bcw.s.s.00315.00732

SHEAR PLATE CONNECTION SUMMARY

Filler Beam profile: W21X50
Column profile: W14X74
Slope: 0 deg.
Skew: 90
Vertical Offset: 0
Horizontal Offset: 0
Span: 45 ft.
Reaction, V: 33 kips
Shear Capacity, Rn: 37.8 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: 8.500 in. x 17.500 in. x 0.500 in.
Configuration Geometry:
Welds at shear plate to support: 5/16 FILLET, 5/16 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 = 5.38 in.
Beam centerline setback = 5.38 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: 1.62 in.
Horizontal distance to first hole: 7 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 = 7.000 in.
Angle = 0.000 deg.
C = 3.171
Using Table 7-1 to determine (1/omega) * rn:
Rn = (1/omega) * rn * C = 11.93 * 3.17 = 37.82 kips

BOLT BEARING AT BEAM SIDE:
Vertical Shear Only Load Case:
ICR cordinate relative to CG = (2.79, 0.00)
At Row 1, At Column 1:
Ri1 = 11.71 kips
Ri vector at Beam   = <10.97, 4.09>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 8.19 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * na * (0.38/1) * 65.00 = na
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 8.19 * (0.38/1) * 65.00 = 121.32 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.38/1) * 65.00 = 22.23 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(na, 121.32, 22.23) = 22.23 kips/bolt
Ri vector at Shear Plate   = <-10.97, -4.09>
Lcsshpl at Shear Plate spacing  = na
Lceshpl at Shear Plate edge    = 6.94 in.
1/omegaRnsshpl at Shear Plate spacing = 1/omega * hf1 * Lcs * t * Fu = 0.50 * 1.20 * na * 0.50 * 58.00 = na
1/omegaRneshpl at Shear Plate edge = 1/omega * hf1 * Lce * t * Fu = 0.50 * 1.20 * 6.94 * 0.50 * 58.00 = 120.70 kips/bolt
1/omegaRndshpl on Shear Plate at Bolt Diameter   = 1/omega * hf2 * db * t * Fu = 0.50 * 2.40 * 0.75 * 0.50 * 58.00 = 26.10 kips/bolt
Shear Plate bearing capacity, 1/omegaRnshpl = min(1/omegaRnsshpl,1/omegaRneshpl,1/omegaRndshpl) = min(na, 120.70, 26.10) = 26.10 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(22.230, 26.100) = 22.23 kips/bolt
Bolt Shear Demand to Bearing ratio = 22.23 / 11.71 = 1.90

At Row 2, At Column 1:
Ri1 = 11.22 kips
Ri vector at Beam   = <9.53, 5.92>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 10.97 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * na * (0.38/1) * 65.00 = na
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 10.97 * (0.38/1) * 65.00 = 162.53 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.38/1) * 65.00 = 22.23 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(na, 162.53, 22.23) = 22.23 kips/bolt
Ri vector at Shear Plate   = <-9.53, -5.92>
Lcsshpl at Shear Plate spacing  = na
Lceshpl at Shear Plate edge    = 7.65 in.
1/omegaRnsshpl at Shear Plate spacing = 1/omega * hf1 * Lcs * t * Fu = 0.50 * 1.20 * na * 0.50 * 58.00 = na
1/omegaRneshpl at Shear Plate edge = 1/omega * hf1 * Lce * t * Fu = 0.50 * 1.20 * 7.65 * 0.50 * 58.00 = 133.13 kips/bolt
1/omegaRndshpl on Shear Plate at Bolt Diameter   = 1/omega * hf2 * db * t * Fu = 0.50 * 2.40 * 0.75 * 0.50 * 58.00 = 26.10 kips/bolt
Shear Plate bearing capacity, 1/omegaRnshpl = min(1/omegaRnsshpl,1/omegaRneshpl,1/omegaRndshpl) = min(na, 133.13, 26.10) = 26.10 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(22.230, 26.100) = 22.23 kips/bolt
Bolt Shear Demand to Bearing ratio = 22.23 / 11.22 = 1.98

At Row 3, At Column 1:
Ri1 = 10.11 kips
Ri vector at Beam   = <4.78, 8.91>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 9.81 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * na * (0.38/1) * 65.00 = na
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 9.81 * (0.38/1) * 65.00 = 145.35 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.38/1) * 65.00 = 22.23 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(na, 145.35, 22.23) = 22.23 kips/bolt
Ri vector at Shear Plate   = <-4.78, -8.91>
Lcsshpl at Shear Plate spacing  = na
Lceshpl at Shear Plate edge    = 11.17 in.
1/omegaRnsshpl at Shear Plate spacing = 1/omega * hf1 * Lcs * t * Fu = 0.50 * 1.20 * na * 0.50 * 58.00 = na
1/omegaRneshpl at Shear Plate edge = 1/omega * hf1 * Lce * t * Fu = 0.50 * 1.20 * 11.17 * 0.50 * 58.00 = 194.38 kips/bolt
1/omegaRndshpl on Shear Plate at Bolt Diameter   = 1/omega * hf2 * db * t * Fu = 0.50 * 2.40 * 0.75 * 0.50 * 58.00 = 26.10 kips/bolt
Shear Plate bearing capacity, 1/omegaRnshpl = min(1/omegaRnsshpl,1/omegaRneshpl,1/omegaRndshpl) = min(na, 194.38, 26.10) = 26.10 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(22.230, 26.100) = 22.23 kips/bolt
Bolt Shear Demand to Bearing ratio = 22.23 / 10.11 = 2.20

At Row 4, At Column 1:
Ri1 = 10.11 kips
Ri vector at Beam   = <-4.78, 8.90>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 3.03 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * na * (0.38/1) * 65.00 = na
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 3.03 * (0.38/1) * 65.00 = 44.87 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.38/1) * 65.00 = 22.23 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(na, 44.87, 22.23) = 22.23 kips/bolt
Ri vector at Shear Plate   = <4.78, -8.90>
Lcsshpl at Shear Plate spacing  = na
Lceshpl at Shear Plate edge    = 2.71 in.
1/omegaRnsshpl at Shear Plate spacing = 1/omega * hf1 * Lcs * t * Fu = 0.50 * 1.20 * na * 0.50 * 58.00 = na
1/omegaRneshpl at Shear Plate edge = 1/omega * hf1 * Lce * t * Fu = 0.50 * 1.20 * 2.71 * 0.50 * 58.00 = 47.13 kips/bolt
1/omegaRndshpl on Shear Plate at Bolt Diameter   = 1/omega * hf2 * db * t * Fu = 0.50 * 2.40 * 0.75 * 0.50 * 58.00 = 26.10 kips/bolt
Shear Plate bearing capacity, 1/omegaRnshpl = min(1/omegaRnsshpl,1/omegaRneshpl,1/omegaRndshpl) = min(na, 47.13, 26.10) = 26.10 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(22.230, 26.100) = 22.23 kips/bolt
Bolt Shear Demand to Bearing ratio = 22.23 / 10.11 = 2.20

At Row 5, At Column 1:
Ri1 = 11.22 kips
Ri vector at Beam   = <-9.53, 5.92>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 1.51 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * na * (0.38/1) * 65.00 = na
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 1.51 * (0.38/1) * 65.00 = 22.32 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.38/1) * 65.00 = 22.23 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(na, 22.32, 22.23) = 22.23 kips/bolt
Ri vector at Shear Plate   = <9.53, -5.92>
Lcsshpl at Shear Plate spacing  = na
Lceshpl at Shear Plate edge    = 1.18 in.
1/omegaRnsshpl at Shear Plate spacing = 1/omega * hf1 * Lcs * t * Fu = 0.50 * 1.20 * na * 0.50 * 58.00 = na
1/omegaRneshpl at Shear Plate edge = 1/omega * hf1 * Lce * t * Fu = 0.50 * 1.20 * 1.18 * 0.50 * 58.00 = 20.48 kips/bolt
1/omegaRndshpl on Shear Plate at Bolt Diameter   = 1/omega * hf2 * db * t * Fu = 0.50 * 2.40 * 0.75 * 0.50 * 58.00 = 26.10 kips/bolt
Shear Plate bearing capacity, 1/omegaRnshpl = min(1/omegaRnsshpl,1/omegaRneshpl,1/omegaRndshpl) = min(na, 20.48, 26.10) = 20.48 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(22.230, 20.480) = 20.48 kips/bolt
Bolt Shear Demand to Bearing ratio = 20.48 / 11.22 = 1.83

At Row 6, At Column 1:
Ri1 = 11.71 kips
Ri vector at Beam   = <-10.97, 4.09>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 1.33 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * na * (0.38/1) * 65.00 = na
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 1.33 * (0.38/1) * 65.00 = 19.68 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.38/1) * 65.00 = 22.23 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(na, 19.68, 22.23) = 19.68 kips/bolt
Ri vector at Shear Plate   = <10.97, -4.09>
Lcsshpl at Shear Plate spacing  = na
Lceshpl at Shear Plate edge    = 1.07 in.
1/omegaRnsshpl at Shear Plate spacing = 1/omega * hf1 * Lcs * t * Fu = 0.50 * 1.20 * na * 0.50 * 58.00 = na
1/omegaRneshpl at Shear Plate edge = 1/omega * hf1 * Lce * t * Fu = 0.50 * 1.20 * 1.07 * 0.50 * 58.00 = 18.57 kips/bolt
1/omegaRndshpl on Shear Plate at Bolt Diameter   = 1/omega * hf2 * db * t * Fu = 0.50 * 2.40 * 0.75 * 0.50 * 58.00 = 26.10 kips/bolt
Shear Plate bearing capacity, 1/omegaRnshpl = min(1/omegaRnsshpl,1/omegaRneshpl,1/omegaRndshpl) = min(na, 18.57, 26.10) = 18.57 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(19.678, 18.568) = 18.57 kips/bolt
Bolt Shear Demand to Bearing ratio = 18.57 / 11.71 = 1.59

Min Bolt Shear Demand to Bearing ratio for vertical shear only = min(1.0, 1.89879, 1.98142, 2.19939, 2.19925, 1.82538, 1.58597) = 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 * 37.82 = 37.82 kips

Web Depth = d - [Top Cope Depth] - [Bottom Cope Depth] = 20.8 - 0 - 0 = 20.8 in.
Gross Area (Shear) = [Web Depth] * tw = 20.80 * 0.38 = 7.90 in^2
Net Shear Area (Shear) = ([Web Depth] - ([# rows] * [Diameter + 0.0625])) * tw 
    = (20.80 - (6 * 0.88)) * 0.38 = 5.91 in^2

Using Eq.J4-3:
Shear Yielding = (1/omega) * 0.6 * Fybeam * [Gross Area] = 0.67 * 0.6 * 50.00 * 7.90 = 158.08 kips

Using Eq.J4-4:
Shear Rupture = (1/omega) * 0.6 * Fubeam * [Net Area] = 0.50 * 0.6 * 65.00 * 5.91 = 115.23 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 = 0.50 * 17.50 = 8.75 in^2
Net Area = (17.50 - (6 *(0.81 + 1/16))) * 0.50 = 6.12 in^2

Using Eq.J4-3:
Shear Yielding = (1/omega) * 0.6 * Fypl * [Gross Area] = 0.67 * 0.6 * 36.00 * 8.75 = 126.00 kips

Using Eq.J4-4:
Shear Rupture = (1/omega) * 0.6 * Fupl * [Net Area] = 0.50 * 0.6 * 58.00 * 6.12 = 106.57 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 * 0.50 * ((0.60 * 58.00 * 11.44) + (1.00 * 58.00 * 0.97)) = 113.55 kips
2. (1/omega) * [material thickness] * ((0.60 * Fypl * [gross shear length]) + (Ubs * Fupl * [net tension length])) 
    = 0.50 * 0.50 * ((0.60 * 36.00 * 16.25) + (1.00 * 58.00 * 0.97)) = 101.80 kips
Block Shear = 101.80 kips

Flexural and Buckling Strength:

Eccentricity at first line of bolts, e = 7.00 in.
Zgross = 38.28 in^3
Znet   = 26.47 in^3
Sgross = 25.52 in^3
Snet   = 17.65 in^3

Using Eq. 9-4
Flexural Rupture = (1/omega) * Fu * Znet / e = 0.50 * 58.00 * 26.47 / 7.00 = 109.66 kips


Using Eq. 9-14 through 9-18, Fcr = Fy * Q
tw = 0.50 in.
ho = 17.50 in.
c = 7.00 in.
lambda = (ho * Fy ^ 0.5) / ( 10 * tw * ( 475.00 + 280.00 * (ho / c)^2 ) ^0.5 ) = 
 = 17.50 * 36.00^0.5 / (10 * 0.50 * (475.00 + 280.00 * (17.50/7.00)^2 )^0.5) = 0.45
When lambda <= 0.70, Q=1
Q = 1.00
Fcrmin =1/omega * Fcr = 0.60 * 36.00 * 1.00 = 21.60 ksi

Using Eq. 9-6
Buckling = Fcr * Sgross / e = 21.60 * 25.52 / 7.00 = 78.75 kips

Interaction Check of Flexural Yielding, Per AISC 10-5: 
Eccentricity at CG of Bolt Group, e = 7.00 in.
Zgross = 38.28
Znet = 26.47
Mr = Vr * e = 33.00 * 7.00 = 231.00 kips-in
Mc = 1/omega * Mn = 1/omega * Fy * Zgross = 0.60 * 36.00 * 38.28 = 826.87 kips-in
Vr = 33.00 kips
Vc = 1/omega * Vn = 1/omega * 0.60 * Fy * Ag = 0.67 * 0.60 * 36.00 * 8.75 = 126.00 kips
Interaction due to moment and shear, (Vr/Vc)^2 + (Mr/Mc)^2 <= 1.0
(Vr/Vc)^2 + (Mr/Mc)^2 = (33.00 / 126.00)^2 + (231.00 / 826.87)^2 = 0.15 <= 1  (OK)

Note: Mn <= 1.6My by inspection

MAXIMUM PLATE THICKNESS:
No of bolt columns = 1
tw  < = db/2 + 1/16 = 0.38 <= 0.4375 OK
Leh(plate) >= 2 * db = 1.5 >= 1.5 OK
Leh(bm) >= 2 * db = 1.625 >= 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 * 0.50^3 / 7.00^2 = 126.22 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 = 33.00 * ((0.38 + 0.50) / 2) = 14.44 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) - (33.00 / (17.50 * 0.50))) * 0.5 * 17.50 * 0.50^2 = 23.25 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 = 33.000 / 17.500 / 2 = 0.943 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) = 0.943 / (0.500 * 1.856) = 1.016/16

Minimum fillet weld size : 
   At shear only load case = 0.06 in.
   per Table J2.4     = 0.19 in.
   5/8(tp)            = 0.31 in.
   user preference    = 0.25 in.

Dmax1 (using eqn 9-3)
 = tshpl * Fushpl / ( Fexx * C1 * 0.088)
 = 0.500 * 58.000 / ( 70.000 * 1.000 * 0.088 ) 
 = 4.687 
Dmax2 (using eqn 9-3)
 = twsupport * Fusupport / ( Fexx * C1 * 0.088 )
 = 0.450 * 65.000 / ( 70.000 * 1.000 * 0.088 ) 
 = 4.728 
Dmax3 = project max fillet weld = 12.000
Dmax=min(Dmax1, Dmax2, Dmax3) = min(4.687, 4.728, 12.000)
 = 4.687 

Use weld size
D1 = 5.00
D2 = 5.00

Weld Strength :
Vertical weld capacity during shear only load, 1/omega * Rnv1 = 0.50 * 1.86 * 17.50 * (4.69 + 4.69) = 152.25 kips