bcw.s.s.00034.00554

SHEAR PLATE CONNECTION SUMMARY

Filler Beam profile: W30X108
Column profile: W14X145
Slope: 0 deg.
Skew: 90
Vertical Offset: 0
Horizontal Offset: 0
Span: 44.9 ft.
Reaction, V: 41 kips
Shear Capacity, Rn: 70.8 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 0.500 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 = 7.94 in.
Beam centerline setback = 7.94 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: 1.56 in.
Horizontal distance to first hole: 9.5 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 = 11.000 in.
Angle = 0.000 deg.
C = 5.934
Using Table 7-1 to determine (1/omega) * rn:
Rn = (1/omega) * rn * C = 11.93 * 5.93 = 70.78 kips

BOLT BEARING AT BEAM SIDE:
Vertical Shear Only Load Case:
ICR cordinate relative to CG = (2.65, -0.00)
At Row 1, At Column 1:
Ri1 = 11.71 kips
Ri vector at Beam   = <10.63, 4.90>
Lcsbm at Beam spacing  = 3.12 in.
Lcebm at Beam edge    = 6.76 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * 3.12 * (0.55/1) * 65.00 = 66.23 kips/bolt
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 6.76 * (0.55/1) * 65.00 = 143.72 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.55/1) * 65.00 = 31.88 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(66.23, 143.72, 31.88) = 31.88 kips/bolt
Ri vector at Shear Plate   = <-10.63, -4.90>
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 * 0.50 * 58.00 = 53.07 kips/bolt
1/omegaRneshpl at Shear Plate edge = 1/omega * hf1 * Lce * t * Fu = 0.50 * 1.20 * 9.91 * 0.50 * 58.00 = 172.43 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, 172.43, 26.10) = 26.10 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(31.883, 26.100) = 26.10 kips/bolt
Bolt Shear Demand to Bearing ratio = 26.10 / 11.71 = 2.23

At Row 1, At Column 2:
Ri1 = 11.63 kips
Ri vector at Beam   = <11.54, 1.47>
Lcsbm at Beam spacing  = 2.19 in.
Lcebm at Beam edge    = 23.31 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * 2.19 * (0.55/1) * 65.00 = 46.50 kips/bolt
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 23.31 * (0.55/1) * 65.00 = 495.47 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.55/1) * 65.00 = 31.88 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(46.50, 495.47, 31.88) = 31.88 kips/bolt
Ri vector at Shear Plate   = <-11.54, -1.47>
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 * 0.50 * 58.00 = 34.80 kips/bolt
1/omegaRneshpl at Shear Plate edge = 1/omega * hf1 * Lce * t * Fu = 0.50 * 1.20 * 12.10 * 0.50 * 58.00 = 210.49 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(34.80, 210.49, 26.10) = 26.10 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(31.883, 26.100) = 26.10 kips/bolt
Bolt Shear Demand to Bearing ratio = 26.10 / 11.63 = 2.24

At Row 2, At Column 1:
Ri1 = 11.38 kips
Ri vector at Beam   = <9.36, 6.47>
Lcsbm at Beam spacing  = 3.12 in.
Lcebm at Beam edge    = 10.15 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * 3.12 * (0.55/1) * 65.00 = 66.23 kips/bolt
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 10.15 * (0.55/1) * 65.00 = 215.65 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.55/1) * 65.00 = 31.88 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(66.23, 215.65, 31.88) = 31.88 kips/bolt
Ri vector at Shear Plate   = <-9.36, -6.47>
Lcsshpl at Shear Plate spacing  = 3.05 in.
Lceshpl at Shear Plate edge    = 10.94 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 * 10.94 * 0.50 * 58.00 = 190.37 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, 190.37, 26.10) = 26.10 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(31.883, 26.100) = 26.10 kips/bolt
Bolt Shear Demand to Bearing ratio = 26.10 / 11.38 = 2.29

At Row 2, At Column 2:
Ri1 = 11.10 kips
Ri vector at Beam   = <10.90, 2.08>
Lcsbm at Beam spacing  = 2.19 in.
Lcebm at Beam edge    = 31.53 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * 2.19 * (0.55/1) * 65.00 = 46.50 kips/bolt
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 31.53 * (0.55/1) * 65.00 = 670.21 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.55/1) * 65.00 = 31.88 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(46.50, 670.21, 31.88) = 31.88 kips/bolt
Ri vector at Shear Plate   = <-10.90, -2.08>
Lcsshpl at Shear Plate spacing  = 2.00 in.
Lceshpl at Shear Plate edge    = 12.22 in.
1/omegaRnsshpl at Shear Plate spacing = 1/omega * hf1 * Lcs * t * Fu = 0.50 * 1.20 * 2 * 0.50 * 58.00 = 34.80 kips/bolt
1/omegaRneshpl at Shear Plate edge = 1/omega * hf1 * Lce * t * Fu = 0.50 * 1.20 * 12.22 * 0.50 * 58.00 = 212.58 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(34.80, 212.58, 26.10) = 26.10 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(31.883, 26.100) = 26.10 kips/bolt
Bolt Shear Demand to Bearing ratio = 26.10 / 11.10 = 2.35

At Row 3, At Column 1:
Ri1 = 10.75 kips
Ri vector at Beam   = <6.30, 8.71>
Lcsbm at Beam spacing  = 3.12 in.
Lcebm at Beam edge    = 10.70 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * 3.12 * (0.55/1) * 65.00 = 66.23 kips/bolt
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 10.70 * (0.55/1) * 65.00 = 227.47 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.55/1) * 65.00 = 31.88 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(66.23, 227.47, 31.88) = 31.88 kips/bolt
Ri vector at Shear Plate   = <-6.30, -8.71>
Lcsshpl at Shear Plate spacing  = 3.05 in.
Lceshpl at Shear Plate edge    = 15.71 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 * 15.71 * 0.50 * 58.00 = 273.29 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, 273.29, 26.10) = 26.10 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(31.883, 26.100) = 26.10 kips/bolt
Bolt Shear Demand to Bearing ratio = 26.10 / 10.75 = 2.43

At Row 3, At Column 2:
Ri1 = 9.55 kips
Ri vector at Beam   = <8.92, 3.41>
Lcsbm at Beam spacing  = 3.12 in.
Lcebm at Beam edge    = 24.79 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * 3.12 * (0.55/1) * 65.00 = 66.23 kips/bolt
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 24.79 * (0.55/1) * 65.00 = 526.82 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.55/1) * 65.00 = 31.88 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(66.23, 526.82, 31.88) = 31.88 kips/bolt
Ri vector at Shear Plate   = <-8.92, -3.41>
Lcsshpl at Shear Plate spacing  = 3.05 in.
Lceshpl at Shear Plate edge    = 12.85 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 * 12.85 * 0.50 * 58.00 = 223.55 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, 223.55, 26.10) = 26.10 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(31.883, 26.100) = 26.10 kips/bolt
Bolt Shear Demand to Bearing ratio = 26.10 / 9.55 = 2.73

At Row 4, At Column 1:
Ri1 = 10.25 kips
Ri vector at Beam   = <0.00, 10.25>
Lcsbm at Beam spacing  = 2.19 in.
Lcebm at Beam edge    = 11.59 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * 2.19 * (0.55/1) * 65.00 = 46.50 kips/bolt
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 11.59 * (0.55/1) * 65.00 = 246.43 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.55/1) * 65.00 = 31.88 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(46.50, 246.43, 31.88) = 31.88 kips/bolt
Ri vector at Shear Plate   = <-0.00, -10.25>
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(31.883, 26.100) = 26.10 kips/bolt
Bolt Shear Demand to Bearing ratio = 26.10 / 10.25 = 2.55

At Row 4, At Column 2:
Ri1 = 6.43 kips
Ri vector at Beam   = <0.00, 6.43>
Lcsbm at Beam spacing  = 2.19 in.
Lcebm at Beam edge    = 11.59 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * 2.19 * (0.55/1) * 65.00 = 46.50 kips/bolt
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 11.59 * (0.55/1) * 65.00 = 246.43 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.55/1) * 65.00 = 31.88 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(46.50, 246.43, 31.88) = 31.88 kips/bolt
Ri vector at Shear Plate   = <-0.00, -6.43>
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(31.883, 26.100) = 26.10 kips/bolt
Bolt Shear Demand to Bearing ratio = 26.10 / 6.43 = 4.06

At Row 5, At Column 1:
Ri1 = 10.75 kips
Ri vector at Beam   = <-6.30, 8.71>
Lcsbm at Beam spacing  = 3.12 in.
Lcebm at Beam edge    = 2.26 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * 3.12 * (0.55/1) * 65.00 = 66.23 kips/bolt
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 2.26 * (0.55/1) * 65.00 = 48.04 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.55/1) * 65.00 = 31.88 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(66.23, 48.04, 31.88) = 31.88 kips/bolt
Ri vector at Shear Plate   = <6.30, -8.71>
Lcsshpl at Shear Plate spacing  = 3.05 in.
Lceshpl at Shear Plate edge    = 7.18 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 * 7.18 * 0.50 * 58.00 = 124.90 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, 124.90, 26.10) = 26.10 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(31.883, 26.100) = 26.10 kips/bolt
Bolt Shear Demand to Bearing ratio = 26.10 / 10.75 = 2.43

At Row 5, At Column 2:
Ri1 = 9.55 kips
Ri vector at Beam   = <-8.92, 3.41>
Lcsbm at Beam spacing  = 3.12 in.
Lcebm at Beam edge    = 4.48 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * 3.12 * (0.55/1) * 65.00 = 66.23 kips/bolt
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 4.48 * (0.55/1) * 65.00 = 95.20 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.55/1) * 65.00 = 31.88 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(66.23, 95.20, 31.88) = 31.88 kips/bolt
Ri vector at Shear Plate   = <8.92, -3.41>
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 * 0.50 * 58.00 = 53.07 kips/bolt
1/omegaRneshpl at Shear Plate edge = 1/omega * hf1 * Lce * t * Fu = 0.50 * 1.20 * 1.07 * 0.50 * 58.00 = 18.63 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, 18.63, 26.10) = 18.63 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(31.883, 18.630) = 18.63 kips/bolt
Bolt Shear Demand to Bearing ratio = 18.63 / 9.55 = 1.95

At Row 6, At Column 1:
Ri1 = 11.38 kips
Ri vector at Beam   = <-9.36, 6.47>
Lcsbm at Beam spacing  = 3.12 in.
Lcebm at Beam edge    = 1.49 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * 3.12 * (0.55/1) * 65.00 = 66.23 kips/bolt
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 1.49 * (0.55/1) * 65.00 = 31.74 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.55/1) * 65.00 = 31.88 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(66.23, 31.74, 31.88) = 31.74 kips/bolt
Ri vector at Shear Plate   = <9.36, -6.47>
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 * 0.50 * 58.00 = 53.07 kips/bolt
1/omegaRneshpl at Shear Plate edge = 1/omega * hf1 * Lce * t * Fu = 0.50 * 1.20 * 4.86 * 0.50 * 58.00 = 84.61 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, 84.61, 26.10) = 26.10 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(31.740, 26.100) = 26.10 kips/bolt
Bolt Shear Demand to Bearing ratio = 26.10 / 11.38 = 2.29

At Row 6, At Column 2:
Ri1 = 11.10 kips
Ri vector at Beam   = <-10.90, 2.09>
Lcsbm at Beam spacing  = 2.19 in.
Lcebm at Beam edge    = 4.24 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * 2.19 * (0.55/1) * 65.00 = 46.50 kips/bolt
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 4.24 * (0.55/1) * 65.00 = 90.10 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.55/1) * 65.00 = 31.88 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(46.50, 90.10, 31.88) = 31.88 kips/bolt
Ri vector at Shear Plate   = <10.90, -2.09>
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 * 0.50 * 58.00 = 34.80 kips/bolt
1/omegaRneshpl at Shear Plate edge = 1/omega * hf1 * Lce * t * Fu = 0.50 * 1.20 * 1.02 * 0.50 * 58.00 = 17.72 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(34.80, 17.72, 26.10) = 17.72 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(31.883, 17.716) = 17.72 kips/bolt
Bolt Shear Demand to Bearing ratio = 17.72 / 11.10 = 1.60

At Row 7, At Column 1:
Ri1 = 11.71 kips
Ri vector at Beam   = <-10.63, 4.90>
Lcsbm at Beam spacing  = 3.12 in.
Lcebm at Beam edge    = 1.31 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * 3.12 * (0.55/1) * 65.00 = 66.23 kips/bolt
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 1.31 * (0.55/1) * 65.00 = 27.93 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.55/1) * 65.00 = 31.88 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(66.23, 27.93, 31.88) = 27.93 kips/bolt
Ri vector at Shear Plate   = <10.63, -4.90>
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 * 0.50 * 58.00 = 53.07 kips/bolt
1/omegaRneshpl at Shear Plate edge = 1/omega * hf1 * Lce * t * Fu = 0.50 * 1.20 * 2.44 * 0.50 * 58.00 = 42.38 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, 42.38, 26.10) = 26.10 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(27.934, 26.100) = 26.10 kips/bolt
Bolt Shear Demand to Bearing ratio = 26.10 / 11.71 = 2.23

At Row 7, At Column 2:
Ri1 = 11.63 kips
Ri vector at Beam   = <-11.54, 1.47>
Lcsbm at Beam spacing  = 2.19 in.
Lcebm at Beam edge    = 4.19 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * 2.19 * (0.55/1) * 65.00 = 46.50 kips/bolt
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 4.19 * (0.55/1) * 65.00 = 89.13 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.55/1) * 65.00 = 31.88 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(46.50, 89.13, 31.88) = 31.88 kips/bolt
Ri vector at Shear Plate   = <11.54, -1.47>
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 * 0.50 * 58.00 = 34.80 kips/bolt
1/omegaRneshpl at Shear Plate edge = 1/omega * hf1 * Lce * t * Fu = 0.50 * 1.20 * 1.01 * 0.50 * 58.00 = 17.54 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(34.80, 17.54, 26.10) = 17.54 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(31.883, 17.541) = 17.54 kips/bolt
Bolt Shear Demand to Bearing ratio = 17.54 / 11.63 = 1.51

Min Bolt Shear Demand to Bearing ratio for vertical shear only = min(1.0, 2.22932, 2.24352, 2.29334, 2.3518, 2.42853, 2.73207, 2.54641, 4.05673, 2.4286, 1.95035, 2.29337, 1.59635, 2.22933, 1.50781) = 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 * 70.78 = 70.78 kips

Web Depth = d - [Top Cope Depth] - [Bottom Cope Depth] = 29.8 - 0 - 0 = 29.8 in.
Gross Area (Shear) = [Web Depth] * tw = 29.80 * 0.55 = 16.24 in^2
Net Shear Area (Shear) = ([Web Depth] - ([# rows] * [Diameter + 0.0625])) * tw 
    = (29.80 - (7 * 0.88)) * 0.55 = 12.90 in^2

Using Eq.J4-3:
Shear Yielding = (1/omega) * 0.6 * Fybeam * [Gross Area] = 0.67 * 0.6 * 50.00 * 16.24 = 324.82 kips

Using Eq.J4-4:
Shear Rupture = (1/omega) * 0.6 * Fubeam * [Net Area] = 0.50 * 0.6 * 65.00 * 12.90 = 251.61 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 = 9.50 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 / 9.50 = 111.99 kips


Using Eq. 9-14 through 9-18, Fcr = Fy * Q
tw = 0.50 in.
ho = 20.50 in.
c = 9.50 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 * (20.50/9.50)^2 )^0.5) = 0.58
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 / 9.50 = 79.63 kips

Interaction Check of Flexural Yielding, Per AISC 10-5: 
Eccentricity at CG of Bolt Group, e = 11.00 in.
Zgross = 52.53
Znet = 52.53
Mr = Vr * e = 41.00 * 11.00 = 451.00 kips-in
Mc = 1/omega * Mn = 1/omega * Fy * Zgross = 0.60 * 36.00 * 52.53 = 1134.67 kips-in
Vr = 41.00 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 = (41.00 / 147.60)^2 + (451.00 / 1134.67)^2 = 0.24 <= 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 * 0.50^3 / 9.50^2 = 80.28 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 = 41.00 * ((0.56 + 0.50) / 2) = 21.78 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) - (41.00 / (20.50 * 0.50))) * 0.5 * 20.50 * 0.50^2 = 26.65 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 = 41.000 / 20.500 / 2 = 1.000 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) = 1.000 / (0.500 * 1.856) = 1.077/16

Minimum fillet weld size : 
   At shear only load case = 0.07 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 9-3)
 = twsupport * Fusupport / ( Fexx * C1 * 0.088 )
 = 0.680 * 65.000 / ( 70.000 * 1.000 * 0.088 ) 
 = 7.144 
Dmax3 = project max fillet weld = 12.000
Dmax=min(Dmax1, Dmax2, Dmax3) = min(4.687, 7.144, 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