BOLT BEARING AT BEAM AND SHEAR PLATE SIDE
Vertical Shear Only Load Case:
ICR cordinate relative to CG = (1.76, 0.00)
At Row 1, At Column 1:
Ribolt = 23.90 kips
Ri vector at Beam = <0.88, 0.48>
Lcsbm at Beam spacing = 3.64 in.
Lcebm at Beam edge = 5.78 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.75 * 1.20 * 3.64 * (0.39/1) * 65.00 = 83.06 kips/bolt
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 5.78 * (0.39/1) * 65.00 = 131.82 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.88 * (0.39/1) * 65.00 = 39.93 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(83.06, 131.82, 39.93) = 39.93 kips/bolt
Ri vector at Shear Plate = <-0.88, -0.48>
Lcsshpl at Shear Plate spacing = 3.59 in.
Lceshpl at Shear Plate edge = 10.00 in.
(phi)Rnsshpl at Shear Plate spacing = (phi) * hf1 * Lcs * t * Fu = 0.75 * 1.20 * 3.59 * 0.38 * 65.00 = 78.72 kips/bolt
(phi)Rneshpl at Shear Plate edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 10.00 * 0.38 * 65.00 = 219.31 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(78.72, 219.31, 38.39) = 38.39 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(39.93, 38.39) = 38.39 kips/bolt
Bolt Shear Demand to Bearing ratio = 38.39 / 23.90 = 1.61
At Row 1, At Column 2:
Ribolt = 23.67 kips
Ri vector at Beam = <1.00, 0.04>
Lcsbm at Beam spacing = 2.00 in.
Lcebm at Beam edge = 67.86 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.75 * 1.20 * 2.00 * (0.39/1) * 65.00 = 45.63 kips/bolt
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 67.86 * (0.39/1) * 65.00 = 1548.32 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.88 * (0.39/1) * 65.00 = 39.93 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(45.63, 1548.32, 39.93) = 39.93 kips/bolt
Ri vector at Shear Plate = <-1.00, -0.04>
Lcsshpl at Shear Plate spacing = 1.81 in.
Lceshpl at Shear Plate edge = 11.79 in.
(phi)Rnsshpl at Shear Plate spacing = (phi) * hf1 * Lcs * t * Fu = 0.75 * 1.20 * 1.81 * 0.38 * 65.00 = 39.76 kips/bolt
(phi)Rneshpl at Shear Plate edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 11.79 * 0.38 * 65.00 = 258.71 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(39.76, 258.71, 38.39) = 38.39 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(39.93, 38.39) = 38.39 kips/bolt
Bolt Shear Demand to Bearing ratio = 38.39 / 23.67 = 1.62
At Row 2, At Column 1:
Ribolt = 22.29 kips
Ri vector at Beam = <0.52, 0.85>
Lcsbm at Beam spacing = 3.64 in.
Lcebm at Beam edge = 7.71 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.75 * 1.20 * 3.64 * (0.39/1) * 65.00 = 83.06 kips/bolt
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 7.71 * (0.39/1) * 65.00 = 175.88 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.88 * (0.39/1) * 65.00 = 39.93 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(83.06, 175.88, 39.93) = 39.93 kips/bolt
Ri vector at Shear Plate = <-0.52, -0.85>
Lcsshpl at Shear Plate spacing = 3.59 in.
Lceshpl at Shear Plate edge = 10.11 in.
(phi)Rnsshpl at Shear Plate spacing = (phi) * hf1 * Lcs * t * Fu = 0.75 * 1.20 * 3.59 * 0.38 * 65.00 = 78.72 kips/bolt
(phi)Rneshpl at Shear Plate edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 10.11 * 0.38 * 65.00 = 221.89 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(78.72, 221.89, 38.39) = 38.39 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(39.93, 38.39) = 38.39 kips/bolt
Bolt Shear Demand to Bearing ratio = 38.39 / 22.29 = 1.72
At Row 2, At Column 2:
Ribolt = 18.95 kips
Ri vector at Beam = <0.99, 0.13>
Lcsbm at Beam spacing = 2.00 in.
Lcebm at Beam edge = 53.06 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.75 * 1.20 * 2.00 * (0.39/1) * 65.00 = 45.63 kips/bolt
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 53.06 * (0.39/1) * 65.00 = 1210.57 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.88 * (0.39/1) * 65.00 = 39.93 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(45.63, 1210.57, 39.93) = 39.93 kips/bolt
Ri vector at Shear Plate = <-0.99, -0.13>
Lcsshpl at Shear Plate spacing = 1.81 in.
Lceshpl at Shear Plate edge = 11.88 in.
(phi)Rnsshpl at Shear Plate spacing = (phi) * hf1 * Lcs * t * Fu = 0.75 * 1.20 * 1.81 * 0.38 * 65.00 = 39.76 kips/bolt
(phi)Rneshpl at Shear Plate edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 11.88 * 0.38 * 65.00 = 260.69 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(39.76, 260.69, 38.39) = 38.39 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(39.93, 38.39) = 38.39 kips/bolt
Bolt Shear Demand to Bearing ratio = 38.39 / 18.95 = 2.03
At Row 3, At Column 1:
Ribolt = 22.29 kips
Ri vector at Beam = <-0.52, 0.85>
Lcsbm at Beam spacing = 3.64 in.
Lcebm at Beam edge = 2.85 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.75 * 1.20 * 3.64 * (0.39/1) * 65.00 = 83.06 kips/bolt
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 2.85 * (0.39/1) * 65.00 = 64.97 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.88 * (0.39/1) * 65.00 = 39.93 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(83.06, 64.97, 39.93) = 39.93 kips/bolt
Ri vector at Shear Plate = <0.52, -0.85>
Lcsshpl at Shear Plate spacing = 3.59 in.
Lceshpl at Shear Plate edge = 5.43 in.
(phi)Rnsshpl at Shear Plate spacing = (phi) * hf1 * Lcs * t * Fu = 0.75 * 1.20 * 3.59 * 0.38 * 65.00 = 78.72 kips/bolt
(phi)Rneshpl at Shear Plate edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 5.43 * 0.38 * 65.00 = 119.02 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(78.72, 119.02, 38.39) = 38.39 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(39.93, 38.39) = 38.39 kips/bolt
Bolt Shear Demand to Bearing ratio = 38.39 / 22.29 = 1.72
At Row 3, At Column 2:
Ribolt = 18.95 kips
Ri vector at Beam = <-0.99, 0.13>
Lcsbm at Beam spacing = 2.00 in.
Lcebm at Beam edge = 4.29 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.75 * 1.20 * 2.00 * (0.39/1) * 65.00 = 45.63 kips/bolt
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 4.29 * (0.39/1) * 65.00 = 97.90 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.88 * (0.39/1) * 65.00 = 39.93 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(45.63, 97.90, 39.93) = 39.93 kips/bolt
Ri vector at Shear Plate = <0.99, -0.13>
Lcsshpl at Shear Plate spacing = 1.81 in.
Lceshpl at Shear Plate edge = 1.17 in.
(phi)Rnsshpl at Shear Plate spacing = (phi) * hf1 * Lcs * t * Fu = 0.75 * 1.20 * 1.81 * 0.38 * 65.00 = 39.76 kips/bolt
(phi)Rneshpl at Shear Plate edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 1.17 * 0.38 * 65.00 = 25.58 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(39.76, 25.58, 38.39) = 25.58 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(39.93, 25.58) = 25.58 kips/bolt
Bolt Shear Demand to Bearing ratio = 25.58 / 18.95 = 1.35
At Row 4, At Column 1:
Ribolt = 23.90 kips
Ri vector at Beam = <-0.88, 0.48>
Lcsbm at Beam spacing = 3.64 in.
Lcebm at Beam edge = 1.49 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.75 * 1.20 * 3.64 * (0.39/1) * 65.00 = 83.06 kips/bolt
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 1.49 * (0.39/1) * 65.00 = 34.04 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.88 * (0.39/1) * 65.00 = 39.93 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(83.06, 34.04, 39.93) = 34.04 kips/bolt
Ri vector at Shear Plate = <0.88, -0.48>
Lcsshpl at Shear Plate spacing = 3.59 in.
Lceshpl at Shear Plate edge = 1.68 in.
(phi)Rnsshpl at Shear Plate spacing = (phi) * hf1 * Lcs * t * Fu = 0.75 * 1.20 * 3.59 * 0.38 * 65.00 = 78.72 kips/bolt
(phi)Rneshpl at Shear Plate edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 1.68 * 0.38 * 65.00 = 36.83 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(78.72, 36.83, 38.39) = 36.83 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(34.04, 36.83) = 34.04 kips/bolt
Bolt Shear Demand to Bearing ratio = 34.04 / 23.90 = 1.42
At Row 4, At Column 2:
Ribolt = 23.67 kips
Ri vector at Beam = <-1.00, 0.04>
Lcsbm at Beam spacing = 2.00 in.
Lcebm at Beam edge = 4.25 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.75 * 1.20 * 2.00 * (0.39/1) * 65.00 = 45.63 kips/bolt
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 4.25 * (0.39/1) * 65.00 = 97.07 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.88 * (0.39/1) * 65.00 = 39.93 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(45.63, 97.07, 39.93) = 39.93 kips/bolt
Ri vector at Shear Plate = <1.00, -0.04>
Lcsshpl at Shear Plate spacing = 1.81 in.
Lceshpl at Shear Plate edge = 1.16 in.
(phi)Rnsshpl at Shear Plate spacing = (phi) * hf1 * Lcs * t * Fu = 0.75 * 1.20 * 1.81 * 0.38 * 65.00 = 39.76 kips/bolt
(phi)Rneshpl at Shear Plate edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 1.16 * 0.38 * 65.00 = 25.39 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(39.76, 25.39, 38.39) = 25.39 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(39.93, 25.39) = 25.39 kips/bolt
Bolt Shear Demand to Bearing ratio = 25.39 / 23.67 = 1.07
Min Bolt Shear Demand to Bearing ratio Beam and Shear Plate for vertical shear only
= min(1.00, 1.61, 1.62, 1.72, 2.03, 1.72, 1.35, 1.42, 1.07) = 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 * 67.88 = 67.88 kips
Rbv = 67.88 kips >= Reaction V = 45.00 kips (OK) |
Using AISC 15th Ed. Equation J4-3
Gross Area, Ag = 0.38 * 14.25 = 5.34 in^2
Shear Yielding, (phi)Vny = (phi) * 0.6 * Fypl * Ag = 1.00 * 0.6 * 50.00 * 5.34 = 160.31 kips
160.31 kips >= Reaction V = 45.00 kips (OK)
Shear Rupture:
Using AISC 15th Ed. Equation J4-4
Net Area, An = (14.25 - (4 * (0.94 + 0.06))) * 0.38 = 3.84 in^2
Shear Rupture, (phi)Vnu = (phi) * 0.6 * Fupl * An = 0.75 * 0.6 * 65.00 * 3.84 = 112.43 kips
112.43 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 - (4 - 0.5) * (0.94 + 0.06) = 9.62 in.
Gross Tension Length = (3.00 + 1.75) = 4.75 in.
Net Tension Length = 4.75 - (2 - 0.5) * (1.12 + 0.06) = 2.97 in.
1. (phi) * [material thickness] * ((0.60 * Fupl* [net shear length]) + (Ubs * Fupl * [net tension length]))
= 0.75 * 0.38 * ((0.60 * 65.00 * 9.62) + (0.50 * 65.00 * 2.97)) = 132.71 kips
2. (phi) * [material thickness] * ((0.60 * Fypl * [gross shear length]) + (Ubs * Fupl * [net tension length]))
= 0.75 * 0.38 * ((0.60 * 50.00 * 13.12) + (0.50 * 65.00 * 2.97)) = 137.88 kips
Block Shear = 132.71 kips
Block 2 (Shear):
Gross Shear Length = 2 * (14.25 - 1.12) = 26.25 in.
Net Shear Length = 2 * ( 13.12 - (4 - 0.5) * (0.94 + 0.06) ) = 19.25 in.
Gross Tension Length = (3.00 + 1.75) - 1.75 = 3.00 in.
Net Tension Length = 3.00 - (2 - 1) * (1.12 + 0.06) = 1.81 in.
1. (phi) * [material thickness] * ((0.60 * Fupl* [net shear length]) + (Ubs * Fupl * [net tension length]))
= 0.75 * 0.38 * ((0.60 * 65.00 * 19.25) + (0.50 * 65.00 * 1.81)) = 227.72 kips
2. (phi) * [material thickness] * ((0.60 * Fypl * [gross shear length]) + (Ubs * Fupl * [net tension length]))
= 0.75 * 0.38 * ((0.60 * 50.00 * 26.25) + (0.50 * 65.00 * 1.81)) = 238.06 kips
Block Shear = 227.72 kips
Block Shear Total = min(Block Shear (1), Block Shear (2)) = min(132.71,227.72) = 132.71
132.71 kips >= Reaction V = 45.00 kips (OK)
Block Shear for Axial T/C is not required.
Check Flexural Yielding and Rupture:
Eccentricity at first line of bolts, e = 9.38 in.
Zgross = 19.04 in^3
Znet = 13.04 in^3
Sgross = 12.69 in^3
Snet = 8.46 in^3
Fypl = 50.00 ksi
Fupl = 65.00 ksi
Mp = Fypl * Zgross = 50.00 * 19.04 = 951.86 kips-in
My = Fypl * Sgross = 50.00 * 12.69 = 634.57 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 * 951.86 / 9.38, 0.90 * 1.6 * 50.00 * 12.69 / 9.38) = 91.38 kips
91.38 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 * 13.04 / 9.38 = 67.79 kips
67.79 kips >= 45.00 kips (OK)
Flexural and Buckling Strength:
Lateral Torsional Buckling using AISC 15th Ed. Equations 9-15 to 9-16, F11-1 to F11-4
t = tshpl = 0.38 in.
d = hshpl = 14.25 in.
drect = hshpl = 14.25 in.
dc = down distance (per AISC Example II.A-19B) = 3.00 in.
Lb = horizontal distance to first hole = 9.38 in.
Fypl = 50.00 ksi
Cb = max((3 + ln(Lb / d)) * (1 - dc / d), 1.84) =
= max((3 + ln(9.38 / 14.25)) * (1 - 3.00 / 14.25), 1.84) = 2.04
Lb * drect / t^2 = 9.38 * 14.25 / 0.38^2 = 950.00
0.08 * E / Fypl = 0.08 * 29000 / 50.00 = 46.40
1.9 * E / Fypl = 1.9 * 29000 / 50.00 = 1102.00
For case when 0.08 * E / Fypl < Lb * drect / t^2 <= 1.9 * E / Fypl
Mn = min(Cb * (1.52 - 0.274 * (Lb * drect / t^2) * Fypl / E) * My, Mp)
= min(2.04 * (1.52 - 0.274 * (9.38 * 14.25 / 0.38^2) * 50.00 / 29000) * 634.57, 951.86)
= min(1385.25, 951.86) = 951.86 kips-in
Flexural Local Buckling Reaction Capacity, (phi)Rn = (phi) * Mn / e = 0.90 * 951.86 / 9.38 = 91.38 kips
91.38 kips >= 45.00 kips (OK)
Interaction Check of Flexural Yielding:
Using AISC 15th Ed. Equation 10-5
Eccentricity at first line of bolts, e = 9.38 in.
Sgross = 12.69 in^3
Zgross = 19.04 in^3
Mr = Vr * e = 45.00 * 9.38 = 421.88 kips-in
Mc = phi * Mn = min(phi * Fypl * Zgross, phi * 1.6 * Fypl * Sgross) =
= min(0.90 * 50.00 * 19.04, 0.90 * 1.6 * 50.00 * 12.69) = 856.67 kips-in
Vr = 45.00 kips
Vc = phi * Vn = phi * 0.60 * Fypl * Ag = 1.00 * 0.60 * 50.00 * 5.34 = 160.31 kips
Interaction due to moment and shear, (Vr/Vc)^2 + (Mr/Mc)^2 <= 1.0
(Vr/Vc)^2 + (Mr/Mc)^2 = (45.00 / 160.31)^2 + (421.88 / 856.67)^2 = 0.32
0.32 <= 1.00 (OK)
MAXIMUM PLATE THICKNESS:
No of bolt columns = 2
tp < = db/2 + 0.06 = 0.38 <= 0.50 OK
tw < = db/2 + 0.06 = 0.39 <= 0.50 OK
Leh(plate) >= 2 * db = 1.75 >= 1.75 OK
Leh(bm) >= 2 * db = 1.75 >= 1.75 OK
Maximum Plate Thickness is Not a Limiting Criteria.
STABILIZER PLATE:
Available Strength to Resist Lateral Displacement:
Using Eq. 6, Thornton and Fortney 2011 Engineering Journal
(phi)Rn = 1500.00 * 3.14 * L * tp^3 / a^2 = 0.90 * 1500.00 * 3.14 * 14.25 * 0.38^3 / 9.38^2 = 36.26 kips
36.26 kips < Reaction V = 45.00 kips (NG)
Stabilizer Plate Required for lateral displacement
Torsional Strength:
Using Eq. 10 and Eq. 16, Thornton and Fortney 2011 Engineering Journal
Required, Mtu = Ru * (tw + tp) / 2 = 45.00 * ((0.38 + 0.38) / 2) = 16.88 kips-in
Lateral Shear Strength of Shear Plate, Mtn (no slab) = [(phiv) * (0.6 * Fyp) - (Ru / (L * tp))] * L * tp^2 / 2 =
= [(1.00) * (0.6 * 50.00) - (45.00 / (14.25 * 0.38))] * 14.25 * 0.38^2 / 2 = 21.62 kips-in
21.62 kips-in >= Mtu = 16.88 kips-in (OK)
Stabilizer Plate Not Required for torsional strength |