BOLT BEARING AT BEAM SIDE:
Vertical Shear Only Load Case:
ICR cordinate relative to CG = (3.68, 0.00)
At Row 1, At Column 1:
Ri1 = 11.71 kips
Ri vector at Beam = <7.40, 9.07>
Lcsbm at Beam spacing = na
Lcebm at Beam edge = 3.47 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * na * (0.23/1) * 65.00 = na
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 3.47 * (0.23/1) * 65.00 = 31.08 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.23/1) * 65.00 = 13.46 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(na, 31.08, 13.46) = 13.46 kips/bolt
Ri vector at Shear Plate = <-7.40, -9.07>
Lcsshpl at Shear Plate spacing = na
Lceshpl at Shear Plate edge = 4.22 in.
1/omegaRnsshpl at Shear Plate spacing = 1/omega * hf1 * Lcs * t * Fu = 0.50 * 1.20 * na * 0.38 * 58.00 = na
1/omegaRneshpl at Shear Plate edge = 1/omega * hf1 * Lce * t * Fu = 0.50 * 1.20 * 4.22 * 0.38 * 58.00 = 55.10 kips/bolt
1/omegaRndshpl on Shear Plate at Bolt Diameter = 1/omega * hf2 * db * t * Fu = 0.50 * 2.40 * 0.75 * 0.38 * 58.00 = 19.57 kips/bolt
Shear Plate bearing capacity, 1/omegaRnshpl = min(1/omegaRnsshpl,1/omegaRneshpl,1/omegaRndshpl) = min(na, 55.10, 19.57) = 19.57 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(13.455, 19.575) = 13.46 kips/bolt
Bolt Shear Demand to Bearing ratio = 13.46 / 11.71 = 1.15
At Row 2, At Column 1:
Ri1 = 11.45 kips
Ri vector at Beam = <-0.00, 11.45>
Lcsbm at Beam spacing = 2.19 in.
Lcebm at Beam edge = 5.59 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * 2.19 * (0.23/1) * 65.00 = 19.62 kips/bolt
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 5.59 * (0.23/1) * 65.00 = 50.18 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.23/1) * 65.00 = 13.46 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(19.62, 50.18, 13.46) = 13.46 kips/bolt
Ri vector at Shear Plate = <0.00, -11.45>
Lcsshpl at Shear Plate spacing = 2.19 in.
Lceshpl at Shear Plate edge = 3.84 in.
1/omegaRnsshpl at Shear Plate spacing = 1/omega * hf1 * Lcs * t * Fu = 0.50 * 1.20 * 2.19 * 0.38 * 58.00 = 28.55 kips/bolt
1/omegaRneshpl at Shear Plate edge = 1/omega * hf1 * Lce * t * Fu = 0.50 * 1.20 * 3.84 * 0.38 * 58.00 = 50.16 kips/bolt
1/omegaRndshpl on Shear Plate at Bolt Diameter = 1/omega * hf2 * db * t * Fu = 0.50 * 2.40 * 0.75 * 0.38 * 58.00 = 19.57 kips/bolt
Shear Plate bearing capacity, 1/omegaRnshpl = min(1/omegaRnsshpl,1/omegaRneshpl,1/omegaRndshpl) = min(28.55, 50.16, 19.57) = 19.57 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(13.455, 19.575) = 13.46 kips/bolt
Bolt Shear Demand to Bearing ratio = 13.46 / 11.45 = 1.18
At Row 3, At Column 1:
Ri1 = 11.71 kips
Ri vector at Beam = <-7.40, 9.07>
Lcsbm at Beam spacing = na
Lcebm at Beam edge = 2.76 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * na * (0.23/1) * 65.00 = na
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 2.76 * (0.23/1) * 65.00 = 24.74 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.23/1) * 65.00 = 13.46 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(na, 24.74, 13.46) = 13.46 kips/bolt
Ri vector at Shear Plate = <7.40, -9.07>
Lcsshpl at Shear Plate spacing = na
Lceshpl at Shear Plate edge = 1.09 in.
1/omegaRnsshpl at Shear Plate spacing = 1/omega * hf1 * Lcs * t * Fu = 0.50 * 1.20 * na * 0.38 * 58.00 = na
1/omegaRneshpl at Shear Plate edge = 1/omega * hf1 * Lce * t * Fu = 0.50 * 1.20 * 1.09 * 0.38 * 58.00 = 14.21 kips/bolt
1/omegaRndshpl on Shear Plate at Bolt Diameter = 1/omega * hf2 * db * t * Fu = 0.50 * 2.40 * 0.75 * 0.38 * 58.00 = 19.57 kips/bolt
Shear Plate bearing capacity, 1/omegaRnshpl = min(1/omegaRnsshpl,1/omegaRneshpl,1/omegaRndshpl) = min(na, 14.21, 19.57) = 14.21 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(13.455, 14.210) = 13.46 kips/bolt
Bolt Shear Demand to Bearing ratio = 13.46 / 11.71 = 1.15
Min Bolt Shear Demand to Bearing ratio for vertical shear only = min(1.0, 1.14926, 1.17514, 1.14925) = 1.00
Bearing Capacity at Beam and Shear Plate at Vertical Shear Load Only, Rbv1 = Min Bolt Shear Demand to Bearing Ratio * Bolt Shear = 1.00 * 29.59 = 29.59 kips |
Gross Area = 0.38 * 8.50 = 3.19 in^2
Net Area = (8.50 - (3 *(0.81 + 1/16))) * 0.38 = 2.20 in^2
Using Eq.J4-3:
Shear Yielding = (1/omega) * 0.6 * Fypl * [Gross Area] = 0.67 * 0.6 * 36.00 * 3.19 = 45.90 kips
Using Eq.J4-4:
Shear Rupture = (1/omega) * 0.6 * Fupl * [Net Area] = 0.50 * 0.6 * 58.00 * 2.20 = 38.33 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 1 (Shear):
Gross Shear Length = (8.5 - 1.25) = 7.25 in.
Net Shear Length = 7.25 - (2.5 * (0.812 + 0.0625)) = 5.06 in.
Gross Tension Length = (0 + 1.5) = 1.50 in.
Net Tension Length = 1.5 - (0.5 * (1 + 0.0625)) = 0.97 in.
1. (1/omega) * [material thickness] * ((0.60 * Fupl* [net shear length]) + (Ubs * Fupl * [net tension length]))
= 0.50 * 0.38 * ((0.60 * 58.00 * 5.06) + (1.00 * 58.00 * 0.97)) = 43.57 kips
2. (1/omega) * [material thickness] * ((0.60 * Fypl * [gross shear length]) + (Ubs * Fupl * [net tension length]))
= 0.50 * 0.38 * ((0.60 * 36.00 * 7.25) + (1.00 * 58.00 * 0.97)) = 39.90 kips
Block Shear = 39.90 kips
Interaction Check of Flexural Yielding, Per AISC 10-5:
Eccentricity due to Conventional Config. (e = a/2), e = 1.50 in.
Zgross = 6.77
Znet = 4.73
Mr = Vr * e = 18.93 * 1.50 = 28.40 kips-in
Mc = 1/omega * Mn = 1/omega * Fy * Zgross = 0.60 * 36.00 * 6.77 = 146.31 kips-in
Vr = 18.93 kips
Vc = 1/omega * Vn = 1/omega * 0.60 * Fy * Ag = 0.67 * 0.60 * 36.00 * 3.19 = 45.90 kips
Interaction due to moment and shear, (Vr/Vc)^2 + (Mr/Mc)^2 <= 1.0
(Vr/Vc)^2 + (Mr/Mc)^2 = (18.93 / 45.90)^2 + (28.40 / 146.31)^2 = 0.21 <= 1 (OK)
Note: Mn <= 1.6My by inspection
MAXIMUM PLATE THICKNESS:
No of columns = 1
Distance cl top to cl bot bolts <= 12" (Equivalent depth of n = 1 to 5 at 3", AISC Table 10-9)
Slot shape = SSL
tmax = Unlimited
Maximum Plate Thickness is Not a Limiting Criteria.
Check Limits of Applicability Table K1.2A
Plate load angle:
theta = 90.00 >= 30 deg (OK)
HSS wall slenderness:
B/t or H/t = 16 / 0.465 = 34.4086 <= 35 (OK)
(B-3t)/t <= 1.40 * (E / Fy)^0.5 for loaded wall, for branch plate shear loading
(16.00 - 3 * 0.47) / 0.47 = 31.41 <= 1.40 * (29000 / 46.00)^0.5 = 35.15 (OK)
Width Ratio:
Bp/B = 8.5 / 16 = 0.53
0.25 <= 0.53 <= 1.0 (OK)
Material Strength:
Fy = 46.00 <= 52 ksi (OK)
Ductility:
Fy/Fu = 46.00 / 58.00 <= 0.80 (OK)
AISC K1-3, Plate Limit States and HSS Punching Shear :
tpl <= thss * Fuhss/Fypl
0.38 <= 0.47 * 58.00 / 36.00 = 0.75 in. (OK) |
WELD:
Weld Requirements:
At shear only case:
Weld Length for shear, Lv = 8.500 in.
Shear Load per inch per weld, fv = R/Lv/2 = 18.934 / 8.500 / 2 = 1.114 kips/in/ weld
theta = 0 deg.
cPhi = 1.0 + 0.5 * sin(0)^1.5 = 1.000
Weld Coefficient = 0.6 * 70.000 * 1.000 * 1.000 * (2^0.5/2)*(1/16) = 1.856
Required weld size, Dv = fv/ (1/omega * coeff) = 1.114 / (0.500 * 1.856) = 1.200/16
Minimum fillet weld size :
At shear only load case = 0.08 in.
per Table J2.4 = 0.19 in.
5/8(tp) = 0.23 in.
user preference = 0.25 in.
Dmax1 (using eqn 9-3)
= tshpl * Fushpl / ( Fexx * C1 * 0.088)
= 0.375 * 58.000 / ( 70.000 * 1.000 * 0.088 )
= 3.515
Dmax2 (using eqn 9-2)
= thss * Fuhss / ( Fexx * C1 * 0.044 )
= 0.465 * 58.000 / ( 70.000 * 1.000 * 0.044 )
= 8.718
Dmax3 = project max fillet weld = 12.000
Dmax=min(Dmax1, Dmax2, Dmax3) = min(3.515, 8.718, 12.000)
= 3.515
Use weld size
D1 = 4.00
D2 = 4.00
Weld Strength :
Vertical weld capacity during shear only load, 1/omega * Rnv1 = 0.50 * 1.86 * 8.50 * (3.52 + 3.52) = 55.46 kips |
