BOLT BEARING AT BEAM AND SHEAR PLATE SIDE
Vertical Shear Only Load Case:
ICR cordinate relative to CG = (5.77, 0.00)
At Row 1, At Column 1:
Ribolt = 17.56 kips
Ri vector at Beam = <8.10, 15.58>
Lcsbm at Beam spacing = na
Lcebm at Beam edge = 1.85 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 * 1.85 * (0.23/1) * 65.00 = 24.86 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.75 * (0.23/1) * 65.00 = 20.18 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(na, 24.86, 20.18) = 20.18 kips/bolt
Ri vector at Shear Plate = <-8.10, -15.58>
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 = 85.13 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, 85.13, 32.91) = 32.91 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(20.18, 32.91) = 20.18 kips/bolt
Bolt Shear Demand to Bearing ratio = 20.18 / 17.56 = 1.15
At Row 2, At Column 1:
Ribolt = 17.41 kips
Ri vector at Beam = <-0.00, 17.41>
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 * (0.23/1) * 65.00 = 29.43 kips/bolt
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 4.59 * (0.23/1) * 65.00 = 61.81 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.75 * (0.23/1) * 65.00 = 20.18 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(29.43, 61.81, 20.18) = 20.18 kips/bolt
Ri vector at Shear Plate = <0.00, -17.41>
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(20.18, 32.91) = 20.18 kips/bolt
Bolt Shear Demand to Bearing ratio = 20.18 / 17.41 = 1.16
At Row 3, At Column 1:
Ribolt = 17.56 kips
Ri vector at Beam = <-8.10, 15.58>
Lcsbm at Beam spacing = na
Lcebm at Beam edge = 2.85 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 * 2.85 * (0.23/1) * 65.00 = 38.31 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.75 * (0.23/1) * 65.00 = 20.18 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(na, 38.31, 20.18) = 20.18 kips/bolt
Ri vector at Shear Plate = <8.10, -15.58>
Lcsshpl at Shear Plate spacing = na
Lceshpl at Shear Plate edge = 0.95 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 * 0.95 * 0.38 * 65.00 = 20.86 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, 20.86, 32.91) = 20.86 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(20.18, 20.86) = 20.18 kips/bolt
Bolt Shear Demand to Bearing ratio = 20.18 / 17.56 = 1.15
Min Bolt Shear Demand to Bearing ratio Beam and Shear Plate for vertical shear only
= min(1.00, 1.15, 1.16, 1.15) = 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 * 48.57 = 48.57 kips
Rbv = 48.57 kips >= Reaction V = 20.70 kips (OK) |
Web Depth = d - [Top Cope Depth] - [Bottom Cope Depth] = 13.70 - 1.00 - 0.00 = 12.70 in.
Using AISC 14th Ed. Equation J4-3
Gross Area (Shear), Agross = [Web Depth] * tw = 12.70 * 0.23 = 2.92 in^2
Shear Yielding, (phi)Vny = (phi) * 0.6 * Fybeam * Agross = 1.00 * 0.6 * 50.00 * 2.92 = 87.63 kips
Using AISC 14th Ed. Equation J4-4
Net Area (Shear), Anet = ([Web Depth] - ([# rows] * [Diameter + 0.06])) * tw
= (12.70 - (3 * 0.88)) * 0.23 = 2.32 in^2
Shear Rupture, (phi)Vnu = (phi) * 0.6 * Fubeam * Anet = 0.75 * 0.6 * 65.00 * 2.32 = 67.78 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 * 0.23 * ((0.60 * 65.00 * 5.81) + (1.00 * 65.00 * 1.06)) = 51.02 kips
2. (phi) * [material thickness] * ((0.60 * Fybeam * [gross shear length]) + (Ubs * Fubeam * [net tension length]))
= 0.75 * 0.23 * ((0.60 * 50.00 * 8.00) + (1.00 * 65.00 * 1.06)) = 53.31 kips
Block Shear = 51.02 kips
Block Shear (1) Total = Block Shear (1) = 51.02 kips
51.02 kips >= Reaction V = 20.70 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 = 3.66 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 = 0.23 in.
h1 = 8.54 in.
c = 3.00 in.
When c/h1<=1.0, k=2.2(h1/c)^1.65
k = 2.20 * (8.54 / 3.00)^1.65 = 12.35
When c/d<=1.0, f=2c/d
f = 2 * (3.00 / 13.70) = 0.44
Fy = 50.00 ksi
Fcr = (phi) * 26210.00 * f * k * (tw/h1)^2 = 0.90 * 26210.00 * 0.44 * 12.35 * (0.23 / 8.54)^2 = 92.65 ksi
Fcrmin =phi * min(Fcr, Fy) = 45.00 ksi
Snet1 (bolt holes not applicable) = 9.23 in^3
Snet2 (bolt holes applicable) = 9.23 in^3
Znet1 (bolt holes not applicable) = 16.38 in^3
Znet2 (bolt holes applicable) = 16.38 in^3
Using AISC 14th Ed. Equation 9-6
Buckling = Fcr * Snet1 / e = 45.00 * 9.23 / 3.66 = 113.51 kips
Using AISC 14th Ed. Equation 9-19
Flexural Yielding = (phi) * Fy * Snet1 / e = 0.90 * 50.00 * 9.23 / 3.66 = 113.51 kips
Using AISC 14th Ed. Equation 9-4
Flexural Rupture = (phi) * Fu * Znet2 / e = 0.75 * 65.00 * 16.38 / 3.66 = 218.30 kips
Buckling and Flexure at Furthest Bolt Line within Cope (Top Cope Only at Section)
Eccentricity at Section, e = 2.16 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 = 0.23 in.
h1 = 9.08 in.
c = 3.00 in.
When c/h1<=1.0, k=2.2(h1/c)^1.65
k = 2.20 * (9.08 / 3.00)^1.65 = 13.68
When c/d<=1.0, f=2c/d
f = 2 * (3.00 / 13.70) = 0.44
Fy = 50.00 ksi
Fcr = (phi) * 26210.00 * f * k * (tw/h1)^2 = 0.90 * 26210.00 * 0.44 * 13.68 * (0.23 / 9.08)^2 = 90.66 ksi
Fcrmin =phi * min(Fcr, Fy) = 45.00 ksi
Snet1 (bolt holes not applicable) = 9.23 in^3
Snet2 (bolt holes applicable) = 7.31 in^3
Znet1 (bolt holes not applicable) = 16.38 in^3
Znet2 (bolt holes applicable) = 13.07 in^3
Using AISC 14th Ed. Equation 9-6
Buckling = Fcr * Snet1 / e = 45.00 * 9.23 / 2.16 = 192.43 kips
Using AISC 14th Ed. Equation 9-19
Flexural Yielding = (phi) * Fy * Snet1 / e = 0.90 * 50.00 * 9.23 / 2.16 = 192.43 kips
Using AISC 14th Ed. Equation 9-4
Flexural Rupture = (phi) * Fu * Znet2 / e = 0.75 * 65.00 * 13.07 / 2.16 = 295.32 kips
Section Bending Strength Calculations Summary:
Coped Beam Buckling and Flexure at Longest Cope (Top Cope Only at Section)
Buckling : 113.51 >= 20.70 kips (OK)
Flexural Yielding : 113.51 >= 20.70 kips (OK)
Flexural Rupture : 218.30 >= 20.70 kips (OK)
Coped Beam Buckling and Flexure at Furthest Bolt Line within Cope (Top Cope Only at Section)
Buckling : 192.43 >= 20.70 kips (OK)
Flexural Yielding : 192.43 >= 20.70 kips (OK)
Flexural Rupture : 295.32 >= 20.70 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 = 20.70 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 = 20.70 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 = 20.70 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 = 1.00 in.
Zgross = 6.77
Znet = 4.73
Mr = Vr * e = 20.70 * 1.00 = 20.70 kips-in
Mc = phi * Mn = phi * Fy * Zgross = 0.90 * 50.00 * 6.77 = 304.80 kips-in
Vr = 20.70 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 = (20.70 / 95.62)^2 + (20.70 / 304.80)^2 = 0.05 <= 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 = 20.70 / 8.50 / 2 = 1.22 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) = 1.22 / (0.75 * 1.86) = 0.87/16
Minimum fillet weld size :
At shear only load case = 0.05 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 )
= 0.32 * 65.00 / ( 70.00 * 1.00 * 0.09 )
= 3.31
Dmax3 = project max fillet weld = 12.00
Dmax=min(Dmax1, Dmax2, Dmax3) = min(3.94, 3.31, 12.00)
= 3.31
Use weld size
D1 = 4.00
D2 = 4.00
Weld Strength :
Vertical weld capacity during shear only load, phi * Rnv1 = 0.75 * 1.86 * 8.50 * (3.31 + 3.31) = 78.32 kips
78.32 kips >= Reaction V = 20.70 kips (OK) |
