BOLT BEARING AT BEAM AND SHEAR PLATE SIDE
Vertical Shear Only Load Case:
ICR cordinate relative to CG = (13.00, 0.00)
At Row 1, At Column 1:
Ribolt = 23.90 kips
Ri vector at Beam = <0.42, 0.91>
Lcsbm at Beam spacing = na
Lcebm at Beam edge = 1.15 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 * 1.15 * (0.48/1) * 65.00 = 32.35 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.88 * (0.48/1) * 65.00 = 49.14 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(na, 32.35, 49.14) = 32.35 kips/bolt
Ri vector at Shear Plate = <-0.42, -0.91>
Lcsshpl at Shear Plate spacing = na
Lceshpl at Shear Plate edge = 5.71 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 * 5.71 * 0.25 * 65.00 = 83.58 kips/bolt
(phi)Rndshpl on Shear Plate at Bolt Diameter = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.88 * 0.25 * 65.00 = 25.59 kips/bolt
Shear Plate bearing capacity, (phi)Rnshpl = min((phi)Rnsshpl,(phi)Rneshpl,(phi)Rndshpl) = min(na, 83.58, 25.59) = 25.59 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(32.35, 25.59) = 25.59 kips/bolt
Bolt Shear Demand to Bearing ratio = 25.59 / 23.90 = 1.07
At Row 2, At Column 1:
Ribolt = 23.79 kips
Ri vector at Beam = <0.22, 0.97>
Lcsbm at Beam spacing = 2.00 in.
Lcebm at Beam edge = 4.12 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.75 * 1.20 * 2.00 * (0.48/1) * 65.00 = 56.16 kips/bolt
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 4.12 * (0.48/1) * 65.00 = 115.64 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.88 * (0.48/1) * 65.00 = 49.14 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(56.16, 115.64, 49.14) = 49.14 kips/bolt
Ri vector at Shear Plate = <-0.22, -0.97>
Lcsshpl at Shear Plate spacing = 2.00 in.
Lceshpl at Shear Plate edge = 9.88 in.
(phi)Rnsshpl at Shear Plate spacing = (phi) * hf1 * Lcs * t * Fu = 0.75 * 1.20 * 2.00 * 0.25 * 65.00 = 29.25 kips/bolt
(phi)Rneshpl at Shear Plate edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 9.88 * 0.25 * 65.00 = 144.47 kips/bolt
(phi)Rndshpl on Shear Plate at Bolt Diameter = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.88 * 0.25 * 65.00 = 25.59 kips/bolt
Shear Plate bearing capacity, (phi)Rnshpl = min((phi)Rnsshpl,(phi)Rneshpl,(phi)Rndshpl) = min(29.25, 144.47, 25.59) = 25.59 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(49.14, 25.59) = 25.59 kips/bolt
Bolt Shear Demand to Bearing ratio = 25.59 / 23.79 = 1.08
At Row 3, At Column 1:
Ribolt = 23.74 kips
Ri vector at Beam = <0.00, 1.00>
Lcsbm at Beam spacing = 2.00 in.
Lcebm at Beam edge = 7.00 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.75 * 1.20 * 2.00 * (0.48/1) * 65.00 = 56.16 kips/bolt
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 7.00 * (0.48/1) * 65.00 = 196.56 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.88 * (0.48/1) * 65.00 = 49.14 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(56.16, 196.56, 49.14) = 49.14 kips/bolt
Ri vector at Shear Plate = <0.00, -1.00>
Lcsshpl at Shear Plate spacing = 2.00 in.
Lceshpl at Shear Plate edge = 6.62 in.
(phi)Rnsshpl at Shear Plate spacing = (phi) * hf1 * Lcs * t * Fu = 0.75 * 1.20 * 2.00 * 0.25 * 65.00 = 29.25 kips/bolt
(phi)Rneshpl at Shear Plate edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 6.62 * 0.25 * 65.00 = 96.89 kips/bolt
(phi)Rndshpl on Shear Plate at Bolt Diameter = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.88 * 0.25 * 65.00 = 25.59 kips/bolt
Shear Plate bearing capacity, (phi)Rnshpl = min((phi)Rnsshpl,(phi)Rneshpl,(phi)Rndshpl) = min(29.25, 96.89, 25.59) = 25.59 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(49.14, 25.59) = 25.59 kips/bolt
Bolt Shear Demand to Bearing ratio = 25.59 / 23.74 = 1.08
At Row 4, At Column 1:
Ribolt = 23.79 kips
Ri vector at Beam = <-0.22, 0.97>
Lcsbm at Beam spacing = 2.00 in.
Lcebm at Beam edge = 7.28 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.75 * 1.20 * 2.00 * (0.48/1) * 65.00 = 56.16 kips/bolt
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 7.28 * (0.48/1) * 65.00 = 204.53 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.88 * (0.48/1) * 65.00 = 49.14 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(56.16, 204.53, 49.14) = 49.14 kips/bolt
Ri vector at Shear Plate = <0.22, -0.97>
Lcsshpl at Shear Plate spacing = 2.00 in.
Lceshpl at Shear Plate edge = 3.72 in.
(phi)Rnsshpl at Shear Plate spacing = (phi) * hf1 * Lcs * t * Fu = 0.75 * 1.20 * 2.00 * 0.25 * 65.00 = 29.25 kips/bolt
(phi)Rneshpl at Shear Plate edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 3.72 * 0.25 * 65.00 = 54.41 kips/bolt
(phi)Rndshpl on Shear Plate at Bolt Diameter = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.88 * 0.25 * 65.00 = 25.59 kips/bolt
Shear Plate bearing capacity, (phi)Rnshpl = min((phi)Rnsshpl,(phi)Rneshpl,(phi)Rndshpl) = min(29.25, 54.41, 25.59) = 25.59 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(49.14, 25.59) = 25.59 kips/bolt
Bolt Shear Demand to Bearing ratio = 25.59 / 23.79 = 1.08
At Row 5, At Column 1:
Ribolt = 23.90 kips
Ri vector at Beam = <-0.42, 0.91>
Lcsbm at Beam spacing = na
Lcebm at Beam edge = 3.68 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 * 3.68 * (0.48/1) * 65.00 = 103.24 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.88 * (0.48/1) * 65.00 = 49.14 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(na, 103.24, 49.14) = 49.14 kips/bolt
Ri vector at Shear Plate = <0.42, -0.91>
Lcsshpl at Shear Plate spacing = na
Lceshpl at Shear Plate edge = 0.69 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 * 0.69 * 0.25 * 65.00 = 10.07 kips/bolt
(phi)Rndshpl on Shear Plate at Bolt Diameter = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.88 * 0.25 * 65.00 = 25.59 kips/bolt
Shear Plate bearing capacity, (phi)Rnshpl = min((phi)Rnsshpl,(phi)Rneshpl,(phi)Rndshpl) = min(na, 10.07, 25.59) = 10.07 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(49.14, 10.07) = 10.07 kips/bolt
Bolt Shear Demand to Bearing ratio = 10.07 / 23.90 = 0.42
Min Bolt Shear Demand to Bearing ratio Beam and Shear Plate for vertical shear only
= min(1.00, 1.07, 1.08, 1.08, 1.08, 0.42) = 0.42
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 = 0.42 * 113.50 = 47.80 kips
Rbv = 47.80 kips >= Reaction V = 45.00 kips (OK) |
Web Depth = d - [Top Cope Depth] - [Bottom Cope Depth] = 18.40 - 1.50 - 1.50 = 15.40 in.
Using AISC 15th Ed. Equation J4-3
Gross Area (Shear), Agross = [Web Depth] * tw = 15.40 * 0.48 = 7.39 in^2
Shear Yielding, (phi)Vny = (phi) * 0.6 * Fybeam * Agross = 1.00 * 0.6 * 50.00 * 7.39 = 221.76 kips
221.76 kips >= Reaction V = 45.00 kips (OK)
Shear Rupture:
Using AISC 15th Ed. Equation J4-4
Net Area (Shear), Anet = ([Web Depth] - [# rows] * (hole width + 0.06)) * tw
= (15.40 - 5 * (0.94 + 0.06)) * 0.48 = 4.99 in^2
Shear Rupture, (phi)Vnu = (phi) * 0.6 * Fubeam * Anet = 0.75 * 0.6 * 65.00 * 4.99 = 146.02 kips
146.02 kips >= Reaction V = 45.00 kips (OK)
Check Vertical Block Shear
Using AISC 15th 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]) = 1.50 + (5 - 1) * 3.00 = 13.50 in.
Net Shear Length = Gross Shear Length - (# rows - 0.5) * (hole width + 0.06) = 13.50 - (5 - 0.5) * (0.94 + 0.06) = 9.00 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 length + 0.06) = 1.75 - (1 - 0.5) * (0.94 + 0.06) = 1.25 in.
1. (phi) * [material thickness] * ((0.60 * Fubeam* [net shear length]) + (Ubs * Fubeam * [net tension length]))
= 0.75 * 0.48 * ((0.60 * 65.00 * 9.00) + (1.00 * 65.00 * 1.25)) = 155.61 kips
2. (phi) * [material thickness] * ((0.60 * Fybeam * [gross shear length]) + (Ubs * Fubeam * [net tension length]))
= 0.75 * 0.48 * ((0.60 * 50.00 * 13.50) + (1.00 * 65.00 * 1.25)) = 175.05 kips
Block Shear = 155.61 kips
Block Shear (1) Total = Block Shear (1) = 155.61 kips
155.61 kips >= Reaction V = 45.00 kips (OK)
Block Shear for Axial T/C is not required.
Buckling and Flexure at End of Cope
(Top and Bottom Copes at Section - Using AISC 15th Ed. Equations 9-4, 9-15, 9-16, F11-1 to F11-4)
Eccentricity at Section, e = 6.95 in.
tw = 0.48 in.
d = 18.40 in.
dctop = 1.50 in.
dcbot = 1.50 in.
ctop = 5.75 in.
cbot = 5.75 in.
ho = d - [Top Cope Depth] - [Bottom Cope Depth] = 18.40 - 1.50 - 1.50 = 15.40 in.
Fybeam = 50.00 ksi
Snet1 (bolt holes not applicable) = 18.97 in^3
Snet2 (bolt holes applicable) = 18.97 in^3
Znet1 (bolt holes not applicable) = 28.46 in^3
Znet2 (bolt holes applicable) = 28.46 in^3
Mp = Fybeam * Znet1 = 50.00 * 28.46 = 1422.96 kips-in
My = Fybeam * Snet1 = 50.00 * 18.97 = 948.64 kips-in
Lateral Torsional Buckling using AISC 15th Ed. Equations 9-15 to 9-16, F11-1 to F11-4
t = tw = 0.48 in.
d = depth of beam = 18.40 in.
drect = ho = 15.40 in.
dc = dctop = 1.50 in.
Lb = top cope length = 5.75 in.
Fybeam = 50.00 ksi
Cb = max((3 + ln(Lb / d)) * (1 - dc / d), 1.84) =
= max((3 + ln(5.75 / 18.40)) * (1 - 1.50 / 18.40), 1.84) = 1.84
Lb * drect / t^2 = 5.75 * 15.40 / 0.48^2 = 384.33
0.08 * E / Fybeam = 0.08 * 29000 / 50.00 = 46.40
1.9 * E / Fybeam = 1.9 * 29000 / 50.00 = 1102.00
For case when 0.08 * E / Fybeam < Lb * drect / t^2 <= 1.9 * E / Fybeam
Mn = min(Cb * (1.52 - 0.274 * (Lb * drect / t^2) * Fybeam / E) * My, Mp)
= min(1.84 * (1.52 - 0.274 * (5.75 * 15.40 / 0.48^2) * 50.00 / 29000) * 948.64, 1422.96)
= min(2336.24, 1422.96) = 1422.96 kips-in
Flexural Local Buckling Reaction Capacity, (phi)Rn = (phi) * Mn / e = 0.90 * 1422.96 / 6.95 = 184.38 kips
Flexural Yielding using AISC 15th Ed. Equation F11-1
Reaction Capacity, (phi)Rn = min((phi) * Mp / e, (phi) * 1.6 * Fybeam * Snet1 / e) =
= min(0.90 * 1422.96 / 6.95, 0.90 * 1.6 * 50.00 * 18.97 / 6.95) = 184.38 kips
Flexural Rupture using AISC 15th Ed. Equation 9-4
Reaction Capacity, (phi)Rn = (phi)Mn / e = (phi) * Fubeam * Znet2 / e =
= 0.75 * 65.00 * 28.46 / 6.95 = 199.75 kips
Buckling and Flexure at Furthest Bolt Line within Cope
(Top and Bottom Copes at Section - Using AISC 15th Ed. Equations 9-4, 9-15, 9-16, F11-1 to F11-4)
Eccentricity at Section, e = 2.95 in.
tw = 0.48 in.
d = 18.40 in.
dctop = 1.50 in.
dcbot = 1.50 in.
ctop = 5.75 in.
cbot = 5.75 in.
ho = d - [Top Cope Depth] - [Bottom Cope Depth] = 18.40 - 1.50 - 1.50 = 15.40 in.
Fybeam = 50.00 ksi
Snet1 (bolt holes not applicable) = 18.97 in^3
Snet2 (bolt holes applicable) = 13.15 in^3
Znet1 (bolt holes not applicable) = 28.46 in^3
Znet2 (bolt holes applicable) = 19.60 in^3
Mp = Fybeam * Znet1 = 50.00 * 28.46 = 1422.96 kips-in
My = Fybeam * Snet1 = 50.00 * 18.97 = 948.64 kips-in
Lateral Torsional Buckling using AISC 15th Ed. Equations 9-15 to 9-16, F11-1 to F11-4
t = tw = 0.48 in.
d = depth of beam = 18.40 in.
drect = ho = 15.40 in.
dc = dctop = 1.50 in.
Lb = top cope length = 5.75 in.
Fybeam = 50.00 ksi
Cb = max((3 + ln(Lb / d)) * (1 - dc / d), 1.84) =
= max((3 + ln(5.75 / 18.40)) * (1 - 1.50 / 18.40), 1.84) = 1.84
Lb * drect / t^2 = 5.75 * 15.40 / 0.48^2 = 384.33
0.08 * E / Fybeam = 0.08 * 29000 / 50.00 = 46.40
1.9 * E / Fybeam = 1.9 * 29000 / 50.00 = 1102.00
For case when 0.08 * E / Fybeam < Lb * drect / t^2 <= 1.9 * E / Fybeam
Mn = min(Cb * (1.52 - 0.274 * (Lb * drect / t^2) * Fybeam / E) * My, Mp)
= min(1.84 * (1.52 - 0.274 * (5.75 * 15.40 / 0.48^2) * 50.00 / 29000) * 948.64, 1422.96)
= min(2336.24, 1422.96) = 1422.96 kips-in
Flexural Local Buckling Reaction Capacity, (phi)Rn = (phi) * Mn / e = 0.90 * 1422.96 / 2.95 = 434.76 kips
Flexural Yielding using AISC 15th Ed. Equation F11-1
Reaction Capacity, (phi)Rn = min((phi) * Mp / e, (phi) * 1.6 * Fybeam * Snet1 / e) =
= min(0.90 * 1422.96 / 2.95, 0.90 * 1.6 * 50.00 * 18.97 / 2.95) = 434.76 kips
Flexural Rupture using AISC 15th Ed. Equation 9-4
Reaction Capacity, (phi)Rn = (phi)Mn / e = (phi) * Fubeam * Znet2 / e =
= 0.75 * 65.00 * 19.60 / 2.95 = 324.43 kips
Section Bending Strength Calculations Summary:
Buckling : 184.38 kips >= 45.00 kips (OK)
Flexural Yielding : 184.38 kips >= 45.00 kips (OK)
Flexural Rupture : 199.75 kips >= 45.00 kips (OK)
Buckling : 434.76 kips >= 45.00 kips (OK)
Flexural Yielding : 434.76 kips >= 45.00 kips (OK)
Flexural Rupture : 324.43 kips >= 45.00 kips (OK) |
Using AISC 15th Ed. Equation J4-3
Gross Area, Ag = 0.25 * 14.25 = 3.56 in^2
Shear Yielding, (phi)Vny = (phi) * 0.6 * Fypl * Ag = 1.00 * 0.6 * 50.00 * 3.56 = 106.88 kips
106.88 kips >= Reaction V = 45.00 kips (OK)
Shear Rupture:
Using AISC 15th Ed. Equation J4-4
Net Area, An = (14.25 - (5 * (0.94 + 0.06))) * 0.25 = 2.31 in^2
Shear Rupture, (phi)Vnu = (phi) * 0.6 * Fupl * An = 0.75 * 0.6 * 65.00 * 2.31 = 67.64 kips
67.64 kips >= Reaction V = 45.00 kips (OK)
Check Vertical Block Shear
Using AISC 15th 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 = (14.25 - 1.12) = 13.12 in.
Net Shear Length = 13.12 - (5 - 0.5) * (0.94 + 0.06) = 8.62 in.
Gross Tension Length = (0.00 + 1.75) = 1.75 in.
Net Tension Length = 1.75 - (1 - 0.5) * (1.12 + 0.06) = 1.16 in.
1. (phi) * [material thickness] * ((0.60 * Fupl* [net shear length]) + (Ubs * Fupl * [net tension length]))
= 0.75 * 0.25 * ((0.60 * 65.00 * 8.62) + (1.00 * 65.00 * 1.16)) = 77.16 kips
2. (phi) * [material thickness] * ((0.60 * Fypl * [gross shear length]) + (Ubs * Fupl * [net tension length]))
= 0.75 * 0.25 * ((0.60 * 50.00 * 13.12) + (1.00 * 65.00 * 1.16)) = 87.92 kips
Block Shear = 77.16 kips
77.16 kips >= Reaction V = 45.00 kips (OK)
Block Shear for Axial T/C is not required.
Check Flexural Yielding and Rupture:
Eccentricity due to Conventional Config. (e = a/2), e = 1.34 in.
Zgross = 12.69 in^3
Znet = 8.13 in^3
Sgross = 8.46 in^3
Snet = 5.29 in^3
Fypl = 50.00 ksi
Fupl = 65.00 ksi
Mp = Fypl * Zgross = 50.00 * 12.69 = 634.57 kips-in
My = Fypl * Sgross = 50.00 * 8.46 = 423.05 kips-in
Flexural Yielding using AISC 15th Ed. Equation F11-1
Reaction Capacity, (phi)Rn = min((phi) * Mp / e, (phi) * 1.6 * Fypl * Sgross / e) =
= min(0.90 * 634.57 / 1.34, 0.90 * 1.6 * 50.00 * 8.46 / 1.34) = 425.89 kips
425.89 kips >= 45.00 kips (OK)
Flexural Rupture using AISC 15th Ed. Equation 9-4
Reaction Capacity, (phi)Rn = (phi)Mn / e = (phi) * Fupl * Znet / e =
= 0.75 * 65.00 * 8.13 / 1.34 = 295.53 kips
295.53 kips >= 45.00 kips (OK)
Interaction Check of Flexural Yielding:
Using AISC 15th Ed. Equation 10-5
Eccentricity due to Conventional Config. (e = a/2), e = 1.34 in.
Sgross = 8.46 in^3
Zgross = 12.69 in^3
Mr = Vr * e = 45.00 * 1.34 = 60.34 kips-in
Mc = phi * Mn = min(phi * Fypl * Zgross, phi * 1.6 * Fypl * Sgross) =
= min(0.90 * 50.00 * 12.69, 0.90 * 1.6 * 50.00 * 8.46) = 571.11 kips-in
Vr = 45.00 kips
Vc = phi * Vn = phi * 0.60 * Fypl * Ag = 1.00 * 0.60 * 50.00 * 3.56 = 106.88 kips
Interaction due to moment and shear, (Vr/Vc)^2 + (Mr/Mc)^2 <= 1.0
(Vr/Vc)^2 + (Mr/Mc)^2 = (45.00 / 106.88)^2 + (60.34 / 571.11)^2 = 0.19
0.19 <= 1.00 (OK)
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 15th Ed. Table 10-9)
Slot shape = SSL
tmax = Unlimited
Maximum Plate Thickness is Not a Limiting Criteria. |
Plate Thickness, tshpl = 0.25 in.
Skew = 65.50 deg.
Dihedral Angle, DA = Skew = 65.50 deg.
Gap on Obtuse Angle Side Without Shear Plate Bevel = 0.10 in., 0.19 in. >= 0.10 in. >= 0.06 in., account for gap in weld size
Weld Length for shear, Lv = 14.25 in.
Minimum weld sizes:
Acute Side Weld per Table J2.4 = 0.12 in.
Obtuse Side Weld per Table J2.4 = 0.12 in.
Per User Preference = 0.19 in.
Per 5/8*tshpl:
Required Effective Throat (Square Case), teff = 5/8 * tshpl * 2^0.5/2 = 0.62 * 0.25 * 2^0.5/2 = 0.11 in.
Required Acute Side Weld, treqa = (teff/cos(DA/2)) * sin(DA) = (0.11 / cos(65.50/2)) * sin(65.50) = 0.12 in.
Required Obtuse Side Weld, treqo = ((teff/sin(DA/2)) + tshpl/tan(DA)) * sin(DA) = ((0.11 / sin(65.50/2)) + 0.25/tan(65.50)) * sin(65.50) = 0.29 in.
Weld design size:
Acute Side Weld, D1 = max(Table J2.4 Min, User Pref Min, treqa) = max(0.12, 0.19, 0.12) = RoundUp(0.19) = 0.19 in., USE D1 = 3.00
Acute Side Effective Throat, teffa = ((D1/16)/sin(DA)) * cos(DA/2) = ((3.00/16) / sin(65.50)) * cos(65.50/2) = 0.17 in. >= 0.11 in. (OK)
Obtuse Side Weld, D2 = max(Table J2.4, User Pref Min, treqo) = max(0.12, 0.19, 0.29) = RoundUp(0.29) = 0.31 in., USE D2 = 5.00
(Weld size increased on obtuse side for gap at skew per AWS D1.1/D1.1M (2015, p.511, C-5.21.1))
Obtuse Side Effective throat, teffo = ((D2/16)/sin(DA) - tshpl/tan(DA)) * sin(DA/2)
= ((5.00/16)/sin(65.50) - 0.25/tan(65.50)) * sin(65.50/2) = 0.12 in. >= 0.11 in. (OK)
Dmax1 (using AISC 15th Ed. eqn 9-3)
= tshpl * Fushpl / ( Fexx * C1 * 0.09)
= 0.25 * 65.00 / ( 70.00 * 1.00 * 0.09 )
= 2.63
Dmax2 (using AISC 15th Ed. eqn 9-3)
= twbm * Fusupport / ( Fexx * C1 * 0.09 )
= 0.48 * 65.00 / ( 70.00 * 1.00 * 0.09 )
= 5.04
Dmax3 = project max fillet weld = 16.00
Dmax=min(Dmax1, Dmax2, Dmax3) = min(2.63, 5.04, 16.00)
= 2.63
Maximum effective throat, tmax = 2.63/16 * 2^0.5/2 = 0.12 in.
Weld Strength:
Vertical weld capacity during shear only load:
theta = 0 deg.
cPhi = 1.0 + 0.5 * sin(theta)^1.5 = 1.0 + 0.5 * sin(0.00)^1.5 = 1.00
(phi) * Rnv1 = (phi) * 0.60 * Fexx * cPhi * C1 * Lv * (min(teffa, tmax) + min(teffo, tmax))
= 0.75 * 0.60 * 70.00 * 1.00 * 1.00 * 14.25 * (min(0.17,0.12) + min(0.12,0.12)) = 104.21 kips
104.21 kips >= Reaction V = 45.00 kips (OK) |
