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 * (0.30/1) * 65.00 = 39.03 kips/bolt
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 1.34 * (0.30/1) * 65.00 = 23.98 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(39.03, 23.98, 26.76) = 23.98 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 * 65.00 = 47.99 kips/bolt
(phi)Rneang1 at Angle 1 edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 9.84 * 0.38 * 65.00 = 215.95 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, 215.95, 32.91) = 32.91 kips/bolt
(phi)Rn = min((phi)Rnbolt, (phi)Rnbm, (phi)Rnang1) = min(17.89, 23.98, 32.91) = 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 * (0.30/1) * 65.00 = 39.03 kips/bolt
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 4.34 * (0.30/1) * 65.00 = 77.51 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(39.03, 77.51, 26.76) = 26.76 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 * 65.00 = 47.99 kips/bolt
(phi)Rneang1 at Angle 1 edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 6.84 * 0.38 * 65.00 = 150.14 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, 150.14, 32.91) = 32.91 kips/bolt
(phi)Rn = min((phi)Rnbolt, (phi)Rnbm, (phi)Rnang1) = min(17.89, 26.76, 32.91) = 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 * (0.30/1) * 65.00 = 39.03 kips/bolt
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 7.34 * (0.30/1) * 65.00 = 131.03 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(39.03, 131.03, 26.76) = 26.76 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 * 65.00 = 47.99 kips/bolt
(phi)Rneang1 at Angle 1 edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 3.84 * 0.38 * 65.00 = 84.32 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, 84.32, 32.91) = 32.91 kips/bolt
(phi)Rn = min((phi)Rnbolt, (phi)Rnbm, (phi)Rnang1) = min(17.89, 26.76, 32.91) = 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 * (0.30/1) * 65.00 = 39.03 kips/bolt
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 10.34 * (0.30/1) * 65.00 = 184.56 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(39.03, 184.56, 26.76) = 26.76 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 * 65.00 = 47.99 kips/bolt
(phi)Rneang1 at Angle 1 edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 0.84 * 0.38 * 65.00 = 18.51 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, 18.51, 32.91) = 18.51 kips/bolt
(phi)Rn = min((phi)Rnbolt, (phi)Rnbm, (phi)Rnang1) = min(17.89, 26.76, 18.51) = 17.89 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 = 71.57 kips
BEARING AT BEAM AND ANGLE SIDE SUMMARY:
Bearing Capacity at Vertical Shear Load Only, Rbv = Sum{ [(Row)i,(Column)i] } = 71.57 kips
Rbv = 71.57 kips >= Reaction V = 2.00 kips (OK) |
Web Depth = d - [Top Cope Depth] - [Bottom Cope Depth] = 16.00 - 1.25 - 0.00 = 14.75 in.
Using AISC 14th Ed. Equation J4-3
Gross Area (Shear), Agross = [Web Depth] * tw = 14.75 * 0.30 = 4.50 in^2
Shear Yielding, (phi)Vny = (phi) * 0.6 * Fybeam * Agross = 1.00 * 0.6 * 50.00 * 4.50 = 134.96 kips
Using AISC 14th Ed. Equation J4-4
Net Area (Shear), Anet = ([Web Depth] - ([# rows] * [Diameter + 0.06])) * tw
= (14.75 - (4 * 0.88)) * 0.30 = 3.43 in^2
Shear Rupture, (phi)Vnu = (phi) * 0.6 * Fubeam * Anet = 0.75 * 0.6 * 65.00 * 3.43 = 100.37 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 + 9.00 = 10.75 in.
Net Shear Length = Gross Shear Length - (# rows - 0.5) * (hole size + 0.06) = 10.75 - (4 - 0.5) * 0.88 = 7.69 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 * 0.30 * ((0.60 * 65.00 * 7.69) + (1.00 * 65.00 * 1.06)) = 84.38 kips
2. (phi) * [material thickness] * ((0.60 * Fybeam * [gross shear length]) + (Ubs * Fubeam * [net tension length]))
= 0.75 * 0.30 * ((0.60 * 50.00 * 10.75) + (1.00 * 65.00 * 1.06)) = 89.57 kips
Block Shear = 84.38 kips
Block Shear (1) Total = Block Shear (1) = 84.38 kips
84.38 kips >= Reaction V = 2.00 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 = 4.43 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 = 0.30 in.
h1 = 10.43 in.
c = 3.75 in.
When c/h1<=1.0, k=2.2(h1/c)^1.65
k = 2.20 * (10.43 / 3.75)^1.65 = 11.90
When c/d<=1.0, f=2c/d
f = 2 * (3.75 / 16.00) = 0.47
Fy = 50.00 ksi
Fcr = (phi) * 26210.00 * f * k * (tw/h1)^2 = 0.90 * 26210.00 * 0.47 * 11.90 * (0.30 / 10.43)^2 = 112.49 ksi
Fcrmin =phi * min(Fcr, Fy) = 45.00 ksi
Snet1 (bolt holes not applicable) = 17.21 in^3
Snet2 (bolt holes applicable) = 17.21 in^3
Znet1 (bolt holes not applicable) = 31.30 in^3
Znet2 (bolt holes applicable) = 31.30 in^3
Using AISC 14th Ed. Equation 9-6
Buckling = Fcr * Snet1 / e = 45.00 * 17.21 / 4.43 = 174.96 kips
Using AISC 14th Ed. Equation 9-19
Flexural Yielding = (phi) * Fy * Snet1 / e = 0.90 * 50.00 * 17.21 / 4.43 = 174.96 kips
Using AISC 14th Ed. Equation 9-4
Flexural Rupture = (phi) * Fu * Znet2 / e = 0.75 * 65.00 * 31.30 / 4.43 = 344.65 kips
Buckling and Flexure at Furthest Bolt Line within Cope (Top Cope Only at Section)
Eccentricity at Section, e = 2.18 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 = 0.30 in.
h1 = 11.09 in.
c = 3.75 in.
When c/h1<=1.0, k=2.2(h1/c)^1.65
k = 2.20 * (11.09 / 3.75)^1.65 = 13.16
When c/d<=1.0, f=2c/d
f = 2 * (3.75 / 16.00) = 0.47
Fy = 50.00 ksi
Fcr = (phi) * 26210.00 * f * k * (tw/h1)^2 = 0.90 * 26210.00 * 0.47 * 13.16 * (0.30 / 11.09)^2 = 110.12 ksi
Fcrmin =phi * min(Fcr, Fy) = 45.00 ksi
Snet1 (bolt holes not applicable) = 17.21 in^3
Snet2 (bolt holes applicable) = 13.16 in^3
Znet1 (bolt holes not applicable) = 31.30 in^3
Znet2 (bolt holes applicable) = 23.30 in^3
Using AISC 14th Ed. Equation 9-6
Buckling = Fcr * Snet1 / e = 45.00 * 17.21 / 2.18 = 355.74 kips
Using AISC 14th Ed. Equation 9-19
Flexural Yielding = (phi) * Fy * Snet1 / e = 0.90 * 50.00 * 17.21 / 2.18 = 355.74 kips
Using AISC 14th Ed. Equation 9-4
Flexural Rupture = (phi) * Fu * Znet2 / e = 0.75 * 65.00 * 23.30 / 2.18 = 521.67 kips
Section Bending Strength Calculations Summary:
Coped Beam Buckling and Flexure at Longest Cope (Top Cope Only at Section)
Buckling : 174.96 >= 2.00 kips (OK)
Flexural Yielding : 174.96 >= 2.00 kips (OK)
Flexural Rupture : 344.65 >= 2.00 kips (OK)
Coped Beam Buckling and Flexure at Furthest Bolt Line within Cope (Top Cope Only at Section)
Buckling : 355.74 >= 2.00 kips (OK)
Flexural Yielding : 355.74 >= 2.00 kips (OK)
Flexural Rupture : 521.67 >= 2.00 kips (OK) |
Support Angle Leg
Using AISC 14th Ed. Equation J4-3
Gross Area, Ag = 0.38 * 11.50 = 4.31 in^2
Shear Yielding, (phi)Vny = (phi) * 0.6 * Fyangle * Ag = 1.00 * 0.6 * 50.00 * 4.31 = 129.38 kips
Using AISC 14th Ed. Equation J4-4
Net Area, An = 0.38 * 11.50 = 4.31 in^2
Shear Rupture, (phi)Vnu = (phi) * 0.6 * Fuangle * An = 0.75 * 0.6 * 65.00 * 4.31 = 126.14 kips
Flexural and Buckling Strength:
Eccentricity at Weld = 2.43
Zgross = 12.40 in^3
Znet = 12.40 in^3
Sgross = 8.27 in^3
Snet = 8.27 in^3
Using AISC 14th Ed. Equation 9-19
Flexural Yielding = (phi) * Fy * Sgross / e = 0.90 * 50.00 * 8.27 / 2.43 = 153.11 kips
Using AISC 14th Ed. Equation 9-4
Flexural Rupture = (phi) * Fu * Znet / e = 0.75 * 65.00 * 12.40 / 2.43 = 248.81 kips
Using AISC 14th Ed. Equation 9-14 through 9-18, Fcr = Fy * Q
tw = 0.38 in.
ho = 11.50 in.
c = 2.28 in.
lambda = (ho * Fy ^ 0.5) / ( 10 * tw * ( 475.00 + 280.00 * (ho / c)^2 ) ^0.5 ) =
= 11.50 * 50.00^0.5 / (10 * 0.38 * (475.00 + 280.00 * (11.50/2.28)^2 )^0.5) = 0.25
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 * 8.27 / 2.43 = 153.11 kips
Beam Angle Leg
Using AISC 14th Ed. Equation J4-3
Gross Area, Ag = 0.38 * 11.50 = 4.31 in^2
Shear Yielding, (phi)Vny = (phi) * 0.6 * Fya * Ag = 1.00 * 0.6 * 50.00 * 4.31 = 129.38 kips
Using AISC 14th Ed. Equation J4-4
Net Area, An = (11.50 - (4 * (0.81 + 1/16))) * 0.38 = 3.00 in^2
Shear Rupture, (phi)Vnu = (phi) * 0.6 * Fua * An = 0.75 * 0.6 * 65.00 * 3.00 = 87.75 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 = (11.50 - 1.25) = 10.25 in.
Net Shear Length = 10.25 - (3.50 * (0.81 + 1/16) = 7.19 in.
Gross Tension Length = [edge dist.] = 1.50 in.
Net Tension Length = (1.50 - (1.00 + 1/16)/2) = 0.97 in.
1. (phi) * [material thickness] * ((0.60 * Fua* [net shear length]) + (Ubs * Fua * [net tension length]))
= 0.75 * 0.38 * ((0.60 * 65.00 * 7.19) + (1.00 * 65.00 * 0.97)) = 96.55 kips
2. (phi) * [material thickness] * ((0.60 * Fya * [gross shear length]) + (Ubs * Fua * [net tension length]))
= 0.75 * 0.38 * ((0.60 * 50.00 * 10.25) + (1.00 * 65.00 * 0.97)) = 104.20 kips
Block Shear = 96.55 kips
Block Shear for Axial T/C is not required.
Support Side Shear Yielding Capacity = 129.38 kips
129.38 kips >= Reaction V = 2.00 kips (OK)
Support Side Shear Rupture Capacity = 126.14 kips
126.14 kips >= Reaction V = 2.00 kips (OK)
Beam Side Shear Yielding Capacity = 129.38 kips
129.38 kips >= Reaction V = 2.00 kips (OK)
Beam Side Shear Rupture Capacity = 87.75 kips
87.75 kips >= Reaction V = 2.00 kips (OK)
Support Side Flexure Yielding Capacity = 153.11 kips
153.11 kips >= Reaction V = 2.00 kips (OK)
Support Side Flexure Rupture Capacity = 248.81 kips
248.81 kips >= Reaction V = 2.00 kips (OK)
Support Side Bending Buckling Capacity = 153.11 kips
153.11 kips >= Reaction V = 2.00 kips (OK)
Beam Side Vertical Block Shear Capacity = 96.55 kips
96.55 kips >= Reaction V = 2.00 kips (OK) |
Angles Welded to Support:
Single Angle Girder Weld:
k = 0.22
ex = 2.43
a = ex / l = 2.43 / 11.50 = 0.21
Weld Coefficient = 0.60 * Fexx * cphi * arrangement coefficient = 2.20
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)
= twsupport * Fusupport / ( Fexx * C1 * 0.09 )
= 0.35 * 65.00 / ( 70.00 * 1.00 * 0.09 )
= 3.73
Dmax3 = project max fillet weld = 12.00
Dmax=min(Dmax1, Dmax2, Dmax3) = min(5.00, 3.73, 12.00)
= 3.73
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 * 2.20 * 11.50 * 3.73 = 70.68 kips |
