bb.s.s.00808.00810

SHEAR PLATE CONNECTION SUMMARY

Filler Beam profile: W21X50
Support Girder profile: W18X40
Slope: 0 deg.
Skew: 90
Vertical Offset: 0
Horizontal Offset: 0
Span: 45 ft.
Reaction, V: 37 kips
Shear Capacity, Rn: 44.1 kips
Design/Reference according to AISC 14th Ed. - ASD
Shear Plate: Conventional Configuration
Beam material grade: A992
Support material grade: A992
Plate material grade: A572-GR.50
Weld grade: E70
Shear Plate Size: 4.750 in. x 11.500 in. x 0.500 in.
Configuration Geometry:
Welds at shear plate to support: 5/16 FILLET, 5/16 FILLET
Bolt: 3 rows x 1 column 0.875 in. Diameter A325N_TC bolts
Vertical spacing: 4.5 in.
Horizontal spacing: 3 in.
Shear plate edge setback = 1 in.
Beam centerline setback = 1 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: 2 in.
Edge distance at top edge of beam: 1.75 in.
Edge distance at bottom edge of beam: 4.88 in.
Top cope depth: 1.25 in.
Top cope length: 2.5 in.
Bottom cope depth: 4 in.
Bottom cope length: 2.5 in.
Horizontal distance to first hole: 3 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 SHEAR CAPACITY AT BEAM AND SHEAR PLATE SIDE:
Bolt Shear Capacity at Shear Load Only:
Using Instantaneous Center Of Rotation Method (AISC 7-1)
ex = 1.500 in.
Angle = 0.000 deg.
C = 2.715
Using Table 7-1 to determine (1/omega)rn:
(1/omega)Rn = (1/omega)rn * C = 16.24 * 2.71 = 44.07 kips


Total Vertical Bolt Shear Capacity = 44.07 kips
44.07 kips >= 37.00 kips (OK)

BOLT BEARING AT BEAM AND SHEAR PLATE SIDE
Vertical Shear Only Load Case:
ICR cordinate relative to CG = (8.66, -0.00)
At Row 1, At Column 1:
Ribolt = 15.94 kips
Ri vector at Beam   = <7.35, 14.14>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 2.91 in.
(1/omega)Rnsbm at Beam spacing = (1/omega) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * na * (0.38/1) * 65.00 = na
(1/omega)Rnebm at Beam edge = (1/omega) * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 2.91 * (0.38/1) * 65.00 = 43.16 kips/bolt
(1/omega)Rndbm on Beam at Bolt Diameter   = (1/omega) * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.88 * (0.38/1) * 65.00 = 25.94 kips/bolt
Beam bearing capacity, (1/omega)Rnbm = min((1/omega)Rnsbm,(1/omega)Rnebm,(1/omega)Rndbm) = min(na, 43.16, 25.94) = 25.94 kips/bolt
Ri vector at Shear Plate   = <-7.35, -14.14>
Lcsshpl at Shear Plate spacing  = na
Lceshpl at Shear Plate edge    = 5.98 in.
(1/omega)Rnsshpl at Shear Plate spacing = (1/omega) * hf1 * Lcs * t * Fu = 0.50 * 1.20 * na * 0.50 * 65.00 = na
(1/omega)Rneshpl at Shear Plate edge = (1/omega) * hf1 * Lce * t * Fu = 0.50 * 1.20 * 5.98 * 0.50 * 65.00 = 116.53 kips/bolt
(1/omega)Rndshpl on Shear Plate at Bolt Diameter   = (1/omega) * hf2 * db * t * Fu = 0.50 * 2.40 * 0.88 * 0.50 * 65.00 = 34.12 kips/bolt
Shear Plate bearing capacity, (1/omega)Rnshpl = min((1/omega)Rnsshpl,(1/omega)Rneshpl,(1/omega)Rndshpl) = min(na, 116.53, 34.12) = 34.12 kips/bolt
(1/omega)Rn = min((1/omega)Rnbm, (1/omega)Rnshpl) = min(25.935, 34.125) = 25.94 kips/bolt
Bolt Shear Demand to Bearing ratio = 25.94 / 15.94 = 1.63

At Row 2, At Column 1:
Ribolt = 15.79 kips
Ri vector at Beam   = <0.00, 15.79>
Lcsbm at Beam spacing  = 3.56 in.
Lcebm at Beam edge    = 5.78 in.
(1/omega)Rnsbm at Beam spacing = (1/omega) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * 3.56 * (0.38/1) * 65.00 = 52.80 kips/bolt
(1/omega)Rnebm at Beam edge = (1/omega) * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 5.78 * (0.38/1) * 65.00 = 85.68 kips/bolt
(1/omega)Rndbm on Beam at Bolt Diameter   = (1/omega) * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.88 * (0.38/1) * 65.00 = 25.94 kips/bolt
Beam bearing capacity, (1/omega)Rnbm = min((1/omega)Rnsbm,(1/omega)Rnebm,(1/omega)Rndbm) = min(52.80, 85.68, 25.94) = 25.94 kips/bolt
Ri vector at Shear Plate   = <-0.00, -15.79>
Lcsshpl at Shear Plate spacing  = 3.56 in.
Lceshpl at Shear Plate edge    = 5.28 in.
(1/omega)Rnsshpl at Shear Plate spacing = (1/omega) * hf1 * Lcs * t * Fu = 0.50 * 1.20 * 3.56 * 0.50 * 65.00 = 69.47 kips/bolt
(1/omega)Rneshpl at Shear Plate edge = (1/omega) * hf1 * Lce * t * Fu = 0.50 * 1.20 * 5.28 * 0.50 * 65.00 = 102.98 kips/bolt
(1/omega)Rndshpl on Shear Plate at Bolt Diameter   = (1/omega) * hf2 * db * t * Fu = 0.50 * 2.40 * 0.88 * 0.50 * 65.00 = 34.12 kips/bolt
Shear Plate bearing capacity, (1/omega)Rnshpl = min((1/omega)Rnsshpl,(1/omega)Rneshpl,(1/omega)Rndshpl) = min(69.47, 102.98, 34.12) = 34.12 kips/bolt
(1/omega)Rn = min((1/omega)Rnbm, (1/omega)Rnshpl) = min(25.935, 34.125) = 25.94 kips/bolt
Bolt Shear Demand to Bearing ratio = 25.94 / 15.79 = 1.64

At Row 3, At Column 1:
Ribolt = 15.94 kips
Ri vector at Beam   = <-7.35, 14.14>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 3.87 in.
(1/omega)Rnsbm at Beam spacing = (1/omega) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * na * (0.38/1) * 65.00 = na
(1/omega)Rnebm at Beam edge = (1/omega) * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 3.87 * (0.38/1) * 65.00 = 57.33 kips/bolt
(1/omega)Rndbm on Beam at Bolt Diameter   = (1/omega) * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.88 * (0.38/1) * 65.00 = 25.94 kips/bolt
Beam bearing capacity, (1/omega)Rnbm = min((1/omega)Rnsbm,(1/omega)Rnebm,(1/omega)Rndbm) = min(na, 57.33, 25.94) = 25.94 kips/bolt
Ri vector at Shear Plate   = <7.35, -14.14>
Lcsshpl at Shear Plate spacing  = na
Lceshpl at Shear Plate edge    = 0.88 in.
(1/omega)Rnsshpl at Shear Plate spacing = (1/omega) * hf1 * Lcs * t * Fu = 0.50 * 1.20 * na * 0.50 * 65.00 = na
(1/omega)Rneshpl at Shear Plate edge = (1/omega) * hf1 * Lce * t * Fu = 0.50 * 1.20 * 0.88 * 0.50 * 65.00 = 17.17 kips/bolt
(1/omega)Rndshpl on Shear Plate at Bolt Diameter   = (1/omega) * hf2 * db * t * Fu = 0.50 * 2.40 * 0.88 * 0.50 * 65.00 = 34.12 kips/bolt
Shear Plate bearing capacity, (1/omega)Rnshpl = min((1/omega)Rnsshpl,(1/omega)Rneshpl,(1/omega)Rndshpl) = min(na, 17.17, 34.12) = 17.17 kips/bolt
(1/omega)Rn = min((1/omega)Rnbm, (1/omega)Rnshpl) = min(25.935, 17.169) = 17.17 kips/bolt
Bolt Shear Demand to Bearing ratio = 17.17 / 15.94 = 1.08

Min Bolt Shear Demand to Bearing ratio Beam and Shear Plate for vertical shear only
 = min(1.00, 1.63, 1.64, 1.08) = 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 * 44.07 = 44.07 kips
Rbv = 44.07 kips >= V = 37.00 kips (OK)

Web Depth = d - [Top Cope Depth] - [Bottom Cope Depth] = 20.8 - 1.25 - 4 = 15.55 in.
Gross Area (Shear) = [Web Depth] * tw = 15.55 * 0.38 = 5.91 in^2
Net Shear Area (Shear) = ([Web Depth] - ([# rows] * [Diameter + 0.0625])) * tw 
    = (15.55 - (3 * 1.00)) * 0.38 = 4.77 in^2

Using Eq.J4-3:
Shear Yielding = (1/omega) * 0.6 * Fybeam * [Gross Area] = 0.67 * 0.6 * 50.00 * 5.91 = 118.18 kips

Using Eq.J4-4:
Shear Rupture = (1/omega) * 0.6 * Fubeam * [Net Area] = 0.50 * 0.6 * 65.00 * 4.77 = 93.00 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]) = 1.75 + 9 = 10.75 in.
Net Shear Length = Gross Shear Length - (# rows - 0.5) * (hole size + 0.0625) = 10.8 - (3 - 0.5) * 1 = 8.25 in.
Gross Tension Length = [edge dist. at beam edge] + ([# cols - 1] * [spacing]) = 2 + (1 - 1) * 3 = 2.00 in.
Net Tension Length = Gross Tension Length - (# cols - 0.5) * (hole size + 0.0625) = 2 - (1 - 0.5) * 1 = 1.50 in.
1. (1/omega) * [material thickness] * ((0.60 * Fubeam* [net shear length]) + (Ubs * Fubeam * [net tension length])) 
    = 0.50 * 0.38 * ((0.60 * 65.00 * 8.25) + (1.00 * 65.00 * 1.50)) = 79.66 kips
2. (1/omega) * [material thickness] * ((0.60 * Fybeam * [gross shear length]) + (Ubs * Fubeam * [net tension length])) 
    = 0.50 * 0.38 * ((0.60 * 50.00 * 10.75) + (1.00 * 65.00 * 1.50)) = 79.80 kips
Block Shear = 79.66 kips

Block Shear (1) Total = Block Shear (1) = 79.66 kips


Buckling and Flexure at Longest Cope (Top and Bottom Copes at Section)
Eccentricity at Section, e = 3.66 in.
If beam is coped at both top and bottom flanges,

Using Eq. 9-14 through 9-18, Fcr = Fy * Q
tw = 0.38 in.
ho = 15.55 in.
c = 2.50 in.
lambda = (ho * Fy ^ 0.5) / ( 10 * tw * ( 475.00 + 280.00 * (ho / c)^2 ) ^0.5 ) = 
 = 15.55 * 50.00^0.5 / (10 * 0.38 * (475.00 + 280.00 * (15.55/2.50)^2 )^0.5) = 0.27
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) = 15.31 in^3
Snet2 (bolt holes applicable) = 15.31 in^3
Znet = 22.97 in^3

Using Eq. 9-6
Buckling = Fcr * Snet1 / e = 30.00 * 15.31 / 3.66 = 125.61 kips

Using Eq. 9-19
Flexural Yielding = (1/omega) * Fy * Snet1 / e = 0.60 * 50.00 * 15.31 / 3.66 = 125.61 kips

Using Eq. 9-4
Flexural Rupture = (1/omega) * Fu * Znet / e = 0.50 * 65.00 * 22.97 / 3.66 = 204.12 kips


Buckling and Flexure at Furthest Bolt Line within Cope (Top and Bottom Copes at Section)
Eccentricity at Section, e = 3.16 in.
If beam is coped at both top and bottom flanges,

Using Eq. 9-14 through 9-18, Fcr = Fy * Q
tw = 0.38 in.
ho = 15.55 in.
c = 2.50 in.
lambda = (ho * Fy ^ 0.5) / ( 10 * tw * ( 475.00 + 280.00 * (ho / c)^2 ) ^0.5 ) = 
 = 15.55 * 50.00^0.5 / (10 * 0.38 * (475.00 + 280.00 * (15.55/2.50)^2 )^0.5) = 0.27
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) = 15.31 in^3
Snet2 (bolt holes applicable) = 12.32 in^3
Znet = 18.88 in^3

Using Eq. 9-6
Buckling = Fcr * Snet1 / e = 30.00 * 15.31 / 3.16 = 145.50 kips

Using Eq. 9-19
Flexural Yielding = (1/omega) * Fy * Snet1 / e = 0.60 * 50.00 * 15.31 / 3.16 = 145.50 kips

Using Eq. 9-4
Flexural Rupture = (1/omega) * Fu * Znet / e = 0.50 * 65.00 * 18.88 / 3.16 = 194.30 kips


Section Bending Strength Calculations Summary:

   Coped Beam Buckling and Flexure at Longest Cope (Top and Bottom Copes at Section)
   Buckling : 125.61 >= 37.00 kips (OK)
   Flexural Yielding : 125.61 >= 37.00 kips (OK)
   Flexural Rupture : 204.12 >= 37.00 kips (OK)

   Coped Beam Buckling and Flexure at Furthest Bolt Line within Cope (Top and Bottom Copes at Section)
   Buckling : 145.50 >= 37.00 kips (OK)
   Flexural Yielding : 145.50 >= 37.00 kips (OK)
   Flexural Rupture : 194.30 >= 37.00 kips (OK)

Gross Area = 0.50 * 11.50 = 5.75 in^2
Net Area = (11.50 - (3 *(0.94 + 1/16))) * 0.50 = 4.25 in^2

Using Eq.J4-3:
Shear Yielding = (1/omega) * 0.6 * Fypl * [Gross Area] = 0.67 * 0.6 * 50.00 * 5.75 = 115.00 kips

Using Eq.J4-4:
Shear Rupture = (1/omega) * 0.6 * Fupl * [Net Area] = 0.50 * 0.6 * 65.00 * 4.25 = 82.88 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 - (2.5 * (0.938 + 0.0625)) = 7.75 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 * 0.50 * ((0.60 * 65.00 * 7.75) + (1.00 * 65.00 * 1.16)) = 94.35 kips
2. (1/omega) * [material thickness] * ((0.60 * Fypl * [gross shear length]) + (Ubs * Fupl * [net tension length])) 
    = 0.50 * 0.50 * ((0.60 * 50.00 * 10.25) + (1.00 * 65.00 * 1.16)) = 95.66 kips
Block Shear = 94.35 kips

94.35 kips >= Vbm = 37.00 kips (OK)


Interaction Check of Flexural Yielding, Per AISC 10-5: 
Eccentricity due to Conventional Config. (e = a/2), e = 1.50 in.
Zgross = 16.53
Znet = 11.91
Mr = Vr * e = 37.00 * 1.50 = 55.50 kips-in
Mc = 1/omega * Mn = 1/omega * Fy * Zgross = 0.60 * 50.00 * 16.53 = 495.94 kips-in
Vr = 37.00 kips
Vc = 1/omega * Vn = 1/omega * 0.60 * Fy * Ag = 0.67 * 0.60 * 50.00 * 5.75 = 115.00 kips
Interaction due to moment and shear, (Vr/Vc)^2 + (Mr/Mc)^2 <= 1.0
(Vr/Vc)^2 + (Mr/Mc)^2 = (37.00 / 115.00)^2 + (55.50 / 495.94)^2 = 0.12 <= 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 = 37.000 / 11.500 / 2 = 1.609 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) = 1.609 / (0.500 * 1.856) = 1.733/16

Minimum fillet weld size : 
   At shear only load case = 0.11 in.
   per Table J2.4     = 0.19 in.
   5/8tp              = 0.31 in.
   user preference    = 0.25 in.

Dmax1 (using eqn 9-3)
 = tshpl * Fushpl / ( Fexx * C1 * 0.088)
 = 0.500 * 65.000 / ( 70.000 * 1.000 * 0.088 ) 
 = 5.253 
Dmax2 (using eqn 9-3)
 = twsupport * Fusupport / ( Fexx * C1 * 0.088 )
 = 0.315 * 65.000 / ( 70.000 * 1.000 * 0.088 ) 
 = 3.309 
Dmax3 = project max fillet weld = 12.000
Dmax=min(Dmax1, Dmax2, Dmax3) = min(5.253, 3.309, 12.000)
 = 3.309 

Use weld size
D1 = 5.00
D2 = 5.00

Weld Strength :

Vertical weld capacity during shear only load, 1/omega * Rnv1 = 0.50 * 1.86 * 11.50 * (3.31 + 3.31) = 70.64 kips

70.64 kips >= Vbm = 37.00 kips (OK)