bcf.s.s.00897.00897

SHEAR PLATE CONNECTION SUMMARY

Filler Beam profile: W21X111
Column profile: W14X176
Slope: 0 deg.
Skew: 90
Vertical Offset: 0
Horizontal Offset: 0
Span: 32.5 ft.
Reaction, V: 49 kips
Shear Capacity, Rn: 59 kips
Design/Reference according to AISC 14th Ed. - ASD
Shear Plate: Conventional Configuration
Beam material grade: A992
Support material grade: A992
Plate material grade: A572-GR.50
Weld grade: E70
Shear Plate Size: 4.000 in. x 14.500 in. x 0.375 in.
Configuration Geometry:
Welds at shear plate to support: 4/16 FILLET, 4/16 FILLET
Bolt: 5 rows x 1 column 0.875 in. Diameter A325N_TC bolts
Vertical spacing: 3 in.
Horizontal spacing: 3 in.
Shear plate edge setback = 0.5 in.
Beam centerline setback = 0.5 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: 1.75 in.
Horizontal distance to first hole: 2.25 in.
Down distance from top of filler beam flange: 3.5 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 = 1.125 in.
Angle = 0.000 deg.
C = 4.731
Using Table 7-1 to determine (1/omega)rn:
(1/omega)Rn = (1/omega)rn * C = 16.24 * 4.73 = 76.80 kips


Total Vertical Bolt Shear Capacity = 76.80 kips
76.80 kips >= 49.00 kips (OK)

BOLT BEARING AT BEAM AND SHEAR PLATE SIDE
Vertical Shear Only Load Case:
ICR cordinate relative to CG = (15.64, 0.00)
At Row 1, At Column 1:
Ribolt = 15.94 kips
Ri vector at Beam   = <5.71, 14.88>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 3.28 in.
(1/omega)Rnsbm at Beam spacing = (1/omega) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * na * (0.55/1) * 65.00 = na
(1/omega)Rnebm at Beam edge = (1/omega) * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 3.28 * (0.55/1) * 65.00 = 70.36 kips/bolt
(1/omega)Rndbm on Beam at Bolt Diameter   = (1/omega) * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.88 * (0.55/1) * 65.00 = 37.54 kips/bolt
Beam bearing capacity, (1/omega)Rnbm = min((1/omega)Rnsbm,(1/omega)Rnebm,(1/omega)Rndbm) = min(na, 70.36, 37.54) = 37.54 kips/bolt
Ri vector at Shear Plate   = <-5.71, -14.88>
Lcsshpl at Shear Plate spacing  = na
Lceshpl at Shear Plate edge    = 5.78 in.
(1/omega)Rnsshpl at Shear Plate spacing = (1/omega) * hf1 * Lcs * t * Fu = 0.50 * 1.20 * na * 0.38 * 65.00 = na
(1/omega)Rneshpl at Shear Plate edge = (1/omega) * hf1 * Lce * t * Fu = 0.50 * 1.20 * 5.78 * 0.38 * 65.00 = 84.51 kips/bolt
(1/omega)Rndshpl on Shear Plate at Bolt Diameter   = (1/omega) * hf2 * db * t * Fu = 0.50 * 2.40 * 0.88 * 0.38 * 65.00 = 25.59 kips/bolt
Shear Plate bearing capacity, (1/omega)Rnshpl = min((1/omega)Rnsshpl,(1/omega)Rneshpl,(1/omega)Rndshpl) = min(na, 84.51, 25.59) = 25.59 kips/bolt
(1/omega)Rn = min((1/omega)Rnbm, (1/omega)Rnshpl) = min(37.538, 25.594) = 25.59 kips/bolt
Bolt Shear Demand to Bearing ratio = 25.59 / 15.94 = 1.61

At Row 2, At Column 1:
Ribolt = 15.88 kips
Ri vector at Beam   = <2.99, 15.60>
Lcsbm at Beam spacing  = 2.06 in.
Lcebm at Beam edge    = 6.15 in.
(1/omega)Rnsbm at Beam spacing = (1/omega) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * 2.06 * (0.55/1) * 65.00 = 44.24 kips/bolt
(1/omega)Rnebm at Beam edge = (1/omega) * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 6.15 * (0.55/1) * 65.00 = 131.91 kips/bolt
(1/omega)Rndbm on Beam at Bolt Diameter   = (1/omega) * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.88 * (0.55/1) * 65.00 = 37.54 kips/bolt
Beam bearing capacity, (1/omega)Rnbm = min((1/omega)Rnsbm,(1/omega)Rnebm,(1/omega)Rndbm) = min(44.24, 131.91, 37.54) = 37.54 kips/bolt
Ri vector at Shear Plate   = <-2.99, -15.60>
Lcsshpl at Shear Plate spacing  = 2.06 in.
Lceshpl at Shear Plate edge    = 9.96 in.
(1/omega)Rnsshpl at Shear Plate spacing = (1/omega) * hf1 * Lcs * t * Fu = 0.50 * 1.20 * 2.06 * 0.38 * 65.00 = 30.16 kips/bolt
(1/omega)Rneshpl at Shear Plate edge = (1/omega) * hf1 * Lce * t * Fu = 0.50 * 1.20 * 9.96 * 0.38 * 65.00 = 145.66 kips/bolt
(1/omega)Rndshpl on Shear Plate at Bolt Diameter   = (1/omega) * hf2 * db * t * Fu = 0.50 * 2.40 * 0.88 * 0.38 * 65.00 = 25.59 kips/bolt
Shear Plate bearing capacity, (1/omega)Rnshpl = min((1/omega)Rnsshpl,(1/omega)Rneshpl,(1/omega)Rndshpl) = min(30.16, 145.66, 25.59) = 25.59 kips/bolt
(1/omega)Rn = min((1/omega)Rnbm, (1/omega)Rnshpl) = min(37.538, 25.594) = 25.59 kips/bolt
Bolt Shear Demand to Bearing ratio = 25.59 / 15.88 = 1.61

At Row 3, At Column 1:
Ribolt = 15.86 kips
Ri vector at Beam   = <-0.00, 15.86>
Lcsbm at Beam spacing  = 2.06 in.
Lcebm at Beam edge    = 9.03 in.
(1/omega)Rnsbm at Beam spacing = (1/omega) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * 2.06 * (0.55/1) * 65.00 = 44.24 kips/bolt
(1/omega)Rnebm at Beam edge = (1/omega) * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 9.03 * (0.55/1) * 65.00 = 193.72 kips/bolt
(1/omega)Rndbm on Beam at Bolt Diameter   = (1/omega) * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.88 * (0.55/1) * 65.00 = 37.54 kips/bolt
Beam bearing capacity, (1/omega)Rnbm = min((1/omega)Rnsbm,(1/omega)Rnebm,(1/omega)Rndbm) = min(44.24, 193.72, 37.54) = 37.54 kips/bolt
Ri vector at Shear Plate   = <0.00, -15.86>
Lcsshpl at Shear Plate spacing  = 2.06 in.
Lceshpl at Shear Plate edge    = 6.78 in.
(1/omega)Rnsshpl at Shear Plate spacing = (1/omega) * hf1 * Lcs * t * Fu = 0.50 * 1.20 * 2.06 * 0.38 * 65.00 = 30.16 kips/bolt
(1/omega)Rneshpl at Shear Plate edge = (1/omega) * hf1 * Lce * t * Fu = 0.50 * 1.20 * 6.78 * 0.38 * 65.00 = 99.18 kips/bolt
(1/omega)Rndshpl on Shear Plate at Bolt Diameter   = (1/omega) * hf2 * db * t * Fu = 0.50 * 2.40 * 0.88 * 0.38 * 65.00 = 25.59 kips/bolt
Shear Plate bearing capacity, (1/omega)Rnshpl = min((1/omega)Rnsshpl,(1/omega)Rneshpl,(1/omega)Rndshpl) = min(30.16, 99.18, 25.59) = 25.59 kips/bolt
(1/omega)Rn = min((1/omega)Rnbm, (1/omega)Rnshpl) = min(37.538, 25.594) = 25.59 kips/bolt
Bolt Shear Demand to Bearing ratio = 25.59 / 15.86 = 1.61

At Row 4, At Column 1:
Ribolt = 15.88 kips
Ri vector at Beam   = <-2.99, 15.60>
Lcsbm at Beam spacing  = 2.06 in.
Lcebm at Beam edge    = 8.82 in.
(1/omega)Rnsbm at Beam spacing = (1/omega) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * 2.06 * (0.55/1) * 65.00 = 44.24 kips/bolt
(1/omega)Rnebm at Beam edge = (1/omega) * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 8.82 * (0.55/1) * 65.00 = 189.16 kips/bolt
(1/omega)Rndbm on Beam at Bolt Diameter   = (1/omega) * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.88 * (0.55/1) * 65.00 = 37.54 kips/bolt
Beam bearing capacity, (1/omega)Rnbm = min((1/omega)Rnsbm,(1/omega)Rnebm,(1/omega)Rndbm) = min(44.24, 189.16, 37.54) = 37.54 kips/bolt
Ri vector at Shear Plate   = <2.99, -15.60>
Lcsshpl at Shear Plate spacing  = 2.06 in.
Lceshpl at Shear Plate edge    = 3.85 in.
(1/omega)Rnsshpl at Shear Plate spacing = (1/omega) * hf1 * Lcs * t * Fu = 0.50 * 1.20 * 2.06 * 0.38 * 65.00 = 30.16 kips/bolt
(1/omega)Rneshpl at Shear Plate edge = (1/omega) * hf1 * Lce * t * Fu = 0.50 * 1.20 * 3.85 * 0.38 * 65.00 = 56.31 kips/bolt
(1/omega)Rndshpl on Shear Plate at Bolt Diameter   = (1/omega) * hf2 * db * t * Fu = 0.50 * 2.40 * 0.88 * 0.38 * 65.00 = 25.59 kips/bolt
Shear Plate bearing capacity, (1/omega)Rnshpl = min((1/omega)Rnsshpl,(1/omega)Rneshpl,(1/omega)Rndshpl) = min(30.16, 56.31, 25.59) = 25.59 kips/bolt
(1/omega)Rn = min((1/omega)Rnbm, (1/omega)Rnshpl) = min(37.538, 25.594) = 25.59 kips/bolt
Bolt Shear Demand to Bearing ratio = 25.59 / 15.88 = 1.61

At Row 5, At Column 1:
Ribolt = 15.94 kips
Ri vector at Beam   = <-5.71, 14.88>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 4.42 in.
(1/omega)Rnsbm at Beam spacing = (1/omega) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * na * (0.55/1) * 65.00 = na
(1/omega)Rnebm at Beam edge = (1/omega) * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 4.42 * (0.55/1) * 65.00 = 94.72 kips/bolt
(1/omega)Rndbm on Beam at Bolt Diameter   = (1/omega) * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.88 * (0.55/1) * 65.00 = 37.54 kips/bolt
Beam bearing capacity, (1/omega)Rnbm = min((1/omega)Rnsbm,(1/omega)Rnebm,(1/omega)Rndbm) = min(na, 94.72, 37.54) = 37.54 kips/bolt
Ri vector at Shear Plate   = <5.71, -14.88>
Lcsshpl at Shear Plate spacing  = na
Lceshpl at Shear Plate edge    = 0.84 in.
(1/omega)Rnsshpl at Shear Plate spacing = (1/omega) * hf1 * Lcs * t * Fu = 0.50 * 1.20 * na * 0.38 * 65.00 = na
(1/omega)Rneshpl at Shear Plate edge = (1/omega) * hf1 * Lce * t * Fu = 0.50 * 1.20 * 0.84 * 0.38 * 65.00 = 12.24 kips/bolt
(1/omega)Rndshpl on Shear Plate at Bolt Diameter   = (1/omega) * hf2 * db * t * Fu = 0.50 * 2.40 * 0.88 * 0.38 * 65.00 = 25.59 kips/bolt
Shear Plate bearing capacity, (1/omega)Rnshpl = min((1/omega)Rnsshpl,(1/omega)Rneshpl,(1/omega)Rndshpl) = min(na, 12.24, 25.59) = 12.24 kips/bolt
(1/omega)Rn = min((1/omega)Rnbm, (1/omega)Rnshpl) = min(37.538, 12.238) = 12.24 kips/bolt
Bolt Shear Demand to Bearing ratio = 12.24 / 15.94 = 0.77

Min Bolt Shear Demand to Bearing ratio Beam and Shear Plate for vertical shear only
 = min(1.00, 1.61, 1.61, 1.61, 1.61, 0.77) = 0.77

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 = 0.77 * 76.80 = 58.99 kips
Rbv = 58.99 kips >= V = 49.00 kips (OK)

Web Depth = d - [Top Cope Depth] - [Bottom Cope Depth] = 21.5 - 0 - 0 = 21.5 in.
Gross Area (Shear) = [Web Depth] * tw = 21.50 * 0.55 = 11.83 in^2
Net Shear Area (Shear) = ([Web Depth] - ([# rows] * [Diameter + 0.0625])) * tw 
    = (21.50 - (5 * 1.00)) * 0.55 = 9.08 in^2

Using Eq.J4-3:
Shear Yielding = (1/omega) * 0.6 * Fybeam * [Gross Area] = 0.67 * 0.6 * 50.00 * 11.83 = 236.50 kips

Using Eq.J4-4:
Shear Rupture = (1/omega) * 0.6 * Fubeam * [Net Area] = 0.50 * 0.6 * 65.00 * 9.08 = 176.96 kips


Block Shear

Using Eq.J4-5:
Block Shear = {(1/omega) * ((0.6 * Fu * Anv) + (Ubs * Fu * Ant))} <= {(1/omega) * ((0.6 * Fy * Agv) + (Ubs * Fu * Ant))}

Block Shear not required.

Gross Area = 0.38 * 14.50 = 5.44 in^2
Net Area = (14.50 - (5 *(0.94 + 1/16))) * 0.38 = 3.56 in^2

Using Eq.J4-3:
Shear Yielding = (1/omega) * 0.6 * Fypl * [Gross Area] = 0.67 * 0.6 * 50.00 * 5.44 = 108.75 kips

Using Eq.J4-4:
Shear Rupture = (1/omega) * 0.6 * Fupl * [Net Area] = 0.50 * 0.6 * 65.00 * 3.56 = 69.47 kips


Block Shear

Using Eq.J4-5:
Block Shear = {(1/omega) * ((0.6 * Fu * Anv) + (Ubs * Fu * Ant))} <= {(1/omega) * ((0.6 * Fy * Agv) + (Ubs * Fu * Ant))}
Block 1 (Shear): 
Gross Shear Length = (14.5 - 1.25) = 13.25 in.
Net Shear Length = 13.2 - (4.5 * (0.938 + 0.0625)) = 8.75 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. (1/omega) * [material thickness] * ((0.60 * Fupl* [net shear length]) + (Ubs * Fupl * [net tension length])) 
    = 0.50 * 0.38 * ((0.60 * 65.00 * 8.75) + (1.00 * 65.00 * 1.16)) = 78.08 kips
2. (1/omega) * [material thickness] * ((0.60 * Fypl * [gross shear length]) + (Ubs * Fupl * [net tension length])) 
    = 0.50 * 0.38 * ((0.60 * 50.00 * 13.25) + (1.00 * 65.00 * 1.16)) = 88.62 kips
Block Shear = 78.08 kips

78.08 kips >= Reaction V = 49.00 kips (OK)


Interaction Check of Flexural Yielding, Per AISC 10-5: 
Eccentricity due to Conventional Config. (e = a/2), e = 1.12 in.
Zgross = 19.71
Znet = 12.87
Mr = Vr * e = 49.00 * 1.12 = 55.12 kips-in
Mc = 1/omega * Mn = 1/omega * Fy * Zgross = 0.60 * 50.00 * 19.71 = 591.33 kips-in
Vr = 49.00 kips
Vc = 1/omega * Vn = 1/omega * 0.60 * Fy * Ag = 0.67 * 0.60 * 50.00 * 5.44 = 108.75 kips
Interaction due to moment and shear, (Vr/Vc)^2 + (Mr/Mc)^2 <= 1.0
(Vr/Vc)^2 + (Mr/Mc)^2 = (49.00 / 108.75)^2 + (55.12 / 591.33)^2 = 0.21 <= 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 = 14.500 in.
Shear Load per inch per weld, fv = R/Lv/2 = 49.000 / 14.500 / 2 = 1.690 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/ (1/omega * coeff) = 1.690 / (0.500 * 1.856) = 1.821/16

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 eqn 9-3)
 = tshpl * Fushpl / ( Fexx * C1 * 0.088)
 = 0.375 * 65.000 / ( 70.000 * 1.000 * 0.088 ) 
 = 3.940 
Dmax2 (using eqn 9-2)
 = tfsupport * Fusupport / ( Fexx * C1 * 0.044 )
 = 1.310 * 65.000 / ( 70.000 * 1.000 * 0.044 ) 
 = 27.525 
Dmax3 = project max fillet weld = 12.000
Dmax=min(Dmax1, Dmax2, Dmax3) = min(3.940, 27.525, 12.000)
 = 3.940 

Use weld size
D1 = 4.00
D2 = 4.00

Weld Strength :

Vertical weld capacity during shear only load, 1/omega * Rnv1 = 0.50 * 1.86 * 14.50 * (3.94 + 3.94) = 106.03 kips

106.03 kips >= Vbm = 49.00 kips (OK)