SHEAR PLATE CONNECTION SUMMARY
Filler Beam profile: W16X40
Support Girder profile: W16X40
Slope: 0 deg.
Skew: 90
Vertical Offset: 0
Horizontal Offset: 0
Span: 15 ft.
Reaction, V: 2 kips
Shear Capacity, Rn: 11.6 kips
Design/Reference according to AISC 14th Ed. - ASD
Shear Plate: Extended Configuration
Beam material grade: A992
Support material grade: A992
Plate material grade: A572-GR.50
Weld grade: E70
Shear Plate Size: 7.375 in. x 7.000 in. x 0.375 in.
Configuration Geometry:
Welds at shear plate to support: 4/16 FILLET, 4/16 FILLET
Bolt: 2 rows x 1 column 0.875 in. Diameter A325N_TC bolts
Vertical spacing: 4.5 in.
Horizontal spacing: 3 in.
Shear plate edge setback = 3.88 in.
Beam centerline setback = 3.88 in.
Edge distance at vertical edge of plate: 1.75 in.
Edge distance at top edge of plate: 1.25 in.
Edge distance at bottom edge of plate: 1.25 in.
Edge distance at vertical edge of beam: 1.75 in.
Horizontal distance to first hole: 5.62 in.
Down distance from top of filler beam flange: 3 in.
Holes in beam web: STD diameter = 0.938 in.
Holes in shear plate: SSL diameter = 0.938 in., slot width = 1.12 in. |
BOLT BEARING AT BEAM AND SHEAR PLATE SIDE
Vertical Shear Only Load Case:
ICR cordinate relative to CG = (0.88, -0.00)
At Row 1, At Column 1:
Ribolt = 15.94 kips
Ri vector at Beam = <14.85, 5.78>
Lcsbm at Beam spacing = na
Lcebm at Beam edge = 7.80 in.
(1/omega)Rnsbm at Beam spacing = (1/omega) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * na * (0.30/1) * 65.00 = na
(1/omega)Rnebm at Beam edge = (1/omega) * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 7.80 * (0.30/1) * 65.00 = 92.75 kips/bolt
(1/omega)Rndbm on Beam at Bolt Diameter = (1/omega) * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.88 * (0.30/1) * 65.00 = 20.82 kips/bolt
Beam bearing capacity, (1/omega)Rnbm = min((1/omega)Rnsbm,(1/omega)Rnebm,(1/omega)Rndbm) = min(na, 92.75, 20.82) = 20.82 kips/bolt
Ri vector at Shear Plate = <-14.85, -5.78>
Lcsshpl at Shear Plate spacing = na
Lceshpl at Shear Plate edge = 5.43 in.
(1/omega)Rnsshpl at Shear Plate spacing = (1/omega) * hf1 * Lcs * t * Fu = 0.50 * 1.20 * na * 0.38 * 65.00 = na
(1/omega)Rneshpl at Shear Plate edge = (1/omega) * hf1 * Lce * t * Fu = 0.50 * 1.20 * 5.43 * 0.38 * 65.00 = 79.46 kips/bolt
(1/omega)Rndshpl on Shear Plate at Bolt Diameter = (1/omega) * hf2 * db * t * Fu = 0.50 * 2.40 * 0.88 * 0.38 * 65.00 = 25.59 kips/bolt
Shear Plate bearing capacity, (1/omega)Rnshpl = min((1/omega)Rnsshpl,(1/omega)Rneshpl,(1/omega)Rndshpl) = min(na, 79.46, 25.59) = 25.59 kips/bolt
(1/omega)Rn = min((1/omega)Rnbm, (1/omega)Rnshpl) = min(20.816, 25.594) = 20.82 kips/bolt
Bolt Shear Demand to Bearing ratio = 20.82 / 15.94 = 1.31
At Row 2, At Column 1:
Ribolt = 15.94 kips
Ri vector at Beam = <-14.85, 5.78>
Lcsbm at Beam spacing = na
Lcebm at Beam edge = 1.41 in.
(1/omega)Rnsbm at Beam spacing = (1/omega) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * na * (0.30/1) * 65.00 = na
(1/omega)Rnebm at Beam edge = (1/omega) * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 1.41 * (0.30/1) * 65.00 = 16.76 kips/bolt
(1/omega)Rndbm on Beam at Bolt Diameter = (1/omega) * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.88 * (0.30/1) * 65.00 = 20.82 kips/bolt
Beam bearing capacity, (1/omega)Rnbm = min((1/omega)Rnsbm,(1/omega)Rnebm,(1/omega)Rndbm) = min(na, 16.76, 20.82) = 16.76 kips/bolt
Ri vector at Shear Plate = <14.85, -5.78>
Lcsshpl at Shear Plate spacing = na
Lceshpl at Shear Plate edge = 1.27 in.
(1/omega)Rnsshpl at Shear Plate spacing = (1/omega) * hf1 * Lcs * t * Fu = 0.50 * 1.20 * na * 0.38 * 65.00 = na
(1/omega)Rneshpl at Shear Plate edge = (1/omega) * hf1 * Lce * t * Fu = 0.50 * 1.20 * 1.27 * 0.38 * 65.00 = 18.64 kips/bolt
(1/omega)Rndshpl on Shear Plate at Bolt Diameter = (1/omega) * hf2 * db * t * Fu = 0.50 * 2.40 * 0.88 * 0.38 * 65.00 = 25.59 kips/bolt
Shear Plate bearing capacity, (1/omega)Rnshpl = min((1/omega)Rnsshpl,(1/omega)Rneshpl,(1/omega)Rndshpl) = min(na, 18.64, 25.59) = 18.64 kips/bolt
(1/omega)Rn = min((1/omega)Rnbm, (1/omega)Rnshpl) = min(16.764, 18.638) = 16.76 kips/bolt
Bolt Shear Demand to Bearing ratio = 16.76 / 15.94 = 1.05
Min Bolt Shear Demand to Bearing ratio Beam and Shear Plate for vertical shear only
= min(1.00, 1.31, 1.05) = 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 * 11.57 = 11.57 kips
Rbv = 11.57 kips >= Reaction V = 2.00 kips (OK) |
Gross Area = 0.38 * 7.00 = 2.62 in^2
Net Area = (7.00 - (2 *(0.94 + 1/16))) * 0.38 = 1.88 in^2
Using Eq.J4-3:
Shear Yielding = (1/omega) * 0.6 * Fypl * [Gross Area] = 0.67 * 0.6 * 50.00 * 2.62 = 52.50 kips
Using Eq.J4-4:
Shear Rupture = (1/omega) * 0.6 * Fupl * [Net Area] = 0.50 * 0.6 * 65.00 * 1.88 = 36.56 kips
Block Shear
Using Eq.J4-5:
Block Shear = {(1/omega) * ((0.6 * Fu * Anv) + (Ubs * Fu * Ant))} <= {(1/omega) * ((0.6 * Fy * Agv) + (Ubs * Fu * Ant))}
Block 1 (Shear):
Gross Shear Length = (7 - 1.25) = 5.75 in.
Net Shear Length = 5.75 - (1.5 * (0.938 + 0.0625)) = 4.25 in.
Gross Tension Length = (0 + 1.75) = 1.75 in.
Net Tension Length = 1.75 - (0.5 * (1.12 + 0.0625)) = 1.16 in.
1. (1/omega) * [material thickness] * ((0.60 * Fupl* [net shear length]) + (Ubs * Fupl * [net tension length]))
= 0.50 * 0.38 * ((0.60 * 65.00 * 4.25) + (1.00 * 65.00 * 1.16)) = 45.17 kips
2. (1/omega) * [material thickness] * ((0.60 * Fypl * [gross shear length]) + (Ubs * Fupl * [net tension length]))
= 0.50 * 0.38 * ((0.60 * 50.00 * 5.75) + (1.00 * 65.00 * 1.16)) = 46.44 kips
Block Shear = 45.17 kips
45.17 kips >= Reaction V = 2.00 kips (OK)
Block Shear for Axial T/C is not required.
Flexural and Buckling Strength:
Eccentricity at first line of bolts, e = 5.78 in.
Zgross = 4.59 in^3
Znet = 2.91 in^3
Sgross = 3.06 in^3
Snet = 1.98 in^3
Using Eq. 9-4
Flexural Rupture = (1/omega) * Fu * Znet / e = 0.50 * 65.00 * 2.91 / 5.78 = 16.35 kips
Using Eq. 9-14 through 9-18, Fcr = Fy * Q
tw = 0.38 in.
ho = 7.00 in.
c = 5.62 in.
lambda = (ho * Fy ^ 0.5) / ( 10 * tw * ( 475.00 + 280.00 * (ho / c)^2 ) ^0.5 ) =
= 7.00 * 50.00^0.5 / (10 * 0.38 * (475.00 + 280.00 * (7.00/5.62)^2 )^0.5) = 0.44
When lambda <= 0.70, Q=1
Q = 1.00
Fcrmin =1/omega * Fcr = 0.60 * 50.00 * 1.00 = 30.00 ksi
Using Eq. 9-6
Buckling = Fcr * Sgross / e = 30.00 * 3.06 / 5.78 = 15.90 kips
Interaction Check of Flexural Yielding, Per AISC 10-5:
Eccentricity at CG of Bolt Group, e = 5.78 in.
Zgross = 4.59
Znet = 2.91
Mr = Vr * e = 2.00 * 5.78 = 11.55 kips-in
Mc = 1/omega * Mn = 1/omega * Fy * Zgross = 0.60 * 50.00 * 4.59 = 137.81 kips-in
Vr = 2.00 kips
Vc = 1/omega * Vn = 1/omega * 0.60 * Fy * Ag = 0.67 * 0.60 * 50.00 * 2.62 = 52.50 kips
Interaction due to moment and shear, (Vr/Vc)^2 + (Mr/Mc)^2 <= 1.0
(Vr/Vc)^2 + (Mr/Mc)^2 = (2.00 / 52.50)^2 + (11.55 / 137.81)^2 = 0.01 <= 1 (OK)
Note: Mn <= 1.6My by inspection
MAXIMUM PLATE THICKNESS:
No of bolt columns = 1
tp < = db/2 + 1/16 = 0.375 <= 0.5 OK
tw < = db/2 + 1/16 = 0.305 <= 0.5 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 = 7.000 in.
Shear Load per inch per weld, fv = R/Lv/2 = 2.000 / 7.000 / 2 = 0.143 kips/in/ weld
theta = 0 deg.
cPhi = 1.0 + 0.5 * sin(0)^1.5 = 1.000
Weld Coefficient = 0.6 * 70.000 * 1.000 * 1.000 * (2^0.5/2)*(1/16) = 1.856
Required weld size, Dv = fv/ (1/omega * coeff) = 0.143 / (0.500 * 1.856) = 0.154/16
Minimum fillet weld size :
At shear only load case = 0.01 in.
per Table J2.4 = 0.19 in.
5/8tp = 0.23 in.
user preference = 0.25 in.
Dmax1 (using eqn 9-3)
= tshpl * Fushpl / ( Fexx * C1 * 0.088)
= 0.375 * 65.000 / ( 70.000 * 1.000 * 0.088 )
= 3.940
Dmax2 (using eqn 9-3)
= twsupport * Fusupport / ( Fexx * C1 * 0.088 )
= 0.305 * 65.000 / ( 70.000 * 1.000 * 0.088 )
= 3.204
Dmax3 = project max fillet weld = 12.000
Dmax=min(Dmax1, Dmax2, Dmax3) = min(3.940, 3.204, 12.000)
= 3.204
Use weld size
D1 = 4.00
D2 = 4.00
Weld Strength :
Vertical weld capacity during shear only load, 1/omega * Rnv1 = 0.50 * 1.86 * 7.00 * (3.20 + 3.20) = 41.63 kips
41.63 kips >= Reaction V = 2.00 kips (OK) |
