bepl.2bw.s.00001.00001

DOUBLE ANGLES Bolted to Beam, Welded to Support CONNECTION SUMMARY

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

Embed Plate profile: PL0.75X10.00X24.00
Filler Beam profile: W16X40
Slope: 0.00 deg.
Skew: 90.00
Vertical Offset: -1.00
Horizontal Offset: 0.00
Span: 2.00 ft.
Reaction, V: 2.00 kips
Shear Capacity, Rn: 36.98 kips
Design/Reference according to AISC 14th Ed. - LRFD
Beam material grade: A992
Support material grade: A36
Angle material grade: A529-GR.50
Weld grade: E70
Angle1 Profile: L5X3X5/16
       Length = 11.00 in.
       Beam side bolts: 4 rows x 1 column 0.75 in. Diameter A325SCA_TC bolts
       Beam side bolt vertical spacing: 3.00 in.
Angle2 Profile: L5X3X5/16
       Length = 11.00 in.
       Beam side bolts: 4 rows x 1 column 0.75 in. Diameter A325SCA_TC bolts
       Beam side bolt vertical spacing: 3.00 in.
Plate Washer Size: 3.00 in. x 11.00 in. x 0.31 in.

Configuration Geometry:
Weld Size at Angle 1 Support Weld:
4/16 FILLET
Weld Size at Angle 2 Support Weld:
4/16 FILLET

Beam setback = 1.00 in.
Edge distance at vertical edge of beam: 1.50 in.
Edge distance at bottom edge of beam: 2.75 in.
Bottom cope depth: 1.25 in.
Bottom cope length: 4.50 in.

Horizontal distance to first hole: 2.50 in.

Bolted Angle Leg At Beam : 
Angle 1 Leg Distances : 
   Down distance from top of filler beam flange : 3.00 in.
   Edge distance at vertical edge : 2.50 in.
   Edge distance at top edge : 1.00 in.
   Edge distance at bottom edge : 1.00 in.

Angle 2 Leg Distances : 
   Down distance from top of filler beam flange : 3.00 in.
   Edge distance at vertical edge : 2.50 in.
   Edge distance at top edge : 1.00 in.
   Edge distance at bottom edge : 1.00 in.

Holes in Beam Web : STD diameter = 0.81 in.
Holes in Beam Angle Leg : LSL slot width = 0.81 in., slot length = 1.88 in.
(Design eccentricity accounts for potential movement in Long Slots)

BOLT SHEAR CAPACITY AT BEAM AND ANGLE 1 SIDE:
At Angle 1 side:
Bolt Shear Capacity at Shear Load Only:
Using Instantaneous Center Of Rotation Method (AISC 7-1)
ex = 3.06 in.
Angle = 0.00 deg.
C = 2.78
Slip Critical, Surface A, determining (phi)Rn:
Using AISC 14th Ed. Equation J3-4
slip coefficient, mu = 0.30
pretension ratio, Du = 1.13
Minimum Bolt Pretension from Table J3.1, Tb = 28.00 kips
factor for fillers, hf = 1.00
number of slip planes, ns = 1.00
rn = mu * Du * hf * Tb * ns = 0.30 * 1.13 * 1.00 * 28.00 * 1.00 = 9.49 kips
(phi)v = 0.70
(phi)rn = (phi)v * rn = 0.70 * 9.49 = 6.64 kips
(phi)Rn = (phi)rn * C = 6.64 * 2.78 = 18.49 kips


BOLT SHEAR CAPACITY AT BEAM AND ANGLE 2 SIDE:
At Angle 2 side:
Bolt Shear Capacity at Shear Load Only:
Using Instantaneous Center Of Rotation Method (AISC 7-1)
ex = 3.06 in.
Angle = 0.00 deg.
C = 2.78
Slip Critical, Surface A, determining (phi)Rn:
Using AISC 14th Ed. Equation J3-4
slip coefficient, mu = 0.30
pretension ratio, Du = 1.13
Minimum Bolt Pretension from Table J3.1, Tb = 28.00 kips
factor for fillers, hf = 1.00
number of slip planes, ns = 1.00
rn = mu * Du * hf * Tb * ns = 0.30 * 1.13 * 1.00 * 28.00 * 1.00 = 9.49 kips
(phi)v = 0.70
(phi)rn = (phi)v * rn = 0.70 * 9.49 = 6.64 kips
(phi)Rn = (phi)rn * C = 6.64 * 2.78 = 18.49 kips


Total Vertical Bolt Shear Capacity = 
 = min(Shear Load Only at Angle 1 side/gage1 ratio, 
       Shear Load Only at Angle 2 side/gage2 ratio) = 
 = min(18.49/0.50, 18.49/0.50) = 36.98 kips
36.98 kips >= Reaction V = 2.00 kips (OK)

BOLT BEARING AT BEAM AND ANGLE 1 SIDE
Vertical Shear Only Load Case:
ICR cordinate relative to CG = (3.07, -0.00)
At Row 1, At Column 1:
Ribolt = 6.52 kips
Ri vector at Beam   = <7.70, 5.25>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 4.92 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = na
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 4.92 * (0.30/2) * 65.00 = 43.86 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.75 * (0.30/2) * 65.00 = 13.38 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(na, 43.86, 13.38) = 13.38 kips/bolt
Ri vector at Angle 1   = <-5.39, -3.68>
Lcsang1 at Angle 1 spacing  = na
Lceang1 at Angle 1 edge    = 2.31 in.
(phi)Rnsang1 at Angle 1 spacing = (phi) * hf1 * Lcs * t * Fu = na
(phi)Rneang1 at Angle 1 edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.00 * 2.31 * 0.31 * 65.00 = 35.18 kips/bolt
(phi)Rndang1 on Angle 1 at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.00 * 0.75 * 0.31 * 65.00 = 22.89 kips/bolt
Angle 1 bearing capacity, (phi)Rnang1 = min((phi)Rnsang1,(phi)Rneang1,(phi)Rndang1) = min(na, 35.18, 22.89) = 22.89 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnang1) = min(13.38, 22.89) = 13.38 kips/bolt
Bolt Shear Demand to Bearing ratio = 13.38 / 6.52 = 2.05

At Row 2, At Column 1:
Ribolt = 6.20 kips
Ri vector at Beam   = <3.89, 7.96>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 6.27 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = na
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 6.27 * (0.30/2) * 65.00 = 55.95 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.75 * (0.30/2) * 65.00 = 13.38 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(na, 55.95, 13.38) = 13.38 kips/bolt
Ri vector at Angle 1   = <-2.72, -5.57>
Lcsang1 at Angle 1 spacing  = na
Lceang1 at Angle 1 edge    = 5.24 in.
(phi)Rnsang1 at Angle 1 spacing = (phi) * hf1 * Lcs * t * Fu = na
(phi)Rneang1 at Angle 1 edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.00 * 5.24 * 0.31 * 65.00 = 80.00 kips/bolt
(phi)Rndang1 on Angle 1 at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.00 * 0.75 * 0.31 * 65.00 = 22.89 kips/bolt
Angle 1 bearing capacity, (phi)Rnang1 = min((phi)Rnsang1,(phi)Rneang1,(phi)Rndang1) = min(na, 80.00, 22.89) = 22.89 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnang1) = min(13.38, 22.89) = 13.38 kips/bolt
Bolt Shear Demand to Bearing ratio = 13.38 / 6.20 = 2.16

At Row 3, At Column 1:
Ribolt = 6.20 kips
Ri vector at Beam   = <-3.89, 7.96>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 3.01 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = na
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 3.01 * (0.30/2) * 65.00 = 26.87 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.75 * (0.30/2) * 65.00 = 13.38 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(na, 26.87, 13.38) = 13.38 kips/bolt
Ri vector at Angle 1   = <2.72, -5.57>
Lcsang1 at Angle 1 spacing  = na
Lceang1 at Angle 1 edge    = 4.00 in.
(phi)Rnsang1 at Angle 1 spacing = (phi) * hf1 * Lcs * t * Fu = na
(phi)Rneang1 at Angle 1 edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.00 * 4.00 * 0.31 * 65.00 = 61.03 kips/bolt
(phi)Rndang1 on Angle 1 at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.00 * 0.75 * 0.31 * 65.00 = 22.89 kips/bolt
Angle 1 bearing capacity, (phi)Rnang1 = min((phi)Rnsang1,(phi)Rneang1,(phi)Rndang1) = min(na, 61.03, 22.89) = 22.89 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnang1) = min(13.38, 22.89) = 13.38 kips/bolt
Bolt Shear Demand to Bearing ratio = 13.38 / 6.20 = 2.16

At Row 4, At Column 1:
Ribolt = 6.52 kips
Ri vector at Beam   = <-7.70, 5.25>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 1.41 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = na
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 1.41 * (0.30/2) * 65.00 = 12.58 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.75 * (0.30/2) * 65.00 = 13.38 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(na, 12.58, 13.38) = 12.58 kips/bolt
Ri vector at Angle 1   = <5.39, -3.68>
Lcsang1 at Angle 1 spacing  = na
Lceang1 at Angle 1 edge    = 1.05 in.
(phi)Rnsang1 at Angle 1 spacing = (phi) * hf1 * Lcs * t * Fu = na
(phi)Rneang1 at Angle 1 edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.00 * 1.05 * 0.31 * 65.00 = 16.07 kips/bolt
(phi)Rndang1 on Angle 1 at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.00 * 0.75 * 0.31 * 65.00 = 22.89 kips/bolt
Angle 1 bearing capacity, (phi)Rnang1 = min((phi)Rnsang1,(phi)Rneang1,(phi)Rndang1) = min(na, 16.07, 22.89) = 16.07 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnang1) = min(12.58, 16.07) = 12.58 kips/bolt
Bolt Shear Demand to Bearing ratio = 12.58 / 6.52 = 1.93

Min Bolt Shear Demand to Bearing ratio Beam and Angle for vertical shear only
 = min(1.00, 2.05, 2.16, 2.16, 1.93) = 1.00

BOLT BEARING AT BEAM AND ANGLE 2 SIDE
Vertical Shear Only Load Case:
ICR cordinate relative to CG = (3.07, -0.00)
At Row 1, At Column 1:
Ribolt = 6.52 kips
Ri vector at Beam   = <7.70, 5.25>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 4.92 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = na
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 4.92 * (0.30/2) * 65.00 = 43.86 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.75 * (0.30/2) * 65.00 = 13.38 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(na, 43.86, 13.38) = 13.38 kips/bolt
Ri vector at Angle 2   = <-5.39, -3.68>
Lcsang2 at Angle 2 spacing  = na
Lceang2 at Angle 2 edge    = 2.31 in.
(phi)Rnsang2 at Angle 2 spacing = (phi) * hf1 * Lcs * t * Fu = na
(phi)Rneang2 at Angle 2 edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.00 * 2.31 * 0.31 * 65.00 = 35.18 kips/bolt
(phi)Rndang2 on Angle 2 at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.00 * 0.75 * 0.31 * 65.00 = 22.89 kips/bolt
Angle 2 bearing capacity, (phi)Rnang2 = min((phi)Rnsang2,(phi)Rneang2,(phi)Rndang2) = min(na, 35.18, 22.89) = 22.89 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnang2) = min(13.38, 22.89) = 13.38 kips/bolt
Bolt Shear Demand to Bearing ratio = 13.38 / 6.52 = 2.05

At Row 2, At Column 1:
Ribolt = 6.20 kips
Ri vector at Beam   = <3.89, 7.96>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 6.27 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = na
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 6.27 * (0.30/2) * 65.00 = 55.95 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.75 * (0.30/2) * 65.00 = 13.38 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(na, 55.95, 13.38) = 13.38 kips/bolt
Ri vector at Angle 2   = <-2.72, -5.57>
Lcsang2 at Angle 2 spacing  = na
Lceang2 at Angle 2 edge    = 5.24 in.
(phi)Rnsang2 at Angle 2 spacing = (phi) * hf1 * Lcs * t * Fu = na
(phi)Rneang2 at Angle 2 edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.00 * 5.24 * 0.31 * 65.00 = 80.00 kips/bolt
(phi)Rndang2 on Angle 2 at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.00 * 0.75 * 0.31 * 65.00 = 22.89 kips/bolt
Angle 2 bearing capacity, (phi)Rnang2 = min((phi)Rnsang2,(phi)Rneang2,(phi)Rndang2) = min(na, 80.00, 22.89) = 22.89 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnang2) = min(13.38, 22.89) = 13.38 kips/bolt
Bolt Shear Demand to Bearing ratio = 13.38 / 6.20 = 2.16

At Row 3, At Column 1:
Ribolt = 6.20 kips
Ri vector at Beam   = <-3.89, 7.96>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 3.01 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = na
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 3.01 * (0.30/2) * 65.00 = 26.87 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.75 * (0.30/2) * 65.00 = 13.38 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(na, 26.87, 13.38) = 13.38 kips/bolt
Ri vector at Angle 2   = <2.72, -5.57>
Lcsang2 at Angle 2 spacing  = na
Lceang2 at Angle 2 edge    = 4.00 in.
(phi)Rnsang2 at Angle 2 spacing = (phi) * hf1 * Lcs * t * Fu = na
(phi)Rneang2 at Angle 2 edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.00 * 4.00 * 0.31 * 65.00 = 61.03 kips/bolt
(phi)Rndang2 on Angle 2 at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.00 * 0.75 * 0.31 * 65.00 = 22.89 kips/bolt
Angle 2 bearing capacity, (phi)Rnang2 = min((phi)Rnsang2,(phi)Rneang2,(phi)Rndang2) = min(na, 61.03, 22.89) = 22.89 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnang2) = min(13.38, 22.89) = 13.38 kips/bolt
Bolt Shear Demand to Bearing ratio = 13.38 / 6.20 = 2.16

At Row 4, At Column 1:
Ribolt = 6.52 kips
Ri vector at Beam   = <-7.70, 5.25>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 1.41 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = na
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 1.41 * (0.30/2) * 65.00 = 12.58 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.75 * (0.30/2) * 65.00 = 13.38 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(na, 12.58, 13.38) = 12.58 kips/bolt
Ri vector at Angle 2   = <5.39, -3.68>
Lcsang2 at Angle 2 spacing  = na
Lceang2 at Angle 2 edge    = 1.05 in.
(phi)Rnsang2 at Angle 2 spacing = (phi) * hf1 * Lcs * t * Fu = na
(phi)Rneang2 at Angle 2 edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.00 * 1.05 * 0.31 * 65.00 = 16.07 kips/bolt
(phi)Rndang2 on Angle 2 at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.00 * 0.75 * 0.31 * 65.00 = 22.89 kips/bolt
Angle 2 bearing capacity, (phi)Rnang2 = min((phi)Rnsang2,(phi)Rneang2,(phi)Rndang2) = min(na, 16.07, 22.89) = 16.07 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnang2) = min(12.58, 16.07) = 12.58 kips/bolt
Bolt Shear Demand to Bearing ratio = 12.58 / 6.52 = 1.93

Min Bolt Shear Demand to Bearing ratio Beam and Angle for vertical shear only
 = min(1.00, 2.05, 2.16, 2.16, 1.93) = 1.00


BEARING AT BEAM AND ANGLE SIDE SUMMARY:
Bearing Capacity at Vertical Shear Load Only, Rbv
 = Min(Side 1 [Min Bolt Shear Demand to Bearing Ratio * Bolt Shear / gage1 ratio],
       Side 2 [Min Bolt Shear Demand to Bearing Ratio * Bolt Shear / gage2 ratio])
 = Min(1.00 * 18.49 / 0.50, 1.00 * 18.49 / 0.50) = 36.98 kips
Rbv = 36.98 kips >= Reaction V = 2.00 kips (OK)

Web Depth = d - [Top Cope Depth] - [Bottom Cope Depth] = 16.00 - 0.00 - 1.25 = 14.75 in.

Using AISC 14th Ed. Equation J4-3
Gross Area (Shear), Agross = [Web Depth] * tw = 14.75 * 0.30 = 4.50 in^2
Shear Yielding, (phi)Vny = (phi) * 0.6 * Fybeam * Agross = 1.00 * 0.6 * 50.00 * 4.50 = 134.96 kips

Using AISC 14th Ed. Equation J4-4
Net Area (Shear), Anet = ([Web Depth] - ([# rows] * [Diameter + 0.06])) * tw 
    = (14.75 - (4 * 0.88)) * 0.30 = 3.43 in^2
Shear Rupture, (phi)Vnu = (phi) * 0.6 * Fubeam * Anet = 0.75 * 0.6 * 65.00 * 3.43 = 100.37 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 for Reaction V is not required.

Block Shear for Axial T/C is not required.

Flexure at Longest Cope (Bottom Cope Only at Section)
Eccentricity at Section, e = 6.06 in.
Fy = 50.00 ksi
Snet1 (bolt holes not applicable) = 17.21 in^3
Snet2 (bolt holes applicable) = 17.21 in^3
Znet1 (bolt holes not applicable) = 31.30 in^3
Znet2 (bolt holes applicable) = 31.30 in^3

Using AISC 14th Ed. Equation 9-19
Flexural Yielding = (phi) * Fy * Snet1 / e = 0.90 * 50.00 * 17.21 / 6.06 = 127.77 kips

Using AISC 14th Ed. Equation 9-4
Flexural Rupture = (phi) * Fu * Znet2 / e = 0.75 * 65.00 * 31.30 / 6.06 = 251.70 kips


Flexure at Furthest Bolt Line within Cope (Bottom Cope Only at Section)
Eccentricity at Section, e = 3.06 in.
Fy = 50.00 ksi
Snet1 (bolt holes not applicable) = 17.21 in^3
Snet2 (bolt holes applicable) = 14.18 in^3
Znet1 (bolt holes not applicable) = 31.30 in^3
Znet2 (bolt holes applicable) = 24.37 in^3

Using AISC 14th Ed. Equation 9-19
Flexural Yielding = (phi) * Fy * Snet1 / e = 0.90 * 50.00 * 17.21 / 3.06 = 252.94 kips

Using AISC 14th Ed. Equation 9-4
Flexural Rupture = (phi) * Fu * Znet2 / e = 0.75 * 65.00 * 24.37 / 3.06 = 387.91 kips


Section Bending Strength Calculations Summary:

   Coped Beam Flexure at Longest Cope (Bottom Cope Only at Section)
   Flexural Yielding : 127.77 >= 2.00 kips (OK)
   Flexural Rupture : 251.70 >= 2.00 kips (OK)

   Coped Beam Flexure at Furthest Bolt Line within Cope (Bottom Cope Only at Section)
   Flexural Yielding : 252.94 >= 2.00 kips (OK)
   Flexural Rupture : 387.91 >= 2.00 kips (OK)

Angle1 

Support Angle Leg 


Using AISC 14th Ed. Equation J4-3
Gross Area, Ag = 0.31 * 11.00 = 3.44 in^2
Shear Yielding, (phi)Vny = (phi) * 0.6 * Fyangle * Ag = 1.00 * 0.6 * 50.00 * 3.44 = 103.29 kips

Using AISC 14th Ed. Equation J4-4
Net Area, An = 0.31 * 11.00 = 3.44 in^2
Shear Rupture, (phi)Vnu = (phi) * 0.6 * Fuangle * An = 0.75 * 0.6 * 65.00 * 3.44 = 100.71 kips


Flexural and Buckling Strength:

Eccentricity at Weld = 3.15
Zgross = 9.47 in^3
Znet   = 9.47 in^3
Sgross = 6.31 in^3
Snet   = 6.31 in^3

Using AISC 14th Ed. Equation 9-19
Flexural Yielding = (phi) * Fy * Sgross / e = 0.90 * 50.00 * 6.31 / 3.15 = 90.10 kips

Using AISC 14th Ed. Equation 9-4
Flexural Rupture = (phi) * Fu * Znet / e = 0.75 * 65.00 * 9.47 / 3.15 = 146.42 kips


Using AISC 14th Ed. Equation 9-14 through 9-18, Fcr = Fy * Q
tw = 0.31 in.
ho = 11.00 in.
c = 3.00 in.
lambda = (ho * Fy ^ 0.5) / ( 10 * tw * ( 475.00 + 280.00 * (ho / c)^2 ) ^0.5 ) = 
 = 11.00 * 50.00^0.5 / (10 * 0.31 * (475.00 + 280.00 * (11.00/3.00)^2 )^0.5) = 0.38
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 * 6.31 / 3.15 = 90.10 kips

Beam Angle Leg 


Using AISC 14th Ed. Equation J4-3
Gross Area, Ag = 0.31 * 11.00 = 3.44 in^2
Shear Yielding, (phi)Vny = (phi) * 0.6 * Fya * Ag = 1.00 * 0.6 * 50.00 * 3.44 = 103.29 kips

Using AISC 14th Ed. Equation J4-4
Net Area, An = (11.00 - (4 * (0.81 + 1/16))) * 0.31 = 2.35 in^2
Shear Rupture, (phi)Vnu = (phi) * 0.6 * Fua * An = 0.75 * 0.6 * 65.00 * 2.35 = 68.67 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 1 (Shear): 
Gross Shear Length = (11.00 - 1.00) = 10.00 in.
Net Shear Length = 10.00 - (3.50 * (0.81 + 1/16) = 6.94 in.
Gross Tension Length = [edge dist.] = 2.50 in.
Net Tension Length = (2.50 - (1.88 + 1/16)/2) = 1.53 in.
1. (phi) * [material thickness] * ((0.60 * Fua* [net shear length]) + (Ubs * Fua * [net tension length])) 
    = 0.75 * 0.31 * ((0.60 * 65.00 * 6.94) + (1.00 * 65.00 * 1.53)) = 86.88 kips
2. (phi) * [material thickness] * ((0.60 * Fya * [gross shear length]) + (Ubs * Fua * [net tension length])) 
    = 0.75 * 0.31 * ((0.60 * 50.00 * 10.00) + (1.00 * 65.00 * 1.53)) = 93.79 kips
Block Shear = 86.88 kips

Block Shear for Axial T/C is not required.

Flexural and Buckling Strength:

Eccentricity at Bolt Column = 3.06
Zgross = 9.47 in^3
Znet   = 6.18 in^3
Sgross = 6.31 in^3
Snet   = 4.06 in^3

Using AISC 14th Ed. Equation 9-19
Flexural Yielding = (phi) * Fy * Sgross / e = 0.90 * 50.00 * 6.31 / 3.06 = 92.75 kips

Using AISC 14th Ed. Equation 9-4
Flexural Rupture = (phi) * Fu * Znet / e = 0.75 * 65.00 * 6.18 / 3.06 = 98.41 kips


Using AISC 14th Ed. Equation 9-14 through 9-18, Fcr = Fy * Q
tw = 0.31 in.
ho = 11.00 in.
c = 3.06 in.
lambda = (ho * Fy ^ 0.5) / ( 10 * tw * ( 475.00 + 280.00 * (ho / c)^2 ) ^0.5 ) = 
 = 11.00 * 50.00^0.5 / (10 * 0.31 * (475.00 + 280.00 * (11.00/3.06)^2 )^0.5) = 0.39
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 * 6.31 / 3.06 = 92.75 kips

Stress Interaction on Angle due to Combined Shear, Axial and Moment Loading:

Zgx = 9.47 in^3
Znx = 6.18 in^3
Zgy = 0.27 in^3
Zny = 0.18 in^3

Mrx = vertical reaction * ex = 1.00 * 3.06 = 3.06 kips-in
Mry = axial reaction * ey = 0.00 * 0.31 = 0.00 kips-in
Mcx = (phi) * Zgx * Min(Fy, Fcr) = 0.90 * 9.47 * Min(50.00, 50.00) = 426.07 kips-in
Mcy = (phi) * Zgy * Fy = 0.90 * 0.27 * 50.00 = 12.12 kips-in
Shear Stress on Gross Section = 1.00 / 3.44 = 0.29 ksi
Shear Stress on Net Section = 1.00 / 2.35 = 0.43 ksi
Axial Stress on Gross Section due to Axial force = 0.00 / 3.44 = 0.00 ksi
Axial Stress on Net Section due to Axial force = 0.00 / 2.35 = 0.00 ksi
Axial Stress on Gross Section due to Moment (shear) = 3.06 / 9.47 = 0.32 ksi
Axial Stress on Net Section due to Moment (shear) = 3.06 / 6.18 = 0.50 ksi
Axial Stress on Gross Section due to Moment (axial) = 0.00 / 0.27 = 0.00 ksi
Axial Stress on Net Section due to Moment (axial) = 0.00 / 0.18 = 0.00 ksi
Axial Stress on Gross Section (total) = 0.00 + 0.00 + 0.32 = 0.32 ksi
Axial Stress on Net Section (total) = 0.00 + 0.00 + 0.50 = 0.50 ksi

Shear Yield Stress Capacity (SYSC) = phi * 0.6 * Fy = 1.00 * 0.60 * 50.00 = 30.00 ksi
Tensile Yield Stress Capacity (TYSC) = phi * Fy = 0.90 * 50.00 = 45.00 ksi
Stress Interaction at Gross Section (elliptical):
(fvg / SYSC)^2 + (fag / TYSC )^2 = (0.29 / 30.00)^2 + (0.32 / 45.00 )^2 = 0.00 <= 1.0 (OK)
Shear Rupture Stress Capacity (SRSC) = phi * 0.6 * Fu = 0.75 * 0.60 * 65.00 = 29.25 ksi
Tensile Rupture Stress Capacity (TRSC) = phi * Fu = 0.75 * 65.00 = 48.75 ksi
Stress Interaction at Net Section (elliptical):
(fvn / SRSC)^2 + (fan / TRSC )^2 = (0.43 / 29.25)^2 + (0.50 / 48.75 )^2 = 0.00 <= 1.0 (OK)


Angle2 

Support Angle Leg 


Using AISC 14th Ed. Equation J4-3
Gross Area, Ag = 0.31 * 11.00 = 3.44 in^2
Shear Yielding, (phi)Vny = (phi) * 0.6 * Fyangle * Ag = 1.00 * 0.6 * 50.00 * 3.44 = 103.29 kips

Using AISC 14th Ed. Equation J4-4
Net Area, An = 0.31 * 11.00 = 3.44 in^2
Shear Rupture, (phi)Vnu = (phi) * 0.6 * Fuangle * An = 0.75 * 0.6 * 65.00 * 3.44 = 100.71 kips


Flexural and Buckling Strength:

Eccentricity at Weld = 3.15
Zgross = 9.47 in^3
Znet   = 9.47 in^3
Sgross = 6.31 in^3
Snet   = 6.31 in^3

Using AISC 14th Ed. Equation 9-19
Flexural Yielding = (phi) * Fy * Sgross / e = 0.90 * 50.00 * 6.31 / 3.15 = 90.10 kips

Using AISC 14th Ed. Equation 9-4
Flexural Rupture = (phi) * Fu * Znet / e = 0.75 * 65.00 * 9.47 / 3.15 = 146.42 kips


Using AISC 14th Ed. Equation 9-14 through 9-18, Fcr = Fy * Q
tw = 0.31 in.
ho = 11.00 in.
c = 3.00 in.
lambda = (ho * Fy ^ 0.5) / ( 10 * tw * ( 475.00 + 280.00 * (ho / c)^2 ) ^0.5 ) = 
 = 11.00 * 50.00^0.5 / (10 * 0.31 * (475.00 + 280.00 * (11.00/3.00)^2 )^0.5) = 0.38
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 * 6.31 / 3.15 = 90.10 kips

Beam Angle Leg 


Using AISC 14th Ed. Equation J4-3
Gross Area, Ag = 0.31 * 11.00 = 3.44 in^2
Shear Yielding, (phi)Vny = (phi) * 0.6 * Fya * Ag = 1.00 * 0.6 * 50.00 * 3.44 = 103.29 kips

Using AISC 14th Ed. Equation J4-4
Net Area, An = (11.00 - (4 * (0.81 + 1/16))) * 0.31 = 2.35 in^2
Shear Rupture, (phi)Vnu = (phi) * 0.6 * Fua * An = 0.75 * 0.6 * 65.00 * 2.35 = 68.67 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 1 (Shear): 
Gross Shear Length = (11.00 - 1.00) = 10.00 in.
Net Shear Length = 10.00 - (3.50 * (0.81 + 1/16) = 6.94 in.
Gross Tension Length = [edge dist.] = 2.50 in.
Net Tension Length = (2.50 - (1.88 + 1/16)/2) = 1.53 in.
1. (phi) * [material thickness] * ((0.60 * Fua* [net shear length]) + (Ubs * Fua * [net tension length])) 
    = 0.75 * 0.31 * ((0.60 * 65.00 * 6.94) + (1.00 * 65.00 * 1.53)) = 86.88 kips
2. (phi) * [material thickness] * ((0.60 * Fya * [gross shear length]) + (Ubs * Fua * [net tension length])) 
    = 0.75 * 0.31 * ((0.60 * 50.00 * 10.00) + (1.00 * 65.00 * 1.53)) = 93.79 kips
Block Shear = 86.88 kips

Block Shear for Axial T/C is not required.

Flexural and Buckling Strength:

Eccentricity at Bolt Column = 3.06
Zgross = 9.47 in^3
Znet   = 6.18 in^3
Sgross = 6.31 in^3
Snet   = 4.06 in^3

Using AISC 14th Ed. Equation 9-19
Flexural Yielding = (phi) * Fy * Sgross / e = 0.90 * 50.00 * 6.31 / 3.06 = 92.75 kips

Using AISC 14th Ed. Equation 9-4
Flexural Rupture = (phi) * Fu * Znet / e = 0.75 * 65.00 * 6.18 / 3.06 = 98.41 kips


Using AISC 14th Ed. Equation 9-14 through 9-18, Fcr = Fy * Q
tw = 0.31 in.
ho = 11.00 in.
c = 3.06 in.
lambda = (ho * Fy ^ 0.5) / ( 10 * tw * ( 475.00 + 280.00 * (ho / c)^2 ) ^0.5 ) = 
 = 11.00 * 50.00^0.5 / (10 * 0.31 * (475.00 + 280.00 * (11.00/3.06)^2 )^0.5) = 0.39
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 * 6.31 / 3.06 = 92.75 kips

Stress Interaction on Angle due to Combined Shear, Axial and Moment Loading:

Zgx = 9.47 in^3
Znx = 6.18 in^3
Zgy = 0.27 in^3
Zny = 0.18 in^3

Mrx = vertical reaction * ex = 1.00 * 3.06 = 3.06 kips-in
Mry = axial reaction * ey = 0.00 * 0.31 = 0.00 kips-in
Mcx = (phi) * Zgx * Min(Fy, Fcr) = 0.90 * 9.47 * Min(50.00, 50.00) = 426.07 kips-in
Mcy = (phi) * Zgy * Fy = 0.90 * 0.27 * 50.00 = 12.12 kips-in
Shear Stress on Gross Section = 1.00 / 3.44 = 0.29 ksi
Shear Stress on Net Section = 1.00 / 2.35 = 0.43 ksi
Axial Stress on Gross Section due to Axial force = 0.00 / 3.44 = 0.00 ksi
Axial Stress on Net Section due to Axial force = 0.00 / 2.35 = 0.00 ksi
Axial Stress on Gross Section due to Moment (shear) = 3.06 / 9.47 = 0.32 ksi
Axial Stress on Net Section due to Moment (shear) = 3.06 / 6.18 = 0.50 ksi
Axial Stress on Gross Section due to Moment (axial) = 0.00 / 0.27 = 0.00 ksi
Axial Stress on Net Section due to Moment (axial) = 0.00 / 0.18 = 0.00 ksi
Axial Stress on Gross Section (total) = 0.00 + 0.00 + 0.32 = 0.32 ksi
Axial Stress on Net Section (total) = 0.00 + 0.00 + 0.50 = 0.50 ksi

Shear Yield Stress Capacity (SYSC) = phi * 0.6 * Fy = 1.00 * 0.60 * 50.00 = 30.00 ksi
Tensile Yield Stress Capacity (TYSC) = phi * Fy = 0.90 * 50.00 = 45.00 ksi
Stress Interaction at Gross Section (elliptical):
(fvg / SYSC)^2 + (fag / TYSC )^2 = (0.29 / 30.00)^2 + (0.32 / 45.00 )^2 = 0.00 <= 1.0 (OK)
Shear Rupture Stress Capacity (SRSC) = phi * 0.6 * Fu = 0.75 * 0.60 * 65.00 = 29.25 ksi
Tensile Rupture Stress Capacity (TRSC) = phi * Fu = 0.75 * 65.00 = 48.75 ksi
Stress Interaction at Net Section (elliptical):
(fvn / SRSC)^2 + (fan / TRSC )^2 = (0.43 / 29.25)^2 + (0.50 / 48.75 )^2 = 0.00 <= 1.0 (OK)


Total Support Side Shear Yielding Capacity =  min(YieldAngle1/Gage1 Ratio, YieldAngle2/Gage2 Ratio) =  min(206.58 , 206.58) = 206.58 kips
206.58 kips >= Reaction V = 2.00 kips (OK)
Total Support Side Shear Rupture Capacity =  min(RuptureAngle1/Gage1 Ratio, RuptureAngle2/Gage2 Ratio) = min(201.42 , 201.42) = 201.42 kips
201.42 kips >= Reaction V = 2.00 kips (OK)
Total Beam Side Shear Yielding Capacity =  min (YieldAngle1/Gage1 Ratio , YieldAngle2/Gage2 Ratio) = min(206.58 , 206.58) = 206.58 kips
206.58 kips >= Reaction V = 2.00 kips (OK)
Total Beam Side Shear Rupture Capacity =  min (RuptureAngle1/Gage1 Ratio , RuptureAngle2/Gage2 Ratio) = min(137.33 , 137.33) = 137.33 kips
137.33 kips >= Reaction V = 2.00 kips (OK)
Total Support Side Flexure Yielding Capacity =  min (FlexureYieldAngle1/Gage1 Ratio , FlexureYieldAngle2/Gage2 Ratio) = min(180.20 , 180.20) = 180.20 kips
180.20 kips >= Reaction V = 2.00 kips (OK)
Total Support Side Flexure Rupture Capacity =  min (FlexureRuptureAngle1/Gage1 Ratio , FlexureRuptureAngle2/Gage2 Ratio) = min(292.84 , 292.84) = 292.84 kips
292.84 kips >= Reaction V = 2.00 kips (OK)
Total Support Side Bending Buckling Capacity =  min (BendingBucklingAngle1/Gage1 Ratio , BendingBucklingAngle2/Gage2 Ratio) = min(180.20 , 180.20) = 180.20 kips
180.20 kips >= Reaction V = 2.00 kips (OK)
Total Beam Side Flexure Yielding Capacity =  min (FlexureYieldAngle1/Gage1 Ratio , FlexureYieldAngle2/Gage2 Ratio) = min(185.50 , 185.50) = 185.50 kips
185.50 kips >= Reaction V = 2.00 kips (OK)
Total Beam Side Flexure Rupture Capacity =  min (FlexureRuptureAngle1/Gage1 Ratio , FlexureRuptureAngle2/Gage2 Ratio) = min(196.81 , 196.81) = 196.81 kips
196.81 kips >= Reaction V = 2.00 kips (OK)
Total Beam Side Bending Buckling Capacity =  min (BendingBucklingAngle1/Gage1 Ratio , BendingBucklingAngle2/Gage2 Ratio) = min(185.50 , 185.50) = 185.50 kips
185.50 kips >= Reaction V = 2.00 kips (OK)
Total Beam Side Vertical Block Shear Capacity =  min (BlockAngle1/Gage1 Ratio , BlockAngle2/Gage2 Ratio) = min(173.76 , 173.76) = 173.76 kips
173.76 kips >= Reaction V = 2.00 kips (OK)

Angles Welded to Support:

'B' Type Welds - Using Equation 10-1, p.10-11:
(phi) * Rn = (2 * (1.39 * D * L / (1 + (12.96 * e^2 /L^2) ) ^ .5)

Angle1 Girder Weld:
Rotational Ductility Check not required as the Leg thickness not greater than 5/8
Dmax1 using min(eqn 9-2, tang - 0.06) 
 = min(tang * Fuang / ( Fexx * C1 * 0.04), tang - 0.06) 
 = min(0.31 * 65.00 / ( 70.00 * 1.00 * 0.04), 0.31 - 0.06) 
 = min(6.58, 4.01)
 = 4.01 
Dmax2 (using eqn 9-2)
 = tembpl * Fuembpl / ( Fexx * C1 * 0.04 )
 = 0.75 * 58.00 / ( 70.00 * 1.00 * 0.04 ) 
 = 14.06 
Dmax3 = project max fillet weld = 12.00
Dmax=min(Dmax1, Dmax2, Dmax3) = min(4.01, 14.06, 12.00)
 = 4.01 

Use D = Min(angle thickness - 1/16, Max(Design Req, Table J2.4, User Pref Min)) = Min(4.01, Max(1.00, 3.00, 4.00)) = 4.00/16
(phi) * Rn = 1.39 * 4.00 * 11.00 /  ( 1 + (12.96 * 9.00 / 121.00))^0.5 = 43.71 kips

Angle2 Girder Weld:
Rotational Ductility Check not required as the Leg thickness not greater than 5/8
Dmax1 using min(eqn 9-2, tang - 0.06) 
 = min(tang * Fuang / ( Fexx * C1 * 0.04), tang - 0.06) 
 = min(0.31 * 65.00 / ( 70.00 * 1.00 * 0.04), 0.31 - 0.06) 
 = min(6.58, 4.01)
 = 4.01 
Dmax2 (using eqn 9-2)
 = tembpl * Fuembpl / ( Fexx * C1 * 0.04 )
 = 0.75 * 58.00 / ( 70.00 * 1.00 * 0.04 ) 
 = 14.06 
Dmax3 = project max fillet weld = 12.00
Dmax=min(Dmax1, Dmax2, Dmax3) = min(4.01, 14.06, 12.00)
 = 4.01 

Use D = Min(angle thickness - 1/16, Max(Design Req, Table J2.4, User Pref Min)) = Min(4.01, Max(1.00, 3.00, 4.00)) = 4.00/16
(phi) * Rn = 1.39 * 4.00 * 11.00 /  ( 1 + (12.96 * 9.00 / 121.00))^0.5 = 43.71 kips


Total Weld Strength = min ( Angle1 Weld Strength/Gage Ratio at Angle1 , Angle2 Weld Strength/Gage Ratio at Angle2 ) = min (87.42 , 87.42) = 87.42 kips