BOLT BEARING AT BEAM AND SHEAR PLATE SIDE
Vertical Shear Only Load Case:
ICR cordinate relative to CG = (5.08, 0.00)
At Row 1, At Column 1:
Ribolt = 23.90 kips
Ri vector at Beam = <0.51, 0.86>
Lcsbm at Beam spacing = na
Lcebm at Beam edge = 2.98 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 * 2.98 * (0.23/1) * 65.00 = 40.16 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, 40.16, 23.55) = 23.55 kips/bolt
Ri vector at Shear Plate = <-0.51, -0.86>
Lcsshpl at Shear Plate spacing = na
Lceshpl at Shear Plate edge = 3.84 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 * 3.84 * 0.25 * 65.00 = 56.19 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, 56.19, 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 = 23.63 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 = 3.62 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 * 3.62 * 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 / 23.63 = 1.00
At Row 3, At Column 1:
Ribolt = 23.90 kips
Ri vector at Beam = <-0.51, 0.86>
Lcsbm at Beam spacing = na
Lcebm at Beam edge = 2.94 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 * 2.94 * (0.23/1) * 65.00 = 39.54 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, 39.54, 23.55) = 23.55 kips/bolt
Ri vector at Shear Plate = <0.51, -0.86>
Lcsshpl at Shear Plate spacing = na
Lceshpl at Shear Plate edge = 0.73 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 * 0.73 * 0.25 * 65.00 = 10.62 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, 10.62, 25.59) = 10.62 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(23.55, 10.62) = 10.62 kips/bolt
Bolt Shear Demand to Bearing ratio = 10.62 / 23.90 = 0.44
Min Bolt Shear Demand to Bearing ratio Beam and Shear Plate for vertical shear only
= min(1.00, 0.99, 1.00, 0.44) = 0.44
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 = 0.44 * 64.78 = 28.78 kips
Rbv = 28.78 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 = 1.12 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 / 1.12, 0.90 * 1.6 * 50.00 * 2.84 / 1.12) = 170.16 kips
170.16 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 / 1.12 = 116.63 kips
116.63 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 = 1.12 in.
Sgross = 2.84 in^3
Zgross = 4.25 in^3
Mr = Vr * e = 20.00 * 1.12 = 22.50 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 + (22.50 / 191.43)^2 = 0.12
0.12 <= 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. |
WELD:
Weld Requirements:
At shear only case:
Weld Length for shear, Lv = 8.25 in.
Shear Load per inch per weld, fv = R/Lv/2 = 20.00 / 8.25 / 2 = 1.21 kips/in/ weld
theta = 0 deg.
cPhi = 1.0 + 0.5 * sin(theta)^1.5 = 1.0 + 0.5 * sin(0.00)^1.5 = 1.00
Weld Coefficient = 0.60 * 70.00 * 1.00 * 1.00 * (2^0.5/2)*(1/16) = 1.86
Required weld size, Dv = fv/ (phi * coeff) = 1.21 / (0.75 * 1.86) = 0.87/16
Minimum fillet weld size :
At shear only load case = 0.05 in.
per Table J2.4 = 0.12 in.
5/8tp = 0.16 in.
user preference = 0.19 in.
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 9-2)
= tfcol * Fusupport / ( Fexx * C1 * 0.04 )
= 0.43 * 65.00 / ( 70.00 * 1.00 * 0.04 )
= 9.14
Dmax3 = project max fillet weld = 16.00
Dmax=min(Dmax1, Dmax2, Dmax3) = min(2.63, 9.14, 16.00)
= 2.63
Use weld size
D1 = 3.00
D2 = 3.00
Weld Strength :
Vertical weld capacity during shear only load, phi * Rnv1 = 0.75 * 1.86 * 8.25 * (2.63 + 2.63) = 60.33 kips
60.33 kips >= Reaction V = 20.00 kips (OK) |
