bb.s.s.00004.00004

SHEAR PLATE CONNECTION SUMMARY

Filler Beam profile: W18X35
Support Girder profile: W18X60
Slope: 0.00 deg.
Skew: 67.90
Vertical Offset: 0.00 in.
Horizontal Offset: 0.00 in.
Span: 24.05 ft.
Reaction, V: 15.00 kips
Shear Capacity, Rn: 80.81 kips
Design/Reference according to AISC 14th Ed. - LRFD
Shear Plate: Conventional Configuration
Beam material grade: A992
Support material grade: A992
Plate material grade: A572-GR.50
Weld grade: E70
Shear Plate Size: 4.75 in. x 12.00 in. x 0.38 in.
Configuration Geometry:
Welds at shear plate to support: 4/16 FILLET, 7/16 FILLET
Bolt: 4 rows x 1 column 1.00 in. Diameter A490N_TC bolts
Vertical spacing: 3.00 in.
Horizontal spacing: 3.00 in.
Shear plate edge setback = 0.75 in.
Beam centerline setback = 0.97 in.
Edge distance at vertical edge of plate: 2.00 in.
Edge distance at top edge of plate: 1.50 in.
Edge distance at bottom edge of plate: 1.50 in.
Edge distance at vertical edge of beam: 2.00 in.
Edge distance at top edge of beam: 1.75 in.
Edge distance at bottom edge of beam: 4.70 in.
Top cope depth: 1.25 in.
Top cope length: 3.75 in.
Bottom cope depth: 1.00 in.
Bottom cope length: 3.75 in.
Horizontal distance to first hole: 2.75 in.
Down distance from top of filler beam flange: 3.00 in.
Holes in beam web: STD diameter = 1.06 in.
Holes in shear plate: SSL diameter = 1.06 in., slot width = 1.31 in.

BOLT SHEAR CAPACITY AT BEAM AND SHEAR PLATE SIDE:
Bolt Shear Capacity at Shear Load Only:
Using Instantaneous Center Of Rotation Method (AISC 14th Ed. Equation (7-1))
ex = 1.45 in.
Angle = 0.00 deg.
C = 3.58
Using Table 7-1 to determine (phi)rn:
(phi)Rn = (phi)rn * C = 40.06 * 3.58 = 143.28 kips


Total Vertical Bolt Shear Capacity = 143.28 kips
143.28 kips >= Reaction V = 15.00 kips (OK)

BOLT BEARING AT BEAM AND SHEAR PLATE SIDE
Vertical Shear Only Load Case:
ICR cordinate relative to CG = (7.35, -0.00)
At Row 1, At Column 1:
Ribolt = 39.32 kips
Ri vector at Beam   = <20.54, 33.52>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 1.52 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 * 1.52 * (0.30/1) * 65.00 = 26.70 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 1.00 * (0.30/1) * 65.00 = 35.10 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(na, 26.70, 35.10) = 26.70 kips/bolt
Ri vector at Shear Plate   = <-20.54, -33.52>
Lcsshpl at Shear Plate spacing  = na
Lceshpl at Shear Plate edge    = 4.64 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 * 4.64 * 0.38 * 65.00 = 101.81 kips/bolt
(phi)Rndshpl on Shear Plate at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 1.00 * 0.38 * 65.00 = 43.88 kips/bolt
Shear Plate bearing capacity, (phi)Rnshpl = min((phi)Rnsshpl,(phi)Rneshpl,(phi)Rndshpl) = min(na, 101.81, 43.88) = 43.88 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(26.70, 43.88) = 26.70 kips/bolt
Bolt Shear Demand to Bearing ratio = 26.70 / 39.32 = 0.68

At Row 2, At Column 1:
Ribolt = 38.90 kips
Ri vector at Beam   = <7.79, 38.11>
Lcsbm at Beam spacing  = 1.94 in.
Lcebm at Beam edge    = 4.32 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.75 * 1.20 * 1.94 * (0.30/1) * 65.00 = 34.00 kips/bolt
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 4.32 * (0.30/1) * 65.00 = 75.76 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 1.00 * (0.30/1) * 65.00 = 35.10 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(34.00, 75.76, 35.10) = 34.00 kips/bolt
Ri vector at Shear Plate   = <-7.79, -38.11>
Lcsshpl at Shear Plate spacing  = 1.94 in.
Lceshpl at Shear Plate edge    = 7.11 in.
(phi)Rnsshpl at Shear Plate spacing = (phi) * hf1 * Lcs * t * Fu = 0.75 * 1.20 * 1.94 * 0.38 * 65.00 = 42.50 kips/bolt
(phi)Rneshpl at Shear Plate edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 7.11 * 0.38 * 65.00 = 156.04 kips/bolt
(phi)Rndshpl on Shear Plate at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 1.00 * 0.38 * 65.00 = 43.88 kips/bolt
Shear Plate bearing capacity, (phi)Rnshpl = min((phi)Rnsshpl,(phi)Rneshpl,(phi)Rndshpl) = min(42.50, 156.04, 43.88) = 42.50 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(34.00, 42.50) = 34.00 kips/bolt
Bolt Shear Demand to Bearing ratio = 34.00 / 38.90 = 0.87

At Row 3, At Column 1:
Ribolt = 38.90 kips
Ri vector at Beam   = <-7.77, 38.11>
Lcsbm at Beam spacing  = 1.94 in.
Lcebm at Beam edge    = 7.38 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.75 * 1.20 * 1.94 * (0.30/1) * 65.00 = 34.00 kips/bolt
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 7.38 * (0.30/1) * 65.00 = 129.49 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 1.00 * (0.30/1) * 65.00 = 35.10 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(34.00, 129.49, 35.10) = 34.00 kips/bolt
Ri vector at Shear Plate   = <7.77, -38.11>
Lcsshpl at Shear Plate spacing  = 1.94 in.
Lceshpl at Shear Plate edge    = 4.05 in.
(phi)Rnsshpl at Shear Plate spacing = (phi) * hf1 * Lcs * t * Fu = 0.75 * 1.20 * 1.94 * 0.38 * 65.00 = 42.50 kips/bolt
(phi)Rneshpl at Shear Plate edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 4.05 * 0.38 * 65.00 = 88.86 kips/bolt
(phi)Rndshpl on Shear Plate at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 1.00 * 0.38 * 65.00 = 43.88 kips/bolt
Shear Plate bearing capacity, (phi)Rnshpl = min((phi)Rnsshpl,(phi)Rneshpl,(phi)Rndshpl) = min(42.50, 88.86, 43.88) = 42.50 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(34.00, 42.50) = 34.00 kips/bolt
Bolt Shear Demand to Bearing ratio = 34.00 / 38.90 = 0.87

At Row 4, At Column 1:
Ribolt = 39.31 kips
Ri vector at Beam   = <-20.53, 33.53>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 3.30 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 * 3.30 * (0.30/1) * 65.00 = 57.90 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 1.00 * (0.30/1) * 65.00 = 35.10 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(na, 57.90, 35.10) = 35.10 kips/bolt
Ri vector at Shear Plate   = <20.53, -33.53>
Lcsshpl at Shear Plate spacing  = na
Lceshpl at Shear Plate edge    = 1.14 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 * 1.14 * 0.38 * 65.00 = 24.92 kips/bolt
(phi)Rndshpl on Shear Plate at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 1.00 * 0.38 * 65.00 = 43.88 kips/bolt
Shear Plate bearing capacity, (phi)Rnshpl = min((phi)Rnsshpl,(phi)Rneshpl,(phi)Rndshpl) = min(na, 24.92, 43.88) = 24.92 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(35.10, 24.92) = 24.92 kips/bolt
Bolt Shear Demand to Bearing ratio = 24.92 / 39.31 = 0.63

Min Bolt Shear Demand to Bearing ratio Beam and Shear Plate for vertical shear only
 = min(1.00, 0.68, 0.87, 0.87, 0.63) = 0.63

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 = 0.63 * 143.28 = 90.82 kips
Rbv = 90.82 kips >= Reaction V = 15.00 kips (OK)

Web Depth = d - [Top Cope Depth] - [Bottom Cope Depth] = 17.70 - 1.25 - 1.00 = 15.45 in.

Using AISC 14th Ed. Equation J4-3
Gross Area (Shear), Agross = [Web Depth] * tw = 15.45 * 0.30 = 4.63 in^2
Shear Yielding, (phi)Vny = (phi) * 0.6 * Fybeam * Agross = 1.00 * 0.6 * 50.00 * 4.63 = 139.05 kips
139.05 kips >= Reaction V = 15.00 kips (OK)

Shear Rupture:
Using AISC 14th Ed. Equation J4-4
Net Area (Shear), Anet = ([Web Depth] - ([# rows] * [Diameter + 0.06])) * tw 
    = (15.45 - (4 * 1.12)) * 0.30 = 3.28 in^2
Shear Rupture, (phi)Vnu = (phi) * 0.6 * Fubeam * Anet = 0.75 * 0.6 * 65.00 * 3.28 = 96.09 kips
96.09 kips >= Reaction V = 15.00 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 Shear (1)
Gross Shear Length = [edge dist. at beam edge] + ([# rows - 1] * [spacing]) = 1.75 + (4 - 1) * 3.00 = 10.75 in.
Net Shear Length = Gross Shear Length - (# rows - 0.5) * (hole size + 0.06) = 10.75 - (4 - 0.5) * 1.12 = 6.81 in.
Gross Tension Length = [edge dist. at beam edge] + ([# cols - 1] * [spacing]) = 2.00 + (1 - 1) * 3.00 = 2.00 in.
Net Tension Length = Gross Tension Length - (# cols - 0.5) * (hole size + 0.06) = 2.00 - (1 - 0.5) * 1.12 = 1.44 in.
1. (phi) * [material thickness] * ((0.60 * Fubeam* [net shear length]) + (Ubs * Fubeam * [net tension length])) 
    = 0.75 * 0.30 * ((0.60 * 65.00 * 6.81) + (1.00 * 65.00 * 1.44)) = 80.81 kips
2. (phi) * [material thickness] * ((0.60 * Fybeam * [gross shear length]) + (Ubs * Fubeam * [net tension length])) 
    = 0.75 * 0.30 * ((0.60 * 50.00 * 10.75) + (1.00 * 65.00 * 1.44)) = 93.59 kips
Block Shear = 80.81 kips

Block Shear (1) Total = Block Shear (1) = 80.81 kips
80.81 kips >= Reaction V = 15.00 kips (OK)

Block Shear for Axial T/C is not required.

Buckling and Flexure at Longest Cope (Top and Bottom Copes at Section)
Eccentricity at Section, e = 4.80 in.
If beam is coped at both top and bottom flanges,

Using AISC 14th Ed. Equation 9-14 through 9-18, Fcr = Fy * Q
tw = 0.30 in.
ho = 15.45 in.
c = 3.75 in.
lambda = (ho * Fy ^ 0.5) / ( 10 * tw * ( 475.00 + 280.00 * (ho / c)^2 ) ^0.5 ) = 
 = 15.45 * 50.00^0.5 / (10 * 0.30 * (475.00 + 280.00 * (15.45/3.75)^2 )^0.5) = 0.50
When lambda <= 0.70, Q=1
Q = 1.00
Fcrmin =phi * Fcr = 0.90 * 50.00 * 1.00 = 45.00 ksi
Snet1 (bolt holes not applicable) = 11.94 in^3
Snet2 (bolt holes applicable) = 11.94 in^3
Znet1 (bolt holes not applicable) = 17.90 in^3
Znet2 (bolt holes applicable) = 17.90 in^3

Using AISC 14th Ed. Equation 9-6
Buckling = Fcr * Snet1 / e = 45.00 * 11.94 / 4.80 = 111.89 kips

Using AISC 14th Ed. Equation 9-19
Flexural Yielding = (phi) * Fy * Snet1 / e = 0.90 * 50.00 * 11.94 / 4.80 = 111.89 kips

Using AISC 14th Ed. Equation 9-4
Flexural Rupture = (phi) * Fu * Znet2 / e = 0.75 * 65.00 * 17.90 / 4.80 = 181.83 kips


Buckling and Flexure at Furthest Bolt Line within Cope (Top and Bottom Copes at Section)
Eccentricity at Section, e = 3.05 in.
If beam is coped at both top and bottom flanges,

Using AISC 14th Ed. Equation 9-14 through 9-18, Fcr = Fy * Q
tw = 0.30 in.
ho = 15.45 in.
c = 3.75 in.
lambda = (ho * Fy ^ 0.5) / ( 10 * tw * ( 475.00 + 280.00 * (ho / c)^2 ) ^0.5 ) = 
 = 15.45 * 50.00^0.5 / (10 * 0.30 * (475.00 + 280.00 * (15.45/3.75)^2 )^0.5) = 0.50
When lambda <= 0.70, Q=1
Q = 1.00
Fcrmin =phi * Fcr = 0.90 * 50.00 * 1.00 = 45.00 ksi
Snet1 (bolt holes not applicable) = 11.94 in^3
Snet2 (bolt holes applicable) = 8.73 in^3
Znet1 (bolt holes not applicable) = 17.90 in^3
Znet2 (bolt holes applicable) = 13.49 in^3

Using AISC 14th Ed. Equation 9-6
Buckling = Fcr * Snet1 / e = 45.00 * 11.94 / 3.05 = 176.09 kips

Using AISC 14th Ed. Equation 9-19
Flexural Yielding = (phi) * Fy * Snet1 / e = 0.90 * 50.00 * 11.94 / 3.05 = 176.09 kips

Using AISC 14th Ed. Equation 9-4
Flexural Rupture = (phi) * Fu * Znet2 / e = 0.75 * 65.00 * 13.49 / 3.05 = 215.62 kips


Section Bending Strength Calculations Summary:

   Coped Beam Buckling and Flexure at Longest Cope (Top and Bottom Copes at Section)
   Buckling : 111.89 >= 15.00 kips (OK)
   Flexural Yielding : 111.89 >= 15.00 kips (OK)
   Flexural Rupture : 181.83 >= 15.00 kips (OK)

   Coped Beam Buckling and Flexure at Furthest Bolt Line within Cope (Top and Bottom Copes at Section)
   Buckling : 176.09 >= 15.00 kips (OK)
   Flexural Yielding : 176.09 >= 15.00 kips (OK)
   Flexural Rupture : 215.62 >= 15.00 kips (OK)

Using AISC 14th Ed. Equation J4-3
Gross Area, Ag = 0.38 * 12.00 = 4.50 in^2
Shear Yielding, (phi)Vny = (phi) * 0.6 * Fypl * Ag = 1.00 * 0.6 * 50.00 * 4.50 = 135.00 kips
135.00 kips >= Reaction V = 15.00 kips (OK)

Shear Rupture:
Using AISC 14th Ed. Equation J4-4
Net Area, An = (12.00 - (4 * (1.06 + 1/16))) * 0.38 = 2.81 in^2
Shear Rupture, (phi)Vnu = (phi) * 0.6 * Fupl * An = 0.75 * 0.6 * 65.00 * 2.81 = 82.27 kips
82.27 kips >= Reaction V = 15.00 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 = (12.00 - 1.50) = 10.50 in.
Net Shear Length = 10.50 - (3.50 * (1.06 + 0.06)) = 6.56 in.
Gross Tension Length = (0.00 + 2.00) = 2.00 in.
Net Tension Length = 2.00 - (0.50 * (1.31 + 0.06)) = 1.31 in.
1. (phi) * [material thickness] * ((0.60 * Fupl* [net shear length]) + (Ubs * Fupl * [net tension length])) 
    = 0.75 * 0.38 * ((0.60 * 65.00 * 6.56) + (1.00 * 65.00 * 1.31)) = 95.98 kips
2. (phi) * [material thickness] * ((0.60 * Fypl * [gross shear length]) + (Ubs * Fupl * [net tension length])) 
    = 0.75 * 0.38 * ((0.60 * 50.00 * 10.50) + (1.00 * 65.00 * 1.31)) = 112.59 kips
Block Shear = 95.98 kips
95.98 kips >= Reaction V = 15.00 kips (OK)

Block Shear for Axial T/C is not required.

Interaction Check of Flexural Yielding:
Using AISC 14th Ed. Equation 10-5
Eccentricity due to Conventional Config. (e = a/2), e = 1.45 in.
Zgross = 13.50
Znet = 8.44
Mr = Vr * e = 15.00 * 1.45 = 21.77 kips-in
Mc = phi * Mn = phi * Fy * Zgross = 0.90 * 50.00 * 13.50 = 607.50 kips-in
Vr = 15.00 kips
Vc = phi * Vn = phi * 0.60 * Fy * Ag = 1.00 * 0.60 * 50.00 * 4.50 = 135.00 kips
Interaction due to moment and shear, (Vr/Vc)^2 + (Mr/Mc)^2 <= 1.0
(Vr/Vc)^2 + (Mr/Mc)^2 = (15.00 / 135.00)^2 + (21.77 / 607.50)^2 = 0.01 <= 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 14th Ed. 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 = 12.00 in.
Shear Load per inch per weld, fv = R/Lv/2 = 15.00 / 12.00 / 2 = 0.62 kips/in/ weld 
theta = 0 deg.
cPhi  = 1.0 + 0.5 * sin(theta)^1.5 = 1.0 + 0.5 * sin(0.00)^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) = 0.62 / (0.75 * 1.86) = 0.45/16

Minimum fillet weld size : 
   At shear only load case = 0.03 in.
   per Table J2.4     = 0.19 in.
   5/8tp              = 0.23 in.
   user preference    = 0.25 in.

Dmax1 (using AISC 14th Ed. eqn 9-3)
 = tshpl * Fushpl / ( Fexx * C1 * 0.09)
 = 0.38 * 65.00 / ( 70.00 * 1.00 * 0.09 ) 
 = 3.94 
Dmax2 (using AISC 14th Ed. eqn 9-3)
 = twbm * Fusupport / ( Fexx * C1 * 0.09 )
 = 0.41 * 65.00 / ( 70.00 * 1.00 * 0.09 ) 
 = 4.36 
Dmax3 = project max fillet weld = 12.00
Dmax=min(Dmax1, Dmax2, Dmax3) = min(3.94, 4.36, 12.00)
 = 3.94 

Dihedral Angle, DA = 67.90 deg.
Gap on Obtuse Angle Side if No Bevel = 0.14 in.
Use weld size
Acute Side  D1 = 4.00
Obtuse Side D2 = 7.00 (weld size increased on obtuse side for gap at skew per AWS D1.1/D1.1M (2015, p.511, C-5.21.1))

Weld Strength :

Vertical weld capacity during shear only load, phi * Rnv1 = 0.75 * 1.86 * 12.00 * (3.94 + 3.94) = 131.63 kips

131.63 kips >= Reaction V = 15.00 kips (OK)

Check Effective Throat:
Acute Side Effect throat  = (D1/sin(DA)) * cos(DA/2) = (0.25/ sin( 67.90)) * cos( 33.95) = 0.22 in.
Obtuse Side Effect throat = (D2/sin(DA)-tshpl/tan(DA))*sin(DA/2) = (0.44 / sin(67.90) - 0.38 / tan(67.90)) * sin(67.90 / 2) = 0.18 in.
Total Effective Throat    = 0.22 + 0.18 = 0.40 in.
Total Effective Throat of Square Case = 5/8tp * 2^0.5 = 0.23 * 2^0.5 = 0.33 in.
0.40 >= 0.33 (OK)