BOLT BEARING AT BEAM AND SHEAR PLATE SIDE
Vertical Shear Only Load Case:
ICR cordinate relative to CG = (17.66, 0.00)
At Row 1, At Column 1:
Ribolt = 17.56 kips
Ri vector at Beam = <5.65, 16.63>
Lcsbm at Beam spacing = na
Lcebm at Beam edge = 1.71 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 * 1.71 * (0.32/1) * 65.00 = 31.44 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.75 * (0.32/1) * 65.00 = 27.64 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(na, 31.44, 27.64) = 27.64 kips/bolt
Ri vector at Shear Plate = <-5.65, -16.63>
Lcsshpl at Shear Plate spacing = na
Lceshpl at Shear Plate edge = 5.79 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 * 5.79 * 0.38 * 65.00 = 127.01 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, 127.01, 32.91) = 32.91 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(27.64, 32.91) = 27.64 kips/bolt
Bolt Shear Demand to Bearing ratio = 27.64 / 17.56 = 1.57
At Row 2, At Column 1:
Ribolt = 17.51 kips
Ri vector at Beam = <2.93, 17.27>
Lcsbm at Beam spacing = 2.19 in.
Lcebm at Beam edge = 4.67 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.75 * 1.20 * 2.19 * (0.32/1) * 65.00 = 40.31 kips/bolt
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 4.67 * (0.32/1) * 65.00 = 85.97 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.75 * (0.32/1) * 65.00 = 27.64 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(40.31, 85.97, 27.64) = 27.64 kips/bolt
Ri vector at Shear Plate = <-2.93, -17.27>
Lcsshpl at Shear Plate spacing = 2.19 in.
Lceshpl at Shear Plate edge = 9.98 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 * 9.98 * 0.38 * 65.00 = 219.04 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, 219.04, 32.91) = 32.91 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(27.64, 32.91) = 27.64 kips/bolt
Bolt Shear Demand to Bearing ratio = 27.64 / 17.51 = 1.58
At Row 3, At Column 1:
Ribolt = 17.50 kips
Ri vector at Beam = <-0.00, 17.50>
Lcsbm at Beam spacing = 2.19 in.
Lcebm at Beam edge = 7.59 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.75 * 1.20 * 2.19 * (0.32/1) * 65.00 = 40.31 kips/bolt
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 7.59 * (0.32/1) * 65.00 = 139.94 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.75 * (0.32/1) * 65.00 = 27.64 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(40.31, 139.94, 27.64) = 27.64 kips/bolt
Ri vector at Shear Plate = <0.00, -17.50>
Lcsshpl at Shear Plate spacing = 2.19 in.
Lceshpl at Shear Plate edge = 6.84 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 * 6.84 * 0.38 * 65.00 = 150.14 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, 150.14, 32.91) = 32.91 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(27.64, 32.91) = 27.64 kips/bolt
Bolt Shear Demand to Bearing ratio = 27.64 / 17.50 = 1.58
At Row 4, At Column 1:
Ribolt = 17.51 kips
Ri vector at Beam = <-2.93, 17.27>
Lcsbm at Beam spacing = 2.19 in.
Lcebm at Beam edge = 8.55 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.75 * 1.20 * 2.19 * (0.32/1) * 65.00 = 40.31 kips/bolt
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 8.55 * (0.32/1) * 65.00 = 157.50 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.75 * (0.32/1) * 65.00 = 27.64 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(40.31, 157.50, 27.64) = 27.64 kips/bolt
Ri vector at Shear Plate = <2.93, -17.27>
Lcsshpl at Shear Plate spacing = 2.19 in.
Lceshpl at Shear Plate edge = 3.90 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 * 3.90 * 0.38 * 65.00 = 85.53 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, 85.53, 32.91) = 32.91 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(27.64, 32.91) = 27.64 kips/bolt
Bolt Shear Demand to Bearing ratio = 27.64 / 17.51 = 1.58
At Row 5, At Column 1:
Ribolt = 17.56 kips
Ri vector at Beam = <-5.65, 16.63>
Lcsbm at Beam spacing = na
Lcebm at Beam edge = 4.26 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 * 4.26 * (0.32/1) * 65.00 = 78.43 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.75 * (0.32/1) * 65.00 = 27.64 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(na, 78.43, 27.64) = 27.64 kips/bolt
Ri vector at Shear Plate = <5.65, -16.63>
Lcsshpl at Shear Plate spacing = na
Lceshpl at Shear Plate edge = 0.89 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 * 0.89 * 0.38 * 65.00 = 19.55 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, 19.55, 32.91) = 19.55 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(27.64, 19.55) = 19.55 kips/bolt
Bolt Shear Demand to Bearing ratio = 19.55 / 17.56 = 1.11
Min Bolt Shear Demand to Bearing ratio Beam and Shear Plate for vertical shear only
= min(1.00, 1.57, 1.58, 1.58, 1.58, 1.11) = 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 * 85.29 = 85.29 kips
Rbv = 85.29 kips >= Reaction V = 58.80 kips (OK) |
Web Depth = d - [Top Cope Depth] - [Bottom Cope Depth] = 17.90 - 1.00 - 0.00 = 16.90 in.
Using AISC 14th Ed. Equation J4-3
Gross Area (Shear), Agross = [Web Depth] * tw = 16.90 * 0.32 = 5.32 in^2
Shear Yielding, (phi)Vny = (phi) * 0.6 * Fybeam * Agross = 1.00 * 0.6 * 50.00 * 5.32 = 159.70 kips
Using AISC 14th Ed. Equation J4-4
Net Area (Shear), Anet = ([Web Depth] - ([# rows] * [Diameter + 0.06])) * tw
= (16.90 - (5 * 0.88)) * 0.32 = 3.95 in^2
Shear Rupture, (phi)Vnu = (phi) * 0.6 * Fubeam * Anet = 0.75 * 0.6 * 65.00 * 3.95 = 115.41 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 + 12.00 = 14.00 in.
Net Shear Length = Gross Shear Length - (# rows - 0.5) * (hole size + 0.06) = 14.00 - (5 - 0.5) * 0.88 = 10.06 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 * 0.32 * ((0.60 * 65.00 * 10.06) + (1.00 * 65.00 * 1.06)) = 109.03 kips
2. (phi) * [material thickness] * ((0.60 * Fybeam * [gross shear length]) + (Ubs * Fubeam * [net tension length]))
= 0.75 * 0.32 * ((0.60 * 50.00 * 14.00) + (1.00 * 65.00 * 1.06)) = 115.54 kips
Block Shear = 109.03 kips
Block Shear (1) Total = Block Shear (1) = 109.03 kips
109.03 kips >= Reaction V = 58.80 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 = 6.75 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 Equation 9-7 through 9-11
tw = 0.32 in.
h1 = 11.40 in.
c = 6.00 in.
When c/h1<=1.0, k=2.2(h1/c)^1.65
k = 2.20 * (11.40 / 6.00)^1.65 = 6.34
When c/d<=1.0, f=2c/d
f = 2 * (6.00 / 17.90) = 0.67
Fy = 50.00 ksi
Fcr = (phi) * 26210.00 * f * k * (tw/h1)^2 = 0.90 * 26210.00 * 0.67 * 6.34 * (0.32 / 11.40)^2 = 76.60 ksi
Fcrmin =phi * min(Fcr, Fy) = 45.00 ksi
Snet1 (bolt holes not applicable) = 22.40 in^3
Snet2 (bolt holes applicable) = 22.40 in^3
Znet1 (bolt holes not applicable) = 39.89 in^3
Znet2 (bolt holes applicable) = 39.89 in^3
Using AISC 14th Ed. Equation 9-6
Buckling = Fcr * Snet1 / e = 45.00 * 22.40 / 6.75 = 149.30 kips
Using AISC 14th Ed. Equation 9-19
Flexural Yielding = (phi) * Fy * Snet1 / e = 0.90 * 50.00 * 22.40 / 6.75 = 149.30 kips
Using AISC 14th Ed. Equation 9-4
Flexural Rupture = (phi) * Fu * Znet2 / e = 0.75 * 65.00 * 39.89 / 6.75 = 288.14 kips
Buckling and Flexure at Furthest Bolt Line within Cope (Top Cope Only at Section)
Eccentricity at Section, e = 2.25 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 Equation 9-7 through 9-11
tw = 0.32 in.
h1 = 12.07 in.
c = 6.00 in.
When c/h1<=1.0, k=2.2(h1/c)^1.65
k = 2.20 * (12.07 / 6.00)^1.65 = 6.97
When c/d<=1.0, f=2c/d
f = 2 * (6.00 / 17.90) = 0.67
Fy = 50.00 ksi
Fcr = (phi) * 26210.00 * f * k * (tw/h1)^2 = 0.90 * 26210.00 * 0.67 * 6.97 * (0.32 / 12.07)^2 = 75.08 ksi
Fcrmin =phi * min(Fcr, Fy) = 45.00 ksi
Snet1 (bolt holes not applicable) = 22.40 in^3
Snet2 (bolt holes applicable) = 17.50 in^3
Znet1 (bolt holes not applicable) = 39.89 in^3
Znet2 (bolt holes applicable) = 31.22 in^3
Using AISC 14th Ed. Equation 9-6
Buckling = Fcr * Snet1 / e = 45.00 * 22.40 / 2.25 = 447.91 kips
Using AISC 14th Ed. Equation 9-19
Flexural Yielding = (phi) * Fy * Snet1 / e = 0.90 * 50.00 * 22.40 / 2.25 = 447.91 kips
Using AISC 14th Ed. Equation 9-4
Flexural Rupture = (phi) * Fu * Znet2 / e = 0.75 * 65.00 * 31.22 / 2.25 = 676.35 kips
Section Bending Strength Calculations Summary:
Coped Beam Buckling and Flexure at Longest Cope (Top Cope Only at Section)
Buckling : 149.30 >= 58.80 kips (OK)
Flexural Yielding : 149.30 >= 58.80 kips (OK)
Flexural Rupture : 288.14 >= 58.80 kips (OK)
Coped Beam Buckling and Flexure at Furthest Bolt Line within Cope (Top Cope Only at Section)
Buckling : 447.91 >= 58.80 kips (OK)
Flexural Yielding : 447.91 >= 58.80 kips (OK)
Flexural Rupture : 676.35 >= 58.80 kips (OK) |