bb.s.s.00106.00264

SHEAR PLATE CONNECTION SUMMARY

Filler Beam profile: W12X14
Support Girder profile: W16X36
Slope: 0 deg.
Skew: 81.4
Vertical Offset: -4
Horizontal Offset: 12.1
Span: 7.57 ft.
Reaction, V: 38 kips
Shear Capacity, Rn: 44.8 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
Doubler plate grade: A36
Shear Plate Size: 10.500 in. x 8.500 in. x 0.750 in.
Doubler plate size: 9.56 in. x 8 in. x 0.312 in.
Configuration Geometry:
Welds at shear plate to support: 8/16 FILLET, 10/16 FILLET
Welds at doubler plate: 
At Top, 4/16 FILLET
At Side, 4/16 FILLET
At Bottom, 4/16 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 = 0.938 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: 2.06 in.
Edge distance at bottom edge of beam: 2.9 in.
Bottom cope depth: 1 in.
Bottom cope length: 3 in.
Edge distance at vertical edge of doubler: 1.5 in.
Edge distance at top edge of doubler: 1 in.
Edge distance at bottom edge of doubler: 1 in.
Horizontal distance to first hole: 3 in.
Down distance from top of filler beam flange: 2 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 = 6.206 in.
Angle = 0.000 deg.
C = 3.757
Using Table 7-1 to determine (1/omega) * rn:
Rn = (1/omega) * rn * C = 11.93 * 3.76 = 44.82 kips

BOLT BEARING AT BEAM SIDE:
Vertical Shear Only Load Case:
ICR cordinate relative to CG = (2.34, -0.00)
At Row 1, At Column 1:
Ri1 = 11.71 kips
Ri vector at Beam   = <5.74, 10.21>
Lcsdblr at Doubler spacing = 3.12 in.
Lcedblr at Doubler edge = 0.74 in.
1/omegaRnsdblr at Doubler spacing = 1/omega * hf1 * Lcs * (dblrt/# shear planes) * Fu = 0.50 * 1.20 * 3.12 * (0.31/1) * 58.00 = 33.9 kips
1/omegaRnedblr at Doubler edge = 1/omega * hf1 * Lce * (dblrt/# shear planes) * Fu = 0.50 * 1.20 * 0.74 * (0.31/1) * 58.00 = 8.06 kips
1/omegaRnddblr on Beam at Doubler = 1/omega * hf2 * db * (dblrt/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.31/1) * 58.00 = 16.31 kips/bolt
Lcsbm at Beam spacing  = 3.12 in.
Lcebm at Beam edge    = 1.89 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * 3.12 * (0.20/1) * 65.00 = 24.30 kips/bolt
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 1.89 * (0.20/1) * 65.00 = 14.73 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.20/1) * 65.00 = 11.70 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm+ Rnsdblr,1/omegaRnebm+ Rnedblr,1/omegaRndbm+ Rnddblr) = min(58.19, 22.78, 28.01) = 22.78 kips/bolt
Ri vector at Shear Plate   = <-5.74, -10.21>
Lcsshpl at Shear Plate spacing  = 3.05 in.
Lceshpl at Shear Plate edge    = 5.66 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 * 5.66 * 0.75 * 58.00 = 147.64 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, 147.64, 39.15) = 39.15 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(22.784, 39.150) = 22.78 kips/bolt
Bolt Shear Demand to Bearing ratio = 22.78 / 11.71 = 1.95

At Row 1, At Column 2:
Ri1 = 11.11 kips
Ri vector at Beam   = <8.76, 6.83>
Lcsdblr at Doubler spacing = 3.12 in.
Lcedblr at Doubler edge = 1.22 in.
1/omegaRnsdblr at Doubler spacing = 1/omega * hf1 * Lcs * (dblrt/# shear planes) * Fu = 0.50 * 1.20 * 3.12 * (0.31/1) * 58.00 = 33.9 kips
1/omegaRnedblr at Doubler edge = 1/omega * hf1 * Lce * (dblrt/# shear planes) * Fu = 0.50 * 1.20 * 1.22 * (0.31/1) * 58.00 = 13.28 kips
1/omegaRnddblr on Beam at Doubler = 1/omega * hf2 * db * (dblrt/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.31/1) * 58.00 = 16.31 kips/bolt
Lcsbm at Beam spacing  = 3.12 in.
Lcebm at Beam edge    = 2.85 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * 3.12 * (0.20/1) * 65.00 = 24.30 kips/bolt
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 2.85 * (0.20/1) * 65.00 = 22.21 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.20/1) * 65.00 = 11.70 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm+ Rnsdblr,1/omegaRnebm+ Rnedblr,1/omegaRndbm+ Rnddblr) = min(58.19, 35.49, 28.01) = 28.01 kips/bolt
Ri vector at Shear Plate   = <-8.76, -6.83>
Lcsshpl at Shear Plate spacing  = 3.05 in.
Lceshpl at Shear Plate edge    = 6.97 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 * 6.97 * 0.75 * 58.00 = 181.98 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, 181.98, 39.15) = 39.15 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(28.012, 39.150) = 28.01 kips/bolt
Bolt Shear Demand to Bearing ratio = 28.01 / 11.11 = 2.52

At Row 1, At Column 3:
Ri1 = 10.68 kips
Ri vector at Beam   = <10.43, -2.30>
Lcsdblr at Doubler spacing = 2.19 in.
Lcedblr at Doubler edge = 1.13 in.
1/omegaRnsdblr at Doubler spacing = 1/omega * hf1 * Lcs * (dblrt/# shear planes) * Fu = 0.50 * 1.20 * 2.19 * (0.31/1) * 58.00 = 23.8 kips
1/omegaRnedblr at Doubler edge = 1/omega * hf1 * Lce * (dblrt/# shear planes) * Fu = 0.50 * 1.20 * 1.13 * (0.31/1) * 58.00 = 12.29 kips
1/omegaRnddblr on Beam at Doubler = 1/omega * hf2 * db * (dblrt/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.31/1) * 58.00 = 16.31 kips/bolt
Lcsbm at Beam spacing  = 2.19 in.
Lcebm at Beam edge    = 45.50 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * 2.19 * (0.20/1) * 65.00 = 17.06 kips/bolt
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 45.50 * (0.20/1) * 65.00 = 354.90 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.20/1) * 65.00 = 11.70 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm+ Rnsdblr,1/omegaRnebm+ Rnedblr,1/omegaRndbm+ Rnddblr) = min(40.85, 367.19, 28.01) = 28.01 kips/bolt
Ri vector at Shear Plate   = <-10.43, 2.30>
Lcsshpl at Shear Plate spacing  = 2.00 in.
Lceshpl at Shear Plate edge    = 5.28 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 * 5.28 * 0.75 * 58.00 = 137.92 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, 137.92, 39.15) = 39.15 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(28.012, 39.150) = 28.01 kips/bolt
Bolt Shear Demand to Bearing ratio = 28.01 / 10.68 = 2.62

At Row 2, At Column 1:
Ri1 = 11.59 kips
Ri vector at Beam   = <0.00, 11.59>
Lcsdblr at Doubler spacing = 2.19 in.
Lcedblr at Doubler edge = 3.59 in.
1/omegaRnsdblr at Doubler spacing = 1/omega * hf1 * Lcs * (dblrt/# shear planes) * Fu = 0.50 * 1.20 * 2.19 * (0.31/1) * 58.00 = 23.8 kips
1/omegaRnedblr at Doubler edge = 1/omega * hf1 * Lce * (dblrt/# shear planes) * Fu = 0.50 * 1.20 * 3.59 * (0.31/1) * 58.00 = 39.08 kips
1/omegaRnddblr on Beam at Doubler = 1/omega * hf2 * db * (dblrt/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.31/1) * 58.00 = 16.31 kips/bolt
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 * (0.20/1) * 65.00 = 17.06 kips/bolt
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 4.59 * (0.20/1) * 65.00 = 35.83 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.20/1) * 65.00 = 11.70 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm+ Rnsdblr,1/omegaRnebm+ Rnedblr,1/omegaRndbm+ Rnddblr) = min(40.85, 74.91, 28.01) = 28.01 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(28.012, 39.150) = 28.01 kips/bolt
Bolt Shear Demand to Bearing ratio = 28.01 / 11.59 = 2.42

At Row 2, At Column 2:
Ri1 = 10.01 kips
Ri vector at Beam   = <0.00, 10.01>
Lcsdblr at Doubler spacing = 2.19 in.
Lcedblr at Doubler edge = 3.59 in.
1/omegaRnsdblr at Doubler spacing = 1/omega * hf1 * Lcs * (dblrt/# shear planes) * Fu = 0.50 * 1.20 * 2.19 * (0.31/1) * 58.00 = 23.8 kips
1/omegaRnedblr at Doubler edge = 1/omega * hf1 * Lce * (dblrt/# shear planes) * Fu = 0.50 * 1.20 * 3.59 * (0.31/1) * 58.00 = 39.08 kips
1/omegaRnddblr on Beam at Doubler = 1/omega * hf2 * db * (dblrt/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.31/1) * 58.00 = 16.31 kips/bolt
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 * (0.20/1) * 65.00 = 17.06 kips/bolt
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 4.59 * (0.20/1) * 65.00 = 35.83 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.20/1) * 65.00 = 11.70 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm+ Rnsdblr,1/omegaRnebm+ Rnedblr,1/omegaRndbm+ Rnddblr) = min(40.85, 74.91, 28.01) = 28.01 kips/bolt
Ri vector at Shear Plate   = <-0.00, -10.01>
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(28.012, 39.150) = 28.01 kips/bolt
Bolt Shear Demand to Bearing ratio = 28.01 / 10.01 = 2.80

At Row 2, At Column 3:
Ri1 = 6.24 kips
Ri vector at Beam   = <0.00, -6.24>
Lcsdblr at Doubler spacing = 2.19 in.
Lcedblr at Doubler edge = 3.59 in.
1/omegaRnsdblr at Doubler spacing = 1/omega * hf1 * Lcs * (dblrt/# shear planes) * Fu = 0.50 * 1.20 * 2.19 * (0.31/1) * 58.00 = 23.8 kips
1/omegaRnedblr at Doubler edge = 1/omega * hf1 * Lce * (dblrt/# shear planes) * Fu = 0.50 * 1.20 * 3.59 * (0.31/1) * 58.00 = 39.08 kips
1/omegaRnddblr on Beam at Doubler = 1/omega * hf2 * db * (dblrt/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.31/1) * 58.00 = 16.31 kips/bolt
Lcsbm at Beam spacing  = 2.19 in.
Lcebm at Beam edge    = 6.49 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * 2.19 * (0.20/1) * 65.00 = 17.06 kips/bolt
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 6.49 * (0.20/1) * 65.00 = 50.65 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.20/1) * 65.00 = 11.70 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm+ Rnsdblr,1/omegaRnebm+ Rnedblr,1/omegaRndbm+ Rnddblr) = min(40.85, 89.73, 28.01) = 28.01 kips/bolt
Ri vector at Shear Plate   = <-0.00, 6.24>
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(28.012, 39.150) = 28.01 kips/bolt
Bolt Shear Demand to Bearing ratio = 28.01 / 6.24 = 4.49

At Row 3, At Column 1:
Ri1 = 11.71 kips
Ri vector at Beam   = <-5.74, 10.21>
Lcsdblr at Doubler spacing = 3.12 in.
Lcedblr at Doubler edge = 3.80 in.
1/omegaRnsdblr at Doubler spacing = 1/omega * hf1 * Lcs * (dblrt/# shear planes) * Fu = 0.50 * 1.20 * 3.12 * (0.31/1) * 58.00 = 33.9 kips
1/omegaRnedblr at Doubler edge = 1/omega * hf1 * Lce * (dblrt/# shear planes) * Fu = 0.50 * 1.20 * 3.80 * (0.31/1) * 58.00 = 41.36 kips
1/omegaRnddblr on Beam at Doubler = 1/omega * hf2 * db * (dblrt/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.31/1) * 58.00 = 16.31 kips/bolt
Lcsbm at Beam spacing  = 3.12 in.
Lcebm at Beam edge    = 3.80 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * 3.12 * (0.20/1) * 65.00 = 24.30 kips/bolt
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 3.80 * (0.20/1) * 65.00 = 29.66 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.20/1) * 65.00 = 11.70 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm+ Rnsdblr,1/omegaRnebm+ Rnedblr,1/omegaRndbm+ Rnddblr) = min(58.19, 71.02, 28.01) = 28.01 kips/bolt
Ri vector at Shear Plate   = <5.74, -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 = 25.26 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, 25.26, 39.15) = 25.26 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(28.012, 25.262) = 25.26 kips/bolt
Bolt Shear Demand to Bearing ratio = 25.26 / 11.71 = 2.16

At Row 3, At Column 2:
Ri1 = 11.11 kips
Ri vector at Beam   = <-8.76, 6.83>
Lcsdblr at Doubler spacing = 3.12 in.
Lcedblr at Doubler edge = 6.01 in.
1/omegaRnsdblr at Doubler spacing = 1/omega * hf1 * Lcs * (dblrt/# shear planes) * Fu = 0.50 * 1.20 * 3.12 * (0.31/1) * 58.00 = 33.9 kips
1/omegaRnedblr at Doubler edge = 1/omega * hf1 * Lce * (dblrt/# shear planes) * Fu = 0.50 * 1.20 * 6.01 * (0.31/1) * 58.00 = 65.38 kips
1/omegaRnddblr on Beam at Doubler = 1/omega * hf2 * db * (dblrt/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.31/1) * 58.00 = 16.31 kips/bolt
Lcsbm at Beam spacing  = 3.12 in.
Lcebm at Beam edge    = 6.01 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * 3.12 * (0.20/1) * 65.00 = 24.30 kips/bolt
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 6.01 * (0.20/1) * 65.00 = 46.89 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.20/1) * 65.00 = 11.70 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm+ Rnsdblr,1/omegaRnebm+ Rnedblr,1/omegaRndbm+ Rnddblr) = min(58.19, 112.26, 28.01) = 28.01 kips/bolt
Ri vector at Shear Plate   = <8.76, -6.83>
Lcsshpl at Shear Plate spacing  = 3.05 in.
Lceshpl at Shear Plate edge    = 1.40 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 * 1.40 * 0.75 * 58.00 = 36.54 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, 36.54, 39.15) = 36.54 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(28.012, 36.539) = 28.01 kips/bolt
Bolt Shear Demand to Bearing ratio = 28.01 / 11.11 = 2.52

At Row 3, At Column 3:
Ri1 = 10.68 kips
Ri vector at Beam   = <-10.43, -2.30>
Lcsdblr at Doubler spacing = 2.19 in.
Lcedblr at Doubler edge = 4.23 in.
1/omegaRnsdblr at Doubler spacing = 1/omega * hf1 * Lcs * (dblrt/# shear planes) * Fu = 0.50 * 1.20 * 2.19 * (0.31/1) * 58.00 = 23.8 kips
1/omegaRnedblr at Doubler edge = 1/omega * hf1 * Lce * (dblrt/# shear planes) * Fu = 0.50 * 1.20 * 4.23 * (0.31/1) * 58.00 = 46.01 kips
1/omegaRnddblr on Beam at Doubler = 1/omega * hf2 * db * (dblrt/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.31/1) * 58.00 = 16.31 kips/bolt
Lcsbm at Beam spacing  = 2.19 in.
Lcebm at Beam edge    = 7.85 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * 2.19 * (0.20/1) * 65.00 = 17.06 kips/bolt
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 7.85 * (0.20/1) * 65.00 = 61.23 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.20/1) * 65.00 = 11.70 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm+ Rnsdblr,1/omegaRnebm+ Rnedblr,1/omegaRndbm+ Rnddblr) = min(40.85, 107.24, 28.01) = 28.01 kips/bolt
Ri vector at Shear Plate   = <10.43, 2.30>
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 = 26.73 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, 26.73, 39.15) = 26.73 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(28.012, 26.729) = 26.73 kips/bolt
Bolt Shear Demand to Bearing ratio = 26.73 / 10.68 = 2.50

Min Bolt Shear Demand to Bearing ratio for vertical shear only = min(1.0, 1.94606, 2.52107, 2.62204, 2.41788, 2.79871, 4.48958, 2.15775, 2.52107, 2.50189) = 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 * 44.82 = 44.82 kips

Web Depth = d - [Top Cope Depth] - [Bottom Cope Depth] = 11.9 - 0 - 1 = 10.9 in.
Gross Area (Shear) = [Web Depth] * tw = 10.90 * 0.20 = 2.18 in^2
Net Shear Area (Shear) = ([Web Depth] - ([# rows] * [Diameter + 0.0625])) * tw 
    = (10.90 - (3 * 0.88)) * 0.20 = 1.66 in^2

Using Eq.J4-3:
Shear Yielding = (1/omega) * 0.6 * Fybeam * [Gross Area] = 0.67 * 0.6 * 50.00 * 2.18 = 43.60 kips

Using Eq.J4-3:
Shear Yielding = (1/omega) * 0.6 * Fydoubler * [Gross Area] = 0.67 * 0.6 * 36.00 * 2.50 = 36.00 kips

Doubler Contribution = Min(Doubler Plate Shear Yielding, Doubler Vertical Component Weld Strength) = 
Min(36.00, 37.23) = 36.00 kips

   Total Shear Yield Capacity = 43.60 + 36.00 = 79.60 kips

Using Eq.J4-4:
Shear Rupture = (1/omega) * 0.6 * Fubeam * [Net Area] = 0.50 * 0.6 * 65.00 * 1.66 = 32.27 kips


Using Eq.J4-4:
Shear Rupture = (1/omega) * 0.6 * Fudoubler * [Net Area] = 0.50 * 0.6 * 58.00 * 1.68 = 29.23 kips


Doubler Contribution = Min(Doubler Plate Shear Rupture, Doubler Vertical Component Weld Strength) = 
Min(29.23, 37.23) = 29.23 kips

   Total Shear Rupture Capacity = 32.27 + 29.23 = 61.50 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))}

Coped Beam Bending Calculations w/o Doubler Plate:

Flexure at Longest Cope (Bottom Cope Only at Section)
Eccentricity at Section, e = 4.14 in.
Fy = 50.00 ksi
Snet1 (bolt holes not applicable) = 5.61 in^3
Snet2 (bolt holes applicable) = 5.61 in^3
Znet = 9.57 in^3

Using Eq. 9-19
Flexural Yielding = (1/omega) * Fy * Snet1 / e = 0.60 * 50.00 * 5.61 / 4.14 = 40.64 kips

Using Eq. 9-4
Flexural Rupture = (1/omega) * Fu * Znet / e = 0.50 * 65.00 * 9.57 / 4.14 = 75.05 kips


Flexure at Furthest Bolt Line within Cope (Bottom Cope Only at Section)
Eccentricity at Section, e = 3.21 in.
Fy = 50.00 ksi
Snet1 (bolt holes not applicable) = 5.61 in^3
Snet2 (bolt holes applicable) = 4.90 in^3
Znet = 8.19 in^3

Using Eq. 9-19
Flexural Yielding = (1/omega) * Fy * Snet1 / e = 0.60 * 50.00 * 5.61 / 3.21 = 52.53 kips

Using Eq. 9-4
Flexural Rupture = (1/omega) * Fu * Znet / e = 0.50 * 65.00 * 8.19 / 3.21 = 83.01 kips


Coped Beam Bending Calculations with Doubler Plate:

Flexure at Longest Cope (Bottom Cope Only at Section)
Eccentricity at Section, e = 4.14 in.
Fy = 50.00 ksi
Snet1 (bolt holes not applicable) = 7.62 in^3
Snet2 (bolt holes applicable) = 7.62 in^3
Znet = 13.47 in^3

Using Eq. 9-19
Flexural Yielding = (1/omega) * Fy * Snet1 / e = 0.60 * 50.00 * 7.62 / 4.14 = 55.17 kips

Using Eq. 9-4
Flexural Rupture = (1/omega) * Fu * Znet / e = 0.50 * 65.00 * 13.47 / 4.14 = 105.68 kips


Flexure at Furthest Bolt Line within Cope (Bottom Cope Only at Section) (with web doubler):
Eccentricity at Section, e = 3.21 in.
Fy = 50.00 ksi
Snet1 (bolt holes not applicable) = 7.62 in^3
Snet2 (bolt holes applicable) = 6.31 in^3
Znet = 10.87 in^3

Using Eq. 9-19
Flexural Yielding = (1/omega) * Fy * Snet1 / e = 0.60 * 50.00 * 7.62 / 3.21 = 71.30 kips

Using Eq. 9-4
Flexural Rupture = (1/omega) * Fu * Znet / e = 0.50 * 65.00 * 10.87 / 3.21 = 110.23 kips


Coped Beam Flexure at Longest Cope (Bottom Cope Only at Section)
Min(Beam Section w/o Doubler + Doubler Plate Weld Strength, Beam Section with Doubler Plate):
Flexural Yielding = Min(40.64 + 37.23, 55.17) = 55.17 kips
Flexural Rupture = Min(75.05 + 37.23, 105.68) = 105.68 kips

Coped Beam Flexure at Furthest Bolt Line within Cope (Bottom Cope Only at Section)
Min(Beam Section w/o Doubler + Doubler Plate Weld Strength, Beam Section with Doubler Plate):
Flexural Yielding = Min(52.53 + 37.23, 71.30) = 71.30 kips
Flexural Rupture = Min(83.01 + 37.23, 110.23) = 110.23 kips

Section Bending Strength Calculations Summary:

   Coped Beam Flexure at Longest Cope (Bottom Cope Only at Section)
   Flexural Yielding : 55.17 >= 38.00 kips (OK)
   Flexural Rupture : 105.68 >= 38.00 kips (OK)

   Coped Beam Flexure at Furthest Bolt Line within Cope (Bottom Cope Only at Section)
   Flexural Yielding : 71.30 >= 38.00 kips (OK)
   Flexural Rupture : 110.23 >= 38.00 kips (OK)

DOUBLER PLATE WELD:


Shear Reaction = 38.00 kips
Beam Shear Failure Reaction = 32.27 kips
 Required Shear Reinforcement = MAX(38.00 - 32.27, 0) = 5.73 kips
Axial Reaction = 0.00 kips

theta = sin(0.00 / (38.00^2 + 0.00^2)^0.5)^-1 = 0.00 deg.
load angle, theta = 0.00 deg.
k = 0.82
ex = 8.67
a = ex / l = 8.67 / 8.00 = 1.08
Weld Coefficient = 0.6 * Fexx * cphi * arrangement coefficient = 2.33
Dmax1 using min(eqn 9-2, tdoub - 0.062) 
 = min(tdoub * Fudoub / ( Fexx * C1 * 0.044), tdoub - 0.062) 
 = min(0.312 * 58.000 / ( 70.000 * 1.000 * 0.044), 0.312 - 0.062) 
 = min(5.859, 4.000)
 = 4.000 
Dmax2 (using eqn 9-2)
 = twbeam * Fubeam / ( Fexx * C1 * 0.044 )
 = 0.200 * 65.000 / ( 70.000 * 1.000 * 0.044 ) 
 = 4.202 
Dmax3 = project max fillet weld = 12.000
Dmax=min(Dmax1, Dmax2, Dmax3) = min(4.000, 4.202, 12.000)
 = 4.000 

D = 4.00/16
Weld Strength = 1/omega * weld coefficient * l * D  = 0.50 * 2.33 * 8.00 * 4.00 = 37.23 kips

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 = 3.21 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 / 3.21 = 85.63 kips


Using Eq. 9-14 through 9-18, Fcr = Fy * Q
tw = 0.75 in.
ho = 8.50 in.
c = 3.06 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 * (8.50/3.06)^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 / 3.21 = 60.85 kips

Interaction Check of Flexural Yielding, Per AISC 10-5: 
Eccentricity at CG of Bolt Group, e = 6.21 in.
Zgross = 13.55
Znet = 9.47
Mr = Vr * e = 38.00 * 6.21 = 235.82 kips-in
Mc = 1/omega * Mn = 1/omega * Fy * Zgross = 0.60 * 36.00 * 13.55 = 292.61 kips-in
Vr = 38.00 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 = (38.00 / 91.80)^2 + (235.82 / 292.61)^2 = 0.82 <= 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 = 38.000 / 8.500 / 2 = 2.235 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) = 2.235 / (0.500 * 1.856) = 2.409/16

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 )
 = 0.295 * 65.000 / ( 70.000 * 1.000 * 0.088 ) 
 = 3.099 
Dmax3 = project max fillet weld = 12.000
Dmax=min(Dmax1, Dmax2, Dmax3) = min(7.031, 3.099, 12.000)
 = 3.099 

Dihedral Angle, DA       = 81.40 deg.
Gap on Obtuse Angle Side = 0.11 in.
Use weld size
Acute Side  D1 = 8.00
Obtuse Side D2 = 10.00

Weld Strength :
Vertical weld capacity during shear only load, 1/omega * Rnv1 = 0.50 * 1.86 * 8.50 * (3.10 + 3.10) = 48.90 kips
Check Effective Throat:
Acute Side Effect throat  = (D1/sin(DA)) * cos(DA/2) = (0.50/ sin( 81.40)) * cos( 40.70) = 0.38 in.
Obtuse Side Effect throat = ((D2/sin(DA)-tshpl/tan(DA))*sin((180-(180-DA))/2))= ((0.62 / sin(81.40) -0.75 / tan(81.40)) * sin((180 - (180 - 81.40)) / 2)) = 0.34 in.
Total Effective Throat    = 0.38 + 0.34 = 0.72 in.
Total Effective Throat of Square Case = D1 * 2^0.5 = 0.50 * 2^0.5 = 0.71 in.
0.71 in. <= 0.72 in. (OK)