Qnect Logo

Connection Calcs Report

Company: - Josh Qnect -
Job Title: - Qnect Demo 2000 Tons -
Session Title: Baseline
Session Date: 2018-08-31 18:06:55
Model Name: Josh_Demo_2000_Tons.db1
B+Op Status: B+Op was disabled
Building Code: AISC-14
Design Type: LRFD
Engineering Units: Imperial
Bolt Catalog: ASTM Imperial
Profile Catalog: ASTM Imperial
Plate Material Grade Catalog: ASTM Imperial
Plate Thickness Catalog: Imperial
Detailing Distances Dimensions: Imperial
Materials:
Weld Shear Plate Angle Bm Web Doubler Plate Stabilizer Plate End Plate Col Moment Plate Col Stiffener Plate Col Web Doubler Plate
E70 A572-GR.50 A36 A572-GR.50 A572-GR.50 A572-GR.50 A572-GR.50 A572-GR.50 A572-GR.50

Summary Reports: Job Standard Summary  |  Job Sample Calcs Report  |  B+Op Comparison Report
Job Preferences Report  |  No Connections Summary  |  No Connections Detailed  |  No Connections Reference Map
 
Shear Plate Reports: Specs  Strengths (Shear Only Connections)  Strengths (Shear & Axial Connections)  Welds  Doublers
Single Angle Reports:  Specs  Strengths (Shear & Axial)  Welds  Doublers
Double Angle Reports:  Support Side Specs  Beam Side Specs  Strengths (Shear & Axial)  Welds  Doublers
Moment Reports:  Specs  Support Strengths  Support Reinforcement Strengths  Moment Plate Strengths  Welds
Moment Group Reports:  Doubler Plate Specs  Doubler Plate Welds  Stiffener / Moment Plate Specs  Stiffener / Moment Plate Welds

Connection Number:
bb.2wb.s.00001.00002
 
Main Calcs:
DOUBLE ANGLES Welded to Beam, Bolted to Support CONNECTION SUMMARY

Girder profile: W16X26
Filler Beam profile: W16X26
Slope: 0.00 deg.
Skew: 90.00
Vertical Offset: 0.00
Horizontal Offset: 3.34
Span: 35.92 ft.
Reaction, V: 12.28 kips
Shear Capacity, Rn: 55.11 kips
Design/Reference according to AISC 14th Ed. - ASD
Beam material grade: A992
Support material grade: A992
Angle material grade: A36
Angle1 Profile: L6X6X1
       Length = 8.500 in.
       Support side bolts: 3 rows x 1 column 1 in. Diameter A325N_TC bolts
       Support side bolt vertical spacing: 3 in.
Angle2 Profile: L8X6X1
       Length = 8.500 in.
       Support side bolts: 3 rows x 1 column 1 in. Diameter A325N_TC bolts
       Support side bolt vertical spacing: 3 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 = 0.5 in.
Top cope depth: 1 in.
Top cope length: 2.75 in.
Bottom cope depth: 1 in.
Bottom cope length: 2.75 in.


Welded Angle Leg At Beam : 
Angle 1 Leg Edge Distances : 
   Distance from top of Angle to top flange of beam : 2 in.
   Distance from bottom of Angle to bottom flange of beam : 5.2 in.

Angle 2 Leg Edge Distances : 
   Distance from top of Angle to top flange of beam : 2 in.
   Distance from bottom of Angle to bottom flange of beam : 5.2 in.

Bolted Angle Leg At Support : 
Angle 1 Leg Distances : 
   Down distance from top of filler beam flange : 3.25 in.
   Gage at Bolt : 3.25 in.
   Edge distance at vertical edge : 2.88 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 : 3.25 in.
   Gage at Bolt : 6.59 in.
   Edge distance at vertical edge : 1.54 in.
   Edge distance at top edge : 1.25 in.
   Edge distance at bottom edge : 1.25 in.

Holes in Support Girder : STD diameter = 1.0625 in.
Holes in Support Angle Leg : SSL slot width = 1.0625 in., slot length = 1.3125 in.
Bolt Strength Calcs:
BOLT STRENGTH SUPPORT SIDE:

Angle 1 Bolt Strength (at Shear Load Only):
Gage ratio:  gage1 ratio = gage2 / (gage1 + gage2) = 6.59 / (3.25 + 6.59) = 0.67
Required tension stress (frt) = gage1 ratio * axial reaction    / shared bolt row count / bolt area  = 0.670 * 0.000 / 2 / 0.785 = 0.000 ksi
Required shear stress   (frv) = gage1 ratio * vertical reaction / bolt row count  / bolt area  = 0.67 * 12.28 / 3 / 0.79 = 3.49 ksi
C = no of bolts = 3.000
Using Table 7-1 to determine (1/omega) * rn:
Rn = (1/omega) * rn * C = 21.21 * 3.00 = 63.62 kips

Angle 1 Bolt Shear Strength Subtotal = 63.62 kips

Angle 2 Bolt Strength (at Shear Load Only):
Gage ratio:  gage2 ratio = gage1 / (gage1 + gage2) = 3.25 / (3.25 + 6.59) = 0.33
Required tension stress (frt) = gage2 ratio * axial reaction    / shared bolt row count / bolt area  = 0.330 * 0.000 / 2 / 0.785 = 0.000 ksi
Required shear stress   (frv) = gage2 ratio * vertical reaction / bolt row count  / bolt area  = 0.33 * 12.28 / 3 / 0.79 = 1.72 ksi
C = no of bolts = 3.000
Using Table 7-1 to determine (1/omega) * rn:
Rn = (1/omega) * rn * C = 21.21 * 3.00 = 63.62 kips

Angle 2 Bolt Shear Strength Subtotal = 63.62 kips


Total Support Side Bolt Shear Strength = min( Angle1 Bolt Shear/Gage1 Ratio , Angle2 Bolt Shear/Gage2 Ratio ) = min (94.99, 192.61) = 94.99 kips
Bolt Bearing Calcs:
BOLT BEARING AT SUPPORT SIDE:
Angle 1, Vertical Shear Loading: 
At Row 1, At Column 1:
Ri1 = 21.21 kips
Lcssupp at Support spacing  = 1.94 in.
Lcesupp at Support edge    = 11.92 in.
1/omegaRnssupp at Support spacing = 1/omega * hf1 * Lcs * (twsup/# bolt sides supported) * Fu = 0.50 * 1.20 * 1.94 * (0.25/1) * 65.00 = 18.89 kips/bolt
1/omegaRnesupp at Support edge = 1/omega * hf1 * Lce * (twsup/# bolt sides supported) * Fu = 0.50 * 1.20 * 11.92 * (0.25/1) * 65.00 = 116.21 kips/bolt
1/omegaRndsupp on Support at Bolt Diameter   = 1/omega * hf2 * db * (twsup/# bolt sides supported) * Fu = 0.50 * 2.40 * 1.00 * (0.25/1) * 65.00 = 19.50 kips/bolt
Support bearing capacity, 1/omegaRnsupp = min(1/omegaRnssupp,1/omegaRnesupp,1/omegaRndsupp) = min(18.89, 116.21, 19.50) = 18.89 kips/bolt
Lcsang1 at Angle 1 spacing  = 1.94 in.
Lceang1 at Angle 1 edge    = 0.72 in.
1/omegaRnsang1 at Angle 1 spacing = 1/omega * hf1 * Lcs * t * Fu = 0.50 * 1.20 * 1.94 * 1.00 * 58.00 = 67.42 kips/bolt
1/omegaRneang1 at Angle 1 edge = 1/omega * hf1 * Lce * t * Fu = 0.50 * 1.20 * 0.72 * 1.00 * 58.00 = 25.01 kips/bolt
1/omegaRndang1 on Angle 1 at Bolt Diameter   = 1/omega * hf2 * db * t * Fu = 0.50 * 2.40 * 1.00 * 1.00 * 58.00 = 69.60 kips/bolt
Angle 1 bearing capacity, 1/omegaRnang1 = min(1/omegaRnsang1,1/omegaRneang1,1/omegaRndang1) = min(67.42, 25.01, 69.60) = 25.01 kips/bolt
1/omegaRn = min(Ri1, 1/omegaRnsupp, 1/omegaRnang1) = min(21.21, 18.891, 25.012) = 18.89 kips/bolt


At Row 2, At Column 1:
Ri1 = 21.21 kips
Lcssupp at Support spacing  = 1.94 in.
Lcesupp at Support edge    = 8.92 in.
1/omegaRnssupp at Support spacing = 1/omega * hf1 * Lcs * (twsup/# bolt sides supported) * Fu = 0.50 * 1.20 * 1.94 * (0.25/2) * 65.00 = 9.45 kips/bolt
1/omegaRnesupp at Support edge = 1/omega * hf1 * Lce * (twsup/# bolt sides supported) * Fu = 0.50 * 1.20 * 8.92 * (0.25/2) * 65.00 = 43.48 kips/bolt
1/omegaRndsupp on Support at Bolt Diameter   = 1/omega * hf2 * db * (twsup/# bolt sides supported) * Fu = 0.50 * 2.40 * 1.00 * (0.25/2) * 65.00 = 9.75 kips/bolt
Support bearing capacity, 1/omegaRnsupp = min(1/omegaRnssupp,1/omegaRnesupp,1/omegaRndsupp) = min(9.45, 43.48, 9.75) = 9.45 kips/bolt
Lcsang1 at Angle 1 spacing  = 1.94 in.
Lceang1 at Angle 1 edge    = 3.72 in.
1/omegaRnsang1 at Angle 1 spacing = 1/omega * hf1 * Lcs * t * Fu = 0.50 * 1.20 * 1.94 * 1.00 * 58.00 = 67.42 kips/bolt
1/omegaRneang1 at Angle 1 edge = 1/omega * hf1 * Lce * t * Fu = 0.50 * 1.20 * 3.72 * 1.00 * 58.00 = 129.41 kips/bolt
1/omegaRndang1 on Angle 1 at Bolt Diameter   = 1/omega * hf2 * db * t * Fu = 0.50 * 2.40 * 1.00 * 1.00 * 58.00 = 69.60 kips/bolt
Angle 1 bearing capacity, 1/omegaRnang1 = min(1/omegaRnsang1,1/omegaRneang1,1/omegaRndang1) = min(67.42, 129.41, 69.60) = 67.42 kips/bolt
1/omegaRn = min(Ri1, 1/omegaRnsupp, 1/omegaRnang1) = min(21.21, 9.445, 67.425) = 9.45 kips/bolt


At Row 3, At Column 1:
Ri1 = 21.21 kips
Lcssupp at Support spacing  = 1.94 in.
Lcesupp at Support edge    = 5.92 in.
1/omegaRnssupp at Support spacing = 1/omega * hf1 * Lcs * (twsup/# bolt sides supported) * Fu = 0.50 * 1.20 * 1.94 * (0.25/2) * 65.00 = 9.45 kips/bolt
1/omegaRnesupp at Support edge = 1/omega * hf1 * Lce * (twsup/# bolt sides supported) * Fu = 0.50 * 1.20 * 5.92 * (0.25/2) * 65.00 = 28.85 kips/bolt
1/omegaRndsupp on Support at Bolt Diameter   = 1/omega * hf2 * db * (twsup/# bolt sides supported) * Fu = 0.50 * 2.40 * 1.00 * (0.25/2) * 65.00 = 9.75 kips/bolt
Support bearing capacity, 1/omegaRnsupp = min(1/omegaRnssupp,1/omegaRnesupp,1/omegaRndsupp) = min(9.45, 28.85, 9.75) = 9.45 kips/bolt
Lcsang1 at Angle 1 spacing  = 1.94 in.
Lceang1 at Angle 1 edge    = 6.72 in.
1/omegaRnsang1 at Angle 1 spacing = 1/omega * hf1 * Lcs * t * Fu = 0.50 * 1.20 * 1.94 * 1.00 * 58.00 = 67.42 kips/bolt
1/omegaRneang1 at Angle 1 edge = 1/omega * hf1 * Lce * t * Fu = 0.50 * 1.20 * 6.72 * 1.00 * 58.00 = 233.81 kips/bolt
1/omegaRndang1 on Angle 1 at Bolt Diameter   = 1/omega * hf2 * db * t * Fu = 0.50 * 2.40 * 1.00 * 1.00 * 58.00 = 69.60 kips/bolt
Angle 1 bearing capacity, 1/omegaRnang1 = min(1/omegaRnsang1,1/omegaRneang1,1/omegaRndang1) = min(67.42, 233.81, 69.60) = 67.42 kips/bolt
1/omegaRn = min(Ri1, 1/omegaRnsupp, 1/omegaRnang1) = min(21.21, 9.445, 67.425) = 9.45 kips/bolt


Bearing Capacity at Shear Plane  = Sum{ Bearing At [(Row)i,(Column)i] } = 
18.891 + 9.445 + 9.445 = 37.78 kips


BOLT BEARING AT SUPPORT SIDE:
Angle 2, Vertical Shear Loading: 
At Row 1, At Column 1:
Ri1 = 21.21 kips
Lcssupp at Support spacing  = 1.94 in.
Lcesupp at Support edge    = 11.92 in.
1/omegaRnssupp at Support spacing = 1/omega * hf1 * Lcs * (twsup/# bolt sides supported) * Fu = 0.50 * 1.20 * 1.94 * (0.25/1) * 65.00 = 18.89 kips/bolt
1/omegaRnesupp at Support edge = 1/omega * hf1 * Lce * (twsup/# bolt sides supported) * Fu = 0.50 * 1.20 * 11.92 * (0.25/1) * 65.00 = 116.21 kips/bolt
1/omegaRndsupp on Support at Bolt Diameter   = 1/omega * hf2 * db * (twsup/# bolt sides supported) * Fu = 0.50 * 2.40 * 1.00 * (0.25/1) * 65.00 = 19.50 kips/bolt
Support bearing capacity, 1/omegaRnsupp = min(1/omegaRnssupp,1/omegaRnesupp,1/omegaRndsupp) = min(18.89, 116.21, 19.50) = 18.89 kips/bolt
Lcsang2 at Angle 2 spacing  = 1.94 in.
Lceang2 at Angle 2 edge    = 0.72 in.
1/omegaRnsang2 at Angle 2 spacing = 1/omega * hf1 * Lcs * t * Fu = 0.50 * 1.20 * 1.94 * 1.00 * 58.00 = 67.42 kips/bolt
1/omegaRneang2 at Angle 2 edge = 1/omega * hf1 * Lce * t * Fu = 0.50 * 1.20 * 0.72 * 1.00 * 58.00 = 25.01 kips/bolt
1/omegaRndang2 on Angle 2 at Bolt Diameter   = 1/omega * hf2 * db * t * Fu = 0.50 * 2.40 * 1.00 * 1.00 * 58.00 = 69.60 kips/bolt
Angle 2 bearing capacity, 1/omegaRnang2 = min(1/omegaRnsang2,1/omegaRneang2,1/omegaRndang2) = min(67.42, 25.01, 69.60) = 25.01 kips/bolt
1/omegaRn = min(Ri1, 1/omegaRnsupp, 1/omegaRnang2) = min(21.21, 18.891, 25.012) = 18.89 kips/bolt


At Row 2, At Column 1:
Ri1 = 21.21 kips
Lcssupp at Support spacing  = 1.94 in.
Lcesupp at Support edge    = 8.92 in.
1/omegaRnssupp at Support spacing = 1/omega * hf1 * Lcs * (twsup/# bolt sides supported) * Fu = 0.50 * 1.20 * 1.94 * (0.25/2) * 65.00 = 9.45 kips/bolt
1/omegaRnesupp at Support edge = 1/omega * hf1 * Lce * (twsup/# bolt sides supported) * Fu = 0.50 * 1.20 * 8.92 * (0.25/2) * 65.00 = 43.48 kips/bolt
1/omegaRndsupp on Support at Bolt Diameter   = 1/omega * hf2 * db * (twsup/# bolt sides supported) * Fu = 0.50 * 2.40 * 1.00 * (0.25/2) * 65.00 = 9.75 kips/bolt
Support bearing capacity, 1/omegaRnsupp = min(1/omegaRnssupp,1/omegaRnesupp,1/omegaRndsupp) = min(9.45, 43.48, 9.75) = 9.45 kips/bolt
Lcsang2 at Angle 2 spacing  = 1.94 in.
Lceang2 at Angle 2 edge    = 3.72 in.
1/omegaRnsang2 at Angle 2 spacing = 1/omega * hf1 * Lcs * t * Fu = 0.50 * 1.20 * 1.94 * 1.00 * 58.00 = 67.42 kips/bolt
1/omegaRneang2 at Angle 2 edge = 1/omega * hf1 * Lce * t * Fu = 0.50 * 1.20 * 3.72 * 1.00 * 58.00 = 129.41 kips/bolt
1/omegaRndang2 on Angle 2 at Bolt Diameter   = 1/omega * hf2 * db * t * Fu = 0.50 * 2.40 * 1.00 * 1.00 * 58.00 = 69.60 kips/bolt
Angle 2 bearing capacity, 1/omegaRnang2 = min(1/omegaRnsang2,1/omegaRneang2,1/omegaRndang2) = min(67.42, 129.41, 69.60) = 67.42 kips/bolt
1/omegaRn = min(Ri1, 1/omegaRnsupp, 1/omegaRnang2) = min(21.21, 9.445, 67.425) = 9.45 kips/bolt


At Row 3, At Column 1:
Ri1 = 21.21 kips
Lcssupp at Support spacing  = 1.94 in.
Lcesupp at Support edge    = 5.92 in.
1/omegaRnssupp at Support spacing = 1/omega * hf1 * Lcs * (twsup/# bolt sides supported) * Fu = 0.50 * 1.20 * 1.94 * (0.25/2) * 65.00 = 9.45 kips/bolt
1/omegaRnesupp at Support edge = 1/omega * hf1 * Lce * (twsup/# bolt sides supported) * Fu = 0.50 * 1.20 * 5.92 * (0.25/2) * 65.00 = 28.85 kips/bolt
1/omegaRndsupp on Support at Bolt Diameter   = 1/omega * hf2 * db * (twsup/# bolt sides supported) * Fu = 0.50 * 2.40 * 1.00 * (0.25/2) * 65.00 = 9.75 kips/bolt
Support bearing capacity, 1/omegaRnsupp = min(1/omegaRnssupp,1/omegaRnesupp,1/omegaRndsupp) = min(9.45, 28.85, 9.75) = 9.45 kips/bolt
Lcsang2 at Angle 2 spacing  = 1.94 in.
Lceang2 at Angle 2 edge    = 6.72 in.
1/omegaRnsang2 at Angle 2 spacing = 1/omega * hf1 * Lcs * t * Fu = 0.50 * 1.20 * 1.94 * 1.00 * 58.00 = 67.42 kips/bolt
1/omegaRneang2 at Angle 2 edge = 1/omega * hf1 * Lce * t * Fu = 0.50 * 1.20 * 6.72 * 1.00 * 58.00 = 233.81 kips/bolt
1/omegaRndang2 on Angle 2 at Bolt Diameter   = 1/omega * hf2 * db * t * Fu = 0.50 * 2.40 * 1.00 * 1.00 * 58.00 = 69.60 kips/bolt
Angle 2 bearing capacity, 1/omegaRnang2 = min(1/omegaRnsang2,1/omegaRneang2,1/omegaRndang2) = min(67.42, 233.81, 69.60) = 67.42 kips/bolt
1/omegaRn = min(Ri1, 1/omegaRnsupp, 1/omegaRnang2) = min(21.21, 9.445, 67.425) = 9.45 kips/bolt


Bearing Capacity at Shear Plane  = Sum{ Bearing At [(Row)i,(Column)i] } = 
18.891 + 9.445 + 9.445 = 37.78 kips


Bearing At Support Side Summary:
Bearing Capacity = min(At Angle1 Shear Only/Gage1 Ratio, At Angle2 Shear Only/Gage2 Ratio) = min(37.78/0.67, 37.78/0.33) = 56.41 kips
Beam Strength Calcs:
Web Depth = d - [Top Cope Depth] - [Bottom Cope Depth] = 15.7 - 1 - 1 = 13.7 in.
Gross Area (Shear) = [Gross Shear Length] * tw = 13.70 * 0.25 = 3.42 in^2
Net Area (Shear) = [Gross Shear Length] * tw = 13.70 * 0.25 = 3.42 in^2

Using Eq.J4-3:
Shear Yielding = (1/omega) * 0.6 * Fybeam * [Gross Area] = 0.67 * 0.6 * 50.00 * 3.42 = 68.50 kips

Using Eq.J4-4:
Shear Rupture = (1/omega) * 0.6 * Fubeam * [Net Area] = 0.50 * 0.6 * 65.00 * 3.42 = 66.79 kips


Block Shear

Using Eq.J4-5:
Block Shear = {(1/omega) * ((0.6 * Fu * Anv) + (Ubs * Fu * Ant))} <= {(1/omega) * ((0.6 * Fy * Agv) + (Ubs * Fu * Ant))}

Block Shear not required.


Buckling and Flexure at Longest Cope (Top and Bottom Copes at Section)
Eccentricity at Section, e = 3.38 in.
If beam is coped at both top and bottom flanges,

Using Eq. 9-14 through 9-18, Fcr = Fy * Q
tw = 0.25 in.
ho = 13.70 in.
c = 2.75 in.
lambda = (ho * Fy ^ 0.5) / ( 10 * tw * ( 475.00 + 280.00 * (ho / c)^2 ) ^0.5 ) = 
 = 13.70 * 50.00^0.5 / (10 * 0.25 * (475.00 + 280.00 * (13.70/2.75)^2 )^0.5) = 0.45
When lambda <= 0.70, Q=1
Q = 1.00
Fcrmin =1/omega * Fcr = 0.60 * 50.00 * 1.00 = 30.00 ksi
Snet1 (bolt holes not applicable) = 7.82 in^3
Snet2 (bolt holes applicable) = 7.82 in^3
Znet = 11.73 in^3

Using Eq. 9-6
Buckling = Fcr * Snet1 / e = 30.00 * 7.82 / 3.38 = 69.51 kips

Using Eq. 9-19
Flexural Yielding = (1/omega) * Fy * Snet1 / e = 0.60 * 50.00 * 7.82 / 3.38 = 69.51 kips

Using Eq. 9-4
Flexural Rupture = (1/omega) * Fu * Znet / e = 0.50 * 65.00 * 11.73 / 3.38 = 112.96 kips


Section Bending Strength Calculations Summary:

   Coped Beam Buckling and Flexure at Longest Cope (Top and Bottom Copes at Section)
   Buckling : 69.51 >= 12.28 kips (OK)
   Flexural Yielding : 69.51 >= 12.28 kips (OK)
   Flexural Rupture : 112.96 >= 12.28 kips (OK)
Double Angles Welded Bolted Calcs:
Angle1 

Support Angle Leg 


Block Shear

Using Eq.J4-5:
Block Shear = {(1/omega) * ((0.6 * Fu * Anv) + (Ubs * Fu * Ant))} <= {(1/omega) * ((0.6 * Fy * Agv) + (Ubs * Fu * Ant))}
Block 1 (Shear): 
Gross Shear Length = (8.5 - 1.25) = 7.25 in.
Net Shear Length = 7.25 - (2.5 * (1.06 + 1/16)) = 4.44 in.
Gross Tension Length = [edge dist.] = 2.88 in.
Net Tension Length = (2.88 - (1.31 + 1/16)/2) = 2.19 in.
1. (1/omega) * [material thickness] * ((0.60 * Fua* [net shear length]) + (Ubs * Fua * [net tension length])) 
    = 0.50 * 1.00 * ((0.60 * 58.00 * 4.44) + (1.00 * 58.00 * 2.19)) = 140.65 kips
2. (1/omega) * [material thickness] * ((0.60 * Fya * [gross shear length]) + (Ubs * Fua * [net tension length])) 
    = 0.50 * 1.00 * ((0.60 * 36.00 * 7.25) + (1.00 * 58.00 * 2.19)) = 141.74 kips
Block Shear = 140.65 kips

Gross Area = 1.00 * 8.50 = 8.50 in^2
Net Area = (8.50 - (3 *(1.06 + 1/16)) * 1.00 = 5.12 in^2

Using Eq.J4-3:
Shear Yielding = (1/omega) * 0.6 * Fya * [Gross Area] = 0.67 * 0.6 * 36.00 * 8.50 = 122.40 kips

Using Eq.J4-4:
Shear Rupture = (1/omega) * 0.6 * Fua * [Net Area] = 0.50 * 0.6 * 58.00 * 5.12 = 89.17 kips


Rotational Ductility Check
Using Eq. 9-37
Minimum bolt diameter = 0.16*tf*sqrt(Fy/b * (b^2/L^2 + 2)) = 0.16*1.00*sqrt(36.00/1.62 * (1.62^2/8.50^2 + 2)) = 1.09 in.
Bolt diameter required = min(minimum bolt diameter, 0.69*sqrt(ts)) = min(1.09, 0.98) = 0.98 in.


Beam Angle Leg 

Gross Area = 1.00 * 8.50 = 8.50 in^2
Net Area = 8.50 in^2

Using Eq.J4-3:
Shear Yielding = (1/omega) * 0.6 * Fyangle * [Gross Area] = 0.67 * 0.6 * 36.00 * 8.50 = 122.40 kips

Using Eq.J4-4:
Shear Rupture = (1/omega) * 0.6 * Fuangle * [Net Area] = 0.50 * 0.6 * 58.00 * 8.50 = 147.90 kips


Flexural and Buckling Strength:

Eccentricity at Weld = 4.45
Zgross = 18.06 in^3
Znet   = 18.06 in^3
Sgross = 12.04 in^3
Snet   = 12.04 in^3

Using Eq. 9-19
Flexural Yielding = (1/omega) * Fy * Sgross / e = 0.60 * 36.00 * 12.04 / 4.45 = 58.47 kips

Using Eq. 9-4
Flexural Rupture = (1/omega) * Fu * Znet / e = 0.50 * 58.00 * 18.06 / 4.45 = 117.74 kips


Using Eq. 9-14 through 9-18, Fcr = Fy * Q
tw = 1.00 in.
ho = 8.50 in.
c = 4.45 in.
lambda = (ho * Fy ^ 0.5) / ( 10 * tw * ( 475.00 + 280.00 * (ho / c)^2 ) ^0.5 ) = 
 = 8.50 * 36.00^0.5 / (10 * 1.00 * (475.00 + 280.00 * (8.50/4.45)^2 )^0.5) = 0.13
When lambda <= 0.70, Q=1
Q = 1.00
Fcrmin =1/omega * Fcr = 0.60 * 36.00 * 1.00 = 21.60 ksi

Using Eq. 9-6
Buckling = Fcr * Sgross / e = 21.60 * 12.04 / 4.45 = 58.47 kips

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

Zgx = 18.06 in^3
Znx = 18.06 in^3
Zgy = 2.12 in^3
Zny = 2.12 in^3

Mrx = vertical reaction * ex = 8.22 * 4.45 = 36.59 kips-in
Mry = axial reaction * ey = 0.00 * 0.62 = 0.00 kips-in
Mcx = 1/omega * Zgx * Min(Fy, Fcr) = 0.60 * 18.06 * Min(36, 36) = 390.15 kips-in
Mcy = 1/omega * Zgy * Fy = 0.60 * 2.12 * 36 = 45.90 kips-in
Shear Stress on Gross Section = 8.22 / 8.50 = 0.97 ksi
Shear Stress on Net Section = 8.22 / 8.50 = 0.97 ksi
Axial Stress on Gross Section due to Axial force = 0.00 / 8.50 = 0.00 ksi
Axial Stress on Net Section due to Axial force = 0.00 / 8.50 = 0.00 ksi
Axial Stress on Gross Section due to Moment (shear) = 36.59 / 18.06 = 2.03 ksi
Axial Stress on Net Section due to Moment (shear) = 36.59 / 18.06 = 2.03 ksi
Axial Stress on Gross Section due to Moment (axial) = 0.00 / 2.12 = 0.00 ksi
Axial Stress on Net Section due to Moment (axial) = 0.00 / 2.12 = 0.00 ksi
Axial Stress on Gross Section (total) = 0.00 + 0.00 + 2.03 = 2.03 ksi
Axial Stress on Net Section (total) = 0.00 + 0.00 + 2.03 = 2.03 ksi

Shear Yield Stress Capacity (SYSC) = 1/omega * 0.6 * Fy =0.67 * 0.60 * 36.00 = 14.40 ksi
Tensile Yield Stress Capacity (TYSC) = 1/omega * Fy =0.60 * 36.00 = 21.60 ksi
Stress Interaction at Gross Section (elliptical):
(fvg / SYSC)^2 + (fag / TYSC )^2 = (0.97 / 14.40)^2 + (2.03 / 21.60 )^2 = 0.01 <= 1.0 (OK)
Shear Rupture Stress Capacity (SRSC) = 1/omega * 0.6 * Fu =0.50 * 0.60 * 58.00 = 17.40 ksi
Tensile Rupture Stress Capacity (TRSC) = 1/omega * Fu =0.50 * 58.00 = 29.00 ksi
Stress Interaction at Net Section (elliptical):
(fvn / SRSC)^2 + (fan / TRSC )^2 = (0.97 / 17.40)^2 + (2.03 / 29.00 )^2 = 0.01 <= 1.0 (OK)


Angle2 

Support Angle Leg 


Block Shear

Using Eq.J4-5:
Block Shear = {(1/omega) * ((0.6 * Fu * Anv) + (Ubs * Fu * Ant))} <= {(1/omega) * ((0.6 * Fy * Agv) + (Ubs * Fu * Ant))}
Block 1 (Shear): 
Gross Shear Length = (8.5 - 1.25) = 7.25 in.
Net Shear Length = 7.25 - (2.5 * (1.06 + 1/16)) = 4.44 in.
Gross Tension Length = [edge dist.] = 1.54 in.
Net Tension Length = (1.54 - (1.31 + 1/16)/2) = 0.85 in.
1. (1/omega) * [material thickness] * ((0.60 * Fua* [net shear length]) + (Ubs * Fua * [net tension length])) 
    = 0.50 * 1.00 * ((0.60 * 58.00 * 4.44) + (1.00 * 58.00 * 0.85)) = 101.79 kips
2. (1/omega) * [material thickness] * ((0.60 * Fya * [gross shear length]) + (Ubs * Fua * [net tension length])) 
    = 0.50 * 1.00 * ((0.60 * 36.00 * 7.25) + (1.00 * 58.00 * 0.85)) = 102.88 kips
Block Shear = 101.79 kips

Gross Area = 1.00 * 8.50 = 8.50 in^2
Net Area = (8.50 - (3 *(1.06 + 1/16)) * 1.00 = 5.12 in^2

Using Eq.J4-3:
Shear Yielding = (1/omega) * 0.6 * Fya * [Gross Area] = 0.67 * 0.6 * 36.00 * 8.50 = 122.40 kips

Using Eq.J4-4:
Shear Rupture = (1/omega) * 0.6 * Fua * [Net Area] = 0.50 * 0.6 * 58.00 * 5.12 = 89.17 kips


Rotational Ductility Check
Using Eq. 9-37
Minimum bolt diameter = 0.16*tf*sqrt(Fy/b * (b^2/L^2 + 2)) = 0.16*1.00*sqrt(36.00/4.96 * (4.96^2/8.50^2 + 2)) = 0.67 in.
Bolt diameter required = min(minimum bolt diameter, 0.69*sqrt(ts)) = min(0.67, 0.98) = 0.67 in.


Beam Angle Leg 

Gross Area = 1.00 * 8.50 = 8.50 in^2
Net Area = 8.50 in^2

Using Eq.J4-3:
Shear Yielding = (1/omega) * 0.6 * Fyangle * [Gross Area] = 0.67 * 0.6 * 36.00 * 8.50 = 122.40 kips

Using Eq.J4-4:
Shear Rupture = (1/omega) * 0.6 * Fuangle * [Net Area] = 0.50 * 0.6 * 58.00 * 8.50 = 147.90 kips


Flexural and Buckling Strength:

Eccentricity at Weld = 4.45
Zgross = 18.06 in^3
Znet   = 18.06 in^3
Sgross = 12.04 in^3
Snet   = 12.04 in^3

Using Eq. 9-19
Flexural Yielding = (1/omega) * Fy * Sgross / e = 0.60 * 36.00 * 12.04 / 4.45 = 58.47 kips

Using Eq. 9-4
Flexural Rupture = (1/omega) * Fu * Znet / e = 0.50 * 58.00 * 18.06 / 4.45 = 117.74 kips


Using Eq. 9-14 through 9-18, Fcr = Fy * Q
tw = 1.00 in.
ho = 8.50 in.
c = 4.45 in.
lambda = (ho * Fy ^ 0.5) / ( 10 * tw * ( 475.00 + 280.00 * (ho / c)^2 ) ^0.5 ) = 
 = 8.50 * 36.00^0.5 / (10 * 1.00 * (475.00 + 280.00 * (8.50/4.45)^2 )^0.5) = 0.13
When lambda <= 0.70, Q=1
Q = 1.00
Fcrmin =1/omega * Fcr = 0.60 * 36.00 * 1.00 = 21.60 ksi

Using Eq. 9-6
Buckling = Fcr * Sgross / e = 21.60 * 12.04 / 4.45 = 58.47 kips

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

Zgx = 18.06 in^3
Znx = 18.06 in^3
Zgy = 2.12 in^3
Zny = 2.12 in^3

Mrx = vertical reaction * ex = 4.06 * 4.45 = 18.05 kips-in
Mry = axial reaction * ey = 0.00 * 0.62 = 0.00 kips-in
Mcx = 1/omega * Zgx * Min(Fy, Fcr) = 0.60 * 18.06 * Min(36, 36) = 390.15 kips-in
Mcy = 1/omega * Zgy * Fy = 0.60 * 2.12 * 36 = 45.90 kips-in
Shear Stress on Gross Section = 4.06 / 8.50 = 0.48 ksi
Shear Stress on Net Section = 4.06 / 8.50 = 0.48 ksi
Axial Stress on Gross Section due to Axial force = 0.00 / 8.50 = 0.00 ksi
Axial Stress on Net Section due to Axial force = 0.00 / 8.50 = 0.00 ksi
Axial Stress on Gross Section due to Moment (shear) = 18.05 / 18.06 = 1.00 ksi
Axial Stress on Net Section due to Moment (shear) = 18.05 / 18.06 = 1.00 ksi
Axial Stress on Gross Section due to Moment (axial) = 0.00 / 2.12 = 0.00 ksi
Axial Stress on Net Section due to Moment (axial) = 0.00 / 2.12 = 0.00 ksi
Axial Stress on Gross Section (total) = 0.00 + 0.00 + 1.00 = 1.00 ksi
Axial Stress on Net Section (total) = 0.00 + 0.00 + 1.00 = 1.00 ksi

Shear Yield Stress Capacity (SYSC) = 1/omega * 0.6 * Fy =0.67 * 0.60 * 36.00 = 14.40 ksi
Tensile Yield Stress Capacity (TYSC) = 1/omega * Fy =0.60 * 36.00 = 21.60 ksi
Stress Interaction at Gross Section (elliptical):
(fvg / SYSC)^2 + (fag / TYSC )^2 = (0.48 / 14.40)^2 + (1.00 / 21.60 )^2 = 0.00 <= 1.0 (OK)
Shear Rupture Stress Capacity (SRSC) = 1/omega * 0.6 * Fu =0.50 * 0.60 * 58.00 = 17.40 ksi
Tensile Rupture Stress Capacity (TRSC) = 1/omega * Fu =0.50 * 58.00 = 29.00 ksi
Stress Interaction at Net Section (elliptical):
(fvn / SRSC)^2 + (fan / TRSC )^2 = (0.48 / 17.40)^2 + (1.00 / 29.00 )^2 = 0.00 <= 1.0 (OK)


Total Support Side Shear Yielding Capacity =  min(YieldAngle1/Gage1 Ratio, YieldAngle2/Gage2 Ratio) =  min(182.764 , 370.59) = 182.764 kips
Total Support Side Shear Rupture Capacity =  min(RuptureAngle1/Gage1 Ratio, RuptureAngle2/Gage2 Ratio) = min(133.154 , 269.994) = 133.154 kips
Total Support Side Vertical Block Shear Capacity =  min(BlockAngle1/Gage1 Ratio, BlockAngle2/Gage2 Ratio) = min(210.015 , 308.189) = 210.015 kips
Total Beam Side Shear Yielding Capacity =  min (YieldAngle1/Gage1 Ratio , YieldAngle2/Gage2 Ratio) = min(182.764 , 370.59) = 182.764 kips
Total Beam Side Shear Rupture Capacity =  min (RuptureAngle1/Gage1 Ratio , RuptureAngle2/Gage2 Ratio) = min(220.84 , 447.796) = 220.84 kips
Total Beam Side Flexure Yielding Capacity =  min (FlexureYieldAngle1/Gage1 Ratio , FlexureYieldAngle2/Gage2 Ratio) = min(87.3002 , 177.018) = 87.3002 kips
Total Beam Side Flexure Rupture Capacity =  min (FlexureRuptureAngle1/Gage1 Ratio , FlexureRuptureAngle2/Gage2 Ratio) = min(175.813 , 356.494) = 175.813 kips
Total Beam Side Bending Buckling Capacity =  min (BendingBucklingAngle1/Gage1 Ratio , BendingBucklingAngle2/Gage2 Ratio) = min(87.3002 , 177.018) = 87.3002 kips
Weld Calcs:
Angles Welded to Beam:

Angle1 Beam Weld
k = 0.65
ex = 4.45
a = ex / l = 4.45 / 8.50 = 0.52
Loadangle = 0.00 deg 
Weld Coefficient = 0.6 * Fexx * cphi * arrangement coefficient = 3.31
Dmax1 using min(eqn 9-2, tang - 0.062) 
 = min(tang * Fuang / ( Fexx * C1 * 0.044), tang - 0.062) 
 = min(1.000 * 58.000 / ( 70.000 * 1.000 * 0.044), 1.000 - 0.062) 
 = min(18.748, 15.000)
 = 15.000 
Dmax2 (using eqn 9-3)
 = twbeam * Fubeam / ( Fexx * C1 * 0.088 )
 = 0.250 * 65.000 / ( 70.000 * 1.000 * 0.088 ) 
 = 2.626 
Dmax3 = project max fillet weld = 12.000
Dmax=min(Dmax1, Dmax2, Dmax3) = min(15.000, 2.626, 12.000)
 = 2.626 

D = 4.00
Weld Strength = 1/omega * weld coefficient * l * D  = 0.50 * 3.31 * 8.50 * 2.63 = 36.91 kips

Angle2 Beam Weld
k = 0.65
ex = 4.45
a = ex / l = 4.45 / 8.50 = 0.52
Loadangle = 0.00 deg 
Weld Coefficient = 0.6 * Fexx * cphi * arrangement coefficient = 3.31
Dmax1 using min(eqn 9-2, tang - 0.062) 
 = min(tang * Fuang / ( Fexx * C1 * 0.044), tang - 0.062) 
 = min(1.000 * 58.000 / ( 70.000 * 1.000 * 0.044), 1.000 - 0.062) 
 = min(18.748, 15.000)
 = 15.000 
Dmax2 (using eqn 9-3)
 = twbeam * Fubeam / ( Fexx * C1 * 0.088 )
 = 0.250 * 65.000 / ( 70.000 * 1.000 * 0.088 ) 
 = 2.626 
Dmax3 = project max fillet weld = 12.000
Dmax=min(Dmax1, Dmax2, Dmax3) = min(15.000, 2.626, 12.000)
 = 2.626 

D = 4.00
Weld Strength = 1/omega * weld coefficient * l * D  = 0.50 * 3.31 * 8.50 * 2.63 = 36.91 kips

Total Welds Shear Strength = min( Angle1 Weld Shear/Gage Ratio at Angle1 , Angle2 Weld Shear/Gage Ratio at Angle2 ) = min ( 55.1, 112) = 55.1 kips