BOLT BEARING AT BEAM AND SHEAR PLATE SIDE
Vertical Shear Only Load Case:
ICR cordinate relative to CG = (9.21, 0.00)
At Row 1, At Column 1:
Ribolt = 23.90 kips
Ri vector at Beam = <9.52, 21.93>
Lcsbm at Beam spacing = na
Lcebm at Beam edge = 1.44 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 * 1.44 * (0.30/1) * 65.00 = 25.68 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, 25.68, 31.23) = 25.68 kips/bolt
Ri vector at Shear Plate = <-9.52, -21.93>
Lcsshpl at Shear Plate spacing = na
Lceshpl at Shear Plate edge = 5.14 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 * 5.14 * 0.50 * 65.00 = 150.36 kips/bolt
(phi)Rndshpl on Shear Plate at Bolt Diameter = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.88 * 0.50 * 65.00 = 51.19 kips/bolt
Shear Plate bearing capacity, (phi)Rnshpl = min((phi)Rnsshpl,(phi)Rneshpl,(phi)Rndshpl) = min(na, 150.36, 51.19) = 51.19 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(25.68, 51.19) = 25.68 kips/bolt
Bolt Shear Demand to Bearing ratio = 25.68 / 23.90 = 1.07
At Row 2, At Column 1:
Ribolt = 23.76 kips
Ri vector at Beam = <-0.00, 23.76>
Lcsbm at Beam spacing = 3.06 in.
Lcebm at Beam edge = 5.28 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.75 * 1.20 * 3.06 * (0.30/1) * 65.00 = 54.64 kips/bolt
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 5.28 * (0.30/1) * 65.00 = 94.23 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(54.64, 94.23, 31.23) = 31.23 kips/bolt
Ri vector at Shear Plate = <0.00, -23.76>
Lcsshpl at Shear Plate spacing = 3.06 in.
Lceshpl at Shear Plate edge = 4.78 in.
(phi)Rnsshpl at Shear Plate spacing = (phi) * hf1 * Lcs * t * Fu = 0.75 * 1.20 * 3.06 * 0.50 * 65.00 = 89.58 kips/bolt
(phi)Rneshpl at Shear Plate edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 4.78 * 0.50 * 65.00 = 139.86 kips/bolt
(phi)Rndshpl on Shear Plate at Bolt Diameter = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.88 * 0.50 * 65.00 = 51.19 kips/bolt
Shear Plate bearing capacity, (phi)Rnshpl = min((phi)Rnsshpl,(phi)Rneshpl,(phi)Rndshpl) = min(89.58, 139.86, 51.19) = 51.19 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(31.23, 51.19) = 31.23 kips/bolt
Bolt Shear Demand to Bearing ratio = 31.23 / 23.76 = 1.31
At Row 3, At Column 1:
Ribolt = 23.90 kips
Ri vector at Beam = <-9.52, 21.93>
Lcsbm at Beam spacing = na
Lcebm at Beam edge = 3.92 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 * 3.92 * (0.30/1) * 65.00 = 70.03 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, 70.03, 31.23) = 31.23 kips/bolt
Ri vector at Shear Plate = <9.52, -21.93>
Lcsshpl at Shear Plate spacing = na
Lceshpl at Shear Plate edge = 0.85 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 * 0.85 * 0.50 * 65.00 = 24.91 kips/bolt
(phi)Rndshpl on Shear Plate at Bolt Diameter = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.88 * 0.50 * 65.00 = 51.19 kips/bolt
Shear Plate bearing capacity, (phi)Rnshpl = min((phi)Rnsshpl,(phi)Rneshpl,(phi)Rndshpl) = min(na, 24.91, 51.19) = 24.91 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(31.23, 24.91) = 24.91 kips/bolt
Bolt Shear Demand to Bearing ratio = 24.91 / 23.90 = 1.04
Min Bolt Shear Demand to Bearing ratio Beam and Shear Plate for vertical shear only
= min(1.00, 1.07, 1.31, 1.04) = 1.00
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 = 1.00 * 67.61 = 67.61 kips
Rbv = 67.61 kips >= Reaction V = 54.75 kips (OK) |
Web Depth = d - [Top Cope Depth] - [Bottom Cope Depth] = 16.00 - 1.25 - 1.25 = 13.50 in.
Using AISC 14th Ed. Equation J4-3
Gross Area (Shear), Agross = [Web Depth] * tw = 13.50 * 0.30 = 4.12 in^2
Shear Yielding, (phi)Vny = (phi) * 0.6 * Fybeam * Agross = 1.00 * 0.6 * 50.00 * 4.12 = 123.52 kips
Using AISC 14th Ed. Equation J4-4
Net Area (Shear), Anet = ([Web Depth] - ([# rows] * [Diameter + 0.06])) * tw
= (13.50 - (3 * 1.00)) * 0.30 = 3.20 in^2
Shear Rupture, (phi)Vnu = (phi) * 0.6 * Fubeam * Anet = 0.75 * 0.6 * 65.00 * 3.20 = 93.68 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 + 8.00 = 9.75 in.
Net Shear Length = Gross Shear Length - (# rows - 0.5) * (hole size + 0.06) = 9.75 - (3 - 0.5) * 1.00 = 7.25 in.
Gross Tension Length = [edge dist. at beam edge] + ([# cols - 1] * [spacing]) = 1.75 + (1 - 1) * 3.00 = 1.75 in.
Net Tension Length = Gross Tension Length - (# cols - 0.5) * (hole size + 0.06) = 1.75 - (1 - 0.5) * 1.00 = 1.25 in.
1. (phi) * [material thickness] * ((0.60 * Fubeam* [net shear length]) + (Ubs * Fubeam * [net tension length]))
= 0.75 * 0.30 * ((0.60 * 65.00 * 7.25) + (1.00 * 65.00 * 1.25)) = 83.27 kips
2. (phi) * [material thickness] * ((0.60 * Fybeam * [gross shear length]) + (Ubs * Fubeam * [net tension length]))
= 0.75 * 0.30 * ((0.60 * 50.00 * 9.75) + (1.00 * 65.00 * 1.25)) = 85.50 kips
Block Shear = 83.27 kips
Block Shear (1) Total = Block Shear (1) = 83.27 kips
83.27 kips >= Reaction V = 54.75 kips (OK)
Block Shear for Axial T/C is not required.
Buckling and Flexure at Longest Cope (Top and Bottom Copes at Section)
Eccentricity at Section, e = 4.15 in.
If beam is coped at both top and bottom flanges,
Using AISC 14th Ed. Equation 9-14 through 9-18, Fcr = Fy * Q
tw = 0.30 in.
ho = 13.50 in.
c = 3.50 in.
lambda = (ho * Fy ^ 0.5) / ( 10 * tw * ( 475.00 + 280.00 * (ho / c)^2 ) ^0.5 ) =
= 13.50 * 50.00^0.5 / (10 * 0.30 * (475.00 + 280.00 * (13.50/3.50)^2 )^0.5) = 0.46
When lambda <= 0.70, Q=1
Q = 1.00
Fcrmin =phi * Fcr = 0.90 * 50.00 * 1.00 = 45.00 ksi
Snet1 (bolt holes not applicable) = 9.26 in^3
Snet2 (bolt holes applicable) = 9.26 in^3
Znet1 (bolt holes not applicable) = 13.90 in^3
Znet2 (bolt holes applicable) = 13.90 in^3
Using AISC 14th Ed. Equation 9-6
Buckling = Fcr * Snet1 / e = 45.00 * 9.26 / 4.15 = 100.40 kips
Using AISC 14th Ed. Equation 9-19
Flexural Yielding = (phi) * Fy * Snet1 / e = 0.90 * 50.00 * 9.26 / 4.15 = 100.40 kips
Using AISC 14th Ed. Equation 9-4
Flexural Rupture = (phi) * Fu * Znet2 / e = 0.75 * 65.00 * 13.90 / 4.15 = 163.15 kips
Buckling and Flexure at Furthest Bolt Line within Cope (Top and Bottom Copes at Section)
Eccentricity at Section, e = 2.40 in.
If beam is coped at both top and bottom flanges,
Using AISC 14th Ed. Equation 9-14 through 9-18, Fcr = Fy * Q
tw = 0.30 in.
ho = 13.50 in.
c = 3.50 in.
lambda = (ho * Fy ^ 0.5) / ( 10 * tw * ( 475.00 + 280.00 * (ho / c)^2 ) ^0.5 ) =
= 13.50 * 50.00^0.5 / (10 * 0.30 * (475.00 + 280.00 * (13.50/3.50)^2 )^0.5) = 0.46
When lambda <= 0.70, Q=1
Q = 1.00
Fcrmin =phi * Fcr = 0.90 * 50.00 * 1.00 = 45.00 ksi
Snet1 (bolt holes not applicable) = 9.26 in^3
Snet2 (bolt holes applicable) = 7.32 in^3
Znet1 (bolt holes not applicable) = 13.90 in^3
Znet2 (bolt holes applicable) = 11.08 in^3
Using AISC 14th Ed. Equation 9-6
Buckling = Fcr * Snet1 / e = 45.00 * 9.26 / 2.40 = 173.53 kips
Using AISC 14th Ed. Equation 9-19
Flexural Yielding = (phi) * Fy * Snet1 / e = 0.90 * 50.00 * 9.26 / 2.40 = 173.53 kips
Using AISC 14th Ed. Equation 9-4
Flexural Rupture = (phi) * Fu * Znet2 / e = 0.75 * 65.00 * 11.08 / 2.40 = 224.74 kips
Section Bending Strength Calculations Summary:
Coped Beam Buckling and Flexure at Longest Cope (Top and Bottom Copes at Section)
Buckling : 100.40 >= 54.75 kips (OK)
Flexural Yielding : 100.40 >= 54.75 kips (OK)
Flexural Rupture : 163.15 >= 54.75 kips (OK)
Coped Beam Buckling and Flexure at Furthest Bolt Line within Cope (Top and Bottom Copes at Section)
Buckling : 173.53 >= 54.75 kips (OK)
Flexural Yielding : 173.53 >= 54.75 kips (OK)
Flexural Rupture : 224.74 >= 54.75 kips (OK) |
Using AISC 14th Ed. Equation J4-3
Gross Area, Ag = 0.50 * 10.50 = 5.25 in^2
Shear Yielding, (phi)Vny = (phi) * 0.6 * Fypl * Ag = 1.00 * 0.6 * 50.00 * 5.25 = 157.50 kips
157.50 kips >= Reaction V = 54.75 kips (OK)
Using AISC 14th Ed. Equation J4-4
Net Area, An = (10.50 - (3 * (0.94 + 1/16))) * 0.50 = 3.75 in^2
Shear Rupture, (phi)Vnu = (phi) * 0.6 * Fupl * An = 0.75 * 0.6 * 65.00 * 3.75 = 109.69 kips
109.69 kips >= Reaction V = 54.75 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 = (10.50 - 1.25) = 9.25 in.
Net Shear Length = 9.25 - (2.50 * (0.94 + 0.06)) = 6.75 in.
Gross Tension Length = (0.00 + 1.75) = 1.75 in.
Net Tension Length = 1.75 - (0.50 * (1.12 + 0.06)) = 1.16 in.
1. (phi) * [material thickness] * ((0.60 * Fupl* [net shear length]) + (Ubs * Fupl * [net tension length]))
= 0.75 * 0.50 * ((0.60 * 65.00 * 6.75) + (1.00 * 65.00 * 1.16)) = 126.91 kips
2. (phi) * [material thickness] * ((0.60 * Fypl * [gross shear length]) + (Ubs * Fupl * [net tension length]))
= 0.75 * 0.50 * ((0.60 * 50.00 * 9.25) + (1.00 * 65.00 * 1.16)) = 132.25 kips
Block Shear = 126.91 kips
126.91 kips >= Reaction V = 54.75 kips (OK)
Block Shear for Axial T/C is not required.
Interaction Check of Flexural Yielding, Per AISC 10-5:
Eccentricity due to Conventional Config. (e = a/2), e = 1.12 in.
Zgross = 13.78
Znet = 9.66
Mr = Vr * e = 54.75 * 1.12 = 61.59 kips-in
Mc = phi * Mn = phi * Fy * Zgross = 0.90 * 50.00 * 13.78 = 620.16 kips-in
Vr = 54.75 kips
Vc = phi * Vn = phi * 0.60 * Fy * Ag = 1.00 * 0.60 * 50.00 * 5.25 = 157.50 kips
Interaction due to moment and shear, (Vr/Vc)^2 + (Mr/Mc)^2 <= 1.0
(Vr/Vc)^2 + (Mr/Mc)^2 = (54.75 / 157.50)^2 + (61.59 / 620.16)^2 = 0.13 <= 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. |
WELD:
Weld Requirements:
At shear only case:
Weld Length for shear, Lv = 13.38 in.
Shear Load per inch per weld, fv = R/Lv/2 = 54.75 / 13.38 / 2 = 2.05 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) = 2.05 / (0.75 * 1.86) = 1.47/16
Minimum fillet weld size :
At shear only load case = 0.09 in.
per Table J2.4 = 0.19 in.
5/8tp = 0.31 in.
user preference = 0.25 in.
Dmax1 (using eqn 9-3)
= tshpl * Fushpl / ( Fexx * C1 * 0.09)
= 0.50 * 65.00 / ( 70.00 * 1.00 * 0.09 )
= 5.25
Dmax2 (using eqn 9-3)
= twsupport * Fusupport / ( Fexx * C1 * 0.09 )
= 0.30 * 65.00 / ( 70.00 * 1.00 * 0.09 )
= 3.20
Dmax3 = project max fillet weld = 12.00
Dmax=min(Dmax1, Dmax2, Dmax3) = min(5.25, 3.20, 12.00)
= 3.20
Use weld size
D1 = 5.00
D2 = 5.00
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 = 54.75 kips (OK) |
