bb.s.s.00349.00349

SHEAR PLATE CONNECTION SUMMARY

Filler Beam profile: W12X26
Support Girder profile: W16X40
Slope: 0 deg.
Skew: 90
Vertical Offset: 0
Horizontal Offset: 0
Span: 15 ft.
Reaction, V: 37.2 kips
Shear Capacity, Rn: 38.5 kips
Design/Reference according to AISC 14th Ed. - ASD
Shear Plate: Extended Configuration
Beam material grade: A992
Support material grade: A992
Plate material grade: A36
Weld grade: E70
Shear Plate Size: 10.500 in. x 8.500 in. x 0.750 in.
Configuration Geometry:
Welds at shear plate to support: 8/16 FILLET, 8/16 FILLET
Bolt: 3 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 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: 2 in.
Top cope depth: 1 in.
Top cope length: 3 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 = 6.152 in.
Angle = 0.000 deg.
C = 3.780
Using Table 7-1 to determine (1/omega) * rn:
Rn = (1/omega) * rn * C = 11.93 * 3.78 = 45.09 kips

BOLT BEARING AT BEAM SIDE:
Vertical Shear Only Load Case:
ICR cordinate relative to CG = (2.35, -0.00)
At Row 1, At Column 1:
Ri1 = 11.71 kips
Ri vector at Beam   = <5.72, 10.21>
Lcsbm at Beam spacing  = 3.12 in.
Lcebm at Beam edge    = 3.03 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * 3.12 * (0.23/1) * 65.00 = 27.95 kips/bolt
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 3.03 * (0.23/1) * 65.00 = 27.20 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.23/1) * 65.00 = 13.46 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(27.95, 27.20, 13.46) = 13.46 kips/bolt
Ri vector at Shear Plate   = <-5.72, -10.21>
Lcsshpl at Shear Plate spacing  = 3.05 in.
Lceshpl at Shear Plate edge    = 5.67 in.
1/omegaRnsshpl at Shear Plate spacing = 1/omega * hf1 * Lcs * t * Fu = 0.50 * 1.20 * 3.05 * 0.75 * 58.00 = 79.60 kips/bolt
1/omegaRneshpl at Shear Plate edge = 1/omega * hf1 * Lce * t * Fu = 0.50 * 1.20 * 5.67 * 0.75 * 58.00 = 148.02 kips/bolt
1/omegaRndshpl on Shear Plate at Bolt Diameter   = 1/omega * hf2 * db * t * Fu = 0.50 * 2.40 * 0.75 * 0.75 * 58.00 = 39.15 kips/bolt
Shear Plate bearing capacity, 1/omegaRnshpl = min(1/omegaRnsshpl,1/omegaRneshpl,1/omegaRndshpl) = min(79.60, 148.02, 39.15) = 39.15 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(13.455, 39.150) = 13.46 kips/bolt
Bolt Shear Demand to Bearing ratio = 13.46 / 11.71 = 1.15

At Row 1, At Column 2:
Ri1 = 11.11 kips
Ri vector at Beam   = <8.74, 6.86>
Lcsbm at Beam spacing  = 3.12 in.
Lcebm at Beam edge    = 4.45 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * 3.12 * (0.23/1) * 65.00 = 27.95 kips/bolt
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 4.45 * (0.23/1) * 65.00 = 39.95 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.23/1) * 65.00 = 13.46 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(27.95, 39.95, 13.46) = 13.46 kips/bolt
Ri vector at Shear Plate   = <-8.74, -6.86>
Lcsshpl at Shear Plate spacing  = 3.05 in.
Lceshpl at Shear Plate edge    = 6.99 in.
1/omegaRnsshpl at Shear Plate spacing = 1/omega * hf1 * Lcs * t * Fu = 0.50 * 1.20 * 3.05 * 0.75 * 58.00 = 79.60 kips/bolt
1/omegaRneshpl at Shear Plate edge = 1/omega * hf1 * Lce * t * Fu = 0.50 * 1.20 * 6.99 * 0.75 * 58.00 = 182.46 kips/bolt
1/omegaRndshpl on Shear Plate at Bolt Diameter   = 1/omega * hf2 * db * t * Fu = 0.50 * 2.40 * 0.75 * 0.75 * 58.00 = 39.15 kips/bolt
Shear Plate bearing capacity, 1/omegaRnshpl = min(1/omegaRnsshpl,1/omegaRneshpl,1/omegaRndshpl) = min(79.60, 182.46, 39.15) = 39.15 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(13.455, 39.150) = 13.46 kips/bolt
Bolt Shear Demand to Bearing ratio = 13.46 / 11.11 = 1.21

At Row 1, At Column 3:
Ri1 = 10.68 kips
Ri vector at Beam   = <10.44, -2.25>
Lcsbm at Beam spacing  = 2.19 in.
Lcebm at Beam edge    = 43.27 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * 2.19 * (0.23/1) * 65.00 = 19.62 kips/bolt
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 43.27 * (0.23/1) * 65.00 = 388.17 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.23/1) * 65.00 = 13.46 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(19.62, 388.17, 13.46) = 13.46 kips/bolt
Ri vector at Shear Plate   = <-10.44, 2.25>
Lcsshpl at Shear Plate spacing  = 2.00 in.
Lceshpl at Shear Plate edge    = 5.42 in.
1/omegaRnsshpl at Shear Plate spacing = 1/omega * hf1 * Lcs * t * Fu = 0.50 * 1.20 * 2 * 0.75 * 58.00 = 52.20 kips/bolt
1/omegaRneshpl at Shear Plate edge = 1/omega * hf1 * Lce * t * Fu = 0.50 * 1.20 * 5.42 * 0.75 * 58.00 = 141.55 kips/bolt
1/omegaRndshpl on Shear Plate at Bolt Diameter   = 1/omega * hf2 * db * t * Fu = 0.50 * 2.40 * 0.75 * 0.75 * 58.00 = 39.15 kips/bolt
Shear Plate bearing capacity, 1/omegaRnshpl = min(1/omegaRnsshpl,1/omegaRneshpl,1/omegaRndshpl) = min(52.20, 141.55, 39.15) = 39.15 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(13.455, 39.150) = 13.46 kips/bolt
Bolt Shear Demand to Bearing ratio = 13.46 / 10.68 = 1.26

At Row 2, At Column 1:
Ri1 = 11.59 kips
Ri vector at Beam   = <0.00, 11.59>
Lcsbm at Beam spacing  = 2.19 in.
Lcebm at Beam edge    = 4.59 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * 2.19 * (0.23/1) * 65.00 = 19.62 kips/bolt
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 4.59 * (0.23/1) * 65.00 = 41.21 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.23/1) * 65.00 = 13.46 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(19.62, 41.21, 13.46) = 13.46 kips/bolt
Ri vector at Shear Plate   = <-0.00, -11.59>
Lcsshpl at Shear Plate spacing  = 2.19 in.
Lceshpl at Shear Plate edge    = 3.84 in.
1/omegaRnsshpl at Shear Plate spacing = 1/omega * hf1 * Lcs * t * Fu = 0.50 * 1.20 * 2.19 * 0.75 * 58.00 = 57.09 kips/bolt
1/omegaRneshpl at Shear Plate edge = 1/omega * hf1 * Lce * t * Fu = 0.50 * 1.20 * 3.84 * 0.75 * 58.00 = 100.32 kips/bolt
1/omegaRndshpl on Shear Plate at Bolt Diameter   = 1/omega * hf2 * db * t * Fu = 0.50 * 2.40 * 0.75 * 0.75 * 58.00 = 39.15 kips/bolt
Shear Plate bearing capacity, 1/omegaRnshpl = min(1/omegaRnsshpl,1/omegaRneshpl,1/omegaRndshpl) = min(57.09, 100.32, 39.15) = 39.15 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(13.455, 39.150) = 13.46 kips/bolt
Bolt Shear Demand to Bearing ratio = 13.46 / 11.59 = 1.16

At Row 2, At Column 2:
Ri1 = 10.02 kips
Ri vector at Beam   = <0.00, 10.02>
Lcsbm at Beam spacing  = 2.19 in.
Lcebm at Beam edge    = 5.59 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * 2.19 * (0.23/1) * 65.00 = 19.62 kips/bolt
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 5.59 * (0.23/1) * 65.00 = 50.18 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.23/1) * 65.00 = 13.46 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(19.62, 50.18, 13.46) = 13.46 kips/bolt
Ri vector at Shear Plate   = <-0.00, -10.02>
Lcsshpl at Shear Plate spacing  = 2.19 in.
Lceshpl at Shear Plate edge    = 3.84 in.
1/omegaRnsshpl at Shear Plate spacing = 1/omega * hf1 * Lcs * t * Fu = 0.50 * 1.20 * 2.19 * 0.75 * 58.00 = 57.09 kips/bolt
1/omegaRneshpl at Shear Plate edge = 1/omega * hf1 * Lce * t * Fu = 0.50 * 1.20 * 3.84 * 0.75 * 58.00 = 100.32 kips/bolt
1/omegaRndshpl on Shear Plate at Bolt Diameter   = 1/omega * hf2 * db * t * Fu = 0.50 * 2.40 * 0.75 * 0.75 * 58.00 = 39.15 kips/bolt
Shear Plate bearing capacity, 1/omegaRnshpl = min(1/omegaRnsshpl,1/omegaRneshpl,1/omegaRndshpl) = min(57.09, 100.32, 39.15) = 39.15 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(13.455, 39.150) = 13.46 kips/bolt
Bolt Shear Demand to Bearing ratio = 13.46 / 10.02 = 1.34

At Row 2, At Column 3:
Ri1 = 6.16 kips
Ri vector at Beam   = <0.00, -6.16>
Lcsbm at Beam spacing  = 2.19 in.
Lcebm at Beam edge    = 5.79 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * 2.19 * (0.23/1) * 65.00 = 19.62 kips/bolt
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 5.79 * (0.23/1) * 65.00 = 51.97 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.23/1) * 65.00 = 13.46 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(19.62, 51.97, 13.46) = 13.46 kips/bolt
Ri vector at Shear Plate   = <-0.00, 6.16>
Lcsshpl at Shear Plate spacing  = 2.19 in.
Lceshpl at Shear Plate edge    = 3.84 in.
1/omegaRnsshpl at Shear Plate spacing = 1/omega * hf1 * Lcs * t * Fu = 0.50 * 1.20 * 2.19 * 0.75 * 58.00 = 57.09 kips/bolt
1/omegaRneshpl at Shear Plate edge = 1/omega * hf1 * Lce * t * Fu = 0.50 * 1.20 * 3.84 * 0.75 * 58.00 = 100.32 kips/bolt
1/omegaRndshpl on Shear Plate at Bolt Diameter   = 1/omega * hf2 * db * t * Fu = 0.50 * 2.40 * 0.75 * 0.75 * 58.00 = 39.15 kips/bolt
Shear Plate bearing capacity, 1/omegaRnshpl = min(1/omegaRnsshpl,1/omegaRneshpl,1/omegaRndshpl) = min(57.09, 100.32, 39.15) = 39.15 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(13.455, 39.150) = 13.46 kips/bolt
Bolt Shear Demand to Bearing ratio = 13.46 / 6.16 = 2.18

At Row 3, At Column 1:
Ri1 = 11.71 kips
Ri vector at Beam   = <-5.72, 10.21>
Lcsbm at Beam spacing  = 3.12 in.
Lcebm at Beam edge    = 3.69 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * 3.12 * (0.23/1) * 65.00 = 27.95 kips/bolt
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 3.69 * (0.23/1) * 65.00 = 33.05 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.23/1) * 65.00 = 13.46 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(27.95, 33.05, 13.46) = 13.46 kips/bolt
Ri vector at Shear Plate   = <5.72, -10.21>
Lcsshpl at Shear Plate spacing  = 3.05 in.
Lceshpl at Shear Plate edge    = 0.97 in.
1/omegaRnsshpl at Shear Plate spacing = 1/omega * hf1 * Lcs * t * Fu = 0.50 * 1.20 * 3.05 * 0.75 * 58.00 = 79.60 kips/bolt
1/omegaRneshpl at Shear Plate edge = 1/omega * hf1 * Lce * t * Fu = 0.50 * 1.20 * 0.97 * 0.75 * 58.00 = 25.24 kips/bolt
1/omegaRndshpl on Shear Plate at Bolt Diameter   = 1/omega * hf2 * db * t * Fu = 0.50 * 2.40 * 0.75 * 0.75 * 58.00 = 39.15 kips/bolt
Shear Plate bearing capacity, 1/omegaRnshpl = min(1/omegaRnsshpl,1/omegaRneshpl,1/omegaRndshpl) = min(79.60, 25.24, 39.15) = 25.24 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(13.455, 25.244) = 13.46 kips/bolt
Bolt Shear Demand to Bearing ratio = 13.46 / 11.71 = 1.15

At Row 3, At Column 2:
Ri1 = 11.11 kips
Ri vector at Beam   = <-8.74, 6.86>
Lcsbm at Beam spacing  = 3.12 in.
Lcebm at Beam edge    = 5.95 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * 3.12 * (0.23/1) * 65.00 = 27.95 kips/bolt
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 5.95 * (0.23/1) * 65.00 = 53.36 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.23/1) * 65.00 = 13.46 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(27.95, 53.36, 13.46) = 13.46 kips/bolt
Ri vector at Shear Plate   = <8.74, -6.86>
Lcsshpl at Shear Plate spacing  = 3.05 in.
Lceshpl at Shear Plate edge    = 1.39 in.
1/omegaRnsshpl at Shear Plate spacing = 1/omega * hf1 * Lcs * t * Fu = 0.50 * 1.20 * 3.05 * 0.75 * 58.00 = 79.60 kips/bolt
1/omegaRneshpl at Shear Plate edge = 1/omega * hf1 * Lce * t * Fu = 0.50 * 1.20 * 1.39 * 0.75 * 58.00 = 36.27 kips/bolt
1/omegaRndshpl on Shear Plate at Bolt Diameter   = 1/omega * hf2 * db * t * Fu = 0.50 * 2.40 * 0.75 * 0.75 * 58.00 = 39.15 kips/bolt
Shear Plate bearing capacity, 1/omegaRnshpl = min(1/omegaRnsshpl,1/omegaRneshpl,1/omegaRndshpl) = min(79.60, 36.27, 39.15) = 36.27 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(13.455, 36.268) = 13.46 kips/bolt
Bolt Shear Demand to Bearing ratio = 13.46 / 11.11 = 1.21

At Row 3, At Column 3:
Ri1 = 10.68 kips
Ri vector at Beam   = <-10.44, -2.25>
Lcsbm at Beam spacing  = 2.19 in.
Lcebm at Beam edge    = 7.78 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * 2.19 * (0.23/1) * 65.00 = 19.62 kips/bolt
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 7.78 * (0.23/1) * 65.00 = 69.76 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.23/1) * 65.00 = 13.46 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(19.62, 69.76, 13.46) = 13.46 kips/bolt
Ri vector at Shear Plate   = <10.44, 2.25>
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 * 0.75 * 58.00 = 52.20 kips/bolt
1/omegaRneshpl at Shear Plate edge = 1/omega * hf1 * Lce * t * Fu = 0.50 * 1.20 * 1.02 * 0.75 * 58.00 = 26.70 kips/bolt
1/omegaRndshpl on Shear Plate at Bolt Diameter   = 1/omega * hf2 * db * t * Fu = 0.50 * 2.40 * 0.75 * 0.75 * 58.00 = 39.15 kips/bolt
Shear Plate bearing capacity, 1/omegaRnshpl = min(1/omegaRnsshpl,1/omegaRneshpl,1/omegaRndshpl) = min(52.20, 26.70, 39.15) = 26.70 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(13.455, 26.699) = 13.46 kips/bolt
Bolt Shear Demand to Bearing ratio = 13.46 / 10.68 = 1.26

Min Bolt Shear Demand to Bearing ratio for vertical shear only = min(1.0, 1.14925, 1.21086, 1.26032, 1.16128, 1.34263, 2.18323, 1.14925, 1.21086, 1.26032) = 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 * 45.09 = 45.09 kips

Web Depth = d - [Top Cope Depth] - [Bottom Cope Depth] = 12.2 - 1 - 0 = 11.2 in.
Gross Area (Shear) = [Web Depth] * tw = 11.20 * 0.23 = 2.58 in^2
Net Shear Area (Shear) = ([Web Depth] - ([# rows] * [Diameter + 0.0625])) * tw 
    = (11.20 - (3 * 0.88)) * 0.23 = 1.97 in^2

Using Eq.J4-3:
Shear Yielding = (1/omega) * 0.6 * Fybeam * [Gross Area] = 0.67 * 0.6 * 50.00 * 2.58 = 51.52 kips

Using Eq.J4-4:
Shear Rupture = (1/omega) * 0.6 * Fubeam * [Net Area] = 0.50 * 0.6 * 65.00 * 1.97 = 38.46 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 = 4.15 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 = 0.23 in.
h1 = 8.20 in.
c = 3.00 in.
When c/h1<=1.0, k=2.2(h1/c)^1.65
k  = 2.20 * (8.20 / 3.00)^1.65 = 11.55
When c/d<=1.0, f=2c/d
f = 2 * (3.00 / 12.20) = 0.49
Fy = 50.00 ksi
Fcr = (1/omega) * 26210.00 * f * k * (tw/h1)^2 = 0.60 * 26210.00 * 0.49 * 11.55 * (0.23 / 8.20)^2 = 70.35 ksi
Fcrmin =1/omega * min(Fcr, Fy) = 30.00 ksi
Snet1 (bolt holes not applicable) = 7.70 in^3
Snet2 (bolt holes applicable) = 7.70 in^3
Znet = 13.93 in^3

Using Eq. 9-6
Buckling = Fcr * Snet1 / e = 30.00 * 7.70 / 4.15 = 55.66 kips

Using Eq. 9-19
Flexural Yielding = (1/omega) * Fy * Snet1 / e = 0.60 * 50.00 * 7.70 / 4.15 = 55.66 kips

Using Eq. 9-4
Flexural Rupture = (1/omega) * Fu * Znet / e = 0.50 * 65.00 * 13.93 / 4.15 = 109.04 kips


Buckling and Flexure at Furthest Bolt Line within Cope (Top Cope Only at Section)
Eccentricity at Section, e = 3.15 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 = 0.23 in.
h1 = 8.64 in.
c = 3.00 in.
When c/h1<=1.0, k=2.2(h1/c)^1.65
k  = 2.20 * (8.64 / 3.00)^1.65 = 12.60
When c/d<=1.0, f=2c/d
f = 2 * (3.00 / 12.20) = 0.49
Fy = 50.00 ksi
Fcr = (1/omega) * 26210.00 * f * k * (tw/h1)^2 = 0.60 * 26210.00 * 0.49 * 12.60 * (0.23 / 8.64)^2 = 69.06 ksi
Fcrmin =1/omega * min(Fcr, Fy) = 30.00 ksi
Snet1 (bolt holes not applicable) = 7.70 in^3
Snet2 (bolt holes applicable) = 6.07 in^3
Znet = 10.41 in^3

Using Eq. 9-6
Buckling = Fcr * Snet1 / e = 30.00 * 7.70 / 3.15 = 73.31 kips

Using Eq. 9-19
Flexural Yielding = (1/omega) * Fy * Snet1 / e = 0.60 * 50.00 * 7.70 / 3.15 = 73.31 kips

Using Eq. 9-4
Flexural Rupture = (1/omega) * Fu * Znet / e = 0.50 * 65.00 * 10.41 / 3.15 = 107.27 kips


Section Bending Strength Calculations Summary:

   Coped Beam Buckling and Flexure at Longest Cope (Top Cope Only at Section)
   Buckling : 55.66 >= 37.20 kips (OK)
   Flexural Yielding : 55.66 >= 37.20 kips (OK)
   Flexural Rupture : 109.04 >= 37.20 kips (OK)

   Coped Beam Buckling and Flexure at Furthest Bolt Line within Cope (Top Cope Only at Section)
   Buckling : 73.31 >= 37.20 kips (OK)
   Flexural Yielding : 73.31 >= 37.20 kips (OK)
   Flexural Rupture : 107.27 >= 37.20 kips (OK)

Gross Area = 0.75 * 8.50 = 6.38 in^2
Net Area = (8.50 - (3 *(0.81 + 1/16))) * 0.75 = 4.41 in^2

Using Eq.J4-3:
Shear Yielding = (1/omega) * 0.6 * Fypl * [Gross Area] = 0.67 * 0.6 * 36.00 * 6.38 = 91.80 kips

Using Eq.J4-4:
Shear Rupture = (1/omega) * 0.6 * Fupl * [Net Area] = 0.50 * 0.6 * 58.00 * 4.41 = 76.67 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 = (8.5 - 1.25) = 7.25 in.
Net Shear Length = 7.25 - (2.5 * (0.812 + 0.0625)) = 5.06 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 * 0.75 * ((0.60 * 58.00 * 5.06) + (0.50 * 58.00 * 4.84)) = 118.74 kips
2. (1/omega) * [material thickness] * ((0.60 * Fypl * [gross shear length]) + (Ubs * Fupl * [net tension length])) 
    = 0.50 * 0.75 * ((0.60 * 36.00 * 7.25) + (0.50 * 58.00 * 4.84)) = 111.40 kips
Block Shear = 111.40 kips

Block 2 (Shear): 
Gross Shear Length = 2 * (8.5 - 1.25) = 14.50 in.
Net Shear Length = 2 * ( 7.25 - (2.5 * (0.812 + 0.0625)) ) = 10.12 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 * 0.75 * ((0.60 * 58.00 * 10.12) + (0.50 * 58.00 * 3.88)) = 174.27 kips
2. (1/omega) * [material thickness] * ((0.60 * Fypl * [gross shear length]) + (Ubs * Fupl * [net tension length])) 
    = 0.50 * 0.75 * ((0.60 * 36.00 * 14.50) + (0.50 * 58.00 * 3.88)) = 159.59 kips
Block Shear = 159.59 kips

Flexural and Buckling Strength:

Eccentricity at first line of bolts, e = 3.15 in.
Zgross = 13.55 in^3
Znet   = 9.47 in^3
Sgross = 9.03 in^3
Snet   = 6.25 in^3

Using Eq. 9-4
Flexural Rupture = (1/omega) * Fu * Znet / e = 0.50 * 58.00 * 9.47 / 3.15 = 87.08 kips


Using Eq. 9-14 through 9-18, Fcr = Fy * Q
tw = 0.75 in.
ho = 8.50 in.
c = 3.00 in.
lambda = (ho * Fy ^ 0.5) / ( 10 * tw * ( 475.00 + 280.00 * (ho / c)^2 ) ^0.5 ) = 
 = 8.50 * 36.00^0.5 / (10 * 0.75 * (475.00 + 280.00 * (8.50/3.00)^2 )^0.5) = 0.13
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 * 9.03 / 3.15 = 61.88 kips

Interaction Check of Flexural Yielding, Per AISC 10-5: 
Eccentricity at CG of Bolt Group, e = 6.15 in.
Zgross = 13.55
Znet = 9.47
Mr = Vr * e = 37.20 * 6.15 = 228.87 kips-in
Mc = 1/omega * Mn = 1/omega * Fy * Zgross = 0.60 * 36.00 * 13.55 = 292.61 kips-in
Vr = 37.20 kips
Vc = 1/omega * Vn = 1/omega * 0.60 * Fy * Ag = 0.67 * 0.60 * 36.00 * 6.38 = 91.80 kips
Interaction due to moment and shear, (Vr/Vc)^2 + (Mr/Mc)^2 <= 1.0
(Vr/Vc)^2 + (Mr/Mc)^2 = (37.20 / 91.80)^2 + (228.87 / 292.61)^2 = 0.78 <= 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 * 28.0478 = 743.467 kips-in
tmax = 6 * 743.467 / (36 * 8.5^2) = 1.72 in.
Maximum Plate Thickness is Not a Limiting Criteria.

WELD:

 Weld Requirements:

At shear only case: 
Weld Length for shear, Lv = 8.500 in.
Shear Load per inch per weld, fv = R/Lv/2 = 37.200 / 8.500 / 2 = 2.188 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) = 2.188 / (0.500 * 1.856) = 2.358/16

Minimum fillet weld size : 
   At shear only load case = 0.15 in.
   per Table J2.4     = 0.19 in.
   5/8(tp)            = 0.47 in.
   user preference    = 0.25 in.

Dmax1 (using eqn 9-3)
 = tshpl * Fushpl / ( Fexx * C1 * 0.088)
 = 0.750 * 58.000 / ( 70.000 * 1.000 * 0.088 ) 
 = 7.031 
Dmax2 (using eqn 9-3)
 = twsupport * Fusupport / ( Fexx * C1 * 0.088 )
 = 0.305 * 65.000 / ( 70.000 * 1.000 * 0.088 ) 
 = 3.204 
Dmax3 = project max fillet weld = 12.000
Dmax=min(Dmax1, Dmax2, Dmax3) = min(7.031, 3.204, 12.000)
 = 3.204 

Use weld size
D1 = 8.00
D2 = 8.00

Weld Strength :
Vertical weld capacity during shear only load, 1/omega * Rnv1 = 0.50 * 1.86 * 8.50 * (3.20 + 3.20) = 50.55 kips