bepl.1bw.s.00001.00001

SINGLE ANGLE Bolted to Beam, Welded to Support CONNECTION SUMMARY

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

Embed Plate profile: PL0.75X10.00X24.00
Filler Beam profile: W16X40
Slope: 0.00 deg.
Skew: 90.00
Vertical Offset: -1.00
Horizontal Offset: 0.00
Span: 2.00 ft.
Reaction, V: 2.00 kips
Shear Capacity, Rn: 18.49 kips
Design/Reference according to AISC 14th Ed. - LRFD
Beam material grade: A992
Support material grade: A36
Angle material grade: A529-GR.50
Weld grade: E70
Angle1 Profile: L5X3X3/8
       Length = 11.00 in.
       Beam side bolts: 4 rows x 1 column 0.75 in. Diameter A325SCA_TC bolts
       Beam side bolt vertical spacing: 3.00 in.
Plate Washer Size: 3.00 in. x 11.00 in. x 0.31 in.

Configuration Geometry:
Weld Size at Angle 1 Support Weld:
4/16 FILLET

Beam setback = 1.00 in.
Edge distance at vertical edge of beam: 1.50 in.

Horizontal distance to first hole: 2.50 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 : 2.50 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 : LSL slot width = 0.81 in., slot length = 1.88 in.
(Design eccentricity accounts for potential movement in Long Slots)

BOLT SHEAR CAPACITY AT BEAM AND ANGLE SIDE:
Bolt Shear Capacity at Shear Load Only:
Using Instantaneous Center Of Rotation Method (AISC 7-1)
ex = 3.06 in.
Angle = 0.00 deg.
C = 2.78
Slip Critical, Surface A, determining (phi)Rn:
Using AISC 14th Ed. Equation J3-4
slip coefficient, mu = 0.30
pretension ratio, Du = 1.13
Minimum Bolt Pretension from Table J3.1, Tb = 28.00 kips
factor for fillers, hf = 1.00
number of slip planes, ns = 1.00
rn = mu * Du * hf * Tb * ns = 0.30 * 1.13 * 1.00 * 28.00 * 1.00 = 9.49 kips
(phi)v = 0.70
(phi)rn = (phi)v * rn = 0.70 * 9.49 = 6.64 kips
(phi)Rn = (phi)rn * C = 6.64 * 2.78 = 18.49 kips


Total Vertical Bolt Shear Capacity = 18.49 kips
18.49 kips >= Reaction V = 2.00 kips (OK)

BOLT BEARING AT BEAM AND ANGLE SIDE
Vertical Shear Only Load Case:
ICR cordinate relative to CG = (3.07, -0.00)
At Row 1, At Column 1:
Ribolt = 6.52 kips
Ri vector at Beam   = <7.70, 5.25>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 4.92 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = na
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 4.92 * (0.30/1) * 65.00 = 87.73 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.75 * (0.30/1) * 65.00 = 26.76 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(na, 87.73, 26.76) = 26.76 kips/bolt
Ri vector at Angle 1   = <-5.39, -3.68>
Lcsang1 at Angle 1 spacing  = na
Lceang1 at Angle 1 edge    = 2.31 in.
(phi)Rnsang1 at Angle 1 spacing = (phi) * hf1 * Lcs * t * Fu = na
(phi)Rneang1 at Angle 1 edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.00 * 2.31 * 0.38 * 65.00 = 42.15 kips/bolt
(phi)Rndang1 on Angle 1 at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.00 * 0.75 * 0.38 * 65.00 = 27.42 kips/bolt
Angle 1 bearing capacity, (phi)Rnang1 = min((phi)Rnsang1,(phi)Rneang1,(phi)Rndang1) = min(na, 42.15, 27.42) = 27.42 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnang1) = min(26.76, 27.42) = 26.76 kips/bolt
Bolt Shear Demand to Bearing ratio = 26.76 / 6.52 = 4.10

At Row 2, At Column 1:
Ribolt = 6.20 kips
Ri vector at Beam   = <3.89, 7.96>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 6.27 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = na
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 6.27 * (0.30/1) * 65.00 = 111.90 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.75 * (0.30/1) * 65.00 = 26.76 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(na, 111.90, 26.76) = 26.76 kips/bolt
Ri vector at Angle 1   = <-2.72, -5.57>
Lcsang1 at Angle 1 spacing  = na
Lceang1 at Angle 1 edge    = 5.24 in.
(phi)Rnsang1 at Angle 1 spacing = (phi) * hf1 * Lcs * t * Fu = na
(phi)Rneang1 at Angle 1 edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.00 * 5.24 * 0.38 * 65.00 = 95.85 kips/bolt
(phi)Rndang1 on Angle 1 at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.00 * 0.75 * 0.38 * 65.00 = 27.42 kips/bolt
Angle 1 bearing capacity, (phi)Rnang1 = min((phi)Rnsang1,(phi)Rneang1,(phi)Rndang1) = min(na, 95.85, 27.42) = 27.42 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnang1) = min(26.76, 27.42) = 26.76 kips/bolt
Bolt Shear Demand to Bearing ratio = 26.76 / 6.20 = 4.32

At Row 3, At Column 1:
Ribolt = 6.20 kips
Ri vector at Beam   = <-3.89, 7.96>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 3.01 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = na
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 3.01 * (0.30/1) * 65.00 = 53.73 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.75 * (0.30/1) * 65.00 = 26.76 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(na, 53.73, 26.76) = 26.76 kips/bolt
Ri vector at Angle 1   = <2.72, -5.57>
Lcsang1 at Angle 1 spacing  = na
Lceang1 at Angle 1 edge    = 4.00 in.
(phi)Rnsang1 at Angle 1 spacing = (phi) * hf1 * Lcs * t * Fu = na
(phi)Rneang1 at Angle 1 edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.00 * 4.00 * 0.38 * 65.00 = 73.12 kips/bolt
(phi)Rndang1 on Angle 1 at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.00 * 0.75 * 0.38 * 65.00 = 27.42 kips/bolt
Angle 1 bearing capacity, (phi)Rnang1 = min((phi)Rnsang1,(phi)Rneang1,(phi)Rndang1) = min(na, 73.12, 27.42) = 27.42 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnang1) = min(26.76, 27.42) = 26.76 kips/bolt
Bolt Shear Demand to Bearing ratio = 26.76 / 6.20 = 4.32

At Row 4, At Column 1:
Ribolt = 6.52 kips
Ri vector at Beam   = <-7.70, 5.25>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 1.41 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = na
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 1.41 * (0.30/1) * 65.00 = 25.15 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.75 * (0.30/1) * 65.00 = 26.76 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(na, 25.15, 26.76) = 25.15 kips/bolt
Ri vector at Angle 1   = <5.39, -3.68>
Lcsang1 at Angle 1 spacing  = na
Lceang1 at Angle 1 edge    = 1.05 in.
(phi)Rnsang1 at Angle 1 spacing = (phi) * hf1 * Lcs * t * Fu = na
(phi)Rneang1 at Angle 1 edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.00 * 1.05 * 0.38 * 65.00 = 19.26 kips/bolt
(phi)Rndang1 on Angle 1 at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.00 * 0.75 * 0.38 * 65.00 = 27.42 kips/bolt
Angle 1 bearing capacity, (phi)Rnang1 = min((phi)Rnsang1,(phi)Rneang1,(phi)Rndang1) = min(na, 19.26, 27.42) = 19.26 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnang1) = min(25.15, 19.26) = 19.26 kips/bolt
Bolt Shear Demand to Bearing ratio = 19.26 / 6.52 = 2.95

Min Bolt Shear Demand to Bearing ratio Beam and Angle for vertical shear only
 = min(1.00, 4.10, 4.32, 4.32, 2.95) = 1.00


BEARING AT BEAM AND ANGLE SIDE SUMMARY:
Bearing Capacity at Vertical Shear Load Only, Rbv = Min Bolt Shear Demand to Bearing Ratio * Bolt Shear = 1.00 * 18.49 = 18.49 kips
Rbv = 18.49 kips >= Reaction V = 2.00 kips (OK)

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

Using AISC 14th Ed. Equation J4-3
Gross Area (Shear), Agross = [Web Depth] * tw = 16.00 * 0.30 = 4.88 in^2
Shear Yielding, (phi)Vny = (phi) * 0.6 * Fybeam * Agross = 1.00 * 0.6 * 50.00 * 4.88 = 146.40 kips

Using AISC 14th Ed. Equation J4-4
Net Area (Shear), Anet = ([Web Depth] - ([# rows] * [Diameter + 0.06])) * tw 
    = (16.00 - (4 * 0.88)) * 0.30 = 3.81 in^2
Shear Rupture, (phi)Vnu = (phi) * 0.6 * Fubeam * Anet = 0.75 * 0.6 * 65.00 * 3.81 = 111.52 kips


Check Horizontal 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 for Axial T/C is not required.

Support Angle Leg 


Using AISC 14th Ed. Equation J4-3
Gross Area, Ag = 0.38 * 11.00 = 4.12 in^2
Shear Yielding, (phi)Vny = (phi) * 0.6 * Fyangle * Ag = 1.00 * 0.6 * 50.00 * 4.12 = 123.75 kips

Using AISC 14th Ed. Equation J4-4
Net Area, An = 0.38 * 11.00 = 4.12 in^2
Shear Rupture, (phi)Vnu = (phi) * 0.6 * Fuangle * An = 0.75 * 0.6 * 65.00 * 4.12 = 120.66 kips


Flexural and Buckling Strength:

Eccentricity at Weld = 2.83
Zgross = 11.34 in^3
Znet   = 11.34 in^3
Sgross = 7.56 in^3
Snet   = 7.56 in^3

Using AISC 14th Ed. Equation 9-19
Flexural Yielding = (phi) * Fy * Sgross / e = 0.90 * 50.00 * 7.56 / 2.83 = 120.21 kips

Using AISC 14th Ed. Equation 9-4
Flexural Rupture = (phi) * Fu * Znet / e = 0.75 * 65.00 * 11.34 / 2.83 = 195.34 kips


Using AISC 14th Ed. Equation 9-14 through 9-18, Fcr = Fy * Q
tw = 0.38 in.
ho = 11.00 in.
c = 2.68 in.
lambda = (ho * Fy ^ 0.5) / ( 10 * tw * ( 475.00 + 280.00 * (ho / c)^2 ) ^0.5 ) = 
 = 11.00 * 50.00^0.5 / (10 * 0.38 * (475.00 + 280.00 * (11.00/2.68)^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 * 7.56 / 2.83 = 120.21 kips

Beam Angle Leg 


Using AISC 14th Ed. Equation J4-3
Gross Area, Ag = 0.38 * 11.00 = 4.12 in^2
Shear Yielding, (phi)Vny = (phi) * 0.6 * Fya * Ag = 1.00 * 0.6 * 50.00 * 4.12 = 123.75 kips

Using AISC 14th Ed. Equation J4-4
Net Area, An = (11.00 - (4 * (0.81 + 1/16))) * 0.38 = 2.81 in^2
Shear Rupture, (phi)Vnu = (phi) * 0.6 * Fua * An = 0.75 * 0.6 * 65.00 * 2.81 = 82.27 kips


Check Vertical Block Shear

Using AISC 14th Ed. Equation J4-5
Block Shear = {(phi) * ((0.6 * Fu * Anv) + (Ubs * Fu * Ant))} <= {(phi) * ((0.6 * Fy * Agv) + (Ubs * Fu * Ant))}

Block 1 (Shear): 
Gross Shear Length = (11.00 - 1.00) = 10.00 in.
Net Shear Length = 10.00 - (3.50 * (0.81 + 1/16) = 6.94 in.
Gross Tension Length = [edge dist.] = 2.50 in.
Net Tension Length = (2.50 - (1.88 + 1/16)/2) = 1.53 in.
1. (phi) * [material thickness] * ((0.60 * Fua* [net shear length]) + (Ubs * Fua * [net tension length])) 
    = 0.75 * 0.38 * ((0.60 * 65.00 * 6.94) + (1.00 * 65.00 * 1.53)) = 104.09 kips
2. (phi) * [material thickness] * ((0.60 * Fya * [gross shear length]) + (Ubs * Fua * [net tension length])) 
    = 0.75 * 0.38 * ((0.60 * 50.00 * 10.00) + (1.00 * 65.00 * 1.53)) = 112.37 kips
Block Shear = 104.09 kips

Block Shear for Axial T/C is not required.

Flexural and Buckling Strength:

Eccentricity at Bolt Column = 3.06
Zgross = 11.34 in^3
Znet   = 7.41 in^3
Sgross = 7.56 in^3
Snet   = 4.86 in^3

Using AISC 14th Ed. Equation 9-19
Flexural Yielding = (phi) * Fy * Sgross / e = 0.90 * 50.00 * 7.56 / 3.06 = 111.12 kips

Using AISC 14th Ed. Equation 9-4
Flexural Rupture = (phi) * Fu * Znet / e = 0.75 * 65.00 * 7.41 / 3.06 = 117.90 kips


Using AISC 14th Ed. Equation 9-14 through 9-18, Fcr = Fy * Q
tw = 0.38 in.
ho = 11.00 in.
c = 3.06 in.
lambda = (ho * Fy ^ 0.5) / ( 10 * tw * ( 475.00 + 280.00 * (ho / c)^2 ) ^0.5 ) = 
 = 11.00 * 50.00^0.5 / (10 * 0.38 * (475.00 + 280.00 * (11.00/3.06)^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

Using AISC 14th Ed. Equation 9-6
Buckling = Fcr * Sgross / e = 45.00 * 7.56 / 3.06 = 111.12 kips

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

Zgx = 11.34 in^3
Znx = 7.41 in^3
Zgy = 0.39 in^3
Zny = 0.26 in^3

Mrx = vertical reaction * ex = 2.00 * 3.06 = 6.12 kips-in
Shear Stress on Gross Section = 2.00 / 4.12 = 0.48 ksi
Shear Stress on Net Section = 2.00 / 2.81 = 0.71 ksi
Axial Stress on Gross Section due to Moment (shear) = 6.12 / 11.34 = 0.54 ksi
Axial Stress on Net Section due to Moment (shear) = 6.12 / 7.41 = 0.83 ksi

Shear Yield Stress Capacity (SYSC) = phi * 0.6 * Fy = 1.00 * 0.60 * 50.00 = 30.00 ksi
Tensile Yield Stress Capacity (TYSC) = phi * Fy = 0.90 * 50.00 = 45.00 ksi
Stress Interaction at Gross Section (elliptical):
(fvg / SYSC)^2 + (fag / TYSC )^2 = (0.48 / 30.00)^2 + (0.54 / 45.00 )^2 = 0.00 <= 1.0 (OK)
Shear Rupture Stress Capacity (SRSC) = phi * 0.6 * Fu = 0.75 * 0.60 * 65.00 = 29.25 ksi
Tensile Rupture Stress Capacity (TRSC) = phi * Fu = 0.75 * 65.00 = 48.75 ksi
Stress Interaction at Net Section (elliptical):
(fvn / SRSC)^2 + (fan / TRSC )^2 = (0.71 / 29.25)^2 + (0.83 / 48.75 )^2 = 0.00 <= 1.0 (OK)


Support Side Shear Yielding Capacity = 123.75 kips
123.75 kips >= Reaction V = 2.00 kips (OK)
Support Side Shear Rupture Capacity = 120.66 kips
120.66 kips >= Reaction V = 2.00 kips (OK)
Beam Side Shear Yielding Capacity = 123.75 kips
123.75 kips >= Reaction V = 2.00 kips (OK)
Beam Side Shear Rupture Capacity = 82.27 kips
82.27 kips >= Reaction V = 2.00 kips (OK)
Support Side Flexure Yielding Capacity = 120.21 kips
120.21 kips >= Reaction V = 2.00 kips (OK)
Support Side Flexure Rupture Capacity = 195.34 kips
195.34 kips >= Reaction V = 2.00 kips (OK)
Support Side Bending Buckling Capacity = 120.21 kips
120.21 kips >= Reaction V = 2.00 kips (OK)
Beam Side Flexure Yielding Capacity = 111.12 kips
111.12 kips >= Reaction V = 2.00 kips (OK)
Beam Side Flexure Rupture Capacity = 117.90 kips
117.90 kips >= Reaction V = 2.00 kips (OK)
Beam Side Bending Buckling Capacity = 111.12 kips
111.12 kips >= Reaction V = 2.00 kips (OK)
Beam Side Vertical Block Shear Capacity = 104.09 kips
104.09 kips >= Reaction V = 2.00 kips (OK)

Angles Welded to Support:

Single Angle Girder Weld:
k = 0.27
ex = 2.83
a = ex / l = 2.83 / 11.00 = 0.26
Weld Coefficient = 0.60 * Fexx * cphi * arrangement coefficient = 2.21
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 9-2)
 = tembpl * Fuembpl / ( Fexx * C1 * 0.04 )
 = 0.75 * 58.00 / ( 70.00 * 1.00 * 0.04 ) 
 = 14.06 
Dmax3 = project max fillet weld = 12.00
Dmax=min(Dmax1, Dmax2, Dmax3) = min(5.00, 14.06, 12.00)
 = 5.00 

Use D = Min(angle thickness - 1/16, Max(Design Req, Table J2.4, User Pref Min)) = Min(5.00, Max(1.00, 3.00, 4.00)) = 4.00/16

Weld Strength = phi * weld coefficient * l * D  = 0.75 * 2.21 * 11.00 * 4.00 = 72.98 kips