SHEAR PLATE CONNECTION SUMMARY
Filler Beam profile: W8X10
Support Girder profile: W21X50
Slope: 0 deg.
Skew: 90
Vertical Offset: -13
Horizontal Offset: 0
Span: 10 ft.
Reaction, V: 15 kips
Shear Capacity, Rn: 16.6 kips
Design/Reference according to AISC 14th Ed. - ASD
Shear Plate: Conventional Configuration
Beam material grade: A992
Support material grade: A992
Plate material grade: A36
Weld grade: E70
Doubler plate grade: A36
Shear Plate Size: 4.500 in. x 5.500 in. x 0.375 in.
Doubler plate size: 4 in. x 5 in. x 0.312 in.
Configuration Geometry:
Welds at shear plate to support: 4/16 FILLET, 4/16 FILLET
Welds at doubler plate:
At Top, 4/16 FILLET
At Side, 4/16 FILLET
At Bottom, 4/16 FILLET
Bolt: 2 rows x 1 columns 0.75 in. Diameter A325N_TC bolts
Vertical spacing: 3 in.
Horizontal spacing: 3 in.
Shear plate edge setback = 1 in.
Beam centerline setback = 1 in.
Edge distance at vertical edge of plate: 1.5 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: 2 in.
Edge distance at bottom edge of beam: 1.64 in.
Bottom cope depth: 1.25 in.
Bottom cope length: 2.75 in.
Edge distance at vertical edge of doubler: 2 in.
Edge distance at top edge of doubler: 1 in.
Edge distance at bottom edge of doubler: 1 in.
Horizontal distance to first hole: 3 in.
Down distance from top of filler beam flange: 2 in.
Holes in beam web: STD diameter = 0.812 in.
Holes in shear plate: SSL diameter = 0.812 in., slot width = 1 in. |
BOLT BEARING AT BEAM SIDE:
Vertical Shear Only Load Case:
ICR cordinate relative to CG = (1.50, -0.00)
At Row 1, At Column 1:
Ri1 = 11.71 kips
Ri vector at Beam = <8.28, 8.28>
Lcsdblr at Doubler spacing = na
Lcedblr at Doubler edge = 1.01 in.
1/omegaRnsdblr at Doubler spacing = 1/omega * hf1 * Lcs * (dblrt/# shear planes) * Fu = 0.50 * 1.20 * na * (0.31/1) * 58.00 = na
1/omegaRnedblr at Doubler edge = 1/omega * hf1 * Lce * (dblrt/# shear planes) * Fu = 0.50 * 1.20 * 1.01 * (0.31/1) * 58.00 = 10.96 kips
1/omegaRnddblr on Beam at Doubler = 1/omega * hf2 * db * (dblrt/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.31/1) * 58.00 = 16.31 kips/bolt
Lcsbm at Beam spacing = na
Lcebm at Beam edge = 2.42 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * na * (0.17/1) * 65.00 = na
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 2.42 * (0.17/1) * 65.00 = 16.06 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.17/1) * 65.00 = 9.95 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm+ Rnsdblr,1/omegaRnebm+ Rnedblr,1/omegaRndbm+ Rnddblr) = min(na, 27.02, 26.26) = 26.26 kips/bolt
Ri vector at Shear Plate = <-8.28, -8.28>
Lcsshpl at Shear Plate spacing = na
Lceshpl at Shear Plate edge = 3.67 in.
1/omegaRnsshpl at Shear Plate spacing = 1/omega * hf1 * Lcs * t * Fu = 0.50 * 1.20 * na * 0.38 * 58.00 = na
1/omegaRneshpl at Shear Plate edge = 1/omega * hf1 * Lce * t * Fu = 0.50 * 1.20 * 3.67 * 0.38 * 58.00 = 47.86 kips/bolt
1/omegaRndshpl on Shear Plate at Bolt Diameter = 1/omega * hf2 * db * t * Fu = 0.50 * 2.40 * 0.75 * 0.38 * 58.00 = 19.57 kips/bolt
Shear Plate bearing capacity, 1/omegaRnshpl = min(1/omegaRnsshpl,1/omegaRneshpl,1/omegaRndshpl) = min(na, 47.86, 19.57) = 19.57 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(26.258, 19.575) = 19.57 kips/bolt
Bolt Shear Demand to Bearing ratio = 19.57 / 11.71 = 1.67
At Row 2, At Column 1:
Ri1 = 11.71 kips
Ri vector at Beam = <-8.28, 8.28>
Lcsdblr at Doubler spacing = na
Lcedblr at Doubler edge = 2.42 in.
1/omegaRnsdblr at Doubler spacing = 1/omega * hf1 * Lcs * (dblrt/# shear planes) * Fu = 0.50 * 1.20 * na * (0.31/1) * 58.00 = na
1/omegaRnedblr at Doubler edge = 1/omega * hf1 * Lce * (dblrt/# shear planes) * Fu = 0.50 * 1.20 * 2.42 * (0.31/1) * 58.00 = 26.34 kips
1/omegaRnddblr on Beam at Doubler = 1/omega * hf2 * db * (dblrt/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.31/1) * 58.00 = 16.31 kips/bolt
Lcsbm at Beam spacing = na
Lcebm at Beam edge = 2.42 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * na * (0.17/1) * 65.00 = na
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 2.42 * (0.17/1) * 65.00 = 16.06 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.17/1) * 65.00 = 9.95 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm+ Rnsdblr,1/omegaRnebm+ Rnedblr,1/omegaRndbm+ Rnddblr) = min(na, 42.40, 26.26) = 26.26 kips/bolt
Ri vector at Shear Plate = <8.28, -8.28>
Lcsshpl at Shear Plate spacing = na
Lceshpl at Shear Plate edge = 1.19 in.
1/omegaRnsshpl at Shear Plate spacing = 1/omega * hf1 * Lcs * t * Fu = 0.50 * 1.20 * na * 0.38 * 58.00 = na
1/omegaRneshpl at Shear Plate edge = 1/omega * hf1 * Lce * t * Fu = 0.50 * 1.20 * 1.19 * 0.38 * 58.00 = 15.57 kips/bolt
1/omegaRndshpl on Shear Plate at Bolt Diameter = 1/omega * hf2 * db * t * Fu = 0.50 * 2.40 * 0.75 * 0.38 * 58.00 = 19.57 kips/bolt
Shear Plate bearing capacity, 1/omegaRnshpl = min(1/omegaRnsshpl,1/omegaRneshpl,1/omegaRndshpl) = min(na, 15.57, 19.57) = 15.57 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(26.258, 15.573) = 15.57 kips/bolt
Bolt Shear Demand to Bearing ratio = 15.57 / 11.71 = 1.33
Min Bolt Shear Demand to Bearing ratio for vertical shear only = min(1.0, 1.67199, 1.33017) = 1.00
Bearing Capacity at Beam and Shear Plate at Vertical Shear Load Only, Rbv1 = Min Bolt Shear Demand to Bearing Ratio * Bolt Shear = 1.00 * 16.56 = 16.56 kips |
Web Depth = d - [Top Cope Depth] - [Bottom Cope Depth] = 7.89 - 0 - 1.25 = 6.64 in.
Gross Area (Shear) = [Web Depth] * tw = 6.64 * 0.17 = 1.13 in^2
Net Shear Area (Shear) = ([Web Depth] - ([# rows] * [Diameter + 0.0625])) * tw
= (6.64 - (2 * 0.88)) * 0.17 = 0.83 in^2
Using Eq.J4-3:
Shear Yielding = (1/omega) * 0.6 * Fybeam * [Gross Area] = 0.67 * 0.6 * 50.00 * 1.13 = 22.58 kips
Using Eq.J4-3:
Shear Yielding = (1/omega) * 0.6 * Fydoubler * [Gross Area] = 0.67 * 0.6 * 36.00 * 1.56 = 22.50 kips
Doubler Contribution = Min(Doubler Plate Shear Yielding, Doubler Vertical Component Weld Strength) =
Min(22.50, 9.93) = 9.93 kips
Total Shear Yield Capacity = 22.58 + 9.93 = 32.51 kips
Using Eq.J4-4:
Shear Rupture = (1/omega) * 0.6 * Fubeam * [Net Area] = 0.50 * 0.6 * 65.00 * 0.83 = 16.21 kips
Using Eq.J4-4:
Shear Rupture = (1/omega) * 0.6 * Fudoubler * [Net Area] = 0.50 * 0.6 * 58.00 * 1.02 = 17.67 kips
Doubler Contribution = Min(Doubler Plate Shear Rupture, Doubler Vertical Component Weld Strength) =
Min(17.67, 9.93) = 9.93 kips
Total Shear Rupture Capacity = 16.21 + 9.93 = 26.14 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))}
Coped Beam Bending Calculations w/o Doubler Plate:
Flexure at Longest Cope (Bottom Cope Only at Section)
Eccentricity at Section, e = 3.94 in.
Fy = 50.00 ksi
Snet1 (bolt holes not applicable) = 1.92 in^3
Snet2 (bolt holes applicable) = 1.92 in^3
Znet = 3.48 in^3
Using Eq. 9-19
Flexural Yielding = (1/omega) * Fy * Snet1 / e = 0.60 * 50.00 * 1.92 / 3.94 = 14.64 kips
Using Eq. 9-4
Flexural Rupture = (1/omega) * Fu * Znet / e = 0.50 * 65.00 * 3.48 / 3.94 = 28.72 kips
Flexure at Furthest Bolt Line within Cope (Bottom Cope Only at Section)
Eccentricity at Section, e = 3.19 in.
Fy = 50.00 ksi
Snet1 (bolt holes not applicable) = 1.92 in^3
Snet2 (bolt holes applicable) = 1.52 in^3
Znet = 2.62 in^3
Using Eq. 9-19
Flexural Yielding = (1/omega) * Fy * Snet1 / e = 0.60 * 50.00 * 1.92 / 3.19 = 18.09 kips
Using Eq. 9-4
Flexural Rupture = (1/omega) * Fu * Znet / e = 0.50 * 65.00 * 2.62 / 3.19 = 26.72 kips
Coped Beam Bending Calculations with Doubler Plate:
Flexure at Longest Cope (Bottom Cope Only at Section)
Eccentricity at Section, e = 3.94 in.
Fy = 50.00 ksi
Snet1 (bolt holes not applicable) = 3.16 in^3
Snet2 (bolt holes applicable) = 3.16 in^3
Znet = 5.48 in^3
Using Eq. 9-19
Flexural Yielding = (1/omega) * Fy * Snet1 / e = 0.60 * 50.00 * 3.16 / 3.94 = 24.02 kips
Using Eq. 9-4
Flexural Rupture = (1/omega) * Fu * Znet / e = 0.50 * 65.00 * 5.48 / 3.94 = 45.19 kips
Flexure at Furthest Bolt Line within Cope (Bottom Cope Only at Section) (with web doubler):
Eccentricity at Section, e = 3.19 in.
Fy = 50.00 ksi
Snet1 (bolt holes not applicable) = 3.16 in^3
Snet2 (bolt holes applicable) = 2.41 in^3
Znet = 4.44 in^3
Using Eq. 9-19
Flexural Yielding = (1/omega) * Fy * Snet1 / e = 0.60 * 50.00 * 3.16 / 3.19 = 29.67 kips
Using Eq. 9-4
Flexural Rupture = (1/omega) * Fu * Znet / e = 0.50 * 65.00 * 4.44 / 3.19 = 45.25 kips
Coped Beam Flexure at Longest Cope (Bottom Cope Only at Section)
Min(Beam Section w/o Doubler + Doubler Plate Weld Strength, Beam Section with Doubler Plate):
Flexural Yielding = Min(14.64 + 9.93, 24.02) = 24.02 kips
Flexural Rupture = Min(28.72 + 9.93, 45.19) = 38.65 kips
Coped Beam Flexure at Furthest Bolt Line within Cope (Bottom Cope Only at Section)
Min(Beam Section w/o Doubler + Doubler Plate Weld Strength, Beam Section with Doubler Plate):
Flexural Yielding = Min(18.09 + 9.93, 29.67) = 28.02 kips
Flexural Rupture = Min(26.72 + 9.93, 45.25) = 36.65 kips
Section Bending Strength Calculations Summary:
Coped Beam Flexure at Longest Cope (Bottom Cope Only at Section)
Flexural Yielding : 24.02 >= 15.00 kips (OK)
Flexural Rupture : 38.65 >= 15.00 kips (OK)
Coped Beam Flexure at Furthest Bolt Line within Cope (Bottom Cope Only at Section)
Flexural Yielding : 28.02 >= 15.00 kips (OK)
Flexural Rupture : 36.65 >= 15.00 kips (OK)
DOUBLER PLATE WELD:
Shear Reaction = 15.00 kips
Beam Shear Failure Reaction = 14.64 kips
Required Shear Reinforcement = MAX(15.00 - 14.64, 0) = 0.36 kips
Axial Reaction = 0.00 kips
theta = sin(0.00 / (15.00^2 + 0.00^2)^0.5)^-1 = 0.00 deg.
load angle, theta = 0.00 deg.
k = 0.25
ex = 4.98
a = ex / l = 4.98 / 5.00 = 1.00
Weld Coefficient = 0.6 * Fexx * cphi * arrangement coefficient = 1.11
Dmax1 using min(eqn 9-2, tdoub - 0.062)
= min(tdoub * Fudoub / ( Fexx * C1 * 0.044), tdoub - 0.062)
= min(0.312 * 58.000 / ( 70.000 * 1.000 * 0.044), 0.312 - 0.062)
= min(5.859, 4.000)
= 4.000
Dmax2 (using eqn 9-2)
= twbeam * Fubeam / ( Fexx * C1 * 0.044 )
= 0.170 * 65.000 / ( 70.000 * 1.000 * 0.044 )
= 3.572
Dmax3 = project max fillet weld = 12.000
Dmax=min(Dmax1, Dmax2, Dmax3) = min(4.000, 3.572, 12.000)
= 3.572
D = 4.00/16
Weld Strength = 1/omega * weld coefficient * l * D = 0.50 * 1.11 * 5.00 * 3.57 = 9.93 kips |
Gross Area = 0.38 * 5.50 = 2.06 in^2
Net Area = (5.50 - (2 *(0.81 + 1/16))) * 0.38 = 1.41 in^2
Using Eq.J4-3:
Shear Yielding = (1/omega) * 0.6 * Fypl * [Gross Area] = 0.67 * 0.6 * 36.00 * 2.06 = 29.70 kips
Using Eq.J4-4:
Shear Rupture = (1/omega) * 0.6 * Fupl * [Net Area] = 0.50 * 0.6 * 58.00 * 1.41 = 24.47 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 = (5.5 - 1.25) = 4.25 in.
Net Shear Length = 4.25 - (1.5 * (0.812 + 0.0625)) = 2.94 in.
Gross Tension Length = (0 + 1.5) = 1.50 in.
Net Tension Length = 1.5 - (0.5 * (1 + 0.0625)) = 0.97 in.
1. (1/omega) * [material thickness] * ((0.60 * Fupl* [net shear length]) + (Ubs * Fupl * [net tension length]))
= 0.50 * 0.38 * ((0.60 * 58.00 * 2.94) + (1.00 * 58.00 * 0.97)) = 29.70 kips
2. (1/omega) * [material thickness] * ((0.60 * Fypl * [gross shear length]) + (Ubs * Fupl * [net tension length]))
= 0.50 * 0.38 * ((0.60 * 36.00 * 4.25) + (1.00 * 58.00 * 0.97)) = 27.75 kips
Block Shear = 27.75 kips
Interaction Check of Flexural Yielding, Per AISC 10-5:
Eccentricity due to Conventional Config. (e = a/2), e = 1.50 in.
Zgross = 2.84
Znet = 1.85
Mr = Vr * e = 15.00 * 1.50 = 22.50 kips-in
Mc = 1/omega * Mn = 1/omega * Fy * Zgross = 0.60 * 36.00 * 2.84 = 61.26 kips-in
Vr = 15.00 kips
Vc = 1/omega * Vn = 1/omega * 0.60 * Fy * Ag = 0.67 * 0.60 * 36.00 * 2.06 = 29.70 kips
Interaction due to moment and shear, (Vr/Vc)^2 + (Mr/Mc)^2 <= 1.0
(Vr/Vc)^2 + (Mr/Mc)^2 = (15.00 / 29.70)^2 + (22.50 / 61.26)^2 = 0.39 <= 1 (OK)
Note: Mn <= 1.6My by inspection
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 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 = 5.500 in.
Shear Load per inch per weld, fv = R/Lv/2 = 15.000 / 5.500 / 2 = 1.364 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) = 1.364 / (0.500 * 1.856) = 1.469/16
Minimum fillet weld size :
At shear only load case = 0.09 in.
per Table J2.4 = 0.19 in.
5/8(tp) = 0.23 in.
user preference = 0.25 in.
Dmax1 (using eqn 9-3)
= tshpl * Fushpl / ( Fexx * C1 * 0.088)
= 0.375 * 58.000 / ( 70.000 * 1.000 * 0.088 )
= 3.515
Dmax2 (using eqn 9-3)
= twsupport * Fusupport / ( Fexx * C1 * 0.088 )
= 0.380 * 65.000 / ( 70.000 * 1.000 * 0.088 )
= 3.992
Dmax3 = project max fillet weld = 12.000
Dmax=min(Dmax1, Dmax2, Dmax3) = min(3.515, 3.992, 12.000)
= 3.515
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 * 5.50 * (3.52 + 3.52) = 35.89 kips |
