bb.s.s.01028.01028

SHEAR PLATE CONNECTION SUMMARY

Filler Beam profile: W18X40
Support Girder profile: W21X111
Slope: -0.641 deg.
Skew: 90
Vertical Offset: 2.68
Horizontal Offset: 0
Span: 20 ft.
Reaction, V: 26 kips
Shear Capacity, Rn: 72.1 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: 4.250 in. x 11.500 in. x 0.375 in.
Configuration Geometry:
Welds at shear plate to support: 4/16 FILLET, 4/16 FILLET
Bolt: 4 rows x 1 column 0.875 in. Diameter A325N_TC bolts
Vertical spacing: 3 in.
Horizontal spacing: 3 in.
Shear plate edge setback = 0.617 in.
Beam centerline setback = 0.617 in.
Edge distance at vertical edge of plate: 1.75 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 at top bolt: 1.75 in.
Edge distance at vertical edge of beam at bottom bolt: 1.85 in.
Edge distance at top edge of beam: 1.75 in.
Top cope depth: 4.25 in.
Top cope length: 5.75 in.
Horizontal distance to first hole: 2.5 in.
Down distance from top of filler beam flange: 6 in.
Holes in beam web: STD diameter = 0.938 in.
Holes in shear plate: SSL diameter = 0.938 in., slot width = 1.12 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 = 1.250 in.
Angle = 0.000 deg.
C = 3.661
Using Table 7-1 to determine (phi)rn:
(phi)Rn = (phi)rn * C = 24.35 * 3.66 = 89.15 kips


Total Vertical Bolt Shear Capacity = 89.15 kips
89.15 kips >= 26.00 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 = 23.90 kips
Ri vector at Beam   = <11.03, 21.21>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 1.49 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.75 * 1.20 * na * (0.32/1) * 65.00 = na
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 1.49 * (0.32/1) * 65.00 = 27.51 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.88 * (0.32/1) * 65.00 = 32.25 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(na, 27.51, 32.25) = 27.51 kips/bolt
Ri vector at Shear Plate   = <-11.03, -21.21>
Lcsshpl at Shear Plate spacing  = na
Lceshpl at Shear Plate edge    = 4.89 in.
(phi)Rnsshpl at Shear Plate spacing = (phi) * hf1 * Lcs * t * Fu = 0.75 * 1.20 * na * 0.38 * 65.00 = na
(phi)Rneshpl at Shear Plate edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 4.89 * 0.38 * 65.00 = 107.24 kips/bolt
(phi)Rndshpl on Shear Plate at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.88 * 0.38 * 65.00 = 38.39 kips/bolt
Shear Plate bearing capacity, (phi)Rnshpl = min((phi)Rnsshpl,(phi)Rneshpl,(phi)Rndshpl) = min(na, 107.24, 38.39) = 38.39 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(27.506, 38.392) = 27.51 kips/bolt
Bolt Shear Demand to Bearing ratio = 27.51 / 23.90 = 1.15

At Row 2, At Column 1:
Ribolt = 23.72 kips
Ri vector at Beam   = <4.05, 23.37>
Lcsbm at Beam spacing  = 2.06 in.
Lcebm at Beam edge    = 4.34 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.75 * 1.20 * 2.06 * (0.32/1) * 65.00 = 38.01 kips/bolt
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 4.34 * (0.32/1) * 65.00 = 80.03 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.88 * (0.32/1) * 65.00 = 32.25 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(38.01, 80.03, 32.25) = 32.25 kips/bolt
Ri vector at Shear Plate   = <-4.05, -23.37>
Lcsshpl at Shear Plate spacing  = 2.06 in.
Lceshpl at Shear Plate edge    = 6.88 in.
(phi)Rnsshpl at Shear Plate spacing = (phi) * hf1 * Lcs * t * Fu = 0.75 * 1.20 * 2.06 * 0.38 * 65.00 = 45.25 kips/bolt
(phi)Rneshpl at Shear Plate edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 6.88 * 0.38 * 65.00 = 150.99 kips/bolt
(phi)Rndshpl on Shear Plate at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.88 * 0.38 * 65.00 = 38.39 kips/bolt
Shear Plate bearing capacity, (phi)Rnshpl = min((phi)Rnsshpl,(phi)Rneshpl,(phi)Rndshpl) = min(45.25, 150.99, 38.39) = 38.39 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(32.249, 38.392) = 32.25 kips/bolt
Bolt Shear Demand to Bearing ratio = 32.25 / 23.72 = 1.36

At Row 3, At Column 1:
Ribolt = 23.72 kips
Ri vector at Beam   = <-4.05, 23.37>
Lcsbm at Beam spacing  = 2.06 in.
Lcebm at Beam edge    = 7.41 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.75 * 1.20 * 2.06 * (0.32/1) * 65.00 = 38.01 kips/bolt
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 7.41 * (0.32/1) * 65.00 = 136.59 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.88 * (0.32/1) * 65.00 = 32.25 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(38.01, 136.59, 32.25) = 32.25 kips/bolt
Ri vector at Shear Plate   = <4.05, -23.37>
Lcsshpl at Shear Plate spacing  = 2.06 in.
Lceshpl at Shear Plate edge    = 3.84 in.
(phi)Rnsshpl at Shear Plate spacing = (phi) * hf1 * Lcs * t * Fu = 0.75 * 1.20 * 2.06 * 0.38 * 65.00 = 45.25 kips/bolt
(phi)Rneshpl at Shear Plate edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 3.84 * 0.38 * 65.00 = 84.19 kips/bolt
(phi)Rndshpl on Shear Plate at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.88 * 0.38 * 65.00 = 38.39 kips/bolt
Shear Plate bearing capacity, (phi)Rnshpl = min((phi)Rnsshpl,(phi)Rneshpl,(phi)Rndshpl) = min(45.25, 84.19, 38.39) = 38.39 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(32.249, 38.392) = 32.25 kips/bolt
Bolt Shear Demand to Bearing ratio = 32.25 / 23.72 = 1.36

At Row 4, At Column 1:
Ribolt = 23.90 kips
Ri vector at Beam   = <-11.03, 21.21>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 3.44 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.75 * 1.20 * na * (0.32/1) * 65.00 = na
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 3.44 * (0.32/1) * 65.00 = 63.39 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.88 * (0.32/1) * 65.00 = 32.25 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(na, 63.39, 32.25) = 32.25 kips/bolt
Ri vector at Shear Plate   = <11.03, -21.21>
Lcsshpl at Shear Plate spacing  = na
Lceshpl at Shear Plate edge    = 0.88 in.
(phi)Rnsshpl at Shear Plate spacing = (phi) * hf1 * Lcs * t * Fu = 0.75 * 1.20 * na * 0.38 * 65.00 = na
(phi)Rneshpl at Shear Plate edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 0.88 * 0.38 * 65.00 = 19.32 kips/bolt
(phi)Rndshpl on Shear Plate at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.88 * 0.38 * 65.00 = 38.39 kips/bolt
Shear Plate bearing capacity, (phi)Rnshpl = min((phi)Rnsshpl,(phi)Rneshpl,(phi)Rndshpl) = min(na, 19.32, 38.39) = 19.32 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(32.249, 19.320) = 19.32 kips/bolt
Bolt Shear Demand to Bearing ratio = 19.32 / 23.90 = 0.81

Min Bolt Shear Demand to Bearing ratio Beam and Shear Plate for vertical shear only
 = min(1.00, 1.15, 1.36, 1.36, 0.81) = 0.81

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 = 0.81 * 89.15 = 72.06 kips
Rbv = 72.06 kips >= Reaction V = 26.00 kips (OK)

Web Depth = d - [Top Cope Depth] - [Bottom Cope Depth] = 17.9 - 4.25 - 0 = 13.65 in.
Gross Area (Shear) = [Web Depth] * tw = 13.65 * 0.32 = 4.30 in^2
Net Shear Area (Shear) = ([Web Depth] - ([# rows] * [Diameter + 0.0625])) * tw 
    = (13.65 - (4 * 1.00)) * 0.32 = 3.04 in^2

Using Eq.J4-3:
Shear Yielding = (phi) * 0.6 * Fybeam * [Gross Area] = 1.00 * 0.6 * 50.00 * 4.30 = 128.99 kips

Using Eq.J4-4:
Shear Rupture = (phi) * 0.6 * Fubeam * [Net Area] = 0.75 * 0.6 * 65.00 * 3.04 = 88.91 kips


Block Shear

Using Eq.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 + 9 = 10.75 in.
Net Shear Length = Gross Shear Length - (# rows - 0.5) * (hole size + 0.0625) = 10.8 - (4 - 0.5) * 1 = 7.25 in.
Gross Tension Length = [edge dist. at beam edge] + ([# cols - 1] * [spacing]) = 1.75 + (1 - 1) * 3 = 1.75 in.
Net Tension Length = Gross Tension Length - (# cols - 0.5) * (hole size + 0.0625) = 1.75 - (1 - 0.5) * 1 = 1.25 in.
1. (phi) * [material thickness] * ((0.60 * Fubeam* [net shear length]) + (Ubs * Fubeam * [net tension length])) 
    = 0.75 * 0.32 * ((0.60 * 65.00 * 7.25) + (1.00 * 65.00 * 1.25)) = 86.00 kips
2. (phi) * [material thickness] * ((0.60 * Fybeam * [gross shear length]) + (Ubs * Fubeam * [net tension length])) 
    = 0.75 * 0.32 * ((0.60 * 50.00 * 10.75) + (1.00 * 65.00 * 1.25)) = 95.39 kips
Block Shear = 86.00 kips

Block Shear (1) Total = Block Shear (1) = 86.00 kips
86.00 kips >= Reaction V = 26.00 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 = 6.64 in.
If coped at top/bottom flange only and c <= 2d and dc <= d/2, use Eq. 9-7, Fcr = 26210.00 * f * k * (tw/h1)^2 <= Fy

Using Eq. 9-7 through 9-11
tw = 0.32 in.
h1 = 9.52 in.
c = 5.75 in.
When c/h1<=1.0, k=2.2(h1/c)^1.65
k  = 2.20 * (9.52 / 5.75)^1.65 = 5.05
When c/d<=1.0, f=2c/d
f = 2 * (5.75 / 17.90) = 0.64
Fy = 50.00 ksi
Fcr = (phi) * 26210.00 * f * k * (tw/h1)^2 = 0.90 * 26210.00 * 0.64 * 5.05 * (0.32 / 9.52)^2 = 83.87 ksi
Fcrmin =phi * min(Fcr, Fy) = 45.00 ksi
Snet1 (bolt holes not applicable) = 15.01 in^3
Snet2 (bolt holes applicable) = 15.01 in^3
Znet = 27.21 in^3

Using Eq. 9-6
Buckling = Fcr * Snet1 / e = 45.00 * 15.01 / 6.64 = 101.67 kips

Using Eq. 9-19
Flexural Yielding = (phi) * Fy * Snet1 / e = 0.90 * 50.00 * 15.01 / 6.64 = 101.67 kips

Using Eq. 9-4
Flexural Rupture = (phi) * Fu * Znet / e = 0.75 * 65.00 * 27.21 / 6.64 = 199.71 kips


Buckling and Flexure at Furthest Bolt Line within Cope (Top Cope Only at Section)
Eccentricity at Section, e = 2.74 in.
If coped at top/bottom flange only and c <= 2d and dc <= d/2, use Eq. 9-7, Fcr = 26210.00 * f * k * (tw/h1)^2 <= Fy

Using Eq. 9-7 through 9-11
tw = 0.32 in.
h1 = 10.20 in.
c = 5.75 in.
When c/h1<=1.0, k=2.2(h1/c)^1.65
k  = 2.20 * (10.20 / 5.75)^1.65 = 5.67
When c/d<=1.0, f=2c/d
f = 2 * (5.75 / 17.90) = 0.64
Fy = 50.00 ksi
Fcr = (phi) * 26210.00 * f * k * (tw/h1)^2 = 0.90 * 26210.00 * 0.64 * 5.67 * (0.32 / 10.20)^2 = 81.87 ksi
Fcrmin =phi * min(Fcr, Fy) = 45.00 ksi
Snet1 (bolt holes not applicable) = 15.01 in^3
Snet2 (bolt holes applicable) = 11.01 in^3
Znet = 19.30 in^3

Using Eq. 9-6
Buckling = Fcr * Snet1 / e = 45.00 * 15.01 / 2.74 = 246.23 kips

Using Eq. 9-19
Flexural Yielding = (phi) * Fy * Snet1 / e = 0.90 * 50.00 * 15.01 / 2.74 = 246.23 kips

Using Eq. 9-4
Flexural Rupture = (phi) * Fu * Znet / e = 0.75 * 65.00 * 19.30 / 2.74 = 342.98 kips


Section Bending Strength Calculations Summary:

   Coped Beam Buckling and Flexure at Longest Cope (Top Cope Only at Section)
   Buckling : 101.67 >= 26.00 kips (OK)
   Flexural Yielding : 101.67 >= 26.00 kips (OK)
   Flexural Rupture : 199.71 >= 26.00 kips (OK)

   Coped Beam Buckling and Flexure at Furthest Bolt Line within Cope (Top Cope Only at Section)
   Buckling : 246.23 >= 26.00 kips (OK)
   Flexural Yielding : 246.23 >= 26.00 kips (OK)
   Flexural Rupture : 342.98 >= 26.00 kips (OK)

Gross Area = 0.38 * 11.50 = 4.31 in^2
Net Area = (11.50 - (4 *(0.94 + 1/16))) * 0.38 = 2.81 in^2

Using Eq.J4-3:
Shear Yielding = (phi) * 0.6 * Fypl * [Gross Area] = 1.00 * 0.6 * 50.00 * 4.31 = 129.38 kips

Using Eq.J4-4:
Shear Rupture = (phi) * 0.6 * Fupl * [Net Area] = 0.75 * 0.6 * 65.00 * 2.81 = 82.27 kips


Block Shear

Using Eq.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 = (11.5 - 1.25) = 10.25 in.
Net Shear Length = 10.2 - (3.5 * (0.938 + 0.0625)) = 6.75 in.
Gross Tension Length = (0 + 1.75) = 1.75 in.
Net Tension Length = 1.75 - (0.5 * (1.12 + 0.0625)) = 1.16 in.
1. (phi) * [material thickness] * ((0.60 * Fupl* [net shear length]) + (Ubs * Fupl * [net tension length])) 
    = 0.75 * 0.38 * ((0.60 * 65.00 * 6.75) + (1.00 * 65.00 * 1.16)) = 95.18 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 * 1.16)) = 107.62 kips
Block Shear = 95.18 kips
95.18 kips >= Reaction V = 26.00 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 = 1.25 in.
Zgross = 12.40
Znet = 7.90
Mr = Vr * e = 26.00 * 1.25 = 32.50 kips-in
Mc = phi * Mn = phi * Fy * Zgross = 0.90 * 50.00 * 12.40 = 557.93 kips-in
Vr = 26.00 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 = (26.00 / 129.38)^2 + (32.50 / 557.93)^2 = 0.04 <= 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 = 11.500 in.
Shear Load per inch per weld, fv = R/Lv/2 = 26.000 / 11.500 / 2 = 1.130 kips/in/ weld 
theta = 0 deg.
cPhi  = 1.0 + 0.5 * sin(0)^1.5 = 1.000
Weld Coefficient = 0.6 * 70.000 * 1.000 * 1.000 * (2^0.5/2)*(1/16) = 1.856
Required weld size, Dv = fv/ (phi * coeff) = 1.130 / (0.750 * 1.856) = 0.812/16

Minimum fillet weld size : 
   At shear only load case = 0.05 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 * 0.088)
 = 0.375 * 65.000 / ( 70.000 * 1.000 * 0.088 ) 
 = 3.940 
Dmax2 (using eqn 9-3)
 = twsupport * Fusupport / ( Fexx * C1 * 0.088 )
 = 0.550 * 65.000 / ( 70.000 * 1.000 * 0.088 ) 
 = 5.778 
Dmax3 = project max fillet weld = 12.000
Dmax=min(Dmax1, Dmax2, Dmax3) = min(3.940, 5.778, 12.000)
 = 3.940 

Use weld size
D1 = 4.00
D2 = 4.00

Weld Strength :

Vertical weld capacity during shear only load, phi * Rnv1 = 0.75 * 1.86 * 11.50 * (3.94 + 3.94) = 126.14 kips

126.14 kips >= Reaction V = 26.00 kips (OK)