BOLT BEARING AT BEAM AND SHEAR PLATE SIDE
Vertical Shear Only Load Case:
ICR cordinate relative to CG = (1.54, -0.00)
At Row 1, At Column 1:
Ribolt = 39.32 kips
Ri vector at Beam = <37.20, 12.73>
Lcsbm at Beam spacing = na
Lcebm at Beam edge = 8.73 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 * 8.73 * (0.32/1) * 65.00 = 160.94 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 1.00 * (0.32/1) * 65.00 = 36.86 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(na, 160.94, 36.86) = 36.86 kips/bolt
Ri vector at Shear Plate = <-37.20, -12.73>
Lcsshpl at Shear Plate spacing = na
Lceshpl at Shear Plate edge = 5.25 in.
(phi)Rnsshpl at Shear Plate spacing = (phi) * hf1 * Lcs * t * Fu = na
(phi)Rneshpl at Shear Plate edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 5.25 * 0.38 * 65.00 = 115.21 kips/bolt
(phi)Rndshpl on Shear Plate at Bolt Diameter = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 1.00 * 0.38 * 65.00 = 43.88 kips/bolt
Shear Plate bearing capacity, (phi)Rnshpl = min((phi)Rnsshpl,(phi)Rneshpl,(phi)Rndshpl) = min(na, 115.21, 43.88) = 43.88 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(36.86, 43.88) = 36.86 kips/bolt
Bolt Shear Demand to Bearing ratio = 36.86 / 39.32 = 0.94
At Row 2, At Column 1:
Ribolt = 32.07 kips
Ri vector at Beam = <0.00, 32.07>
Lcsbm at Beam spacing = 3.44 in.
Lcebm at Beam edge = 6.97 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.75 * 1.20 * 3.44 * (0.32/1) * 65.00 = 63.35 kips/bolt
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 6.97 * (0.32/1) * 65.00 = 128.42 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 1.00 * (0.32/1) * 65.00 = 36.86 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(63.35, 128.42, 36.86) = 36.86 kips/bolt
Ri vector at Shear Plate = <-0.00, -32.07>
Lcsshpl at Shear Plate spacing = 3.44 in.
Lceshpl at Shear Plate edge = 5.47 in.
(phi)Rnsshpl at Shear Plate spacing = (phi) * hf1 * Lcs * t * Fu = 0.75 * 1.20 * 3.44 * 0.38 * 65.00 = 75.41 kips/bolt
(phi)Rneshpl at Shear Plate edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 5.47 * 0.38 * 65.00 = 119.97 kips/bolt
(phi)Rndshpl on Shear Plate at Bolt Diameter = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 1.00 * 0.38 * 65.00 = 43.88 kips/bolt
Shear Plate bearing capacity, (phi)Rnshpl = min((phi)Rnsshpl,(phi)Rneshpl,(phi)Rndshpl) = min(75.41, 119.97, 43.88) = 43.88 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(36.86, 43.88) = 36.86 kips/bolt
Bolt Shear Demand to Bearing ratio = 36.86 / 32.07 = 1.15
At Row 3, At Column 1:
Ribolt = 39.32 kips
Ri vector at Beam = <-37.20, 12.73>
Lcsbm at Beam spacing = na
Lcebm at Beam edge = 1.58 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 * 1.58 * (0.32/1) * 65.00 = 29.16 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 1.00 * (0.32/1) * 65.00 = 36.86 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(na, 29.16, 36.86) = 29.16 kips/bolt
Ri vector at Shear Plate = <37.20, -12.73>
Lcsshpl at Shear Plate spacing = na
Lceshpl at Shear Plate edge = 1.42 in.
(phi)Rnsshpl at Shear Plate spacing = (phi) * hf1 * Lcs * t * Fu = na
(phi)Rneshpl at Shear Plate edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 1.42 * 0.38 * 65.00 = 31.16 kips/bolt
(phi)Rndshpl on Shear Plate at Bolt Diameter = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 1.00 * 0.38 * 65.00 = 43.88 kips/bolt
Shear Plate bearing capacity, (phi)Rnshpl = min((phi)Rnsshpl,(phi)Rneshpl,(phi)Rndshpl) = min(na, 31.16, 43.88) = 31.16 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(29.16, 31.16) = 29.16 kips/bolt
Bolt Shear Demand to Bearing ratio = 29.16 / 39.32 = 0.74
Min Bolt Shear Demand to Bearing ratio Beam and Shear Plate for vertical shear only
= min(1.00, 0.94, 1.15, 0.74) = 0.74
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 = 0.74 * 57.53 = 42.68 kips
Rbv = 42.68 kips >= Reaction V = 30.00 kips (OK) |
Using AISC 14th Ed. Equation J4-3
Gross Area, Ag = 0.38 * 12.00 = 4.50 in^2
Shear Yielding, (phi)Vny = (phi) * 0.6 * Fypl * Ag = 1.00 * 0.6 * 50.00 * 4.50 = 135.00 kips
135.00 kips >= Reaction V = 30.00 kips (OK)
Using AISC 14th Ed. Equation J4-4
Net Area, An = (12.00 - (3 * (1.06 + 1/16))) * 0.38 = 3.23 in^2
Shear Rupture, (phi)Vnu = (phi) * 0.6 * Fupl * An = 0.75 * 0.6 * 65.00 * 3.23 = 94.61 kips
94.61 kips >= Reaction V = 30.00 kips (OK)
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 = (12.00 - 1.50) = 10.50 in.
Net Shear Length = 10.50 - (2.50 * (1.06 + 0.06)) = 7.69 in.
Gross Tension Length = (0.00 + 2.00) = 2.00 in.
Net Tension Length = 2.00 - (0.50 * (1.31 + 0.06)) = 1.31 in.
1. (phi) * [material thickness] * ((0.60 * Fupl* [net shear length]) + (Ubs * Fupl * [net tension length]))
= 0.75 * 0.38 * ((0.60 * 65.00 * 7.69) + (1.00 * 65.00 * 1.31)) = 108.32 kips
2. (phi) * [material thickness] * ((0.60 * Fypl * [gross shear length]) + (Ubs * Fupl * [net tension length]))
= 0.75 * 0.38 * ((0.60 * 50.00 * 10.50) + (1.00 * 65.00 * 1.31)) = 112.59 kips
Block Shear = 108.32 kips
108.32 kips >= Reaction V = 30.00 kips (OK)
Block Shear for Axial T/C is not required.
Flexural and Buckling Strength:
Eccentricity at first line of bolts, e = 5.82 in.
Zgross = 13.50 in^3
Znet = 9.58 in^3
Sgross = 9.00 in^3
Snet = 6.15 in^3
Using AISC 14th Ed. Equation 9-4
Flexural Rupture = (phi) * Fu * Znet / e = 0.75 * 65.00 * 9.58 / 5.82 = 80.35 kips
Using AISC 14th Ed. Equation 9-14 through 9-18, Fcr = Fy * Q
tw = 0.38 in.
ho = 12.00 in.
c = 5.62 in.
lambda = (ho * Fy ^ 0.5) / ( 10 * tw * ( 475.00 + 280.00 * (ho / c)^2 ) ^0.5 ) =
= 12.00 * 50.00^0.5 / (10 * 0.38 * (475.00 + 280.00 * (12.00/5.62)^2 )^0.5) = 0.54
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 * 9.00 / 5.82 = 69.65 kips
Interaction Check of Flexural Yielding, Per AISC 10-5:
Eccentricity at CG of Bolt Group, e = 5.82 in.
Zgross = 13.50
Znet = 9.58
Mr = Vr * e = 30.00 * 5.82 = 174.45 kips-in
Mc = phi * Mn = phi * Fy * Zgross = 0.90 * 50.00 * 13.50 = 607.50 kips-in
Vr = 30.00 kips
Vc = phi * Vn = phi * 0.60 * Fy * Ag = 1.00 * 0.60 * 50.00 * 4.50 = 135.00 kips
Interaction due to moment and shear, (Vr/Vc)^2 + (Mr/Mc)^2 <= 1.0
(Vr/Vc)^2 + (Mr/Mc)^2 = (30.00 / 135.00)^2 + (174.45 / 607.50)^2 = 0.13 <= 1 (OK)
Note: Mn <= 1.6My by inspection
MAXIMUM PLATE THICKNESS:
No of bolt columns = 1
tp < = db/2 + 1/16 = 0.38 <= 0.56 OK
tw < = db/2 + 1/16 = 0.32 <= 0.56 OK
Leh(plate) >= 2 * db = 2.00 >= 2.00 OK
Leh(bm) >= 2 * db = 2.00 >= 2.00 OK
Maximum Plate Thickness is Not a Limiting Criteria. |
WELD:
Weld Requirements:
At shear only case:
Weld Length for shear, Lv = 12.00 in.
Shear Load per inch per weld, fv = R/Lv/2 = 30.00 / 12.00 / 2 = 1.25 kips/in/ weld
theta = 0 deg.
cPhi = 1.0 + 0.5 * sin(0)^1.5 = 1.00
Weld Coefficient = 0.60 * 70.00 * 1.00 * 1.00 * (2^0.5/2)*(1/16) = 1.86
Required weld size, Dv = fv/ (phi * coeff) = 1.25 / (0.75 * 1.86) = 0.90/16
Minimum fillet weld size :
At shear only load case = 0.06 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 * 0.09)
= 0.38 * 65.00 / ( 70.00 * 1.00 * 0.09 )
= 3.94
Dmax2 (using eqn 9-3)
= twsupport * Fusupport / ( Fexx * C1 * 0.09 )
= 0.38 * 65.00 / ( 70.00 * 1.00 * 0.09 )
= 3.99
Dmax3 = project max fillet weld = 12.00
Dmax=min(Dmax1, Dmax2, Dmax3) = min(3.94, 3.99, 12.00)
= 3.94
Use weld size
D1 = 4.00
D2 = 4.00
Weld Strength :
Vertical weld capacity during shear only load, phi * Rnv1 = 0.75 * 1.86 * 12.00 * (3.94 + 3.94) = 131.63 kips
131.63 kips >= Reaction V = 30.00 kips (OK) |
