bb.2wb.s.00001.00001

DOUBLE ANGLES Welded to Beam, Bolted to Support CONNECTION SUMMARY

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

Girder profile: W18X50
Filler Beam profile: W16X40
Slope: 0.00 deg.
Skew: 90.00
Vertical Offset: 0.00
Horizontal Offset: 0.00
Span: 2.00 ft.
Reaction, V: 2.00 kips
Shear Capacity, Rn: 119.52 kips
Design/Reference according to AISC 14th Ed. - LRFD
Beam material grade: A992
Support material grade: A992
Angle material grade: A529-GR.50
Angle1 Profile: L5X3X5/16
       Length = 11.50 in.
       Support side bolts: 4 rows x 1 column 0.75 in. Diameter A325N_TC bolts
       Support side bolt vertical spacing: 3.00 in.
Angle2 Profile: L5X3X5/16
       Length = 11.50 in.
       Support side bolts: 4 rows x 1 column 0.75 in. Diameter A325N_TC bolts
       Support side bolt vertical spacing: 3.00 in.

Configuration Geometry:
Weld Size at Angle 1 Beam Weld:
4/16 FILLET - 3 sides
Weld Size at Angle 2 Beam Weld:
4/16 FILLET - 3 sides

Beam setback = 0.50 in.
Top cope depth: 1.25 in.
Top cope length: 3.75 in.


Welded Angle Leg At Beam : 
Angle 1 Leg Edge Distances : 
   Distance from top of Angle to top flange of beam : 1.75 in.
   Distance from bottom of Angle to bottom flange of beam : 2.75 in.

Angle 2 Leg Edge Distances : 
   Distance from top of Angle to top flange of beam : 1.75 in.
   Distance from bottom of Angle to bottom flange of beam : 2.75 in.

Bolted Angle Leg At Support : 
Angle 1 Leg Distances : 
   Down distance from top of filler beam flange : 3.00 in.
   Gage at Bolt : 3.25 in.
   Edge distance at vertical edge : 1.90 in.
   Edge distance at top edge : 1.25 in.
   Edge distance at bottom edge : 1.25 in.

Angle 2 Leg Distances : 
   Down distance from top of filler beam flange : 3.00 in.
   Gage at Bolt : 3.25 in.
   Edge distance at vertical edge : 1.90 in.
   Edge distance at top edge : 1.25 in.
   Edge distance at bottom edge : 1.25 in.

Holes in Support Girder : STD diameter = 0.81 in.
Holes in Support Angle Leg : SSL slot width = 0.81 in., slot length = 1.00 in.

BOLT SHEAR CAPACITY AT SUPPORT AND ANGLE 1 SIDE:
Bolt Shear Capacity at Shear Load Only:
Gage ratio:  gage1 ratio = gage2 / (gage1 + gage2) = 3.25 / (3.25 + 3.25) = 0.50
Required tension stress (frt) = gage1 ratio * axial reaction    / bolt row count / bolt area  = 0.50 * 0.00 / 4 / 0.44 = 0.00 ksi
Required shear stress   (frv) = gage1 ratio * vertical reaction / bolt row count  / bolt area  = 0.50 * 2.00 / 4 / 0.44 = 0.57 ksi
C = no of bolts = 4.00
Using Table 7-1 to determine (phi)rn:
(phi)Rn = (phi)rn * C = 17.89 * 4.00 = 71.57 kips


BOLT SHEAR CAPACITY AT SUPPORT AND ANGLE 2 SIDE:
Bolt Shear Capacity at Shear Load Only:
Gage ratio:  gage2 ratio = gage1 / (gage1 + gage2) = 3.25 / (3.25 + 3.25) = 0.50
Required tension stress (frt) = gage2 ratio * axial reaction    / bolt row count / bolt area  = 0.50 * 0.00 / 4 / 0.44 = 0.00 ksi
Required shear stress   (frv) = gage2 ratio * vertical reaction / bolt row count  / bolt area  = 0.50 * 2.00 / 4 / 0.44 = 0.57 ksi
C = no of bolts = 4.00
Using Table 7-1 to determine (phi)rn:
(phi)Rn = (phi)rn * C = 17.89 * 4.00 = 71.57 kips


Vertical Bolt Shear Capacity at Support and Angle 1 = 
 = Shear Load Only Angle 1 side/gage1 ratio = 71.57/0.50 = 143.14 kips
Vertical Bolt Shear Capacity at Support and Angle 2 = 
 = Shear Load Only Angle 2 side/gage2 ratio = 71.57/0.50 = 143.14 kips
Total Support Side Bolt Shear Capacity = min(143.14, 143.14) = 143.14 kips
143.14 kips >= Reaction V = 2.00 kips (OK)

BOLT BEARING AT SUPPORT AND ANGLE 1 SIDE
Vertical Shear Only Load Case:
At Row 1, At Column 1:
(phi)Rnbolt = 17.89 kips
Lcssupp at Support spacing  = 2.19 in.
Lcesupp at Support edge    = 14.59 in.
(phi)Rnssupp at Support spacing = (phi) * hf1 * Lcs * (twsup/# bolt sides supported) * Fu = 0.75 * 1.20 * 2.19 * (0.35/1) * 65.00 = 45.43 kips/bolt
(phi)Rnesupp at Support edge = (phi) * hf1 * Lce * (twsup/# bolt sides supported) * Fu = 0.75 * 1.20 * 14.59 * (0.35/1) * 65.00 = 303.08 kips/bolt
(phi)Rndsupp on Support at Bolt Diameter   = (phi) * hf2 * db * (twsup/# bolt sides supported) * Fu = 0.75 * 2.40 * 0.75 * (0.35/1) * 65.00 = 31.15 kips/bolt
Support bearing capacity, (phi)Rnsupp = min((phi)Rnssupp,(phi)Rnesupp,(phi)Rndsupp) = min(45.43, 303.08, 31.15) = 31.15 kips/bolt
Lcsang1 at Angle 1 spacing  = 2.19 in.
Lceang1 at Angle 1 edge    = 0.84 in.
(phi)Rnsang1 at Angle 1 spacing = (phi) * hf1 * Lcs * t * Fu = 0.75 * 1.20 * 2.19 * 0.31 * 65.00 = 40.06 kips/bolt
(phi)Rneang1 at Angle 1 edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 0.84 * 0.31 * 65.00 = 15.45 kips/bolt
(phi)Rndang1 on Angle 1 at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.75 * 0.31 * 65.00 = 27.47 kips/bolt
Angle 1 bearing capacity, (phi)Rnang1 = min((phi)Rnsang1,(phi)Rneang1,(phi)Rndang1) = min(40.06, 15.45, 27.47) = 15.45 kips/bolt
(phi)Rn = min((phi)Rnbolt, (phi)Rnsupp, (phi)Rnang1) = min(17.89, 31.15, 15.45) = 15.45 kips/bolt

At Row 2, At Column 1:
(phi)Rnbolt = 17.89 kips
Lcssupp at Support spacing  = 2.19 in.
Lcesupp at Support edge    = 11.59 in.
(phi)Rnssupp at Support spacing = (phi) * hf1 * Lcs * (twsup/# bolt sides supported) * Fu = 0.75 * 1.20 * 2.19 * (0.35/1) * 65.00 = 45.43 kips/bolt
(phi)Rnesupp at Support edge = (phi) * hf1 * Lce * (twsup/# bolt sides supported) * Fu = 0.75 * 1.20 * 11.59 * (0.35/1) * 65.00 = 240.78 kips/bolt
(phi)Rndsupp on Support at Bolt Diameter   = (phi) * hf2 * db * (twsup/# bolt sides supported) * Fu = 0.75 * 2.40 * 0.75 * (0.35/1) * 65.00 = 31.15 kips/bolt
Support bearing capacity, (phi)Rnsupp = min((phi)Rnssupp,(phi)Rnesupp,(phi)Rndsupp) = min(45.43, 240.78, 31.15) = 31.15 kips/bolt
Lcsang1 at Angle 1 spacing  = 2.19 in.
Lceang1 at Angle 1 edge    = 3.84 in.
(phi)Rnsang1 at Angle 1 spacing = (phi) * hf1 * Lcs * t * Fu = 0.75 * 1.20 * 2.19 * 0.31 * 65.00 = 40.06 kips/bolt
(phi)Rneang1 at Angle 1 edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 3.84 * 0.31 * 65.00 = 70.38 kips/bolt
(phi)Rndang1 on Angle 1 at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.75 * 0.31 * 65.00 = 27.47 kips/bolt
Angle 1 bearing capacity, (phi)Rnang1 = min((phi)Rnsang1,(phi)Rneang1,(phi)Rndang1) = min(40.06, 70.38, 27.47) = 27.47 kips/bolt
(phi)Rn = min((phi)Rnbolt, (phi)Rnsupp, (phi)Rnang1) = min(17.89, 31.15, 27.47) = 17.89 kips/bolt

At Row 3, At Column 1:
(phi)Rnbolt = 17.89 kips
Lcssupp at Support spacing  = 2.19 in.
Lcesupp at Support edge    = 8.59 in.
(phi)Rnssupp at Support spacing = (phi) * hf1 * Lcs * (twsup/# bolt sides supported) * Fu = 0.75 * 1.20 * 2.19 * (0.35/1) * 65.00 = 45.43 kips/bolt
(phi)Rnesupp at Support edge = (phi) * hf1 * Lce * (twsup/# bolt sides supported) * Fu = 0.75 * 1.20 * 8.59 * (0.35/1) * 65.00 = 178.48 kips/bolt
(phi)Rndsupp on Support at Bolt Diameter   = (phi) * hf2 * db * (twsup/# bolt sides supported) * Fu = 0.75 * 2.40 * 0.75 * (0.35/1) * 65.00 = 31.15 kips/bolt
Support bearing capacity, (phi)Rnsupp = min((phi)Rnssupp,(phi)Rnesupp,(phi)Rndsupp) = min(45.43, 178.48, 31.15) = 31.15 kips/bolt
Lcsang1 at Angle 1 spacing  = 2.19 in.
Lceang1 at Angle 1 edge    = 6.84 in.
(phi)Rnsang1 at Angle 1 spacing = (phi) * hf1 * Lcs * t * Fu = 0.75 * 1.20 * 2.19 * 0.31 * 65.00 = 40.06 kips/bolt
(phi)Rneang1 at Angle 1 edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 6.84 * 0.31 * 65.00 = 125.32 kips/bolt
(phi)Rndang1 on Angle 1 at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.75 * 0.31 * 65.00 = 27.47 kips/bolt
Angle 1 bearing capacity, (phi)Rnang1 = min((phi)Rnsang1,(phi)Rneang1,(phi)Rndang1) = min(40.06, 125.32, 27.47) = 27.47 kips/bolt
(phi)Rn = min((phi)Rnbolt, (phi)Rnsupp, (phi)Rnang1) = min(17.89, 31.15, 27.47) = 17.89 kips/bolt

At Row 4, At Column 1:
(phi)Rnbolt = 17.89 kips
Lcssupp at Support spacing  = 2.19 in.
Lcesupp at Support edge    = 5.59 in.
(phi)Rnssupp at Support spacing = (phi) * hf1 * Lcs * (twsup/# bolt sides supported) * Fu = 0.75 * 1.20 * 2.19 * (0.35/1) * 65.00 = 45.43 kips/bolt
(phi)Rnesupp at Support edge = (phi) * hf1 * Lce * (twsup/# bolt sides supported) * Fu = 0.75 * 1.20 * 5.59 * (0.35/1) * 65.00 = 116.17 kips/bolt
(phi)Rndsupp on Support at Bolt Diameter   = (phi) * hf2 * db * (twsup/# bolt sides supported) * Fu = 0.75 * 2.40 * 0.75 * (0.35/1) * 65.00 = 31.15 kips/bolt
Support bearing capacity, (phi)Rnsupp = min((phi)Rnssupp,(phi)Rnesupp,(phi)Rndsupp) = min(45.43, 116.17, 31.15) = 31.15 kips/bolt
Lcsang1 at Angle 1 spacing  = 2.19 in.
Lceang1 at Angle 1 edge    = 9.84 in.
(phi)Rnsang1 at Angle 1 spacing = (phi) * hf1 * Lcs * t * Fu = 0.75 * 1.20 * 2.19 * 0.31 * 65.00 = 40.06 kips/bolt
(phi)Rneang1 at Angle 1 edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 9.84 * 0.31 * 65.00 = 180.25 kips/bolt
(phi)Rndang1 on Angle 1 at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.75 * 0.31 * 65.00 = 27.47 kips/bolt
Angle 1 bearing capacity, (phi)Rnang1 = min((phi)Rnsang1,(phi)Rneang1,(phi)Rndang1) = min(40.06, 180.25, 27.47) = 27.47 kips/bolt
(phi)Rn = min((phi)Rnbolt, (phi)Rnsupp, (phi)Rnang1) = min(17.89, 31.15, 27.47) = 17.89 kips/bolt

Bearing Capacity at Support and Angle 1 for vertical shear only
 = Sum{ Bearing At [(Row)i,(Column)i] }
 = 15.45 + 17.89 + 17.89 + 17.89 = 69.13 kips

BOLT BEARING AT SUPPORT AND ANGLE 2 SIDE
Vertical Shear Only Load Case:
At Row 1, At Column 1:
(phi)Rnbolt = 17.89 kips
Lcssupp at Support spacing  = 2.19 in.
Lcesupp at Support edge    = 14.59 in.
(phi)Rnssupp at Support spacing = (phi) * hf1 * Lcs * (twsup/# bolt sides supported) * Fu = 0.75 * 1.20 * 2.19 * (0.35/1) * 65.00 = 45.43 kips/bolt
(phi)Rnesupp at Support edge = (phi) * hf1 * Lce * (twsup/# bolt sides supported) * Fu = 0.75 * 1.20 * 14.59 * (0.35/1) * 65.00 = 303.08 kips/bolt
(phi)Rndsupp on Support at Bolt Diameter   = (phi) * hf2 * db * (twsup/# bolt sides supported) * Fu = 0.75 * 2.40 * 0.75 * (0.35/1) * 65.00 = 31.15 kips/bolt
Support bearing capacity, (phi)Rnsupp = min((phi)Rnssupp,(phi)Rnesupp,(phi)Rndsupp) = min(45.43, 303.08, 31.15) = 31.15 kips/bolt
Lcsang2 at Angle 2 spacing  = 2.19 in.
Lceang2 at Angle 2 edge    = 0.84 in.
(phi)Rnsang2 at Angle 2 spacing = (phi) * hf1 * Lcs * t * Fu = 0.75 * 1.20 * 2.19 * 0.31 * 65.00 = 40.06 kips/bolt
(phi)Rneang2 at Angle 2 edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 0.84 * 0.31 * 65.00 = 15.45 kips/bolt
(phi)Rndang2 on Angle 2 at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.75 * 0.31 * 65.00 = 27.47 kips/bolt
Angle 2 bearing capacity, (phi)Rnang2 = min((phi)Rnsang2,(phi)Rneang2,(phi)Rndang2) = min(40.06, 15.45, 27.47) = 15.45 kips/bolt
(phi)Rn = min((phi)Rnbolt, (phi)Rnsupp, (phi)Rnang2) = min(17.89, 31.15, 15.45) = 15.45 kips/bolt

At Row 2, At Column 1:
(phi)Rnbolt = 17.89 kips
Lcssupp at Support spacing  = 2.19 in.
Lcesupp at Support edge    = 11.59 in.
(phi)Rnssupp at Support spacing = (phi) * hf1 * Lcs * (twsup/# bolt sides supported) * Fu = 0.75 * 1.20 * 2.19 * (0.35/1) * 65.00 = 45.43 kips/bolt
(phi)Rnesupp at Support edge = (phi) * hf1 * Lce * (twsup/# bolt sides supported) * Fu = 0.75 * 1.20 * 11.59 * (0.35/1) * 65.00 = 240.78 kips/bolt
(phi)Rndsupp on Support at Bolt Diameter   = (phi) * hf2 * db * (twsup/# bolt sides supported) * Fu = 0.75 * 2.40 * 0.75 * (0.35/1) * 65.00 = 31.15 kips/bolt
Support bearing capacity, (phi)Rnsupp = min((phi)Rnssupp,(phi)Rnesupp,(phi)Rndsupp) = min(45.43, 240.78, 31.15) = 31.15 kips/bolt
Lcsang2 at Angle 2 spacing  = 2.19 in.
Lceang2 at Angle 2 edge    = 3.84 in.
(phi)Rnsang2 at Angle 2 spacing = (phi) * hf1 * Lcs * t * Fu = 0.75 * 1.20 * 2.19 * 0.31 * 65.00 = 40.06 kips/bolt
(phi)Rneang2 at Angle 2 edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 3.84 * 0.31 * 65.00 = 70.38 kips/bolt
(phi)Rndang2 on Angle 2 at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.75 * 0.31 * 65.00 = 27.47 kips/bolt
Angle 2 bearing capacity, (phi)Rnang2 = min((phi)Rnsang2,(phi)Rneang2,(phi)Rndang2) = min(40.06, 70.38, 27.47) = 27.47 kips/bolt
(phi)Rn = min((phi)Rnbolt, (phi)Rnsupp, (phi)Rnang2) = min(17.89, 31.15, 27.47) = 17.89 kips/bolt

At Row 3, At Column 1:
(phi)Rnbolt = 17.89 kips
Lcssupp at Support spacing  = 2.19 in.
Lcesupp at Support edge    = 8.59 in.
(phi)Rnssupp at Support spacing = (phi) * hf1 * Lcs * (twsup/# bolt sides supported) * Fu = 0.75 * 1.20 * 2.19 * (0.35/1) * 65.00 = 45.43 kips/bolt
(phi)Rnesupp at Support edge = (phi) * hf1 * Lce * (twsup/# bolt sides supported) * Fu = 0.75 * 1.20 * 8.59 * (0.35/1) * 65.00 = 178.48 kips/bolt
(phi)Rndsupp on Support at Bolt Diameter   = (phi) * hf2 * db * (twsup/# bolt sides supported) * Fu = 0.75 * 2.40 * 0.75 * (0.35/1) * 65.00 = 31.15 kips/bolt
Support bearing capacity, (phi)Rnsupp = min((phi)Rnssupp,(phi)Rnesupp,(phi)Rndsupp) = min(45.43, 178.48, 31.15) = 31.15 kips/bolt
Lcsang2 at Angle 2 spacing  = 2.19 in.
Lceang2 at Angle 2 edge    = 6.84 in.
(phi)Rnsang2 at Angle 2 spacing = (phi) * hf1 * Lcs * t * Fu = 0.75 * 1.20 * 2.19 * 0.31 * 65.00 = 40.06 kips/bolt
(phi)Rneang2 at Angle 2 edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 6.84 * 0.31 * 65.00 = 125.32 kips/bolt
(phi)Rndang2 on Angle 2 at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.75 * 0.31 * 65.00 = 27.47 kips/bolt
Angle 2 bearing capacity, (phi)Rnang2 = min((phi)Rnsang2,(phi)Rneang2,(phi)Rndang2) = min(40.06, 125.32, 27.47) = 27.47 kips/bolt
(phi)Rn = min((phi)Rnbolt, (phi)Rnsupp, (phi)Rnang2) = min(17.89, 31.15, 27.47) = 17.89 kips/bolt

At Row 4, At Column 1:
(phi)Rnbolt = 17.89 kips
Lcssupp at Support spacing  = 2.19 in.
Lcesupp at Support edge    = 5.59 in.
(phi)Rnssupp at Support spacing = (phi) * hf1 * Lcs * (twsup/# bolt sides supported) * Fu = 0.75 * 1.20 * 2.19 * (0.35/1) * 65.00 = 45.43 kips/bolt
(phi)Rnesupp at Support edge = (phi) * hf1 * Lce * (twsup/# bolt sides supported) * Fu = 0.75 * 1.20 * 5.59 * (0.35/1) * 65.00 = 116.17 kips/bolt
(phi)Rndsupp on Support at Bolt Diameter   = (phi) * hf2 * db * (twsup/# bolt sides supported) * Fu = 0.75 * 2.40 * 0.75 * (0.35/1) * 65.00 = 31.15 kips/bolt
Support bearing capacity, (phi)Rnsupp = min((phi)Rnssupp,(phi)Rnesupp,(phi)Rndsupp) = min(45.43, 116.17, 31.15) = 31.15 kips/bolt
Lcsang2 at Angle 2 spacing  = 2.19 in.
Lceang2 at Angle 2 edge    = 9.84 in.
(phi)Rnsang2 at Angle 2 spacing = (phi) * hf1 * Lcs * t * Fu = 0.75 * 1.20 * 2.19 * 0.31 * 65.00 = 40.06 kips/bolt
(phi)Rneang2 at Angle 2 edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 9.84 * 0.31 * 65.00 = 180.25 kips/bolt
(phi)Rndang2 on Angle 2 at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.75 * 0.31 * 65.00 = 27.47 kips/bolt
Angle 2 bearing capacity, (phi)Rnang2 = min((phi)Rnsang2,(phi)Rneang2,(phi)Rndang2) = min(40.06, 180.25, 27.47) = 27.47 kips/bolt
(phi)Rn = min((phi)Rnbolt, (phi)Rnsupp, (phi)Rnang2) = min(17.89, 31.15, 27.47) = 17.89 kips/bolt

Bearing Capacity at Support and Angle 2 for vertical shear only
 = Sum{ Bearing At [(Row)i,(Column)i] }
 = 15.45 + 17.89 + 17.89 + 17.89 = 69.13 kips

BEARING AT SUPPORT AND ANGLES SUMMARY:
Bearing Capacity at Vertical Shear Load Only, Rbv1 = Sum{ [(Row)i,(Column)i] } / gage1 ratio = 69.13 / 0.50 = 138.26 kips
Bearing Capacity at Vertical Shear Load Only, Rbv2 = Sum{ [(Row)i,(Column)i] } / gage2 ratio = 69.13 / 0.50 = 138.26 kips
Overall vertical Bearing Capacity Rbv = min(Rbv1, Rbv2) = min(138.26, 138.26) = 138.26 kips
138.26 kips >= 2.00 kips (OK)

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

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

Using AISC 14th Ed. Equation J4-4
Net Area (Shear), Anet = [Gross Shear Length] * tw = 14.75 * 0.30 = 4.50 in^2
Shear Rupture, (phi)Vnu = (phi) * 0.6 * Fubeam * Anet = 0.75 * 0.6 * 65.00 * 4.50 = 131.59 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 = [dist. bottom most weld line to top edge of beam cope] = 12.00 in.
Net Shear Length = 12.00 in.
Gross Tension Length = [horizontal weld length] = 2.50 in.
Net Tension Length = 2.50 in.
1. (phi) * [material thickness] * ((0.60 * Fubeam* [net shear length]) + (Ubs * Fubeam * [net tension length])) 
    = 0.75 * 0.30 * ((0.60 * 65.00 * 12.00) + (1.00 * 65.00 * 2.50)) = 144.23 kips
2. (phi) * [material thickness] * ((0.60 * Fybeam * [gross shear length]) + (Ubs * Fubeam * [net tension length])) 
    = 0.75 * 0.30 * ((0.60 * 50.00 * 12.00) + (1.00 * 65.00 * 2.50)) = 119.52 kips
Block Shear = 119.52 kips
119.52 kips >= Reaction V = 2.00 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 = 4.43 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 = 10.43 in.
c = 3.75 in.
When c/h1<=1.0, k=2.2(h1/c)^1.65
k  = 2.20 * (10.43 / 3.75)^1.65 = 11.90
When c/d<=1.0, f=2c/d
f = 2 * (3.75 / 16.00) = 0.47
Fy = 50.00 ksi
Fcr = (phi) * 26210.00 * f * k * (tw/h1)^2 = 0.90 * 26210.00 * 0.47 * 11.90 * (0.30 / 10.43)^2 = 112.49 ksi
Fcrmin =phi * min(Fcr, Fy) = 45.00 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 9-6
Buckling = Fcr * Snet1 / e = 45.00 * 17.21 / 4.43 = 174.96 kips

Using AISC 14th Ed. Equation 9-19
Flexural Yielding = (phi) * Fy * Snet1 / e = 0.90 * 50.00 * 17.21 / 4.43 = 174.96 kips

Using AISC 14th Ed. Equation 9-4
Flexural Rupture = (phi) * Fu * Znet2 / e = 0.75 * 65.00 * 31.30 / 4.43 = 344.65 kips


Section Bending Strength Calculations Summary:

   Coped Beam Buckling and Flexure at Longest Cope (Top Cope Only at Section)
   Buckling : 174.96 >= 2.00 kips (OK)
   Flexural Yielding : 174.96 >= 2.00 kips (OK)
   Flexural Rupture : 344.65 >= 2.00 kips (OK)

Angle1 

Support Angle Leg 


Using AISC 14th Ed. Equation J4-3
Gross Area, Ag = 0.31 * 11.50 = 3.60 in^2
Shear Yielding, (phi)Vny = (phi) * 0.6 * Fya * Ag = 1.00 * 0.6 * 50.00 * 3.60 = 107.98 kips

Using AISC 14th Ed. Equation J4-4
Net Area, An = (11.50 - (4 * (0.81 + 1/16))) * 0.31 = 2.50 in^2
Shear Rupture, (phi)Vnu = (phi) * 0.6 * Fua * An = 0.75 * 0.6 * 65.00 * 2.50 = 73.24 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 = (11.50 - 1.25) = 10.25 in.
Net Shear Length = 10.25 - (3.50 * (0.81 + 1/16)) = 7.19 in.
Gross Tension Length = [edge dist.] = 1.90 in.
Net Tension Length = (1.90 - (1.00 + 1/16)/2) = 1.37 in.
1. (phi) * [material thickness] * ((0.60 * Fua* [net shear length]) + (Ubs * Fua * [net tension length])) 
    = 0.75 * 0.31 * ((0.60 * 65.00 * 7.19) + (1.00 * 65.00 * 1.37)) = 86.73 kips
2. (phi) * [material thickness] * ((0.60 * Fya * [gross shear length]) + (Ubs * Fua * [net tension length])) 
    = 0.75 * 0.31 * ((0.60 * 50.00 * 10.25) + (1.00 * 65.00 * 1.37)) = 93.11 kips
Block Shear = 86.73 kips

Beam Angle Leg 


Using AISC 14th Ed. Equation J4-3
Gross Area, Ag = 0.31 * 11.50 = 3.60 in^2
Shear Yielding, (phi)Vny = (phi) * 0.6 * Fyangle * Ag = 1.00 * 0.6 * 50.00 * 3.60 = 107.98 kips

Using AISC 14th Ed. Equation J4-4
Net Area, An = 0.31 * 11.50 = 3.60 in^2
Shear Rupture, (phi)Vnu = (phi) * 0.6 * Fuangle * An = 0.75 * 0.6 * 65.00 * 3.60 = 105.29 kips


Flexural and Buckling Strength:

Eccentricity at Weld = 2.62
Zgross = 10.35 in^3
Znet   = 10.35 in^3
Sgross = 6.90 in^3
Snet   = 6.90 in^3

Using AISC 14th Ed. Equation 9-19
Flexural Yielding = (phi) * Fy * Sgross / e = 0.90 * 50.00 * 6.90 / 2.62 = 118.44 kips

Using AISC 14th Ed. Equation 9-4
Flexural Rupture = (phi) * Fu * Znet / e = 0.75 * 65.00 * 10.35 / 2.62 = 192.47 kips


Using AISC 14th Ed. Equation 9-14 through 9-18, Fcr = Fy * Q
tw = 0.31 in.
ho = 11.50 in.
c = 2.62 in.
lambda = (ho * Fy ^ 0.5) / ( 10 * tw * ( 475.00 + 280.00 * (ho / c)^2 ) ^0.5 ) = 
 = 11.50 * 50.00^0.5 / (10 * 0.31 * (475.00 + 280.00 * (11.50/2.62)^2 )^0.5) = 0.34
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 * 6.90 / 2.62 = 118.44 kips

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

Zgx = 10.35 in^3
Znx = 10.35 in^3
Zgy = 0.28 in^3
Zny = 0.28 in^3

Mrx = vertical reaction * ex = 1.00 * 2.62 = 2.62 kips-in
Mry = axial reaction * ey = 0.00 * 0.31 = 0.00 kips-in
Mcx = (phi) * Zgx * Min(Fy, Fcr) = 0.90 * 10.35 * Min(50.00, 50.00) = 465.69 kips-in
Mcy = (phi) * Zgy * Fy = 0.90 * 0.28 * 50.00 = 12.67 kips-in
Shear Stress on Gross Section = 1.00 / 3.60 = 0.28 ksi
Shear Stress on Net Section = 1.00 / 3.60 = 0.28 ksi
Axial Stress on Gross Section due to Axial force = 0.00 / 3.60 = 0.00 ksi
Axial Stress on Net Section due to Axial force = 0.00 / 3.60 = 0.00 ksi
Axial Stress on Gross Section due to Moment (shear) = 2.62 / 10.35 = 0.25 ksi
Axial Stress on Net Section due to Moment (shear) = 2.62 / 10.35 = 0.25 ksi
Axial Stress on Gross Section due to Moment (axial) = 0.00 / 0.28 = 0.00 ksi
Axial Stress on Net Section due to Moment (axial) = 0.00 / 0.28 = 0.00 ksi
Axial Stress on Gross Section (total) = 0.00 + 0.00 + 0.25 = 0.25 ksi
Axial Stress on Net Section (total) = 0.00 + 0.00 + 0.25 = 0.25 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 = (0.28 / 30.00)^2 + (0.25 / 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 = (0.28 / 29.25)^2 + (0.25 / 48.75 )^2 = 0.00 <= 1.0 (OK)


Angle2 

Support Angle Leg 


Using AISC 14th Ed. Equation J4-3
Gross Area, Ag = 0.31 * 11.50 = 3.60 in^2
Shear Yielding, (phi)Vny = (phi) * 0.6 * Fya * Ag = 1.00 * 0.6 * 50.00 * 3.60 = 107.98 kips

Using AISC 14th Ed. Equation J4-4
Net Area, An = (11.50 - (4 * (0.81 + 1/16))) * 0.31 = 2.50 in^2
Shear Rupture, (phi)Vnu = (phi) * 0.6 * Fua * An = 0.75 * 0.6 * 65.00 * 2.50 = 73.24 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 = (11.50 - 1.25) = 10.25 in.
Net Shear Length = 10.25 - (3.50 * (0.81 + 1/16)) = 7.19 in.
Gross Tension Length = [edge dist.] = 1.90 in.
Net Tension Length = (1.90 - (1.00 + 1/16)/2) = 1.37 in.
1. (phi) * [material thickness] * ((0.60 * Fua* [net shear length]) + (Ubs * Fua * [net tension length])) 
    = 0.75 * 0.31 * ((0.60 * 65.00 * 7.19) + (1.00 * 65.00 * 1.37)) = 86.73 kips
2. (phi) * [material thickness] * ((0.60 * Fya * [gross shear length]) + (Ubs * Fua * [net tension length])) 
    = 0.75 * 0.31 * ((0.60 * 50.00 * 10.25) + (1.00 * 65.00 * 1.37)) = 93.11 kips
Block Shear = 86.73 kips

Beam Angle Leg 


Using AISC 14th Ed. Equation J4-3
Gross Area, Ag = 0.31 * 11.50 = 3.60 in^2
Shear Yielding, (phi)Vny = (phi) * 0.6 * Fyangle * Ag = 1.00 * 0.6 * 50.00 * 3.60 = 107.98 kips

Using AISC 14th Ed. Equation J4-4
Net Area, An = 0.31 * 11.50 = 3.60 in^2
Shear Rupture, (phi)Vnu = (phi) * 0.6 * Fuangle * An = 0.75 * 0.6 * 65.00 * 3.60 = 105.29 kips


Flexural and Buckling Strength:

Eccentricity at Weld = 2.62
Zgross = 10.35 in^3
Znet   = 10.35 in^3
Sgross = 6.90 in^3
Snet   = 6.90 in^3

Using AISC 14th Ed. Equation 9-19
Flexural Yielding = (phi) * Fy * Sgross / e = 0.90 * 50.00 * 6.90 / 2.62 = 118.44 kips

Using AISC 14th Ed. Equation 9-4
Flexural Rupture = (phi) * Fu * Znet / e = 0.75 * 65.00 * 10.35 / 2.62 = 192.47 kips


Using AISC 14th Ed. Equation 9-14 through 9-18, Fcr = Fy * Q
tw = 0.31 in.
ho = 11.50 in.
c = 2.62 in.
lambda = (ho * Fy ^ 0.5) / ( 10 * tw * ( 475.00 + 280.00 * (ho / c)^2 ) ^0.5 ) = 
 = 11.50 * 50.00^0.5 / (10 * 0.31 * (475.00 + 280.00 * (11.50/2.62)^2 )^0.5) = 0.34
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 * 6.90 / 2.62 = 118.44 kips

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

Zgx = 10.35 in^3
Znx = 10.35 in^3
Zgy = 0.28 in^3
Zny = 0.28 in^3

Mrx = vertical reaction * ex = 1.00 * 2.62 = 2.62 kips-in
Mry = axial reaction * ey = 0.00 * 0.31 = 0.00 kips-in
Mcx = (phi) * Zgx * Min(Fy, Fcr) = 0.90 * 10.35 * Min(50.00, 50.00) = 465.69 kips-in
Mcy = (phi) * Zgy * Fy = 0.90 * 0.28 * 50.00 = 12.67 kips-in
Shear Stress on Gross Section = 1.00 / 3.60 = 0.28 ksi
Shear Stress on Net Section = 1.00 / 3.60 = 0.28 ksi
Axial Stress on Gross Section due to Axial force = 0.00 / 3.60 = 0.00 ksi
Axial Stress on Net Section due to Axial force = 0.00 / 3.60 = 0.00 ksi
Axial Stress on Gross Section due to Moment (shear) = 2.62 / 10.35 = 0.25 ksi
Axial Stress on Net Section due to Moment (shear) = 2.62 / 10.35 = 0.25 ksi
Axial Stress on Gross Section due to Moment (axial) = 0.00 / 0.28 = 0.00 ksi
Axial Stress on Net Section due to Moment (axial) = 0.00 / 0.28 = 0.00 ksi
Axial Stress on Gross Section (total) = 0.00 + 0.00 + 0.25 = 0.25 ksi
Axial Stress on Net Section (total) = 0.00 + 0.00 + 0.25 = 0.25 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 = (0.28 / 30.00)^2 + (0.25 / 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 = (0.28 / 29.25)^2 + (0.25 / 48.75 )^2 = 0.00 <= 1.0 (OK)


Total Support Side Shear Yielding Capacity =  min(YieldAngle1/Gage1 Ratio, YieldAngle2/Gage2 Ratio) =  min(215.97 , 215.97) = 215.97 kips
215.97 kips >= Reaction V = 2.00 kips (OK)
Total Support Side Shear Rupture Capacity =  min(RuptureAngle1/Gage1 Ratio, RuptureAngle2/Gage2 Ratio) = min(146.49 , 146.49) = 146.49 kips
146.49 kips >= Reaction V = 2.00 kips (OK)
Total Support Side Vertical Block Shear Capacity =  min(BlockAngle1/Gage1 Ratio, BlockAngle2/Gage2 Ratio) = min(173.46 , 173.46) = 173.46 kips
173.46 kips >= Reaction V = 2.00 kips (OK)
Total Beam Side Shear Yielding Capacity =  min (YieldAngle1/Gage1 Ratio , YieldAngle2/Gage2 Ratio) = min(215.97 , 215.97) = 215.97 kips
215.97 kips >= Reaction V = 2.00 kips (OK)
Total Beam Side Shear Rupture Capacity =  min (RuptureAngle1/Gage1 Ratio , RuptureAngle2/Gage2 Ratio) = min(210.58 , 210.58) = 210.58 kips
210.58 kips >= Reaction V = 2.00 kips (OK)
Total Beam Side Flexure Yielding Capacity =  min (FlexureYieldAngle1/Gage1 Ratio , FlexureYieldAngle2/Gage2 Ratio) = min(236.88 , 236.88) = 236.88 kips
236.88 kips >= Reaction V = 2.00 kips (OK)
Total Beam Side Flexure Rupture Capacity =  min (FlexureRuptureAngle1/Gage1 Ratio , FlexureRuptureAngle2/Gage2 Ratio) = min(384.94 , 384.94) = 384.94 kips
384.94 kips >= Reaction V = 2.00 kips (OK)
Total Beam Side Bending Buckling Capacity =  min (BendingBucklingAngle1/Gage1 Ratio , BendingBucklingAngle2/Gage2 Ratio) = min(236.88 , 236.88) = 236.88 kips
236.88 kips >= Reaction V = 2.00 kips (OK)

Angles Welded to Beam:

Angle1 Beam Weld
k = 0.22
ex = 2.62
a = ex / l = 2.62 / 11.50 = 0.23
Loadangle = 0.00 deg 
Weld Coefficient = 0.60 * Fexx * cphi * arrangement coefficient = 2.65
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 9-3)
 = twbeam * Fubeam / ( Fexx * C1 * 0.09 )
 = 0.30 * 65.00 / ( 70.00 * 1.00 * 0.09 ) 
 = 3.20 
Dmax3 = project max fillet weld = 12.00
Dmax=min(Dmax1, Dmax2, Dmax3) = min(4.01, 3.20, 12.00)
 = 3.20 

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

Weld Strength = phi * weld coefficient * l * D  = 0.75 * 2.65 * 11.50 * 3.20 = 73.12 kips

Angle2 Beam Weld
k = 0.22
ex = 2.62
a = ex / l = 2.62 / 11.50 = 0.23
Loadangle = 0.00 deg 
Weld Coefficient = 0.60 * Fexx * cphi * arrangement coefficient = 2.65
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 9-3)
 = twbeam * Fubeam / ( Fexx * C1 * 0.09 )
 = 0.30 * 65.00 / ( 70.00 * 1.00 * 0.09 ) 
 = 3.20 
Dmax3 = project max fillet weld = 12.00
Dmax=min(Dmax1, Dmax2, Dmax3) = min(4.01, 3.20, 12.00)
 = 3.20 

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

Weld Strength = phi * weld coefficient * l * D  = 0.75 * 2.65 * 11.50 * 3.20 = 73.12 kips

Total Welds Shear Strength = min( Angle1 Weld Shear/Gage Ratio at Angle1 , Angle2 Weld Shear/Gage Ratio at Angle2 ) = min ( 146.24, 146.24) = 146.24 kips