BOLT BEARING AT BEAM AND SHEAR PLATE SIDE
Vertical Shear Only Load Case:
ICR cordinate relative to CG = (1.10, 0.00)
At Row 1, At Column 1:
Ribolt = 23.90 kips
Ri vector at Beam = <0.96, 0.27>
Lcsbm at Beam spacing = na
Lcebm at Beam edge = 10.79 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 * 10.79 * (0.27/1) * 65.00 = 170.38 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.88 * (0.27/1) * 65.00 = 27.64 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(na, 170.38, 27.64) = 27.64 kips/bolt
Ri vector at Shear Plate = <-0.96, -0.27>
Lcsshpl at Shear Plate spacing = na
Lceshpl at Shear Plate edge = 5.35 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 * 5.35 * 0.38 * 65.00 = 117.34 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(na, 117.34, 38.39) = 38.39 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(27.64, 38.39) = 27.64 kips/bolt
Bolt Shear Demand to Bearing ratio = 27.64 / 23.90 = 1.16
At Row 2, At Column 1:
Ribolt = 18.30 kips
Ri vector at Beam = <0.00, 1.00>
Lcsbm at Beam spacing = 3.00 in.
Lcebm at Beam edge = 6.50 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.75 * 1.20 * 3.00 * (0.27/1) * 65.00 = 47.39 kips/bolt
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 6.50 * (0.27/1) * 65.00 = 102.67 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.88 * (0.27/1) * 65.00 = 27.64 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(47.39, 102.67, 27.64) = 27.64 kips/bolt
Ri vector at Shear Plate = <0.00, -1.00>
Lcsshpl at Shear Plate spacing = 3.00 in.
Lceshpl at Shear Plate edge = 4.62 in.
(phi)Rnsshpl at Shear Plate spacing = (phi) * hf1 * Lcs * t * Fu = 0.75 * 1.20 * 3.00 * 0.38 * 65.00 = 65.81 kips/bolt
(phi)Rneshpl at Shear Plate edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 4.62 * 0.38 * 65.00 = 101.46 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(65.81, 101.46, 38.39) = 38.39 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(27.64, 38.39) = 27.64 kips/bolt
Bolt Shear Demand to Bearing ratio = 27.64 / 18.30 = 1.51
At Row 3, At Column 1:
Ribolt = 23.90 kips
Ri vector at Beam = <-0.96, 0.27>
Lcsbm at Beam spacing = na
Lcebm at Beam edge = 1.32 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 * 1.32 * (0.27/1) * 65.00 = 20.78 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.88 * (0.27/1) * 65.00 = 27.64 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(na, 20.78, 27.64) = 20.78 kips/bolt
Ri vector at Shear Plate = <0.96, -0.27>
Lcsshpl at Shear Plate spacing = na
Lceshpl at Shear Plate edge = 1.20 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 * 1.20 * 0.38 * 65.00 = 26.31 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(na, 26.31, 38.39) = 26.31 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(20.78, 26.31) = 20.78 kips/bolt
Bolt Shear Demand to Bearing ratio = 20.78 / 23.90 = 0.87
Min Bolt Shear Demand to Bearing ratio Beam and Shear Plate for vertical shear only
= min(1.00, 1.16, 1.51, 0.87) = 0.87
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 = 0.87 * 31.01 = 26.95 kips
Rbv = 26.95 kips >= Reaction V = 25.00 kips (OK) |
Using AISC 15th Ed. Equation J4-3
Gross Area, Ag = 0.38 * 10.25 = 3.84 in^2
Shear Yielding, (phi)Vny = (phi) * 0.6 * Fypl * Ag = 1.00 * 0.6 * 50.00 * 3.84 = 115.31 kips
115.31 kips >= Reaction V = 25.00 kips (OK)
Shear Rupture:
Using AISC 15th Ed. Equation J4-4
Net Area, An = (10.25 - (3 * (0.94 + 0.06))) * 0.38 = 2.72 in^2
Shear Rupture, (phi)Vnu = (phi) * 0.6 * Fupl * An = 0.75 * 0.6 * 65.00 * 2.72 = 79.53 kips
79.53 kips >= Reaction V = 25.00 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 = (10.25 - 1.12) = 9.12 in.
Net Shear Length = 9.12 - (3 - 0.5) * (0.94 + 0.06) = 6.62 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 * 0.38 * ((0.60 * 65.00 * 6.62) + (1.00 * 65.00 * 1.16)) = 93.81 kips
2. (phi) * [material thickness] * ((0.60 * Fypl * [gross shear length]) + (Ubs * Fupl * [net tension length]))
= 0.75 * 0.38 * ((0.60 * 50.00 * 9.12) + (1.00 * 65.00 * 1.16)) = 98.13 kips
Block Shear = 93.81 kips
93.81 kips >= Reaction V = 25.00 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 = 9.85 in^3
Znet = 6.76 in^3
Sgross = 6.57 in^3
Snet = 4.21 in^3
Fypl = 50.00 ksi
Fupl = 65.00 ksi
Mp = Fypl * Zgross = 50.00 * 9.85 = 492.48 kips-in
My = Fypl * Sgross = 50.00 * 6.57 = 328.32 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 * 492.48 / 5.95, 0.90 * 1.6 * 50.00 * 6.57 / 5.95) = 74.56 kips
74.56 kips >= 25.00 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 * 6.76 / 5.95 = 55.40 kips
55.40 kips >= 25.00 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 = 10.25 in.
drect = hshpl = 10.25 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 / 10.25)) * (1 - 3.00 / 10.25), 1.84) = 1.84
Lb * drect / t^2 = 5.75 * 10.25 / 0.38^2 = 419.11
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 * 10.25 / 0.38^2) * 50.00 / 29000) * 328.32, 492.48)
= min(798.64, 492.48) = 492.48 kips-in
Flexural Local Buckling Reaction Capacity, (phi)Rn = (phi) * Mn / e = 0.90 * 492.48 / 5.95 = 74.56 kips
74.56 kips >= 25.00 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 = 6.57 in^3
Zgross = 9.85 in^3
Mr = Vr * e = 25.00 * 5.95 = 148.62 kips-in
Mc = phi * Mn = min(phi * Fypl * Zgross, phi * 1.6 * Fypl * Sgross) =
= min(0.90 * 50.00 * 9.85, 0.90 * 1.6 * 50.00 * 6.57) = 443.23 kips-in
Vr = 25.00 kips
Vc = phi * Vn = phi * 0.60 * Fypl * Ag = 1.00 * 0.60 * 50.00 * 3.84 = 115.31 kips
Interaction due to moment and shear, (Vr/Vc)^2 + (Mr/Mc)^2 <= 1.0
(Vr/Vc)^2 + (Mr/Mc)^2 = (25.00 / 115.31)^2 + (148.62 / 443.23)^2 = 0.16
0.16 <= 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 * 10.25 * 0.38^3 / 5.75^2 = 69.34 kips
69.34 kips >= Reaction V = 25.00 kips (OK)
Torsional Strength:
Using Eq. 10 and Eq. 16, Thornton and Fortney 2011 Engineering Journal
Required, Mtu = Ru * (tw + tp) / 2 = 25.00 * ((0.25 + 0.38) / 2) = 7.81 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) - (25.00 / (10.25 * 0.38))] * 10.25 * 0.38^2 / 2 = 16.93 kips-in
16.93 kips-in >= Mtu = 7.81 kips-in (OK)
MAXIMUM PLATE THICKNESS:
No of bolt columns = 1
tp < = db/2 + 0.06 = 0.38 <= 0.50 OK
tw < = db/2 + 0.06 = 0.27 <= 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. |
WELD:
Weld Requirements:
At shear only case:
Weld Length for shear, Lv = 10.25 in.
Shear Load per inch per weld, fv = R/Lv/2 = 25.00 / 10.25 / 2 = 1.22 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) = 1.22 / (0.75 * 1.86) = 0.88/16
Minimum fillet weld size :
At shear only load case = 0.05 in.
per Table J2.4 = 0.19 in.
5/8tp = 0.23 in.
user preference = 0.19 in.
Dmax1 (using AISC 15th Ed. eqn 9-3)
= tshpl * Fushpl / ( Fexx * C1 * 0.09)
= 0.38 * 65.00 / ( 70.00 * 1.00 * 0.09 )
= 3.94
Dmax2 (using AISC 15th Ed. eqn 9-3)
= twbm * Fusupport / ( Fexx * C1 * 0.09 )
= 0.39 * 65.00 / ( 70.00 * 1.00 * 0.09 )
= 4.10
Dmax3 = project max fillet weld = 16.00
Dmax=min(Dmax1, Dmax2, Dmax3) = min(3.94, 4.10, 16.00)
= 3.94
Use weld size
D1 = 4.00
D2 = 4.00
Weld Strength :
Vertical weld capacity during shear only load, phi * Rnv1 = 0.75 * 1.86 * 10.25 * (3.94 + 3.94) = 112.43 kips
112.43 kips >= Reaction V = 25.00 kips (OK) |
