bb.s.s.00001.00001

SHEAR PLATE CONNECTION SUMMARY

Filler Beam profile: W14X74
Support Girder profile: W14X74
Slope: 0 deg.
Skew: 90
Vertical Offset: 0
Horizontal Offset: 0
Span: 30 ft.
Reaction, V: 70 kips
Shear Capacity, Rn: 70.3 kips
Design/Reference according to AISC 14th Ed. - ASD
Shear Plate: Extended Configuration
Beam material grade: A992
Support material grade: A992
Plate material grade: A572-GR.50
Weld grade: E70
Doubler plate grade: A572-GR.50
Shear Plate Size: 13.750 in. x 9.500 in. x 1.000 in.
Doubler plate size: 12.8 in. x 9.25 in. x 0.375 in.
Configuration Geometry:
Welds at shear plate to support: 10/16 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 4 columns 0.875 in. Diameter A325N_TC bolts
Vertical spacing: 3.5 in.
Horizontal spacing: 3 in.
Shear plate edge setback = 1 in.
Beam centerline setback = 1 in.
Edge distance at vertical edge of plate: 1.75 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: 1.5 in.
Edge distance at bottom edge of beam: 2.7 in.
Top cope depth: 1.5 in.
Top cope length: 4.5 in.
Bottom cope depth: 1.5 in.
Bottom cope length: 4.5 in.
Edge distance at vertical edge of doubler: 1.75 in.
Edge distance at top edge of doubler: 1.12 in.
Edge distance at bottom edge of doubler: 1.12 in.
Horizontal distance to first hole: 3 in.
Down distance from top of filler beam flange: 3 in.
Holes in beam web: STD diameter = 0.938 in.
Holes in shear plate: SSL diameter = 0.938 in., slot width = 1.12 in.

BOLT SHEAR CAPACITY AT BEAM AND SHEAR PLATE SIDE:
Bolt Shear Capacity at Shear Load Only:
Using Instantaneous Center Of Rotation Method (AISC 7-1)
ex = 7.725 in.
Angle = 0.000 deg.
C = 5.016
Using Table 7-1 to determine (1/omega)rn:
(1/omega)Rn = (1/omega)rn * C = 16.24 * 5.02 = 81.45 kips


Total Vertical Bolt Shear Capacity = 81.45 kips
81.45 kips >= 70.00 kips (OK)

BOLT BEARING AT BEAM AND SHEAR PLATE SIDE
Vertical Shear Only Load Case:
ICR cordinate relative to CG = (2.90, 0.00)
At Row 1, At Column 1:
Ribolt = 15.94 kips
Ri vector at Beam   = <6.82, 14.40>
Lcsdblr at Doubler spacing = 3.31 in.
Lcedblr at Doubler edge = 0.78 in.
(1/omega)Rnsdblr at Doubler spacing = (1/omega) * hf1 * Lcs * (dblrt/# shear planes) * Fu = 0.50 * 1.20 * 3.31 * (0.38/1) * 65.00 = 48.4 kips
(1/omega)Rnedblr at Doubler edge = (1/omega) * hf1 * Lce * (dblrt/# shear planes) * Fu = 0.50 * 1.20 * 0.78 * (0.38/1) * 65.00 = 11.35 kips
(1/omega)Rnddblr on Beam at Doubler = (1/omega) * hf2 * db * (dblrt/# shear planes) * Fu = 0.50 * 2.40 * 0.88 * (0.38/1) * 65.00 = 25.59 kips/bolt
Lcsbm at Beam spacing  = 3.31 in.
Lcebm at Beam edge    = 1.19 in.
(1/omega)Rnsbm at Beam spacing = (1/omega) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * 3.31 * (0.45/1) * 65.00 = 58.07 kips/bolt
(1/omega)Rnebm at Beam edge = (1/omega) * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 1.19 * (0.45/1) * 65.00 = 20.90 kips/bolt
(1/omega)Rndbm on Beam at Bolt Diameter   = (1/omega) * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.88 * (0.45/1) * 65.00 = 30.71 kips/bolt
Beam bearing capacity, (1/omega)Rnbm = min((1/omega)Rnsbm+ Rnsdblr,(1/omega)Rnebm+ Rnedblr,(1/omega)Rndbm+ Rnddblr) = min(106.47, 32.24, 56.31) = 32.24 kips/bolt
Ri vector at Shear Plate   = <-6.82, -14.40>
Lcsshpl at Shear Plate spacing  = 3.25 in.
Lceshpl at Shear Plate edge    = 6.50 in.
(1/omega)Rnsshpl at Shear Plate spacing = (1/omega) * hf1 * Lcs * t * Fu = 0.50 * 1.20 * 3.25 * 1.00 * 65.00 = 126.77 kips/bolt
(1/omega)Rneshpl at Shear Plate edge = (1/omega) * hf1 * Lce * t * Fu = 0.50 * 1.20 * 6.50 * 1.00 * 65.00 = 253.33 kips/bolt
(1/omega)Rndshpl on Shear Plate at Bolt Diameter   = (1/omega) * hf2 * db * t * Fu = 0.50 * 2.40 * 0.88 * 1.00 * 65.00 = 68.25 kips/bolt
Shear Plate bearing capacity, (1/omega)Rnshpl = min((1/omega)Rnsshpl,(1/omega)Rneshpl,(1/omega)Rndshpl) = min(126.77, 253.33, 68.25) = 68.25 kips/bolt
(1/omega)Rn = min((1/omega)Rnbm, (1/omega)Rnshpl) = min(32.243, 68.250) = 32.24 kips/bolt
Bolt Shear Demand to Bearing ratio = 32.24 / 15.94 = 2.02

At Row 1, At Column 2:
Ribolt = 15.35 kips
Ri vector at Beam   = <9.56, 12.01>
Lcsdblr at Doubler spacing = 3.31 in.
Lcedblr at Doubler edge = 0.97 in.
(1/omega)Rnsdblr at Doubler spacing = (1/omega) * hf1 * Lcs * (dblrt/# shear planes) * Fu = 0.50 * 1.20 * 3.31 * (0.38/1) * 65.00 = 48.4 kips
(1/omega)Rnedblr at Doubler edge = (1/omega) * hf1 * Lce * (dblrt/# shear planes) * Fu = 0.50 * 1.20 * 0.97 * (0.38/1) * 65.00 = 14.17 kips
(1/omega)Rnddblr on Beam at Doubler = (1/omega) * hf2 * db * (dblrt/# shear planes) * Fu = 0.50 * 2.40 * 0.88 * (0.38/1) * 65.00 = 25.59 kips/bolt
Lcsbm at Beam spacing  = 3.31 in.
Lcebm at Beam edge    = 3.37 in.
(1/omega)Rnsbm at Beam spacing = (1/omega) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * 3.31 * (0.45/1) * 65.00 = 58.07 kips/bolt
(1/omega)Rnebm at Beam edge = (1/omega) * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 3.37 * (0.45/1) * 65.00 = 59.07 kips/bolt
(1/omega)Rndbm on Beam at Bolt Diameter   = (1/omega) * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.88 * (0.45/1) * 65.00 = 30.71 kips/bolt
Beam bearing capacity, (1/omega)Rnbm = min((1/omega)Rnsbm+ Rnsdblr,(1/omega)Rnebm+ Rnedblr,(1/omega)Rndbm+ Rnddblr) = min(106.47, 73.24, 56.31) = 56.31 kips/bolt
Ri vector at Shear Plate   = <-9.56, -12.01>
Lcsshpl at Shear Plate spacing  = 3.25 in.
Lceshpl at Shear Plate edge    = 9.03 in.
(1/omega)Rnsshpl at Shear Plate spacing = (1/omega) * hf1 * Lcs * t * Fu = 0.50 * 1.20 * 3.25 * 1.00 * 65.00 = 126.77 kips/bolt
(1/omega)Rneshpl at Shear Plate edge = (1/omega) * hf1 * Lce * t * Fu = 0.50 * 1.20 * 9.03 * 1.00 * 65.00 = 352.36 kips/bolt
(1/omega)Rndshpl on Shear Plate at Bolt Diameter   = (1/omega) * hf2 * db * t * Fu = 0.50 * 2.40 * 0.88 * 1.00 * 65.00 = 68.25 kips/bolt
Shear Plate bearing capacity, (1/omega)Rnshpl = min((1/omega)Rnsshpl,(1/omega)Rneshpl,(1/omega)Rndshpl) = min(126.77, 352.36, 68.25) = 68.25 kips/bolt
(1/omega)Rn = min((1/omega)Rnbm, (1/omega)Rnshpl) = min(56.306, 68.250) = 56.31 kips/bolt
Bolt Shear Demand to Bearing ratio = 56.31 / 15.35 = 3.67

At Row 1, At Column 3:
Ribolt = 14.27 kips
Ri vector at Beam   = <13.26, 5.29>
Lcsdblr at Doubler spacing = 3.31 in.
Lcedblr at Doubler edge = 2.57 in.
(1/omega)Rnsdblr at Doubler spacing = (1/omega) * hf1 * Lcs * (dblrt/# shear planes) * Fu = 0.50 * 1.20 * 3.31 * (0.38/1) * 65.00 = 48.4 kips
(1/omega)Rnedblr at Doubler edge = (1/omega) * hf1 * Lce * (dblrt/# shear planes) * Fu = 0.50 * 1.20 * 2.57 * (0.38/1) * 65.00 = 37.53 kips
(1/omega)Rnddblr on Beam at Doubler = (1/omega) * hf2 * db * (dblrt/# shear planes) * Fu = 0.50 * 2.40 * 0.88 * (0.38/1) * 65.00 = 25.59 kips/bolt
Lcsbm at Beam spacing  = 3.31 in.
Lcebm at Beam edge    = 7.62 in.
(1/omega)Rnsbm at Beam spacing = (1/omega) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * 3.31 * (0.45/1) * 65.00 = 58.07 kips/bolt
(1/omega)Rnebm at Beam edge = (1/omega) * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 7.62 * (0.45/1) * 65.00 = 133.81 kips/bolt
(1/omega)Rndbm on Beam at Bolt Diameter   = (1/omega) * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.88 * (0.45/1) * 65.00 = 30.71 kips/bolt
Beam bearing capacity, (1/omega)Rnbm = min((1/omega)Rnsbm+ Rnsdblr,(1/omega)Rnebm+ Rnedblr,(1/omega)Rndbm+ Rnddblr) = min(106.47, 171.35, 56.31) = 56.31 kips/bolt
Ri vector at Shear Plate   = <-13.26, -5.29>
Lcsshpl at Shear Plate spacing  = 3.25 in.
Lceshpl at Shear Plate edge    = 9.08 in.
(1/omega)Rnsshpl at Shear Plate spacing = (1/omega) * hf1 * Lcs * t * Fu = 0.50 * 1.20 * 3.25 * 1.00 * 65.00 = 126.77 kips/bolt
(1/omega)Rneshpl at Shear Plate edge = (1/omega) * hf1 * Lce * t * Fu = 0.50 * 1.20 * 9.08 * 1.00 * 65.00 = 354.30 kips/bolt
(1/omega)Rndshpl on Shear Plate at Bolt Diameter   = (1/omega) * hf2 * db * t * Fu = 0.50 * 2.40 * 0.88 * 1.00 * 65.00 = 68.25 kips/bolt
Shear Plate bearing capacity, (1/omega)Rnshpl = min((1/omega)Rnsshpl,(1/omega)Rneshpl,(1/omega)Rndshpl) = min(126.77, 354.30, 68.25) = 68.25 kips/bolt
(1/omega)Rn = min((1/omega)Rnbm, (1/omega)Rnshpl) = min(56.306, 68.250) = 56.31 kips/bolt
Bolt Shear Demand to Bearing ratio = 56.31 / 14.27 = 3.95

At Row 1, At Column 4:
Ribolt = 14.34 kips
Ri vector at Beam   = <13.04, -5.97>
Lcsdblr at Doubler spacing = 3.31 in.
Lcedblr at Doubler edge = 1.46 in.
(1/omega)Rnsdblr at Doubler spacing = (1/omega) * hf1 * Lcs * (dblrt/# shear planes) * Fu = 0.50 * 1.20 * 3.31 * (0.38/1) * 65.00 = 48.4 kips
(1/omega)Rnedblr at Doubler edge = (1/omega) * hf1 * Lce * (dblrt/# shear planes) * Fu = 0.50 * 1.20 * 1.46 * (0.38/1) * 65.00 = 21.30 kips
(1/omega)Rnddblr on Beam at Doubler = (1/omega) * hf2 * db * (dblrt/# shear planes) * Fu = 0.50 * 2.40 * 0.88 * (0.38/1) * 65.00 = 25.59 kips/bolt
Lcsbm at Beam spacing  = 3.31 in.
Lcebm at Beam edge    = 26.43 in.
(1/omega)Rnsbm at Beam spacing = (1/omega) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * 3.31 * (0.45/1) * 65.00 = 58.07 kips/bolt
(1/omega)Rnebm at Beam edge = (1/omega) * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 26.43 * (0.45/1) * 65.00 = 463.77 kips/bolt
(1/omega)Rndbm on Beam at Bolt Diameter   = (1/omega) * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.88 * (0.45/1) * 65.00 = 30.71 kips/bolt
Beam bearing capacity, (1/omega)Rnbm = min((1/omega)Rnsbm+ Rnsdblr,(1/omega)Rnebm+ Rnedblr,(1/omega)Rndbm+ Rnddblr) = min(106.47, 485.07, 56.31) = 56.31 kips/bolt
Ri vector at Shear Plate   = <-13.04, 5.97>
Lcsshpl at Shear Plate spacing  = 3.25 in.
Lceshpl at Shear Plate edge    = 2.38 in.
(1/omega)Rnsshpl at Shear Plate spacing = (1/omega) * hf1 * Lcs * t * Fu = 0.50 * 1.20 * 3.25 * 1.00 * 65.00 = 126.77 kips/bolt
(1/omega)Rneshpl at Shear Plate edge = (1/omega) * hf1 * Lce * t * Fu = 0.50 * 1.20 * 2.38 * 1.00 * 65.00 = 92.93 kips/bolt
(1/omega)Rndshpl on Shear Plate at Bolt Diameter   = (1/omega) * hf2 * db * t * Fu = 0.50 * 2.40 * 0.88 * 1.00 * 65.00 = 68.25 kips/bolt
Shear Plate bearing capacity, (1/omega)Rnshpl = min((1/omega)Rnsshpl,(1/omega)Rneshpl,(1/omega)Rndshpl) = min(126.77, 92.93, 68.25) = 68.25 kips/bolt
(1/omega)Rn = min((1/omega)Rnbm, (1/omega)Rnshpl) = min(56.306, 68.250) = 56.31 kips/bolt
Bolt Shear Demand to Bearing ratio = 56.31 / 14.34 = 3.93

At Row 2, At Column 1:
Ribolt = 15.82 kips
Ri vector at Beam   = <-0.00, 15.82>
Lcsdblr at Doubler spacing = 2.56 in.
Lcedblr at Doubler edge = 4.16 in.
(1/omega)Rnsdblr at Doubler spacing = (1/omega) * hf1 * Lcs * (dblrt/# shear planes) * Fu = 0.50 * 1.20 * 2.56 * (0.38/1) * 65.00 = 37.5 kips
(1/omega)Rnedblr at Doubler edge = (1/omega) * hf1 * Lce * (dblrt/# shear planes) * Fu = 0.50 * 1.20 * 4.16 * (0.38/1) * 65.00 = 60.79 kips
(1/omega)Rnddblr on Beam at Doubler = (1/omega) * hf2 * db * (dblrt/# shear planes) * Fu = 0.50 * 2.40 * 0.88 * (0.38/1) * 65.00 = 25.59 kips/bolt
Lcsbm at Beam spacing  = 2.56 in.
Lcebm at Beam edge    = 4.53 in.
(1/omega)Rnsbm at Beam spacing = (1/omega) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * 2.56 * (0.45/1) * 65.00 = 44.97 kips/bolt
(1/omega)Rnebm at Beam edge = (1/omega) * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 4.53 * (0.45/1) * 65.00 = 79.52 kips/bolt
(1/omega)Rndbm on Beam at Bolt Diameter   = (1/omega) * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.88 * (0.45/1) * 65.00 = 30.71 kips/bolt
Beam bearing capacity, (1/omega)Rnbm = min((1/omega)Rnsbm+ Rnsdblr,(1/omega)Rnebm+ Rnedblr,(1/omega)Rndbm+ Rnddblr) = min(82.45, 140.31, 56.31) = 56.31 kips/bolt
Ri vector at Shear Plate   = <0.00, -15.82>
Lcsshpl at Shear Plate spacing  = 2.56 in.
Lceshpl at Shear Plate edge    = 4.28 in.
(1/omega)Rnsshpl at Shear Plate spacing = (1/omega) * hf1 * Lcs * t * Fu = 0.50 * 1.20 * 2.56 * 1.00 * 65.00 = 99.94 kips/bolt
(1/omega)Rneshpl at Shear Plate edge = (1/omega) * hf1 * Lce * t * Fu = 0.50 * 1.20 * 4.28 * 1.00 * 65.00 = 166.97 kips/bolt
(1/omega)Rndshpl on Shear Plate at Bolt Diameter   = (1/omega) * hf2 * db * t * Fu = 0.50 * 2.40 * 0.88 * 1.00 * 65.00 = 68.25 kips/bolt
Shear Plate bearing capacity, (1/omega)Rnshpl = min((1/omega)Rnsshpl,(1/omega)Rneshpl,(1/omega)Rndshpl) = min(99.94, 166.97, 68.25) = 68.25 kips/bolt
(1/omega)Rn = min((1/omega)Rnbm, (1/omega)Rnshpl) = min(56.306, 68.250) = 56.31 kips/bolt
Bolt Shear Demand to Bearing ratio = 56.31 / 15.82 = 3.56

At Row 2, At Column 2:
Ribolt = 14.74 kips
Ri vector at Beam   = <-0.00, 14.74>
Lcsdblr at Doubler spacing = 2.56 in.
Lcedblr at Doubler edge = 4.16 in.
(1/omega)Rnsdblr at Doubler spacing = (1/omega) * hf1 * Lcs * (dblrt/# shear planes) * Fu = 0.50 * 1.20 * 2.56 * (0.38/1) * 65.00 = 37.5 kips
(1/omega)Rnedblr at Doubler edge = (1/omega) * hf1 * Lce * (dblrt/# shear planes) * Fu = 0.50 * 1.20 * 4.16 * (0.38/1) * 65.00 = 60.79 kips
(1/omega)Rnddblr on Beam at Doubler = (1/omega) * hf2 * db * (dblrt/# shear planes) * Fu = 0.50 * 2.40 * 0.88 * (0.38/1) * 65.00 = 25.59 kips/bolt
Lcsbm at Beam spacing  = 2.56 in.
Lcebm at Beam edge    = 6.03 in.
(1/omega)Rnsbm at Beam spacing = (1/omega) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * 2.56 * (0.45/1) * 65.00 = 44.97 kips/bolt
(1/omega)Rnebm at Beam edge = (1/omega) * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 6.03 * (0.45/1) * 65.00 = 105.85 kips/bolt
(1/omega)Rndbm on Beam at Bolt Diameter   = (1/omega) * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.88 * (0.45/1) * 65.00 = 30.71 kips/bolt
Beam bearing capacity, (1/omega)Rnbm = min((1/omega)Rnsbm+ Rnsdblr,(1/omega)Rnebm+ Rnedblr,(1/omega)Rndbm+ Rnddblr) = min(82.45, 166.63, 56.31) = 56.31 kips/bolt
Ri vector at Shear Plate   = <0.00, -14.74>
Lcsshpl at Shear Plate spacing  = 2.56 in.
Lceshpl at Shear Plate edge    = 4.28 in.
(1/omega)Rnsshpl at Shear Plate spacing = (1/omega) * hf1 * Lcs * t * Fu = 0.50 * 1.20 * 2.56 * 1.00 * 65.00 = 99.94 kips/bolt
(1/omega)Rneshpl at Shear Plate edge = (1/omega) * hf1 * Lce * t * Fu = 0.50 * 1.20 * 4.28 * 1.00 * 65.00 = 166.97 kips/bolt
(1/omega)Rndshpl on Shear Plate at Bolt Diameter   = (1/omega) * hf2 * db * t * Fu = 0.50 * 2.40 * 0.88 * 1.00 * 65.00 = 68.25 kips/bolt
Shear Plate bearing capacity, (1/omega)Rnshpl = min((1/omega)Rnsshpl,(1/omega)Rneshpl,(1/omega)Rndshpl) = min(99.94, 166.97, 68.25) = 68.25 kips/bolt
(1/omega)Rn = min((1/omega)Rnbm, (1/omega)Rnshpl) = min(56.306, 68.250) = 56.31 kips/bolt
Bolt Shear Demand to Bearing ratio = 56.31 / 14.74 = 3.82

At Row 2, At Column 3:
Ribolt = 10.34 kips
Ri vector at Beam   = <-0.00, 10.34>
Lcsdblr at Doubler spacing = 2.56 in.
Lcedblr at Doubler edge = 4.16 in.
(1/omega)Rnsdblr at Doubler spacing = (1/omega) * hf1 * Lcs * (dblrt/# shear planes) * Fu = 0.50 * 1.20 * 2.56 * (0.38/1) * 65.00 = 37.5 kips
(1/omega)Rnedblr at Doubler edge = (1/omega) * hf1 * Lce * (dblrt/# shear planes) * Fu = 0.50 * 1.20 * 4.16 * (0.38/1) * 65.00 = 60.79 kips
(1/omega)Rnddblr on Beam at Doubler = (1/omega) * hf2 * db * (dblrt/# shear planes) * Fu = 0.50 * 2.40 * 0.88 * (0.38/1) * 65.00 = 25.59 kips/bolt
Lcsbm at Beam spacing  = 2.56 in.
Lcebm at Beam edge    = 6.03 in.
(1/omega)Rnsbm at Beam spacing = (1/omega) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * 2.56 * (0.45/1) * 65.00 = 44.97 kips/bolt
(1/omega)Rnebm at Beam edge = (1/omega) * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 6.03 * (0.45/1) * 65.00 = 105.85 kips/bolt
(1/omega)Rndbm on Beam at Bolt Diameter   = (1/omega) * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.88 * (0.45/1) * 65.00 = 30.71 kips/bolt
Beam bearing capacity, (1/omega)Rnbm = min((1/omega)Rnsbm+ Rnsdblr,(1/omega)Rnebm+ Rnedblr,(1/omega)Rndbm+ Rnddblr) = min(82.45, 166.63, 56.31) = 56.31 kips/bolt
Ri vector at Shear Plate   = <0.00, -10.34>
Lcsshpl at Shear Plate spacing  = 2.56 in.
Lceshpl at Shear Plate edge    = 4.28 in.
(1/omega)Rnsshpl at Shear Plate spacing = (1/omega) * hf1 * Lcs * t * Fu = 0.50 * 1.20 * 2.56 * 1.00 * 65.00 = 99.94 kips/bolt
(1/omega)Rneshpl at Shear Plate edge = (1/omega) * hf1 * Lce * t * Fu = 0.50 * 1.20 * 4.28 * 1.00 * 65.00 = 166.97 kips/bolt
(1/omega)Rndshpl on Shear Plate at Bolt Diameter   = (1/omega) * hf2 * db * t * Fu = 0.50 * 2.40 * 0.88 * 1.00 * 65.00 = 68.25 kips/bolt
Shear Plate bearing capacity, (1/omega)Rnshpl = min((1/omega)Rnsshpl,(1/omega)Rneshpl,(1/omega)Rndshpl) = min(99.94, 166.97, 68.25) = 68.25 kips/bolt
(1/omega)Rn = min((1/omega)Rnbm, (1/omega)Rnshpl) = min(56.306, 68.250) = 56.31 kips/bolt
Bolt Shear Demand to Bearing ratio = 56.31 / 10.34 = 5.45

At Row 2, At Column 4:
Ribolt = 10.92 kips
Ri vector at Beam   = <-0.00, -10.92>
Lcsdblr at Doubler spacing = 2.56 in.
Lcedblr at Doubler edge = 4.16 in.
(1/omega)Rnsdblr at Doubler spacing = (1/omega) * hf1 * Lcs * (dblrt/# shear planes) * Fu = 0.50 * 1.20 * 2.56 * (0.38/1) * 65.00 = 37.5 kips
(1/omega)Rnedblr at Doubler edge = (1/omega) * hf1 * Lce * (dblrt/# shear planes) * Fu = 0.50 * 1.20 * 4.16 * (0.38/1) * 65.00 = 60.79 kips
(1/omega)Rnddblr on Beam at Doubler = (1/omega) * hf2 * db * (dblrt/# shear planes) * Fu = 0.50 * 2.40 * 0.88 * (0.38/1) * 65.00 = 25.59 kips/bolt
Lcsbm at Beam spacing  = 2.56 in.
Lcebm at Beam edge    = 7.23 in.
(1/omega)Rnsbm at Beam spacing = (1/omega) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * 2.56 * (0.45/1) * 65.00 = 44.97 kips/bolt
(1/omega)Rnebm at Beam edge = (1/omega) * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 7.23 * (0.45/1) * 65.00 = 126.91 kips/bolt
(1/omega)Rndbm on Beam at Bolt Diameter   = (1/omega) * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.88 * (0.45/1) * 65.00 = 30.71 kips/bolt
Beam bearing capacity, (1/omega)Rnbm = min((1/omega)Rnsbm+ Rnsdblr,(1/omega)Rnebm+ Rnedblr,(1/omega)Rndbm+ Rnddblr) = min(82.45, 187.69, 56.31) = 56.31 kips/bolt
Ri vector at Shear Plate   = <0.00, 10.92>
Lcsshpl at Shear Plate spacing  = 2.56 in.
Lceshpl at Shear Plate edge    = 4.28 in.
(1/omega)Rnsshpl at Shear Plate spacing = (1/omega) * hf1 * Lcs * t * Fu = 0.50 * 1.20 * 2.56 * 1.00 * 65.00 = 99.94 kips/bolt
(1/omega)Rneshpl at Shear Plate edge = (1/omega) * hf1 * Lce * t * Fu = 0.50 * 1.20 * 4.28 * 1.00 * 65.00 = 166.97 kips/bolt
(1/omega)Rndshpl on Shear Plate at Bolt Diameter   = (1/omega) * hf2 * db * t * Fu = 0.50 * 2.40 * 0.88 * 1.00 * 65.00 = 68.25 kips/bolt
Shear Plate bearing capacity, (1/omega)Rnshpl = min((1/omega)Rnsshpl,(1/omega)Rneshpl,(1/omega)Rndshpl) = min(99.94, 166.97, 68.25) = 68.25 kips/bolt
(1/omega)Rn = min((1/omega)Rnbm, (1/omega)Rnshpl) = min(56.306, 68.250) = 56.31 kips/bolt
Bolt Shear Demand to Bearing ratio = 56.31 / 10.92 = 5.16

At Row 3, At Column 1:
Ribolt = 15.94 kips
Ri vector at Beam   = <-6.82, 14.40>
Lcsdblr at Doubler spacing = 3.31 in.
Lcedblr at Doubler edge = 4.21 in.
(1/omega)Rnsdblr at Doubler spacing = (1/omega) * hf1 * Lcs * (dblrt/# shear planes) * Fu = 0.50 * 1.20 * 3.31 * (0.38/1) * 65.00 = 48.4 kips
(1/omega)Rnedblr at Doubler edge = (1/omega) * hf1 * Lce * (dblrt/# shear planes) * Fu = 0.50 * 1.20 * 4.21 * (0.38/1) * 65.00 = 61.53 kips
(1/omega)Rnddblr on Beam at Doubler = (1/omega) * hf2 * db * (dblrt/# shear planes) * Fu = 0.50 * 2.40 * 0.88 * (0.38/1) * 65.00 = 25.59 kips/bolt
Lcsbm at Beam spacing  = 3.31 in.
Lcebm at Beam edge    = 4.21 in.
(1/omega)Rnsbm at Beam spacing = (1/omega) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * 3.31 * (0.45/1) * 65.00 = 58.07 kips/bolt
(1/omega)Rnebm at Beam edge = (1/omega) * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 4.21 * (0.45/1) * 65.00 = 73.84 kips/bolt
(1/omega)Rndbm on Beam at Bolt Diameter   = (1/omega) * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.88 * (0.45/1) * 65.00 = 30.71 kips/bolt
Beam bearing capacity, (1/omega)Rnbm = min((1/omega)Rnsbm+ Rnsdblr,(1/omega)Rnebm+ Rnedblr,(1/omega)Rndbm+ Rnddblr) = min(106.47, 135.37, 56.31) = 56.31 kips/bolt
Ri vector at Shear Plate   = <6.82, -14.40>
Lcsshpl at Shear Plate spacing  = 3.25 in.
Lceshpl at Shear Plate edge    = 0.86 in.
(1/omega)Rnsshpl at Shear Plate spacing = (1/omega) * hf1 * Lcs * t * Fu = 0.50 * 1.20 * 3.25 * 1.00 * 65.00 = 126.77 kips/bolt
(1/omega)Rneshpl at Shear Plate edge = (1/omega) * hf1 * Lce * t * Fu = 0.50 * 1.20 * 0.86 * 1.00 * 65.00 = 33.71 kips/bolt
(1/omega)Rndshpl on Shear Plate at Bolt Diameter   = (1/omega) * hf2 * db * t * Fu = 0.50 * 2.40 * 0.88 * 1.00 * 65.00 = 68.25 kips/bolt
Shear Plate bearing capacity, (1/omega)Rnshpl = min((1/omega)Rnsshpl,(1/omega)Rneshpl,(1/omega)Rndshpl) = min(126.77, 33.71, 68.25) = 33.71 kips/bolt
(1/omega)Rn = min((1/omega)Rnbm, (1/omega)Rnshpl) = min(56.306, 33.708) = 33.71 kips/bolt
Bolt Shear Demand to Bearing ratio = 33.71 / 15.94 = 2.12

At Row 3, At Column 2:
Ribolt = 15.35 kips
Ri vector at Beam   = <-9.56, 12.01>
Lcsdblr at Doubler spacing = 3.31 in.
Lcedblr at Doubler edge = 7.56 in.
(1/omega)Rnsdblr at Doubler spacing = (1/omega) * hf1 * Lcs * (dblrt/# shear planes) * Fu = 0.50 * 1.20 * 3.31 * (0.38/1) * 65.00 = 48.4 kips
(1/omega)Rnedblr at Doubler edge = (1/omega) * hf1 * Lce * (dblrt/# shear planes) * Fu = 0.50 * 1.20 * 7.56 * (0.38/1) * 65.00 = 110.56 kips
(1/omega)Rnddblr on Beam at Doubler = (1/omega) * hf2 * db * (dblrt/# shear planes) * Fu = 0.50 * 2.40 * 0.88 * (0.38/1) * 65.00 = 25.59 kips/bolt
Lcsbm at Beam spacing  = 3.31 in.
Lcebm at Beam edge    = 7.56 in.
(1/omega)Rnsbm at Beam spacing = (1/omega) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * 3.31 * (0.45/1) * 65.00 = 58.07 kips/bolt
(1/omega)Rnebm at Beam edge = (1/omega) * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 7.56 * (0.45/1) * 65.00 = 132.67 kips/bolt
(1/omega)Rndbm on Beam at Bolt Diameter   = (1/omega) * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.88 * (0.45/1) * 65.00 = 30.71 kips/bolt
Beam bearing capacity, (1/omega)Rnbm = min((1/omega)Rnsbm+ Rnsdblr,(1/omega)Rnebm+ Rnedblr,(1/omega)Rndbm+ Rnddblr) = min(106.47, 243.23, 56.31) = 56.31 kips/bolt
Ri vector at Shear Plate   = <9.56, -12.01>
Lcsshpl at Shear Plate spacing  = 3.25 in.
Lceshpl at Shear Plate edge    = 1.00 in.
(1/omega)Rnsshpl at Shear Plate spacing = (1/omega) * hf1 * Lcs * t * Fu = 0.50 * 1.20 * 3.25 * 1.00 * 65.00 = 126.77 kips/bolt
(1/omega)Rneshpl at Shear Plate edge = (1/omega) * hf1 * Lce * t * Fu = 0.50 * 1.20 * 1.00 * 1.00 * 65.00 = 38.94 kips/bolt
(1/omega)Rndshpl on Shear Plate at Bolt Diameter   = (1/omega) * hf2 * db * t * Fu = 0.50 * 2.40 * 0.88 * 1.00 * 65.00 = 68.25 kips/bolt
Shear Plate bearing capacity, (1/omega)Rnshpl = min((1/omega)Rnsshpl,(1/omega)Rneshpl,(1/omega)Rndshpl) = min(126.77, 38.94, 68.25) = 38.94 kips/bolt
(1/omega)Rn = min((1/omega)Rnbm, (1/omega)Rnshpl) = min(56.306, 38.944) = 38.94 kips/bolt
Bolt Shear Demand to Bearing ratio = 38.94 / 15.35 = 2.54

At Row 3, At Column 3:
Ribolt = 14.27 kips
Ri vector at Beam   = <-13.26, 5.29>
Lcsdblr at Doubler spacing = 3.31 in.
Lcedblr at Doubler edge = 8.14 in.
(1/omega)Rnsdblr at Doubler spacing = (1/omega) * hf1 * Lcs * (dblrt/# shear planes) * Fu = 0.50 * 1.20 * 3.31 * (0.38/1) * 65.00 = 48.4 kips
(1/omega)Rnedblr at Doubler edge = (1/omega) * hf1 * Lce * (dblrt/# shear planes) * Fu = 0.50 * 1.20 * 8.14 * (0.38/1) * 65.00 = 119.12 kips
(1/omega)Rnddblr on Beam at Doubler = (1/omega) * hf2 * db * (dblrt/# shear planes) * Fu = 0.50 * 2.40 * 0.88 * (0.38/1) * 65.00 = 25.59 kips/bolt
Lcsbm at Beam spacing  = 3.31 in.
Lcebm at Beam edge    = 8.14 in.
(1/omega)Rnsbm at Beam spacing = (1/omega) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * 3.31 * (0.45/1) * 65.00 = 58.07 kips/bolt
(1/omega)Rnebm at Beam edge = (1/omega) * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 8.14 * (0.45/1) * 65.00 = 142.94 kips/bolt
(1/omega)Rndbm on Beam at Bolt Diameter   = (1/omega) * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.88 * (0.45/1) * 65.00 = 30.71 kips/bolt
Beam bearing capacity, (1/omega)Rnbm = min((1/omega)Rnsbm+ Rnsdblr,(1/omega)Rnebm+ Rnedblr,(1/omega)Rndbm+ Rnddblr) = min(106.47, 262.06, 56.31) = 56.31 kips/bolt
Ri vector at Shear Plate   = <13.26, -5.29>
Lcsshpl at Shear Plate spacing  = 3.25 in.
Lceshpl at Shear Plate edge    = 2.77 in.
(1/omega)Rnsshpl at Shear Plate spacing = (1/omega) * hf1 * Lcs * t * Fu = 0.50 * 1.20 * 3.25 * 1.00 * 65.00 = 126.77 kips/bolt
(1/omega)Rneshpl at Shear Plate edge = (1/omega) * hf1 * Lce * t * Fu = 0.50 * 1.20 * 2.77 * 1.00 * 65.00 = 107.90 kips/bolt
(1/omega)Rndshpl on Shear Plate at Bolt Diameter   = (1/omega) * hf2 * db * t * Fu = 0.50 * 2.40 * 0.88 * 1.00 * 65.00 = 68.25 kips/bolt
Shear Plate bearing capacity, (1/omega)Rnshpl = min((1/omega)Rnsshpl,(1/omega)Rneshpl,(1/omega)Rndshpl) = min(126.77, 107.90, 68.25) = 68.25 kips/bolt
(1/omega)Rn = min((1/omega)Rnbm, (1/omega)Rnshpl) = min(56.306, 68.250) = 56.31 kips/bolt
Bolt Shear Demand to Bearing ratio = 56.31 / 14.27 = 3.95

At Row 3, At Column 4:
Ribolt = 14.34 kips
Ri vector at Beam   = <-13.04, -5.97>
Lcsdblr at Doubler spacing = 3.31 in.
Lcedblr at Doubler edge = 2.23 in.
(1/omega)Rnsdblr at Doubler spacing = (1/omega) * hf1 * Lcs * (dblrt/# shear planes) * Fu = 0.50 * 1.20 * 3.31 * (0.38/1) * 65.00 = 48.4 kips
(1/omega)Rnedblr at Doubler edge = (1/omega) * hf1 * Lce * (dblrt/# shear planes) * Fu = 0.50 * 1.20 * 2.23 * (0.38/1) * 65.00 = 32.65 kips
(1/omega)Rnddblr on Beam at Doubler = (1/omega) * hf2 * db * (dblrt/# shear planes) * Fu = 0.50 * 2.40 * 0.88 * (0.38/1) * 65.00 = 25.59 kips/bolt
Lcsbm at Beam spacing  = 3.31 in.
Lcebm at Beam edge    = 6.68 in.
(1/omega)Rnsbm at Beam spacing = (1/omega) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * 3.31 * (0.45/1) * 65.00 = 58.07 kips/bolt
(1/omega)Rnebm at Beam edge = (1/omega) * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 6.68 * (0.45/1) * 65.00 = 117.25 kips/bolt
(1/omega)Rndbm on Beam at Bolt Diameter   = (1/omega) * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.88 * (0.45/1) * 65.00 = 30.71 kips/bolt
Beam bearing capacity, (1/omega)Rnbm = min((1/omega)Rnsbm+ Rnsdblr,(1/omega)Rnebm+ Rnedblr,(1/omega)Rndbm+ Rnddblr) = min(106.47, 149.90, 56.31) = 56.31 kips/bolt
Ri vector at Shear Plate   = <13.04, 5.97>
Lcsshpl at Shear Plate spacing  = 3.25 in.
Lceshpl at Shear Plate edge    = 1.31 in.
(1/omega)Rnsshpl at Shear Plate spacing = (1/omega) * hf1 * Lcs * t * Fu = 0.50 * 1.20 * 3.25 * 1.00 * 65.00 = 126.77 kips/bolt
(1/omega)Rneshpl at Shear Plate edge = (1/omega) * hf1 * Lce * t * Fu = 0.50 * 1.20 * 1.31 * 1.00 * 65.00 = 50.94 kips/bolt
(1/omega)Rndshpl on Shear Plate at Bolt Diameter   = (1/omega) * hf2 * db * t * Fu = 0.50 * 2.40 * 0.88 * 1.00 * 65.00 = 68.25 kips/bolt
Shear Plate bearing capacity, (1/omega)Rnshpl = min((1/omega)Rnsshpl,(1/omega)Rneshpl,(1/omega)Rndshpl) = min(126.77, 50.94, 68.25) = 50.94 kips/bolt
(1/omega)Rn = min((1/omega)Rnbm, (1/omega)Rnshpl) = min(56.306, 50.940) = 50.94 kips/bolt
Bolt Shear Demand to Bearing ratio = 50.94 / 14.34 = 3.55

Min Bolt Shear Demand to Bearing ratio Beam and Shear Plate for vertical shear only
 = min(1.00, 2.02, 3.67, 3.95, 3.93, 3.56, 3.82, 5.45, 5.16, 2.12, 
       2.54, 3.95, 3.55) = 1.00

BEARING AT BEAM AND SHEAR PLATE SIDE SUMMARY:
Bearing Capacity at Vertical Shear Load Only, Rbv = Min Bolt Shear Demand to Bearing Ratio * Bolt Shear = 1.00 * 81.45 = 81.45 kips
Rbv = 81.45 kips >= V = 70.00 kips (OK)

Web Depth = d - [Top Cope Depth] - [Bottom Cope Depth] = 14.2 - 1.5 - 1.5 = 11.2 in.
Gross Area (Shear) = [Web Depth] * tw = 11.20 * 0.45 = 5.04 in^2
Net Shear Area (Shear) = ([Web Depth] - ([# rows] * [Diameter + 0.0625])) * tw 
    = (11.20 - (3 * 1.00)) * 0.45 = 3.69 in^2

Using Eq.J4-3:
Shear Yielding = (1/omega) * 0.6 * Fybeam * [Gross Area] = 0.67 * 0.6 * 50.00 * 5.04 = 100.80 kips

Using Eq.J4-3:
Shear Yielding = (1/omega) * 0.6 * Fydoubler * [Gross Area] = 0.67 * 0.6 * 50.00 * 3.47 = 69.38 kips

Doubler Contribution = Min(Doubler Plate Shear Yielding, Doubler Vertical Component Weld Strength) = 
Min(69.38, 42.04) = 42.04 kips

   Total Shear Yield Capacity = 100.80 + 42.04 = 142.84 kips

Using Eq.J4-4:
Shear Rupture = (1/omega) * 0.6 * Fubeam * [Net Area] = 0.50 * 0.6 * 65.00 * 3.69 = 71.95 kips


Using Eq.J4-4:
Shear Rupture = (1/omega) * 0.6 * Fudoubler * [Net Area] = 0.50 * 0.6 * 65.00 * 2.34 = 45.70 kips


Doubler Contribution = Min(Doubler Plate Shear Rupture, Doubler Vertical Component Weld Strength) = 
Min(45.70, 42.04) = 42.04 kips

   Total Shear Rupture Capacity = 71.95 + 42.04 = 114.00 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))}

Coped Beam Bending Calculations w/o Doubler Plate:

Buckling and Flexure at Longest Cope (Top and Bottom Copes at Section)
Eccentricity at Section, e = 5.72 in.
If beam is coped at both top and bottom flanges,

Using Eq. 9-14 through 9-18, Fcr = Fy * Q
tw = 0.45 in.
ho = 11.20 in.
c = 4.50 in.
lambda = (ho * Fy ^ 0.5) / ( 10 * tw * ( 475.00 + 280.00 * (ho / c)^2 ) ^0.5 ) = 
 = 11.20 * 50.00^0.5 / (10 * 0.45 * (475.00 + 280.00 * (11.20/4.50)^2 )^0.5) = 0.37
When lambda <= 0.70, Q=1
Q = 1.00
Fcrmin =1/omega * Fcr = 0.60 * 50.00 * 1.00 = 30.00 ksi
Snet1 (bolt holes not applicable) = 9.41 in^3
Snet2 (bolt holes applicable) = 9.41 in^3
Znet = 14.11 in^3

Using Eq. 9-6
Buckling = Fcr * Snet1 / e = 30.00 * 9.41 / 5.72 = 49.30 kips

Using Eq. 9-19
Flexural Yielding = (1/omega) * Fy * Snet1 / e = 0.60 * 50.00 * 9.41 / 5.72 = 49.30 kips

Using Eq. 9-4
Flexural Rupture = (1/omega) * Fu * Znet / e = 0.50 * 65.00 * 14.11 / 5.72 = 80.11 kips


Buckling and Flexure at Furthest Bolt Line within Cope (Top and Bottom Copes at Section)
Eccentricity at Section, e = 3.23 in.
If beam is coped at both top and bottom flanges,

Using Eq. 9-14 through 9-18, Fcr = Fy * Q
tw = 0.45 in.
ho = 11.20 in.
c = 4.50 in.
lambda = (ho * Fy ^ 0.5) / ( 10 * tw * ( 475.00 + 280.00 * (ho / c)^2 ) ^0.5 ) = 
 = 11.20 * 50.00^0.5 / (10 * 0.45 * (475.00 + 280.00 * (11.20/4.50)^2 )^0.5) = 0.37
When lambda <= 0.70, Q=1
Q = 1.00
Fcrmin =1/omega * Fcr = 0.60 * 50.00 * 1.00 = 30.00 ksi
Snet1 (bolt holes not applicable) = 9.41 in^3
Snet2 (bolt holes applicable) = 7.03 in^3
Znet = 10.58 in^3

Using Eq. 9-6
Buckling = Fcr * Snet1 / e = 30.00 * 9.41 / 3.23 = 87.52 kips

Using Eq. 9-19
Flexural Yielding = (1/omega) * Fy * Snet1 / e = 0.60 * 50.00 * 9.41 / 3.23 = 87.52 kips

Using Eq. 9-4
Flexural Rupture = (1/omega) * Fu * Znet / e = 0.50 * 65.00 * 10.58 / 3.23 = 106.62 kips


Coped Beam Bending Calculations with Doubler Plate:

Buckling and Flexure at Longest Cope (Top and Bottom Copes at Section)
Eccentricity at Section, e = 5.72 in.
If beam is coped at both top and bottom flanges,

Using Eq. 9-14 through 9-18, Fcr = Fy * Q
tw = 0.45 in.
ho = 11.20 in.
c = 4.50 in.
lambda = (ho * Fy ^ 0.5) / ( 10 * tw * ( 475.00 + 280.00 * (ho / c)^2 ) ^0.5 ) = 
 = 11.20 * 50.00^0.5 / (10 * 0.45 * (475.00 + 280.00 * (11.20/4.50)^2 )^0.5) = 0.37
When lambda <= 0.70, Q=1
Q = 1.00
Fcrmin =1/omega * Fcr = 0.60 * 50.00 * 1.00 = 30.00 ksi
Snet1 (bolt holes not applicable) = 13.41 in^3
Snet2 (bolt holes applicable) = 13.41 in^3
Znet = 22.19 in^3

Using Eq. 9-6
Buckling = Fcr * Snet1 / e = 30.00 * 13.41 / 5.72 = 70.29 kips

Using Eq. 9-19
Flexural Yielding = (1/omega) * Fy * Snet1 / e = 0.60 * 50.00 * 13.41 / 5.72 = 70.29 kips

Using Eq. 9-4
Flexural Rupture = (1/omega) * Fu * Znet / e = 0.50 * 65.00 * 22.19 / 5.72 = 125.97 kips


Buckling and Flexure at Furthest Bolt Line within Cope (Top and Bottom Copes at Section) (with web doubler):
Eccentricity at Section, e = 3.23 in.
If beam is coped at both top and bottom flanges,

Using Eq. 9-14 through 9-18, Fcr = Fy * Q
tw = 0.45 in.
ho = 11.20 in.
c = 4.50 in.
lambda = (ho * Fy ^ 0.5) / ( 10 * tw * ( 475.00 + 280.00 * (ho / c)^2 ) ^0.5 ) = 
 = 11.20 * 50.00^0.5 / (10 * 0.45 * (475.00 + 280.00 * (11.20/4.50)^2 )^0.5) = 0.37
When lambda <= 0.70, Q=1
Q = 1.00
Fcrmin =1/omega * Fcr = 0.60 * 50.00 * 1.00 = 30.00 ksi
Snet1 (bolt holes not applicable) = 13.41 in^3
Snet2 (bolt holes applicable) = 10.09 in^3
Znet = 15.91 in^3

Using Eq. 9-6
Buckling = Fcr * Snet1 / e = 30.00 * 13.41 / 3.23 = 124.77 kips

Using Eq. 9-19
Flexural Yielding = (1/omega) * Fy * Snet1 / e = 0.60 * 50.00 * 13.41 / 3.23 = 124.77 kips

Using Eq. 9-4
Flexural Rupture = (1/omega) * Fu * Znet / e = 0.50 * 65.00 * 15.91 / 3.23 = 160.34 kips


Coped Beam Buckling and Flexure at Longest Cope (Top and Bottom Copes at Section)
Min(Beam Section w/o Doubler + Doubler Plate Weld Strength, Beam Section with Doubler Plate):
Buckling = Min(49.30 + 42.04, 70.29) = 70.29 kips
Flexural Yielding = Min(49.30 + 42.04, 70.29) = 70.29 kips
Flexural Rupture = Min(80.11 + 42.04, 125.97) = 122.16 kips

Coped Beam Buckling and Flexure at Furthest Bolt Line within Cope (Top and Bottom Copes at Section)
Min(Beam Section w/o Doubler + Doubler Plate Weld Strength, Beam Section with Doubler Plate):
Buckling = Min(87.52 + 42.04, 124.77) = 124.77 kips
Flexural Yielding = Min(87.52 + 42.04, 124.77) = 124.77 kips
Flexural Rupture = Min(106.62 + 42.04, 160.34) = 148.66 kips

Section Bending Strength Calculations Summary:

   Coped Beam Buckling and Flexure at Longest Cope (Top and Bottom Copes at Section)
   Buckling : 70.29 >= 70.00 kips (OK)
   Flexural Yielding : 70.29 >= 70.00 kips (OK)
   Flexural Rupture : 122.16 >= 70.00 kips (OK)

   Coped Beam Buckling and Flexure at Furthest Bolt Line within Cope (Top and Bottom Copes at Section)
   Buckling : 124.77 >= 70.00 kips (OK)
   Flexural Yielding : 124.77 >= 70.00 kips (OK)
   Flexural Rupture : 148.66 >= 70.00 kips (OK)

DOUBLER PLATE WELD:


Shear Reaction = 70.00 kips
Beam Shear Failure Reaction = 49.30 kips
 Required Shear Reinforcement = MAX(70.00 - 49.30, 0) = 20.70 kips
Axial Reaction = 0.00 kips

theta = sin(0.00 / (70.00^2 + 0.00^2)^0.5)^-1 = 0.00 deg.
load angle, theta = 0.00 deg.
k = 0.89
ex = 11.33
a = ex / l = 11.33 / 9.25 = 1.23
Weld Coefficient = 0.6 * Fexx * cphi * arrangement coefficient = 2.27
Dmax1 using min(eqn 9-2, tdoub - 0.062) 
 = min(tdoub * Fudoub / ( Fexx * C1 * 0.044), tdoub - 0.062) 
 = min(0.375 * 65.000 / ( 70.000 * 1.000 * 0.044), 0.375 - 0.062) 
 = min(7.879, 5.000)
 = 5.000 
Dmax2 (using eqn 9-2)
 = twbeam * Fubeam / ( Fexx * C1 * 0.044 )
 = 0.450 * 65.000 / ( 70.000 * 1.000 * 0.044 ) 
 = 9.455 
Dmax3 = project max fillet weld = 12.000
Dmax=min(Dmax1, Dmax2, Dmax3) = min(5.000, 9.455, 12.000)
 = 5.000 

Use D = Min(doubler thickness - 1/16, 5/16, Max(Design Req, J Req, User Pref Min)) = Min(5.00, 5.00, Max(2.00, 3.00, 4.00)) = 4.00/16

Weld Strength = 1/omega * weld coefficient * l * D  = 0.50 * 2.27 * 9.25 * 4.00 = 42.04 kips

Gross Area = 1.00 * 9.50 = 9.50 in^2
Net Area = (9.50 - (3 *(0.94 + 1/16))) * 1.00 = 6.50 in^2

Using Eq.J4-3:
Shear Yielding = (1/omega) * 0.6 * Fypl * [Gross Area] = 0.67 * 0.6 * 50.00 * 9.50 = 190.00 kips

Using Eq.J4-4:
Shear Rupture = (1/omega) * 0.6 * Fupl * [Net Area] = 0.50 * 0.6 * 65.00 * 6.50 = 126.75 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 = (9.5 - 1.25) = 8.25 in.
Net Shear Length = 8.25 - (2.5 * (0.938 + 0.0625)) = 5.75 in.
Gross Tension Length = (9 + 1.75) = 10.75 in.
Net Tension Length = 10.8 - (3.5 * (1.12 + 0.0625)) = 6.59 in.
1. (1/omega) * [material thickness] * ((0.60 * Fupl* [net shear length]) + (Ubs * Fupl * [net tension length])) 
    = 0.50 * 1.00 * ((0.60 * 65.00 * 5.75) + (0.50 * 65.00 * 6.59)) = 219.27 kips
2. (1/omega) * [material thickness] * ((0.60 * Fypl * [gross shear length]) + (Ubs * Fupl * [net tension length])) 
    = 0.50 * 1.00 * ((0.60 * 50.00 * 8.25) + (0.50 * 65.00 * 6.59)) = 230.90 kips
Block Shear = 219.27 kips

Block 2 (Shear): 
Gross Shear Length = 2 * (9.5 - 1.25) = 16.50 in.
Net Shear Length = 2 * ( 8.25 - (2.5 * (0.938 + 0.0625)) ) = 11.50 in.
Gross Tension Length = (9 + 1.75) - 1.75 = 9.00 in.
Net Tension Length = 9 - 3 * (1.12 + 0.0625) = 5.44 in.
1. (1/omega) * [material thickness] * ((0.60 * Fupl* [net shear length]) + (Ubs * Fupl * [net tension length])) 
    = 0.50 * 1.00 * ((0.60 * 65.00 * 11.50) + (0.50 * 65.00 * 5.44)) = 312.61 kips
2. (1/omega) * [material thickness] * ((0.60 * Fypl * [gross shear length]) + (Ubs * Fupl * [net tension length])) 
    = 0.50 * 1.00 * ((0.60 * 50.00 * 16.50) + (0.50 * 65.00 * 5.44)) = 335.86 kips
Block Shear = 312.61 kips

219.27 kips >= Vbm = 70.00 kips (OK)

Flexural and Buckling Strength:

Eccentricity at first line of bolts, e = 3.23 in.
Zgross = 22.56 in^3
Znet   = 15.31 in^3
Sgross = 15.04 in^3
Snet   = 9.88 in^3

Using Eq. 9-4
Flexural Rupture = (1/omega) * Fu * Znet / e = 0.50 * 65.00 * 15.31 / 3.23 = 154.31 kips


Using Eq. 9-14 through 9-18, Fcr = Fy * Q
tw = 1.00 in.
ho = 9.50 in.
c = 3.00 in.
lambda = (ho * Fy ^ 0.5) / ( 10 * tw * ( 475.00 + 280.00 * (ho / c)^2 ) ^0.5 ) = 
 = 9.50 * 50.00^0.5 / (10 * 1.00 * (475.00 + 280.00 * (9.50/3.00)^2 )^0.5) = 0.12
When lambda <= 0.70, Q=1
Q = 1.00
Fcrmin =1/omega * Fcr = 0.60 * 50.00 * 1.00 = 30.00 ksi

Using Eq. 9-6
Buckling = Fcr * Sgross / e = 30.00 * 15.04 / 3.23 = 139.92 kips

Interaction Check of Flexural Yielding, Per AISC 10-5: 
Eccentricity at CG of Bolt Group, e = 7.72 in.
Zgross = 22.56
Znet = 22.56
Mr = Vr * e = 70.00 * 7.72 = 540.75 kips-in
Mc = 1/omega * Mn = 1/omega * Fy * Zgross = 0.60 * 50.00 * 22.56 = 676.87 kips-in
Vr = 70.00 kips
Vc = 1/omega * Vn = 1/omega * 0.60 * Fy * Ag = 0.67 * 0.60 * 50.00 * 9.50 = 190.00 kips
Interaction due to moment and shear, (Vr/Vc)^2 + (Mr/Mc)^2 <= 1.0
(Vr/Vc)^2 + (Mr/Mc)^2 = (70.00 / 190.00)^2 + (540.75 / 676.87)^2 = 0.77 <= 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 * 0.60132 * 47.631 = 1718.49 kips-in
tmax = 6 * 1718.49 / (50 * 9.5^2) = 2.28 in.
Maximum Plate Thickness is Not a Limiting Criteria.

WELD:

 Weld Requirements:

At shear only case: 
Weld Length for shear, Lv = 9.500 in.
Shear Load per inch per weld, fv = R/Lv/2 = 70.000 / 9.500 / 2 = 3.684 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) = 3.684 / (0.500 * 1.856) = 3.970/16

Minimum fillet weld size : 
   At shear only load case = 0.25 in.
   per Table J2.4     = 0.19 in.
   5/8tp              = 0.62 in.
   user preference    = 0.25 in.

Dmax1 (using eqn 9-3)
 = tshpl * Fushpl / ( Fexx * C1 * 0.088)
 = 1.000 * 65.000 / ( 70.000 * 1.000 * 0.088 ) 
 = 10.506 
Dmax2 (using eqn 9-3)
 = twsupport * Fusupport / ( Fexx * C1 * 0.088 )
 = 0.450 * 65.000 / ( 70.000 * 1.000 * 0.088 ) 
 = 4.728 
Dmax3 = project max fillet weld = 12.000
Dmax=min(Dmax1, Dmax2, Dmax3) = min(10.506, 4.728, 12.000)
 = 4.728 

Use weld size
D1 = 10.00
D2 = 10.00

Weld Strength :

Vertical weld capacity during shear only load, 1/omega * Rnv1 = 0.50 * 1.86 * 9.50 * (4.73 + 4.73) = 83.36 kips

83.36 kips >= Vbm = 70.00 kips (OK)