BOLT BEARING AT BEAM AND SHEAR PLATE SIDE
Vertical Shear Only Load Case:
ICR cordinate relative to CG = (5.08, 0.00)
At Row 1, At Column 1:
Ribolt = 23.90 kips
Ri vector at Beam = <12.16, 20.58>
Lcsbm at Beam spacing = na
Lcebm at Beam edge = 1.56 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 * 1.56 * (0.30/1) * 65.00 = 27.91 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, 27.91, 31.23) = 27.91 kips/bolt
Ri vector at Shear Plate = <-12.16, -20.58>
Lcsshpl at Shear Plate spacing = na
Lceshpl at Shear Plate edge = 3.88 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 * 3.88 * 0.38 * 65.00 = 85.07 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, 85.07, 38.39) = 38.39 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(27.91, 38.39) = 27.91 kips/bolt
Bolt Shear Demand to Bearing ratio = 27.91 / 23.90 = 1.17
At Row 2, At Column 1:
Ribolt = 23.63 kips
Ri vector at Beam = <-0.00, 23.63>
Lcsbm at Beam spacing = 2.06 in.
Lcebm at Beam edge = 4.28 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 * 4.28 * (0.30/1) * 65.00 = 76.39 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, 76.39, 31.23) = 31.23 kips/bolt
Ri vector at Shear Plate = <0.00, -23.63>
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(31.23, 38.39) = 31.23 kips/bolt
Bolt Shear Demand to Bearing ratio = 31.23 / 23.63 = 1.32
At Row 3, At Column 1:
Ribolt = 23.90 kips
Ri vector at Beam = <-12.16, 20.58>
Lcsbm at Beam spacing = na
Lcebm at Beam edge = 2.97 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 * 2.97 * (0.30/1) * 65.00 = 52.99 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, 52.99, 31.23) = 31.23 kips/bolt
Ri vector at Shear Plate = <12.16, -20.58>
Lcsshpl at Shear Plate spacing = na
Lceshpl at Shear Plate edge = 0.91 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 * 0.91 * 0.38 * 65.00 = 19.91 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, 19.91, 38.39) = 19.91 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(31.23, 19.91) = 19.91 kips/bolt
Bolt Shear Demand to Bearing ratio = 19.91 / 23.90 = 0.83
Min Bolt Shear Demand to Bearing ratio Beam and Shear Plate for vertical shear only
= min(1.00, 1.17, 1.32, 0.83) = 0.83
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 = 0.83 * 64.78 = 53.96 kips
Rbv = 53.96 kips >= Reaction V = 51.00 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 + 6.00 = 7.75 in.
Net Shear Length = Gross Shear Length - (# rows - 0.5) * (hole size + 0.06) = 7.75 - (3 - 0.5) * 1.00 = 5.25 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 * 5.25) + (1.00 * 65.00 * 1.25)) = 65.42 kips
2. (phi) * [material thickness] * ((0.60 * Fybeam * [gross shear length]) + (Ubs * Fubeam * [net tension length]))
= 0.75 * 0.30 * ((0.60 * 50.00 * 7.75) + (1.00 * 65.00 * 1.25)) = 71.77 kips
Block Shear = 65.42 kips
Block Shear (1) Total = Block Shear (1) = 65.42 kips
65.42 kips >= Reaction V = 51.00 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 = 4.21 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 / 4.21 = 98.91 kips
Using AISC 14th Ed. Equation 9-19
Flexural Yielding = (phi) * Fy * Snet1 / e = 0.90 * 50.00 * 9.26 / 4.21 = 98.91 kips
Using AISC 14th Ed. Equation 9-4
Flexural Rupture = (phi) * Fu * Znet2 / e = 0.75 * 65.00 * 13.90 / 4.21 = 160.73 kips
Buckling and Flexure at Furthest Bolt Line within Cope (Top and Bottom Copes at Section)
Eccentricity at Section, e = 2.46 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) = 7.14 in^3
Znet1 (bolt holes not applicable) = 13.90 in^3
Znet2 (bolt holes applicable) = 11.38 in^3
Using AISC 14th Ed. Equation 9-6
Buckling = Fcr * Snet1 / e = 45.00 * 9.26 / 2.46 = 169.13 kips
Using AISC 14th Ed. Equation 9-19
Flexural Yielding = (phi) * Fy * Snet1 / e = 0.90 * 50.00 * 9.26 / 2.46 = 169.13 kips
Using AISC 14th Ed. Equation 9-4
Flexural Rupture = (phi) * Fu * Znet2 / e = 0.75 * 65.00 * 11.38 / 2.46 = 225.07 kips
Section Bending Strength Calculations Summary:
Coped Beam Buckling and Flexure at Longest Cope (Top and Bottom Copes at Section)
Buckling : 98.91 >= 51.00 kips (OK)
Flexural Yielding : 98.91 >= 51.00 kips (OK)
Flexural Rupture : 160.73 >= 51.00 kips (OK)
Coped Beam Buckling and Flexure at Furthest Bolt Line within Cope (Top and Bottom Copes at Section)
Buckling : 169.13 >= 51.00 kips (OK)
Flexural Yielding : 169.13 >= 51.00 kips (OK)
Flexural Rupture : 225.07 >= 51.00 kips (OK) |
Using AISC 14th Ed. Equation J4-3
Gross Area, Ag = 0.38 * 8.50 = 3.19 in^2
Shear Yielding, (phi)Vny = (phi) * 0.6 * Fypl * Ag = 1.00 * 0.6 * 50.00 * 3.19 = 95.62 kips
95.62 kips >= Reaction V = 51.00 kips (OK)
Using AISC 14th Ed. Equation J4-4
Net Area, An = (8.50 - (3 * (0.94 + 1/16))) * 0.38 = 2.06 in^2
Shear Rupture, (phi)Vnu = (phi) * 0.6 * Fupl * An = 0.75 * 0.6 * 65.00 * 2.06 = 60.33 kips
60.33 kips >= Reaction V = 51.00 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 = (8.50 - 1.25) = 7.25 in.
Net Shear Length = 7.25 - (2.50 * (0.94 + 0.06)) = 4.75 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 * 0.38 * ((0.60 * 65.00 * 4.75) + (1.00 * 65.00 * 1.16)) = 73.24 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 * 1.16)) = 82.31 kips
Block Shear = 73.24 kips
73.24 kips >= Reaction V = 51.00 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 = 6.77
Znet = 4.43
Mr = Vr * e = 51.00 * 1.12 = 57.37 kips-in
Mc = phi * Mn = phi * Fy * Zgross = 0.90 * 50.00 * 6.77 = 304.80 kips-in
Vr = 51.00 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 = (51.00 / 95.62)^2 + (57.37 / 304.80)^2 = 0.32 <= 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 = 51.00 / 13.38 / 2 = 1.91 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) = 1.91 / (0.75 * 1.86) = 1.37/16
Minimum fillet weld size :
At shear only load case = 0.09 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 )
= 0.43 * 65.00 / ( 70.00 * 1.00 * 0.09 )
= 4.52
Dmax3 = project max fillet weld = 12.00
Dmax=min(Dmax1, Dmax2, Dmax3) = min(3.94, 4.52, 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 * 13.38 * (3.94 + 3.94) = 146.71 kips
146.71 kips >= Reaction V = 51.00 kips (OK) |
