bb.s.s.01374.01375

SHEAR PLATE CONNECTION SUMMARY

Filler Beam profile: W18X40
Support Girder profile: W21X111
Slope: 0.00 deg.
Skew: 90.00
Vertical Offset: 0.00 in.
Horizontal Offset: 0.00 in.
Span: 20.00 ft.
Reaction, V: 58.80 kips
Shear Capacity, Rn: 82.27 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: 4.50 in. x 12.00 in. x 0.38 in.
Configuration Geometry:
Welds at shear plate to support: 4/16 FILLET, 4/16 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 = 0.50 in.
Beam centerline setback = 0.50 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: 2.25 in.
Top cope depth: 1.50 in.
Top cope length: 6.00 in.
Horizontal distance to first hole: 2.50 in.
Down distance from top of filler beam flange: 3.75 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 7-1)
ex = 1.25 in.
Angle = 0.00 deg.
C = 3.66
Using Table 7-1 to determine (phi)rn:
(phi)Rn = (phi)rn * C = 40.06 * 3.66 = 146.63 kips


Total Vertical Bolt Shear Capacity = 146.63 kips
146.63 kips >= Reaction V = 58.80 kips (OK)

BOLT BEARING AT BEAM AND SHEAR PLATE SIDE
Vertical Shear Only Load Case:
ICR cordinate relative to CG = (8.65, 0.00)
At Row 1, At Column 1:
Ribolt = 39.32 kips
Ri vector at Beam   = <18.15, 34.88>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 2.01 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 * 2.01 * (0.32/1) * 65.00 = 36.95 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 1.00 * (0.32/1) * 65.00 = 36.86 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(na, 36.95, 36.86) = 36.86 kips/bolt
Ri vector at Shear Plate   = <-18.15, -34.88>
Lcsshpl at Shear Plate spacing  = na
Lceshpl at Shear Plate edge    = 4.82 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 * 4.82 * 0.38 * 65.00 = 105.69 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, 105.69, 43.88) = 43.88 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(36.86, 43.88) = 36.86 kips/bolt
Bolt Shear Demand to Bearing ratio = 36.86 / 39.32 = 0.94

At Row 2, At Column 1:
Ribolt = 39.01 kips
Ri vector at Beam   = <6.67, 38.44>
Lcsbm at Beam spacing  = 1.94 in.
Lcebm at Beam edge    = 4.80 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.75 * 1.20 * 1.94 * (0.32/1) * 65.00 = 35.70 kips/bolt
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 4.80 * (0.32/1) * 65.00 = 88.40 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 1.00 * (0.32/1) * 65.00 = 36.86 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(35.70, 88.40, 36.86) = 35.70 kips/bolt
Ri vector at Shear Plate   = <-6.67, -38.44>
Lcsshpl at Shear Plate spacing  = 1.94 in.
Lceshpl at Shear Plate edge    = 7.07 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 * 7.07 * 0.38 * 65.00 = 155.16 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, 155.16, 43.88) = 42.50 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(35.70, 42.50) = 35.70 kips/bolt
Bolt Shear Demand to Bearing ratio = 35.70 / 39.01 = 0.92

At Row 3, At Column 1:
Ribolt = 39.01 kips
Ri vector at Beam   = <-6.67, 38.44>
Lcsbm at Beam spacing  = 1.94 in.
Lcebm at Beam edge    = 7.84 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.75 * 1.20 * 1.94 * (0.32/1) * 65.00 = 35.70 kips/bolt
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 7.84 * (0.32/1) * 65.00 = 144.51 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 1.00 * (0.32/1) * 65.00 = 36.86 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(35.70, 144.51, 36.86) = 35.70 kips/bolt
Ri vector at Shear Plate   = <6.67, -38.44>
Lcsshpl at Shear Plate spacing  = 1.94 in.
Lceshpl at Shear Plate edge    = 4.03 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 * 4.03 * 0.38 * 65.00 = 88.37 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, 88.37, 43.88) = 42.50 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(35.70, 42.50) = 35.70 kips/bolt
Bolt Shear Demand to Bearing ratio = 35.70 / 39.01 = 0.92

At Row 4, At Column 1:
Ribolt = 39.32 kips
Ri vector at Beam   = <-18.15, 34.88>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 3.80 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 * 3.80 * (0.32/1) * 65.00 = 70.06 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 1.00 * (0.32/1) * 65.00 = 36.86 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(na, 70.06, 36.86) = 36.86 kips/bolt
Ri vector at Shear Plate   = <18.15, -34.88>
Lcsshpl at Shear Plate spacing  = na
Lceshpl at Shear Plate edge    = 1.09 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 * 1.09 * 0.38 * 65.00 = 23.96 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, 23.96, 43.88) = 23.96 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(36.86, 23.96) = 23.96 kips/bolt
Bolt Shear Demand to Bearing ratio = 23.96 / 39.32 = 0.61

Min Bolt Shear Demand to Bearing ratio Beam and Shear Plate for vertical shear only
 = min(1.00, 0.94, 0.92, 0.92, 0.61) = 0.61

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 = 0.61 * 146.63 = 89.35 kips
Rbv = 89.35 kips >= Reaction V = 58.80 kips (OK)

Web Depth = d - [Top Cope Depth] - [Bottom Cope Depth] = 17.90 - 1.50 - 0.00 = 16.40 in.

Using AISC 14th Ed. Equation J4-3
Gross Area (Shear), Agross = [Web Depth] * tw = 16.40 * 0.32 = 5.17 in^2
Shear Yielding, (phi)Vny = (phi) * 0.6 * Fybeam * Agross = 1.00 * 0.6 * 50.00 * 5.17 = 154.98 kips
154.98 kips >= Reaction V = 58.80 kips (OK)

Using AISC 14th Ed. Equation J4-4
Net Area (Shear), Anet = ([Web Depth] - ([# rows] * [Diameter + 0.06])) * tw 
    = (16.40 - (4 * 1.12)) * 0.32 = 3.75 in^2
Shear Rupture, (phi)Vnu = (phi) * 0.6 * Fubeam * Anet = 0.75 * 0.6 * 65.00 * 3.75 = 109.65 kips
109.65 kips >= Reaction V = 58.80 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]) = 2.25 + 9.00 = 11.25 in.
Net Shear Length = Gross Shear Length - (# rows - 0.5) * (hole size + 0.06) = 11.25 - (4 - 0.5) * 1.12 = 7.31 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 * 0.32 * ((0.60 * 65.00 * 7.31) + (1.00 * 65.00 * 1.44)) = 89.45 kips
2. (phi) * [material thickness] * ((0.60 * Fybeam * [gross shear length]) + (Ubs * Fubeam * [net tension length])) 
    = 0.75 * 0.32 * ((0.60 * 50.00 * 11.25) + (1.00 * 65.00 * 1.44)) = 101.81 kips
Block Shear = 89.45 kips

Block Shear (1) Total = Block Shear (1) = 89.45 kips
89.45 kips >= Reaction V = 58.80 kips (OK)

Block Shear for Axial T/C is not required.

Buckling and Flexure at Longest Cope (Top Cope Only at Section)
Eccentricity at Section, e = 6.78 in.
If coped at top/bottom flange only and c <= 2d and dc <= d/2, use AISC 14th Ed. Equation 9-7, Fcr = 26210.00 * f * k * (tw/h1)^2 <= Fy

Using AISC Equations 9-7 through 9-11
tw = 0.32 in.
h1 = 11.11 in.
c = 6.00 in.
When c/h1<=1.0, k=2.2(h1/c)^1.65
k  = 2.20 * (11.11 / 6.00)^1.65 = 6.08
When c/d<=1.0, f=2c/d
f = 2 * (6.00 / 17.90) = 0.67
Fy = 50.00 ksi
Fcr = (phi) * 26210.00 * f * k * (tw/h1)^2 = 0.90 * 26210.00 * 0.67 * 6.08 * (0.32 / 11.11)^2 = 77.28 ksi
Fcrmin =phi * min(Fcr, Fy) = 45.00 ksi
Snet1 (bolt holes not applicable) = 21.17 in^3
Snet2 (bolt holes applicable) = 21.17 in^3
Znet1 (bolt holes not applicable) = 37.83 in^3
Znet2 (bolt holes applicable) = 37.83 in^3

Using AISC 14th Ed. Equation 9-6
Buckling = Fcr * Snet1 / e = 45.00 * 21.17 / 6.78 = 140.64 kips

Using AISC 14th Ed. Equation 9-19
Flexural Yielding = (phi) * Fy * Snet1 / e = 0.90 * 50.00 * 21.17 / 6.78 = 140.64 kips

Using AISC 14th Ed. Equation 9-4
Flexural Rupture = (phi) * Fu * Znet2 / e = 0.75 * 65.00 * 37.83 / 6.78 = 272.25 kips


Buckling and Flexure at Furthest Bolt Line within Cope (Top Cope Only at Section)
Eccentricity at Section, e = 2.77 in.
If coped at top/bottom flange only and c <= 2d and dc <= d/2, use AISC 14th Ed. Equation 9-7, Fcr = 26210.00 * f * k * (tw/h1)^2 <= Fy

Using AISC Equations 9-7 through 9-11
tw = 0.32 in.
h1 = 12.03 in.
c = 6.00 in.
When c/h1<=1.0, k=2.2(h1/c)^1.65
k  = 2.20 * (12.03 / 6.00)^1.65 = 6.93
When c/d<=1.0, f=2c/d
f = 2 * (6.00 / 17.90) = 0.67
Fy = 50.00 ksi
Fcr = (phi) * 26210.00 * f * k * (tw/h1)^2 = 0.90 * 26210.00 * 0.67 * 6.93 * (0.32 / 12.03)^2 = 75.17 ksi
Fcrmin =phi * min(Fcr, Fy) = 45.00 ksi
Snet1 (bolt holes not applicable) = 21.17 in^3
Snet2 (bolt holes applicable) = 15.51 in^3
Znet1 (bolt holes not applicable) = 37.83 in^3
Znet2 (bolt holes applicable) = 27.45 in^3

Using AISC 14th Ed. Equation 9-6
Buckling = Fcr * Snet1 / e = 45.00 * 21.17 / 2.77 = 343.36 kips

Using AISC 14th Ed. Equation 9-19
Flexural Yielding = (phi) * Fy * Snet1 / e = 0.90 * 50.00 * 21.17 / 2.77 = 343.36 kips

Using AISC 14th Ed. Equation 9-4
Flexural Rupture = (phi) * Fu * Znet2 / e = 0.75 * 65.00 * 27.45 / 2.77 = 482.17 kips


Section Bending Strength Calculations Summary:

   Coped Beam Buckling and Flexure at Longest Cope (Top Cope Only at Section)
   Buckling : 140.64 >= 58.80 kips (OK)
   Flexural Yielding : 140.64 >= 58.80 kips (OK)
   Flexural Rupture : 272.25 >= 58.80 kips (OK)

   Coped Beam Buckling and Flexure at Furthest Bolt Line within Cope (Top Cope Only at Section)
   Buckling : 343.36 >= 58.80 kips (OK)
   Flexural Yielding : 343.36 >= 58.80 kips (OK)
   Flexural Rupture : 482.17 >= 58.80 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 = 58.80 kips (OK)

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 = 58.80 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 = 58.80 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 = 1.25 in.
Zgross = 13.50
Znet = 8.44
Mr = Vr * e = 58.80 * 1.25 = 73.50 kips-in
Mc = phi * Mn = phi * Fy * Zgross = 0.90 * 50.00 * 13.50 = 607.50 kips-in
Vr = 58.80 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 = (58.80 / 135.00)^2 + (73.50 / 607.50)^2 = 0.20 <= 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 = 12.00 in.
Shear Load per inch per weld, fv = R/Lv/2 = 58.80 / 12.00 / 2 = 2.45 kips/in/ weld 
theta = 0 deg.
cPhi  = 1.0 + 0.5 * sin(0)^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) = 2.45 / (0.75 * 1.86) = 1.76/16

Minimum fillet weld size : 
   At shear only load case = 0.11 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 )
 = 0.55 * 65.00 / ( 70.00 * 1.00 * 0.09 ) 
 = 5.78 
Dmax3 = project max fillet weld = 12.00
Dmax=min(Dmax1, Dmax2, Dmax3) = min(3.94, 5.78, 12.00)
 = 3.94 

Use weld size
D1 = 4.00
D2 = 4.00

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 = 58.80 kips (OK)