BOLT BEARING AT BEAM AND SHEAR PLATE SIDE
Vertical Shear Only Load Case:
ICR cordinate relative to CG = (1.70, 0.00)
At Row 1, At Column 1:
Ribolt = 23.90 kips
Ri vector at Beam = <0.82, 0.58>
Lcsbm at Beam spacing = 2.87 in.
Lcebm at Beam edge = 4.68 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.75 * 1.20 * 2.87 * (0.39/1) * 65.00 = 65.55 kips/bolt
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 4.68 * (0.39/1) * 65.00 = 106.81 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(65.55, 106.81, 39.93) = 39.93 kips/bolt
Ri vector at Shear Plate = <-0.82, -0.58>
Lcsshpl at Shear Plate spacing = 2.81 in.
Lceshpl at Shear Plate edge = 6.32 in.
(phi)Rnsshpl at Shear Plate spacing = (phi) * hf1 * Lcs * t * Fu = 0.75 * 1.20 * 2.81 * 0.50 * 65.00 = 82.09 kips/bolt
(phi)Rneshpl at Shear Plate edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 6.32 * 0.50 * 65.00 = 184.98 kips/bolt
(phi)Rndshpl on Shear Plate at Bolt Diameter = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.88 * 0.50 * 65.00 = 51.19 kips/bolt
Shear Plate bearing capacity, (phi)Rnshpl = min((phi)Rnsshpl,(phi)Rneshpl,(phi)Rndshpl) = min(82.09, 184.98, 51.19) = 51.19 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(39.93, 51.19) = 39.93 kips/bolt
Bolt Shear Demand to Bearing ratio = 39.93 / 23.90 = 1.67
At Row 1, At Column 2:
Ribolt = 23.51 kips
Ri vector at Beam = <1.00, 0.04>
Lcsbm at Beam spacing = 2.00 in.
Lcebm at Beam edge = 68.64 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 * 68.64 * (0.39/1) * 65.00 = 1566.12 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, 1566.12, 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 = 8.16 in.
(phi)Rnsshpl at Shear Plate spacing = (phi) * hf1 * Lcs * t * Fu = 0.75 * 1.20 * 1.81 * 0.50 * 65.00 = 53.02 kips/bolt
(phi)Rneshpl at Shear Plate edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 8.16 * 0.50 * 65.00 = 238.80 kips/bolt
(phi)Rndshpl on Shear Plate at Bolt Diameter = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.88 * 0.50 * 65.00 = 51.19 kips/bolt
Shear Plate bearing capacity, (phi)Rnshpl = min((phi)Rnsshpl,(phi)Rneshpl,(phi)Rndshpl) = min(53.02, 238.80, 51.19) = 51.19 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(39.93, 51.19) = 39.93 kips/bolt
Bolt Shear Demand to Bearing ratio = 39.93 / 23.51 = 1.70
At Row 2, At Column 1:
Ribolt = 22.79 kips
Ri vector at Beam = <0.42, 0.91>
Lcsbm at Beam spacing = 2.87 in.
Lcebm at Beam edge = 6.13 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.75 * 1.20 * 2.87 * (0.39/1) * 65.00 = 65.55 kips/bolt
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 6.13 * (0.39/1) * 65.00 = 139.82 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(65.55, 139.82, 39.93) = 39.93 kips/bolt
Ri vector at Shear Plate = <-0.42, -0.91>
Lcsshpl at Shear Plate spacing = 2.81 in.
Lceshpl at Shear Plate edge = 7.32 in.
(phi)Rnsshpl at Shear Plate spacing = (phi) * hf1 * Lcs * t * Fu = 0.75 * 1.20 * 2.81 * 0.50 * 65.00 = 82.09 kips/bolt
(phi)Rneshpl at Shear Plate edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 7.32 * 0.50 * 65.00 = 214.07 kips/bolt
(phi)Rndshpl on Shear Plate at Bolt Diameter = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.88 * 0.50 * 65.00 = 51.19 kips/bolt
Shear Plate bearing capacity, (phi)Rnshpl = min((phi)Rnsshpl,(phi)Rneshpl,(phi)Rndshpl) = min(82.09, 214.07, 51.19) = 51.19 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(39.93, 51.19) = 39.93 kips/bolt
Bolt Shear Demand to Bearing ratio = 39.93 / 22.79 = 1.75
At Row 2, At Column 2:
Ribolt = 18.49 kips
Ri vector at Beam = <0.99, 0.13>
Lcsbm at Beam spacing = 2.00 in.
Lcebm at Beam edge = 45.94 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 * 45.94 * (0.39/1) * 65.00 = 1048.17 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, 1048.17, 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 = 8.23 in.
(phi)Rnsshpl at Shear Plate spacing = (phi) * hf1 * Lcs * t * Fu = 0.75 * 1.20 * 1.81 * 0.50 * 65.00 = 53.02 kips/bolt
(phi)Rneshpl at Shear Plate edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 8.23 * 0.50 * 65.00 = 240.59 kips/bolt
(phi)Rndshpl on Shear Plate at Bolt Diameter = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.88 * 0.50 * 65.00 = 51.19 kips/bolt
Shear Plate bearing capacity, (phi)Rnshpl = min((phi)Rnsshpl,(phi)Rneshpl,(phi)Rndshpl) = min(53.02, 240.59, 51.19) = 51.19 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(39.93, 51.19) = 39.93 kips/bolt
Bolt Shear Demand to Bearing ratio = 39.93 / 18.49 = 2.16
At Row 3, At Column 1:
Ribolt = 22.79 kips
Ri vector at Beam = <-0.42, 0.91>
Lcsbm at Beam spacing = 2.87 in.
Lcebm at Beam edge = 3.62 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.75 * 1.20 * 2.87 * (0.39/1) * 65.00 = 65.55 kips/bolt
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 3.62 * (0.39/1) * 65.00 = 82.55 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(65.55, 82.55, 39.93) = 39.93 kips/bolt
Ri vector at Shear Plate = <0.42, -0.91>
Lcsshpl at Shear Plate spacing = 2.81 in.
Lceshpl at Shear Plate edge = 4.00 in.
(phi)Rnsshpl at Shear Plate spacing = (phi) * hf1 * Lcs * t * Fu = 0.75 * 1.20 * 2.81 * 0.50 * 65.00 = 82.09 kips/bolt
(phi)Rneshpl at Shear Plate edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 4.00 * 0.50 * 65.00 = 117.14 kips/bolt
(phi)Rndshpl on Shear Plate at Bolt Diameter = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.88 * 0.50 * 65.00 = 51.19 kips/bolt
Shear Plate bearing capacity, (phi)Rnshpl = min((phi)Rnsshpl,(phi)Rneshpl,(phi)Rndshpl) = min(82.09, 117.14, 51.19) = 51.19 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(39.93, 51.19) = 39.93 kips/bolt
Bolt Shear Demand to Bearing ratio = 39.93 / 22.79 = 1.75
At Row 3, At Column 2:
Ribolt = 18.49 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 = 97.88 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(45.63, 97.88, 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 * 0.50 * 65.00 = 53.02 kips/bolt
(phi)Rneshpl at Shear Plate edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 1.17 * 0.50 * 65.00 = 34.11 kips/bolt
(phi)Rndshpl on Shear Plate at Bolt Diameter = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.88 * 0.50 * 65.00 = 51.19 kips/bolt
Shear Plate bearing capacity, (phi)Rnshpl = min((phi)Rnsshpl,(phi)Rneshpl,(phi)Rndshpl) = min(53.02, 34.11, 51.19) = 34.11 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(39.93, 34.11) = 34.11 kips/bolt
Bolt Shear Demand to Bearing ratio = 34.11 / 18.49 = 1.84
At Row 4, At Column 1:
Ribolt = 23.90 kips
Ri vector at Beam = <-0.82, 0.58>
Lcsbm at Beam spacing = 2.87 in.
Lcebm at Beam edge = 1.65 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.75 * 1.20 * 2.87 * (0.39/1) * 65.00 = 65.55 kips/bolt
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 1.65 * (0.39/1) * 65.00 = 37.56 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(65.55, 37.56, 39.93) = 37.56 kips/bolt
Ri vector at Shear Plate = <0.82, -0.58>
Lcsshpl at Shear Plate spacing = 2.81 in.
Lceshpl at Shear Plate edge = 1.21 in.
(phi)Rnsshpl at Shear Plate spacing = (phi) * hf1 * Lcs * t * Fu = 0.75 * 1.20 * 2.81 * 0.50 * 65.00 = 82.09 kips/bolt
(phi)Rneshpl at Shear Plate edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 1.21 * 0.50 * 65.00 = 35.54 kips/bolt
(phi)Rndshpl on Shear Plate at Bolt Diameter = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.88 * 0.50 * 65.00 = 51.19 kips/bolt
Shear Plate bearing capacity, (phi)Rnshpl = min((phi)Rnsshpl,(phi)Rneshpl,(phi)Rndshpl) = min(82.09, 35.54, 51.19) = 35.54 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(37.56, 35.54) = 35.54 kips/bolt
Bolt Shear Demand to Bearing ratio = 35.54 / 23.90 = 1.49
At Row 4, At Column 2:
Ribolt = 23.51 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 * 0.50 * 65.00 = 53.02 kips/bolt
(phi)Rneshpl at Shear Plate edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 1.16 * 0.50 * 65.00 = 33.85 kips/bolt
(phi)Rndshpl on Shear Plate at Bolt Diameter = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.88 * 0.50 * 65.00 = 51.19 kips/bolt
Shear Plate bearing capacity, (phi)Rnshpl = min((phi)Rnsshpl,(phi)Rneshpl,(phi)Rndshpl) = min(53.02, 33.85, 51.19) = 33.85 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(39.93, 33.85) = 33.85 kips/bolt
Bolt Shear Demand to Bearing ratio = 33.85 / 23.51 = 1.44
Min Bolt Shear Demand to Bearing ratio Beam and Shear Plate for vertical shear only
= min(1.00, 1.67, 1.70, 1.75, 2.16, 1.75, 1.84, 1.49, 1.44) = 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 * 75.76 = 75.76 kips
Rbv = 75.76 kips >= Reaction V = 45.00 kips (OK) |
Using AISC 15th Ed. Equation J4-3
Gross Area, Ag = 0.50 * 11.25 = 5.62 in^2
Shear Yielding, (phi)Vny = (phi) * 0.6 * Fypl * Ag = 1.00 * 0.6 * 50.00 * 5.62 = 168.75 kips
168.75 kips >= Reaction V = 45.00 kips (OK)
Shear Rupture:
Using AISC 15th Ed. Equation J4-4
Net Area, An = (11.25 - (4 * (0.94 + 0.06))) * 0.50 = 3.62 in^2
Shear Rupture, (phi)Vnu = (phi) * 0.6 * Fupl * An = 0.75 * 0.6 * 65.00 * 3.62 = 106.03 kips
106.03 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 = (11.25 - 1.12) = 10.12 in.
Net Shear Length = 10.12 - (4 - 0.5) * (0.94 + 0.06) = 6.62 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 * 0.50 * ((0.60 * 65.00 * 6.62) + (0.50 * 65.00 * 2.97)) = 133.08 kips
2. (phi) * [material thickness] * ((0.60 * Fypl * [gross shear length]) + (Ubs * Fupl * [net tension length]))
= 0.75 * 0.50 * ((0.60 * 50.00 * 10.12) + (0.50 * 65.00 * 2.97)) = 150.09 kips
Block Shear = 133.08 kips
Block 2 (Shear):
Gross Shear Length = 2 * (11.25 - 1.12) = 20.25 in.
Net Shear Length = 2 * ( 10.12 - (4 - 0.5) * (0.94 + 0.06) ) = 13.25 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 * 0.50 * ((0.60 * 65.00 * 13.25) + (0.50 * 65.00 * 1.81)) = 215.88 kips
2. (phi) * [material thickness] * ((0.60 * Fypl * [gross shear length]) + (Ubs * Fupl * [net tension length]))
= 0.75 * 0.50 * ((0.60 * 50.00 * 20.25) + (0.50 * 65.00 * 1.81)) = 249.91 kips
Block Shear = 215.88 kips
Block Shear Total = min(Block Shear (1), Block Shear (2)) = min(133.08,215.88) = 133.08
133.08 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 = 5.95 in.
Zgross = 15.82 in^3
Znet = 9.82 in^3
Sgross = 10.55 in^3
Snet = 6.52 in^3
Fypl = 50.00 ksi
Fupl = 65.00 ksi
Mp = Fypl * Zgross = 50.00 * 15.82 = 791.02 kips-in
My = Fypl * Sgross = 50.00 * 10.55 = 527.34 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 * 791.02 / 5.95, 0.90 * 1.6 * 50.00 * 10.55 / 5.95) = 119.75 kips
119.75 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 * 9.82 / 5.95 = 80.53 kips
80.53 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 = 0.50 in.
d = hshpl = 11.25 in.
drect = hshpl = 11.25 in.
dc = down distance (per AISC Example II.A-19B) = 3.00 in.
Lb = horizontal distance to first hole = 5.75 in.
Fypl = 50.00 ksi
Cb = max((3 + ln(Lb / d)) * (1 - dc / d), 1.84) =
= max((3 + ln(5.75 / 11.25)) * (1 - 3.00 / 11.25), 1.84) = 1.84
Lb * drect / t^2 = 5.75 * 11.25 / 0.50^2 = 258.75
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(1.84 * (1.52 - 0.274 * (5.75 * 11.25 / 0.50^2) * 50.00 / 29000) * 527.34, 791.02)
= min(1356.27, 791.02) = 791.02 kips-in
Flexural Local Buckling Reaction Capacity, (phi)Rn = (phi) * Mn / e = 0.90 * 791.02 / 5.95 = 119.75 kips
119.75 kips >= 45.00 kips (OK)
Interaction Check of Flexural Yielding:
Using AISC 15th Ed. Equation 10-5
Eccentricity at first line of bolts, e = 5.95 in.
Sgross = 10.55 in^3
Zgross = 15.82 in^3
Mr = Vr * e = 45.00 * 5.95 = 267.53 kips-in
Mc = phi * Mn = min(phi * Fypl * Zgross, phi * 1.6 * Fypl * Sgross) =
= min(0.90 * 50.00 * 15.82, 0.90 * 1.6 * 50.00 * 10.55) = 711.91 kips-in
Vr = 45.00 kips
Vc = phi * Vn = phi * 0.60 * Fypl * Ag = 1.00 * 0.60 * 50.00 * 5.62 = 168.75 kips
Interaction due to moment and shear, (Vr/Vc)^2 + (Mr/Mc)^2 <= 1.0
(Vr/Vc)^2 + (Mr/Mc)^2 = (45.00 / 168.75)^2 + (267.53 / 711.91)^2 = 0.21
0.21 <= 1.00 (OK)
LATERAL-TORSIONAL STABILITY:
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 * 11.25 * 0.50^3 / 5.75^2 = 180.39 kips
180.39 kips >= Reaction V = 45.00 kips (OK)
Torsional Strength:
Using Eq. 10 and Eq. 16, Thornton and Fortney 2011 Engineering Journal
Required, Mtu = Ru * (tw + tp) / 2 = 45.00 * ((0.38 + 0.50) / 2) = 19.69 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 / (11.25 * 0.50))] * 11.25 * 0.50^2 / 2 = 30.94 kips-in
30.94 kips-in >= Mtu = 19.69 kips-in (OK)
MAXIMUM PLATE THICKNESS:
No of bolt columns = 2
tp < = db/2 + 0.06 = 0.50 <= 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. |