BOLT BEARING AT BEAM AND SHEAR PLATE SIDE
Vertical Shear Only Load Case:
ICR cordinate relative to CG = (3.41, 0.00)
At Row 1, At Column 1:
Ribolt = 23.90 kips
Ri vector at Beam = <0.66, 0.75>
Lcsbm at Beam spacing = na
Lcebm at Beam edge = 3.50 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 * 3.50 * (0.23/1) * 65.00 = 47.06 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.88 * (0.23/1) * 65.00 = 23.55 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(na, 47.06, 23.55) = 23.55 kips/bolt
Ri vector at Shear Plate = <-0.66, -0.75>
Lcsshpl at Shear Plate spacing = na
Lceshpl at Shear Plate edge = 4.06 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 * 4.06 * 0.25 * 65.00 = 59.40 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, 59.40, 25.59) = 25.59 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(23.55, 25.59) = 23.55 kips/bolt
Bolt Shear Demand to Bearing ratio = 23.55 / 23.90 = 0.99
At Row 2, At Column 1:
Ribolt = 23.29 kips
Ri vector at Beam = <-0.00, 1.00>
Lcsbm at Beam spacing = 2.00 in.
Lcebm at Beam edge = 5.50 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.75 * 1.20 * 2.00 * (0.23/1) * 65.00 = 26.91 kips/bolt
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 5.50 * (0.23/1) * 65.00 = 74.00 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.88 * (0.23/1) * 65.00 = 23.55 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(26.91, 74.00, 23.55) = 23.55 kips/bolt
Ri vector at Shear Plate = <0.00, -1.00>
Lcsshpl at Shear Plate spacing = 2.00 in.
Lceshpl at Shear Plate edge = 3.63 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 * 3.63 * 0.25 * 65.00 = 53.02 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, 53.02, 25.59) = 25.59 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(23.55, 25.59) = 23.55 kips/bolt
Bolt Shear Demand to Bearing ratio = 23.55 / 23.29 = 1.01
At Row 3, At Column 1:
Ribolt = 23.90 kips
Ri vector at Beam = <-0.66, 0.75>
Lcsbm at Beam spacing = na
Lcebm at Beam edge = 2.15 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 * 2.15 * (0.23/1) * 65.00 = 28.89 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.88 * (0.23/1) * 65.00 = 23.55 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(na, 28.89, 23.55) = 23.55 kips/bolt
Ri vector at Shear Plate = <0.66, -0.75>
Lcsshpl at Shear Plate spacing = na
Lceshpl at Shear Plate edge = 0.83 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 * 0.83 * 0.25 * 65.00 = 12.18 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, 12.18, 25.59) = 12.18 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(23.55, 12.18) = 12.18 kips/bolt
Bolt Shear Demand to Bearing ratio = 12.18 / 23.90 = 0.51
Min Bolt Shear Demand to Bearing ratio Beam and Shear Plate for vertical shear only
= min(1.00, 0.99, 1.01, 0.51) = 0.51
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 = 0.51 * 59.16 = 30.15 kips
Rbv = 30.15 kips >= Reaction V = 20.00 kips (OK) |
Using AISC 15th Ed. Equation J4-3
Gross Area, Ag = 0.25 * 8.25 = 2.06 in^2
Shear Yielding, (phi)Vny = (phi) * 0.6 * Fypl * Ag = 1.00 * 0.6 * 50.00 * 2.06 = 61.88 kips
61.88 kips >= Reaction V = 20.00 kips (OK)
Shear Rupture:
Using AISC 15th Ed. Equation J4-4
Net Area, An = (8.25 - (3 * (0.94 + 0.06))) * 0.25 = 1.31 in^2
Shear Rupture, (phi)Vnu = (phi) * 0.6 * Fupl * An = 0.75 * 0.6 * 65.00 * 1.31 = 38.39 kips
38.39 kips >= Reaction V = 20.00 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 = (8.25 - 1.12) = 7.12 in.
Net Shear Length = 7.12 - (3 - 0.5) * (0.94 + 0.06) = 4.62 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 * 4.62) + (1.00 * 65.00 * 1.16)) = 47.91 kips
2. (phi) * [material thickness] * ((0.60 * Fypl * [gross shear length]) + (Ubs * Fupl * [net tension length]))
= 0.75 * 0.25 * ((0.60 * 50.00 * 7.12) + (1.00 * 65.00 * 1.16)) = 54.17 kips
Block Shear = 47.91 kips
47.91 kips >= Reaction V = 20.00 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 = 1.60 in.
Zgross = 4.25 in^3
Znet = 2.69 in^3
Sgross = 2.84 in^3
Snet = 1.73 in^3
Fypl = 50.00 ksi
Fupl = 65.00 ksi
Mp = Fypl * Zgross = 50.00 * 4.25 = 212.70 kips-in
My = Fypl * Sgross = 50.00 * 2.84 = 141.80 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 * 212.70 / 1.60, 0.90 * 1.6 * 50.00 * 2.84 / 1.60) = 119.52 kips
119.52 kips >= 20.00 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 * 2.69 / 1.60 = 81.93 kips
81.93 kips >= 20.00 kips (OK)
Interaction Check of Flexural Yielding:
Using AISC 15th Ed. Equation 10-5
Eccentricity due to Conventional Config. (e = a/2), e = 1.60 in.
Sgross = 2.84 in^3
Zgross = 4.25 in^3
Mr = Vr * e = 20.00 * 1.60 = 32.03 kips-in
Mc = phi * Mn = min(phi * Fypl * Zgross, phi * 1.6 * Fypl * Sgross) =
= min(0.90 * 50.00 * 4.25, 0.90 * 1.6 * 50.00 * 2.84) = 191.43 kips-in
Vr = 20.00 kips
Vc = phi * Vn = phi * 0.60 * Fypl * Ag = 1.00 * 0.60 * 50.00 * 2.06 = 61.88 kips
Interaction due to moment and shear, (Vr/Vc)^2 + (Mr/Mc)^2 <= 1.0
(Vr/Vc)^2 + (Mr/Mc)^2 = (20.00 / 61.88)^2 + (32.03 / 191.43)^2 = 0.13
0.13 <= 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. |
WELDS:
PJP Weld Details:
Root Face, f = 0.12 in.
Dihedral Angle, DA = 58.00 deg.
Groove Depth, S = tp - f = 0.25 - 0.12 = 0.12 in.
zloss = 0.00 in.
Epjp Groove Size = S - zloss = 0.12 - 0.00 = 0.12 in. >= 0.12 in. (OK, per Table J2.3)
Epjp max effective groove, Epjp max = (twsupport*Fusupport)/(Fexx*#sides) = (0.43 * 65.00)/(70.00 * 1.00) = 0.40 in.
Epjp str = min(Epjp groove size, Epjp max) = min(0.12, 0.40) = 0.12 in.
Companion Fillet Weld Details:
Dihedral Angle, DA = 58.00 deg.
Z loss value matching AWS D1.1 Table 2.2 for PJP weld process, position and dihedral angle = 0.00 in.
Required Effective Throat (Square Case), teff = 5/8*tshpl*2^0.5/2 = 5/8*0.25*2^0.5/2 = 0.11 in.
Required Fillet Weld for Effective Throat, treqa = ((teff + zloss) / cos(DA/2))*sin(DA) = ((0.11 + 0.00) / cos(58.00/2))*sin(58.00) = 0.11 in.
Required fillet weld for plate tensile strength =
(((Plate tensile strength) - PJP Contribution))/(phi * 0.60 * Fexx * electrode coeff c1 * 1.5) + zloss) * sin(DA)/cos(DA/2) =
(((11.25) - (0.80 * 0.60 * 70.00 * 1.00 * 0.12))/(0.75 * 0.60 * 70.00 * 1.00 * 1.5) + 0.00) * sin(58.00) / cos(29.00) = 0.14 in.
Required fillet weld for plate shear strength =
(((Plate shear strength) - PJP Contribution))/(phi * 0.60 * Fexx * electrode coeff c1) + zloss) * sin(DA)/cos(DA/2) =
(((7.50) - (0.75 * 0.60 * 70.00 * 1.00 * 0.12))/(0.75 * 0.60 * 70.00 * 1.00) + 0.00) * sin(58.00) / cos(29.00) = 0.11 in.
req strength = max(required fillet weld for plate tensile strength, required fillet weld for plate shear strength) = max(0.14,0.11) = 0.14
Minimum required fillet weld per Table J2.4 = 0.12 in.
Fillet Weld Size Use, D = min(max(min user prefs, min Table J2.4, treqa, req strength), max user prefs) = min(max(0.19,0.12,0.11,0.14),1.00) = 0.19 in., use D = 3.00
Fillet Weld Effective Throat, teffa = (D/16/sin(DA)) * cos(DA/2) - zloss = (3.00/16/sin(58.00)) * cos(29.00) - 0.00 = 0.19 in. >= 0.11 in. (OK)
Fillet max effective throat, tmax = (twsupport*Fusupport)/(Fexx*#sides) = (0.43 * 65.00)/(70.00 * 1.00) = 0.40 in.
Fillet str = max(0, min(teffa, tmax) = max(0.00,min(0.19, 0.40)) = 0.19 in.
Combined Weld Strength:
PJP Weld:
Shear Only Weld Capacity
Vertical Capacity, V pjp 1 = phi(Rn) = phi shear * 0.60 * Fexx * electrode coeff c1 * Epjp str * weld length = 0.75 * 0.60 * 70.00 * 1.00 * 0.12 * 8.25 = 32.49 kips
Fillet Weld:
Shear Only Load Capacity
Vertical Capacity, V fil 1 = phi(Rn) = phi * 0.60 * Fexx * electrode coeff c1 * Fillet str * weld length = 0.75 * 0.60 * 70.00 * 1.00 * 0.19 * 8.25 = 50.25 kips
Total Fillet + PJP weld capacities:
Vertical Capacity, V comb = V pjp 1 + V fil 1 = 32.49 + 50.25 = 82.74 kips
82.74 kips >= Reaction V = 20.00 kips (OK)
Check plate tensile strength <= weld tensile strength
Plate Tensile Strength = phi * Fy * tshpl = 11.25 kips/in
Weld Tensile Strength = Fillet Contribution + PJP Contribution = phi * 0.60 * Fexx * electrode coeff c1 * teffa * 1.5 + phi * 0.60 * Fexx * electrode coeff c1 * Epjp groove size =
0.75 * 0.60 * 70.00 * 1.00 * 0.19 * 1.5 + 0.80 * 0.60 * 70.00 * 1.00 * 0.12 = 13.34 kips/in
13.34 kips/in >= 11.25 kips/in (OK)
Check plate shear strength <= weld shear strength
Plate Shear Strength = phi * 0.6 * Fy * tshpl = 7.50 kips/in
Weld Shear Strength = Fillet Contribution + PJP Contribution = phi * 0.60 * Fexx * electrode coeff c1 * teffa + phi * 0.60 * Fexx * electrode coeff c1 * Epjp groove size =
0.75 * 0.60 * 70.00 * 1.00 * 0.19 + 0.75 * 0.60 * 70.00 * 1.00 * 0.12 = 10.03 kips/in
10.03 kips/in >= 7.50 kips/in (OK) |
