BOLT BEARING AT BEAM AND SHEAR PLATE SIDE
Vertical Shear Only Load Case:
ICR cordinate relative to CG = (4.52, -0.00)
At Row 1, At Column 1:
Ribolt = 39.32 kips
Ri vector at Beam = <21.74, 32.76>
Lcsbm at Beam spacing = na
Lcebm at Beam edge = 1.57 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 * 1.57 * (0.23/1) * 65.00 = 21.11 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 1.00 * (0.23/1) * 65.00 = 26.91 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(na, 21.11, 26.91) = 21.11 kips/bolt
Ri vector at Shear Plate = <-21.74, -32.76>
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 = 85.21 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, 85.21, 43.88) = 43.88 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(21.11, 43.88) = 21.11 kips/bolt
Bolt Shear Demand to Bearing ratio = 21.11 / 39.32 = 0.54
At Row 2, At Column 1:
Ribolt = 38.74 kips
Ri vector at Beam = <0.00, 38.74>
Lcsbm at Beam spacing = 1.94 in.
Lcebm at Beam edge = 4.22 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.75 * 1.20 * 1.94 * (0.23/1) * 65.00 = 26.07 kips/bolt
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 4.22 * (0.23/1) * 65.00 = 56.76 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 1.00 * (0.23/1) * 65.00 = 26.91 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(26.07, 56.76, 26.91) = 26.07 kips/bolt
Ri vector at Shear Plate = <-0.00, -38.74>
Lcsshpl at Shear Plate spacing = 1.94 in.
Lceshpl at Shear Plate edge = 3.97 in.
(phi)Rnsshpl at Shear Plate spacing = (phi) * hf1 * Lcs * t * Fu = 0.75 * 1.20 * 1.94 * 0.38 * 65.00 = 42.50 kips/bolt
(phi)Rneshpl at Shear Plate edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 3.97 * 0.38 * 65.00 = 87.07 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(42.50, 87.07, 43.88) = 42.50 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(26.07, 42.50) = 26.07 kips/bolt
Bolt Shear Demand to Bearing ratio = 26.07 / 38.74 = 0.67
At Row 3, At Column 1:
Ribolt = 39.32 kips
Ri vector at Beam = <-21.74, 32.76>
Lcsbm at Beam spacing = na
Lcebm at Beam edge = 3.09 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 * 3.09 * (0.23/1) * 65.00 = 41.53 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 1.00 * (0.23/1) * 65.00 = 26.91 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(na, 41.53, 26.91) = 26.91 kips/bolt
Ri vector at Shear Plate = <21.74, -32.76>
Lcsshpl at Shear Plate spacing = na
Lceshpl at Shear Plate edge = 1.16 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 * 1.16 * 0.38 * 65.00 = 25.51 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, 25.51, 43.88) = 25.51 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(26.91, 25.51) = 25.51 kips/bolt
Bolt Shear Demand to Bearing ratio = 25.51 / 39.32 = 0.65
Min Bolt Shear Demand to Bearing ratio Beam and Shear Plate for vertical shear only
= min(1.00, 0.54, 0.67, 0.65) = 0.54
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 = 0.54 * 104.26 = 55.99 kips
Rbv = 55.99 kips >= Reaction V = 15.00 kips (OK) |
Web Depth = d - [Top Cope Depth] - [Bottom Cope Depth] = 13.70 - 1.25 - 0.00 = 12.45 in.
Using AISC 14th Ed. Equation J4-3
Gross Area (Shear), Agross = [Web Depth] * tw = 12.45 * 0.23 = 2.86 in^2
Shear Yielding, (phi)Vny = (phi) * 0.6 * Fybeam * Agross = 1.00 * 0.6 * 50.00 * 2.86 = 85.91 kips
85.91 kips >= Reaction V = 15.00 kips (OK)
Using AISC 14th Ed. Equation J4-4
Net Area (Shear), Anet = ([Web Depth] - ([# rows] * [Diameter + 0.06])) * tw
= (12.45 - (3 * 1.12)) * 0.23 = 2.09 in^2
Shear Rupture, (phi)Vnu = (phi) * 0.6 * Fubeam * Anet = 0.75 * 0.6 * 65.00 * 2.09 = 61.05 kips
61.05 kips >= Reaction V = 15.00 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 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) * 1.12 = 4.94 in.
Gross Tension Length = [edge dist. at beam edge] + ([# cols - 1] * [spacing]) = 2.00 + (1 - 1) * 3.00 = 2.00 in.
Net Tension Length = Gross Tension Length - (# cols - 0.5) * (hole size + 0.06) = 2.00 - (1 - 0.5) * 1.12 = 1.44 in.
1. (phi) * [material thickness] * ((0.60 * Fubeam* [net shear length]) + (Ubs * Fubeam * [net tension length]))
= 0.75 * 0.23 * ((0.60 * 65.00 * 4.94) + (1.00 * 65.00 * 1.44)) = 49.34 kips
2. (phi) * [material thickness] * ((0.60 * Fybeam * [gross shear length]) + (Ubs * Fubeam * [net tension length]))
= 0.75 * 0.23 * ((0.60 * 50.00 * 7.75) + (1.00 * 65.00 * 1.44)) = 56.23 kips
Block Shear = 49.34 kips
Block Shear (1) Total = Block Shear (1) = 49.34 kips
49.34 kips >= Reaction V = 15.00 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 = 3.94 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 = 8.39 in.
c = 3.25 in.
When c/h1<=1.0, k=2.2(h1/c)^1.65
k = 2.20 * (8.39 / 3.25)^1.65 = 10.53
When c/d<=1.0, f=2c/d
f = 2 * (3.25 / 13.70) = 0.47
Fy = 50.00 ksi
Fcr = (phi) * 26210.00 * f * k * (tw/h1)^2 = 0.90 * 26210.00 * 0.47 * 10.53 * (0.23 / 8.39)^2 = 88.47 ksi
Fcrmin =phi * min(Fcr, Fy) = 45.00 ksi
Snet1 (bolt holes not applicable) = 8.89 in^3
Snet2 (bolt holes applicable) = 8.89 in^3
Znet1 (bolt holes not applicable) = 15.82 in^3
Znet2 (bolt holes applicable) = 15.82 in^3
Using AISC 14th Ed. Equation 9-6
Buckling = Fcr * Snet1 / e = 45.00 * 8.89 / 3.94 = 101.55 kips
Using AISC 14th Ed. Equation 9-19
Flexural Yielding = (phi) * Fy * Snet1 / e = 0.90 * 50.00 * 8.89 / 3.94 = 101.55 kips
Using AISC 14th Ed. Equation 9-4
Flexural Rupture = (phi) * Fu * Znet2 / e = 0.75 * 65.00 * 15.82 / 3.94 = 195.71 kips
Buckling and Flexure at Furthest Bolt Line within Cope (Top Cope Only at Section)
Eccentricity at Section, e = 2.69 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 = 9.16 in.
c = 3.25 in.
When c/h1<=1.0, k=2.2(h1/c)^1.65
k = 2.20 * (9.16 / 3.25)^1.65 = 12.17
When c/d<=1.0, f=2c/d
f = 2 * (3.25 / 13.70) = 0.47
Fy = 50.00 ksi
Fcr = (phi) * 26210.00 * f * k * (tw/h1)^2 = 0.90 * 26210.00 * 0.47 * 12.17 * (0.23 / 9.16)^2 = 85.80 ksi
Fcrmin =phi * min(Fcr, Fy) = 45.00 ksi
Snet1 (bolt holes not applicable) = 8.89 in^3
Snet2 (bolt holes applicable) = 6.27 in^3
Znet1 (bolt holes not applicable) = 15.82 in^3
Znet2 (bolt holes applicable) = 11.32 in^3
Using AISC 14th Ed. Equation 9-6
Buckling = Fcr * Snet1 / e = 45.00 * 8.89 / 2.69 = 148.73 kips
Using AISC 14th Ed. Equation 9-19
Flexural Yielding = (phi) * Fy * Snet1 / e = 0.90 * 50.00 * 8.89 / 2.69 = 148.73 kips
Using AISC 14th Ed. Equation 9-4
Flexural Rupture = (phi) * Fu * Znet2 / e = 0.75 * 65.00 * 11.32 / 2.69 = 205.16 kips
Section Bending Strength Calculations Summary:
Coped Beam Buckling and Flexure at Longest Cope (Top Cope Only at Section)
Buckling : 101.55 >= 15.00 kips (OK)
Flexural Yielding : 101.55 >= 15.00 kips (OK)
Flexural Rupture : 195.71 >= 15.00 kips (OK)
Coped Beam Buckling and Flexure at Furthest Bolt Line within Cope (Top Cope Only at Section)
Buckling : 148.73 >= 15.00 kips (OK)
Flexural Yielding : 148.73 >= 15.00 kips (OK)
Flexural Rupture : 205.16 >= 15.00 kips (OK) |
Using AISC 14th Ed. Equation J4-3
Gross Area, Ag = 0.38 * 9.00 = 3.38 in^2
Shear Yielding, (phi)Vny = (phi) * 0.6 * Fypl * Ag = 1.00 * 0.6 * 50.00 * 3.38 = 101.25 kips
101.25 kips >= Reaction V = 15.00 kips (OK)
Using AISC 14th Ed. Equation J4-4
Net Area, An = (9.00 - (3 * (1.06 + 1/16))) * 0.38 = 2.11 in^2
Shear Rupture, (phi)Vnu = (phi) * 0.6 * Fupl * An = 0.75 * 0.6 * 65.00 * 2.11 = 61.70 kips
61.70 kips >= Reaction V = 15.00 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 = (9.00 - 1.50) = 7.50 in.
Net Shear Length = 7.50 - (2.50 * (1.06 + 0.06)) = 4.69 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 * 4.69) + (1.00 * 65.00 * 1.31)) = 75.41 kips
2. (phi) * [material thickness] * ((0.60 * Fypl * [gross shear length]) + (Ubs * Fupl * [net tension length]))
= 0.75 * 0.38 * ((0.60 * 50.00 * 7.50) + (1.00 * 65.00 * 1.31)) = 87.28 kips
Block Shear = 75.41 kips
75.41 kips >= Reaction V = 15.00 kips (OK)
Block Shear for Axial T/C is not required.
Interaction Check of Flexural Yielding:
Using AISC 14th Ed. Equation 10-5
Eccentricity due to Conventional Config. (e = a/2), e = 1.25 in.
Zgross = 7.59
Znet = 4.94
Mr = Vr * e = 15.00 * 1.25 = 18.75 kips-in
Mc = phi * Mn = phi * Fy * Zgross = 0.90 * 50.00 * 7.59 = 341.72 kips-in
Vr = 15.00 kips
Vc = phi * Vn = phi * 0.60 * Fy * Ag = 1.00 * 0.60 * 50.00 * 3.38 = 101.25 kips
Interaction due to moment and shear, (Vr/Vc)^2 + (Mr/Mc)^2 <= 1.0
(Vr/Vc)^2 + (Mr/Mc)^2 = (15.00 / 101.25)^2 + (18.75 / 341.72)^2 = 0.02 <= 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 = 9.00 in.
Shear Load per inch per weld, fv = R/Lv/2 = 15.00 / 9.00 / 2 = 0.83 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) = 0.83 / (0.75 * 1.86) = 0.60/16
Minimum fillet weld size :
At shear only load case = 0.04 in.
per Table J2.4 = 0.19 in.
5/8tp = 0.23 in.
user preference = 0.25 in.
Dmax1 (using AISC 14th Ed. eqn 9-3)
= tshpl * Fushpl / ( Fexx * C1 * 0.09)
= 0.38 * 65.00 / ( 70.00 * 1.00 * 0.09 )
= 3.94
Dmax2 (using AISC 14th Ed. eqn 9-3)
= twbm * 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 * 9.00 * (3.94 + 3.94) = 98.72 kips
98.72 kips >= Reaction V = 15.00 kips (OK) |
