bcw.s.s.01881.01881

SHEAR PLATE CONNECTION SUMMARY

Filler Beam profile: W18X40
Column profile: W14X145
Slope: 0 deg.
Skew: 90
Vertical Offset: 0
Horizontal Offset: 0
Span: 20 ft.
Reaction, V: 15 kips
Shear Capacity, Rn: 16.1 kips
Design/Reference according to AISC 14th Ed. - ASD
Shear Plate: Extended Configuration
Beam material grade: A992
Support material grade: A992
Plate material grade: A572-GR.50
Weld grade: E70
Shear Plate Size: 11.500 in. x 12.500 in. x 0.375 in.
Configuration Geometry:
Welds at shear plate to support: 4/16 FILLET, 4/16 FILLET
Bolt: 3 rows x 1 column 0.875 in. Diameter A325N_TC bolts
Vertical spacing: 5 in.
Horizontal spacing: 3 in.
Shear plate edge setback = 8 in.
Beam centerline setback = 8 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: 9.75 in.
Down distance from top of filler beam flange: 3 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 = 9.750 in.
Angle = 0.000 deg.
C = 0.991
Using Table 7-1 to determine (1/omega)rn:
(1/omega)Rn = (1/omega)rn * C = 16.24 * 0.99 = 16.09 kips


Total Vertical Bolt Shear Capacity = 16.09 kips
16.09 kips >= 15.00 kips (OK)

BOLT BEARING AT BEAM AND SHEAR PLATE SIDE
Vertical Shear Only Load Case:
ICR cordinate relative to CG = (0.89, -0.00)
At Row 1, At Column 1:
Ribolt = 15.94 kips
Ri vector at Beam   = <15.69, 2.81>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 16.56 in.
(1/omega)Rnsbm at Beam spacing = (1/omega) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * na * (0.32/1) * 65.00 = na
(1/omega)Rnebm at Beam edge = (1/omega) * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 16.56 * (0.32/1) * 65.00 = 203.42 kips/bolt
(1/omega)Rndbm on Beam at Bolt Diameter   = (1/omega) * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.88 * (0.32/1) * 65.00 = 21.50 kips/bolt
Beam bearing capacity, (1/omega)Rnbm = min((1/omega)Rnsbm,(1/omega)Rnebm,(1/omega)Rndbm) = min(na, 203.42, 21.50) = 21.50 kips/bolt
Ri vector at Shear Plate   = <-15.69, -2.81>
Lcsshpl at Shear Plate spacing  = na
Lceshpl at Shear Plate edge    = 9.33 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 * 9.33 * 0.38 * 65.00 = 136.50 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, 136.50, 25.59) = 25.59 kips/bolt
(1/omega)Rn = min((1/omega)Rnbm, (1/omega)Rnshpl) = min(21.499, 25.594) = 21.50 kips/bolt
Bolt Shear Demand to Bearing ratio = 21.50 / 15.94 = 1.35

At Row 2, At Column 1:
Ribolt = 10.47 kips
Ri vector at Beam   = <-0.00, 10.47>
Lcsbm at Beam spacing  = 4.06 in.
Lcebm at Beam edge    = 7.53 in.
(1/omega)Rnsbm at Beam spacing = (1/omega) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * 4.06 * (0.32/1) * 65.00 = 49.91 kips/bolt
(1/omega)Rnebm at Beam edge = (1/omega) * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 7.53 * (0.32/1) * 65.00 = 92.52 kips/bolt
(1/omega)Rndbm on Beam at Bolt Diameter   = (1/omega) * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.88 * (0.32/1) * 65.00 = 21.50 kips/bolt
Beam bearing capacity, (1/omega)Rnbm = min((1/omega)Rnsbm,(1/omega)Rnebm,(1/omega)Rndbm) = min(49.91, 92.52, 21.50) = 21.50 kips/bolt
Ri vector at Shear Plate   = <0.00, -10.47>
Lcsshpl at Shear Plate spacing  = 4.06 in.
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 * 4.06 * 0.38 * 65.00 = 59.41 kips/bolt
(1/omega)Rneshpl at Shear Plate edge = (1/omega) * hf1 * Lce * t * Fu = 0.50 * 1.20 * 5.78 * 0.38 * 65.00 = 84.55 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(59.41, 84.55, 25.59) = 25.59 kips/bolt
(1/omega)Rn = min((1/omega)Rnbm, (1/omega)Rnshpl) = min(21.499, 25.594) = 21.50 kips/bolt
Bolt Shear Demand to Bearing ratio = 21.50 / 10.47 = 2.05

At Row 3, At Column 1:
Ribolt = 15.94 kips
Ri vector at Beam   = <-15.69, 2.81>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 1.31 in.
(1/omega)Rnsbm at Beam spacing = (1/omega) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * na * (0.32/1) * 65.00 = na
(1/omega)Rnebm at Beam edge = (1/omega) * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 1.31 * (0.32/1) * 65.00 = 16.08 kips/bolt
(1/omega)Rndbm on Beam at Bolt Diameter   = (1/omega) * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.88 * (0.32/1) * 65.00 = 21.50 kips/bolt
Beam bearing capacity, (1/omega)Rnbm = min((1/omega)Rnsbm,(1/omega)Rnebm,(1/omega)Rndbm) = min(na, 16.08, 21.50) = 16.08 kips/bolt
Ri vector at Shear Plate   = <15.69, -2.81>
Lcsshpl at Shear Plate spacing  = na
Lceshpl at Shear Plate edge    = 1.21 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 * 1.21 * 0.38 * 65.00 = 17.64 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, 17.64, 25.59) = 17.64 kips/bolt
(1/omega)Rn = min((1/omega)Rnbm, (1/omega)Rnshpl) = min(16.082, 17.643) = 16.08 kips/bolt
Bolt Shear Demand to Bearing ratio = 16.08 / 15.94 = 1.01

Min Bolt Shear Demand to Bearing ratio Beam and Shear Plate for vertical shear only
 = min(1.00, 1.35, 2.05, 1.01) = 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 * 16.09 = 16.09 kips
Rbv = 16.09 kips >= V = 15.00 kips (OK)

Web Depth = d - [Top Cope Depth] - [Bottom Cope Depth] = 17.9 - 0 - 0 = 17.9 in.
Gross Area (Shear) = [Web Depth] * tw = 17.90 * 0.32 = 5.64 in^2
Net Shear Area (Shear) = ([Web Depth] - ([# rows] * [Diameter + 0.0625])) * tw 
    = (17.90 - (3 * 1.00)) * 0.32 = 4.69 in^2

Using Eq.J4-3:
Shear Yielding = (1/omega) * 0.6 * Fybeam * [Gross Area] = 0.67 * 0.6 * 50.00 * 5.64 = 112.77 kips

Using Eq.J4-4:
Shear Rupture = (1/omega) * 0.6 * Fubeam * [Net Area] = 0.50 * 0.6 * 65.00 * 4.69 = 91.52 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 * 12.50 = 4.69 in^2
Net Area = (12.50 - (3 *(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 * 4.69 = 93.75 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 = (12.5 - 1.25) = 11.25 in.
Net Shear Length = 11.2 - (2.5 * (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 * 11.25) + (1.00 * 65.00 * 1.16)) = 77.37 kips
Block Shear = 77.37 kips

77.37 kips >= Reaction V = 15.00 kips (OK)

Flexural and Buckling Strength:

Eccentricity at first line of bolts, e = 9.75 in.
Zgross = 14.65 in^3
Znet   = 10.80 in^3
Sgross = 9.77 in^3
Snet   = 6.77 in^3

Using Eq. 9-4
Flexural Rupture = (1/omega) * Fu * Znet / e = 0.50 * 65.00 * 10.80 / 9.75 = 36.02 kips


Using Eq. 9-14 through 9-18, Fcr = Fy * Q
tw = 0.38 in.
ho = 12.50 in.
c = 9.75 in.
lambda = (ho * Fy ^ 0.5) / ( 10 * tw * ( 475.00 + 280.00 * (ho / c)^2 ) ^0.5 ) = 
 = 12.50 * 50.00^0.5 / (10 * 0.38 * (475.00 + 280.00 * (12.50/9.75)^2 )^0.5) = 0.77
When 0.70 < lambda <= 1.41, Q=1.34 - 0.49 * lambda
Q = 0.97
Fcrmin =1/omega * Fcr = 0.60 * 50.00 * 0.97 = 28.96 ksi

Using Eq. 9-6
Buckling = Fcr * Sgross / e = 28.96 * 9.77 / 9.75 = 29.01 kips

Interaction Check of Flexural Yielding, Per AISC 10-5: 
Eccentricity at CG of Bolt Group, e = 9.75 in.
Zgross = 14.65
Znet = 10.80
Mr = Vr * e = 15.00 * 9.75 = 146.25 kips-in
Mc = 1/omega * Mn = 1/omega * Fy * Zgross = 0.60 * 50.00 * 14.65 = 439.45 kips-in
Vr = 15.00 kips
Vc = 1/omega * Vn = 1/omega * 0.60 * Fy * Ag = 0.67 * 0.60 * 50.00 * 4.69 = 93.75 kips
Interaction due to moment and shear, (Vr/Vc)^2 + (Mr/Mc)^2 <= 1.0
(Vr/Vc)^2 + (Mr/Mc)^2 = (15.00 / 93.75)^2 + (146.25 / 439.45)^2 = 0.14 <= 1  (OK)

Note: Mn <= 1.6My by inspection

MAXIMUM PLATE THICKNESS:
No of bolt columns = 1
tp  < = db/2 + 1/16 = 0.375 <= 0.5 OK
tw  < = db/2 + 1/16 = 0.315 <= 0.5 OK
Leh(plate) >= 2 * db = 1.75 >= 1.75 OK
Leh(bm) >= 2 * db = 1.75 >= 1.75 OK
Maximum Plate Thickness is Not a Limiting Criteria.

STABILIZER PLATE:

Available Strength to Resist Lateral Displacement:
Using Eq. 10-6 (14th Ed.):
Rn/omega = 1500.00  * 3.14159 * L * tp^3 / a^2 = 0.60 * 1500.00 * 3.14159 * 12.50 * 0.38^3 / 9.75^2 = 19.61 kips
Stabilizer Plate Not Required for lateral displacement

Torsional Strength:
Using Eq. 10-8 and Eq. 10-7 (14th Ed.):
Required, Mta or Mtu = Ra * (tw + tp) /2 = 15.00 * ((0.31 + 0.38) / 2) = 5.16 kips-in
Lateral Shear Strength of Shear Plate, Mtn (no slab) = [1/omega*(0.6*Fyp)-(Ra/(L*tp))] *L*tp^2/2 =  ((0.67 * 0.6 * 50.00) - (15.00 / (12.50 * 0.38))) * 0.5 * 12.50 * 0.38^2 = 14.77 kips-in
Stabilizer Plate Not Required for torsional strength

WELD:

 Weld Requirements:

At shear only case: 
Weld Length for shear, Lv = 12.500 in.
Shear Load per inch per weld, fv = R/Lv/2 = 15.000 / 12.500 / 2 = 0.600 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) = 0.600 / (0.500 * 1.856) = 0.646/16

Minimum fillet weld size : 
   At shear only load case = 0.04 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 )
 = 0.680 * 65.000 / ( 70.000 * 1.000 * 0.088 ) 
 = 7.144 
Dmax3 = project max fillet weld = 12.000
Dmax=min(Dmax1, Dmax2, Dmax3) = min(3.940, 7.144, 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 * 12.50 * (3.94 + 3.94) = 91.41 kips

91.41 kips >= Vbm = 15.00 kips (OK)