bcf.s.s.01377.01392

SHEAR PLATE CONNECTION SUMMARY

Filler Beam profile: W18X40
Column profile: W14X90
Slope: 0.00 deg.
Skew: 82.90
Vertical Offset: 0.00 in.
Horizontal Offset: 0.00 in.
Span: 16.96 ft.
Reaction, V: 69.33 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 = 0.57 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.
Horizontal distance to first hole: 2.50 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 7-1)
ex = 1.27 in.
Angle = 0.00 deg.
C = 3.65
Using Table 7-1 to determine (phi)rn:
(phi)Rn = (phi)rn * C = 40.06 * 3.65 = 146.26 kips


Total Vertical Bolt Shear Capacity = 146.26 kips
146.26 kips >= Reaction V = 69.33 kips (OK)

BOLT BEARING AT BEAM AND SHEAR PLATE SIDE
Vertical Shear Only Load Case:
ICR cordinate relative to CG = (8.48, -0.00)
At Row 1, At Column 1:
Ribolt = 39.32 kips
Ri vector at Beam   = <18.43, 34.73>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 2.87 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 * 2.87 * (0.32/1) * 65.00 = 52.80 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, 52.80, 36.86) = 36.86 kips/bolt
Ri vector at Shear Plate   = <-18.43, -34.73>
Lcsshpl at Shear Plate spacing  = na
Lceshpl at Shear Plate edge    = 4.73 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 * 4.73 * 0.38 * 65.00 = 103.78 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, 103.78, 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 = 39.00 kips
Ri vector at Beam   = <6.80, 38.40>
Lcsbm at Beam spacing  = 1.94 in.
Lcebm at Beam edge    = 5.56 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 * 5.56 * (0.32/1) * 65.00 = 102.50 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, 102.50, 36.86) = 35.70 kips/bolt
Ri vector at Shear Plate   = <-6.80, -38.40>
Lcsshpl at Shear Plate spacing  = 1.94 in.
Lceshpl at Shear Plate edge    = 7.08 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 * 7.08 * 0.38 * 65.00 = 155.26 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, 155.26, 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 / 39.00 = 0.92

At Row 3, At Column 1:
Ribolt = 39.00 kips
Ri vector at Beam   = <-6.80, 38.40>
Lcsbm at Beam spacing  = 1.94 in.
Lcebm at Beam edge    = 8.61 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 * 8.61 * (0.32/1) * 65.00 = 158.64 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, 158.64, 36.86) = 35.70 kips/bolt
Ri vector at Shear Plate   = <6.80, -38.40>
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 = 88.42 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, 88.42, 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 / 39.00 = 0.92

At Row 4, At Column 1:
Ribolt = 39.32 kips
Ri vector at Beam   = <-18.43, 34.73>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 3.73 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 * 3.73 * (0.32/1) * 65.00 = 68.82 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, 68.82, 36.86) = 36.86 kips/bolt
Ri vector at Shear Plate   = <18.43, -34.73>
Lcsshpl at Shear Plate spacing  = na
Lceshpl at Shear Plate edge    = 1.10 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 * 1.10 * 0.38 * 65.00 = 24.06 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, 24.06, 43.88) = 24.06 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(36.86, 24.06) = 24.06 kips/bolt
Bolt Shear Demand to Bearing ratio = 24.06 / 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 * 146.26 = 89.51 kips
Rbv = 89.51 kips >= Reaction V = 69.33 kips (OK)

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

Using AISC 14th Ed. Equation J4-3
Gross Area (Shear), Agross = [Web Depth] * tw = 17.90 * 0.32 = 5.64 in^2
Shear Yielding, (phi)Vny = (phi) * 0.6 * Fybeam * Agross = 1.00 * 0.6 * 50.00 * 5.64 = 169.16 kips
169.16 kips >= Reaction V = 69.33 kips (OK)

Using AISC 14th Ed. Equation J4-4
Net Area (Shear), Anet = ([Web Depth] - ([# rows] * [Diameter + 0.06])) * tw 
    = (17.90 - (4 * 1.12)) * 0.32 = 4.22 in^2
Shear Rupture, (phi)Vnu = (phi) * 0.6 * Fubeam * Anet = 0.75 * 0.6 * 65.00 * 4.22 = 123.47 kips
123.47 kips >= Reaction V = 69.33 kips (OK)


Check Horizontal 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 for Axial T/C is not required.

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 = 69.33 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 = 69.33 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 = 69.33 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 = 1.27 in.
Zgross = 13.50
Znet = 8.44
Mr = Vr * e = 69.33 * 1.27 = 88.29 kips-in
Mc = phi * Mn = phi * Fy * Zgross = 0.90 * 50.00 * 13.50 = 607.50 kips-in
Vr = 69.33 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 = (69.33 / 135.00)^2 + (88.29 / 607.50)^2 = 0.28 <= 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 = 69.33 / 12.00 / 2 = 2.89 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) = 2.89 / (0.75 * 1.86) = 2.08/16

Minimum fillet weld size : 
   At shear only load case = 0.13 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 9-2)
 = tfcol * Fusupport / ( Fexx * C1 * 0.04 )
 = 0.71 * 65.00 / ( 70.00 * 1.00 * 0.04 ) 
 = 14.92 
Dmax3 = project max fillet weld = 12.00
Dmax=min(Dmax1, Dmax2, Dmax3) = min(3.94, 14.92, 12.00)
 = 3.94 

Dihedral Angle, DA = 82.90 deg.
Gap on Obtuse Angle Side if No Bevel = 0.05 in.
Use weld size
Acute Side  D1 = 4.00
Obtuse Side D2 = 4.00 (weld size is not increased on obtuse side for gap at skew less 1/16 in (2mm) 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 = 69.33 kips (OK)

Check Effective Throat:
Acute Side Effect throat  = (D1/sin(DA)) * cos(DA/2) = (0.25/ sin( 82.90)) * cos( 41.45) = 0.19 in.
Obtuse Side Effect throat (with gap < 1/16 in (2mm)) = D2/sin(DA)*sin(DA/2) = 0.25 / sin(82.90) * sin(82.90 / 2) = 0.17 in.
Total Effective Throat    = 0.19 + 0.17 = 0.36 in.
Total Effective Throat of Square Case = 5/8tp * 2^0.5 = 0.23 * 2^0.5 = 0.33 in.
0.36 >= 0.33 (OK)