BOLT BEARING AT BEAM AND SHEAR PLATE SIDE
Vertical Shear Only Load Case:
ICR cordinate relative to CG = (1.25, 0.00)
At Row 1, At Column 1:
Ribolt = 23.90 kips
Ri vector at Beam = <0.95, 0.30>
Lcsbm at Beam spacing = na
Lcebm at Beam edge = 6.21 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 * 6.21 * (0.23/1) * 65.00 = 83.57 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, 83.57, 23.55) = 23.55 kips/bolt
Ri vector at Shear Plate = <-0.95, -0.30>
Lcsshpl at Shear Plate spacing = na
Lceshpl at Shear Plate edge = 5.01 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 * 5.01 * 0.25 * 65.00 = 73.26 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, 73.26, 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 = 19.00 kips
Ri vector at Beam = <0.00, 1.00>
Lcsbm at Beam spacing = 3.00 in.
Lcebm at Beam edge = 5.50 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.75 * 1.20 * 3.00 * (0.23/1) * 65.00 = 40.37 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(40.37, 74.00, 23.55) = 23.55 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 * 0.25 * 65.00 = 43.88 kips/bolt
(phi)Rneshpl at Shear Plate edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 4.62 * 0.25 * 65.00 = 67.64 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(43.88, 67.64, 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 / 19.00 = 1.24
At Row 3, At Column 1:
Ribolt = 23.90 kips
Ri vector at Beam = <-0.95, 0.30>
Lcsbm at Beam spacing = na
Lcebm at Beam edge = 1.33 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 * 1.33 * (0.23/1) * 65.00 = 17.94 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, 17.94, 23.55) = 17.94 kips/bolt
Ri vector at Shear Plate = <0.95, -0.30>
Lcsshpl at Shear Plate spacing = na
Lceshpl at Shear Plate edge = 1.21 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 * 1.21 * 0.25 * 65.00 = 17.72 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, 17.72, 25.59) = 17.72 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(17.94, 17.72) = 17.72 kips/bolt
Bolt Shear Demand to Bearing ratio = 17.72 / 23.90 = 0.74
Min Bolt Shear Demand to Bearing ratio Beam and Shear Plate for vertical shear only
= min(1.00, 0.99, 1.24, 0.74) = 0.74
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 = 0.74 * 33.25 = 24.64 kips
Rbv = 24.64 kips >= Reaction V = 20.00 kips (OK) |
Using AISC 15th Ed. Equation J4-3
Gross Area, Ag = 0.25 * 10.25 = 2.56 in^2
Shear Yielding, (phi)Vny = (phi) * 0.6 * Fypl * Ag = 1.00 * 0.6 * 50.00 * 2.56 = 76.88 kips
76.88 kips >= Reaction V = 20.00 kips (OK)
Shear Rupture:
Using AISC 15th Ed. Equation J4-4
Net Area, An = (10.25 - (3 * (0.94 + 0.06))) * 0.25 = 1.81 in^2
Shear Rupture, (phi)Vnu = (phi) * 0.6 * Fupl * An = 0.75 * 0.6 * 65.00 * 1.81 = 53.02 kips
53.02 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 = (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 * 0.25 * ((0.60 * 65.00 * 6.62) + (1.00 * 65.00 * 1.16)) = 62.54 kips
2. (phi) * [material thickness] * ((0.60 * Fypl * [gross shear length]) + (Ubs * Fupl * [net tension length]))
= 0.75 * 0.25 * ((0.60 * 50.00 * 9.12) + (1.00 * 65.00 * 1.16)) = 65.42 kips
Block Shear = 62.54 kips
62.54 kips >= Reaction V = 20.00 kips (OK)
Block Shear for Axial T/C is not required.
Check Flexural Yielding and Rupture:
Eccentricity at first line of bolts, e = 5.49 in.
Zgross = 6.57 in^3
Znet = 4.50 in^3
Sgross = 4.38 in^3
Snet = 2.80 in^3
Fypl = 50.00 ksi
Fupl = 65.00 ksi
Mp = Fypl * Zgross = 50.00 * 6.57 = 328.32 kips-in
My = Fypl * Sgross = 50.00 * 4.38 = 218.88 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 * 328.32 / 5.49, 0.90 * 1.6 * 50.00 * 4.38 / 5.49) = 53.82 kips
53.82 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 * 4.50 / 5.49 = 39.99 kips
39.99 kips >= 20.00 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 = 0.25 in.
d = hshpl = 10.25 in.
drect = hshpl = 10.25 in.
dc = down distance (per AISC Example II.A-19B) = 2.00 in.
Lb = horizontal distance to first hole = 5.38 in.
Fypl = 50.00 ksi
Cb = max((3 + ln(Lb / d)) * (1 - dc / d), 1.84) =
= max((3 + ln(5.38 / 10.25)) * (1 - 2.00 / 10.25), 1.84) = 1.90
Lb * drect / t^2 = 5.38 * 10.25 / 0.25^2 = 881.50
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(1.90 * (1.52 - 0.274 * (5.38 * 10.25 / 0.25^2) * 50.00 / 29000) * 218.88, 328.32)
= min(457.75, 328.32) = 328.32 kips-in
Flexural Local Buckling Reaction Capacity, (phi)Rn = (phi) * Mn / e = 0.90 * 328.32 / 5.49 = 53.82 kips
53.82 kips >= 20.00 kips (OK)
Interaction Check of Flexural Yielding:
Using AISC 15th Ed. Equation 10-5
Eccentricity at first line of bolts, e = 5.49 in.
Sgross = 4.38 in^3
Zgross = 6.57 in^3
Mr = Vr * e = 20.00 * 5.49 = 109.80 kips-in
Mc = phi * Mn = min(phi * Fypl * Zgross, phi * 1.6 * Fypl * Sgross) =
= min(0.90 * 50.00 * 6.57, 0.90 * 1.6 * 50.00 * 4.38) = 295.49 kips-in
Vr = 20.00 kips
Vc = phi * Vn = phi * 0.60 * Fypl * Ag = 1.00 * 0.60 * 50.00 * 2.56 = 76.88 kips
Interaction due to moment and shear, (Vr/Vc)^2 + (Mr/Mc)^2 <= 1.0
(Vr/Vc)^2 + (Mr/Mc)^2 = (20.00 / 76.88)^2 + (109.80 / 295.49)^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 * 10.25 * 0.25^3 / 5.38^2 = 23.51 kips
23.51 kips >= Reaction V = 20.00 kips (OK)
Torsional Strength:
Using Eq. 10 and Eq. 16, Thornton and Fortney 2011 Engineering Journal
Required, Mtu = Ru * (tw + tp) / 2 = 20.00 * ((0.25 + 0.25) / 2) = 5.00 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) - (20.00 / (10.25 * 0.25))] * 10.25 * 0.25^2 / 2 = 7.11 kips-in
7.11 kips-in >= Mtu = 5.00 kips-in (OK)
MAXIMUM PLATE THICKNESS:
No of bolt columns = 1
tp < = db/2 + 0.06 = 0.25 <= 0.50 OK
tw < = db/2 + 0.06 = 0.23 <= 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 = 20.00 / 10.25 / 2 = 0.98 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) = 0.98 / (0.75 * 1.86) = 0.70/16
Minimum fillet weld size :
At shear only load case = 0.04 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 9-3)
= twbm * Fusupport / ( Fexx * C1 * 0.09 )
= 0.23 * 65.00 / ( 70.00 * 1.00 * 0.09 )
= 2.42
Dmax3 = project max fillet weld = 16.00
Dmax=min(Dmax1, Dmax2, Dmax3) = min(2.63, 2.42, 16.00)
= 2.42
Use weld size
D1 = 3.00
D2 = 3.00
Weld Strength :
Vertical weld capacity during shear only load, phi * Rnv1 = 0.75 * 1.86 * 10.25 * (2.42 + 2.42) = 68.96 kips
68.96 kips >= Reaction V = 20.00 kips (OK) |
