bb.2bb.s.01455.01462

DOUBLE ANGLES Bolted to Beam, Bolted to Support CONNECTION SUMMARY

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

Girder profile: W18X40
Filler Beam profile: W12X19
Slope: 0.00 deg.
Skew: 90.00
Vertical Offset: 0.00
Horizontal Offset: 0.00
Span: 20.00 ft.
Reaction, V: 17.00 kips
Shear Capacity, Rn: 40.96 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: L4X3-1/2X3/8
       Length = 5.50 in.
       Beam side bolts: 2 rows x 1 column 0.75 in. Diameter A325N_TC bolts
       Beam side bolt vertical spacing: 3.50 in.
       Support side bolts: 2 rows x 1 column 0.75 in. Diameter A325N_TC bolts
       Support side bolt vertical spacing: 3.50 in.
Angle2 Profile: L4X3-1/2X3/8
       Length = 5.50 in.
       Beam side bolts: 2 rows x 1 column 0.75 in. Diameter A325N_TC bolts
       Beam side bolt vertical spacing: 3.50 in.
       Support side bolts: 2 rows x 1 column 0.75 in. Diameter A325N_TC bolts
       Support side bolt vertical spacing: 3.50 in.

Configuration Geometry:

Beam setback = 0.50 in.
Edge distance at vertical edge of beam: 1.50 in.
Edge distance at top edge of beam: 2.00 in.
Top cope depth: 1.00 in.
Top cope length: 3.00 in.

Horizontal distance to first hole: 2.00 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 : 1.50 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 : 1.50 in.
   Edge distance at top edge : 1.00 in.
   Edge distance at bottom edge : 1.00 in.

Bolted Angle Leg At Support : 
Angle 1 Leg Distances : 
   Down distance from top of filler beam flange : 3.00 in.
   Gage at Bolt : 2.75 in.
   Edge distance at vertical edge : 1.37 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.
   Gage at Bolt : 2.75 in.
   Edge distance at vertical edge : 1.37 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 : STD diameter = 0.81 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 BEAM AND ANGLE 1 SIDE:
At Angle 1 side:
Bolt Shear Capacity at Shear Load Only:
C = no of bolts = 2.00
Using Table 7-1 to determine (phi)rn:
(phi)Rn = (phi)rn * C = 17.89 * 2.00 = 35.79 kips


BOLT SHEAR CAPACITY AT BEAM AND ANGLE 2 SIDE:
At Angle 2 side:
Bolt Shear Capacity at Shear Load Only:
C = no of bolts = 2.00
Using Table 7-1 to determine (phi)rn:
(phi)Rn = (phi)rn * C = 17.89 * 2.00 = 35.79 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(35.79/0.50, 35.79/0.50) = 71.57 kips
71.57 kips >= Reaction V = 17.00 kips (OK)

BOLT SHEAR CAPACITY AT SUPPORT AND ANGLE 1 SIDE:
Bolt Shear Capacity at Shear Load Only:
Gage ratio:  gage1 ratio = gage2 / (gage1 + gage2) = 2.75 / (2.75 + 2.75) = 0.50
Required tension stress (frt) = gage1 ratio * axial reaction    / bolt row count / bolt area  = 0.50 * 0.00 / 2 / 0.44 = 0.00 ksi
Required shear stress   (frv) = gage1 ratio * vertical reaction / bolt row count  / bolt area  = 0.50 * 17.00 / 2 / 0.44 = 9.62 ksi
C = no of bolts = 2.00
Using Table 7-1 to determine (phi)rn:
(phi)Rn = (phi)rn * C = 17.89 * 2.00 = 35.79 kips


BOLT SHEAR CAPACITY AT SUPPORT AND ANGLE 2 SIDE:
Bolt Shear Capacity at Shear Load Only:
Gage ratio:  gage2 ratio = gage1 / (gage1 + gage2) = 2.75 / (2.75 + 2.75) = 0.50
Required tension stress (frt) = gage2 ratio * axial reaction    / bolt row count / bolt area  = 0.50 * 0.00 / 2 / 0.44 = 0.00 ksi
Required shear stress   (frv) = gage2 ratio * vertical reaction / bolt row count  / bolt area  = 0.50 * 17.00 / 2 / 0.44 = 9.62 ksi
C = no of bolts = 2.00
Using Table 7-1 to determine (phi)rn:
(phi)Rn = (phi)rn * C = 17.89 * 2.00 = 35.79 kips


Vertical Bolt Shear Capacity at Support and Angle 1 = 
 = Shear Load Only Angle 1 side/gage1 ratio = 35.79/0.50 = 71.57 kips
Vertical Bolt Shear Capacity at Support and Angle 2 = 
 = Shear Load Only Angle 2 side/gage2 ratio = 35.79/0.50 = 71.57 kips
Total Support Side Bolt Shear Capacity = min(71.57, 71.57) = 71.57 kips
71.57 kips >= Reaction V = 17.00 kips (OK)

BOLT BEARING AT BEAM AND ANGLE 1 SIDE
Vertical Shear Only Load Case:
At Row 1, At Column 1:
(phi)Rnbolt = 17.89 kips
Lcsbm at Beam spacing  = 2.69 in.
Lcebm at Beam edge    = 1.59 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.75 * 1.20 * 2.69 * (0.23/2) * 65.00 = 18.47 kips/bolt
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 1.59 * (0.23/2) * 65.00 = 10.96 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.75 * (0.23/2) * 65.00 = 10.31 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(18.47, 10.96, 10.31) = 10.31 kips/bolt
Lcsang1 at Angle 1 spacing  = 2.69 in.
Lceang1 at Angle 1 edge    = 4.09 in.
(phi)Rnsang1 at Angle 1 spacing = (phi) * hf1 * Lcs * t * Fu = 0.75 * 1.20 * 2.69 * 0.38 * 65.00 = 58.96 kips/bolt
(phi)Rneang1 at Angle 1 edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 4.09 * 0.38 * 65.00 = 89.81 kips/bolt
(phi)Rndang1 on Angle 1 at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.75 * 0.38 * 65.00 = 32.91 kips/bolt
Angle 1 bearing capacity, (phi)Rnang1 = min((phi)Rnsang1,(phi)Rneang1,(phi)Rndang1) = min(58.96, 89.81, 32.91) = 32.91 kips/bolt
(phi)Rn = min((phi)Rnbolt, (phi)Rnbm, (phi)Rnang1) = min(17.89, 10.31, 32.91) = 10.31 kips/bolt

At Row 2, At Column 1:
(phi)Rnbolt = 17.89 kips
Lcsbm at Beam spacing  = 2.69 in.
Lcebm at Beam edge    = 5.09 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.75 * 1.20 * 2.69 * (0.23/2) * 65.00 = 18.47 kips/bolt
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 5.09 * (0.23/2) * 65.00 = 35.01 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.75 * (0.23/2) * 65.00 = 10.31 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(18.47, 35.01, 10.31) = 10.31 kips/bolt
Lcsang1 at Angle 1 spacing  = 2.69 in.
Lceang1 at Angle 1 edge    = 0.59 in.
(phi)Rnsang1 at Angle 1 spacing = (phi) * hf1 * Lcs * t * Fu = 0.75 * 1.20 * 2.69 * 0.38 * 65.00 = 58.96 kips/bolt
(phi)Rneang1 at Angle 1 edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 0.59 * 0.38 * 65.00 = 13.03 kips/bolt
(phi)Rndang1 on Angle 1 at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.75 * 0.38 * 65.00 = 32.91 kips/bolt
Angle 1 bearing capacity, (phi)Rnang1 = min((phi)Rnsang1,(phi)Rneang1,(phi)Rndang1) = min(58.96, 13.03, 32.91) = 13.03 kips/bolt
(phi)Rn = min((phi)Rnbolt, (phi)Rnbm, (phi)Rnang1) = min(17.89, 10.31, 13.03) = 10.31 kips/bolt

Bearing Capacity at Beam and Angle for vertical shear only
 = Sum{ Bearing At [(Row)i,(Column)i] }
 = 10.31 + 10.31 = 20.62 kips

BOLT BEARING AT BEAM AND ANGLE 2 SIDE
Vertical Shear Only Load Case:
At Row 1, At Column 1:
(phi)Rnbolt = 17.89 kips
Lcsbm at Beam spacing  = 2.69 in.
Lcebm at Beam edge    = 1.59 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.75 * 1.20 * 2.69 * (0.23/2) * 65.00 = 18.47 kips/bolt
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 1.59 * (0.23/2) * 65.00 = 10.96 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.75 * (0.23/2) * 65.00 = 10.31 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(18.47, 10.96, 10.31) = 10.31 kips/bolt
Lcsang2 at Angle 2 spacing  = 2.69 in.
Lceang2 at Angle 2 edge    = 4.09 in.
(phi)Rnsang2 at Angle 2 spacing = (phi) * hf1 * Lcs * t * Fu = 0.75 * 1.20 * 2.69 * 0.38 * 65.00 = 58.96 kips/bolt
(phi)Rneang2 at Angle 2 edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 4.09 * 0.38 * 65.00 = 89.81 kips/bolt
(phi)Rndang2 on Angle 2 at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.75 * 0.38 * 65.00 = 32.91 kips/bolt
Angle 2 bearing capacity, (phi)Rnang2 = min((phi)Rnsang2,(phi)Rneang2,(phi)Rndang2) = min(58.96, 89.81, 32.91) = 32.91 kips/bolt
(phi)Rn = min((phi)Rnbolt, (phi)Rnbm, (phi)Rnang2) = min(17.89, 10.31, 32.91) = 10.31 kips/bolt

At Row 2, At Column 1:
(phi)Rnbolt = 17.89 kips
Lcsbm at Beam spacing  = 2.69 in.
Lcebm at Beam edge    = 5.09 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.75 * 1.20 * 2.69 * (0.23/2) * 65.00 = 18.47 kips/bolt
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 5.09 * (0.23/2) * 65.00 = 35.01 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.75 * (0.23/2) * 65.00 = 10.31 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(18.47, 35.01, 10.31) = 10.31 kips/bolt
Lcsang2 at Angle 2 spacing  = 2.69 in.
Lceang2 at Angle 2 edge    = 0.59 in.
(phi)Rnsang2 at Angle 2 spacing = (phi) * hf1 * Lcs * t * Fu = 0.75 * 1.20 * 2.69 * 0.38 * 65.00 = 58.96 kips/bolt
(phi)Rneang2 at Angle 2 edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 0.59 * 0.38 * 65.00 = 13.03 kips/bolt
(phi)Rndang2 on Angle 2 at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.75 * 0.38 * 65.00 = 32.91 kips/bolt
Angle 2 bearing capacity, (phi)Rnang2 = min((phi)Rnsang2,(phi)Rneang2,(phi)Rndang2) = min(58.96, 13.03, 32.91) = 13.03 kips/bolt
(phi)Rn = min((phi)Rnbolt, (phi)Rnbm, (phi)Rnang2) = min(17.89, 10.31, 13.03) = 10.31 kips/bolt

Bearing Capacity at Beam and Angle for vertical shear only
 = Sum{ Bearing At [(Row)i,(Column)i] }
 = 10.31 + 10.31 = 20.62 kips


BEARING AT BEAM AND ANGLE SIDE SUMMARY:
Bearing Capacity at Vertical Shear Load Only, Rbv
 = Min(Sum{ Bearing at side 1  [(Row)i,(Column)i] } / gage1 ratio, 
       Sum{ Bearing at side 2  [(Row)i,(Column)i] } / gage2 ratio )
 = Min( 20.62/ 0.50, 20.62/ 0.50 ) = 41.24 kips
Rbv = 41.24 kips >= Reaction V = 17.00 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  = 2.69 in.
Lcesupp at Support edge    = 14.49 in.
(phi)Rnssupp at Support spacing = (phi) * hf1 * Lcs * (twsup/# bolt sides supported) * Fu = 0.75 * 1.20 * 2.69 * (0.32/1) * 65.00 = 49.53 kips/bolt
(phi)Rnesupp at Support edge = (phi) * hf1 * Lce * (twsup/# bolt sides supported) * Fu = 0.75 * 1.20 * 14.49 * (0.32/1) * 65.00 = 267.09 kips/bolt
(phi)Rndsupp on Support at Bolt Diameter   = (phi) * hf2 * db * (twsup/# bolt sides supported) * Fu = 0.75 * 2.40 * 0.75 * (0.32/1) * 65.00 = 27.64 kips/bolt
Support bearing capacity, (phi)Rnsupp = min((phi)Rnssupp,(phi)Rnesupp,(phi)Rndsupp) = min(49.53, 267.09, 27.64) = 27.64 kips/bolt
Lcsang1 at Angle 1 spacing  = 2.69 in.
Lceang1 at Angle 1 edge    = 0.59 in.
(phi)Rnsang1 at Angle 1 spacing = (phi) * hf1 * Lcs * t * Fu = 0.75 * 1.20 * 2.69 * 0.38 * 65.00 = 58.96 kips/bolt
(phi)Rneang1 at Angle 1 edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 0.59 * 0.38 * 65.00 = 13.03 kips/bolt
(phi)Rndang1 on Angle 1 at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.75 * 0.38 * 65.00 = 32.91 kips/bolt
Angle 1 bearing capacity, (phi)Rnang1 = min((phi)Rnsang1,(phi)Rneang1,(phi)Rndang1) = min(58.96, 13.03, 32.91) = 13.03 kips/bolt
(phi)Rn = min((phi)Rnbolt, (phi)Rnsupp, (phi)Rnang1) = min(17.89, 27.64, 13.03) = 13.03 kips/bolt

At Row 2, At Column 1:
(phi)Rnbolt = 17.89 kips
Lcssupp at Support spacing  = 2.69 in.
Lcesupp at Support edge    = 10.99 in.
(phi)Rnssupp at Support spacing = (phi) * hf1 * Lcs * (twsup/# bolt sides supported) * Fu = 0.75 * 1.20 * 2.69 * (0.32/1) * 65.00 = 49.53 kips/bolt
(phi)Rnesupp at Support edge = (phi) * hf1 * Lce * (twsup/# bolt sides supported) * Fu = 0.75 * 1.20 * 10.99 * (0.32/1) * 65.00 = 202.59 kips/bolt
(phi)Rndsupp on Support at Bolt Diameter   = (phi) * hf2 * db * (twsup/# bolt sides supported) * Fu = 0.75 * 2.40 * 0.75 * (0.32/1) * 65.00 = 27.64 kips/bolt
Support bearing capacity, (phi)Rnsupp = min((phi)Rnssupp,(phi)Rnesupp,(phi)Rndsupp) = min(49.53, 202.59, 27.64) = 27.64 kips/bolt
Lcsang1 at Angle 1 spacing  = 2.69 in.
Lceang1 at Angle 1 edge    = 4.09 in.
(phi)Rnsang1 at Angle 1 spacing = (phi) * hf1 * Lcs * t * Fu = 0.75 * 1.20 * 2.69 * 0.38 * 65.00 = 58.96 kips/bolt
(phi)Rneang1 at Angle 1 edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 4.09 * 0.38 * 65.00 = 89.81 kips/bolt
(phi)Rndang1 on Angle 1 at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.75 * 0.38 * 65.00 = 32.91 kips/bolt
Angle 1 bearing capacity, (phi)Rnang1 = min((phi)Rnsang1,(phi)Rneang1,(phi)Rndang1) = min(58.96, 89.81, 32.91) = 32.91 kips/bolt
(phi)Rn = min((phi)Rnbolt, (phi)Rnsupp, (phi)Rnang1) = min(17.89, 27.64, 32.91) = 17.89 kips/bolt

Bearing Capacity at Support and Angle 1 for vertical shear only
 = Sum{ Bearing At [(Row)i,(Column)i] }
 = 13.03 + 17.89 = 30.92 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  = 2.69 in.
Lcesupp at Support edge    = 14.49 in.
(phi)Rnssupp at Support spacing = (phi) * hf1 * Lcs * (twsup/# bolt sides supported) * Fu = 0.75 * 1.20 * 2.69 * (0.32/1) * 65.00 = 49.53 kips/bolt
(phi)Rnesupp at Support edge = (phi) * hf1 * Lce * (twsup/# bolt sides supported) * Fu = 0.75 * 1.20 * 14.49 * (0.32/1) * 65.00 = 267.09 kips/bolt
(phi)Rndsupp on Support at Bolt Diameter   = (phi) * hf2 * db * (twsup/# bolt sides supported) * Fu = 0.75 * 2.40 * 0.75 * (0.32/1) * 65.00 = 27.64 kips/bolt
Support bearing capacity, (phi)Rnsupp = min((phi)Rnssupp,(phi)Rnesupp,(phi)Rndsupp) = min(49.53, 267.09, 27.64) = 27.64 kips/bolt
Lcsang2 at Angle 2 spacing  = 2.69 in.
Lceang2 at Angle 2 edge    = 0.59 in.
(phi)Rnsang2 at Angle 2 spacing = (phi) * hf1 * Lcs * t * Fu = 0.75 * 1.20 * 2.69 * 0.38 * 65.00 = 58.96 kips/bolt
(phi)Rneang2 at Angle 2 edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 0.59 * 0.38 * 65.00 = 13.03 kips/bolt
(phi)Rndang2 on Angle 2 at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.75 * 0.38 * 65.00 = 32.91 kips/bolt
Angle 2 bearing capacity, (phi)Rnang2 = min((phi)Rnsang2,(phi)Rneang2,(phi)Rndang2) = min(58.96, 13.03, 32.91) = 13.03 kips/bolt
(phi)Rn = min((phi)Rnbolt, (phi)Rnsupp, (phi)Rnang2) = min(17.89, 27.64, 13.03) = 13.03 kips/bolt

At Row 2, At Column 1:
(phi)Rnbolt = 17.89 kips
Lcssupp at Support spacing  = 2.69 in.
Lcesupp at Support edge    = 10.99 in.
(phi)Rnssupp at Support spacing = (phi) * hf1 * Lcs * (twsup/# bolt sides supported) * Fu = 0.75 * 1.20 * 2.69 * (0.32/1) * 65.00 = 49.53 kips/bolt
(phi)Rnesupp at Support edge = (phi) * hf1 * Lce * (twsup/# bolt sides supported) * Fu = 0.75 * 1.20 * 10.99 * (0.32/1) * 65.00 = 202.59 kips/bolt
(phi)Rndsupp on Support at Bolt Diameter   = (phi) * hf2 * db * (twsup/# bolt sides supported) * Fu = 0.75 * 2.40 * 0.75 * (0.32/1) * 65.00 = 27.64 kips/bolt
Support bearing capacity, (phi)Rnsupp = min((phi)Rnssupp,(phi)Rnesupp,(phi)Rndsupp) = min(49.53, 202.59, 27.64) = 27.64 kips/bolt
Lcsang2 at Angle 2 spacing  = 2.69 in.
Lceang2 at Angle 2 edge    = 4.09 in.
(phi)Rnsang2 at Angle 2 spacing = (phi) * hf1 * Lcs * t * Fu = 0.75 * 1.20 * 2.69 * 0.38 * 65.00 = 58.96 kips/bolt
(phi)Rneang2 at Angle 2 edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 4.09 * 0.38 * 65.00 = 89.81 kips/bolt
(phi)Rndang2 on Angle 2 at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.75 * 0.38 * 65.00 = 32.91 kips/bolt
Angle 2 bearing capacity, (phi)Rnang2 = min((phi)Rnsang2,(phi)Rneang2,(phi)Rndang2) = min(58.96, 89.81, 32.91) = 32.91 kips/bolt
(phi)Rn = min((phi)Rnbolt, (phi)Rnsupp, (phi)Rnang2) = min(17.89, 27.64, 32.91) = 17.89 kips/bolt

Bearing Capacity at Support and Angle 2 for vertical shear only
 = Sum{ Bearing At [(Row)i,(Column)i] }
 = 13.03 + 17.89 = 30.92 kips

BEARING AT SUPPORT AND ANGLES SUMMARY:
Bearing Capacity at Vertical Shear Load Only, Rbv1 = Sum{ [(Row)i,(Column)i] } / gage1 ratio = 30.92 / 0.50 = 61.84 kips
Bearing Capacity at Vertical Shear Load Only, Rbv2 = Sum{ [(Row)i,(Column)i] } / gage2 ratio = 30.92 / 0.50 = 61.84 kips
Overall vertical Bearing Capacity Rbv = min(Rbv1, Rbv2) = min(61.84, 61.84) = 61.84 kips
61.84 kips >= 17.00 kips (OK)

Web Depth = d - [Top Cope Depth] - [Bottom Cope Depth] = 12.20 - 1.00 - 0.00 = 11.20 in.

Using AISC 14th Ed. Equation J4-3
Gross Area (Shear), Agross = [Web Depth] * tw = 11.20 * 0.23 = 2.63 in^2
Shear Yielding, (phi)Vny = (phi) * 0.6 * Fybeam * Agross = 1.00 * 0.6 * 50.00 * 2.63 = 78.96 kips

Using AISC 14th Ed. Equation J4-4
Net Area (Shear), Anet = ([Web Depth] - ([# rows] * [Diameter + 0.06])) * tw 
    = (11.20 - (2 * 0.88)) * 0.23 = 2.22 in^2
Shear Rupture, (phi)Vnu = (phi) * 0.6 * Fubeam * Anet = 0.75 * 0.6 * 65.00 * 2.22 = 64.96 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]) = 2.00 + 3.50 = 5.50 in.
Net Shear Length = Gross Shear Length - (# rows - 0.5) * (hole size + 0.06) = 5.50 - (2 - 0.5) * 0.88 = 4.19 in.
Gross Tension Length = [edge dist. at beam edge] + ([# cols - 1] * [spacing]) = 1.50 + (1 - 1) * 3.00 = 1.50 in.
Net Tension Length = Gross Tension Length - (# cols - 0.5) * (hole size + 0.06) = 1.50 - (1 - 0.5) * 0.88 = 1.06 in.
1. (phi) * [material thickness] * ((0.60 * Fubeam* [net shear length]) + (Ubs * Fubeam * [net tension length])) 
    = 0.75 * 0.23 * ((0.60 * 65.00 * 4.19) + (1.00 * 65.00 * 1.06)) = 40.96 kips
2. (phi) * [material thickness] * ((0.60 * Fybeam * [gross shear length]) + (Ubs * Fubeam * [net tension length])) 
    = 0.75 * 0.23 * ((0.60 * 50.00 * 5.50) + (1.00 * 65.00 * 1.06)) = 41.25 kips
Block Shear = 40.96 kips

Block Shear (1) Total = Block Shear (1) = 40.96 kips
40.96 kips >= Reaction V = 17.00 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 = 3.66 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 = 0.23 in.
h1 = 7.41 in.
c = 3.00 in.
When c/h1<=1.0, k=2.2(h1/c)^1.65
k  = 2.20 * (7.41 / 3.00)^1.65 = 9.79
When c/d<=1.0, f=2c/d
f = 2 * (3.00 / 12.20) = 0.49
Fy = 50.00 ksi
Fcr = (phi) * 26210.00 * f * k * (tw/h1)^2 = 0.90 * 26210.00 * 0.49 * 9.79 * (0.23 / 7.41)^2 = 114.11 ksi
Fcrmin =phi * min(Fcr, Fy) = 45.00 ksi
Snet1 (bolt holes not applicable) = 7.21 in^3
Snet2 (bolt holes applicable) = 7.21 in^3
Znet1 (bolt holes not applicable) = 12.68 in^3
Znet2 (bolt holes applicable) = 12.68 in^3

Using AISC 14th Ed. Equation 9-6
Buckling = Fcr * Snet1 / e = 45.00 * 7.21 / 3.66 = 88.65 kips

Using AISC 14th Ed. Equation 9-19
Flexural Yielding = (phi) * Fy * Snet1 / e = 0.90 * 50.00 * 7.21 / 3.66 = 88.65 kips

Using AISC 14th Ed. Equation 9-4
Flexural Rupture = (phi) * Fu * Znet2 / e = 0.75 * 65.00 * 12.68 / 3.66 = 169.02 kips


Buckling and Flexure at Furthest Bolt Line within Cope (Top Cope Only at Section)
Eccentricity at Section, e = 2.16 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 = 0.23 in.
h1 = 7.84 in.
c = 3.00 in.
When c/h1<=1.0, k=2.2(h1/c)^1.65
k  = 2.20 * (7.84 / 3.00)^1.65 = 10.73
When c/d<=1.0, f=2c/d
f = 2 * (3.00 / 12.20) = 0.49
Fy = 50.00 ksi
Fcr = (phi) * 26210.00 * f * k * (tw/h1)^2 = 0.90 * 26210.00 * 0.49 * 10.73 * (0.23 / 7.84)^2 = 111.90 ksi
Fcrmin =phi * min(Fcr, Fy) = 45.00 ksi
Snet1 (bolt holes not applicable) = 7.21 in^3
Snet2 (bolt holes applicable) = 5.86 in^3
Znet1 (bolt holes not applicable) = 12.68 in^3
Znet2 (bolt holes applicable) = 10.58 in^3

Using AISC 14th Ed. Equation 9-6
Buckling = Fcr * Snet1 / e = 45.00 * 7.21 / 2.16 = 150.29 kips

Using AISC 14th Ed. Equation 9-19
Flexural Yielding = (phi) * Fy * Snet1 / e = 0.90 * 50.00 * 7.21 / 2.16 = 150.29 kips

Using AISC 14th Ed. Equation 9-4
Flexural Rupture = (phi) * Fu * Znet2 / e = 0.75 * 65.00 * 10.58 / 2.16 = 239.14 kips


Section Bending Strength Calculations Summary:

   Coped Beam Buckling and Flexure at Longest Cope (Top Cope Only at Section)
   Buckling : 88.65 >= 17.00 kips (OK)
   Flexural Yielding : 88.65 >= 17.00 kips (OK)
   Flexural Rupture : 169.02 >= 17.00 kips (OK)

   Coped Beam Buckling and Flexure at Furthest Bolt Line within Cope (Top Cope Only at Section)
   Buckling : 150.29 >= 17.00 kips (OK)
   Flexural Yielding : 150.29 >= 17.00 kips (OK)
   Flexural Rupture : 239.14 >= 17.00 kips (OK)

Angle1 

Support Angle Leg 


Using AISC 14th Ed. Equation J4-3
Gross Area, Ag = 0.38 * 5.50 = 2.06 in^2
Shear Yielding, (phi)Vny = (phi) * 0.6 * Fya * Ag = 1.00 * 0.6 * 50.00 * 2.06 = 61.88 kips

Using AISC 14th Ed. Equation J4-4
Net Area, An = (5.50 - (2 * (0.81 + 1/16))) * 0.38 = 1.41 in^2
Shear Rupture, (phi)Vnu = (phi) * 0.6 * Fua * An = 0.75 * 0.6 * 65.00 * 1.41 = 41.13 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 = (5.50 - 1.00) = 4.50 in.
Net Shear Length = 4.50 - (1.50 * (0.81 + 1/16)) = 3.19 in.
Gross Tension Length = [edge dist.] = 1.37 in.
Net Tension Length = (1.37 - (1.00 + 1/16)/2) = 0.84 in.
1. (phi) * [material thickness] * ((0.60 * Fua* [net shear length]) + (Ubs * Fua * [net tension length])) 
    = 0.75 * 0.38 * ((0.60 * 65.00 * 3.19) + (1.00 * 65.00 * 0.84)) = 50.25 kips
2. (phi) * [material thickness] * ((0.60 * Fya * [gross shear length]) + (Ubs * Fua * [net tension length])) 
    = 0.75 * 0.38 * ((0.60 * 50.00 * 4.50) + (1.00 * 65.00 * 0.84)) = 53.26 kips
Block Shear = 50.25 kips

Beam Angle Leg 


Using AISC 14th Ed. Equation J4-3
Gross Area, Ag = 0.38 * 5.50 = 2.06 in^2
Shear Yielding, (phi)Vny = (phi) * 0.6 * Fya * Ag = 1.00 * 0.6 * 50.00 * 2.06 = 61.88 kips

Using AISC 14th Ed. Equation J4-4
Net Area, An = (5.50 - (2 * (0.81 + 1/16))) * 0.38 = 1.41 in^2
Shear Rupture, (phi)Vnu = (phi) * 0.6 * Fua * An = 0.75 * 0.6 * 65.00 * 1.41 = 41.13 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 = (5.50 - 1.00) = 4.50 in.
Net Shear Length = 4.50 - (1.50 * (0.81 + 1/16) = 3.19 in.
Gross Tension Length = [edge dist.] = 1.50 in.
Net Tension Length = (1.50 - (0.81 + 1/16)/2) = 1.06 in.
1. (phi) * [material thickness] * ((0.60 * Fua* [net shear length]) + (Ubs * Fua * [net tension length])) 
    = 0.75 * 0.38 * ((0.60 * 65.00 * 3.19) + (1.00 * 65.00 * 1.06)) = 54.39 kips
2. (phi) * [material thickness] * ((0.60 * Fya * [gross shear length]) + (Ubs * Fua * [net tension length])) 
    = 0.75 * 0.38 * ((0.60 * 50.00 * 4.50) + (1.00 * 65.00 * 1.06)) = 57.39 kips
Block Shear = 54.39 kips

Block Shear for Axial T/C is not required.


Angle2 

Support Angle Leg 


Using AISC 14th Ed. Equation J4-3
Gross Area, Ag = 0.38 * 5.50 = 2.06 in^2
Shear Yielding, (phi)Vny = (phi) * 0.6 * Fya * Ag = 1.00 * 0.6 * 50.00 * 2.06 = 61.88 kips

Using AISC 14th Ed. Equation J4-4
Net Area, An = (5.50 - (2 * (0.81 + 1/16))) * 0.38 = 1.41 in^2
Shear Rupture, (phi)Vnu = (phi) * 0.6 * Fua * An = 0.75 * 0.6 * 65.00 * 1.41 = 41.13 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 = (5.50 - 1.00) = 4.50 in.
Net Shear Length = 4.50 - (1.50 * (0.81 + 1/16)) = 3.19 in.
Gross Tension Length = [edge dist.] = 1.37 in.
Net Tension Length = (1.37 - (1.00 + 1/16)/2) = 0.84 in.
1. (phi) * [material thickness] * ((0.60 * Fua* [net shear length]) + (Ubs * Fua * [net tension length])) 
    = 0.75 * 0.38 * ((0.60 * 65.00 * 3.19) + (1.00 * 65.00 * 0.84)) = 50.25 kips
2. (phi) * [material thickness] * ((0.60 * Fya * [gross shear length]) + (Ubs * Fua * [net tension length])) 
    = 0.75 * 0.38 * ((0.60 * 50.00 * 4.50) + (1.00 * 65.00 * 0.84)) = 53.26 kips
Block Shear = 50.25 kips

Beam Angle Leg 


Using AISC 14th Ed. Equation J4-3
Gross Area, Ag = 0.38 * 5.50 = 2.06 in^2
Shear Yielding, (phi)Vny = (phi) * 0.6 * Fya * Ag = 1.00 * 0.6 * 50.00 * 2.06 = 61.88 kips

Using AISC 14th Ed. Equation J4-4
Net Area, An = (5.50 - (2 * (0.81 + 1/16))) * 0.38 = 1.41 in^2
Shear Rupture, (phi)Vnu = (phi) * 0.6 * Fua * An = 0.75 * 0.6 * 65.00 * 1.41 = 41.13 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 = (5.50 - 1.00) = 4.50 in.
Net Shear Length = 4.50 - (1.50 * (0.81 + 1/16) = 3.19 in.
Gross Tension Length = [edge dist.] = 1.50 in.
Net Tension Length = (1.50 - (0.81 + 1/16)/2) = 1.06 in.
1. (phi) * [material thickness] * ((0.60 * Fua* [net shear length]) + (Ubs * Fua * [net tension length])) 
    = 0.75 * 0.38 * ((0.60 * 65.00 * 3.19) + (1.00 * 65.00 * 1.06)) = 54.39 kips
2. (phi) * [material thickness] * ((0.60 * Fya * [gross shear length]) + (Ubs * Fua * [net tension length])) 
    = 0.75 * 0.38 * ((0.60 * 50.00 * 4.50) + (1.00 * 65.00 * 1.06)) = 57.39 kips
Block Shear = 54.39 kips

Block Shear for Axial T/C is not required.


Total Support Side Shear Yielding Capacity =  min(YieldAngle1/Gage1 Ratio, YieldAngle2/Gage2 Ratio) =  min(123.75 , 123.75) = 123.75 kips
123.75 kips >= Reaction V = 17.00 kips (OK)
Total Support Side Shear Rupture Capacity =  min(RuptureAngle1/Gage1 Ratio, RuptureAngle2/Gage2 Ratio) = min(82.27 , 82.27) = 82.27 kips
82.27 kips >= Reaction V = 17.00 kips (OK)
Total Support Side Vertical Block Shear Capacity =  min(BlockAngle1/Gage1 Ratio, BlockAngle2/Gage2 Ratio) = min(100.50 , 100.50) = 100.50 kips
100.50 kips >= Reaction V = 17.00 kips (OK)
Total Beam Side Shear Yielding Capacity =  min (YieldAngle1/Gage1 Ratio , YieldAngle2/Gage2 Ratio) = min(123.75 , 123.75) = 123.75 kips
123.75 kips >= Reaction V = 17.00 kips (OK)
Total Beam Side Shear Rupture Capacity =  min (RuptureAngle1/Gage1 Ratio , RuptureAngle2/Gage2 Ratio) = min(82.27 , 82.27) = 82.27 kips
82.27 kips >= Reaction V = 17.00 kips (OK)
Total Beam Side Vertical Block Shear Capacity =  min (BlockAngle1/Gage1 Ratio , BlockAngle2/Gage2 Ratio) = min(108.78 , 108.78) = 108.78 kips
108.78 kips >= Reaction V = 17.00 kips (OK)

(Not applicable / No results )