bcw.s.s.00865.00865

SHEAR PLATE CONNECTION SUMMARY

Filler Beam profile: W24X55
Column profile: W14X109
Slope: 0 deg.
Skew: 83
Vertical Offset: 0
Horizontal Offset: 0
Span: 20 ft.
Reaction, V: 66.9 kips
Shear Capacity, Rn: 70.6 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: 14.000 in. x 20.500 in. x 0.625 in.
Configuration Geometry:
Welds at shear plate to support: 7/16 FILLET, 9/16 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 = 8 in.
Beam centerline setback = 8.1 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: 1.5 in.
Horizontal distance to first hole: 9.5 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 = 11.038 in.
Angle = 0.000 deg.
C = 5.917
Using Table 7-1 to determine (1/omega) * rn:
Rn = (1/omega) * rn * C = 11.93 * 5.92 = 70.58 kips

BOLT BEARING AT BEAM SIDE:
Vertical Shear Only Load Case:
ICR cordinate relative to CG = (2.64, 0.00)
At Row 1, At Column 1:
Ri1 = 11.71 kips
Ri vector at Beam   = <10.64, 4.89>
Lcsbm at Beam spacing  = 3.12 in.
Lcebm at Beam edge    = 6.18 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 * 6.18 * (0.40/1) * 65.00 = 95.16 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, 95.16, 23.11) = 23.11 kips/bolt
Ri vector at Shear Plate   = <-10.64, -4.89>
Lcsshpl at Shear Plate spacing  = 3.05 in.
Lceshpl at Shear Plate edge    = 9.91 in.
1/omegaRnsshpl at Shear Plate spacing = 1/omega * hf1 * Lcs * t * Fu = 0.50 * 1.20 * 3.05 * 0.62 * 58.00 = 66.33 kips/bolt
1/omegaRneshpl at Shear Plate edge = 1/omega * hf1 * Lce * t * Fu = 0.50 * 1.20 * 9.91 * 0.62 * 58.00 = 215.45 kips/bolt
1/omegaRndshpl on Shear Plate at Bolt Diameter   = 1/omega * hf2 * db * t * Fu = 0.50 * 2.40 * 0.75 * 0.62 * 58.00 = 32.62 kips/bolt
Shear Plate bearing capacity, 1/omegaRnshpl = min(1/omegaRnsshpl,1/omegaRneshpl,1/omegaRndshpl) = min(66.33, 215.45, 32.62) = 32.62 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(23.107, 32.625) = 23.11 kips/bolt
Bolt Shear Demand to Bearing ratio = 23.11 / 11.71 = 1.97

At Row 1, At Column 2:
Ri1 = 11.63 kips
Ri vector at Beam   = <11.54, 1.46>
Lcsbm at Beam spacing  = 2.19 in.
Lcebm at Beam edge    = 21.52 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 * 21.52 * (0.40/1) * 65.00 = 331.53 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, 331.53, 23.11) = 23.11 kips/bolt
Ri vector at Shear Plate   = <-11.54, -1.46>
Lcsshpl at Shear Plate spacing  = 2.00 in.
Lceshpl at Shear Plate edge    = 12.10 in.
1/omegaRnsshpl at Shear Plate spacing = 1/omega * hf1 * Lcs * t * Fu = 0.50 * 1.20 * 2 * 0.62 * 58.00 = 43.50 kips/bolt
1/omegaRneshpl at Shear Plate edge = 1/omega * hf1 * Lce * t * Fu = 0.50 * 1.20 * 12.10 * 0.62 * 58.00 = 263.08 kips/bolt
1/omegaRndshpl on Shear Plate at Bolt Diameter   = 1/omega * hf2 * db * t * Fu = 0.50 * 2.40 * 0.75 * 0.62 * 58.00 = 32.62 kips/bolt
Shear Plate bearing capacity, 1/omegaRnshpl = min(1/omegaRnsshpl,1/omegaRneshpl,1/omegaRndshpl) = min(43.50, 263.08, 32.62) = 32.62 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(23.107, 32.625) = 23.11 kips/bolt
Bolt Shear Demand to Bearing ratio = 23.11 / 11.63 = 1.99

At Row 2, At Column 1:
Ri1 = 11.38 kips
Ri vector at Beam   = <9.37, 6.46>
Lcsbm at Beam spacing  = 3.12 in.
Lcebm at Beam edge    = 9.72 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 * 9.72 * (0.40/1) * 65.00 = 149.77 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, 149.77, 23.11) = 23.11 kips/bolt
Ri vector at Shear Plate   = <-9.37, -6.46>
Lcsshpl at Shear Plate spacing  = 3.05 in.
Lceshpl at Shear Plate edge    = 10.93 in.
1/omegaRnsshpl at Shear Plate spacing = 1/omega * hf1 * Lcs * t * Fu = 0.50 * 1.20 * 3.05 * 0.62 * 58.00 = 66.33 kips/bolt
1/omegaRneshpl at Shear Plate edge = 1/omega * hf1 * Lce * t * Fu = 0.50 * 1.20 * 10.93 * 0.62 * 58.00 = 237.79 kips/bolt
1/omegaRndshpl on Shear Plate at Bolt Diameter   = 1/omega * hf2 * db * t * Fu = 0.50 * 2.40 * 0.75 * 0.62 * 58.00 = 32.62 kips/bolt
Shear Plate bearing capacity, 1/omegaRnshpl = min(1/omegaRnsshpl,1/omegaRneshpl,1/omegaRndshpl) = min(66.33, 237.79, 32.62) = 32.62 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(23.107, 32.625) = 23.11 kips/bolt
Bolt Shear Demand to Bearing ratio = 23.11 / 11.38 = 2.03

At Row 2, At Column 2:
Ri1 = 11.10 kips
Ri vector at Beam   = <10.90, 2.07>
Lcsbm at Beam spacing  = 2.19 in.
Lcebm at Beam edge    = 30.46 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 * 30.46 * (0.40/1) * 65.00 = 469.20 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, 469.20, 23.11) = 23.11 kips/bolt
Ri vector at Shear Plate   = <-10.90, -2.07>
Lcsshpl at Shear Plate spacing  = 2.00 in.
Lceshpl at Shear Plate edge    = 12.21 in.
1/omegaRnsshpl at Shear Plate spacing = 1/omega * hf1 * Lcs * t * Fu = 0.50 * 1.20 * 2 * 0.62 * 58.00 = 43.50 kips/bolt
1/omegaRneshpl at Shear Plate edge = 1/omega * hf1 * Lce * t * Fu = 0.50 * 1.20 * 12.21 * 0.62 * 58.00 = 265.65 kips/bolt
1/omegaRndshpl on Shear Plate at Bolt Diameter   = 1/omega * hf2 * db * t * Fu = 0.50 * 2.40 * 0.75 * 0.62 * 58.00 = 32.62 kips/bolt
Shear Plate bearing capacity, 1/omegaRnshpl = min(1/omegaRnsshpl,1/omegaRneshpl,1/omegaRndshpl) = min(43.50, 265.65, 32.62) = 32.62 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(23.107, 32.625) = 23.11 kips/bolt
Bolt Shear Demand to Bearing ratio = 23.11 / 11.10 = 2.08

At Row 3, At Column 1:
Ri1 = 10.74 kips
Ri vector at Beam   = <6.31, 8.70>
Lcsbm at Beam spacing  = 3.12 in.
Lcebm at Beam edge    = 10.40 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 * 10.40 * (0.40/1) * 65.00 = 160.23 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, 160.23, 23.11) = 23.11 kips/bolt
Ri vector at Shear Plate   = <-6.31, -8.70>
Lcsshpl at Shear Plate spacing  = 3.05 in.
Lceshpl at Shear Plate edge    = 15.68 in.
1/omegaRnsshpl at Shear Plate spacing = 1/omega * hf1 * Lcs * t * Fu = 0.50 * 1.20 * 3.05 * 0.62 * 58.00 = 66.33 kips/bolt
1/omegaRneshpl at Shear Plate edge = 1/omega * hf1 * Lce * t * Fu = 0.50 * 1.20 * 15.68 * 0.62 * 58.00 = 341.10 kips/bolt
1/omegaRndshpl on Shear Plate at Bolt Diameter   = 1/omega * hf2 * db * t * Fu = 0.50 * 2.40 * 0.75 * 0.62 * 58.00 = 32.62 kips/bolt
Shear Plate bearing capacity, 1/omegaRnshpl = min(1/omegaRnsshpl,1/omegaRneshpl,1/omegaRndshpl) = min(66.33, 341.10, 32.62) = 32.62 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(23.107, 32.625) = 23.11 kips/bolt
Bolt Shear Demand to Bearing ratio = 23.11 / 10.74 = 2.15

At Row 3, At Column 2:
Ri1 = 9.55 kips
Ri vector at Beam   = <8.93, 3.39>
Lcsbm at Beam spacing  = 3.12 in.
Lcebm at Beam edge    = 24.27 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 * 24.27 * (0.40/1) * 65.00 = 373.87 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, 373.87, 23.11) = 23.11 kips/bolt
Ri vector at Shear Plate   = <-8.93, -3.39>
Lcsshpl at Shear Plate spacing  = 3.05 in.
Lceshpl at Shear Plate edge    = 12.83 in.
1/omegaRnsshpl at Shear Plate spacing = 1/omega * hf1 * Lcs * t * Fu = 0.50 * 1.20 * 3.05 * 0.62 * 58.00 = 66.33 kips/bolt
1/omegaRneshpl at Shear Plate edge = 1/omega * hf1 * Lce * t * Fu = 0.50 * 1.20 * 12.83 * 0.62 * 58.00 = 279.14 kips/bolt
1/omegaRndshpl on Shear Plate at Bolt Diameter   = 1/omega * hf2 * db * t * Fu = 0.50 * 2.40 * 0.75 * 0.62 * 58.00 = 32.62 kips/bolt
Shear Plate bearing capacity, 1/omegaRnshpl = min(1/omegaRnsshpl,1/omegaRneshpl,1/omegaRndshpl) = min(66.33, 279.14, 32.62) = 32.62 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(23.107, 32.625) = 23.11 kips/bolt
Bolt Shear Demand to Bearing ratio = 23.11 / 9.55 = 2.42

At Row 4, At Column 1:
Ri1 = 10.24 kips
Ri vector at Beam   = <-0.00, 10.24>
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, -10.24>
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 * 0.62 * 58.00 = 47.58 kips/bolt
1/omegaRneshpl at Shear Plate edge = 1/omega * hf1 * Lce * t * Fu = 0.50 * 1.20 * 9.84 * 0.62 * 58.00 = 214.10 kips/bolt
1/omegaRndshpl on Shear Plate at Bolt Diameter   = 1/omega * hf2 * db * t * Fu = 0.50 * 2.40 * 0.75 * 0.62 * 58.00 = 32.62 kips/bolt
Shear Plate bearing capacity, 1/omegaRnshpl = min(1/omegaRnsshpl,1/omegaRneshpl,1/omegaRndshpl) = min(47.58, 214.10, 32.62) = 32.62 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(23.107, 32.625) = 23.11 kips/bolt
Bolt Shear Demand to Bearing ratio = 23.11 / 10.24 = 2.26

At Row 4, At Column 2:
Ri1 = 6.41 kips
Ri vector at Beam   = <-0.00, 6.41>
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, -6.41>
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 * 0.62 * 58.00 = 47.58 kips/bolt
1/omegaRneshpl at Shear Plate edge = 1/omega * hf1 * Lce * t * Fu = 0.50 * 1.20 * 9.84 * 0.62 * 58.00 = 214.10 kips/bolt
1/omegaRndshpl on Shear Plate at Bolt Diameter   = 1/omega * hf2 * db * t * Fu = 0.50 * 2.40 * 0.75 * 0.62 * 58.00 = 32.62 kips/bolt
Shear Plate bearing capacity, 1/omegaRnshpl = min(1/omegaRnsshpl,1/omegaRneshpl,1/omegaRndshpl) = min(47.58, 214.10, 32.62) = 32.62 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(23.107, 32.625) = 23.11 kips/bolt
Bolt Shear Demand to Bearing ratio = 23.11 / 6.41 = 3.61

At Row 5, At Column 1:
Ri1 = 10.74 kips
Ri vector at Beam   = <-6.31, 8.70>
Lcsbm at Beam spacing  = 3.12 in.
Lcebm at Beam edge    = 2.15 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 * 2.15 * (0.40/1) * 65.00 = 33.11 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, 33.11, 23.11) = 23.11 kips/bolt
Ri vector at Shear Plate   = <6.31, -8.70>
Lcsshpl at Shear Plate spacing  = 3.05 in.
Lceshpl at Shear Plate edge    = 7.16 in.
1/omegaRnsshpl at Shear Plate spacing = 1/omega * hf1 * Lcs * t * Fu = 0.50 * 1.20 * 3.05 * 0.62 * 58.00 = 66.33 kips/bolt
1/omegaRneshpl at Shear Plate edge = 1/omega * hf1 * Lce * t * Fu = 0.50 * 1.20 * 7.16 * 0.62 * 58.00 = 155.82 kips/bolt
1/omegaRndshpl on Shear Plate at Bolt Diameter   = 1/omega * hf2 * db * t * Fu = 0.50 * 2.40 * 0.75 * 0.62 * 58.00 = 32.62 kips/bolt
Shear Plate bearing capacity, 1/omegaRnshpl = min(1/omegaRnsshpl,1/omegaRneshpl,1/omegaRndshpl) = min(66.33, 155.82, 32.62) = 32.62 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(23.107, 32.625) = 23.11 kips/bolt
Bolt Shear Demand to Bearing ratio = 23.11 / 10.74 = 2.15

At Row 5, At Column 2:
Ri1 = 9.55 kips
Ri vector at Beam   = <-8.93, 3.39>
Lcsbm at Beam spacing  = 3.12 in.
Lcebm at Beam edge    = 4.41 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 * 4.41 * (0.40/1) * 65.00 = 67.88 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, 67.88, 23.11) = 23.11 kips/bolt
Ri vector at Shear Plate   = <8.93, -3.39>
Lcsshpl at Shear Plate spacing  = 3.05 in.
Lceshpl at Shear Plate edge    = 1.07 in.
1/omegaRnsshpl at Shear Plate spacing = 1/omega * hf1 * Lcs * t * Fu = 0.50 * 1.20 * 3.05 * 0.62 * 58.00 = 66.33 kips/bolt
1/omegaRneshpl at Shear Plate edge = 1/omega * hf1 * Lce * t * Fu = 0.50 * 1.20 * 1.07 * 0.62 * 58.00 = 23.26 kips/bolt
1/omegaRndshpl on Shear Plate at Bolt Diameter   = 1/omega * hf2 * db * t * Fu = 0.50 * 2.40 * 0.75 * 0.62 * 58.00 = 32.62 kips/bolt
Shear Plate bearing capacity, 1/omegaRnshpl = min(1/omegaRnsshpl,1/omegaRneshpl,1/omegaRndshpl) = min(66.33, 23.26, 32.62) = 23.26 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(23.107, 23.261) = 23.11 kips/bolt
Bolt Shear Demand to Bearing ratio = 23.11 / 9.55 = 2.42

At Row 6, At Column 1:
Ri1 = 11.38 kips
Ri vector at Beam   = <-9.37, 6.46>
Lcsbm at Beam spacing  = 3.12 in.
Lcebm at Beam edge    = 1.42 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 * 1.42 * (0.40/1) * 65.00 = 21.81 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, 21.81, 23.11) = 21.81 kips/bolt
Ri vector at Shear Plate   = <9.37, -6.46>
Lcsshpl at Shear Plate spacing  = 3.05 in.
Lceshpl at Shear Plate edge    = 4.86 in.
1/omegaRnsshpl at Shear Plate spacing = 1/omega * hf1 * Lcs * t * Fu = 0.50 * 1.20 * 3.05 * 0.62 * 58.00 = 66.33 kips/bolt
1/omegaRneshpl at Shear Plate edge = 1/omega * hf1 * Lce * t * Fu = 0.50 * 1.20 * 4.86 * 0.62 * 58.00 = 105.68 kips/bolt
1/omegaRndshpl on Shear Plate at Bolt Diameter   = 1/omega * hf2 * db * t * Fu = 0.50 * 2.40 * 0.75 * 0.62 * 58.00 = 32.62 kips/bolt
Shear Plate bearing capacity, 1/omegaRnshpl = min(1/omegaRnsshpl,1/omegaRneshpl,1/omegaRndshpl) = min(66.33, 105.68, 32.62) = 32.62 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(21.811, 32.625) = 21.81 kips/bolt
Bolt Shear Demand to Bearing ratio = 21.81 / 11.38 = 1.92

At Row 6, At Column 2:
Ri1 = 11.10 kips
Ri vector at Beam   = <-10.90, 2.07>
Lcsbm at Beam spacing  = 2.19 in.
Lcebm at Beam edge    = 4.17 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 * 4.17 * (0.40/1) * 65.00 = 64.30 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, 64.30, 23.11) = 23.11 kips/bolt
Ri vector at Shear Plate   = <10.90, -2.07>
Lcsshpl at Shear Plate spacing  = 2.00 in.
Lceshpl at Shear Plate edge    = 1.02 in.
1/omegaRnsshpl at Shear Plate spacing = 1/omega * hf1 * Lcs * t * Fu = 0.50 * 1.20 * 2 * 0.62 * 58.00 = 43.50 kips/bolt
1/omegaRneshpl at Shear Plate edge = 1/omega * hf1 * Lce * t * Fu = 0.50 * 1.20 * 1.02 * 0.62 * 58.00 = 22.14 kips/bolt
1/omegaRndshpl on Shear Plate at Bolt Diameter   = 1/omega * hf2 * db * t * Fu = 0.50 * 2.40 * 0.75 * 0.62 * 58.00 = 32.62 kips/bolt
Shear Plate bearing capacity, 1/omegaRnshpl = min(1/omegaRnsshpl,1/omegaRneshpl,1/omegaRndshpl) = min(43.50, 22.14, 32.62) = 22.14 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(23.107, 22.138) = 22.14 kips/bolt
Bolt Shear Demand to Bearing ratio = 22.14 / 11.10 = 1.99

At Row 7, At Column 1:
Ri1 = 11.71 kips
Ri vector at Beam   = <-10.64, 4.89>
Lcsbm at Beam spacing  = 3.12 in.
Lcebm at Beam edge    = 1.24 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 * 1.24 * (0.40/1) * 65.00 = 19.17 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, 19.17, 23.11) = 19.17 kips/bolt
Ri vector at Shear Plate   = <10.64, -4.89>
Lcsshpl at Shear Plate spacing  = 3.05 in.
Lceshpl at Shear Plate edge    = 2.44 in.
1/omegaRnsshpl at Shear Plate spacing = 1/omega * hf1 * Lcs * t * Fu = 0.50 * 1.20 * 3.05 * 0.62 * 58.00 = 66.33 kips/bolt
1/omegaRneshpl at Shear Plate edge = 1/omega * hf1 * Lce * t * Fu = 0.50 * 1.20 * 2.44 * 0.62 * 58.00 = 53.12 kips/bolt
1/omegaRndshpl on Shear Plate at Bolt Diameter   = 1/omega * hf2 * db * t * Fu = 0.50 * 2.40 * 0.75 * 0.62 * 58.00 = 32.62 kips/bolt
Shear Plate bearing capacity, 1/omegaRnshpl = min(1/omegaRnsshpl,1/omegaRneshpl,1/omegaRndshpl) = min(66.33, 53.12, 32.62) = 32.62 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(19.174, 32.625) = 19.17 kips/bolt
Bolt Shear Demand to Bearing ratio = 19.17 / 11.71 = 1.64

At Row 7, At Column 2:
Ri1 = 11.63 kips
Ri vector at Beam   = <-11.54, 1.46>
Lcsbm at Beam spacing  = 2.19 in.
Lcebm at Beam edge    = 4.13 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 * 4.13 * (0.40/1) * 65.00 = 63.62 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, 63.62, 23.11) = 23.11 kips/bolt
Ri vector at Shear Plate   = <11.54, -1.46>
Lcsshpl at Shear Plate spacing  = 2.00 in.
Lceshpl at Shear Plate edge    = 1.01 in.
1/omegaRnsshpl at Shear Plate spacing = 1/omega * hf1 * Lcs * t * Fu = 0.50 * 1.20 * 2 * 0.62 * 58.00 = 43.50 kips/bolt
1/omegaRneshpl at Shear Plate edge = 1/omega * hf1 * Lce * t * Fu = 0.50 * 1.20 * 1.01 * 0.62 * 58.00 = 21.92 kips/bolt
1/omegaRndshpl on Shear Plate at Bolt Diameter   = 1/omega * hf2 * db * t * Fu = 0.50 * 2.40 * 0.75 * 0.62 * 58.00 = 32.62 kips/bolt
Shear Plate bearing capacity, 1/omegaRnshpl = min(1/omegaRnsshpl,1/omegaRneshpl,1/omegaRndshpl) = min(43.50, 21.92, 32.62) = 21.92 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(23.107, 21.923) = 21.92 kips/bolt
Bolt Shear Demand to Bearing ratio = 21.92 / 11.63 = 1.88

Min Bolt Shear Demand to Bearing ratio for vertical shear only = min(1.0, 1.97372, 1.98625, 2.03049, 2.08214, 2.15061, 2.41944, 2.25555, 3.60502, 2.1506, 2.41939, 1.91655, 1.99473, 1.63776, 1.88444) = 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 * 70.58 = 70.58 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 = 0.62 * 20.50 = 12.81 in^2
Net Area = (20.50 - (7 *(0.81 + 1/16))) * 0.62 = 8.98 in^2

Using Eq.J4-3:
Shear Yielding = (1/omega) * 0.6 * Fypl * [Gross Area] = 0.67 * 0.6 * 36.00 * 12.81 = 184.50 kips

Using Eq.J4-4:
Shear Rupture = (1/omega) * 0.6 * Fupl * [Net Area] = 0.50 * 0.6 * 58.00 * 8.98 = 156.33 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 * 0.62 * ((0.60 * 58.00 * 13.56) + (0.50 * 58.00 * 2.91)) = 173.83 kips
2. (1/omega) * [material thickness] * ((0.60 * Fypl * [gross shear length]) + (Ubs * Fupl * [net tension length])) 
    = 0.50 * 0.62 * ((0.60 * 36.00 * 19.25) + (0.50 * 58.00 * 2.91)) = 156.28 kips
Block Shear = 156.28 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 * 0.62 * ((0.60 * 58.00 * 27.12) + (0.50 * 58.00 * 1.94)) = 312.54 kips
2. (1/omega) * [material thickness] * ((0.60 * Fypl * [gross shear length]) + (Ubs * Fupl * [net tension length])) 
    = 0.50 * 0.62 * ((0.60 * 36.00 * 38.50) + (0.50 * 58.00 * 1.94)) = 277.43 kips
Block Shear = 277.43 kips

Flexural and Buckling Strength:

Eccentricity at first line of bolts, e = 9.54 in.
Zgross = 65.66 in^3
Znet   = 45.86 in^3
Sgross = 43.78 in^3
Snet   = 30.33 in^3

Using Eq. 9-4
Flexural Rupture = (1/omega) * Fu * Znet / e = 0.50 * 58.00 * 45.86 / 9.54 = 139.42 kips


Using Eq. 9-14 through 9-18, Fcr = Fy * Q
tw = 0.62 in.
ho = 20.50 in.
c = 9.54 in.
lambda = (ho * Fy ^ 0.5) / ( 10 * tw * ( 475.00 + 280.00 * (ho / c)^2 ) ^0.5 ) = 
 = 20.50 * 36.00^0.5 / (10 * 0.62 * (475.00 + 280.00 * (20.50/9.54)^2 )^0.5) = 0.47
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 * 43.78 / 9.54 = 99.13 kips

Interaction Check of Flexural Yielding, Per AISC 10-5: 
Eccentricity at CG of Bolt Group, e = 11.04 in.
Zgross = 65.66
Znet = 65.66
Mr = Vr * e = 66.87 * 11.04 = 738.09 kips-in
Mc = 1/omega * Mn = 1/omega * Fy * Zgross = 0.60 * 36.00 * 65.66 = 1418.34 kips-in
Vr = 66.87 kips
Vc = 1/omega * Vn = 1/omega * 0.60 * Fy * Ag = 0.67 * 0.60 * 36.00 * 12.81 = 184.50 kips
Interaction due to moment and shear, (Vr/Vc)^2 + (Mr/Mc)^2 <= 1.0
(Vr/Vc)^2 + (Mr/Mc)^2 = (66.87 / 184.50)^2 + (738.09 / 1418.34)^2 = 0.40 <= 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.

STABILIZER PLATE:

Available Strength to Resist Lateral Displacement:
Using Eq. 10-6 (14th Ed.):
Rn/omega = 1500.00  * 3.14159 * L * tp^3 / a^2 = 0.60 * 1500.00 * 3.14159 * 20.50 * 0.62^3 / 9.50^2 = 156.80 kips
Stabilizer Plate Not Required for lateral displacement

Torsional Strength:
Using Eq. 10-8 and Eq. 10-7 (14th Ed.):
Required, Mta or Mtu = Ra * (tw + tp) /2 = 66.87 * ((0.38 + 0.62) / 2) = 33.43 kips-in
Lateral Shear Strength of Shear Plate, Mtn (no slab) = [1/omega*(0.6*Fyp)-(Ra/(L*tp))] *L*tp^2/2 =  ((0.67 * 0.6 * 36.00) - (66.87 / (20.50 * 0.62))) * 0.5 * 20.50 * 0.62^2 = 36.76 kips-in
Stabilizer Plate Not Required for torsional strength

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 = 66.866 / 20.500 / 2 = 1.631 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) = 1.631 / (0.500 * 1.856) = 1.757/16

Minimum fillet weld size : 
   At shear only load case = 0.11 in.
   per Table J2.4     = 0.25 in.
   5/8(tp)            = 0.39 in.
   user preference    = 0.25 in.

Dmax1 (using eqn 9-3)
 = tshpl * Fushpl / ( Fexx * C1 * 0.088)
 = 0.625 * 58.000 / ( 70.000 * 1.000 * 0.088 ) 
 = 5.859 
Dmax2 (using eqn 9-3)
 = twsupport * Fusupport / ( Fexx * C1 * 0.088 )
 = 0.525 * 65.000 / ( 70.000 * 1.000 * 0.088 ) 
 = 5.515 
Dmax3 = project max fillet weld = 12.000
Dmax=min(Dmax1, Dmax2, Dmax3) = min(5.859, 5.515, 12.000)
 = 5.515 

Dihedral Angle, DA       = 83.00 deg.
Gap on Obtuse Angle Side = 0.08 in.
Use weld size
Acute Side  D1 = 7.00
Obtuse Side D2 = 9.00

Weld Strength :
Vertical weld capacity during shear only load, 1/omega * Rnv1 = 0.50 * 1.86 * 20.50 * (5.52 + 5.52) = 209.87 kips
Check Effective Throat:
Acute Side Effect throat  = (D1/sin(DA)) * cos(DA/2) = (0.44/ sin( 83.00)) * cos( 41.50) = 0.33 in.
Obtuse Side Effect throat = ((D2/sin(DA)-tshpl/tan(DA))*sin((180-(180-DA))/2))= ((0.56 / sin(83.00) -0.62 / tan(83.00)) * sin((180 - (180 - 83.00)) / 2)) = 0.32 in.
Total Effective Throat    = 0.33 + 0.32 = 0.65 in.
Total Effective Throat of Square Case = D1 * 2^0.5 = 0.44 * 2^0.5 = 0.62 in.
0.62 in. <= 0.65 in. (OK)