bb.s.s.00003.00166

SHEAR PLATE CONNECTION SUMMARY

Filler Beam profile: W18X40
Support Girder profile: W21X55
Slope: 0 deg.
Skew: 90
Vertical Offset: -2.88
Horizontal Offset: 0
Span: 20 ft.
Reaction, V: 23 kips
Shear Capacity, Rn: 30.1 kips
Design/Reference according to AISC 14th Ed. - ASD
Shear Plate: Extended Configuration
Beam material grade: A992
Support material grade: A992
Plate material grade: A36
Weld grade: E70
Shear Plate Size: 7.500 in. x 14.500 in. x 0.375 in.
Configuration Geometry:
Welds at shear plate to support: 4/16 FILLET, 4/16 FILLET
Bolt: 5 rows x 1 columns 0.75 in. Diameter A325N_TC bolts
Vertical spacing: 3 in.
Horizontal spacing: 3 in.
Shear plate edge setback = 4.44 in.
Beam centerline setback = 4.44 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: 1.56 in.
Horizontal distance to first hole: 6 in.
Down distance from top of filler beam flange: 3 in.
Holes in beam web: STD diameter = 0.812 in.
Holes in shear plate: SSL diameter = 0.812 in., slot width = 1 in.

BOLT STRENGTH BEAM SIDE:

Bolt Strength:
Using Instantaneous Center Of Rotation Method (AISC 7-1)
ex = 6.188 in.
Angle = 0.000 deg.
C = 2.523
Using Table 7-1 to determine (1/omega) * rn:
Rn = (1/omega) * rn * C = 11.93 * 2.52 = 30.10 kips

BOLT BEARING AT BEAM SIDE:
Vertical Shear Only Load Case:
ICR cordinate relative to CG = (2.12, -0.00)
At Row 1, At Column 1:
Ri1 = 11.71 kips
Ri vector at Beam   = <11.04, 3.90>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 8.60 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * na * (0.32/1) * 65.00 = na
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 8.60 * (0.32/1) * 65.00 = 105.64 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.32/1) * 65.00 = 18.43 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(na, 105.64, 18.43) = 18.43 kips/bolt
Ri vector at Shear Plate   = <-11.04, -3.90>
Lcsshpl at Shear Plate spacing  = na
Lceshpl at Shear Plate edge    = 5.83 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 * 5.83 * 0.38 * 58.00 = 76.12 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, 76.12, 19.57) = 19.57 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(18.427, 19.575) = 18.43 kips/bolt
Bolt Shear Demand to Bearing ratio = 18.43 / 11.71 = 1.57

At Row 2, At Column 1:
Ri1 = 10.98 kips
Ri vector at Beam   = <8.96, 6.33>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 9.99 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * na * (0.32/1) * 65.00 = na
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 9.99 * (0.32/1) * 65.00 = 122.73 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.32/1) * 65.00 = 18.43 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(na, 122.73, 18.43) = 18.43 kips/bolt
Ri vector at Shear Plate   = <-8.96, -6.33>
Lcsshpl at Shear Plate spacing  = na
Lceshpl at Shear Plate edge    = 6.73 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 * 6.73 * 0.38 * 58.00 = 87.89 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, 87.89, 19.57) = 19.57 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(18.427, 19.575) = 18.43 kips/bolt
Bolt Shear Demand to Bearing ratio = 18.43 / 10.98 = 1.68

At Row 3, At Column 1:
Ri1 = 9.63 kips
Ri vector at Beam   = <0.00, 9.63>
Lcsbm at Beam spacing  = 2.19 in.
Lcebm at Beam edge    = 8.59 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * 2.19 * (0.32/1) * 65.00 = 26.87 kips/bolt
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 8.59 * (0.32/1) * 65.00 = 105.57 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.32/1) * 65.00 = 18.43 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(26.87, 105.57, 18.43) = 18.43 kips/bolt
Ri vector at Shear Plate   = <-0.00, -9.63>
Lcsshpl at Shear Plate spacing  = 2.19 in.
Lceshpl at Shear Plate edge    = 6.84 in.
1/omegaRnsshpl at Shear Plate spacing = 1/omega * hf1 * Lcs * t * Fu = 0.50 * 1.20 * 2.19 * 0.38 * 58.00 = 28.55 kips/bolt
1/omegaRneshpl at Shear Plate edge = 1/omega * hf1 * Lce * t * Fu = 0.50 * 1.20 * 6.84 * 0.38 * 58.00 = 89.31 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(28.55, 89.31, 19.57) = 19.57 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(18.427, 19.575) = 18.43 kips/bolt
Bolt Shear Demand to Bearing ratio = 18.43 / 9.63 = 1.91

At Row 4, At Column 1:
Ri1 = 10.98 kips
Ri vector at Beam   = <-8.96, 6.33>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 1.51 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * na * (0.32/1) * 65.00 = na
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 1.51 * (0.32/1) * 65.00 = 18.51 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.32/1) * 65.00 = 18.43 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(na, 18.51, 18.43) = 18.43 kips/bolt
Ri vector at Shear Plate   = <8.96, -6.33>
Lcsshpl at Shear Plate spacing  = na
Lceshpl at Shear Plate edge    = 1.22 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 * 1.22 * 0.38 * 58.00 = 15.98 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, 15.98, 19.57) = 15.98 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(18.427, 15.980) = 15.98 kips/bolt
Bolt Shear Demand to Bearing ratio = 15.98 / 10.98 = 1.46

At Row 5, At Column 1:
Ri1 = 11.71 kips
Ri vector at Beam   = <-11.04, 3.90>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 1.25 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * na * (0.32/1) * 65.00 = na
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 1.25 * (0.32/1) * 65.00 = 15.37 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.32/1) * 65.00 = 18.43 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(na, 15.37, 18.43) = 15.37 kips/bolt
Ri vector at Shear Plate   = <11.04, -3.90>
Lcsshpl at Shear Plate spacing  = na
Lceshpl at Shear Plate edge    = 1.06 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 * 1.06 * 0.38 * 58.00 = 13.84 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, 13.84, 19.57) = 13.84 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(15.368, 13.841) = 13.84 kips/bolt
Bolt Shear Demand to Bearing ratio = 13.84 / 11.71 = 1.18

Min Bolt Shear Demand to Bearing ratio for vertical shear only = min(1.0, 1.57398, 1.67899, 1.91324, 1.45599, 1.1822) = 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 * 30.10 = 30.10 kips

Web Depth = d - [Top Cope Depth] - [Bottom Cope Depth] = 17.9 - 0 - 0 = 17.9 in.
Gross Area (Shear) = [Web Depth] * tw = 17.90 * 0.32 = 5.64 in^2
Net Shear Area (Shear) = ([Web Depth] - ([# rows] * [Diameter + 0.0625])) * tw 
    = (17.90 - (5 * 0.88)) * 0.32 = 4.26 in^2

Using Eq.J4-3:
Shear Yielding = (1/omega) * 0.6 * Fybeam * [Gross Area] = 0.67 * 0.6 * 50.00 * 5.64 = 112.77 kips

Using Eq.J4-4:
Shear Rupture = (1/omega) * 0.6 * Fubeam * [Net Area] = 0.50 * 0.6 * 65.00 * 4.26 = 83.08 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 Shear not required.

Gross Area = 0.38 * 14.50 = 5.44 in^2
Net Area = (14.50 - (5 *(0.81 + 1/16))) * 0.38 = 3.80 in^2

Using Eq.J4-3:
Shear Yielding = (1/omega) * 0.6 * Fypl * [Gross Area] = 0.67 * 0.6 * 36.00 * 5.44 = 78.30 kips

Using Eq.J4-4:
Shear Rupture = (1/omega) * 0.6 * Fupl * [Net Area] = 0.50 * 0.6 * 58.00 * 3.80 = 66.07 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 = (14.5 - 1.25) = 13.25 in.
Net Shear Length = 13.2 - (4.5 * (0.812 + 0.0625)) = 9.31 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 * 9.31) + (1.00 * 58.00 * 0.97)) = 71.30 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 * 13.25) + (1.00 * 58.00 * 0.97)) = 64.20 kips
Block Shear = 64.20 kips

Flexural and Buckling Strength:

Eccentricity at first line of bolts, e = 6.19 in.
Zgross = 19.71 in^3
Znet   = 13.73 in^3
Sgross = 13.14 in^3
Snet   = 9.07 in^3

Using Eq. 9-4
Flexural Rupture = (1/omega) * Fu * Znet / e = 0.50 * 58.00 * 13.73 / 6.19 = 64.36 kips


Using Eq. 9-14 through 9-18, Fcr = Fy * Q
tw = 0.38 in.
ho = 14.50 in.
c = 6.00 in.
lambda = (ho * Fy ^ 0.5) / ( 10 * tw * ( 475.00 + 280.00 * (ho / c)^2 ) ^0.5 ) = 
 = 14.50 * 36.00^0.5 / (10 * 0.38 * (475.00 + 280.00 * (14.50/6.00)^2 )^0.5) = 0.51
When lambda <= 0.70, Q=1
Q = 1.00
Fcrmin =1/omega * Fcr = 0.60 * 36.00 * 1.00 = 21.60 ksi

Using Eq. 9-6
Buckling = Fcr * Sgross / e = 21.60 * 13.14 / 6.19 = 45.87 kips

Interaction Check of Flexural Yielding, Per AISC 10-5: 
Eccentricity at CG of Bolt Group, e = 6.19 in.
Zgross = 19.71
Znet = 13.73
Mr = Vr * e = 23.00 * 6.19 = 142.31 kips-in
Mc = 1/omega * Mn = 1/omega * Fy * Zgross = 0.60 * 36.00 * 19.71 = 425.76 kips-in
Vr = 23.00 kips
Vc = 1/omega * Vn = 1/omega * 0.60 * Fy * Ag = 0.67 * 0.60 * 36.00 * 5.44 = 78.30 kips
Interaction due to moment and shear, (Vr/Vc)^2 + (Mr/Mc)^2 <= 1.0
(Vr/Vc)^2 + (Mr/Mc)^2 = (23.00 / 78.30)^2 + (142.31 / 425.76)^2 = 0.20 <= 1  (OK)

Note: Mn <= 1.6My by inspection

MAXIMUM PLATE THICKNESS:
No of bolt columns = 1
tp  < = db/2 + 1/16 = 0.375 <= 0.4375 OK
tw  < = db/2 + 1/16 = 0.315 <= 0.4375 OK
Leh(plate) >= 2 * db = 1.5 >= 1.5 OK
Leh(bm) >= 2 * db = 1.5625 >= 1.5 OK
Maximum Plate Thickness is Not a Limiting Criteria.

WELD:

 Weld Requirements:

At shear only case: 
Weld Length for shear, Lv = 14.500 in.
Shear Load per inch per weld, fv = R/Lv/2 = 23.000 / 14.500 / 2 = 0.793 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) = 0.793 / (0.500 * 1.856) = 0.855/16

Minimum fillet weld size : 
   At shear only load case = 0.05 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 )
 = 0.375 * 65.000 / ( 70.000 * 1.000 * 0.088 ) 
 = 3.940 
Dmax3 = project max fillet weld = 12.000
Dmax=min(Dmax1, Dmax2, Dmax3) = min(3.515, 3.940, 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 * 14.50 * (3.52 + 3.52) = 94.61 kips