bb.s.s.00347.00347

SHEAR PLATE CONNECTION SUMMARY

Filler Beam profile: W16X40
Support Girder profile: W27X84
Slope: 0 deg.
Skew: 85
Vertical Offset: 0
Horizontal Offset: 0
Span: 9.34 ft.
Reaction, V: 55 kips
Shear Capacity, Rn: 66.9 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 11.500 in. x 0.625 in.
Configuration Geometry:
Welds at shear plate to support: 7/16 FILLET, 8/16 FILLET
Bolt: 4 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 = 1.07 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 top edge of beam: 1.75 in.
Top cope depth: 1.25 in.
Top cope length: 4.5 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 = 6.258 in.
Angle = 0.000 deg.
C = 5.743
Using Table 7-1 to determine (1/omega) * rn:
Rn = (1/omega) * rn * C = 11.93 * 5.74 = 68.50 kips

BOLT BEARING AT BEAM SIDE:
Vertical Shear Only Load Case:
ICR cordinate relative to CG = (2.83, -0.00)
At Row 1, At Column 1:
Ri1 = 11.71 kips
Ri vector at Beam   = <7.15, 9.27>
Lcsbm at Beam spacing  = 3.12 in.
Lcebm at Beam edge    = 1.80 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * 3.12 * (0.30/1) * 65.00 = 37.06 kips/bolt
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 1.80 * (0.30/1) * 65.00 = 21.47 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.30/1) * 65.00 = 17.84 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(37.06, 21.47, 17.84) = 17.84 kips/bolt
Ri vector at Shear Plate   = <-7.15, -9.27>
Lcsshpl at Shear Plate spacing  = 3.05 in.
Lceshpl at Shear Plate edge    = 4.40 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 * 4.40 * 0.62 * 58.00 = 95.61 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, 95.61, 32.62) = 32.62 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(17.842, 32.625) = 17.84 kips/bolt
Bolt Shear Demand to Bearing ratio = 17.84 / 11.71 = 1.52

At Row 1, At Column 2:
Ri1 = 11.35 kips
Ri vector at Beam   = <9.61, 6.04>
Lcsbm at Beam spacing  = 3.12 in.
Lcebm at Beam edge    = 5.23 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * 3.12 * (0.30/1) * 65.00 = 37.06 kips/bolt
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 5.23 * (0.30/1) * 65.00 = 62.23 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.30/1) * 65.00 = 17.84 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(37.06, 62.23, 17.84) = 17.84 kips/bolt
Ri vector at Shear Plate   = <-9.61, -6.04>
Lcsshpl at Shear Plate spacing  = 3.05 in.
Lceshpl at Shear Plate edge    = 6.50 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 * 6.50 * 0.62 * 58.00 = 141.29 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, 141.29, 32.62) = 32.62 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(17.842, 32.625) = 17.84 kips/bolt
Bolt Shear Demand to Bearing ratio = 17.84 / 11.35 = 1.57

At Row 1, At Column 3:
Ri1 = 11.08 kips
Ri vector at Beam   = <11.08, -0.42>
Lcsbm at Beam spacing  = 2.19 in.
Lcebm at Beam edge    = 340.75 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * 2.19 * (0.30/1) * 65.00 = 26.02 kips/bolt
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 340.75 * (0.30/1) * 65.00 = 4053.21 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.30/1) * 65.00 = 17.84 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(26.02, 4053.21, 17.84) = 17.84 kips/bolt
Ri vector at Shear Plate   = <-11.08, 0.42>
Lcsshpl at Shear Plate spacing  = 2.00 in.
Lceshpl at Shear Plate edge    = 8.51 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 * 8.51 * 0.62 * 58.00 = 185.01 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, 185.01, 32.62) = 32.62 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(17.842, 32.625) = 17.84 kips/bolt
Bolt Shear Demand to Bearing ratio = 17.84 / 11.08 = 1.61

At Row 2, At Column 1:
Ri1 = 11.51 kips
Ri vector at Beam   = <2.87, 11.15>
Lcsbm at Beam spacing  = 2.19 in.
Lcebm at Beam edge    = 4.50 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * 2.19 * (0.30/1) * 65.00 = 26.02 kips/bolt
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 4.50 * (0.30/1) * 65.00 = 53.51 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.30/1) * 65.00 = 17.84 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(26.02, 53.51, 17.84) = 17.84 kips/bolt
Ri vector at Shear Plate   = <-2.87, -11.15>
Lcsshpl at Shear Plate spacing  = 2.19 in.
Lceshpl at Shear Plate edge    = 7.07 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 * 7.07 * 0.62 * 58.00 = 153.70 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, 153.70, 32.62) = 32.62 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(17.842, 32.625) = 17.84 kips/bolt
Bolt Shear Demand to Bearing ratio = 17.84 / 11.51 = 1.55

At Row 2, At Column 2:
Ri1 = 10.35 kips
Ri vector at Beam   = <4.85, 9.14>
Lcsbm at Beam spacing  = 3.12 in.
Lcebm at Beam edge    = 6.39 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * 3.12 * (0.30/1) * 65.00 = 37.06 kips/bolt
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 6.39 * (0.30/1) * 65.00 = 75.95 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.30/1) * 65.00 = 17.84 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(37.06, 75.95, 17.84) = 17.84 kips/bolt
Ri vector at Shear Plate   = <-4.85, -9.14>
Lcsshpl at Shear Plate spacing  = 3.05 in.
Lceshpl at Shear Plate edge    = 7.75 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 * 7.75 * 0.62 * 58.00 = 168.49 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, 168.49, 32.62) = 32.62 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(17.842, 32.625) = 17.84 kips/bolt
Bolt Shear Demand to Bearing ratio = 17.84 / 10.35 = 1.72

At Row 2, At Column 3:
Ri1 = 8.17 kips
Ri vector at Beam   = <8.11, -0.93>
Lcsbm at Beam spacing  = 2.19 in.
Lcebm at Beam edge    = 87.58 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * 2.19 * (0.30/1) * 65.00 = 26.02 kips/bolt
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 87.58 * (0.30/1) * 65.00 = 1041.74 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.30/1) * 65.00 = 17.84 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(26.02, 1041.74, 17.84) = 17.84 kips/bolt
Ri vector at Shear Plate   = <-8.11, 0.93>
Lcsshpl at Shear Plate spacing  = 2.00 in.
Lceshpl at Shear Plate edge    = 8.56 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 * 8.56 * 0.62 * 58.00 = 186.08 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, 186.08, 32.62) = 32.62 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(17.842, 32.625) = 17.84 kips/bolt
Bolt Shear Demand to Bearing ratio = 17.84 / 8.17 = 2.19

At Row 3, At Column 1:
Ri1 = 11.51 kips
Ri vector at Beam   = <-2.87, 11.15>
Lcsbm at Beam spacing  = 2.19 in.
Lcebm at Beam edge    = 7.60 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * 2.19 * (0.30/1) * 65.00 = 26.02 kips/bolt
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 7.60 * (0.30/1) * 65.00 = 90.36 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.30/1) * 65.00 = 17.84 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(26.02, 90.36, 17.84) = 17.84 kips/bolt
Ri vector at Shear Plate   = <2.87, -11.15>
Lcsshpl at Shear Plate spacing  = 2.19 in.
Lceshpl at Shear Plate edge    = 3.97 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 * 3.97 * 0.62 * 58.00 = 86.33 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, 86.33, 32.62) = 32.62 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(17.842, 32.625) = 17.84 kips/bolt
Bolt Shear Demand to Bearing ratio = 17.84 / 11.51 = 1.55

At Row 3, At Column 2:
Ri1 = 10.35 kips
Ri vector at Beam   = <-4.85, 9.14>
Lcsbm at Beam spacing  = 3.12 in.
Lcebm at Beam edge    = 8.37 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * 3.12 * (0.30/1) * 65.00 = 37.06 kips/bolt
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 8.37 * (0.30/1) * 65.00 = 99.52 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.30/1) * 65.00 = 17.84 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(37.06, 99.52, 17.84) = 17.84 kips/bolt
Ri vector at Shear Plate   = <4.85, -9.14>
Lcsshpl at Shear Plate spacing  = 3.05 in.
Lceshpl at Shear Plate edge    = 4.35 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 * 4.35 * 0.62 * 58.00 = 94.63 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, 94.63, 32.62) = 32.62 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(17.842, 32.625) = 17.84 kips/bolt
Bolt Shear Demand to Bearing ratio = 17.84 / 10.35 = 1.72

At Row 3, At Column 3:
Ri1 = 8.16 kips
Ri vector at Beam   = <-8.11, -0.93>
Lcsbm at Beam spacing  = 2.19 in.
Lcebm at Beam edge    = 7.65 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * 2.19 * (0.30/1) * 65.00 = 26.02 kips/bolt
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 7.65 * (0.30/1) * 65.00 = 90.95 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.30/1) * 65.00 = 17.84 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(26.02, 90.95, 17.84) = 17.84 kips/bolt
Ri vector at Shear Plate   = <8.11, 0.93>
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 = 21.89 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, 21.89, 32.62) = 21.89 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(17.842, 21.892) = 17.84 kips/bolt
Bolt Shear Demand to Bearing ratio = 17.84 / 8.16 = 2.19

At Row 4, At Column 1:
Ri1 = 11.71 kips
Ri vector at Beam   = <-7.15, 9.27>
Lcsbm at Beam spacing  = 3.12 in.
Lcebm at Beam edge    = 2.87 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * 3.12 * (0.30/1) * 65.00 = 37.06 kips/bolt
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 2.87 * (0.30/1) * 65.00 = 34.10 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.30/1) * 65.00 = 17.84 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(37.06, 34.10, 17.84) = 17.84 kips/bolt
Ri vector at Shear Plate   = <7.15, -9.27>
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 = 23.18 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, 23.18, 32.62) = 23.18 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(17.842, 23.185) = 17.84 kips/bolt
Bolt Shear Demand to Bearing ratio = 17.84 / 11.71 = 1.52

At Row 4, At Column 2:
Ri1 = 11.35 kips
Ri vector at Beam   = <-9.61, 6.04>
Lcsbm at Beam spacing  = 3.12 in.
Lcebm at Beam edge    = 5.50 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * 3.12 * (0.30/1) * 65.00 = 37.06 kips/bolt
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 5.50 * (0.30/1) * 65.00 = 65.42 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.30/1) * 65.00 = 17.84 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(37.06, 65.42, 17.84) = 17.84 kips/bolt
Ri vector at Shear Plate   = <9.61, -6.04>
Lcsshpl at Shear Plate spacing  = 3.05 in.
Lceshpl at Shear Plate edge    = 1.76 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 * 1.76 * 0.62 * 58.00 = 38.25 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, 38.25, 32.62) = 32.62 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(17.842, 32.625) = 17.84 kips/bolt
Bolt Shear Demand to Bearing ratio = 17.84 / 11.35 = 1.57

At Row 4, At Column 3:
Ri1 = 11.08 kips
Ri vector at Beam   = <-11.08, -0.42>
Lcsbm at Beam spacing  = 2.19 in.
Lcebm at Beam edge    = 7.60 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * 2.19 * (0.30/1) * 65.00 = 26.02 kips/bolt
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 7.60 * (0.30/1) * 65.00 = 90.40 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.30/1) * 65.00 = 17.84 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(26.02, 90.40, 17.84) = 17.84 kips/bolt
Ri vector at Shear Plate   = <11.08, 0.42>
Lcsshpl at Shear Plate spacing  = 2.00 in.
Lceshpl at Shear Plate edge    = 1.00 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 * 1.00 * 0.62 * 58.00 = 21.77 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, 21.77, 32.62) = 21.77 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(17.842, 21.766) = 17.84 kips/bolt
Bolt Shear Demand to Bearing ratio = 17.84 / 11.08 = 1.61

Min Bolt Shear Demand to Bearing ratio for vertical shear only = min(1.0, 1.52401, 1.5716, 1.60982, 1.54951, 1.72464, 2.18522, 1.54951, 1.72465, 2.18526, 1.52401, 1.5716, 1.60983) = 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 * 68.50 = 68.50 kips

Web Depth = d - [Top Cope Depth] - [Bottom Cope Depth] = 16 - 1.25 - 0 = 14.75 in.
Gross Area (Shear) = [Web Depth] * tw = 14.75 * 0.30 = 4.50 in^2
Net Shear Area (Shear) = ([Web Depth] - ([# rows] * [Diameter + 0.0625])) * tw 
    = (14.75 - (4 * 0.88)) * 0.30 = 3.43 in^2

Using Eq.J4-3:
Shear Yielding = (1/omega) * 0.6 * Fybeam * [Gross Area] = 0.67 * 0.6 * 50.00 * 4.50 = 89.98 kips

Using Eq.J4-4:
Shear Rupture = (1/omega) * 0.6 * Fubeam * [Net Area] = 0.50 * 0.6 * 65.00 * 3.43 = 66.91 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.


Buckling and Flexure at Longest Cope (Top Cope Only at Section)
Eccentricity at Section, e = 5.76 in.
If coped at top/bottom flange only and c <= 2d and dc <= d/2, use Eq. 9-7, Fcr = 26210.00 * f * k * (tw/h1)^2 <= Fy

Using Eq. 9-7 through 9-11
tw = 0.30 in.
h1 = 10.43 in.
c = 4.50 in.
When c/h1<=1.0, k=2.2(h1/c)^1.65
k  = 2.20 * (10.43 / 4.50)^1.65 = 8.81
When c/d<=1.0, f=2c/d
f = 2 * (4.50 / 16.00) = 0.56
Fy = 50.00 ksi
Fcr = (1/omega) * 26210.00 * f * k * (tw/h1)^2 = 0.60 * 26210.00 * 0.56 * 8.81 * (0.30 / 10.43)^2 = 66.61 ksi
Fcrmin =1/omega * min(Fcr, Fy) = 30.00 ksi
Snet1 (bolt holes not applicable) = 17.21 in^3
Snet2 (bolt holes applicable) = 17.21 in^3
Znet = 31.30 in^3

Using Eq. 9-6
Buckling = Fcr * Snet1 / e = 30.00 * 17.21 / 5.76 = 89.68 kips

Using Eq. 9-19
Flexural Yielding = (1/omega) * Fy * Snet1 / e = 0.60 * 50.00 * 17.21 / 5.76 = 89.68 kips

Using Eq. 9-4
Flexural Rupture = (1/omega) * Fu * Znet / e = 0.50 * 65.00 * 31.30 / 5.76 = 176.66 kips


Buckling and Flexure at Furthest Bolt Line within Cope (Top Cope Only at Section)
Eccentricity at Section, e = 3.26 in.
If coped at top/bottom flange only and c <= 2d and dc <= d/2, use Eq. 9-7, Fcr = 26210.00 * f * k * (tw/h1)^2 <= Fy

Using Eq. 9-7 through 9-11
tw = 0.30 in.
h1 = 11.09 in.
c = 4.50 in.
When c/h1<=1.0, k=2.2(h1/c)^1.65
k  = 2.20 * (11.09 / 4.50)^1.65 = 9.74
When c/d<=1.0, f=2c/d
f = 2 * (4.50 / 16.00) = 0.56
Fy = 50.00 ksi
Fcr = (1/omega) * 26210.00 * f * k * (tw/h1)^2 = 0.60 * 26210.00 * 0.56 * 9.74 * (0.30 / 11.09)^2 = 65.21 ksi
Fcrmin =1/omega * min(Fcr, Fy) = 30.00 ksi
Snet1 (bolt holes not applicable) = 17.21 in^3
Snet2 (bolt holes applicable) = 13.16 in^3
Znet = 23.30 in^3

Using Eq. 9-6
Buckling = Fcr * Snet1 / e = 30.00 * 17.21 / 3.26 = 158.50 kips

Using Eq. 9-19
Flexural Yielding = (1/omega) * Fy * Snet1 / e = 0.60 * 50.00 * 17.21 / 3.26 = 158.50 kips

Using Eq. 9-4
Flexural Rupture = (1/omega) * Fu * Znet / e = 0.50 * 65.00 * 23.30 / 3.26 = 232.42 kips


Section Bending Strength Calculations Summary:

   Coped Beam Buckling and Flexure at Longest Cope (Top Cope Only at Section)
   Buckling : 89.68 >= 55.00 kips (OK)
   Flexural Yielding : 89.68 >= 55.00 kips (OK)
   Flexural Rupture : 176.66 >= 55.00 kips (OK)

   Coped Beam Buckling and Flexure at Furthest Bolt Line within Cope (Top Cope Only at Section)
   Buckling : 158.50 >= 55.00 kips (OK)
   Flexural Yielding : 158.50 >= 55.00 kips (OK)
   Flexural Rupture : 232.42 >= 55.00 kips (OK)

Gross Area = 0.62 * 11.50 = 7.19 in^2
Net Area = (11.50 - (4 *(0.81 + 1/16))) * 0.62 = 5.00 in^2

Using Eq.J4-3:
Shear Yielding = (1/omega) * 0.6 * Fypl * [Gross Area] = 0.67 * 0.6 * 36.00 * 7.19 = 103.50 kips

Using Eq.J4-4:
Shear Rupture = (1/omega) * 0.6 * Fupl * [Net Area] = 0.50 * 0.6 * 58.00 * 5.00 = 87.00 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 = (11.5 - 1.25) = 10.25 in.
Net Shear Length = 10.2 - (3.5 * (0.812 + 0.0625)) = 7.19 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 * 0.62 * ((0.60 * 58.00 * 7.19) + (0.50 * 58.00 * 4.84)) = 122.06 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 * 10.25) + (0.50 * 58.00 * 4.84)) = 113.08 kips
Block Shear = 113.08 kips

Block 2 (Shear): 
Gross Shear Length = 2 * (11.5 - 1.25) = 20.50 in.
Net Shear Length = 2 * ( 10.2 - (3.5 * (0.812 + 0.0625)) ) = 14.38 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 * 0.62 * ((0.60 * 58.00 * 14.38) + (0.50 * 58.00 * 3.88)) = 191.45 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 * 20.50) + (0.50 * 58.00 * 3.88)) = 173.49 kips
Block Shear = 173.49 kips

Flexural and Buckling Strength:

Eccentricity at first line of bolts, e = 3.26 in.
Zgross = 20.66 in^3
Znet   = 14.10 in^3
Sgross = 13.78 in^3
Snet   = 9.50 in^3

Using Eq. 9-4
Flexural Rupture = (1/omega) * Fu * Znet / e = 0.50 * 58.00 * 14.10 / 3.26 = 125.51 kips


Using Eq. 9-14 through 9-18, Fcr = Fy * Q
tw = 0.62 in.
ho = 11.50 in.
c = 3.03 in.
lambda = (ho * Fy ^ 0.5) / ( 10 * tw * ( 475.00 + 280.00 * (ho / c)^2 ) ^0.5 ) = 
 = 11.50 * 36.00^0.5 / (10 * 0.62 * (475.00 + 280.00 * (11.50/3.03)^2 )^0.5) = 0.16
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 * 13.78 / 3.26 = 91.33 kips

Interaction Check of Flexural Yielding, Per AISC 10-5: 
Eccentricity at CG of Bolt Group, e = 6.26 in.
Zgross = 20.66
Znet = 14.10
Mr = Vr * e = 55.00 * 6.26 = 344.20 kips-in
Mc = 1/omega * Mn = 1/omega * Fy * Zgross = 0.60 * 36.00 * 20.66 = 446.34 kips-in
Vr = 55.00 kips
Vc = 1/omega * Vn = 1/omega * 0.60 * Fy * Ag = 0.67 * 0.60 * 36.00 * 7.19 = 103.50 kips
Interaction due to moment and shear, (Vr/Vc)^2 + (Mr/Mc)^2 <= 1.0
(Vr/Vc)^2 + (Mr/Mc)^2 = (55.00 / 103.50)^2 + (344.20 / 446.34)^2 = 0.88 <= 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 * 44.7183 = 1185.36 kips-in
tmax = 6 * 1185.36 / (36 * 11.5^2) = 1.49 in.
Maximum Plate Thickness is Not a Limiting Criteria.

WELD:

 Weld Requirements:

At shear only case: 
Weld Length for shear, Lv = 11.500 in.
Shear Load per inch per weld, fv = R/Lv/2 = 55.000 / 11.500 / 2 = 2.391 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) = 2.391 / (0.500 * 1.856) = 2.577/16

Minimum fillet weld size : 
   At shear only load case = 0.16 in.
   per Table J2.4     = 0.19 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 )
 = 0.460 * 65.000 / ( 70.000 * 1.000 * 0.088 ) 
 = 4.833 
Dmax3 = project max fillet weld = 12.000
Dmax=min(Dmax1, Dmax2, Dmax3) = min(5.859, 4.833, 12.000)
 = 4.833 

Dihedral Angle, DA       = 85.00 deg.
Gap on Obtuse Angle Side = 0.05 in.
Use weld size
Acute Side  D1 = 7.00
Obtuse Side D2 = 8.00

Weld Strength :
Vertical weld capacity during shear only load, 1/omega * Rnv1 = 0.50 * 1.86 * 11.50 * (4.83 + 4.83) = 103.16 kips
Check Effective Throat:
Acute Side Effect throat  = (D1/sin(DA)) * cos(DA/2) = (0.44/ sin( 85.00)) * cos( 42.50) = 0.32 in.
Obtuse Side Effect throat = ((D2/sin(DA)-tshpl/tan(DA))*sin((180-(180-DA))/2))= ((0.50 / sin(85.00) -0.62 / tan(85.00)) * sin((180 - (180 - 85.00)) / 2)) = 0.26 in.
Total Effective Throat    = 0.32 + 0.26 = 0.63 in.
Total Effective Throat of Square Case = D1 * 2^0.5 = 0.44 * 2^0.5 = 0.62 in.
0.62 in. <= 0.63 in. (OK)