bb.s.s.01149.01219

SHEAR PLATE CONNECTION SUMMARY

NOTE: DESIGNED WITH MEMBERS CHOSEN ON ONLY ONE SIDE OF SUPPORT

Filler Beam profile: W16X31
Support Girder profile: W18X35
Slope: 0.00 deg.
Skew: 74.90
Vertical Offset: 0.00 in.
Horizontal Offset: 0.00 in.
Span: 4.10 ft.
Reaction, V: 30.00 kips
Shear Capacity, Rn: 66.42 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 11.50 in. x 0.38 in.
Configuration Geometry:
Welds at shear plate to support: 4/16 FILLET, 6/16 FILLET
Bolt: 4 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 = 0.76 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.
Edge distance at top edge of beam: 2.00 in.
Top cope depth: 1.00 in.
Top cope length: 3.00 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 = 3.71
Using Table 7-1 to determine (phi)rn:
(phi)Rn = (phi)rn * C = 17.89 * 3.71 = 66.42 kips


Total Vertical Bolt Shear Capacity = 66.42 kips
66.42 kips >= Reaction V = 30.00 kips (OK)

BOLT BEARING AT BEAM AND SHEAR PLATE SIDE
Vertical Shear Only Load Case:
ICR cordinate relative to CG = (9.79, 0.00)
At Row 1, At Column 1:
Ribolt = 17.56 kips
Ri vector at Beam   = <7.33, 15.96>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 1.79 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 * 1.79 * (0.28/1) * 65.00 = 28.88 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.75 * (0.28/1) * 65.00 = 24.13 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(na, 28.88, 24.13) = 24.13 kips/bolt
Ri vector at Shear Plate   = <-7.33, -15.96>
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 = 101.83 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(na, 101.83, 32.91) = 32.91 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(24.13, 32.91) = 24.13 kips/bolt
Bolt Shear Demand to Bearing ratio = 24.13 / 17.56 = 1.37

At Row 2, At Column 1:
Ribolt = 17.46 kips
Ri vector at Beam   = <2.64, 17.25>
Lcsbm at Beam spacing  = 2.19 in.
Lcebm at Beam edge    = 4.65 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.75 * 1.20 * 2.19 * (0.28/1) * 65.00 = 35.19 kips/bolt
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 4.65 * (0.28/1) * 65.00 = 74.84 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.75 * (0.28/1) * 65.00 = 24.13 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(35.19, 74.84, 24.13) = 24.13 kips/bolt
Ri vector at Shear Plate   = <-2.64, -17.25>
Lcsshpl at Shear Plate spacing  = 2.19 in.
Lceshpl at Shear Plate edge    = 6.92 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 * 6.92 * 0.38 * 65.00 = 151.89 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, 151.89, 32.91) = 32.91 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(24.13, 32.91) = 24.13 kips/bolt
Bolt Shear Demand to Bearing ratio = 24.13 / 17.46 = 1.38

At Row 3, At Column 1:
Ribolt = 17.46 kips
Ri vector at Beam   = <-2.65, 17.25>
Lcsbm at Beam spacing  = 2.19 in.
Lcebm at Beam edge    = 7.69 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.75 * 1.20 * 2.19 * (0.28/1) * 65.00 = 35.19 kips/bolt
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 7.69 * (0.28/1) * 65.00 = 123.67 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.75 * (0.28/1) * 65.00 = 24.13 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(35.19, 123.67, 24.13) = 24.13 kips/bolt
Ri vector at Shear Plate   = <2.65, -17.25>
Lcsshpl at Shear Plate spacing  = 2.19 in.
Lceshpl at Shear Plate edge    = 3.89 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 * 3.89 * 0.38 * 65.00 = 85.31 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, 85.31, 32.91) = 32.91 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(24.13, 32.91) = 24.13 kips/bolt
Bolt Shear Demand to Bearing ratio = 24.13 / 17.46 = 1.38

At Row 4, At Column 1:
Ribolt = 17.56 kips
Ri vector at Beam   = <-7.34, 15.96>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 3.18 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 * 3.18 * (0.28/1) * 65.00 = 51.23 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.75 * (0.28/1) * 65.00 = 24.13 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(na, 51.23, 24.13) = 24.13 kips/bolt
Ri vector at Shear Plate   = <7.34, -15.96>
Lcsshpl at Shear Plate spacing  = na
Lceshpl at Shear Plate edge    = 0.93 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 * 0.93 * 0.38 * 65.00 = 20.37 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, 20.37, 32.91) = 20.37 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(24.13, 20.37) = 20.37 kips/bolt
Bolt Shear Demand to Bearing ratio = 20.37 / 17.56 = 1.16

Min Bolt Shear Demand to Bearing ratio Beam and Shear Plate for vertical shear only
 = min(1.00, 1.37, 1.38, 1.38, 1.16) = 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 * 66.42 = 66.42 kips
Rbv = 66.42 kips >= Reaction V = 30.00 kips (OK)

Web Depth = d - [Top Cope Depth] - [Bottom Cope Depth] = 15.90 - 1.00 - 0.00 = 14.90 in.

Using AISC 14th Ed. Equation J4-3
Gross Area (Shear), Agross = [Web Depth] * tw = 14.90 * 0.28 = 4.10 in^2
Shear Yielding, (phi)Vny = (phi) * 0.6 * Fybeam * Agross = 1.00 * 0.6 * 50.00 * 4.10 = 122.93 kips

Using AISC 14th Ed. Equation J4-4
Net Area (Shear), Anet = ([Web Depth] - ([# rows] * [Diameter + 0.06])) * tw 
    = (14.90 - (4 * 0.88)) * 0.28 = 3.14 in^2
Shear Rupture, (phi)Vnu = (phi) * 0.6 * Fubeam * Anet = 0.75 * 0.6 * 65.00 * 3.14 = 91.70 kips


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]) = 2.00 + 9.00 = 11.00 in.
Net Shear Length = Gross Shear Length - (# rows - 0.5) * (hole size + 0.06) = 11.00 - (4 - 0.5) * 0.88 = 7.94 in.
Gross Tension Length = [edge dist. at beam edge] + ([# cols - 1] * [spacing]) = 1.50 + (1 - 1) * 3.00 = 1.50 in.
Net Tension Length = Gross Tension Length - (# cols - 0.5) * (hole size + 0.06) = 1.50 - (1 - 0.5) * 0.88 = 1.06 in.
1. (phi) * [material thickness] * ((0.60 * Fubeam* [net shear length]) + (Ubs * Fubeam * [net tension length])) 
    = 0.75 * 0.28 * ((0.60 * 65.00 * 7.94) + (1.00 * 65.00 * 1.06)) = 78.09 kips
2. (phi) * [material thickness] * ((0.60 * Fybeam * [gross shear length]) + (Ubs * Fubeam * [net tension length])) 
    = 0.75 * 0.28 * ((0.60 * 50.00 * 11.00) + (1.00 * 65.00 * 1.06)) = 82.31 kips
Block Shear = 78.09 kips

Block Shear (1) Total = Block Shear (1) = 78.09 kips
78.09 kips >= Reaction V = 30.00 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 = 3.83 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 = 0.28 in.
h1 = 10.06 in.
c = 3.00 in.
When c/h1<=1.0, k=2.2(h1/c)^1.65
k  = 2.20 * (10.06 / 3.00)^1.65 = 16.19
When c/d<=1.0, f=2c/d
f = 2 * (3.00 / 15.90) = 0.38
Fy = 50.00 ksi
Fcr = (phi) * 26210.00 * f * k * (tw/h1)^2 = 0.90 * 26210.00 * 0.38 * 16.19 * (0.28 / 10.06)^2 = 107.75 ksi
Fcrmin =phi * min(Fcr, Fy) = 45.00 ksi
Snet1 (bolt holes not applicable) = 15.22 in^3
Snet2 (bolt holes applicable) = 15.22 in^3
Znet1 (bolt holes not applicable) = 27.12 in^3
Znet2 (bolt holes applicable) = 27.12 in^3

Using AISC 14th Ed. Equation 9-6
Buckling = Fcr * Snet1 / e = 45.00 * 15.22 / 3.83 = 178.81 kips

Using AISC 14th Ed. Equation 9-19
Flexural Yielding = (phi) * Fy * Snet1 / e = 0.90 * 50.00 * 15.22 / 3.83 = 178.81 kips

Using AISC 14th Ed. Equation 9-4
Flexural Rupture = (phi) * Fu * Znet2 / e = 0.75 * 65.00 * 27.12 / 3.83 = 345.12 kips


Buckling and Flexure at Furthest Bolt Line within Cope (Top Cope Only at Section)
Eccentricity at Section, e = 2.33 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 = 0.28 in.
h1 = 10.69 in.
c = 3.00 in.
When c/h1<=1.0, k=2.2(h1/c)^1.65
k  = 2.20 * (10.69 / 3.00)^1.65 = 17.90
When c/d<=1.0, f=2c/d
f = 2 * (3.00 / 15.90) = 0.38
Fy = 50.00 ksi
Fcr = (phi) * 26210.00 * f * k * (tw/h1)^2 = 0.90 * 26210.00 * 0.38 * 17.90 * (0.28 / 10.69)^2 = 105.49 ksi
Fcrmin =phi * min(Fcr, Fy) = 45.00 ksi
Snet1 (bolt holes not applicable) = 15.22 in^3
Snet2 (bolt holes applicable) = 11.97 in^3
Znet1 (bolt holes not applicable) = 27.12 in^3
Znet2 (bolt holes applicable) = 21.32 in^3

Using AISC 14th Ed. Equation 9-6
Buckling = Fcr * Snet1 / e = 45.00 * 15.22 / 2.33 = 293.88 kips

Using AISC 14th Ed. Equation 9-19
Flexural Yielding = (phi) * Fy * Snet1 / e = 0.90 * 50.00 * 15.22 / 2.33 = 293.88 kips

Using AISC 14th Ed. Equation 9-4
Flexural Rupture = (phi) * Fu * Znet2 / e = 0.75 * 65.00 * 21.32 / 2.33 = 445.84 kips


Section Bending Strength Calculations Summary:

   Coped Beam Buckling and Flexure at Longest Cope (Top Cope Only at Section)
   Buckling : 178.81 >= 30.00 kips (OK)
   Flexural Yielding : 178.81 >= 30.00 kips (OK)
   Flexural Rupture : 345.12 >= 30.00 kips (OK)

   Coped Beam Buckling and Flexure at Furthest Bolt Line within Cope (Top Cope Only at Section)
   Buckling : 293.88 >= 30.00 kips (OK)
   Flexural Yielding : 293.88 >= 30.00 kips (OK)
   Flexural Rupture : 445.84 >= 30.00 kips (OK)

Using AISC 14th Ed. Equation J4-3
Gross Area, Ag = 0.38 * 11.50 = 4.31 in^2
Shear Yielding, (phi)Vny = (phi) * 0.6 * Fypl * Ag = 1.00 * 0.6 * 50.00 * 4.31 = 129.38 kips

129.38 kips >= Reaction V = 30.00 kips (OK)

Using AISC 14th Ed. Equation J4-4
Net Area, An = (11.50 - (4 * (0.81 + 1/16))) * 0.38 = 3.00 in^2
Shear Rupture, (phi)Vnu = (phi) * 0.6 * Fupl * An = 0.75 * 0.6 * 65.00 * 3.00 = 87.75 kips

87.75 kips >= Reaction V = 30.00 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 = (11.50 - 1.25) = 10.25 in.
Net Shear Length = 10.25 - (3.50 * (0.81 + 0.06)) = 7.19 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 * 7.19) + (1.00 * 65.00 * 0.97)) = 96.55 kips
2. (phi) * [material thickness] * ((0.60 * Fypl * [gross shear length]) + (Ubs * Fupl * [net tension length])) 
    = 0.75 * 0.38 * ((0.60 * 50.00 * 10.25) + (1.00 * 65.00 * 0.97)) = 104.20 kips
Block Shear = 96.55 kips
96.55 kips >= Reaction V = 30.00 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 = 1.11 in.
Zgross = 12.40
Znet = 8.46
Mr = Vr * e = 30.00 * 1.11 = 33.39 kips-in
Mc = phi * Mn = phi * Fy * Zgross = 0.90 * 50.00 * 12.40 = 557.93 kips-in
Vr = 30.00 kips
Vc = phi * Vn = phi * 0.60 * Fy * Ag = 1.00 * 0.60 * 50.00 * 4.31 = 129.38 kips
Interaction due to moment and shear, (Vr/Vc)^2 + (Mr/Mc)^2 <= 1.0
(Vr/Vc)^2 + (Mr/Mc)^2 = (30.00 / 129.38)^2 + (33.39 / 557.93)^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 = 11.50 in.
Shear Load per inch per weld, fv = R/Lv/2 = 30.00 / 11.50 / 2 = 1.30 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) = 1.30 / (0.75 * 1.86) = 0.94/16

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 9-3)
 = twbm * Fusupport / ( Fexx * C1 * 0.09 )
 = 0.30 * 65.00 / ( 70.00 * 1.00 * 0.09 ) 
 = 3.15 
Dmax3 = project max fillet weld = 12.00
Dmax=min(Dmax1, Dmax2, Dmax3) = min(3.94, 3.15, 12.00)
 = 3.15 

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 * 11.50 * (3.15 + 3.15) = 100.92 kips

100.92 kips >= Reaction V = 30.00 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)