BOLT BEARING AT BEAM AND SHEAR PLATE SIDE
Vertical Shear Only Load Case:
ICR cordinate relative to CG = (5.13, 0.00)
At Row 1, At Column 1:
Ribolt = 17.56 kips
Ri vector at Beam = <8.86, 15.16>
Lcsbm at Beam spacing = na
Lcebm at Beam edge = 1.91 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 * 1.91 * (0.28/1) * 65.00 = 30.73 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.75 * (0.28/1) * 65.00 = 24.13 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(na, 30.73, 24.13) = 24.13 kips/bolt
Ri vector at Shear Plate = <-8.86, -15.16>
Lcsshpl at Shear Plate spacing = na
Lceshpl at Shear Plate edge = 3.74 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 * 3.74 * 0.38 * 65.00 = 82.07 kips/bolt
(phi)Rndshpl on Shear Plate at Bolt Diameter = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.75 * 0.38 * 65.00 = 32.91 kips/bolt
Shear Plate bearing capacity, (phi)Rnshpl = min((phi)Rnsshpl,(phi)Rneshpl,(phi)Rndshpl) = min(na, 82.07, 32.91) = 32.91 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(24.13, 32.91) = 24.13 kips/bolt
Bolt Shear Demand to Bearing ratio = 24.13 / 17.56 = 1.37
At Row 2, At Column 1:
Ribolt = 17.36 kips
Ri vector at Beam = <-0.00, 17.36>
Lcsbm at Beam spacing = 2.19 in.
Lcebm at Beam edge = 4.59 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.75 * 1.20 * 2.19 * (0.28/1) * 65.00 = 35.19 kips/bolt
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 4.59 * (0.28/1) * 65.00 = 73.90 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.75 * (0.28/1) * 65.00 = 24.13 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(35.19, 73.90, 24.13) = 24.13 kips/bolt
Ri vector at Shear Plate = <0.00, -17.36>
Lcsshpl at Shear Plate spacing = 2.19 in.
Lceshpl at Shear Plate edge = 3.84 in.
(phi)Rnsshpl at Shear Plate spacing = (phi) * hf1 * Lcs * t * Fu = 0.75 * 1.20 * 2.19 * 0.38 * 65.00 = 47.99 kips/bolt
(phi)Rneshpl at Shear Plate edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 3.84 * 0.38 * 65.00 = 84.32 kips/bolt
(phi)Rndshpl on Shear Plate at Bolt Diameter = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.75 * 0.38 * 65.00 = 32.91 kips/bolt
Shear Plate bearing capacity, (phi)Rnshpl = min((phi)Rnsshpl,(phi)Rneshpl,(phi)Rndshpl) = min(47.99, 84.32, 32.91) = 32.91 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(24.13, 32.91) = 24.13 kips/bolt
Bolt Shear Demand to Bearing ratio = 24.13 / 17.36 = 1.39
At Row 3, At Column 1:
Ribolt = 17.56 kips
Ri vector at Beam = <-8.86, 15.16>
Lcsbm at Beam spacing = na
Lcebm at Beam edge = 2.57 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 * 2.57 * (0.28/1) * 65.00 = 41.27 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.75 * (0.28/1) * 65.00 = 24.13 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(na, 41.27, 24.13) = 24.13 kips/bolt
Ri vector at Shear Plate = <8.86, -15.16>
Lcsshpl at Shear Plate spacing = na
Lceshpl at Shear Plate edge = 0.98 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 * 0.98 * 0.38 * 65.00 = 21.44 kips/bolt
(phi)Rndshpl on Shear Plate at Bolt Diameter = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.75 * 0.38 * 65.00 = 32.91 kips/bolt
Shear Plate bearing capacity, (phi)Rnshpl = min((phi)Rnsshpl,(phi)Rneshpl,(phi)Rndshpl) = min(na, 21.44, 32.91) = 21.44 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(24.13, 21.44) = 21.44 kips/bolt
Bolt Shear Demand to Bearing ratio = 21.44 / 17.56 = 1.22
Min Bolt Shear Demand to Bearing ratio Beam and Shear Plate for vertical shear only
= min(1.00, 1.37, 1.39, 1.22) = 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 * 47.69 = 47.69 kips
Rbv = 47.69 kips >= Reaction V = 30.00 kips (OK) |
Web Depth = d - [Top Cope Depth] - [Bottom Cope Depth] = 15.90 - 1.00 - 0.00 = 14.90 in.
Using AISC 14th Ed. Equation J4-3
Gross Area (Shear), Agross = [Web Depth] * tw = 14.90 * 0.28 = 4.10 in^2
Shear Yielding, (phi)Vny = (phi) * 0.6 * Fybeam * Agross = 1.00 * 0.6 * 50.00 * 4.10 = 122.93 kips
Using AISC 14th Ed. Equation J4-4
Net Area (Shear), Anet = ([Web Depth] - ([# rows] * [Diameter + 0.06])) * tw
= (14.90 - (3 * 0.88)) * 0.28 = 3.38 in^2
Shear Rupture, (phi)Vnu = (phi) * 0.6 * Fubeam * Anet = 0.75 * 0.6 * 65.00 * 3.38 = 98.74 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]) = 2.00 + 6.00 = 8.00 in.
Net Shear Length = Gross Shear Length - (# rows - 0.5) * (hole size + 0.06) = 8.00 - (3 - 0.5) * 0.88 = 5.81 in.
Gross Tension Length = [edge dist. at beam edge] + ([# cols - 1] * [spacing]) = 1.50 + (1 - 1) * 3.00 = 1.50 in.
Net Tension Length = Gross Tension Length - (# cols - 0.5) * (hole size + 0.06) = 1.50 - (1 - 0.5) * 0.88 = 1.06 in.
1. (phi) * [material thickness] * ((0.60 * Fubeam* [net shear length]) + (Ubs * Fubeam * [net tension length]))
= 0.75 * 0.28 * ((0.60 * 65.00 * 5.81) + (1.00 * 65.00 * 1.06)) = 61.00 kips
2. (phi) * [material thickness] * ((0.60 * Fybeam * [gross shear length]) + (Ubs * Fubeam * [net tension length]))
= 0.75 * 0.28 * ((0.60 * 50.00 * 8.00) + (1.00 * 65.00 * 1.06)) = 63.75 kips
Block Shear = 61.00 kips
Block Shear (1) Total = Block Shear (1) = 61.00 kips
61.00 kips >= Reaction V = 30.00 kips (OK)
Block Shear for Axial T/C is not required.
Buckling and Flexure at Longest Cope (Top Cope Only at Section)
Eccentricity at Section, e = 3.83 in.
If coped at top/bottom flange only and c <= 2d and dc <= d/2, use AISC 14th Ed. Equation 9-7, Fcr = 26210.00 * f * k * (tw/h1)^2 <= Fy
Using AISC Equations 9-7 through 9-11
tw = 0.28 in.
h1 = 10.06 in.
c = 3.00 in.
When c/h1<=1.0, k=2.2(h1/c)^1.65
k = 2.20 * (10.06 / 3.00)^1.65 = 16.19
When c/d<=1.0, f=2c/d
f = 2 * (3.00 / 15.90) = 0.38
Fy = 50.00 ksi
Fcr = (phi) * 26210.00 * f * k * (tw/h1)^2 = 0.90 * 26210.00 * 0.38 * 16.19 * (0.28 / 10.06)^2 = 107.75 ksi
Fcrmin =phi * min(Fcr, Fy) = 45.00 ksi
Snet1 (bolt holes not applicable) = 15.22 in^3
Snet2 (bolt holes applicable) = 15.22 in^3
Znet1 (bolt holes not applicable) = 27.12 in^3
Znet2 (bolt holes applicable) = 27.12 in^3
Using AISC 14th Ed. Equation 9-6
Buckling = Fcr * Snet1 / e = 45.00 * 15.22 / 3.83 = 178.81 kips
Using AISC 14th Ed. Equation 9-19
Flexural Yielding = (phi) * Fy * Snet1 / e = 0.90 * 50.00 * 15.22 / 3.83 = 178.81 kips
Using AISC 14th Ed. Equation 9-4
Flexural Rupture = (phi) * Fu * Znet2 / e = 0.75 * 65.00 * 27.12 / 3.83 = 345.12 kips
Buckling and Flexure at Furthest Bolt Line within Cope (Top Cope Only at Section)
Eccentricity at Section, e = 2.33 in.
If coped at top/bottom flange only and c <= 2d and dc <= d/2, use AISC 14th Ed. Equation 9-7, Fcr = 26210.00 * f * k * (tw/h1)^2 <= Fy
Using AISC Equations 9-7 through 9-11
tw = 0.28 in.
h1 = 10.70 in.
c = 3.00 in.
When c/h1<=1.0, k=2.2(h1/c)^1.65
k = 2.20 * (10.70 / 3.00)^1.65 = 17.93
When c/d<=1.0, f=2c/d
f = 2 * (3.00 / 15.90) = 0.38
Fy = 50.00 ksi
Fcr = (phi) * 26210.00 * f * k * (tw/h1)^2 = 0.90 * 26210.00 * 0.38 * 17.93 * (0.28 / 10.70)^2 = 105.44 ksi
Fcrmin =phi * min(Fcr, Fy) = 45.00 ksi
Snet1 (bolt holes not applicable) = 15.22 in^3
Snet2 (bolt holes applicable) = 11.96 in^3
Znet1 (bolt holes not applicable) = 27.12 in^3
Znet2 (bolt holes applicable) = 21.84 in^3
Using AISC 14th Ed. Equation 9-6
Buckling = Fcr * Snet1 / e = 45.00 * 15.22 / 2.33 = 293.88 kips
Using AISC 14th Ed. Equation 9-19
Flexural Yielding = (phi) * Fy * Snet1 / e = 0.90 * 50.00 * 15.22 / 2.33 = 293.88 kips
Using AISC 14th Ed. Equation 9-4
Flexural Rupture = (phi) * Fu * Znet2 / e = 0.75 * 65.00 * 21.84 / 2.33 = 456.84 kips
Section Bending Strength Calculations Summary:
Coped Beam Buckling and Flexure at Longest Cope (Top Cope Only at Section)
Buckling : 178.81 >= 30.00 kips (OK)
Flexural Yielding : 178.81 >= 30.00 kips (OK)
Flexural Rupture : 345.12 >= 30.00 kips (OK)
Coped Beam Buckling and Flexure at Furthest Bolt Line within Cope (Top Cope Only at Section)
Buckling : 293.88 >= 30.00 kips (OK)
Flexural Yielding : 293.88 >= 30.00 kips (OK)
Flexural Rupture : 456.84 >= 30.00 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 = 30.00 kips (OK)
Using AISC 14th Ed. Equation J4-4
Net Area, An = (8.50 - (3 * (0.81 + 1/16))) * 0.38 = 2.20 in^2
Shear Rupture, (phi)Vnu = (phi) * 0.6 * Fupl * An = 0.75 * 0.6 * 65.00 * 2.20 = 64.44 kips
64.44 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 = (8.50 - 1.25) = 7.25 in.
Net Shear Length = 7.25 - (2.50 * (0.81 + 0.06)) = 5.06 in.
Gross Tension Length = (0.00 + 1.50) = 1.50 in.
Net Tension Length = 1.50 - (0.50 * (1.00 + 0.06)) = 0.97 in.
1. (phi) * [material thickness] * ((0.60 * Fupl* [net shear length]) + (Ubs * Fupl * [net tension length]))
= 0.75 * 0.38 * ((0.60 * 65.00 * 5.06) + (1.00 * 65.00 * 0.97)) = 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 * 0.97)) = 78.88 kips
Block Shear = 73.24 kips
73.24 kips >= Reaction V = 30.00 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 = 1.11 in.
Zgross = 6.77
Znet = 4.73
Mr = Vr * e = 30.00 * 1.11 = 33.39 kips-in
Mc = phi * Mn = phi * Fy * Zgross = 0.90 * 50.00 * 6.77 = 304.80 kips-in
Vr = 30.00 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 = (30.00 / 95.62)^2 + (33.39 / 304.80)^2 = 0.11 <= 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 = 8.50 in.
Shear Load per inch per weld, fv = R/Lv/2 = 30.00 / 8.50 / 2 = 1.76 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) = 1.76 / (0.75 * 1.86) = 1.27/16
Minimum fillet weld size :
At shear only load case = 0.08 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)
= twbm * Fusupport / ( Fexx * C1 * 0.09 )
= 0.30 * 65.00 / ( 70.00 * 1.00 * 0.09 )
= 3.15
Dmax3 = project max fillet weld = 12.00
Dmax=min(Dmax1, Dmax2, Dmax3) = min(3.94, 3.15, 12.00)
= 3.15
Dihedral Angle, DA = 74.90 deg.
Gap on Obtuse Angle Side if No Bevel = 0.10 in.
Use weld size
Acute Side D1 = 4.00
Obtuse Side D2 = 6.00 (weld size increased on obtuse side for gap at skew per AWS D1.1/D1.1M (2015, p.511, C-5.21.1))
Weld Strength :
Vertical weld capacity during shear only load, phi * Rnv1 = 0.75 * 1.86 * 8.50 * (3.15 + 3.15) = 74.59 kips
74.59 kips >= Reaction V = 30.00 kips (OK)
Check Effective Throat:
Acute Side Effect throat = (D1/sin(DA)) * cos(DA/2) = (0.25/ sin( 74.90)) * cos( 37.45) = 0.21 in.
Obtuse Side Effect throat = (D2/sin(DA)-tshpl/tan(DA))*sin(DA/2) = (0.38 / sin(74.90) - 0.38 / tan(74.90)) * sin(74.90 / 2) = 0.17 in.
Total Effective Throat = 0.21 + 0.17 = 0.38 in.
Total Effective Throat of Square Case = 5/8tp * 2^0.5 = 0.23 * 2^0.5 = 0.33 in.
0.38 >= 0.33 (OK) |
