BOLT BEARING AT BEAM AND SHEAR PLATE SIDE
Vertical Shear Only Load Case:
ICR cordinate relative to CG = (0.55, -0.00)
At Row 1, At Column 1:
Ribolt = 23.90 kips
Ri vector at Beam = <23.51, 4.30>
Lcsbm at Beam spacing = na
Lcebm at Beam edge = 16.21 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.75 * 1.20 * na * (0.30/1) * 65.00 = na
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 16.21 * (0.30/1) * 65.00 = 289.23 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.88 * (0.30/1) * 65.00 = 31.23 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(na, 289.23, 31.23) = 31.23 kips/bolt
Ri vector at Shear Plate = <-23.51, -4.30>
Lcsshpl at Shear Plate spacing = na
Lceshpl at Shear Plate edge = 5.15 in.
(phi)Rnsshpl at Shear Plate spacing = (phi) * hf1 * Lcs * t * Fu = 0.75 * 1.20 * na * 0.38 * 65.00 = na
(phi)Rneshpl at Shear Plate edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 5.15 * 0.38 * 65.00 = 112.90 kips/bolt
(phi)Rndshpl on Shear Plate at Bolt Diameter = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.88 * 0.38 * 65.00 = 38.39 kips/bolt
Shear Plate bearing capacity, (phi)Rnshpl = min((phi)Rnsshpl,(phi)Rneshpl,(phi)Rndshpl) = min(na, 112.90, 38.39) = 38.39 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(31.225, 38.392) = 31.23 kips/bolt
Bolt Shear Demand to Bearing ratio = 31.23 / 23.90 = 1.31
At Row 2, At Column 1:
Ribolt = 15.84 kips
Ri vector at Beam = <-0.00, 15.84>
Lcsbm at Beam spacing = 2.06 in.
Lcebm at Beam edge = 5.53 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.75 * 1.20 * 2.06 * (0.30/1) * 65.00 = 36.80 kips/bolt
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 5.53 * (0.30/1) * 65.00 = 98.69 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.88 * (0.30/1) * 65.00 = 31.23 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(36.80, 98.69, 31.23) = 31.23 kips/bolt
Ri vector at Shear Plate = <0.00, -15.84>
Lcsshpl at Shear Plate spacing = 2.06 in.
Lceshpl at Shear Plate edge = 3.78 in.
(phi)Rnsshpl at Shear Plate spacing = (phi) * hf1 * Lcs * t * Fu = 0.75 * 1.20 * 2.06 * 0.38 * 65.00 = 45.25 kips/bolt
(phi)Rneshpl at Shear Plate edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 3.78 * 0.38 * 65.00 = 82.95 kips/bolt
(phi)Rndshpl on Shear Plate at Bolt Diameter = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.88 * 0.38 * 65.00 = 38.39 kips/bolt
Shear Plate bearing capacity, (phi)Rnshpl = min((phi)Rnsshpl,(phi)Rneshpl,(phi)Rndshpl) = min(45.25, 82.95, 38.39) = 38.39 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(31.225, 38.392) = 31.23 kips/bolt
Bolt Shear Demand to Bearing ratio = 31.23 / 15.84 = 1.97
At Row 3, At Column 1:
Ribolt = 23.90 kips
Ri vector at Beam = <-23.51, 4.30>
Lcsbm at Beam spacing = na
Lcebm at Beam edge = 1.31 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.75 * 1.20 * na * (0.30/1) * 65.00 = na
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 1.31 * (0.30/1) * 65.00 = 23.38 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.88 * (0.30/1) * 65.00 = 31.23 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(na, 23.38, 31.23) = 23.38 kips/bolt
Ri vector at Shear Plate = <23.51, -4.30>
Lcsshpl at Shear Plate spacing = na
Lceshpl at Shear Plate edge = 1.33 in.
(phi)Rnsshpl at Shear Plate spacing = (phi) * hf1 * Lcs * t * Fu = 0.75 * 1.20 * na * 0.38 * 65.00 = na
(phi)Rneshpl at Shear Plate edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 1.33 * 0.38 * 65.00 = 29.27 kips/bolt
(phi)Rndshpl on Shear Plate at Bolt Diameter = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.88 * 0.38 * 65.00 = 38.39 kips/bolt
Shear Plate bearing capacity, (phi)Rnshpl = min((phi)Rnsshpl,(phi)Rneshpl,(phi)Rndshpl) = min(na, 29.27, 38.39) = 29.27 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(23.379, 29.271) = 23.38 kips/bolt
Bolt Shear Demand to Bearing ratio = 23.38 / 23.90 = 0.98
Min Bolt Shear Demand to Bearing ratio Beam and Shear Plate for vertical shear only
= min(1.00, 1.31, 1.97, 0.98) = 0.98
BEARING AT BEAM AND SHEAR PLATE SIDE SUMMARY:
Bearing Capacity at Vertical Shear Load Only, Rbv = Min Bolt Shear Demand to Bearing Ratio * Bolt Shear = 0.98 * 24.44 = 23.90 kips
Rbv = 23.90 kips >= Reaction V = 2.00 kips (OK) |
Gross Area = 0.38 * 8.50 = 3.19 in^2
Net Area = (8.50 - (3 *(0.94 + 1/16))) * 0.38 = 2.06 in^2
Using Eq.J4-3:
Shear Yielding = (phi) * 0.6 * Fypl * [Gross Area] = 1.00 * 0.6 * 50.00 * 3.19 = 95.62 kips
Using Eq.J4-4:
Shear Rupture = (phi) * 0.6 * Fupl * [Net Area] = 0.75 * 0.6 * 65.00 * 2.06 = 60.33 kips
Block Shear
Using Eq.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 = (8.5 - 1.25) = 7.25 in.
Net Shear Length = 7.25 - (2.5 * (0.938 + 0.0625)) = 4.75 in.
Gross Tension Length = (0 + 1.88) = 1.88 in.
Net Tension Length = 1.88 - (0.5 * (1.12 + 0.0625)) = 1.28 in.
1. (phi) * [material thickness] * ((0.60 * Fupl* [net shear length]) + (Ubs * Fupl * [net tension length]))
= 0.75 * 0.38 * ((0.60 * 65.00 * 4.75) + (1.00 * 65.00 * 1.28)) = 75.53 kips
2. (phi) * [material thickness] * ((0.60 * Fypl * [gross shear length]) + (Ubs * Fupl * [net tension length]))
= 0.75 * 0.38 * ((0.60 * 50.00 * 7.25) + (1.00 * 65.00 * 1.28)) = 84.60 kips
Block Shear = 75.53 kips
75.53 kips >= Reaction V = 2.00 kips (OK)
Block Shear for Axial T/C is not required.
Flexural and Buckling Strength:
Eccentricity at first line of bolts, e = 5.78 in.
Zgross = 6.77 in^3
Znet = 4.43 in^3
Sgross = 4.52 in^3
Snet = 2.93 in^3
Using Eq. 9-4
Flexural Rupture = (phi) * Fu * Znet / e = 0.75 * 65.00 * 4.43 / 5.78 = 37.38 kips
Using Eq. 9-14 through 9-18, Fcr = Fy * Q
tw = 0.38 in.
ho = 8.50 in.
c = 5.62 in.
lambda = (ho * Fy ^ 0.5) / ( 10 * tw * ( 475.00 + 280.00 * (ho / c)^2 ) ^0.5 ) =
= 8.50 * 50.00^0.5 / (10 * 0.38 * (475.00 + 280.00 * (8.50/5.62)^2 )^0.5) = 0.48
When lambda <= 0.70, Q=1
Q = 1.00
Fcrmin =phi * Fcr = 0.90 * 50.00 * 1.00 = 45.00 ksi
Using Eq. 9-6
Buckling = Fcr * Sgross / e = 45.00 * 4.52 / 5.78 = 35.17 kips
Interaction Check of Flexural Yielding, Per AISC 10-5:
Eccentricity at CG of Bolt Group, e = 5.78 in.
Zgross = 6.77
Znet = 4.43
Mr = Vr * e = 2.00 * 5.78 = 11.55 kips-in
Mc = phi * Mn = phi * Fy * Zgross = 0.90 * 50.00 * 6.77 = 304.80 kips-in
Vr = 2.00 kips
Vc = phi * Vn = phi * 0.60 * Fy * Ag = 1.00 * 0.60 * 50.00 * 3.19 = 95.62 kips
Interaction due to moment and shear, (Vr/Vc)^2 + (Mr/Mc)^2 <= 1.0
(Vr/Vc)^2 + (Mr/Mc)^2 = (2.00 / 95.62)^2 + (11.55 / 304.80)^2 = 0.00 <= 1 (OK)
Note: Mn <= 1.6My by inspection
MAXIMUM PLATE THICKNESS:
No of bolt columns = 1
tp < = db/2 + 1/16 = 0.375 <= 0.5 OK
tw < = db/2 + 1/16 = 0.305 <= 0.5 OK
Leh(plate) >= 2 * db = 1.875 >= 1.75 OK
Leh(bm) >= 2 * db = 1.75 >= 1.75 OK
Maximum Plate Thickness is Not a Limiting Criteria. |
WELD:
Weld Requirements:
At shear only case:
Weld Length for shear, Lv = 13.375 in.
Shear Load per inch per weld, fv = R/Lv/2 = 2.000 / 13.375 / 2 = 0.075 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/ (phi * coeff) = 0.075 / (0.750 * 1.856) = 0.054/16
Minimum fillet weld size :
At shear only load case = 0.00 in.
per Table J2.4 = 0.19 in.
5/8tp = 0.23 in.
user preference = 0.25 in.
Dmax1 (using eqn 9-3)
= tshpl * Fushpl / ( Fexx * C1 * 0.088)
= 0.375 * 65.000 / ( 70.000 * 1.000 * 0.088 )
= 3.940
Dmax2 (using eqn 9-3)
= twsupport * Fusupport / ( Fexx * C1 * 0.088 )
= 0.305 * 65.000 / ( 70.000 * 1.000 * 0.088 )
= 3.204
Dmax3 = project max fillet weld = 12.000
Dmax=min(Dmax1, Dmax2, Dmax3) = min(3.940, 3.204, 12.000)
= 3.204
Use weld size
D1 = 4.00
D2 = 4.00
Weld Strength :
Vertical weld capacity during shear only load, phi * Rnv1 = 0.75 * 1.86 * 13.38 * (3.20 + 3.20) = 119.32 kips
119.32 kips >= Reaction V = 2.00 kips (OK) |
