plate bearing capacity, 1/omegaRnshpl = min(1/omegaRnsshpl,1/omegaRneshpl,1/omegaRndshpl) = min(53.07, 154.57, 26.10) = 26.10 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(23.107, 26.100) = 23.11 kips/bolt
Bolt Shear Demand to Bearing ratio = 23.11 / 11.39 = 2.03

At Row 3, At Column 2:
Ri1 = 10.76 kips
Ri vector at Beam   = <4.93, 9.56>
Lcsbm at Beam spacing  = 3.12 in.
Lcebm at Beam edge    = 9.44 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * 3.12 * (0.40/1) * 65.00 = 48.00 kips/bolt
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 9.44 * (0.40/1) * 65.00 = 145.41 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.40/1) * 65.00 = 23.11 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(48.00, 145.41, 23.11) = 23.11 kips/bolt
Ri vector at Shear Plate   = <-4.93, -9.56>
Lcsshpl at Shear Plate spacing  = 3.05 in.
Lceshpl at Shear Plate edge    = 12.63 in.
1/omegaRnsshpl at Shear Plate spacing = 1/omega * hf1 * Lcs * t * Fu = 0.50 * 1.20 * 3.05 * 0.50 * 58.00 = 53.07 kips/bolt
1/omegaRneshpl at Shear Plate edge = 1/omega * hf1 * Lce * t * Fu = 0.50 * 1.20 * 12.63 * 0.50 * 58.00 = 219.77 kips/bolt
1/omegaRndshpl on Shear Plate at Bolt Diameter   = 1/omega * hf2 * db * t * Fu = 0.50 * 2.40 * 0.75 * 0.50 * 58.00 = 26.10 kips/bolt
Shear Plate bearing capacity, 1/omegaRnshpl = min(1/omegaRnsshpl,1/omegaRneshpl,1/omegaRndshpl) = min(53.07, 219.77, 26.10) = 26.10 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(23.107, 26.100) = 23.11 kips/bolt
Bolt Shear Demand to Bearing ratio = 23.11 / 10.76 = 2.15

At Row 4, At Column 1:
Ri1 = 11.31 kips
Ri vector at Beam   = <-0.00, 11.31>
Lcsbm at Beam spacing  = 2.19 in.
Lcebm at Beam edge    = 11.34 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * 2.19 * (0.40/1) * 65.00 = 33.70 kips/bolt
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 11.34 * (0.40/1) * 65.00 = 174.75 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.40/1) * 65.00 = 23.11 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(33.70, 174.75, 23.11) = 23.11 kips/bolt
Ri vector at Shear Plate   = <0.00, -11.31>
Lcsshpl at Shear Plate spacing  = 2.19 in.
Lceshpl at Shear Plate edge    = 9.84 in.
1/omegaRnsshpl at Shear Plate spacing = 1/omega * hf1 * Lcs * t * Fu = 0.50 * 1.20 * 2.19 * 0.50 * 58.00 = 38.06 kips/bolt
1/omegaRneshpl at Shear Plate edge = 1/omega * hf1 * Lce * t * Fu = 0.50 * 1.20 * 9.84 * 0.50 * 58.00 = 171.28 kips/bolt
1/omegaRndshpl on Shear Plate at Bolt Diameter   = 1/omega * hf2 * db * t * Fu = 0.50 * 2.40 * 0.75 * 0.50 * 58.00 = 26.10 kips/bolt
Shear Plate bearing capacity, 1/omegaRnshpl = min(1/omegaRnsshpl,1/omegaRneshpl,1/omegaRndshpl) = min(38.06, 171.28, 26.10) = 26.10 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(23.107, 26.100) = 23.11 kips/bolt
Bolt Shear Demand to Bearing ratio = 23.11 / 11.31 = 2.04

At Row 4, At Column 2:
Ri1 = 10.49 kips
Ri vector at Beam   = <-0.00, 10.49>
Lcsbm at Beam spacing  = 2.19 in.
Lcebm at Beam edge    = 11.34 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * 2.19 * (0.40/1) * 65.00 = 33.70 kips/bolt
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 11.34 * (0.40/1) * 65.00 = 174.75 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.40/1) * 65.00 = 23.11 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(33.70, 174.75, 23.11) = 23.11 kips/bolt
Ri vector at Shear Plate   = <0.00, -10.49>
Lcsshpl at Shear Plate spacing  = 2.19 in.
Lceshpl at Shear Plate edge    = 9.84 in.
1/omegaRnsshpl at Shear Plate spacing = 1/omega * hf1 * Lcs * t * Fu = 0.50 * 1.20 * 2.19 * 0.50 * 58.00 = 38.06 kips/bolt
1/omegaRneshpl at Shear Plate edge = 1/omega * hf1 * Lce * t * Fu = 0.50 * 1.20 * 9.84 * 0.50 * 58.00 = 171.28 kips/bolt
1/omegaRndshpl on Shear Plate at Bolt Diameter   = 1/omega * hf2 * db * t * Fu = 0.50 * 2.40 * 0.75 * 0.50 * 58.00 = 26.10 kips/bolt
Shear Plate bearing capacity, 1/omegaRnshpl = min(1/omegaRnsshpl,1/omegaRneshpl,1/omegaRndshpl) = min(38.06, 171.28, 26.10) = 26.10 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(23.107, 26.100) = 23.11 kips/bolt
Bolt Shear Demand to Bearing ratio = 23.11 / 10.49 = 2.20

At Row 5, At Column 1:
Ri1 = 11.39 kips
Ri vector at Beam   = <-3.67, 10.78>
Lcsbm at Beam spacing  = 3.12 in.
Lcebm at Beam edge    = 5.80 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * 3.12 * (0.40/1) * 65.00 = 48.00 kips/bolt
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 5.80 * (0.40/1) * 65.00 = 89.37 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.40/1) * 65.00 = 23.11 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(48.00, 89.37, 23.11) = 23.11 kips/bolt
Ri vector at Shear Plate   = <3.67, -10.78>
Lcsshpl at Shear Plate spacing  = 3.05 in.
Lceshpl at Shear Plate edge    = 7.23 in.
1/omegaRnsshpl at Shear Plate spacing = 1/omega * hf1 * Lcs * t * Fu = 0.50 * 1.20 * 3.05 * 0.50 * 58.00 = 53.07 kips/bolt
1/omegaRneshpl at Shear Plate edge = 1/omega * hf1 * Lce * t * Fu = 0.50 * 1.20 * 7.23 * 0.50 * 58.00 = 125.79 kips/bolt
1/omegaRndshpl on Shear Plate at Bolt Diameter   = 1/omega * hf2 * db * t * Fu = 0.50 * 2.40 * 0.75 * 0.50 * 58.00 = 26.10 kips/bolt
Shear Plate bearing capacity, 1/omegaRnshpl = min(1/omegaRnsshpl,1/omegaRneshpl,1/omegaRndshpl) = min(53.07, 125.79, 26.10) = 26.10 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(23.107, 26.100) = 23.11 kips/bolt
Bolt Shear Demand to Bearing ratio = 23.11 / 11.39 = 2.03

At Row 5, At Column 2:
Ri1 = 10.76 kips
Ri vector at Beam   = <-4.93, 9.56>
Lcsbm at Beam spacing  = 3.12 in.
Lcebm at Beam edge    = 10.50 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * 3.12 * (0.40/1) * 65.00 = 48.00 kips/bolt
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 10.50 * (0.40/1) * 65.00 = 161.74 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.40/1) * 65.00 = 23.11 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(48.00, 161.74, 23.11) = 23.11 kips/bolt
Ri vector at Shear Plate   = <4.93, -9.56>
Lcsshpl at Shear Plate spacing  = 3.05 in.
Lceshpl at Shear Plate edge    = 2.81 in.
1/omegaRnsshpl at Shear Plate spacing = 1/omega * hf1 * Lcs * t * Fu = 0.50 * 1.20 * 3.05 * 0.50 * 58.00 = 53.07 kips/bolt
1/omegaRneshpl at Shear Plate edge = 1/omega * hf1 * Lce * t * Fu = 0.50 * 1.20 * 2.81 * 0.50 * 58.00 = 48.97 kips/bolt
1/omegaRndshpl on Shear Plate at Bolt Diameter   = 1/omega * hf2 * db * t * Fu = 0.50 * 2.40 * 0.75 * 0.50 * 58.00 = 26.10 kips/bolt
Shear Plate bearing capacity, 1/omegaRnshpl = min(1/omegaRnsshpl,1/omegaRneshpl,1/omegaRndshpl) = min(53.07, 48.97, 26.10) = 26.10 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(23.107, 26.100) = 23.11 kips/bolt
Bolt Shear Demand to Bearing ratio = 23.11 / 10.76 = 2.15

At Row 6, At Column 1:
Ri1 = 11.55 kips
Ri vector at Beam   = <-6.50, 9.55>
Lcsbm at Beam spacing  = 3.12 in.
Lcebm at Beam edge    = 3.15 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * 3.12 * (0.40/1) * 65.00 = 48.00 kips/bolt
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 3.15 * (0.40/1) * 65.00 = 48.50 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.40/1) * 65.00 = 23.11 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(48.00, 48.50, 23.11) = 23.11 kips/bolt
Ri vector at Shear Plate   = <6.50, -9.55>
Lcsshpl at Shear Plate spacing  = 3.05 in.
Lceshpl at Shear Plate edge    = 4.65 in.
1/omegaRnsshpl at Shear Plate spacing = 1/omega * hf1 * Lcs * t * Fu = 0.50 * 1.20 * 3.05 * 0.50 * 58.00 = 53.07 kips/bolt
1/omegaRneshpl at Shear Plate edge = 1/omega * hf1 * Lce * t * Fu = 0.50 * 1.20 * 4.65 * 0.50 * 58.00 = 80.90 kips/bolt
1/omegaRndshpl on Shear Plate at Bolt Diameter   = 1/omega * hf2 * db * t * Fu = 0.50 * 2.40 * 0.75 * 0.50 * 58.00 = 26.10 kips/bolt
Shear Plate bearing capacity, 1/omegaRnshpl = min(1/omegaRnsshpl,1/omegaRneshpl,1/omegaRndshpl) = min(53.07, 80.90, 26.10) = 26.10 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(23.107, 26.100) = 23.11 kips/bolt
Bolt Shear Demand to Bearing ratio = 23.11 / 11.55 = 2.00

At Row 6, At Column 2:
Ri1 = 11.22 kips
Ri vector at Beam   = <-8.06, 7.81>
Lcsbm at Beam spacing  = 3.12 in.
Lcebm at Beam edge    = 6.56 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * 3.12 * (0.40/1) * 65.00 = 48.00 kips/bolt
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 6.56 * (0.40/1) * 65.00 = 101.01 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.40/1) * 65.00 = 23.11 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(48.00, 101.01, 23.11) = 23.11 kips/bolt
Ri vector at Shear Plate   = <8.06, -7.81>
Lcsshpl at Shear Plate spacing  = 3.05 in.
Lceshpl at Shear Plate edge    = 1.51 in.
1/omegaRnsshpl at Shear Plate spacing = 1/omega * hf1 * Lcs * t * Fu = 0.50 * 1.20 * 3.05 * 0.50 * 58.00 = 53.07 kips/bolt
1/omegaRneshpl at Shear Plate edge = 1/omega * hf1 * Lce * t * Fu = 0.50 * 1.20 * 1.51 * 0.50 * 58.00 = 26.19 kips/bolt
1/omegaRndshpl on Shear Plate at Bolt Diameter   = 1/omega * hf2 * db * t * Fu = 0.50 * 2.40 * 0.75 * 0.50 * 58.00 = 26.10 kips/bolt
Shear Plate bearing capacity, 1/omegaRnshpl = min(1/omegaRnsshpl,1/omegaRneshpl,1/omegaRndshpl) = min(53.07, 26.19, 26.10) = 26.10 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(23.107, 26.100) = 23.11 kips/bolt
Bolt Shear Demand to Bearing ratio = 23.11 / 11.22 = 2.06

At Row 7, At Column 1:
Ri1 = 11.71 kips
Ri vector at Beam   = <-8.36, 8.19>
Lcsbm at Beam spacing  = 3.12 in.
Lcebm at Beam edge    = 2.39 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * 3.12 * (0.40/1) * 65.00 = 48.00 kips/bolt
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 2.39 * (0.40/1) * 65.00 = 36.87 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.40/1) * 65.00 = 23.11 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(48.00, 36.87, 23.11) = 23.11 kips/bolt
Ri vector at Shear Plate   = <8.36, -8.19>
Lcsshpl at Shear Plate spacing  = 3.05 in.
Lceshpl at Shear Plate edge    = 1.21 in.
1/omegaRnsshpl at Shear Plate spacing = 1/omega * hf1 * Lcs * t * Fu = 0.50 * 1.20 * 3.05 * 0.50 * 58.00 = 53.07 kips/bolt
1/omegaRneshpl at Shear Plate edge = 1/omega * hf1 * Lce * t * Fu = 0.50 * 1.20 * 1.21 * 0.50 * 58.00 = 20.98 kips/bolt
1/omegaRndshpl on Shear Plate at Bolt Diameter   = 1/omega * hf2 * db * t * Fu = 0.50 * 2.40 * 0.75 * 0.50 * 58.00 = 26.10 kips/bolt
Shear Plate bearing capacity, 1/omegaRnshpl = min(1/omegaRnsshpl,1/omegaRneshpl,1/omegaRndshpl) = min(53.07, 20.98, 26.10) = 20.98 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(23.107, 20.981) = 20.98 kips/bolt
Bolt Shear Demand to Bearing ratio = 20.98 / 11.71 = 1.79

At Row 7, At Column 2:
Ri1 = 11.56 kips
Ri vector at Beam   = <-9.71, 6.27>
Lcsbm at Beam spacing  = 3.12 in.
Lcebm at Beam edge    = 5.55 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * 3.12 * (0.40/1) * 65.00 = 48.00 kips/bolt
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 5.55 * (0.40/1) * 65.00 = 85.45 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.40/1) * 65.00 = 23.11 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(48.00, 85.45, 23.11) = 23.11 kips/bolt
Ri vector at Shear Plate   = <9.71, -6.27>
Lcsshpl at Shear Plate spacing  = 3.05 in.
Lceshpl at Shear Plate edge    = 1.19 in.
1/omegaRnsshpl at Shear Plate spacing = 1/omega * hf1 * Lcs * t * Fu = 0.50 * 1.20 * 3.05 * 0.50 * 58.00 = 53.07 kips/bolt
1/omegaRneshpl at Shear Plate edge = 1/omega * hf1 * Lce * t * Fu = 0.50 * 1.20 * 1.19 * 0.50 * 58.00 = 20.72 kips/bolt
1/omegaRndshpl on Shear Plate at Bolt Diameter   = 1/omega * hf2 * db * t * Fu = 0.50 * 2.40 * 0.75 * 0.50 * 58.00 = 26.10 kips/bolt
Shear Plate bearing capacity, 1/omegaRnshpl = min(1/omegaRnsshpl,1/omegaRneshpl,1/omegaRndshpl) = min(53.07, 20.72, 26.10) = 20.72 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(23.107, 20.716) = 20.72 kips/bolt
Bolt Shear Demand to Bearing ratio = 20.72 / 11.56 = 1.79

Min Bolt Shear Demand to Bearing ratio for vertical shear only = min(1.0, 1.97372, 1.99898, 1.99989, 2.05892, 2.02936, 2.14773, 2.04361, 2.20256, 2.02935, 2.14772, 1.99989, 2.05891, 1.79212, 1.7921) = 1.00


Bearing Capacity at Beam and Shear Plate at Vertical Shear Load Only, Rbv1 = Min Bolt Shear Demand to Bearing Ratio * Bolt Shear = 1.00 * 126.14 = 126.14 kips

Web Depth = d - [Top Cope Depth] - [Bottom Cope Depth] = 23.6 - 0 - 0 = 23.6 in.
Gross Area (Shear) = [Web Depth] * tw = 23.60 * 0.40 = 9.32 in^2
Net Shear Area (Shear) = ([Web Depth] - ([# rows] * [Diameter + 0.0625])) * tw 
    = (23.60 - (7 * 0.88)) * 0.40 = 6.90 in^2

Using Eq.J4-3:
Shear Yielding = (1/omega) * 0.6 * Fybeam * [Gross Area] = 0.67 * 0.6 * 50.00 * 9.32 = 186.44 kips

Using Eq.J4-4:
Shear Rupture = (1/omega) * 0.6 * Fubeam * [Net Area] = 0.50 * 0.6 * 65.00 * 6.90 = 134.60 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.

Gross Area = 0.50 * 20.50 = 10.25 in^2
Net Area = (20.50 - (7 *(0.81 + 1/16))) * 0.50 = 7.19 in^2

Using Eq.J4-3:
Shear Yielding = (1/omega) * 0.6 * Fypl * [Gross Area] = 0.67 * 0.6 * 36.00 * 10.25 = 147.60 kips

Using Eq.J4-4:
Shear Rupture = (1/omega) * 0.6 * Fupl * [Net Area] = 0.50 * 0.6 * 58.00 * 7.19 = 125.06 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 = (20.5 - 1.25) = 19.25 in.
Net Shear Length = 19.2 - (6.5 * (0.812 + 0.0625)) = 13.56 in.
Gross Tension Length = (3 + 1.5) = 4.50 in.
Net Tension Length = 4.5 - (1.5 * (1 + 0.0625)) = 2.91 in.
1. (1/omega) * [material thickness] * ((0.60 * Fupl* [net shear length]) + (Ubs * Fupl * [net tension length])) 
    = 0.50 * 0.50 * ((0.60 * 58.00 * 13.56) + (0.50 * 58.00 * 2.91)) = 139.06 kips
2. (1/omega) * [material thickness] * ((0.60 * Fypl * [gross shear length]) + (Ubs * Fupl * [net tension length])) 
    = 0.50 * 0.50 * ((0.60 * 36.00 * 19.25) + (0.50 * 58.00 * 2.91)) = 125.02 kips
Block Shear = 125.02 kips

Block 2 (Shear): 
Gross Shear Length = 2 * (20.5 - 1.25) = 38.50 in.
Net Shear Length = 2 * ( 19.2 - (6.5 * (0.812 + 0.0625)) ) = 27.12 in.
Gross Tension Length = (3 + 1.5) - 1.5 = 3.00 in.
Net Tension Length = 3 - 1 * (1 + 0.0625) = 1.94 in.
1. (1/omega) * [material thickness] * ((0.60 * Fupl* [net shear length]) + (Ubs * Fupl * [net tension length])) 
    = 0.50 * 0.50 * ((0.60 * 58.00 * 27.12) + (0.50 * 58.00 * 1.94)) = 250.03 kips
2. (1/omega) * [material thickness] * ((0.60 * Fypl * [gross shear length]) + (Ubs * Fupl * [net tension length])) 
    = 0.50 * 0.50 * ((0.60 * 36.00 * 38.50) + (0.50 * 58.00 * 1.94)) = 221.95 kips
Block Shear = 221.95 kips

Flexural and Buckling Strength:

Eccentricity at first line of bolts, e = 3.00 in.
Zgross = 52.53 in^3
Znet   = 36.69 in^3
Sgross = 35.02 in^3
Snet   = 24.26 in^3

Using Eq. 9-4
Flexural Rupture = (1/omega) * Fu * Znet / e = 0.50 * 58.00 * 36.69 / 3.00 = 354.63 kips


Using Eq. 9-14 through 9-18, Fcr = Fy * Q
tw = 0.50 in.
ho = 20.50 in.
c = 3.00 in.
lambda = (ho * Fy ^ 0.5) / ( 10 * tw * ( 475.00 + 280.00 * (ho / c)^2 ) ^0.5 ) = 
 = 20.50 * 36.00^0.5 / (10 * 0.50 * (475.00 + 280.00 * (20.50/3.00)^2 )^0.5) = 0.21
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 * 35.02 / 3.00 = 252.15 kips

Interaction Check of Flexural Yielding, Per AISC 10-5: 
Eccentricity at CG of Bolt Group, e = 4.50 in.
Zgross = 52.53
Znet = 52.53
Mr = Vr * e = 102.75 * 4.50 = 462.36 kips-in
Mc = 1/omega * Mn = 1/omega * Fy * Zgross = 0.60 * 36.00 * 52.53 = 1134.67 kips-in
Vr = 102.75 kips
Vc = 1/omega * Vn = 1/omega * 0.60 * Fy * Ag = 0.67 * 0.60 * 36.00 * 10.25 = 147.60 kips
Interaction due to moment and shear, (Vr/Vc)^2 + (Mr/Mc)^2 <= 1.0
(Vr/Vc)^2 + (Mr/Mc)^2 = (102.75 / 147.60)^2 + (462.36 / 1134.67)^2 = 0.65 <= 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 * 72.1945 = 1913.67 kips-in
tmax = 6 * 1913.67 / (36 * 20.5^2) = 0.76 in.
Maximum Plate Thickness is Not a Limiting Criteria.

Check Limits of Applicability Table K1.2A
Plate load angle:
   theta = 90.00 >= 30 deg (OK)
HSS wall slenderness:
   B/t or H/t  = 12 / 0.465 = 25.8065 <= 40 (OK)
   (B-3t)/t <= 1.40 * (E / Fy)^0.5 for loaded wall, for branch plate shear loading
   (12.00 - 3 * 0.47) / 0.47 = 22.81 <= 1.40 * (29000 / 46.00)^0.5 = 35.15 (OK)
Material Strength:
   Fy = 46.00 <= 52 ksi (OK)
Ductility: 
   Fy/Fu = 46.00 / 58.00 <= 0.80 (OK)

AISC K1-3, Plate Limit States and HSS Punching Shear : 
tpl <= thss * Fuhss/Fypl
0.50 <= 0.47 * 58.00 / 36.00 = 0.75 in. (OK)

WELD:

 Weld Requirements:

At shear only case: 
Weld Length for shear, Lv = 20.500 in.
Shear Load per inch per weld, fv = R/Lv/2 = 102.747 / 20.500 / 2 = 2.506 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) = 2.506 / (0.500 * 1.856) = 2.700/16

Minimum fillet weld size : 
   At shear only load case = 0.17 in.
   per Table J2.4     = 0.19 in.
   5/8(tp)            = 0.31 in.
   user preference    = 0.25 in.

Dmax1 (using eqn 9-3)
 = tshpl * Fushpl / ( Fexx * C1 * 0.088)
 = 0.500 * 58.000 / ( 70.000 * 1.000 * 0.088 ) 
 = 4.687 
Dmax2 (using eqn 9-2)
 = thss * Fuhss / ( Fexx * C1 * 0.044 )
 = 0.465 * 58.000 / ( 70.000 * 1.000 * 0.044 ) 
 = 8.718 
Dmax3 = project max fillet weld = 12.000
Dmax=min(Dmax1, Dmax2, Dmax3) = min(4.687, 8.718, 12.000)
 = 4.687 

Use weld size
D1 = 5.00
D2 = 5.00

Weld Strength :
Vertical weld capacity during shear only load, 1/omega * Rnv1 = 0.50 * 1.86 * 20.50 * (4.69 + 4.69) = 178.35 kips