bb.s.s.00015.00016

SHEAR PLATE CONNECTION SUMMARY

NOTE: DESIGNED WITH MEMBERS CHOSEN ON ONLY ONE SIDE OF SUPPORT

Filler Beam profile: W16X40
Support Girder profile: W18X97
Slope: 0.00 deg.
Skew: 90.00
Vertical Offset: 0.00
Horizontal Offset: 0.00
Span: 2.00 ft.
Reaction, V: 68.00 kips
Shear Capacity, Rn: 87.75 kips
Design/Reference according to AISC 14th Ed. - LRFD
Shear Plate: Extended Configuration
Beam material grade: A992
Support material grade: A992
Plate material grade: A572-GR.50
Weld grade: E70
Shear Plate Size: 6.50 in. x 11.50 in. x 0.38 in.
Configuration Geometry:
Welds at shear plate to support: 4/16 FILLET, 4/16 FILLET
Bolt: 4 rows x 2 columns 0.75 in. Diameter A325N_TC bolts
Vertical spacing: 3.00 in.
Horizontal spacing: 3.00 in.
Shear plate edge setback = 0.50 in.
Beam centerline setback = 0.50 in.
Edge distance at vertical edge of plate: 1.50 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: 1.50 in.
Edge distance at top edge of beam: 1.50 in.
Top cope depth: 1.50 in.
Top cope length: 5.25 in.
Horizontal distance to first hole: 2.00 in.
Down distance from top of filler beam flange: 3.00 in.
Holes in beam web: STD diameter = 0.81 in.
Holes in shear plate: SSL diameter = 0.81 in., slot width = 1.00 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 = 3.77 in.
Angle = 0.00 deg.
C = 5.03
Using Table 7-1 to determine (phi)rn:
(phi)Rn = (phi)rn * C = 17.89 * 5.03 = 90.08 kips


Total Vertical Bolt Shear Capacity = 90.08 kips
90.08 kips >= Reaction V = 68.00 kips (OK)

BOLT BEARING AT BEAM AND SHEAR PLATE SIDE
Vertical Shear Only Load Case:
ICR cordinate relative to CG = (3.09, 0.00)
At Row 1, At Column 1:
Ribolt = 17.56 kips
Ri vector at Beam   = <12.30, 12.54>
Lcsbm at Beam spacing  = 3.12 in.
Lcebm at Beam edge    = 1.70 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.75 * 1.20 * 3.12 * (0.30/1) * 65.00 = 55.59 kips/bolt
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 1.70 * (0.30/1) * 65.00 = 30.25 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.75 * (0.30/1) * 65.00 = 26.76 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(55.59, 30.25, 26.76) = 26.76 kips/bolt
Ri vector at Shear Plate   = <-12.30, -12.54>
Lcsshpl at Shear Plate spacing  = 3.05 in.
Lceshpl at Shear Plate edge    = 2.29 in.
(phi)Rnsshpl at Shear Plate spacing = (phi) * hf1 * Lcs * t * Fu = 0.75 * 1.20 * 3.05 * 0.38 * 65.00 = 66.90 kips/bolt
(phi)Rneshpl at Shear Plate edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 2.29 * 0.38 * 65.00 = 50.16 kips/bolt
(phi)Rndshpl on Shear Plate at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.75 * 0.38 * 65.00 = 32.91 kips/bolt
Shear Plate bearing capacity, (phi)Rnshpl = min((phi)Rnsshpl,(phi)Rneshpl,(phi)Rndshpl) = min(66.90, 50.16, 32.91) = 32.91 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(26.76, 32.91) = 26.76 kips/bolt
Bolt Shear Demand to Bearing ratio = 26.76 / 17.56 = 1.52

At Row 1, At Column 2:
Ribolt = 17.09 kips
Ri vector at Beam   = <16.12, 5.68>
Lcsbm at Beam spacing  = 3.12 in.
Lcebm at Beam edge    = 8.62 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.75 * 1.20 * 3.12 * (0.30/1) * 65.00 = 55.59 kips/bolt
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 8.62 * (0.30/1) * 65.00 = 153.79 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.75 * (0.30/1) * 65.00 = 26.76 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(55.59, 153.79, 26.76) = 26.76 kips/bolt
Ri vector at Shear Plate   = <-16.12, -5.68>
Lcsshpl at Shear Plate spacing  = 3.05 in.
Lceshpl at Shear Plate edge    = 4.77 in.
(phi)Rnsshpl at Shear Plate spacing = (phi) * hf1 * Lcs * t * Fu = 0.75 * 1.20 * 3.05 * 0.38 * 65.00 = 66.90 kips/bolt
(phi)Rneshpl at Shear Plate edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 4.77 * 0.38 * 65.00 = 104.67 kips/bolt
(phi)Rndshpl on Shear Plate at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.75 * 0.38 * 65.00 = 32.91 kips/bolt
Shear Plate bearing capacity, (phi)Rnshpl = min((phi)Rnsshpl,(phi)Rneshpl,(phi)Rndshpl) = min(66.90, 104.67, 32.91) = 32.91 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(26.76, 32.91) = 26.76 kips/bolt
Bolt Shear Demand to Bearing ratio = 26.76 / 17.09 = 1.57

At Row 2, At Column 1:
Ribolt = 17.11 kips
Ri vector at Beam   = <5.32, 16.27>
Lcsbm at Beam spacing  = 3.12 in.
Lcebm at Beam edge    = 4.33 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.75 * 1.20 * 3.12 * (0.30/1) * 65.00 = 55.59 kips/bolt
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 4.33 * (0.30/1) * 65.00 = 77.23 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.75 * (0.30/1) * 65.00 = 26.76 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(55.59, 77.23, 26.76) = 26.76 kips/bolt
Ri vector at Shear Plate   = <-5.32, -16.27>
Lcsshpl at Shear Plate spacing  = 3.05 in.
Lceshpl at Shear Plate edge    = 6.01 in.
(phi)Rnsshpl at Shear Plate spacing = (phi) * hf1 * Lcs * t * Fu = 0.75 * 1.20 * 3.05 * 0.38 * 65.00 = 66.90 kips/bolt
(phi)Rneshpl at Shear Plate edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 6.01 * 0.38 * 65.00 = 131.76 kips/bolt
(phi)Rndshpl on Shear Plate at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.75 * 0.38 * 65.00 = 32.91 kips/bolt
Shear Plate bearing capacity, (phi)Rnshpl = min((phi)Rnsshpl,(phi)Rneshpl,(phi)Rndshpl) = min(66.90, 131.76, 32.91) = 32.91 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(26.76, 32.91) = 26.76 kips/bolt
Bolt Shear Demand to Bearing ratio = 26.76 / 17.11 = 1.56

At Row 2, At Column 2:
Ribolt = 14.53 kips
Ri vector at Beam   = <9.98, 10.56>
Lcsbm at Beam spacing  = 3.12 in.
Lcebm at Beam edge    = 7.85 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.75 * 1.20 * 3.12 * (0.30/1) * 65.00 = 55.59 kips/bolt
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 7.85 * (0.30/1) * 65.00 = 140.10 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.75 * (0.30/1) * 65.00 = 26.76 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(55.59, 140.10, 26.76) = 26.76 kips/bolt
Ri vector at Shear Plate   = <-9.98, -10.56>
Lcsshpl at Shear Plate spacing  = 3.05 in.
Lceshpl at Shear Plate edge    = 6.72 in.
(phi)Rnsshpl at Shear Plate spacing = (phi) * hf1 * Lcs * t * Fu = 0.75 * 1.20 * 3.05 * 0.38 * 65.00 = 66.90 kips/bolt
(phi)Rneshpl at Shear Plate edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 6.72 * 0.38 * 65.00 = 147.37 kips/bolt
(phi)Rndshpl on Shear Plate at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.75 * 0.38 * 65.00 = 32.91 kips/bolt
Shear Plate bearing capacity, (phi)Rnshpl = min((phi)Rnsshpl,(phi)Rneshpl,(phi)Rndshpl) = min(66.90, 147.37, 32.91) = 32.91 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(26.76, 32.91) = 26.76 kips/bolt
Bolt Shear Demand to Bearing ratio = 26.76 / 14.53 = 1.84

At Row 3, At Column 1:
Ribolt = 17.11 kips
Ri vector at Beam   = <-5.32, 16.27>
Lcsbm at Beam spacing  = 3.12 in.
Lcebm at Beam edge    = 4.42 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.75 * 1.20 * 3.12 * (0.30/1) * 65.00 = 55.59 kips/bolt
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 4.42 * (0.30/1) * 65.00 = 78.84 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.75 * (0.30/1) * 65.00 = 26.76 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(55.59, 78.84, 26.76) = 26.76 kips/bolt
Ri vector at Shear Plate   = <5.32, -16.27>
Lcsshpl at Shear Plate spacing  = 3.05 in.
Lceshpl at Shear Plate edge    = 4.04 in.
(phi)Rnsshpl at Shear Plate spacing = (phi) * hf1 * Lcs * t * Fu = 0.75 * 1.20 * 3.05 * 0.38 * 65.00 = 66.90 kips/bolt
(phi)Rneshpl at Shear Plate edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 4.04 * 0.38 * 65.00 = 88.72 kips/bolt
(phi)Rndshpl on Shear Plate at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.75 * 0.38 * 65.00 = 32.91 kips/bolt
Shear Plate bearing capacity, (phi)Rnshpl = min((phi)Rnsshpl,(phi)Rneshpl,(phi)Rndshpl) = min(66.90, 88.72, 32.91) = 32.91 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(26.76, 32.91) = 26.76 kips/bolt
Bolt Shear Demand to Bearing ratio = 26.76 / 17.11 = 1.56

At Row 3, At Column 2:
Ribolt = 14.53 kips
Ri vector at Beam   = <-9.99, 10.56>
Lcsbm at Beam spacing  = 3.12 in.
Lcebm at Beam edge    = 6.14 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.75 * 1.20 * 3.12 * (0.30/1) * 65.00 = 55.59 kips/bolt
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 6.14 * (0.30/1) * 65.00 = 109.60 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.75 * (0.30/1) * 65.00 = 26.76 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(55.59, 109.60, 26.76) = 26.76 kips/bolt
Ri vector at Shear Plate   = <9.99, -10.56>
Lcsshpl at Shear Plate spacing  = 3.05 in.
Lceshpl at Shear Plate edge    = 1.62 in.
(phi)Rnsshpl at Shear Plate spacing = (phi) * hf1 * Lcs * t * Fu = 0.75 * 1.20 * 3.05 * 0.38 * 65.00 = 66.90 kips/bolt
(phi)Rneshpl at Shear Plate edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 1.62 * 0.38 * 65.00 = 35.62 kips/bolt
(phi)Rndshpl on Shear Plate at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.75 * 0.38 * 65.00 = 32.91 kips/bolt
Shear Plate bearing capacity, (phi)Rnshpl = min((phi)Rnsshpl,(phi)Rneshpl,(phi)Rndshpl) = min(66.90, 35.62, 32.91) = 32.91 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(26.76, 32.91) = 26.76 kips/bolt
Bolt Shear Demand to Bearing ratio = 26.76 / 14.53 = 1.84

At Row 4, At Column 1:
Ribolt = 17.56 kips
Ri vector at Beam   = <-12.30, 12.54>
Lcsbm at Beam spacing  = 3.12 in.
Lcebm at Beam edge    = 1.74 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.75 * 1.20 * 3.12 * (0.30/1) * 65.00 = 55.59 kips/bolt
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 1.74 * (0.30/1) * 65.00 = 30.97 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.75 * (0.30/1) * 65.00 = 26.76 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(55.59, 30.97, 26.76) = 26.76 kips/bolt
Ri vector at Shear Plate   = <12.30, -12.54>
Lcsshpl at Shear Plate spacing  = 3.05 in.
Lceshpl at Shear Plate edge    = 1.18 in.
(phi)Rnsshpl at Shear Plate spacing = (phi) * hf1 * Lcs * t * Fu = 0.75 * 1.20 * 3.05 * 0.38 * 65.00 = 66.90 kips/bolt
(phi)Rneshpl at Shear Plate edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 1.18 * 0.38 * 65.00 = 25.93 kips/bolt
(phi)Rndshpl on Shear Plate at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.75 * 0.38 * 65.00 = 32.91 kips/bolt
Shear Plate bearing capacity, (phi)Rnshpl = min((phi)Rnsshpl,(phi)Rneshpl,(phi)Rndshpl) = min(66.90, 25.93, 32.91) = 25.93 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(26.76, 25.93) = 25.93 kips/bolt
Bolt Shear Demand to Bearing ratio = 25.93 / 17.56 = 1.48

At Row 4, At Column 2:
Ribolt = 17.09 kips
Ri vector at Beam   = <-16.12, 5.68>
Lcsbm at Beam spacing  = 3.12 in.
Lcebm at Beam edge    = 4.37 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.75 * 1.20 * 3.12 * (0.30/1) * 65.00 = 55.59 kips/bolt
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 4.37 * (0.30/1) * 65.00 = 77.89 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.75 * (0.30/1) * 65.00 = 26.76 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(55.59, 77.89, 26.76) = 26.76 kips/bolt
Ri vector at Shear Plate   = <16.12, -5.68>
Lcsshpl at Shear Plate spacing  = 3.05 in.
Lceshpl at Shear Plate edge    = 1.06 in.
(phi)Rnsshpl at Shear Plate spacing = (phi) * hf1 * Lcs * t * Fu = 0.75 * 1.20 * 3.05 * 0.38 * 65.00 = 66.90 kips/bolt
(phi)Rneshpl at Shear Plate edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 1.06 * 0.38 * 65.00 = 23.26 kips/bolt
(phi)Rndshpl on Shear Plate at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.75 * 0.38 * 65.00 = 32.91 kips/bolt
Shear Plate bearing capacity, (phi)Rnshpl = min((phi)Rnsshpl,(phi)Rneshpl,(phi)Rndshpl) = min(66.90, 23.26, 32.91) = 23.26 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(26.76, 23.26) = 23.26 kips/bolt
Bolt Shear Demand to Bearing ratio = 23.26 / 17.09 = 1.36

Min Bolt Shear Demand to Bearing ratio Beam and Shear Plate for vertical shear only
 = min(1.00, 1.52, 1.57, 1.56, 1.84, 1.56, 1.84, 1.48, 1.36) = 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 * 90.08 = 90.08 kips
Rbv = 90.08 kips >= Reaction V = 68.00 kips (OK)

Web Depth = d - [Top Cope Depth] - [Bottom Cope Depth] = 16.00 - 1.50 - 0.00 = 14.50 in.

Using AISC 14th Ed. Equation J4-3
Gross Area (Shear), Agross = [Web Depth] * tw = 14.50 * 0.30 = 4.42 in^2
Shear Yielding, (phi)Vny = (phi) * 0.6 * Fybeam * Agross = 1.00 * 0.6 * 50.00 * 4.42 = 132.68 kips

Using AISC 14th Ed. Equation J4-4
Net Area (Shear), Anet = ([Web Depth] - ([# rows] * [Diameter + 0.06])) * tw 
    = (14.50 - (4 * 0.88)) * 0.30 = 3.35 in^2
Shear Rupture, (phi)Vnu = (phi) * 0.6 * Fubeam * Anet = 0.75 * 0.6 * 65.00 * 3.35 = 98.14 kips


Check Vertical Block Shear

Using AISC 14th Ed. Equation J4-5
Block Shear = {(phi) * ((0.6 * Fu * Anv) + (Ubs * Fu * Ant))} <= {(phi) * ((0.6 * Fy * Agv) + (Ubs * Fu * Ant))}

Block Shear (1)
Gross Shear Length = [edge dist. at beam edge] + ([# rows - 1] * [spacing]) = 1.50 + 9.00 = 10.50 in.
Net Shear Length = Gross Shear Length - (# rows - 0.5) * (hole size + 0.06) = 10.50 - (4 - 0.5) * 0.88 = 7.44 in.
Gross Tension Length = [edge dist. at beam edge] + ([# cols - 1] * [spacing]) = 1.50 + (2 - 1) * 3.00 = 4.50 in.
Net Tension Length = Gross Tension Length - (# cols - 0.5) * (hole size + 0.06) = 4.50 - (2 - 0.5) * 0.88 = 3.19 in.
1. (phi) * [material thickness] * ((0.60 * Fubeam* [net shear length]) + (Ubs * Fubeam * [net tension length])) 
    = 0.75 * 0.30 * ((0.60 * 65.00 * 7.44) + (0.50 * 65.00 * 3.19)) = 90.05 kips
2. (phi) * [material thickness] * ((0.60 * Fybeam * [gross shear length]) + (Ubs * Fubeam * [net tension length])) 
    = 0.75 * 0.30 * ((0.60 * 50.00 * 10.50) + (0.50 * 65.00 * 3.19)) = 95.76 kips
Block Shear = 90.05 kips

Block Shear (1) Total = Block Shear (1) = 90.05 kips
90.05 kips >= Reaction V = 68.00 kips (OK)

Block Shear for Axial T/C is not required.

Buckling and Flexure at Longest Cope (Top Cope Only at Section)
Eccentricity at Section, e = 6.02 in.
If coped at top/bottom flange only and c <= 2d and dc <= d/2, use AISC 14th Ed. Equation 9-7, Fcr = 26210.00 * f * k * (tw/h1)^2 <= Fy

Using Equation 9-7 through 9-11
tw = 0.30 in.
h1 = 10.28 in.
c = 5.25 in.
When c/h1<=1.0, k=2.2(h1/c)^1.65
k  = 2.20 * (10.28 / 5.25)^1.65 = 6.67
When c/d<=1.0, f=2c/d
f = 2 * (5.25 / 16.00) = 0.66
Fy = 50.00 ksi
Fcr = (phi) * 26210.00 * f * k * (tw/h1)^2 = 0.90 * 26210.00 * 0.66 * 6.67 * (0.30 / 10.28)^2 = 90.85 ksi
Fcrmin =phi * min(Fcr, Fy) = 45.00 ksi
Snet1 (bolt holes not applicable) = 16.67 in^3
Snet2 (bolt holes applicable) = 16.67 in^3
Znet1 (bolt holes not applicable) = 30.32 in^3
Znet2 (bolt holes applicable) = 30.32 in^3

Using AISC 14th Ed. Equation 9-6
Buckling = Fcr * Snet1 / e = 45.00 * 16.67 / 6.02 = 124.65 kips

Using AISC 14th Ed. Equation 9-19
Flexural Yielding = (phi) * Fy * Snet1 / e = 0.90 * 50.00 * 16.67 / 6.02 = 124.65 kips

Using AISC 14th Ed. Equation 9-4
Flexural Rupture = (phi) * Fu * Znet2 / e = 0.75 * 65.00 * 30.32 / 6.02 = 245.64 kips


Buckling and Flexure at Furthest Bolt Line within Cope (Top Cope Only at Section)
Eccentricity at Section, e = 5.27 in.
If coped at top/bottom flange only and c <= 2d and dc <= d/2, use AISC 14th Ed. Equation 9-7, Fcr = 26210.00 * f * k * (tw/h1)^2 <= Fy

Using Equation 9-7 through 9-11
tw = 0.30 in.
h1 = 10.96 in.
c = 5.25 in.
When c/h1<=1.0, k=2.2(h1/c)^1.65
k  = 2.20 * (10.96 / 5.25)^1.65 = 7.41
When c/d<=1.0, f=2c/d
f = 2 * (5.25 / 16.00) = 0.66
Fy = 50.00 ksi
Fcr = (phi) * 26210.00 * f * k * (tw/h1)^2 = 0.90 * 26210.00 * 0.66 * 7.41 * (0.30 / 10.96)^2 = 88.84 ksi
Fcrmin =phi * min(Fcr, Fy) = 45.00 ksi
Snet1 (bolt holes not applicable) = 16.67 in^3
Snet2 (bolt holes applicable) = 12.47 in^3
Znet1 (bolt holes not applicable) = 30.32 in^3
Znet2 (bolt holes applicable) = 22.22 in^3

Using AISC 14th Ed. Equation 9-6
Buckling = Fcr * Snet1 / e = 45.00 * 16.67 / 5.27 = 142.40 kips

Using AISC 14th Ed. Equation 9-19
Flexural Yielding = (phi) * Fy * Snet1 / e = 0.90 * 50.00 * 16.67 / 5.27 = 142.40 kips

Using AISC 14th Ed. Equation 9-4
Flexural Rupture = (phi) * Fu * Znet2 / e = 0.75 * 65.00 * 22.22 / 5.27 = 205.67 kips


Section Bending Strength Calculations Summary:

   Coped Beam Buckling and Flexure at Longest Cope (Top Cope Only at Section)
   Buckling : 124.65 >= 68.00 kips (OK)
   Flexural Yielding : 124.65 >= 68.00 kips (OK)
   Flexural Rupture : 245.64 >= 68.00 kips (OK)

   Coped Beam Buckling and Flexure at Furthest Bolt Line within Cope (Top Cope Only at Section)
   Buckling : 142.40 >= 68.00 kips (OK)
   Flexural Yielding : 142.40 >= 68.00 kips (OK)
   Flexural Rupture : 205.67 >= 68.00 kips (OK)

Using AISC 14th Ed. Equation J4-3
Gross Area, Ag = 0.38 * 11.50 = 4.31 in^2
Shear Yielding, (phi)Vny = (phi) * 0.6 * Fypl * Ag = 1.00 * 0.6 * 50.00 * 4.31 = 129.38 kips

129.38 kips >= Reaction V = 68.00 kips (OK)

Using AISC 14th Ed. Equation J4-4
Net Area, An = (11.50 - (4 * (0.81 + 1/16))) * 0.38 = 3.00 in^2
Shear Rupture, (phi)Vnu = (phi) * 0.6 * Fupl * An = 0.75 * 0.6 * 65.00 * 3.00 = 87.75 kips

87.75 kips >= Reaction V = 68.00 kips (OK)


Check Vertical Block Shear

Using AISC 14th Ed. Equation J4-5
Block Shear = {(phi) * ((0.6 * Fu * Anv) + (Ubs * Fu * Ant))} <= {(phi) * ((0.6 * Fy * Agv) + (Ubs * Fu * Ant))}

Block 1 (Shear): 
Gross Shear Length = (11.50 - 1.25) = 10.25 in.
Net Shear Length = 10.25 - (3.50 * (0.81 + 0.06)) = 7.19 in.
Gross Tension Length = (3.00 + 1.50) = 4.50 in.
Net Tension Length = 4.50 - (1.50 * (1.00 + 0.06)) = 2.91 in.
1. (phi) * [material thickness] * ((0.60 * Fupl* [net shear length]) + (Ubs * Fupl * [net tension length])) 
    = 0.75 * 0.38 * ((0.60 * 65.00 * 7.19) + (0.50 * 65.00 * 2.91)) = 105.41 kips
2. (phi) * [material thickness] * ((0.60 * Fypl * [gross shear length]) + (Ubs * Fupl * [net tension length])) 
    = 0.75 * 0.38 * ((0.60 * 50.00 * 10.25) + (0.50 * 65.00 * 2.91)) = 113.05 kips
Block Shear = 105.41 kips

Block 2 (Shear): 
Gross Shear Length = 2 * (11.50 - 1.25) = 20.50 in.
Net Shear Length = 2 * ( 10.25 - (3.50 * (0.81 + 0.06)) ) = 14.38 in.
Gross Tension Length = (3.00 + 1.50) - 1.50 = 3.00 in.
Net Tension Length = 3.00 - 1 * (1.00 + 0.06) = 1.94 in.
1. (phi) * [material thickness] * ((0.60 * Fupl* [net shear length]) + (Ubs * Fupl * [net tension length])) 
    = 0.75 * 0.38 * ((0.60 * 65.00 * 14.38) + (0.50 * 65.00 * 1.94)) = 175.39 kips
2. (phi) * [material thickness] * ((0.60 * Fypl * [gross shear length]) + (Ubs * Fupl * [net tension length])) 
    = 0.75 * 0.38 * ((0.60 * 50.00 * 20.50) + (0.50 * 65.00 * 1.94)) = 190.68 kips
Block Shear = 175.39 kips
105.41 kips >= Reaction V = 68.00 kips (OK)

Block Shear for Axial T/C is not required.

Flexural and Buckling Strength:

Eccentricity at first line of bolts, e = 2.27 in.
Zgross = 12.40 in^3
Znet   = 8.46 in^3
Sgross = 8.27 in^3
Snet   = 5.70 in^3

Using AISC 14th Ed. Equation 9-4
Flexural Rupture = (phi) * Fu * Znet / e = 0.75 * 65.00 * 8.46 / 2.27 = 181.91 kips


Using AISC 14th Ed. Equation 9-14 through 9-18, Fcr = Fy * Q
tw = 0.38 in.
ho = 11.50 in.
c = 2.00 in.
lambda = (ho * Fy ^ 0.5) / ( 10 * tw * ( 475.00 + 280.00 * (ho / c)^2 ) ^0.5 ) = 
 = 11.50 * 50.00^0.5 / (10 * 0.38 * (475.00 + 280.00 * (11.50/2.00)^2 )^0.5) = 0.22
When lambda <= 0.70, Q=1
Q = 1.00
Fcrmin =phi * Fcr = 0.90 * 50.00 * 1.00 = 45.00 ksi

Using AISC 14th Ed. Equation 9-6
Buckling = Fcr * Sgross / e = 45.00 * 8.27 / 2.27 = 164.04 kips

Interaction Check of Flexural Yielding, Per AISC 10-5: 
Eccentricity at CG of Bolt Group, e = 3.77 in.
Zgross = 12.40
Znet = 12.40
Mr = Vr * e = 68.00 * 3.77 = 256.19 kips-in
Mc = phi * Mn = phi * Fy * Zgross = 0.90 * 50.00 * 12.40 = 557.93 kips-in
Vr = 68.00 kips
Vc = phi * Vn = phi * 0.60 * Fy * Ag = 1.00 * 0.60 * 50.00 * 4.31 = 129.38 kips
Interaction due to moment and shear, (Vr/Vc)^2 + (Mr/Mc)^2 <= 1.0
(Vr/Vc)^2 + (Mr/Mc)^2 = (68.00 / 129.38)^2 + (256.19 / 557.93)^2 = 0.49 <= 1  (OK)

Note: Mn <= 1.6My by inspection

MAXIMUM PLATE THICKNESS:
No of bolt columns = 2
tp  < = db/2 + 1/16 = 0.38 <= 0.44 OK
tw  < = db/2 + 1/16 = 0.30 <= 0.44 OK
Leh(plate) >= 2 * db = 1.50 >= 1.50 OK
Leh(bm) >= 2 * db = 1.50 >= 1.50 OK
Maximum Plate Thickness is Not a Limiting Criteria.

WELD:

 Weld Requirements:

At shear only case: 
Weld Length for shear, Lv = 11.50 in.
Shear Load per inch per weld, fv = R/Lv/2 = 68.00 / 11.50 / 2 = 2.96 kips/in/ weld 
theta = 0 deg.
cPhi  = 1.0 + 0.5 * sin(0)^1.5 = 1.00
Weld Coefficient = 0.60 * 70.00 * 1.00 * 1.00 * (2^0.5/2)*(1/16) = 1.86
Required weld size, Dv = fv/ (phi * coeff) = 2.96 / (0.75 * 1.86) = 2.12/16

Minimum fillet weld size : 
   At shear only load case = 0.13 in.
   per Table J2.4     = 0.19 in.
   5/8tp              = 0.23 in.
   user preference    = 0.25 in.

Dmax1 (using eqn 9-3)
 = tshpl * Fushpl / ( Fexx * C1 * 0.09)
 = 0.38 * 65.00 / ( 70.00 * 1.00 * 0.09 ) 
 = 3.94 
Dmax2 (using eqn 9-3)
 = twsupport * Fusupport / ( Fexx * C1 * 0.09 )
 = 0.54 * 65.00 / ( 70.00 * 1.00 * 0.09 ) 
 = 5.62 
Dmax3 = project max fillet weld = 12.00
Dmax=min(Dmax1, Dmax2, Dmax3) = min(3.94, 5.62, 12.00)
 = 3.94 

Use weld size
D1 = 4.00
D2 = 4.00

Weld Strength :

Vertical weld capacity during shear only load, phi * Rnv1 = 0.75 * 1.86 * 11.50 * (3.94 + 3.94) = 126.14 kips

126.14 kips >= Reaction V = 68.00 kips (OK)