bcw.s.s.00329.00747

SHEAR PLATE CONNECTION SUMMARY

Filler Beam profile: W21X44
Column profile: W14X90
Slope: 0 deg.
Skew: 90
Vertical Offset: 0
Horizontal Offset: 0
Span: 20 ft.
Reaction, V: 30 kips
Shear Capacity, Rn: 30.1 kips
Design/Reference according to AISC 14th Ed. - ASD
Shear Plate: Extended Configuration
Beam material grade: A992
Support material grade: A992
Plate material grade: A36
Weld grade: E70
Shear Plate Size: 10.750 in. x 17.500 in. x 0.375 in.
Configuration Geometry:
Welds at shear plate to support: 4/16 FILLET, 4/16 FILLET
Bolt: 6 rows x 1 columns 0.75 in. Diameter A325N_TC bolts
Vertical spacing: 3 in.
Horizontal spacing: 3 in.
Shear plate edge setback = 7.56 in.
Beam centerline setback = 7.56 in.
Edge distance at vertical edge of plate: 1.5 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: 1.69 in.
Horizontal distance to first hole: 9.25 in.
Down distance from top of filler beam flange: 3 in.
Holes in beam web: STD diameter = 0.812 in.
Holes in shear plate: SSL diameter = 0.812 in., slot width = 1 in.

BOLT STRENGTH BEAM SIDE:

Bolt Strength:
Using Instantaneous Center Of Rotation Method (AISC 7-1)
ex = 9.250 in.
Angle = 0.000 deg.
C = 2.527
Using Table 7-1 to determine (1/omega) * rn:
Rn = (1/omega) * rn * C = 11.93 * 2.53 = 30.15 kips

BOLT BEARING AT BEAM SIDE:
Vertical Shear Only Load Case:
ICR cordinate relative to CG = (1.98, -0.00)
At Row 1, At Column 1:
Ri1 = 11.71 kips
Ri vector at Beam   = <11.32, 2.99>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 11.34 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * na * (0.35/1) * 65.00 = na
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 11.34 * (0.35/1) * 65.00 = 154.78 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.35/1) * 65.00 = 20.47 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(na, 154.78, 20.47) = 20.47 kips/bolt
Ri vector at Shear Plate   = <-11.32, -2.99>
Lcsshpl at Shear Plate spacing  = na
Lceshpl at Shear Plate edge    = 9.05 in.
1/omegaRnsshpl at Shear Plate spacing = 1/omega * hf1 * Lcs * t * Fu = 0.50 * 1.20 * na * 0.38 * 58.00 = na
1/omegaRneshpl at Shear Plate edge = 1/omega * hf1 * Lce * t * Fu = 0.50 * 1.20 * 9.05 * 0.38 * 58.00 = 118.11 kips/bolt
1/omegaRndshpl on Shear Plate at Bolt Diameter   = 1/omega * hf2 * db * t * Fu = 0.50 * 2.40 * 0.75 * 0.38 * 58.00 = 19.57 kips/bolt
Shear Plate bearing capacity, 1/omegaRnshpl = min(1/omegaRnsshpl,1/omegaRneshpl,1/omegaRndshpl) = min(na, 118.11, 19.57) = 19.57 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(20.475, 19.575) = 19.57 kips/bolt
Bolt Shear Demand to Bearing ratio = 19.57 / 11.71 = 1.67

At Row 2, At Column 1:
Ri1 = 11.15 kips
Ri vector at Beam   = <10.20, 4.49>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 14.48 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * na * (0.35/1) * 65.00 = na
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 14.48 * (0.35/1) * 65.00 = 197.71 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.35/1) * 65.00 = 20.47 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(na, 197.71, 20.47) = 20.47 kips/bolt
Ri vector at Shear Plate   = <-10.20, -4.49>
Lcsshpl at Shear Plate spacing  = na
Lceshpl at Shear Plate edge    = 9.56 in.
1/omegaRnsshpl at Shear Plate spacing = 1/omega * hf1 * Lcs * t * Fu = 0.50 * 1.20 * na * 0.38 * 58.00 = na
1/omegaRneshpl at Shear Plate edge = 1/omega * hf1 * Lce * t * Fu = 0.50 * 1.20 * 9.56 * 0.38 * 58.00 = 124.76 kips/bolt
1/omegaRndshpl on Shear Plate at Bolt Diameter   = 1/omega * hf2 * db * t * Fu = 0.50 * 2.40 * 0.75 * 0.38 * 58.00 = 19.57 kips/bolt
Shear Plate bearing capacity, 1/omegaRnshpl = min(1/omegaRnsshpl,1/omegaRneshpl,1/omegaRndshpl) = min(na, 124.76, 19.57) = 19.57 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(20.475, 19.575) = 19.57 kips/bolt
Bolt Shear Demand to Bearing ratio = 19.57 / 11.15 = 1.76

At Row 3, At Column 1:
Ri1 = 9.52 kips
Ri vector at Beam   = <5.75, 7.59>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 10.88 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * na * (0.35/1) * 65.00 = na
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 10.88 * (0.35/1) * 65.00 = 148.57 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.35/1) * 65.00 = 20.47 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(na, 148.57, 20.47) = 20.47 kips/bolt
Ri vector at Shear Plate   = <-5.75, -7.59>
Lcsshpl at Shear Plate spacing  = na
Lceshpl at Shear Plate edge    = 12.35 in.
1/omegaRnsshpl at Shear Plate spacing = 1/omega * hf1 * Lcs * t * Fu = 0.50 * 1.20 * na * 0.38 * 58.00 = na
1/omegaRneshpl at Shear Plate edge = 1/omega * hf1 * Lce * t * Fu = 0.50 * 1.20 * 12.35 * 0.38 * 58.00 = 161.15 kips/bolt
1/omegaRndshpl on Shear Plate at Bolt Diameter   = 1/omega * hf2 * db * t * Fu = 0.50 * 2.40 * 0.75 * 0.38 * 58.00 = 19.57 kips/bolt
Shear Plate bearing capacity, 1/omegaRnshpl = min(1/omegaRnsshpl,1/omegaRneshpl,1/omegaRndshpl) = min(na, 161.15, 19.57) = 19.57 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(20.475, 19.575) = 19.57 kips/bolt
Bolt Shear Demand to Bearing ratio = 19.57 / 9.52 = 2.06

At Row 4, At Column 1:
Ri1 = 9.52 kips
Ri vector at Beam   = <-5.74, 7.59>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 2.39 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * na * (0.35/1) * 65.00 = na
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 2.39 * (0.35/1) * 65.00 = 32.63 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.35/1) * 65.00 = 20.47 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(na, 32.63, 20.47) = 20.47 kips/bolt
Ri vector at Shear Plate   = <5.74, -7.59>
Lcsshpl at Shear Plate spacing  = na
Lceshpl at Shear Plate edge    = 1.98 in.
1/omegaRnsshpl at Shear Plate spacing = 1/omega * hf1 * Lcs * t * Fu = 0.50 * 1.20 * na * 0.38 * 58.00 = na
1/omegaRneshpl at Shear Plate edge = 1/omega * hf1 * Lce * t * Fu = 0.50 * 1.20 * 1.98 * 0.38 * 58.00 = 25.80 kips/bolt
1/omegaRndshpl on Shear Plate at Bolt Diameter   = 1/omega * hf2 * db * t * Fu = 0.50 * 2.40 * 0.75 * 0.38 * 58.00 = 19.57 kips/bolt
Shear Plate bearing capacity, 1/omegaRnshpl = min(1/omegaRnsshpl,1/omegaRneshpl,1/omegaRndshpl) = min(na, 25.80, 19.57) = 19.57 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(20.475, 19.575) = 19.57 kips/bolt
Bolt Shear Demand to Bearing ratio = 19.57 / 9.52 = 2.06

At Row 5, At Column 1:
Ri1 = 11.15 kips
Ri vector at Beam   = <-10.20, 4.49>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 1.44 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * na * (0.35/1) * 65.00 = na
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 1.44 * (0.35/1) * 65.00 = 19.62 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.35/1) * 65.00 = 20.47 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(na, 19.62, 20.47) = 19.62 kips/bolt
Ri vector at Shear Plate   = <10.20, -4.49>
Lcsshpl at Shear Plate spacing  = na
Lceshpl at Shear Plate edge    = 1.09 in.
1/omegaRnsshpl at Shear Plate spacing = 1/omega * hf1 * Lcs * t * Fu = 0.50 * 1.20 * na * 0.38 * 58.00 = na
1/omegaRneshpl at Shear Plate edge = 1/omega * hf1 * Lce * t * Fu = 0.50 * 1.20 * 1.09 * 0.38 * 58.00 = 14.26 kips/bolt
1/omegaRndshpl on Shear Plate at Bolt Diameter   = 1/omega * hf2 * db * t * Fu = 0.50 * 2.40 * 0.75 * 0.38 * 58.00 = 19.57 kips/bolt
Shear Plate bearing capacity, 1/omegaRnshpl = min(1/omegaRnsshpl,1/omegaRneshpl,1/omegaRndshpl) = min(na, 14.26, 19.57) = 14.26 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(19.624, 14.260) = 14.26 kips/bolt
Bolt Shear Demand to Bearing ratio = 14.26 / 11.15 = 1.28

At Row 6, At Column 1:
Ri1 = 11.71 kips
Ri vector at Beam   = <-11.32, 2.99>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 1.34 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * na * (0.35/1) * 65.00 = na
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 1.34 * (0.35/1) * 65.00 = 18.28 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.35/1) * 65.00 = 20.47 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(na, 18.28, 20.47) = 18.28 kips/bolt
Ri vector at Shear Plate   = <11.32, -2.99>
Lcsshpl at Shear Plate spacing  = na
Lceshpl at Shear Plate edge    = 1.03 in.
1/omegaRnsshpl at Shear Plate spacing = 1/omega * hf1 * Lcs * t * Fu = 0.50 * 1.20 * na * 0.38 * 58.00 = na
1/omegaRneshpl at Shear Plate edge = 1/omega * hf1 * Lce * t * Fu = 0.50 * 1.20 * 1.03 * 0.38 * 58.00 = 13.50 kips/bolt
1/omegaRndshpl on Shear Plate at Bolt Diameter   = 1/omega * hf2 * db * t * Fu = 0.50 * 2.40 * 0.75 * 0.38 * 58.00 = 19.57 kips/bolt
Shear Plate bearing capacity, 1/omegaRnshpl = min(1/omegaRnsshpl,1/omegaRneshpl,1/omegaRndshpl) = min(na, 13.50, 19.57) = 13.50 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(18.280, 13.498) = 13.50 kips/bolt
Bolt Shear Demand to Bearing ratio = 13.50 / 11.71 = 1.15

Min Bolt Shear Demand to Bearing ratio for vertical shear only = min(1.0, 1.67199, 1.75608, 2.05628, 2.05655, 1.27931, 1.15294) = 1.00


Bearing Capacity at Beam and Shear Plate at Vertical Shear Load Only, Rbv1 = Min Bolt Shear Demand to Bearing Ratio * Bolt Shear = 1.00 * 30.15 = 30.15 kips

Web Depth = d - [Top Cope Depth] - [Bottom Cope Depth] = 20.7 - 0 - 0 = 20.7 in.
Gross Area (Shear) = [Web Depth] * tw = 20.70 * 0.35 = 7.24 in^2
Net Shear Area (Shear) = ([Web Depth] - ([# rows] * [Diameter + 0.0625])) * tw 
    = (20.70 - (6 * 0.88)) * 0.35 = 5.41 in^2

Using Eq.J4-3:
Shear Yielding = (1/omega) * 0.6 * Fybeam * [Gross Area] = 0.67 * 0.6 * 50.00 * 7.24 = 144.90 kips

Using Eq.J4-4:
Shear Rupture = (1/omega) * 0.6 * Fubeam * [Net Area] = 0.50 * 0.6 * 65.00 * 5.41 = 105.45 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 * 17.50 = 6.56 in^2
Net Area = (17.50 - (6 *(0.81 + 1/16))) * 0.38 = 4.59 in^2

Using Eq.J4-3:
Shear Yielding = (1/omega) * 0.6 * Fypl * [Gross Area] = 0.67 * 0.6 * 36.00 * 6.56 = 94.50 kips

Using Eq.J4-4:
Shear Rupture = (1/omega) * 0.6 * Fupl * [Net Area] = 0.50 * 0.6 * 58.00 * 4.59 = 79.93 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 = (17.5 - 1.25) = 16.25 in.
Net Shear Length = 16.2 - (5.5 * (0.812 + 0.0625)) = 11.44 in.
Gross Tension Length = (0 + 1.5) = 1.50 in.
Net Tension Length = 1.5 - (0.5 * (1 + 0.0625)) = 0.97 in.
1. (1/omega) * [material thickness] * ((0.60 * Fupl* [net shear length]) + (Ubs * Fupl * [net tension length])) 
    = 0.50 * 0.38 * ((0.60 * 58.00 * 11.44) + (1.00 * 58.00 * 0.97)) = 85.16 kips
2. (1/omega) * [material thickness] * ((0.60 * Fypl * [gross shear length]) + (Ubs * Fupl * [net tension length])) 
    = 0.50 * 0.38 * ((0.60 * 36.00 * 16.25) + (1.00 * 58.00 * 0.97)) = 76.35 kips
Block Shear = 76.35 kips

Flexural and Buckling Strength:

Eccentricity at first line of bolts, e = 9.25 in.
Zgross = 28.71 in^3
Znet   = 19.85 in^3
Sgross = 19.14 in^3
Snet   = 13.23 in^3

Using Eq. 9-4
Flexural Rupture = (1/omega) * Fu * Znet / e = 0.50 * 58.00 * 19.85 / 9.25 = 62.24 kips


Using Eq. 9-14 through 9-18, Fcr = Fy * Q
tw = 0.38 in.
ho = 17.50 in.
c = 9.25 in.
lambda = (ho * Fy ^ 0.5) / ( 10 * tw * ( 475.00 + 280.00 * (ho / c)^2 ) ^0.5 ) = 
 = 17.50 * 36.00^0.5 / (10 * 0.38 * (475.00 + 280.00 * (17.50/9.25)^2 )^0.5) = 0.73
When 0.70 < lambda <= 1.41, Q=1.34 - 0.49 * lambda
Q = 0.99
Fcrmin =1/omega * Fcr = 0.60 * 36.00 * 0.99 = 21.30 ksi

Using Eq. 9-6
Buckling = Fcr * Sgross / e = 21.30 * 19.14 / 9.25 = 44.07 kips

Interaction Check of Flexural Yielding, Per AISC 10-5: 
Eccentricity at CG of Bolt Group, e = 9.25 in.
Zgross = 28.71
Znet = 19.85
Mr = Vr * e = 30.00 * 9.25 = 277.50 kips-in
Mc = 1/omega * Mn = 1/omega * Fy * Zgross = 0.60 * 36.00 * 28.71 = 620.16 kips-in
Vr = 30.00 kips
Vc = 1/omega * Vn = 1/omega * 0.60 * Fy * Ag = 0.67 * 0.60 * 36.00 * 6.56 = 94.50 kips
Interaction due to moment and shear, (Vr/Vc)^2 + (Mr/Mc)^2 <= 1.0
(Vr/Vc)^2 + (Mr/Mc)^2 = (30.00 / 94.50)^2 + (277.50 / 620.16)^2 = 0.30 <= 1  (OK)

Note: Mn <= 1.6My by inspection

MAXIMUM PLATE THICKNESS:
No of bolt columns = 1
tp  < = db/2 + 1/16 = 0.375 <= 0.4375 OK
tw  < = db/2 + 1/16 = 0.35 <= 0.4375 OK
Leh(plate) >= 2 * db = 1.5 >= 1.5 OK
Leh(bm) >= 2 * db = 1.6875 >= 1.5 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 * 17.50 * 0.38^3 / 9.25^2 = 30.50 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 = 30.00 * ((0.38 + 0.38) / 2) = 11.25 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 * 36.00) - (30.00 / (17.50 * 0.38))) * 0.5 * 17.50 * 0.38^2 = 12.09 kips-in
Stabilizer Plate Not Required for torsional strength

WELD:

 Weld Requirements:

At shear only case: 
Weld Length for shear, Lv = 17.500 in.
Shear Load per inch per weld, fv = R/Lv/2 = 30.000 / 17.500 / 2 = 0.857 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) = 0.857 / (0.500 * 1.856) = 0.924/16

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

Dmax1 (using eqn 9-3)
 = tshpl * Fushpl / ( Fexx * C1 * 0.088)
 = 0.375 * 58.000 / ( 70.000 * 1.000 * 0.088 ) 
 = 3.515 
Dmax2 (using eqn 9-3)
 = twsupport * Fusupport / ( Fexx * C1 * 0.088 )
 = 0.440 * 65.000 / ( 70.000 * 1.000 * 0.088 ) 
 = 4.622 
Dmax3 = project max fillet weld = 12.000
Dmax=min(Dmax1, Dmax2, Dmax3) = min(3.515, 4.622, 12.000)
 = 3.515 

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 * 17.50 * (3.52 + 3.52) = 114.19 kips