bb.s.s.00013.00171

SHEAR PLATE CONNECTION SUMMARY

Filler Beam profile: W21X44
Support Girder profile: W18X60
Slope: 0 deg.
Skew: 68.1
Vertical Offset: 2.38
Horizontal Offset: 0.0112
Span: 40.9 ft.
Reaction, V: 29 kips
Shear Capacity, Rn: 42 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
Shear Plate Size: 4.500 in. x 11.500 in. x 0.375 in.
Configuration Geometry:
Welds at shear plate to support: 4/16 FILLET, 7/16 FILLET
Bolt: 4 rows x 1 columns 0.75 in. Diameter A325N_TC bolts
Vertical spacing: 3 in.
Horizontal spacing: 3 in.
Shear plate edge setback = 0.938 in.
Beam centerline setback = 1.16 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: 2.06 in.
Edge distance at top edge of beam: 1.25 in.
Edge distance at bottom edge of beam: 5.45 in.
Top cope depth: 3.75 in.
Top cope length: 3.5 in.
Bottom cope depth: 1.25 in.
Bottom cope length: 3.5 in.
Horizontal distance to first hole: 3 in.
Down distance from top of filler beam flange: 5 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 = 1.575 in.
Angle = 0.000 deg.
C = 3.522
Using Table 7-1 to determine (1/omega) * rn:
Rn = (1/omega) * rn * C = 11.93 * 3.52 = 42.01 kips

BOLT BEARING AT BEAM SIDE:
Vertical Shear Only Load Case:
ICR cordinate relative to CG = (6.71, 0.00)
At Row 1, At Column 1:
Ri1 = 11.71 kips
Ri vector at Beam   = <6.52, 9.72>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 1.10 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * na * (0.35/1) * 65.00 = na
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 1.10 * (0.35/1) * 65.00 = 15.00 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.35/1) * 65.00 = 20.47 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(na, 15.00, 20.47) = 15.00 kips/bolt
Ri vector at Shear Plate   = <-6.52, -9.72>
Lcsshpl at Shear Plate spacing  = na
Lceshpl at Shear Plate edge    = 4.90 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 * 4.90 * 0.38 * 58.00 = 63.91 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, 63.91, 19.57) = 19.57 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(14.998, 19.575) = 15.00 kips/bolt
Bolt Shear Demand to Bearing ratio = 15.00 / 11.71 = 1.28

At Row 2, At Column 1:
Ri1 = 11.56 kips
Ri vector at Beam   = <2.52, 11.28>
Lcsbm at Beam spacing  = 2.19 in.
Lcebm at Beam edge    = 3.95 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * 2.19 * (0.35/1) * 65.00 = 29.86 kips/bolt
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 3.95 * (0.35/1) * 65.00 = 53.90 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.35/1) * 65.00 = 20.47 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(29.86, 53.90, 20.47) = 20.47 kips/bolt
Ri vector at Shear Plate   = <-2.52, -11.28>
Lcsshpl at Shear Plate spacing  = 2.19 in.
Lceshpl at Shear Plate edge    = 7.01 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 * 7.01 * 0.38 * 58.00 = 91.51 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, 91.51, 19.57) = 19.57 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(20.475, 19.575) = 19.57 kips/bolt
Bolt Shear Demand to Bearing ratio = 19.57 / 11.56 = 1.69

At Row 3, At Column 1:
Ri1 = 11.56 kips
Ri vector at Beam   = <-2.52, 11.28>
Lcsbm at Beam spacing  = 2.19 in.
Lcebm at Beam edge    = 7.02 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * 2.19 * (0.35/1) * 65.00 = 29.86 kips/bolt
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 7.02 * (0.35/1) * 65.00 = 95.86 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.35/1) * 65.00 = 20.47 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(29.86, 95.86, 20.47) = 20.47 kips/bolt
Ri vector at Shear Plate   = <2.52, -11.28>
Lcsshpl at Shear Plate spacing  = 2.19 in.
Lceshpl at Shear Plate edge    = 3.94 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 * 3.94 * 0.38 * 58.00 = 51.40 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, 51.40, 19.57) = 19.57 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(20.475, 19.575) = 19.57 kips/bolt
Bolt Shear Demand to Bearing ratio = 19.57 / 11.56 = 1.69

At Row 4, At Column 1:
Ri1 = 11.71 kips
Ri vector at Beam   = <-6.52, 9.72>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 3.30 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * na * (0.35/1) * 65.00 = na
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 3.30 * (0.35/1) * 65.00 = 45.00 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.35/1) * 65.00 = 20.47 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(na, 45.00, 20.47) = 20.47 kips/bolt
Ri vector at Shear Plate   = <6.52, -9.72>
Lcsshpl at Shear Plate spacing  = na
Lceshpl at Shear Plate edge    = 1.02 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 * 1.02 * 0.38 * 58.00 = 13.26 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, 13.26, 19.57) = 13.26 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(20.475, 13.258) = 13.26 kips/bolt
Bolt Shear Demand to Bearing ratio = 13.26 / 11.71 = 1.13

Min Bolt Shear Demand to Bearing ratio for vertical shear only = min(1.0, 1.28109, 1.69331, 1.69331, 1.13246) = 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 * 42.01 = 42.01 kips

Web Depth = d - [Top Cope Depth] - [Bottom Cope Depth] = 20.7 - 3.75 - 1.25 = 15.7 in.
Gross Area (Shear) = [Web Depth] * tw = 15.70 * 0.35 = 5.49 in^2
Net Shear Area (Shear) = ([Web Depth] - ([# rows] * [Diameter + 0.0625])) * tw 
    = (15.70 - (4 * 0.88)) * 0.35 = 4.27 in^2

Using Eq.J4-3:
Shear Yielding = (1/omega) * 0.6 * Fybeam * [Gross Area] = 0.67 * 0.6 * 50.00 * 5.49 = 109.90 kips

Using Eq.J4-4:
Shear Rupture = (1/omega) * 0.6 * Fubeam * [Net Area] = 0.50 * 0.6 * 65.00 * 4.27 = 83.26 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 (1)
Gross Shear Length = [edge dist. at beam edge] + ([# rows - 1] * [spacing]) = 1.25 + 9 = 10.25 in.
Net Shear Length = Gross Shear Length - (# rows - 0.5) * (hole size + 0.0625) = 10.2 - (4 - 0.5) * 0.875 = 7.19 in.
Gross Tension Length = [edge dist. at beam edge] + ([# cols - 1] * [spacing]) = 2.06 + (1 - 1) * 3 = 2.06 in.
Net Tension Length = Gross Tension Length - (# cols - 0.5) * (hole size + 0.0625) = 2.06 - (1 - 0.5) * 0.875 = 1.62 in.
1. (1/omega) * [material thickness] * ((0.60 * Fubeam* [net shear length]) + (Ubs * Fubeam * [net tension length])) 
    = 0.50 * 0.35 * ((0.60 * 65.00 * 7.19) + (1.00 * 65.00 * 1.62)) = 67.54 kips
2. (1/omega) * [material thickness] * ((0.60 * Fybeam * [gross shear length]) + (Ubs * Fubeam * [net tension length])) 
    = 0.50 * 0.35 * ((0.60 * 50.00 * 10.25) + (1.00 * 65.00 * 1.62)) = 72.30 kips
Block Shear = 67.54 kips

Block Shear (1) Total = Block Shear (1) = 67.54 kips


Buckling and Flexure at Longest Cope (Top and Bottom Copes at Section)
Eccentricity at Section, e = 4.74 in.
If beam is coped at both top and bottom flanges,

Using Eq. 9-14 through 9-18, Fcr = Fy * Q
tw = 0.35 in.
ho = 15.70 in.
c = 3.50 in.
lambda = (ho * Fy ^ 0.5) / ( 10 * tw * ( 475.00 + 280.00 * (ho / c)^2 ) ^0.5 ) = 
 = 15.70 * 50.00^0.5 / (10 * 0.35 * (475.00 + 280.00 * (15.70/3.50)^2 )^0.5) = 0.41
When lambda <= 0.70, Q=1
Q = 1.00
Fcrmin =1/omega * Fcr = 0.60 * 50.00 * 1.00 = 30.00 ksi
Snet1 (bolt holes not applicable) = 14.38 in^3
Snet2 (bolt holes applicable) = 14.38 in^3
Znet = 21.57 in^3

Using Eq. 9-6
Buckling = Fcr * Snet1 / e = 30.00 * 14.38 / 4.74 = 91.07 kips

Using Eq. 9-19
Flexural Yielding = (1/omega) * Fy * Snet1 / e = 0.60 * 50.00 * 14.38 / 4.74 = 91.07 kips

Using Eq. 9-4
Flexural Rupture = (1/omega) * Fu * Znet / e = 0.50 * 65.00 * 21.57 / 4.74 = 147.99 kips


Buckling and Flexure at Furthest Bolt Line within Cope (Top and Bottom Copes at Section)
Eccentricity at Section, e = 3.30 in.
If beam is coped at both top and bottom flanges,

Using Eq. 9-14 through 9-18, Fcr = Fy * Q
tw = 0.35 in.
ho = 15.70 in.
c = 3.50 in.
lambda = (ho * Fy ^ 0.5) / ( 10 * tw * ( 475.00 + 280.00 * (ho / c)^2 ) ^0.5 ) = 
 = 15.70 * 50.00^0.5 / (10 * 0.35 * (475.00 + 280.00 * (15.70/3.50)^2 )^0.5) = 0.41
When lambda <= 0.70, Q=1
Q = 1.00
Fcrmin =1/omega * Fcr = 0.60 * 50.00 * 1.00 = 30.00 ksi
Snet1 (bolt holes not applicable) = 14.38 in^3
Snet2 (bolt holes applicable) = 10.89 in^3
Znet = 17.26 in^3

Using Eq. 9-6
Buckling = Fcr * Snet1 / e = 30.00 * 14.38 / 3.30 = 130.75 kips

Using Eq. 9-19
Flexural Yielding = (1/omega) * Fy * Snet1 / e = 0.60 * 50.00 * 14.38 / 3.30 = 130.75 kips

Using Eq. 9-4
Flexural Rupture = (1/omega) * Fu * Znet / e = 0.50 * 65.00 * 17.26 / 3.30 = 170.01 kips


Section Bending Strength Calculations Summary:

   Coped Beam Buckling and Flexure at Longest Cope (Top and Bottom Copes at Section)
   Buckling : 91.07 >= 29.00 kips (OK)
   Flexural Yielding : 91.07 >= 29.00 kips (OK)
   Flexural Rupture : 147.99 >= 29.00 kips (OK)

   Coped Beam Buckling and Flexure at Furthest Bolt Line within Cope (Top and Bottom Copes at Section)
   Buckling : 130.75 >= 29.00 kips (OK)
   Flexural Yielding : 130.75 >= 29.00 kips (OK)
   Flexural Rupture : 170.01 >= 29.00 kips (OK)

Gross Area = 0.38 * 11.50 = 4.31 in^2
Net Area = (11.50 - (4 *(0.81 + 1/16))) * 0.38 = 3.00 in^2

Using Eq.J4-3:
Shear Yielding = (1/omega) * 0.6 * Fypl * [Gross Area] = 0.67 * 0.6 * 36.00 * 4.31 = 62.10 kips

Using Eq.J4-4:
Shear Rupture = (1/omega) * 0.6 * Fupl * [Net Area] = 0.50 * 0.6 * 58.00 * 3.00 = 52.20 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 = (11.5 - 1.25) = 10.25 in.
Net Shear Length = 10.2 - (3.5 * (0.812 + 0.0625)) = 7.19 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 * 7.19) + (1.00 * 58.00 * 0.97)) = 57.43 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 * 10.25) + (1.00 * 58.00 * 0.97)) = 52.05 kips
Block Shear = 52.05 kips


Interaction Check of Flexural Yielding, Per AISC 10-5: 
Eccentricity due to Conventional Config. (e = a/2), e = 1.58 in.
Zgross = 12.40
Znet = 8.46
Mr = Vr * e = 29.00 * 1.58 = 45.69 kips-in
Mc = 1/omega * Mn = 1/omega * Fy * Zgross = 0.60 * 36.00 * 12.40 = 267.81 kips-in
Vr = 29.00 kips
Vc = 1/omega * Vn = 1/omega * 0.60 * Fy * Ag = 0.67 * 0.60 * 36.00 * 4.31 = 62.10 kips
Interaction due to moment and shear, (Vr/Vc)^2 + (Mr/Mc)^2 <= 1.0
(Vr/Vc)^2 + (Mr/Mc)^2 = (29.00 / 62.10)^2 + (45.69 / 267.81)^2 = 0.25 <= 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 = 11.500 in.
Shear Load per inch per weld, fv = R/Lv/2 = 29.000 / 11.500 / 2 = 1.261 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) = 1.261 / (0.500 * 1.856) = 1.359/16

Minimum fillet weld size : 
   At shear only load case = 0.08 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 )
 = 0.415 * 65.000 / ( 70.000 * 1.000 * 0.088 ) 
 = 4.360 
Dmax3 = project max fillet weld = 12.000
Dmax=min(Dmax1, Dmax2, Dmax3) = min(3.515, 4.360, 12.000)
 = 3.515 

Dihedral Angle, DA       = 68.10 deg.
Gap on Obtuse Angle Side = 0.14 in.
Use weld size
Acute Side  D1 = 4.00
Obtuse Side D2 = 7.00

Weld Strength :
Vertical weld capacity during shear only load, 1/omega * Rnv1 = 0.50 * 1.86 * 11.50 * (3.52 + 3.52) = 75.04 kips
Check Effective Throat:
Acute Side Effect throat  = (D1/sin(DA)) * cos(DA/2) = (0.25/ sin( 68.10)) * cos( 34.05) = 0.22 in.
Obtuse Side Effect throat = ((D2/sin(DA)-tshpl/tan(DA))*sin((180-(180-DA))/2))= ((0.44 / sin(68.10) -0.38 / tan(68.10)) * sin((180 - (180 - 68.10)) / 2)) = 0.18 in.
Total Effective Throat    = 0.22 + 0.18 = 0.40 in.
Total Effective Throat of Square Case = D1 * 2^0.5 = 0.25 * 2^0.5 = 0.35 in.
0.35 in. <= 0.40 in. (OK)