bb.1bb.s.00002.00002

SINGLE ANGLE 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: W21X50
Slope: 0.00 deg.
Skew: 90.00
Vertical Offset: 0.00 in.
Horizontal Offset: 0.00 in.
Span: 45.00 ft.
Reaction, V: 36.67 kips
Shear Capacity, Rn: 67.27 kips
Design/Reference according to AISC 14th Ed. - LRFD
Beam material grade: A992
Support material grade: A992
Angle material grade: A36
Angle1 Profile: L4X3X3/8
       Length = 14.50 in.
       Beam side bolts: 5 rows x 1 column 0.75 in. Diameter A325N_TC bolts
       Beam side bolt vertical spacing: 3.00 in.
       Support side bolts: 5 rows x 1 column 0.75 in. Diameter A325N_TC bolts
       Support side bolt vertical spacing: 3.00 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: 1.75 in.
Edge distance at bottom edge of beam: 1.80 in.
Top cope depth: 1.25 in.
Top cope length: 3.00 in.
Bottom cope depth: 4.00 in.
Bottom 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 : 1.00 in.
   Edge distance at top edge : 1.25 in.
   Edge distance at bottom edge : 1.25 in.

Bolted Angle Leg At Support : 
Angle 1 Leg Distances : 
   Down distance from top of filler beam flange : 3.00 in.
   Gage at Bolt : 3.19 in.
   Edge distance at vertical edge : 1.00 in.
   Edge distance at top edge : 1.25 in.
   Edge distance at bottom edge : 1.25 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 : STD diameter = 0.81 in.

BOLT SHEAR CAPACITY AT BEAM AND ANGLE SIDE:
Bolt Shear Capacity at Shear Load Only:
C = no of bolts = 5.00
Using Table 7-1 to determine (phi)rn:
(phi)Rn = (phi)rn * C = 17.89 * 5.00 = 89.46 kips


Total Vertical Bolt Shear Capacity = 89.46 kips
89.46 kips >= Reaction V = 36.67 kips (OK)

BOLT SHEAR CAPACITY AT SUPPORT AND ANGLE SIDE:
Bolt Shear Capacity at Shear Load Only:
Required tension stress (frt) = axial reaction    / bolt row count / bolt area  = 0.00 / 5 / 0.44 = 0.00 ksi
Required shear stress   (frv) = vertical reaction / bolt row count  / bolt area  = 36.67 / 5 / 0.44 = 16.60 ksi
Using Instantaneous Center Of Rotation Method (AISC 7-1)
ex = 3.19 in.
Angle = 0.00 deg.
C = 3.80
Using Table 7-1 to determine (phi)rn:
(phi)Rn = (phi)rn * C = 17.89 * 3.80 = 68.03 kips


Vertical Bolt Shear Capacity at Support and Angle = 68.03 kips
68.03 kips >= 36.67 kips (OK)

BOLT BEARING AT BEAM AND ANGLE SIDE
Vertical Shear Only Load Case:
At Row 1, At Column 1:
(phi)Rnbolt = 17.89 kips
Lcsbm at Beam spacing  = 2.19 in.
Lcebm at Beam edge    = 1.34 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.75 * 1.20 * 2.19 * (0.38/1) * 65.00 = 48.63 kips/bolt
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 1.34 * (0.38/1) * 65.00 = 29.87 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.75 * (0.38/1) * 65.00 = 33.35 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(48.63, 29.87, 33.35) = 29.87 kips/bolt
Lcsang1 at Angle 1 spacing  = 2.19 in.
Lceang1 at Angle 1 edge    = 12.84 in.
(phi)Rnsang1 at Angle 1 spacing = (phi) * hf1 * Lcs * t * Fu = 0.75 * 1.20 * 2.19 * 0.38 * 58.00 = 42.82 kips/bolt
(phi)Rneang1 at Angle 1 edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 12.84 * 0.38 * 58.00 = 251.42 kips/bolt
(phi)Rndang1 on Angle 1 at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.75 * 0.38 * 58.00 = 29.36 kips/bolt
Angle 1 bearing capacity, (phi)Rnang1 = min((phi)Rnsang1,(phi)Rneang1,(phi)Rndang1) = min(42.82, 251.42, 29.36) = 29.36 kips/bolt
(phi)Rn = min((phi)Rnbolt, (phi)Rnbm, (phi)Rnang1) = min(17.89, 29.87, 29.36) = 17.89 kips/bolt

At Row 2, At Column 1:
(phi)Rnbolt = 17.89 kips
Lcsbm at Beam spacing  = 2.19 in.
Lcebm at Beam edge    = 4.34 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.75 * 1.20 * 2.19 * (0.38/1) * 65.00 = 48.63 kips/bolt
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 4.34 * (0.38/1) * 65.00 = 96.56 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.75 * (0.38/1) * 65.00 = 33.35 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(48.63, 96.56, 33.35) = 33.35 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 * 0.38 * 58.00 = 42.82 kips/bolt
(phi)Rneang1 at Angle 1 edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 9.84 * 0.38 * 58.00 = 192.70 kips/bolt
(phi)Rndang1 on Angle 1 at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.75 * 0.38 * 58.00 = 29.36 kips/bolt
Angle 1 bearing capacity, (phi)Rnang1 = min((phi)Rnsang1,(phi)Rneang1,(phi)Rndang1) = min(42.82, 192.70, 29.36) = 29.36 kips/bolt
(phi)Rn = min((phi)Rnbolt, (phi)Rnbm, (phi)Rnang1) = min(17.89, 33.35, 29.36) = 17.89 kips/bolt

At Row 3, At Column 1:
(phi)Rnbolt = 17.89 kips
Lcsbm at Beam spacing  = 2.19 in.
Lcebm at Beam edge    = 7.34 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.75 * 1.20 * 2.19 * (0.38/1) * 65.00 = 48.63 kips/bolt
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 7.34 * (0.38/1) * 65.00 = 163.26 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.75 * (0.38/1) * 65.00 = 33.35 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(48.63, 163.26, 33.35) = 33.35 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 * 0.38 * 58.00 = 42.82 kips/bolt
(phi)Rneang1 at Angle 1 edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 6.84 * 0.38 * 58.00 = 133.97 kips/bolt
(phi)Rndang1 on Angle 1 at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.75 * 0.38 * 58.00 = 29.36 kips/bolt
Angle 1 bearing capacity, (phi)Rnang1 = min((phi)Rnsang1,(phi)Rneang1,(phi)Rndang1) = min(42.82, 133.97, 29.36) = 29.36 kips/bolt
(phi)Rn = min((phi)Rnbolt, (phi)Rnbm, (phi)Rnang1) = min(17.89, 33.35, 29.36) = 17.89 kips/bolt

At Row 4, At Column 1:
(phi)Rnbolt = 17.89 kips
Lcsbm at Beam spacing  = 2.19 in.
Lcebm at Beam edge    = 10.34 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.75 * 1.20 * 2.19 * (0.38/1) * 65.00 = 48.63 kips/bolt
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 10.34 * (0.38/1) * 65.00 = 229.95 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.75 * (0.38/1) * 65.00 = 33.35 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(48.63, 229.95, 33.35) = 33.35 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 * 0.38 * 58.00 = 42.82 kips/bolt
(phi)Rneang1 at Angle 1 edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 3.84 * 0.38 * 58.00 = 75.24 kips/bolt
(phi)Rndang1 on Angle 1 at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.75 * 0.38 * 58.00 = 29.36 kips/bolt
Angle 1 bearing capacity, (phi)Rnang1 = min((phi)Rnsang1,(phi)Rneang1,(phi)Rndang1) = min(42.82, 75.24, 29.36) = 29.36 kips/bolt
(phi)Rn = min((phi)Rnbolt, (phi)Rnbm, (phi)Rnang1) = min(17.89, 33.35, 29.36) = 17.89 kips/bolt

At Row 5, At Column 1:
(phi)Rnbolt = 17.89 kips
Lcsbm at Beam spacing  = 2.19 in.
Lcebm at Beam edge    = 13.34 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.75 * 1.20 * 2.19 * (0.38/1) * 65.00 = 48.63 kips/bolt
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 13.34 * (0.38/1) * 65.00 = 296.64 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.75 * (0.38/1) * 65.00 = 33.35 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(48.63, 296.64, 33.35) = 33.35 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 * 0.38 * 58.00 = 42.82 kips/bolt
(phi)Rneang1 at Angle 1 edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 0.84 * 0.38 * 58.00 = 16.52 kips/bolt
(phi)Rndang1 on Angle 1 at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.75 * 0.38 * 58.00 = 29.36 kips/bolt
Angle 1 bearing capacity, (phi)Rnang1 = min((phi)Rnsang1,(phi)Rneang1,(phi)Rndang1) = min(42.82, 16.52, 29.36) = 16.52 kips/bolt
(phi)Rn = min((phi)Rnbolt, (phi)Rnbm, (phi)Rnang1) = min(17.89, 33.35, 16.52) = 16.52 kips/bolt

Bearing Capacity at Beam and Angle for vertical shear only
 = Sum{ Bearing At [(Row)i,(Column)i] }
 = 17.89 + 17.89 + 17.89 + 17.89 + 16.52 = 88.09 kips


BEARING AT BEAM AND ANGLE SIDE SUMMARY:
Bearing Capacity at Vertical Shear Load Only, Rbv = Sum{ [(Row)i,(Column)i] } = 88.09 kips
Rbv = 88.09 kips >= Reaction V = 36.67 kips (OK)


BOLT BEARING AT SUPPORT AND ANGLE SIDE
Vertical Shear Only Load Case:
ICR cordinate relative to CG = (4.89, -0.00)
At Row 1, At Column 1:
Ribolt = 17.56 kips
Ri vector at Support   = <-13.61, -11.10>
Lcssupp at Support spacing  = na
Lcesupp at Support edge    = 23.18 in.
(phi)Rnssupp at Support spacing = (phi) * hf1 * Lcs * (twsup/# bolt sides supported) * Fu = na
(phi)Rnesupp at Support edge = (phi) * hf1 * Lce * (twsup/# bolt sides supported) * Fu = 0.75 * 1.20 * 23.18 * (0.32/1) * 65.00 = 427.12 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(na, 427.12, 27.64) = 27.64 kips/bolt
Ri vector at Angle   = <13.61, 11.10>
Lcsang at Angle spacing  = na
Lceang at Angle edge    = 0.89 in.
(phi)Rnsang at Angle spacing = (phi) * hf1 * Lcs * t * Fu = na
(phi)Rneang at Angle edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 0.89 * 0.38 * 58.00 = 17.36 kips/bolt
(phi)Rndang on Angle at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.75 * 0.38 * 58.00 = 29.36 kips/bolt
Angle bearing capacity, (phi)Rnang = min((phi)Rnsang,(phi)Rneang,(phi)Rndang) = min(na, 17.36, 29.36) = 17.36 kips/bolt
(phi)Rn = min((phi)Rnsupp, (phi)Rnang) = min(27.64, 17.36) = 17.36 kips/bolt
Bolt Shear Demand to Bearing ratio = 17.36 / 17.56 = 0.99

At Row 2, At Column 1:
Ribolt = 17.09 kips
Ri vector at Support   = <-8.93, -14.56>
Lcssupp at Support spacing  = na
Lcesupp at Support edge    = 13.55 in.
(phi)Rnssupp at Support spacing = (phi) * hf1 * Lcs * (twsup/# bolt sides supported) * Fu = na
(phi)Rnesupp at Support edge = (phi) * hf1 * Lce * (twsup/# bolt sides supported) * Fu = 0.75 * 1.20 * 13.55 * (0.32/1) * 65.00 = 249.79 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(na, 249.79, 27.64) = 27.64 kips/bolt
Ri vector at Angle   = <8.93, 14.56>
Lcsang at Angle spacing  = na
Lceang at Angle edge    = 1.51 in.
(phi)Rnsang at Angle spacing = (phi) * hf1 * Lcs * t * Fu = na
(phi)Rneang at Angle edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 1.51 * 0.38 * 58.00 = 29.58 kips/bolt
(phi)Rndang on Angle at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.75 * 0.38 * 58.00 = 29.36 kips/bolt
Angle bearing capacity, (phi)Rnang = min((phi)Rnsang,(phi)Rneang,(phi)Rndang) = min(na, 29.58, 29.36) = 29.36 kips/bolt
(phi)Rn = min((phi)Rnsupp, (phi)Rnang) = min(27.64, 29.36) = 27.64 kips/bolt
Bolt Shear Demand to Bearing ratio = 27.64 / 17.09 = 1.62

At Row 3, At Column 1:
Ribolt = 16.71 kips
Ri vector at Support   = <-0.00, -16.71>
Lcssupp at Support spacing  = 2.19 in.
Lcesupp at Support edge    = 8.49 in.
(phi)Rnssupp at Support spacing = (phi) * hf1 * Lcs * (twsup/# bolt sides supported) * Fu = 0.75 * 1.20 * 2.19 * (0.32/1) * 65.00 = 40.31 kips/bolt
(phi)Rnesupp at Support edge = (phi) * hf1 * Lce * (twsup/# bolt sides supported) * Fu = 0.75 * 1.20 * 8.49 * (0.32/1) * 65.00 = 156.52 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(40.31, 156.52, 27.64) = 27.64 kips/bolt
Ri vector at Angle   = <0.00, 16.71>
Lcsang at Angle spacing  = 2.19 in.
Lceang at Angle edge    = 6.84 in.
(phi)Rnsang at Angle spacing = (phi) * hf1 * Lcs * t * Fu = 0.75 * 1.20 * 2.19 * 0.38 * 58.00 = 42.82 kips/bolt
(phi)Rneang at Angle edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 6.84 * 0.38 * 58.00 = 133.97 kips/bolt
(phi)Rndang on Angle at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.75 * 0.38 * 58.00 = 29.36 kips/bolt
Angle bearing capacity, (phi)Rnang = min((phi)Rnsang,(phi)Rneang,(phi)Rndang) = min(42.82, 133.97, 29.36) = 29.36 kips/bolt
(phi)Rn = min((phi)Rnsupp, (phi)Rnang) = min(27.64, 29.36) = 27.64 kips/bolt
Bolt Shear Demand to Bearing ratio = 27.64 / 16.71 = 1.65

At Row 4, At Column 1:
Ribolt = 17.09 kips
Ri vector at Support   = <8.93, -14.56>
Lcssupp at Support spacing  = na
Lcesupp at Support edge    = 6.52 in.
(phi)Rnssupp at Support spacing = (phi) * hf1 * Lcs * (twsup/# bolt sides supported) * Fu = na
(phi)Rnesupp at Support edge = (phi) * hf1 * Lce * (twsup/# bolt sides supported) * Fu = 0.75 * 1.20 * 6.52 * (0.32/1) * 65.00 = 120.06 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(na, 120.06, 27.64) = 27.64 kips/bolt
Ri vector at Angle   = <-8.93, 14.56>
Lcsang at Angle spacing  = na
Lceang at Angle edge    = 5.33 in.
(phi)Rnsang at Angle spacing = (phi) * hf1 * Lcs * t * Fu = na
(phi)Rneang at Angle edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 5.33 * 0.38 * 58.00 = 104.27 kips/bolt
(phi)Rndang on Angle at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.75 * 0.38 * 58.00 = 29.36 kips/bolt
Angle bearing capacity, (phi)Rnang = min((phi)Rnsang,(phi)Rneang,(phi)Rndang) = min(na, 104.27, 29.36) = 29.36 kips/bolt
(phi)Rn = min((phi)Rnsupp, (phi)Rnang) = min(27.64, 29.36) = 27.64 kips/bolt
Bolt Shear Demand to Bearing ratio = 27.64 / 17.09 = 1.62

At Row 5, At Column 1:
Ribolt = 17.56 kips
Ri vector at Support   = <13.61, -11.10>
Lcssupp at Support spacing  = na
Lcesupp at Support edge    = 4.18 in.
(phi)Rnssupp at Support spacing = (phi) * hf1 * Lcs * (twsup/# bolt sides supported) * Fu = na
(phi)Rnesupp at Support edge = (phi) * hf1 * Lce * (twsup/# bolt sides supported) * Fu = 0.75 * 1.20 * 4.18 * (0.32/1) * 65.00 = 77.10 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(na, 77.10, 27.64) = 27.64 kips/bolt
Ri vector at Angle   = <-13.61, 11.10>
Lcsang at Angle spacing  = na
Lceang at Angle edge    = 3.46 in.
(phi)Rnsang at Angle spacing = (phi) * hf1 * Lcs * t * Fu = na
(phi)Rneang at Angle edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 3.46 * 0.38 * 58.00 = 67.75 kips/bolt
(phi)Rndang on Angle at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.75 * 0.38 * 58.00 = 29.36 kips/bolt
Angle bearing capacity, (phi)Rnang = min((phi)Rnsang,(phi)Rneang,(phi)Rndang) = min(na, 67.75, 29.36) = 29.36 kips/bolt
(phi)Rn = min((phi)Rnsupp, (phi)Rnang) = min(27.64, 29.36) = 27.64 kips/bolt
Bolt Shear Demand to Bearing ratio = 27.64 / 17.56 = 1.57

Min Bolt Shear Demand to Bearing ratio Support and Angle for vertical shear only
 = min(1.00, 0.99, 1.62, 1.65, 1.62, 1.57) = 0.99

BEARING AT SUPPORT AND ANGLE SUMMARY:
Bearing Capacity at Vertical Shear Load Only, Rbv = Min Bolt Shear Demand to Bearing Ratio * Bolt Shear = 0.99 * 68.03 = 67.27 kips
67.27 kips >= 36.67 kips (OK)

Web Depth = d - [Top Cope Depth] - [Bottom Cope Depth] = 20.80 - 1.25 - 4.00 = 15.55 in.

Using AISC 14th Ed. Equation J4-3
Gross Area (Shear), Agross = [Web Depth] * tw = 15.55 * 0.38 = 5.91 in^2
Shear Yielding, (phi)Vny = (phi) * 0.6 * Fybeam * Agross = 1.00 * 0.6 * 50.00 * 5.91 = 177.27 kips

Using AISC 14th Ed. Equation J4-4
Net Area (Shear), Anet = ([Web Depth] - ([# rows] * [Diameter + 0.06])) * tw 
    = (15.55 - (5 * 0.88)) * 0.38 = 4.25 in^2
Shear Rupture, (phi)Vnu = (phi) * 0.6 * Fubeam * Anet = 0.75 * 0.6 * 65.00 * 4.25 = 124.21 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]) = 1.75 + 12.00 = 13.75 in.
Net Shear Length = Gross Shear Length - (# rows - 0.5) * (hole size + 0.06) = 13.75 - (5 - 0.5) * 0.88 = 9.81 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 * 0.38 * ((0.60 * 65.00 * 9.81) + (1.00 * 65.00 * 1.06)) = 128.75 kips
2. (phi) * [material thickness] * ((0.60 * Fybeam * [gross shear length]) + (Ubs * Fubeam * [net tension length])) 
    = 0.75 * 0.38 * ((0.60 * 50.00 * 13.75) + (1.00 * 65.00 * 1.06)) = 137.25 kips
Block Shear = 128.75 kips

Block Shear (1) Total = Block Shear (1) = 128.75 kips
128.75 kips >= Reaction V = 36.67 kips (OK)

Block Shear for Axial T/C is not required.

Buckling and Flexure at Longest Cope (Top and Bottom Copes at Section)
Eccentricity at Section, e = 3.66 in.
If beam is coped at both top and bottom flanges,

Using AISC 14th Ed. Equation 9-14 through 9-18, Fcr = Fy * Q
tw = 0.38 in.
ho = 15.55 in.
c = 3.00 in.
lambda = (ho * Fy ^ 0.5) / ( 10 * tw * ( 475.00 + 280.00 * (ho / c)^2 ) ^0.5 ) = 
 = 15.55 * 50.00^0.5 / (10 * 0.38 * (475.00 + 280.00 * (15.55/3.00)^2 )^0.5) = 0.32
When lambda <= 0.70, Q=1
Q = 1.00
Fcrmin =phi * Fcr = 0.90 * 50.00 * 1.00 = 45.00 ksi
Snet1 (bolt holes not applicable) = 15.31 in^3
Snet2 (bolt holes applicable) = 15.31 in^3
Znet1 (bolt holes not applicable) = 22.97 in^3
Znet2 (bolt holes applicable) = 22.97 in^3

Using AISC 14th Ed. Equation 9-6
Buckling = Fcr * Snet1 / e = 45.00 * 15.31 / 3.66 = 188.42 kips

Using AISC 14th Ed. Equation 9-19
Flexural Yielding = (phi) * Fy * Snet1 / e = 0.90 * 50.00 * 15.31 / 3.66 = 188.42 kips

Using AISC 14th Ed. Equation 9-4
Flexural Rupture = (phi) * Fu * Znet2 / e = 0.75 * 65.00 * 22.97 / 3.66 = 306.19 kips


Buckling and Flexure at Furthest Bolt Line within Cope (Top and Bottom Copes at Section)
Eccentricity at Section, e = 2.16 in.
If beam is coped at both top and bottom flanges,

Using AISC 14th Ed. Equation 9-14 through 9-18, Fcr = Fy * Q
tw = 0.38 in.
ho = 15.55 in.
c = 3.00 in.
lambda = (ho * Fy ^ 0.5) / ( 10 * tw * ( 475.00 + 280.00 * (ho / c)^2 ) ^0.5 ) = 
 = 15.55 * 50.00^0.5 / (10 * 0.38 * (475.00 + 280.00 * (15.55/3.00)^2 )^0.5) = 0.32
When lambda <= 0.70, Q=1
Q = 1.00
Fcrmin =phi * Fcr = 0.90 * 50.00 * 1.00 = 45.00 ksi
Snet1 (bolt holes not applicable) = 15.31 in^3
Snet2 (bolt holes applicable) = 11.44 in^3
Znet1 (bolt holes not applicable) = 22.97 in^3
Znet2 (bolt holes applicable) = 16.91 in^3

Using AISC 14th Ed. Equation 9-6
Buckling = Fcr * Snet1 / e = 45.00 * 15.31 / 2.16 = 319.41 kips

Using AISC 14th Ed. Equation 9-19
Flexural Yielding = (phi) * Fy * Snet1 / e = 0.90 * 50.00 * 15.31 / 2.16 = 319.41 kips

Using AISC 14th Ed. Equation 9-4
Flexural Rupture = (phi) * Fu * Znet2 / e = 0.75 * 65.00 * 16.91 / 2.16 = 381.99 kips


Section Bending Strength Calculations Summary:

   Coped Beam Buckling and Flexure at Longest Cope (Top and Bottom Copes at Section)
   Buckling : 188.42 >= 36.67 kips (OK)
   Flexural Yielding : 188.42 >= 36.67 kips (OK)
   Flexural Rupture : 306.19 >= 36.67 kips (OK)

   Coped Beam Buckling and Flexure at Furthest Bolt Line within Cope (Top and Bottom Copes at Section)
   Buckling : 319.41 >= 36.67 kips (OK)
   Flexural Yielding : 319.41 >= 36.67 kips (OK)
   Flexural Rupture : 381.99 >= 36.67 kips (OK)

Support Angle Leg 


Using AISC 14th Ed. Equation J4-3
Gross Area, Ag = 0.38 * 14.50 = 5.44 in^2
Shear Yielding, (phi)Vny = (phi) * 0.6 * Fya * Ag = 1.00 * 0.6 * 36.00 * 5.44 = 117.45 kips

Using AISC 14th Ed. Equation J4-4
Net Area, An = (14.50 - (5 * (0.81 + 1/16))) * 0.38 = 3.80 in^2
Shear Rupture, (phi)Vnu = (phi) * 0.6 * Fua * An = 0.75 * 0.6 * 58.00 * 3.80 = 99.10 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 = (14.50 - 1.25) = 13.25 in.
Net Shear Length = 13.25 - (4.50 * (0.81 + 1/16)) = 9.31 in.
Gross Tension Length = [edge dist.] = 1.00 in.
Net Tension Length = (1.00 - (0.81 + 1/16)/2) = 0.56 in.
1. (phi) * [material thickness] * ((0.60 * Fua* [net shear length]) + (Ubs * Fua * [net tension length])) 
    = 0.75 * 0.38 * ((0.60 * 58.00 * 9.31) + (1.00 * 58.00 * 0.56)) = 100.37 kips
2. (phi) * [material thickness] * ((0.60 * Fya * [gross shear length]) + (Ubs * Fua * [net tension length])) 
    = 0.75 * 0.38 * ((0.60 * 36.00 * 13.25) + (1.00 * 58.00 * 0.56)) = 89.71 kips
Block Shear = 89.71 kips

Flexural and Buckling Strength:

Eccentricity at Bolt Column = 3.19
Zgross = 19.71 in^3
Znet   = 13.73 in^3
Sgross = 13.14 in^3
Snet   = 9.05 in^3

Using AISC 14th Ed. Equation 9-19
Flexural Yielding = (phi) * Fy * Sgross / e = 0.90 * 36.00 * 13.14 / 3.19 = 133.57 kips

Using AISC 14th Ed. Equation 9-4
Flexural Rupture = (phi) * Fu * Znet / e = 0.75 * 58.00 * 13.73 / 3.19 = 187.42 kips


Using AISC 14th Ed. Equation 9-14 through 9-18, Fcr = Fy * Q
tw = 0.38 in.
ho = 14.50 in.
c = 3.00 in.
lambda = (ho * Fy ^ 0.5) / ( 10 * tw * ( 475.00 + 280.00 * (ho / c)^2 ) ^0.5 ) = 
 = 14.50 * 36.00^0.5 / (10 * 0.38 * (475.00 + 280.00 * (14.50/3.00)^2 )^0.5) = 0.28
When lambda <= 0.70, Q=1
Q = 1.00
Fcrmin =phi * Fcr = 0.90 * 36.00 * 1.00 = 32.40 ksi

Using AISC 14th Ed. Equation 9-6
Buckling = Fcr * Sgross / e = 32.40 * 13.14 / 3.19 = 133.57 kips

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

Zgx = 19.71 in^3
Znx = 13.73 in^3

Eccentricity = 3.19 in.
Mrx = 36.67 * 3.19 = 116.89 kips-in

Shear Stress on Gross Section = 36.67 / 5.44 = 6.74 ksi
Shear Stress on Net Section = 36.67 / 3.80 = 9.66 ksi
Axial Stress on Gross Section due to Moment (shear) = 116.89 / 19.71 = 5.93 ksi
Axial Stress on Net Section due to Moment (shear) = 116.89 / 13.73 = 8.51 ksi

Shear Yield Stress Capacity (SYSC) = phi * 0.6 * Fy = 1.00 * 0.60 * 36.00 = 21.60 ksi
Tensile Yield Stress Capacity (TYSC) = phi * Fy = 0.90 * 36.00 = 32.40 ksi
Stress Interaction at Gross Section (elliptical):
(fvg / SYSC)^2 + (fag / TYSC )^2 = (6.74 / 21.60)^2 + (5.93 / 32.40 )^2 = 0.13 <= 1.0 (OK)
Shear Rupture Stress Capacity (SRSC) = phi * 0.6 * Fu = 0.75 * 0.60 * 58.00 = 26.10 ksi
Tensile Rupture Stress Capacity (TRSC) = phi * Fu = 0.75 * 58.00 = 43.50 ksi
Stress Interaction at Net Section (elliptical):
(fvn / SRSC)^2 + (fan / TRSC )^2 = (9.66 / 26.10)^2 + (8.51 / 43.50 )^2 = 0.18 <= 1.0 (OK)

Beam Angle Leg 


Using AISC 14th Ed. Equation J4-3
Gross Area, Ag = 0.38 * 14.50 = 5.44 in^2
Shear Yielding, (phi)Vny = (phi) * 0.6 * Fya * Ag = 1.00 * 0.6 * 36.00 * 5.44 = 117.45 kips

Using AISC 14th Ed. Equation J4-4
Net Area, An = (14.50 - (5 * (0.81 + 1/16))) * 0.38 = 3.80 in^2
Shear Rupture, (phi)Vnu = (phi) * 0.6 * Fua * An = 0.75 * 0.6 * 58.00 * 3.80 = 99.10 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 = (14.50 - 1.25) = 13.25 in.
Net Shear Length = 13.25 - (4.50 * (0.81 + 1/16) = 9.31 in.
Gross Tension Length = [edge dist.] = 1.00 in.
Net Tension Length = (1.00 - (0.81 + 1/16)/2) = 0.56 in.
1. (phi) * [material thickness] * ((0.60 * Fua* [net shear length]) + (Ubs * Fua * [net tension length])) 
    = 0.75 * 0.38 * ((0.60 * 58.00 * 9.31) + (1.00 * 58.00 * 0.56)) = 100.32 kips
2. (phi) * [material thickness] * ((0.60 * Fya * [gross shear length]) + (Ubs * Fua * [net tension length])) 
    = 0.75 * 0.38 * ((0.60 * 36.00 * 13.25) + (1.00 * 58.00 * 0.56)) = 89.67 kips
Block Shear = 89.67 kips

Block Shear for Axial T/C is not required.


Support Side Shear Yielding Capacity = 117.45 kips
117.45 kips >= Reaction V = 36.67 kips (OK)
Support Side Shear Rupture Capacity = 99.10 kips
99.10 kips >= Reaction V = 36.67 kips (OK)
Support Side Vertical Block Shear Capacity = 89.71 kips
89.71 kips >= Reaction V = 36.67 kips (OK)
Beam Side Shear Yielding Capacity = 117.45 kips
117.45 kips >= Reaction V = 36.67 kips (OK)
Beam Side Shear Rupture Capacity = 99.10 kips
99.10 kips >= Reaction V = 36.67 kips (OK)
Support Side Flexure Yielding Capacity = 133.57 kips
133.57 kips >= Reaction V = 36.67 kips (OK)
Support Side Flexure Rupture Capacity = 187.42 kips
187.42 kips >= Reaction V = 36.67 kips (OK)
Support Side Bending Buckling Capacity = 133.57 kips
133.57 kips >= Reaction V = 36.67 kips (OK)
Beam Side Vertical Block Shear Capacity = 89.67 kips
89.67 kips >= Reaction V = 36.67 kips (OK)

(Not applicable / No results )