bcf.s.s.01148.01183

SHEAR PLATE CONNECTION SUMMARY

Filler Beam profile: W18X35
Column profile: W14X90
Slope: 0.00 deg.
Skew: 74.90
Vertical Offset: 0.00 in.
Horizontal Offset: 0.00 in.
Span: 11.09 ft.
Reaction, V: 40.00 kips
Shear Capacity, Rn: 84.71 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: 3.62 in. x 14.50 in. x 0.38 in.
Configuration Geometry:
Welds at shear plate to support: 4/16 FILLET, 6/16 FILLET
Bolt: 5 rows x 1 column 0.75 in. Diameter A325N_TC bolts
Vertical spacing: 3.00 in.
Horizontal spacing: 3.00 in.
Shear plate edge setback = 0.62 in.
Beam centerline setback = 0.77 in.
Edge distance at vertical edge of plate: 1.50 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: 1.50 in.
Horizontal distance to first hole: 2.12 in.
Down distance from top of filler beam flange: 3.00 in.
Holes in beam web: STD diameter = 0.81 in.
Holes in shear plate: SSL diameter = 0.81 in., slot width = 1.00 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 = 1.11 in.
Angle = 0.00 deg.
C = 4.73
Using Table 7-1 to determine (phi)rn:
(phi)Rn = (phi)rn * C = 17.89 * 4.73 = 84.71 kips


Total Vertical Bolt Shear Capacity = 84.71 kips
84.71 kips >= Reaction V = 40.00 kips (OK)

BOLT BEARING AT BEAM AND SHEAR PLATE SIDE
Vertical Shear Only Load Case:
ICR cordinate relative to CG = (15.82, 0.00)
At Row 1, At Column 1:
Ribolt = 17.56 kips
Ri vector at Beam   = <6.23, 16.42>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 2.80 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 * 2.80 * (0.30/1) * 65.00 = 49.18 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.75 * (0.30/1) * 65.00 = 26.33 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(na, 49.18, 26.33) = 26.33 kips/bolt
Ri vector at Shear Plate   = <-6.23, -16.42>
Lcsshpl at Shear Plate spacing  = na
Lceshpl at Shear Plate edge    = 5.56 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 * 5.56 * 0.38 * 65.00 = 121.92 kips/bolt
(phi)Rndshpl on Shear Plate at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.75 * 0.38 * 65.00 = 32.91 kips/bolt
Shear Plate bearing capacity, (phi)Rnshpl = min((phi)Rnsshpl,(phi)Rneshpl,(phi)Rndshpl) = min(na, 121.92, 32.91) = 32.91 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(26.33, 32.91) = 26.33 kips/bolt
Bolt Shear Demand to Bearing ratio = 26.33 / 17.56 = 1.50

At Row 2, At Column 1:
Ribolt = 17.50 kips
Ri vector at Beam   = <3.26, 17.20>
Lcsbm at Beam spacing  = 2.19 in.
Lcebm at Beam edge    = 5.70 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.75 * 1.20 * 2.19 * (0.30/1) * 65.00 = 38.39 kips/bolt
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 5.70 * (0.30/1) * 65.00 = 100.05 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.75 * (0.30/1) * 65.00 = 26.33 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(38.39, 100.05, 26.33) = 26.33 kips/bolt
Ri vector at Shear Plate   = <-3.26, -17.20>
Lcsshpl at Shear Plate spacing  = 2.19 in.
Lceshpl at Shear Plate edge    = 10.02 in.
(phi)Rnsshpl at Shear Plate spacing = (phi) * hf1 * Lcs * t * Fu = 0.75 * 1.20 * 2.19 * 0.38 * 65.00 = 47.99 kips/bolt
(phi)Rneshpl at Shear Plate edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 10.02 * 0.38 * 65.00 = 219.80 kips/bolt
(phi)Rndshpl on Shear Plate at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.75 * 0.38 * 65.00 = 32.91 kips/bolt
Shear Plate bearing capacity, (phi)Rnshpl = min((phi)Rnsshpl,(phi)Rneshpl,(phi)Rndshpl) = min(47.99, 219.80, 32.91) = 32.91 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(26.33, 32.91) = 26.33 kips/bolt
Bolt Shear Demand to Bearing ratio = 26.33 / 17.50 = 1.50

At Row 3, At Column 1:
Ribolt = 17.48 kips
Ri vector at Beam   = <-0.00, 17.48>
Lcsbm at Beam spacing  = 2.19 in.
Lcebm at Beam edge    = 8.59 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.75 * 1.20 * 2.19 * (0.30/1) * 65.00 = 38.39 kips/bolt
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 8.59 * (0.30/1) * 65.00 = 150.82 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.75 * (0.30/1) * 65.00 = 26.33 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(38.39, 150.82, 26.33) = 26.33 kips/bolt
Ri vector at Shear Plate   = <0.00, -17.48>
Lcsshpl at Shear Plate spacing  = 2.19 in.
Lceshpl at Shear Plate edge    = 6.84 in.
(phi)Rnsshpl at Shear Plate spacing = (phi) * hf1 * Lcs * t * Fu = 0.75 * 1.20 * 2.19 * 0.38 * 65.00 = 47.99 kips/bolt
(phi)Rneshpl at Shear Plate edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 6.84 * 0.38 * 65.00 = 150.14 kips/bolt
(phi)Rndshpl on Shear Plate at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.75 * 0.38 * 65.00 = 32.91 kips/bolt
Shear Plate bearing capacity, (phi)Rnshpl = min((phi)Rnsshpl,(phi)Rneshpl,(phi)Rndshpl) = min(47.99, 150.14, 32.91) = 32.91 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(26.33, 32.91) = 26.33 kips/bolt
Bolt Shear Demand to Bearing ratio = 26.33 / 17.48 = 1.51

At Row 4, At Column 1:
Ribolt = 17.50 kips
Ri vector at Beam   = <-3.26, 17.20>
Lcsbm at Beam spacing  = 2.19 in.
Lcebm at Beam edge    = 7.64 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.75 * 1.20 * 2.19 * (0.30/1) * 65.00 = 38.39 kips/bolt
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 7.64 * (0.30/1) * 65.00 = 134.15 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.75 * (0.30/1) * 65.00 = 26.33 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(38.39, 134.15, 26.33) = 26.33 kips/bolt
Ri vector at Shear Plate   = <3.26, -17.20>
Lcsshpl at Shear Plate spacing  = 2.19 in.
Lceshpl at Shear Plate edge    = 3.91 in.
(phi)Rnsshpl at Shear Plate spacing = (phi) * hf1 * Lcs * t * Fu = 0.75 * 1.20 * 2.19 * 0.38 * 65.00 = 47.99 kips/bolt
(phi)Rneshpl at Shear Plate edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 3.91 * 0.38 * 65.00 = 85.83 kips/bolt
(phi)Rndshpl on Shear Plate at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.75 * 0.38 * 65.00 = 32.91 kips/bolt
Shear Plate bearing capacity, (phi)Rnshpl = min((phi)Rnsshpl,(phi)Rneshpl,(phi)Rndshpl) = min(47.99, 85.83, 32.91) = 32.91 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(26.33, 32.91) = 26.33 kips/bolt
Bolt Shear Demand to Bearing ratio = 26.33 / 17.50 = 1.50

At Row 5, At Column 1:
Ribolt = 17.56 kips
Ri vector at Beam   = <-6.23, 16.42>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 3.82 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 * 3.82 * (0.30/1) * 65.00 = 67.10 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.75 * (0.30/1) * 65.00 = 26.33 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(na, 67.10, 26.33) = 26.33 kips/bolt
Ri vector at Shear Plate   = <6.23, -16.42>
Lcsshpl at Shear Plate spacing  = na
Lceshpl at Shear Plate edge    = 0.90 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 * 0.90 * 0.38 * 65.00 = 19.80 kips/bolt
(phi)Rndshpl on Shear Plate at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.75 * 0.38 * 65.00 = 32.91 kips/bolt
Shear Plate bearing capacity, (phi)Rnshpl = min((phi)Rnsshpl,(phi)Rneshpl,(phi)Rndshpl) = min(na, 19.80, 32.91) = 19.80 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(26.33, 19.80) = 19.80 kips/bolt
Bolt Shear Demand to Bearing ratio = 19.80 / 17.56 = 1.13

Min Bolt Shear Demand to Bearing ratio Beam and Shear Plate for vertical shear only
 = min(1.00, 1.50, 1.50, 1.51, 1.50, 1.13) = 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 * 84.71 = 84.71 kips
Rbv = 84.71 kips >= Reaction V = 40.00 kips (OK)

Web Depth = d - [Top Cope Depth] - [Bottom Cope Depth] = 17.70 - 0.00 - 0.00 = 17.70 in.

Using AISC 14th Ed. Equation J4-3
Gross Area (Shear), Agross = [Web Depth] * tw = 17.70 * 0.30 = 5.31 in^2
Shear Yielding, (phi)Vny = (phi) * 0.6 * Fybeam * Agross = 1.00 * 0.6 * 50.00 * 5.31 = 159.30 kips

Using AISC 14th Ed. Equation J4-4
Net Area (Shear), Anet = ([Web Depth] - ([# rows] * [Diameter + 0.06])) * tw 
    = (17.70 - (5 * 0.88)) * 0.30 = 4.00 in^2
Shear Rupture, (phi)Vnu = (phi) * 0.6 * Fubeam * Anet = 0.75 * 0.6 * 65.00 * 4.00 = 116.93 kips


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 * 14.50 = 5.44 in^2
Shear Yielding, (phi)Vny = (phi) * 0.6 * Fypl * Ag = 1.00 * 0.6 * 50.00 * 5.44 = 163.12 kips

163.12 kips >= Reaction V = 40.00 kips (OK)

Using AISC 14th Ed. Equation J4-4
Net Area, An = (14.50 - (5 * (0.81 + 1/16))) * 0.38 = 3.80 in^2
Shear Rupture, (phi)Vnu = (phi) * 0.6 * Fupl * An = 0.75 * 0.6 * 65.00 * 3.80 = 111.06 kips

111.06 kips >= Reaction V = 40.00 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 = (14.50 - 1.25) = 13.25 in.
Net Shear Length = 13.25 - (4.50 * (0.81 + 0.06)) = 9.31 in.
Gross Tension Length = (0.00 + 1.50) = 1.50 in.
Net Tension Length = 1.50 - (0.50 * (1.00 + 0.06)) = 0.97 in.
1. (phi) * [material thickness] * ((0.60 * Fupl* [net shear length]) + (Ubs * Fupl * [net tension length])) 
    = 0.75 * 0.38 * ((0.60 * 65.00 * 9.31) + (1.00 * 65.00 * 0.97)) = 119.86 kips
2. (phi) * [material thickness] * ((0.60 * Fypl * [gross shear length]) + (Ubs * Fupl * [net tension length])) 
    = 0.75 * 0.38 * ((0.60 * 50.00 * 13.25) + (1.00 * 65.00 * 0.97)) = 129.51 kips
Block Shear = 119.86 kips
119.86 kips >= Reaction V = 40.00 kips (OK)

Block Shear for Axial T/C is not required.

Interaction Check of Flexural Yielding, Per AISC 10-5: 
Eccentricity due to Conventional Config. (e = a/2), e = 1.11 in.
Zgross = 19.71
Znet = 13.73
Mr = Vr * e = 40.00 * 1.11 = 44.52 kips-in
Mc = phi * Mn = phi * Fy * Zgross = 0.90 * 50.00 * 19.71 = 886.99 kips-in
Vr = 40.00 kips
Vc = phi * Vn = phi * 0.60 * Fy * Ag = 1.00 * 0.60 * 50.00 * 5.44 = 163.12 kips
Interaction due to moment and shear, (Vr/Vc)^2 + (Mr/Mc)^2 <= 1.0
(Vr/Vc)^2 + (Mr/Mc)^2 = (40.00 / 163.12)^2 + (44.52 / 886.99)^2 = 0.06 <= 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 = 14.50 in.
Shear Load per inch per weld, fv = R/Lv/2 = 40.00 / 14.50 / 2 = 1.38 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) = 1.38 / (0.75 * 1.86) = 0.99/16

Minimum fillet weld size : 
   At shear only load case = 0.06 in.
   per Table J2.4     = 0.19 in.
   5/8tp              = 0.23 in.
   user preference    = 0.25 in.

Dmax1 (using eqn 9-3)
 = tshpl * Fushpl / ( Fexx * C1 * 0.09)
 = 0.38 * 65.00 / ( 70.00 * 1.00 * 0.09 ) 
 = 3.94 
Dmax2 (using 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 = 74.90 deg.
Gap on Obtuse Angle Side if No Bevel = 0.10 in.
Use weld size
Acute Side  D1 = 4.00
Obtuse Side D2 = 6.00 (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 * 14.50 * (3.94 + 3.94) = 159.05 kips

159.05 kips >= Reaction V = 40.00 kips (OK)

Check Effective Throat:
Acute Side Effect throat  = (D1/sin(DA)) * cos(DA/2) = (0.25/ sin( 74.90)) * cos( 37.45) = 0.21 in.
Obtuse Side Effect throat = (D2/sin(DA)-tshpl/tan(DA))*sin(DA/2) = (0.38 / sin(74.90) - 0.38 / tan(74.90)) * sin(74.90 / 2) = 0.17 in.
Total Effective Throat    = 0.21 + 0.17 = 0.38 in.
Total Effective Throat of Square Case = 5/8tp * 2^0.5 = 0.23 * 2^0.5 = 0.33 in.
0.38 >= 0.33 (OK)