SHEAR PLATE CONNECTION SUMMARY
NOTE: DESIGNED WITH MEMBERS CHOSEN ON ONLY ONE SIDE OF SUPPORT
Filler Beam profile: W18X40
Support Girder profile: W21X50
Slope: 0.00 deg.
Skew: 90.00
Vertical Offset: 0.00 in.
Horizontal Offset: 0.00 in.
Span: 2.49 ft.
Reaction, V: 2.00 kips
Shear Capacity, Rn: 17.27 kips
Design/Reference according to AISC 14th Ed. - LRFD
Shear Plate: Extended Configuration
Beam material grade: A992
Support material grade: A992
Plate material grade: A572-GR.50
Weld grade: E70
Shear Plate Size: 6.62 in. x 8.50 in. x 0.38 in.
Configuration Geometry:
Welds at shear plate to support: 4/16 FILLET, 4/16 FILLET
Bolt: 2 rows x 1 column 0.75 in. Diameter A325N_TC bolts
Vertical spacing: 6.00 in.
Horizontal spacing: 3.00 in.
Shear plate edge setback = 3.62 in.
Beam centerline setback = 3.62 in.
Edge distance at vertical edge of plate: 1.50 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: 1.50 in.
Horizontal distance to first hole: 5.12 in.
Down distance from top of filler beam flange: 3.00 in.
Holes in beam web: STD diameter = 0.81 in.
Holes in shear plate: SSL diameter = 0.81 in., slot width = 1.00 in. |
BOLT BEARING AT BEAM AND SHEAR PLATE SIDE
Vertical Shear Only Load Case:
ICR cordinate relative to CG = (1.69, -0.00)
At Row 1, At Column 1:
Ribolt = 17.56 kips
Ri vector at Beam = <15.29, 8.64>
Lcsbm at Beam spacing = na
Lcebm at Beam edge = 5.69 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 * 5.69 * (0.32/1) * 65.00 = 104.93 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.75 * (0.32/1) * 65.00 = 27.64 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(na, 104.93, 27.64) = 27.64 kips/bolt
Ri vector at Shear Plate = <-15.29, -8.64>
Lcsshpl at Shear Plate spacing = na
Lceshpl at Shear Plate edge = 5.31 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 * 5.31 * 0.38 * 65.00 = 116.53 kips/bolt
(phi)Rndshpl on Shear Plate at Bolt Diameter = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.75 * 0.38 * 65.00 = 32.91 kips/bolt
Shear Plate bearing capacity, (phi)Rnshpl = min((phi)Rnsshpl,(phi)Rneshpl,(phi)Rndshpl) = min(na, 116.53, 32.91) = 32.91 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(27.64, 32.91) = 27.64 kips/bolt
Bolt Shear Demand to Bearing ratio = 27.64 / 17.56 = 1.57
At Row 2, At Column 1:
Ribolt = 17.56 kips
Ri vector at Beam = <-15.29, 8.64>
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 * (0.32/1) * 65.00 = 24.26 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.75 * (0.32/1) * 65.00 = 27.64 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(na, 24.26, 27.64) = 24.26 kips/bolt
Ri vector at Shear Plate = <15.29, -8.64>
Lcsshpl at Shear Plate spacing = na
Lceshpl at Shear Plate edge = 1.15 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 * 1.15 * 0.38 * 65.00 = 25.20 kips/bolt
(phi)Rndshpl on Shear Plate at Bolt Diameter = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.75 * 0.38 * 65.00 = 32.91 kips/bolt
Shear Plate bearing capacity, (phi)Rnshpl = min((phi)Rnsshpl,(phi)Rneshpl,(phi)Rndshpl) = min(na, 25.20, 32.91) = 25.20 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(24.26, 25.20) = 24.26 kips/bolt
Bolt Shear Demand to Bearing ratio = 24.26 / 17.56 = 1.38
Min Bolt Shear Demand to Bearing ratio Beam and Shear Plate for vertical shear only
= min(1.00, 1.57, 1.38) = 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 * 17.27 = 17.27 kips
Rbv = 17.27 kips >= Reaction V = 2.00 kips (OK) |
Web Depth = d - [Top Cope Depth] - [Bottom Cope Depth] = 17.90 - 0.00 - 0.00 = 17.90 in.
Using AISC 14th Ed. Equation J4-3
Gross Area (Shear), Agross = [Web Depth] * tw = 17.90 * 0.32 = 5.64 in^2
Shear Yielding, (phi)Vny = (phi) * 0.6 * Fybeam * Agross = 1.00 * 0.6 * 50.00 * 5.64 = 169.16 kips
Using AISC 14th Ed. Equation J4-4
Net Area (Shear), Anet = ([Web Depth] - ([# rows] * [Diameter + 0.06])) * tw
= (17.90 - (2 * 0.88)) * 0.32 = 5.09 in^2
Shear Rupture, (phi)Vnu = (phi) * 0.6 * Fubeam * Anet = 0.75 * 0.6 * 65.00 * 5.09 = 148.81 kips
Check Horizontal Block Shear
Using AISC 14th Ed. Equation J4-5
Block Shear = {(phi) * ((0.6 * Fu * Anv) + (Ubs * Fu * Ant))} <= {(phi) * ((0.6 * Fy * Agv) + (Ubs * Fu * Ant))}
Block Shear for Axial T/C is not required. |
Using AISC 14th Ed. Equation J4-3
Gross Area, Ag = 0.38 * 8.50 = 3.19 in^2
Shear Yielding, (phi)Vny = (phi) * 0.6 * Fypl * Ag = 1.00 * 0.6 * 50.00 * 3.19 = 95.62 kips
95.62 kips >= Reaction V = 2.00 kips (OK)
Using AISC 14th Ed. Equation J4-4
Net Area, An = (8.50 - (2 * (0.81 + 1/16))) * 0.38 = 2.53 in^2
Shear Rupture, (phi)Vnu = (phi) * 0.6 * Fupl * An = 0.75 * 0.6 * 65.00 * 2.53 = 74.04 kips
74.04 kips >= Reaction V = 2.00 kips (OK)
Check Vertical Block Shear
Using AISC 14th 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 = (8.50 - 1.25) = 7.25 in.
Net Shear Length = 7.25 - (1.50 * (0.81 + 0.06)) = 5.94 in.
Gross Tension Length = (0.00 + 1.50) = 1.50 in.
Net Tension Length = 1.50 - (0.50 * (1.00 + 0.06)) = 0.97 in.
1. (phi) * [material thickness] * ((0.60 * Fupl* [net shear length]) + (Ubs * Fupl * [net tension length]))
= 0.75 * 0.38 * ((0.60 * 65.00 * 5.94) + (1.00 * 65.00 * 0.97)) = 82.84 kips
2. (phi) * [material thickness] * ((0.60 * Fypl * [gross shear length]) + (Ubs * Fupl * [net tension length]))
= 0.75 * 0.38 * ((0.60 * 50.00 * 7.25) + (1.00 * 65.00 * 0.97)) = 78.88 kips
Block Shear = 78.88 kips
78.88 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 = 5.32 in.
Zgross = 6.77 in^3
Znet = 4.80 in^3
Sgross = 4.52 in^3
Snet = 3.13 in^3
Using AISC 14th Ed. Equation 9-4
Flexural Rupture = (phi) * Fu * Znet / e = 0.75 * 65.00 * 4.80 / 5.32 = 44.07 kips
Using AISC 14th Ed. Equation 9-14 through 9-18, Fcr = Fy * Q
tw = 0.38 in.
ho = 8.50 in.
c = 5.12 in.
lambda = (ho * Fy ^ 0.5) / ( 10 * tw * ( 475.00 + 280.00 * (ho / c)^2 ) ^0.5 ) =
= 8.50 * 50.00^0.5 / (10 * 0.38 * (475.00 + 280.00 * (8.50/5.12)^2 )^0.5) = 0.45
When lambda <= 0.70, Q=1
Q = 1.00
Fcrmin =phi * Fcr = 0.90 * 50.00 * 1.00 = 45.00 ksi
Using AISC 14th Ed. Equation 9-6
Buckling = Fcr * Sgross / e = 45.00 * 4.52 / 5.32 = 38.23 kips
Interaction Check of Flexural Yielding, Per AISC 10-5:
Eccentricity at CG of Bolt Group, e = 5.32 in.
Zgross = 6.77
Znet = 4.80
Mr = Vr * e = 2.00 * 5.32 = 10.63 kips-in
Mc = phi * Mn = phi * Fy * Zgross = 0.90 * 50.00 * 6.77 = 304.80 kips-in
Vr = 2.00 kips
Vc = phi * Vn = phi * 0.60 * Fy * Ag = 1.00 * 0.60 * 50.00 * 3.19 = 95.62 kips
Interaction due to moment and shear, (Vr/Vc)^2 + (Mr/Mc)^2 <= 1.0
(Vr/Vc)^2 + (Mr/Mc)^2 = (2.00 / 95.62)^2 + (10.63 / 304.80)^2 = 0.00 <= 1 (OK)
Note: Mn <= 1.6My by inspection
MAXIMUM PLATE THICKNESS:
No of bolt columns = 1
tp < = db/2 + 1/16 = 0.38 <= 0.44 OK
tw < = db/2 + 1/16 = 0.32 <= 0.44 OK
Leh(plate) >= 2 * db = 1.50 >= 1.50 OK
Leh(bm) >= 2 * db = 1.50 >= 1.50 OK
Maximum Plate Thickness is Not a Limiting Criteria. |
WELD:
Weld Requirements:
At shear only case:
Weld Length for shear, Lv = 8.50 in.
Shear Load per inch per weld, fv = R/Lv/2 = 2.00 / 8.50 / 2 = 0.12 kips/in/ weld
theta = 0 deg.
cPhi = 1.0 + 0.5 * sin(0)^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) = 0.12 / (0.75 * 1.86) = 0.08/16
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 * 0.09)
= 0.38 * 65.00 / ( 70.00 * 1.00 * 0.09 )
= 3.94
Dmax2 (using eqn 9-3)
= twsupport * Fusupport / ( Fexx * C1 * 0.09 )
= 0.38 * 65.00 / ( 70.00 * 1.00 * 0.09 )
= 3.99
Dmax3 = project max fillet weld = 12.00
Dmax=min(Dmax1, Dmax2, Dmax3) = min(3.94, 3.99, 12.00)
= 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 * 8.50 * (3.94 + 3.94) = 93.24 kips
93.24 kips >= Reaction V = 2.00 kips (OK) |
