BOLT BEARING AT SUPPORT AND ANGLE SIDE
Vertical Shear Only Load Case:
ICR cordinate relative to CG = (5.42, 0.00)
At Row 1, At Column 1:
Ribolt = 17.56 kips
Ri vector at Support = <-11.22, -13.51>
Lcssupp at Support spacing = na
Lcesupp at Support edge = 19.10 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 * 19.10 * (0.35/1) * 65.00 = 396.59 kips/bolt
(phi)Rndsupp on Support at Bolt Diameter = (phi) * hf2 * db * (twsup/# bolt sides supported) * Fu = 0.75 * 2.40 * 0.75 * (0.35/1) * 65.00 = 31.15 kips/bolt
Support bearing capacity, (phi)Rnsupp = min((phi)Rnssupp,(phi)Rnesupp,(phi)Rndsupp) = min(na, 396.59, 31.15) = 31.15 kips/bolt
Ri vector at Angle = <11.22, 13.51>
Lcsang at Angle spacing = na
Lceang at Angle edge = 1.22 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 * 1.22 * 0.38 * 65.00 = 26.74 kips/bolt
(phi)Rndang on Angle at Bolt Diameter = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.75 * 0.38 * 65.00 = 32.91 kips/bolt
Angle bearing capacity, (phi)Rnang = min((phi)Rnsang,(phi)Rneang,(phi)Rndang) = min(na, 26.74, 32.91) = 26.74 kips/bolt
(phi)Rn = min((phi)Rnsupp, (phi)Rnang) = min(31.15, 26.74) = 26.74 kips/bolt
Bolt Shear Demand to Bearing ratio = 26.74 / 17.56 = 1.52
At Row 2, At Column 1:
Ribolt = 17.23 kips
Ri vector at Support = <-4.60, -16.61>
Lcssupp at Support spacing = na
Lcesupp at Support edge = 12.05 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 * 12.05 * (0.35/1) * 65.00 = 250.16 kips/bolt
(phi)Rndsupp on Support at Bolt Diameter = (phi) * hf2 * db * (twsup/# bolt sides supported) * Fu = 0.75 * 2.40 * 0.75 * (0.35/1) * 65.00 = 31.15 kips/bolt
Support bearing capacity, (phi)Rnsupp = min((phi)Rnssupp,(phi)Rnesupp,(phi)Rndsupp) = min(na, 250.16, 31.15) = 31.15 kips/bolt
Ri vector at Angle = <4.60, 16.61>
Lcsang at Angle spacing = na
Lceang at Angle edge = 4.00 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 * 4.00 * 0.38 * 65.00 = 87.83 kips/bolt
(phi)Rndang on Angle at Bolt Diameter = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.75 * 0.38 * 65.00 = 32.91 kips/bolt
Angle bearing capacity, (phi)Rnang = min((phi)Rnsang,(phi)Rneang,(phi)Rndang) = min(na, 87.83, 32.91) = 32.91 kips/bolt
(phi)Rn = min((phi)Rnsupp, (phi)Rnang) = min(31.15, 32.91) = 31.15 kips/bolt
Bolt Shear Demand to Bearing ratio = 31.15 / 17.23 = 1.81
At Row 3, At Column 1:
Ribolt = 17.23 kips
Ri vector at Support = <4.60, -16.60>
Lcssupp at Support spacing = na
Lcesupp at Support edge = 8.93 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 * 8.93 * (0.35/1) * 65.00 = 185.51 kips/bolt
(phi)Rndsupp on Support at Bolt Diameter = (phi) * hf2 * db * (twsup/# bolt sides supported) * Fu = 0.75 * 2.40 * 0.75 * (0.35/1) * 65.00 = 31.15 kips/bolt
Support bearing capacity, (phi)Rnsupp = min((phi)Rnssupp,(phi)Rnesupp,(phi)Rndsupp) = min(na, 185.51, 31.15) = 31.15 kips/bolt
Ri vector at Angle = <-4.60, 16.60>
Lcsang at Angle spacing = na
Lceang at Angle edge = 6.16 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 * 6.16 * 0.38 * 65.00 = 135.21 kips/bolt
(phi)Rndang on Angle at Bolt Diameter = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.75 * 0.38 * 65.00 = 32.91 kips/bolt
Angle bearing capacity, (phi)Rnang = min((phi)Rnsang,(phi)Rneang,(phi)Rndang) = min(na, 135.21, 32.91) = 32.91 kips/bolt
(phi)Rn = min((phi)Rnsupp, (phi)Rnang) = min(31.15, 32.91) = 31.15 kips/bolt
Bolt Shear Demand to Bearing ratio = 31.15 / 17.23 = 1.81
At Row 4, At Column 1:
Ribolt = 17.56 kips
Ri vector at Support = <11.22, -13.51>
Lcssupp at Support spacing = na
Lcesupp at Support edge = 7.39 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 * 7.39 * (0.35/1) * 65.00 = 153.58 kips/bolt
(phi)Rndsupp on Support at Bolt Diameter = (phi) * hf2 * db * (twsup/# bolt sides supported) * Fu = 0.75 * 2.40 * 0.75 * (0.35/1) * 65.00 = 31.15 kips/bolt
Support bearing capacity, (phi)Rnsupp = min((phi)Rnssupp,(phi)Rnesupp,(phi)Rndsupp) = min(na, 153.58, 31.15) = 31.15 kips/bolt
Ri vector at Angle = <-11.22, 13.51>
Lcsang at Angle spacing = na
Lceang at Angle edge = 2.34 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 * 2.34 * 0.38 * 65.00 = 51.29 kips/bolt
(phi)Rndang on Angle at Bolt Diameter = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.75 * 0.38 * 65.00 = 32.91 kips/bolt
Angle bearing capacity, (phi)Rnang = min((phi)Rnsang,(phi)Rneang,(phi)Rndang) = min(na, 51.29, 32.91) = 32.91 kips/bolt
(phi)Rn = min((phi)Rnsupp, (phi)Rnang) = min(31.15, 32.91) = 31.15 kips/bolt
Bolt Shear Demand to Bearing ratio = 31.15 / 17.56 = 1.77
Min Bolt Shear Demand to Bearing ratio Support and Angle for vertical shear only
= min(1.00, 1.52, 1.81, 1.81, 1.77) = 1.00
BEARING AT SUPPORT AND ANGLE SUMMARY:
Bearing Capacity at Vertical Shear Load Only, Rbv = Min Bolt Shear Demand to Bearing Ratio * Bolt Shear = 1.00 * 60.22 = 60.22 kips
60.22 kips >= 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), Ag = [Gross Shear Length] * tw = 14.75 * 0.30 = 4.50 in^2
Shear Yielding, (phi)Vny = (phi) * 0.6 * Fybeam * Ag = 1.00 * 0.6 * 50.00 * 4.50 = 134.96 kips
Using AISC 14th Ed. Equation J4-4
Net Area (Shear), Anet = [Gross Shear Length] * tw = 14.75 * 0.30 = 4.50 in^2
Shear Rupture, (phi)Vnu = (phi) * 0.6 * Fubeam * Anet = 0.75 * 0.6 * 65.00 * 4.50 = 131.59 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] = 12.00 in.
Net Shear Length = 12.00 in.
Gross Tension Length = [horizontal weld length] = 2.00 in.
Net Tension Length = 2.00 in.
1. (phi) * [material thickness] * ((0.60 * Fubeam* [net shear length]) + (Ubs * Fubeam * [net tension length]))
= 0.75 * 0.30 * ((0.60 * 65.00 * 12.00) + (1.00 * 65.00 * 2.00)) = 136.80 kips
2. (phi) * [material thickness] * ((0.60 * Fybeam * [gross shear length]) + (Ubs * Fubeam * [net tension length]))
= 0.75 * 0.30 * ((0.60 * 50.00 * 12.00) + (1.00 * 65.00 * 2.00)) = 112.09 kips
Block Shear = 112.09 kips
112.09 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
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) |
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 * 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.] = 1.25 in.
Net Tension Length = (1.25 - (0.81 + 1/16)/2) = 0.81 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 * 0.81)) = 93.63 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 * 0.81)) = 101.27 kips
Block Shear = 93.63 kips
Flexural and Buckling Strength:
Eccentricity at Bolt Column = 1.91
Zgross = 12.40 in^3
Znet = 8.46 in^3
Sgross = 8.27 in^3
Snet = 5.68 in^3
Using AISC 14th Ed. Equation 9-19
Flexural Yielding = (phi) * Fy * Sgross / e = 0.90 * 50.00 * 8.27 / 1.91 = 195.12 kips
Using AISC 14th Ed. Equation 9-4
Flexural Rupture = (phi) * Fu * Znet / e = 0.75 * 65.00 * 8.46 / 1.91 = 216.38 kips
Using AISC 14th Ed. Equation 9-14 through 9-18, Fcr = Fy * Q
tw = 0.38 in.
ho = 11.50 in.
c = 1.75 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 * (11.50/1.75)^2 )^0.5) = 0.19
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 / 1.91 = 195.12 kips
Stress Interaction on Angle due to Combined Shear and Moment Loading:
Zgx = 12.40 in^3
Znx = 8.46 in^3
Eccentricity = 1.91 in.
Mrx = 2.00 * 1.91 = 3.81 kips-in
Shear Stress on Gross Section = 2.00 / 4.31 = 0.46 ksi
Shear Stress on Net Section = 2.00 / 3.00 = 0.67 ksi
Axial Stress on Gross Section due to Moment (shear) = 3.81 / 12.40 = 0.31 ksi
Axial Stress on Net Section due to Moment (shear) = 3.81 / 8.46 = 0.45 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 = (0.46 / 30.00)^2 + (0.31 / 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 = (0.67 / 29.25)^2 + (0.45 / 48.75 )^2 = 0.00 <= 1.0 (OK)
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 * 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 = 2.24
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 / 2.24 = 165.91 kips
Using AISC 14th Ed. Equation 9-4
Flexural Rupture = (phi) * Fu * Znet / e = 0.75 * 65.00 * 12.40 / 2.24 = 269.61 kips
Using AISC 14th Ed. Equation 9-14 through 9-18, Fcr = Fy * Q
tw = 0.38 in.
ho = 11.50 in.
c = 2.24 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 * (11.50/2.24)^2 )^0.5) = 0.24
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 / 2.24 = 165.91 kips
Support Side Shear Yielding Capacity = 129.38 kips
129.38 kips >= Reaction V = 2.00 kips (OK)
Support Side Shear Rupture Capacity = 87.75 kips
87.75 kips >= Reaction V = 2.00 kips (OK)
Support Side Vertical Block Shear Capacity = 93.63 kips
93.63 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 = 126.14 kips
126.14 kips >= Reaction V = 2.00 kips (OK)
Support Side Flexure Yielding Capacity = 195.12 kips
195.12 kips >= Reaction V = 2.00 kips (OK)
Support Side Flexure Rupture Capacity = 216.38 kips
216.38 kips >= Reaction V = 2.00 kips (OK)
Support Side Bending Buckling Capacity = 195.12 kips
195.12 kips >= Reaction V = 2.00 kips (OK)
Beam Side Flexure Yielding Capacity = 165.91 kips
165.91 kips >= Reaction V = 2.00 kips (OK)
Beam Side Flexure Rupture Capacity = 269.61 kips
269.61 kips >= Reaction V = 2.00 kips (OK)
Beam Side Bending Buckling Capacity = 165.91 kips
165.91 kips >= Reaction V = 2.00 kips (OK) |
Angles Welded to Beam:
Angle1 Beam Weld:
k = 0.17
ex = 2.24
a = ex / l = 2.24 / 11.50 = 0.19
Loadangle = 0.00 deg
Weld Coefficient = 0.60 * Fexx * cphi * arrangement coefficient = 2.52
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)
= twbeam * Fubeam / ( Fexx * C1 * 0.04 )
= 0.30 * 65.00 / ( 70.00 * 1.00 * 0.04 )
= 6.41
Dmax3 = project max fillet weld = 12.00
Dmax=min(Dmax1, Dmax2, Dmax3) = min(5.00, 6.41, 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 * 2.52 * 11.50 * 4.00 = 87.10 kips |
