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Connection Calcs Report

Company: - Josh Qnect -
Job Title: - Qnect Demo 2000 Tons -
B+Op Status: B+Op was disabled for some sessions of this job
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 E70
Shear Plate A572-GR.50
Angle A36
Bm Web Doubler Plate A572-GR.50
Stabilizer Plate A572-GR.50
End Plate A572-GR.50
Col Moment Plate A572-GR.50
Col Stiffener Plate A572-GR.50
Col Web Doubler Plate A572-GR.50

Summary Reports: Job Standard Summary  |  Job Sample Calcs Report    |  B+Op Connection Comparison Report  |  Standard Connection Cost Report
Job Preferences Report  |  No Connections Summary  |  No Connections Detailed    |  No Connections Reference Map
 
Shear and Axial Reports:Shear Plate: Specs  Strengths (Shear Only Connections)  Welds  Doublers  Connection Cost Report
    Strengths (Shear & Axial Connections)      
 Single Angle:  Specs  Strengths (Shear & Axial)  Welds  Doublers  Connection Cost Report
 Double Angle Reports:  Support Side Specs  Strengths (Shear & Axial)  Welds  Doublers  Connection Cost Report
    Beam Side Specs        
 End Plate Reports:  Specs  Strengths (Shear & Axial)  Welds  Connection Cost Report
 
Moment Reports: Specs  Support Strengths  Beam Flange Welds  Connection Cost Report
 Moment Plates:  Specs  Strengths  Welds  
 Column Stiffeners:  Specs  Strengths  Welds  
 Column Web Doublers:  Specs  Strengths  Welds  
 Shear Plate:  Specs  Strengths  Welds  
 Double Angle:  Support Side Specs  Strengths  Welds  
   Beam Side Specs      
 

Connection Number:
bb.2wb.s.00004.00004
 
Main Calcs:
DOUBLE ANGLES Welded to Beam, Bolted to Support CONNECTION SUMMARY

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: 76.99 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 = 8.00 in.
       Support side bolts: 3 rows x 1 column 0.75 in. Diameter A325N_TC bolts
       Support side bolt vertical spacing: 3.00 in.
Angle2 Profile: L4X3-1/2X3/8
       Length = 8.00 in.
       Support side bolts: 3 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: 1.00 in.
Top cope length: 3.00 in.


Welded Angle Leg At Beam : 
Angle 1 Leg Edge Distances : 
   Distance from top of Angle to top flange of beam : 2.00 in.
   Distance from bottom of Angle to bottom flange of beam : 2.20 in.

Angle 2 Leg Edge Distances : 
   Distance from top of Angle to top flange of beam : 2.00 in.
   Distance from bottom of Angle to bottom flange of beam : 2.20 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 Support Girder : STD diameter = 0.81 in.
Holes in Support Angle Leg : SSL slot width = 0.81 in., slot length = 1.00 in.
Bolt Strength Calcs:
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    / shared bolt row count / bolt area  = 0.50 * 0.00 / 3 / 0.44 = 0.00 ksi
Required shear stress   (frv) = gage1 ratio * vertical reaction / bolt row count  / bolt area  = 0.50 * 17.00 / 3 / 0.44 = 6.41 ksi
C = no of bolts = 3.00
Using Table 7-1 to determine (phi)rn:
(phi)Rn = (phi)rn * C = 17.89 * 3.00 = 53.68 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    / shared bolt row count / bolt area  = 0.50 * 0.00 / 3 / 0.44 = 0.00 ksi
Required shear stress   (frv) = gage2 ratio * vertical reaction / bolt row count  / bolt area  = 0.50 * 17.00 / 3 / 0.44 = 6.41 ksi
C = no of bolts = 3.00
Using Table 7-1 to determine (phi)rn:
(phi)Rn = (phi)rn * C = 17.89 * 3.00 = 53.68 kips


Vertical Bolt Shear Capacity at Support and Angle 1 = 
 = Shear Load Only Angle 1 side/gage1 ratio = 53.68/0.50 = 107.36 kips
Vertical Bolt Shear Capacity at Support and Angle 2 = 
 = Shear Load Only Angle 2 side/gage2 ratio = 53.68/0.50 = 107.36 kips
Total Support Side Bolt Shear Capacity = min(107.36, 107.36) = 107.36 kips
107.36 kips >= Reaction V = 17.00 kips (OK)
Bolt Bearing Calcs:
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    = 14.49 in.
(phi)Rnssupp at Support spacing = (phi) * hf1 * Lcs * (twsup/# bolt sides supported) * Fu = 0.75 * 1.20 * 2.19 * (0.32/2) * 65.00 = 20.16 kips/bolt
(phi)Rnesupp at Support edge = (phi) * hf1 * Lce * (twsup/# bolt sides supported) * Fu = 0.75 * 1.20 * 14.49 * (0.32/2) * 65.00 = 133.55 kips/bolt
(phi)Rndsupp on Support at Bolt Diameter   = (phi) * hf2 * db * (twsup/# bolt sides supported) * Fu = 0.75 * 2.40 * 0.75 * (0.32/2) * 65.00 = 13.82 kips/bolt
Support bearing capacity, (phi)Rnsupp = min((phi)Rnssupp,(phi)Rnesupp,(phi)Rndsupp) = min(20.16, 133.55, 13.82) = 13.82 kips/bolt
Lcsang1 at Angle 1 spacing  = 2.19 in.
Lceang1 at Angle 1 edge    = 0.59 in.
(phi)Rnsang1 at Angle 1 spacing = (phi) * hf1 * Lcs * t * Fu = 0.75 * 1.20 * 2.19 * 0.38 * 65.00 = 47.99 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(47.99, 13.03, 32.91) = 13.03 kips/bolt
(phi)Rn = min((phi)Rnbolt, (phi)Rnsupp, (phi)Rnang1) = min(17.89, 13.82, 13.03) = 13.03 kips/bolt

At Row 2, At Column 1:
(phi)Rnbolt = 17.89 kips
Lcssupp at Support spacing  = 2.19 in.
Lcesupp at Support edge    = 11.49 in.
(phi)Rnssupp at Support spacing = (phi) * hf1 * Lcs * (twsup/# bolt sides supported) * Fu = 0.75 * 1.20 * 2.19 * (0.32/2) * 65.00 = 20.16 kips/bolt
(phi)Rnesupp at Support edge = (phi) * hf1 * Lce * (twsup/# bolt sides supported) * Fu = 0.75 * 1.20 * 11.49 * (0.32/2) * 65.00 = 105.90 kips/bolt
(phi)Rndsupp on Support at Bolt Diameter   = (phi) * hf2 * db * (twsup/# bolt sides supported) * Fu = 0.75 * 2.40 * 0.75 * (0.32/2) * 65.00 = 13.82 kips/bolt
Support bearing capacity, (phi)Rnsupp = min((phi)Rnssupp,(phi)Rnesupp,(phi)Rndsupp) = min(20.16, 105.90, 13.82) = 13.82 kips/bolt
Lcsang1 at Angle 1 spacing  = 2.19 in.
Lceang1 at Angle 1 edge    = 3.59 in.
(phi)Rnsang1 at Angle 1 spacing = (phi) * hf1 * Lcs * t * Fu = 0.75 * 1.20 * 2.19 * 0.38 * 65.00 = 47.99 kips/bolt
(phi)Rneang1 at Angle 1 edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 3.59 * 0.38 * 65.00 = 78.84 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(47.99, 78.84, 32.91) = 32.91 kips/bolt
(phi)Rn = min((phi)Rnbolt, (phi)Rnsupp, (phi)Rnang1) = min(17.89, 13.82, 32.91) = 13.82 kips/bolt

At Row 3, At Column 1:
(phi)Rnbolt = 17.89 kips
Lcssupp at Support spacing  = 2.19 in.
Lcesupp at Support edge    = 8.49 in.
(phi)Rnssupp at Support spacing = (phi) * hf1 * Lcs * (twsup/# bolt sides supported) * Fu = 0.75 * 1.20 * 2.19 * (0.32/2) * 65.00 = 20.16 kips/bolt
(phi)Rnesupp at Support edge = (phi) * hf1 * Lce * (twsup/# bolt sides supported) * Fu = 0.75 * 1.20 * 8.49 * (0.32/2) * 65.00 = 78.26 kips/bolt
(phi)Rndsupp on Support at Bolt Diameter   = (phi) * hf2 * db * (twsup/# bolt sides supported) * Fu = 0.75 * 2.40 * 0.75 * (0.32/2) * 65.00 = 13.82 kips/bolt
Support bearing capacity, (phi)Rnsupp = min((phi)Rnssupp,(phi)Rnesupp,(phi)Rndsupp) = min(20.16, 78.26, 13.82) = 13.82 kips/bolt
Lcsang1 at Angle 1 spacing  = 2.19 in.
Lceang1 at Angle 1 edge    = 6.59 in.
(phi)Rnsang1 at Angle 1 spacing = (phi) * hf1 * Lcs * t * Fu = 0.75 * 1.20 * 2.19 * 0.38 * 65.00 = 47.99 kips/bolt
(phi)Rneang1 at Angle 1 edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 6.59 * 0.38 * 65.00 = 144.65 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(47.99, 144.65, 32.91) = 32.91 kips/bolt
(phi)Rn = min((phi)Rnbolt, (phi)Rnsupp, (phi)Rnang1) = min(17.89, 13.82, 32.91) = 13.82 kips/bolt

Bearing Capacity at Support and Angle 1 for vertical shear only
 = Sum{ Bearing At [(Row)i,(Column)i] }
 = 13.03 + 13.82 + 13.82 = 40.67 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    = 14.49 in.
(phi)Rnssupp at Support spacing = (phi) * hf1 * Lcs * (twsup/# bolt sides supported) * Fu = 0.75 * 1.20 * 2.19 * (0.32/2) * 65.00 = 20.16 kips/bolt
(phi)Rnesupp at Support edge = (phi) * hf1 * Lce * (twsup/# bolt sides supported) * Fu = 0.75 * 1.20 * 14.49 * (0.32/2) * 65.00 = 133.55 kips/bolt
(phi)Rndsupp on Support at Bolt Diameter   = (phi) * hf2 * db * (twsup/# bolt sides supported) * Fu = 0.75 * 2.40 * 0.75 * (0.32/2) * 65.00 = 13.82 kips/bolt
Support bearing capacity, (phi)Rnsupp = min((phi)Rnssupp,(phi)Rnesupp,(phi)Rndsupp) = min(20.16, 133.55, 13.82) = 13.82 kips/bolt
Lcsang2 at Angle 2 spacing  = 2.19 in.
Lceang2 at Angle 2 edge    = 0.59 in.
(phi)Rnsang2 at Angle 2 spacing = (phi) * hf1 * Lcs * t * Fu = 0.75 * 1.20 * 2.19 * 0.38 * 65.00 = 47.99 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(47.99, 13.03, 32.91) = 13.03 kips/bolt
(phi)Rn = min((phi)Rnbolt, (phi)Rnsupp, (phi)Rnang2) = min(17.89, 13.82, 13.03) = 13.03 kips/bolt

At Row 2, At Column 1:
(phi)Rnbolt = 17.89 kips
Lcssupp at Support spacing  = 2.19 in.
Lcesupp at Support edge    = 11.49 in.
(phi)Rnssupp at Support spacing = (phi) * hf1 * Lcs * (twsup/# bolt sides supported) * Fu = 0.75 * 1.20 * 2.19 * (0.32/2) * 65.00 = 20.16 kips/bolt
(phi)Rnesupp at Support edge = (phi) * hf1 * Lce * (twsup/# bolt sides supported) * Fu = 0.75 * 1.20 * 11.49 * (0.32/2) * 65.00 = 105.90 kips/bolt
(phi)Rndsupp on Support at Bolt Diameter   = (phi) * hf2 * db * (twsup/# bolt sides supported) * Fu = 0.75 * 2.40 * 0.75 * (0.32/2) * 65.00 = 13.82 kips/bolt
Support bearing capacity, (phi)Rnsupp = min((phi)Rnssupp,(phi)Rnesupp,(phi)Rndsupp) = min(20.16, 105.90, 13.82) = 13.82 kips/bolt
Lcsang2 at Angle 2 spacing  = 2.19 in.
Lceang2 at Angle 2 edge    = 3.59 in.
(phi)Rnsang2 at Angle 2 spacing = (phi) * hf1 * Lcs * t * Fu = 0.75 * 1.20 * 2.19 * 0.38 * 65.00 = 47.99 kips/bolt
(phi)Rneang2 at Angle 2 edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 3.59 * 0.38 * 65.00 = 78.84 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(47.99, 78.84, 32.91) = 32.91 kips/bolt
(phi)Rn = min((phi)Rnbolt, (phi)Rnsupp, (phi)Rnang2) = min(17.89, 13.82, 32.91) = 13.82 kips/bolt

At Row 3, At Column 1:
(phi)Rnbolt = 17.89 kips
Lcssupp at Support spacing  = 2.19 in.
Lcesupp at Support edge    = 8.49 in.
(phi)Rnssupp at Support spacing = (phi) * hf1 * Lcs * (twsup/# bolt sides supported) * Fu = 0.75 * 1.20 * 2.19 * (0.32/2) * 65.00 = 20.16 kips/bolt
(phi)Rnesupp at Support edge = (phi) * hf1 * Lce * (twsup/# bolt sides supported) * Fu = 0.75 * 1.20 * 8.49 * (0.32/2) * 65.00 = 78.26 kips/bolt
(phi)Rndsupp on Support at Bolt Diameter   = (phi) * hf2 * db * (twsup/# bolt sides supported) * Fu = 0.75 * 2.40 * 0.75 * (0.32/2) * 65.00 = 13.82 kips/bolt
Support bearing capacity, (phi)Rnsupp = min((phi)Rnssupp,(phi)Rnesupp,(phi)Rndsupp) = min(20.16, 78.26, 13.82) = 13.82 kips/bolt
Lcsang2 at Angle 2 spacing  = 2.19 in.
Lceang2 at Angle 2 edge    = 6.59 in.
(phi)Rnsang2 at Angle 2 spacing = (phi) * hf1 * Lcs * t * Fu = 0.75 * 1.20 * 2.19 * 0.38 * 65.00 = 47.99 kips/bolt
(phi)Rneang2 at Angle 2 edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 6.59 * 0.38 * 65.00 = 144.65 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(47.99, 144.65, 32.91) = 32.91 kips/bolt
(phi)Rn = min((phi)Rnbolt, (phi)Rnsupp, (phi)Rnang2) = min(17.89, 13.82, 32.91) = 13.82 kips/bolt

Bearing Capacity at Support and Angle 2 for vertical shear only
 = Sum{ Bearing At [(Row)i,(Column)i] }
 = 13.03 + 13.82 + 13.82 = 40.67 kips

BEARING AT SUPPORT AND ANGLES SUMMARY:
Bearing Capacity at Vertical Shear Load Only, Rbv1 = Sum{ [(Row)i,(Column)i] } / gage1 ratio = 40.67 / 0.50 = 81.34 kips
Bearing Capacity at Vertical Shear Load Only, Rbv2 = Sum{ [(Row)i,(Column)i] } / gage2 ratio = 40.67 / 0.50 = 81.34 kips
Overall vertical Bearing Capacity Rbv = min(Rbv1, Rbv2) = min(81.34, 81.34) = 81.34 kips
81.34 kips >= 17.00 kips (OK)
Beam Strength Calcs:
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), Ag = [Gross Shear Length] * tw = 11.20 * 0.23 = 2.63 in^2
Shear Yielding, (phi)Vny = (phi) * 0.6 * Fybeam * Ag = 1.00 * 0.6 * 50.00 * 2.63 = 78.96 kips

Using AISC 14th Ed. Equation J4-4
Net Area (Shear), Anet = [Gross Shear Length] * tw = 11.20 * 0.23 = 2.63 in^2
Shear Rupture, (phi)Vnu = (phi) * 0.6 * Fubeam * Anet = 0.75 * 0.6 * 65.00 * 2.63 = 76.99 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] = 9.00 in.
Net Shear Length = 9.00 in.
Gross Tension Length = [horizontal weld length] = 3.00 in.
Net Tension Length = 3.00 in.
1. (phi) * [material thickness] * ((0.60 * Fubeam* [net shear length]) + (Ubs * Fubeam * [net tension length])) 
    = 0.75 * 0.23 * ((0.60 * 65.00 * 9.00) + (1.00 * 65.00 * 3.00)) = 96.23 kips
2. (phi) * [material thickness] * ((0.60 * Fybeam * [gross shear length]) + (Ubs * Fubeam * [net tension length])) 
    = 0.75 * 0.23 * ((0.60 * 50.00 * 9.00) + (1.00 * 65.00 * 3.00)) = 81.96 kips
Block Shear = 81.96 kips
81.96 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


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)
Double Angles Welded Bolted Calcs:
Angle1 

Support Angle Leg 


Using AISC 14th Ed. Equation J4-3
Gross Area, Ag = 0.38 * 8.00 = 3.00 in^2
Shear Yielding, (phi)Vny = (phi) * 0.6 * Fya * Ag = 1.00 * 0.6 * 50.00 * 3.00 = 90.00 kips

Using AISC 14th Ed. Equation J4-4
Net Area, An = (8.00 - (3 * (0.81 + 1/16))) * 0.38 = 2.02 in^2
Shear Rupture, (phi)Vnu = (phi) * 0.6 * Fua * An = 0.75 * 0.6 * 65.00 * 2.02 = 58.96 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 1 (Shear): 
Gross Shear Length = (8.00 - 1.00) = 7.00 in.
Net Shear Length = 7.00 - (2.50 * (0.81 + 1/16)) = 4.81 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 * 4.81) + (1.00 * 65.00 * 0.84)) = 68.08 kips
2. (phi) * [material thickness] * ((0.60 * Fya * [gross shear length]) + (Ubs * Fua * [net tension length])) 
    = 0.75 * 0.38 * ((0.60 * 50.00 * 7.00) + (1.00 * 65.00 * 0.84)) = 74.35 kips
Block Shear = 68.08 kips

Beam Angle Leg 


Using AISC 14th Ed. Equation J4-3
Gross Area, Ag = 0.38 * 8.00 = 3.00 in^2
Shear Yielding, (phi)Vny = (phi) * 0.6 * Fyangle * Ag = 1.00 * 0.6 * 50.00 * 3.00 = 90.00 kips

Using AISC 14th Ed. Equation J4-4
Net Area, An = 0.38 * 8.00 = 3.00 in^2
Shear Rupture, (phi)Vnu = (phi) * 0.6 * Fuangle * An = 0.75 * 0.6 * 65.00 * 3.00 = 87.75 kips


Flexural and Buckling Strength:

Eccentricity at Weld = 2.86
Zgross = 6.00 in^3
Znet   = 6.00 in^3
Sgross = 4.00 in^3
Snet   = 4.00 in^3

Using AISC 14th Ed. Equation 9-19
Flexural Yielding = (phi) * Fy * Sgross / e = 0.90 * 50.00 * 4.00 / 2.86 = 63.00 kips

Using AISC 14th Ed. Equation 9-4
Flexural Rupture = (phi) * Fu * Znet / e = 0.75 * 65.00 * 6.00 / 2.86 = 102.38 kips


Using AISC 14th Ed. Equation 9-14 through 9-18, Fcr = Fy * Q
tw = 0.38 in.
ho = 8.00 in.
c = 2.86 in.
lambda = (ho * Fy ^ 0.5) / ( 10 * tw * ( 475.00 + 280.00 * (ho / c)^2 ) ^0.5 ) = 
 = 8.00 * 50.00^0.5 / (10 * 0.38 * (475.00 + 280.00 * (8.00/2.86)^2 )^0.5) = 0.29
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 * 4.00 / 2.86 = 63.00 kips

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

Zgx = 6.00 in^3
Znx = 6.00 in^3
Zgy = 0.28 in^3
Zny = 0.28 in^3

Mrx = vertical reaction * ex = 8.50 * 2.86 = 24.29 kips-in
Mry = axial reaction * ey = 0.00 * 0.30 = 0.00 kips-in
Mcx = (phi) * Zgx * Min(Fy, Fcr) = 0.90 * 6.00 * Min(50.00, 50.00) = 270.00 kips-in
Mcy = (phi) * Zgy * Fy = 0.90 * 0.28 * 50.00 = 12.66 kips-in
Shear Stress on Gross Section = 8.50 / 3.00 = 2.83 ksi
Shear Stress on Net Section = 8.50 / 3.00 = 2.83 ksi
Axial Stress on Gross Section due to Axial force = 0.00 / 3.00 = 0.00 ksi
Axial Stress on Net Section due to Axial force = 0.00 / 3.00 = 0.00 ksi
Axial Stress on Gross Section due to Moment (shear) = 24.29 / 6.00 = 4.05 ksi
Axial Stress on Net Section due to Moment (shear) = 24.29 / 6.00 = 4.05 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 + 4.05 = 4.05 ksi
Axial Stress on Net Section (total) = 0.00 + 0.00 + 4.05 = 4.05 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 = (2.83 / 30.00)^2 + (4.05 / 45.00 )^2 = 0.02 <= 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 = (2.83 / 29.25)^2 + (4.05 / 48.75 )^2 = 0.02 <= 1.0 (OK)


Angle2 

Support Angle Leg 


Using AISC 14th Ed. Equation J4-3
Gross Area, Ag = 0.38 * 8.00 = 3.00 in^2
Shear Yielding, (phi)Vny = (phi) * 0.6 * Fya * Ag = 1.00 * 0.6 * 50.00 * 3.00 = 90.00 kips

Using AISC 14th Ed. Equation J4-4
Net Area, An = (8.00 - (3 * (0.81 + 1/16))) * 0.38 = 2.02 in^2
Shear Rupture, (phi)Vnu = (phi) * 0.6 * Fua * An = 0.75 * 0.6 * 65.00 * 2.02 = 58.96 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 1 (Shear): 
Gross Shear Length = (8.00 - 1.00) = 7.00 in.
Net Shear Length = 7.00 - (2.50 * (0.81 + 1/16)) = 4.81 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 * 4.81) + (1.00 * 65.00 * 0.84)) = 68.08 kips
2. (phi) * [material thickness] * ((0.60 * Fya * [gross shear length]) + (Ubs * Fua * [net tension length])) 
    = 0.75 * 0.38 * ((0.60 * 50.00 * 7.00) + (1.00 * 65.00 * 0.84)) = 74.35 kips
Block Shear = 68.08 kips

Beam Angle Leg 


Using AISC 14th Ed. Equation J4-3
Gross Area, Ag = 0.38 * 8.00 = 3.00 in^2
Shear Yielding, (phi)Vny = (phi) * 0.6 * Fyangle * Ag = 1.00 * 0.6 * 50.00 * 3.00 = 90.00 kips

Using AISC 14th Ed. Equation J4-4
Net Area, An = 0.38 * 8.00 = 3.00 in^2
Shear Rupture, (phi)Vnu = (phi) * 0.6 * Fuangle * An = 0.75 * 0.6 * 65.00 * 3.00 = 87.75 kips


Flexural and Buckling Strength:

Eccentricity at Weld = 2.86
Zgross = 6.00 in^3
Znet   = 6.00 in^3
Sgross = 4.00 in^3
Snet   = 4.00 in^3

Using AISC 14th Ed. Equation 9-19
Flexural Yielding = (phi) * Fy * Sgross / e = 0.90 * 50.00 * 4.00 / 2.86 = 63.00 kips

Using AISC 14th Ed. Equation 9-4
Flexural Rupture = (phi) * Fu * Znet / e = 0.75 * 65.00 * 6.00 / 2.86 = 102.38 kips


Using AISC 14th Ed. Equation 9-14 through 9-18, Fcr = Fy * Q
tw = 0.38 in.
ho = 8.00 in.
c = 2.86 in.
lambda = (ho * Fy ^ 0.5) / ( 10 * tw * ( 475.00 + 280.00 * (ho / c)^2 ) ^0.5 ) = 
 = 8.00 * 50.00^0.5 / (10 * 0.38 * (475.00 + 280.00 * (8.00/2.86)^2 )^0.5) = 0.29
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 * 4.00 / 2.86 = 63.00 kips

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

Zgx = 6.00 in^3
Znx = 6.00 in^3
Zgy = 0.28 in^3
Zny = 0.28 in^3

Mrx = vertical reaction * ex = 8.50 * 2.86 = 24.29 kips-in
Mry = axial reaction * ey = 0.00 * 0.30 = 0.00 kips-in
Mcx = (phi) * Zgx * Min(Fy, Fcr) = 0.90 * 6.00 * Min(50.00, 50.00) = 270.00 kips-in
Mcy = (phi) * Zgy * Fy = 0.90 * 0.28 * 50.00 = 12.66 kips-in
Shear Stress on Gross Section = 8.50 / 3.00 = 2.83 ksi
Shear Stress on Net Section = 8.50 / 3.00 = 2.83 ksi
Axial Stress on Gross Section due to Axial force = 0.00 / 3.00 = 0.00 ksi
Axial Stress on Net Section due to Axial force = 0.00 / 3.00 = 0.00 ksi
Axial Stress on Gross Section due to Moment (shear) = 24.29 / 6.00 = 4.05 ksi
Axial Stress on Net Section due to Moment (shear) = 24.29 / 6.00 = 4.05 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 + 4.05 = 4.05 ksi
Axial Stress on Net Section (total) = 0.00 + 0.00 + 4.05 = 4.05 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 = (2.83 / 30.00)^2 + (4.05 / 45.00 )^2 = 0.02 <= 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 = (2.83 / 29.25)^2 + (4.05 / 48.75 )^2 = 0.02 <= 1.0 (OK)


Total Support Side Shear Yielding Capacity =  min(YieldAngle1/Gage1 Ratio, YieldAngle2/Gage2 Ratio) =  min(180.00 , 180.00) = 180.00 kips
180.00 kips >= Reaction V = 17.00 kips (OK)
Total Support Side Shear Rupture Capacity =  min(RuptureAngle1/Gage1 Ratio, RuptureAngle2/Gage2 Ratio) = min(117.92 , 117.92) = 117.92 kips
117.92 kips >= Reaction V = 17.00 kips (OK)
Total Support Side Vertical Block Shear Capacity =  min(BlockAngle1/Gage1 Ratio, BlockAngle2/Gage2 Ratio) = min(136.15 , 136.15) = 136.15 kips
136.15 kips >= Reaction V = 17.00 kips (OK)
Total Beam Side Shear Yielding Capacity =  min (YieldAngle1/Gage1 Ratio , YieldAngle2/Gage2 Ratio) = min(180.00 , 180.00) = 180.00 kips
180.00 kips >= Reaction V = 17.00 kips (OK)
Total Beam Side Shear Rupture Capacity =  min (RuptureAngle1/Gage1 Ratio , RuptureAngle2/Gage2 Ratio) = min(175.50 , 175.50) = 175.50 kips
175.50 kips >= Reaction V = 17.00 kips (OK)
Total Beam Side Flexure Yielding Capacity =  min (FlexureYieldAngle1/Gage1 Ratio , FlexureYieldAngle2/Gage2 Ratio) = min(126.00 , 126.00) = 126.00 kips
126.00 kips >= Reaction V = 17.00 kips (OK)
Total Beam Side Flexure Rupture Capacity =  min (FlexureRuptureAngle1/Gage1 Ratio , FlexureRuptureAngle2/Gage2 Ratio) = min(204.76 , 204.76) = 204.76 kips
204.76 kips >= Reaction V = 17.00 kips (OK)
Total Beam Side Bending Buckling Capacity =  min (BendingBucklingAngle1/Gage1 Ratio , BendingBucklingAngle2/Gage2 Ratio) = min(126.00 , 126.00) = 126.00 kips
126.00 kips >= Reaction V = 17.00 kips (OK)
Weld Calcs:
Angles Welded to Beam:

Angle1 Beam Weld
k = 0.38
ex = 2.86
a = ex / l = 2.86 / 8.00 = 0.36
Loadangle = 0.00 deg 
Weld Coefficient = 0.60 * Fexx * cphi * arrangement coefficient = 2.90
Dmax1 using min(eqn 9-2, tang - 0.06) 
 = min(tang * Fuang / ( Fexx * C1 * 0.04), tang - 0.06) 
 = min(0.38 * 65.00 / ( 70.00 * 1.00 * 0.04), 0.38 - 0.06) 
 = min(7.88, 5.00)
 = 5.00 
Dmax2 (using eqn 9-3)
 = twbeam * Fubeam / ( Fexx * C1 * 0.09 )
 = 0.23 * 65.00 / ( 70.00 * 1.00 * 0.09 ) 
 = 2.47 
Dmax3 = project max fillet weld = 12.00
Dmax=min(Dmax1, Dmax2, Dmax3) = min(5.00, 2.47, 12.00)
 = 2.47 

Use D = Min(angle thickness - 1/16, Max(Design Req, Table J2.4, User Pref Min)) = Min(5.00, Max(1.00, 2.00, 4.00)) = 4.00/16

Weld Strength = phi * weld coefficient * l * D  = 0.75 * 2.90 * 8.00 * 2.47 = 42.97 kips

Angle2 Beam Weld
k = 0.38
ex = 2.86
a = ex / l = 2.86 / 8.00 = 0.36
Loadangle = 0.00 deg 
Weld Coefficient = 0.60 * Fexx * cphi * arrangement coefficient = 2.90
Dmax1 using min(eqn 9-2, tang - 0.06) 
 = min(tang * Fuang / ( Fexx * C1 * 0.04), tang - 0.06) 
 = min(0.38 * 65.00 / ( 70.00 * 1.00 * 0.04), 0.38 - 0.06) 
 = min(7.88, 5.00)
 = 5.00 
Dmax2 (using eqn 9-3)
 = twbeam * Fubeam / ( Fexx * C1 * 0.09 )
 = 0.23 * 65.00 / ( 70.00 * 1.00 * 0.09 ) 
 = 2.47 
Dmax3 = project max fillet weld = 12.00
Dmax=min(Dmax1, Dmax2, Dmax3) = min(5.00, 2.47, 12.00)
 = 2.47 

Use D = Min(angle thickness - 1/16, Max(Design Req, Table J2.4, User Pref Min)) = Min(5.00, Max(1.00, 2.00, 4.00)) = 4.00/16

Weld Strength = phi * weld coefficient * l * D  = 0.75 * 2.90 * 8.00 * 2.47 = 42.97 kips

Total Welds Shear Strength = min( Angle1 Weld Shear/Gage Ratio at Angle1 , Angle2 Weld Shear/Gage Ratio at Angle2 ) = min ( 85.94, 85.94) = 85.94 kips