bcw.s.s.00072.00536

SHEAR PLATE CONNECTION SUMMARY

Filler Beam profile: W16X26
Column profile: W14X43
Slope: 0 deg.
Skew: 90
Vertical Offset: 0
Horizontal Offset: 0
Span: 20 ft.
Reaction, V: 14 kips
Shear Capacity, Rn: 20.6 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: 7.500 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 columns 0.75 in. Diameter A325N_TC bolts
Vertical spacing: 3 in.
Horizontal spacing: 3 in.
Shear plate edge setback = 4.38 in.
Beam centerline setback = 4.38 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: 6 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 = 6.000 in.
Angle = 0.000 deg.
C = 1.730
Using Table 7-1 to determine (1/omega) * rn:
Rn = (1/omega) * rn * C = 11.93 * 1.73 = 20.64 kips

BOLT BEARING AT BEAM SIDE:
Vertical Shear Only Load Case:
ICR cordinate relative to CG = (1.36, -0.00)
At Row 1, At Column 1:
Ri1 = 11.71 kips
Ri vector at Beam   = <11.21, 3.39>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 9.97 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * na * (0.25/1) * 65.00 = na
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 9.97 * (0.25/1) * 65.00 = 97.16 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.25/1) * 65.00 = 14.62 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(na, 97.16, 14.62) = 14.62 kips/bolt
Ri vector at Shear Plate   = <-11.21, -3.39>
Lcsshpl at Shear Plate spacing  = na
Lceshpl at Shear Plate edge    = 5.75 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 * 5.75 * 0.38 * 58.00 = 74.98 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, 74.98, 19.57) = 19.57 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(14.625, 19.575) = 14.62 kips/bolt
Bolt Shear Demand to Bearing ratio = 14.62 / 11.71 = 1.25

At Row 2, At Column 1:
Ri1 = 10.32 kips
Ri vector at Beam   = <7.65, 6.93>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 8.53 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * na * (0.25/1) * 65.00 = na
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 8.53 * (0.25/1) * 65.00 = 83.15 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.25/1) * 65.00 = 14.62 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(na, 83.15, 14.62) = 14.62 kips/bolt
Ri vector at Shear Plate   = <-7.65, -6.93>
Lcsshpl at Shear Plate spacing  = na
Lceshpl at Shear Plate edge    = 7.49 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 * 7.49 * 0.38 * 58.00 = 97.78 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, 97.78, 19.57) = 19.57 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(14.625, 19.575) = 14.62 kips/bolt
Bolt Shear Demand to Bearing ratio = 14.62 / 10.32 = 1.42

At Row 3, At Column 1:
Ri1 = 10.32 kips
Ri vector at Beam   = <-7.65, 6.93>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 1.79 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * na * (0.25/1) * 65.00 = na
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 1.79 * (0.25/1) * 65.00 = 17.43 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.25/1) * 65.00 = 14.62 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(na, 17.43, 14.62) = 14.62 kips/bolt
Ri vector at Shear Plate   = <7.65, -6.93>
Lcsshpl at Shear Plate spacing  = na
Lceshpl at Shear Plate edge    = 1.42 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 * 1.42 * 0.38 * 58.00 = 18.54 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, 18.54, 19.57) = 18.54 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(14.625, 18.536) = 14.62 kips/bolt
Bolt Shear Demand to Bearing ratio = 14.62 / 10.32 = 1.42

At Row 4, At Column 1:
Ri1 = 11.71 kips
Ri vector at Beam   = <-11.21, 3.39>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 1.29 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * na * (0.25/1) * 65.00 = na
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 1.29 * (0.25/1) * 65.00 = 12.59 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.25/1) * 65.00 = 14.62 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(na, 12.59, 14.62) = 12.59 kips/bolt
Ri vector at Shear Plate   = <11.21, -3.39>
Lcsshpl at Shear Plate spacing  = na
Lceshpl at Shear Plate edge    = 1.04 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 * 1.04 * 0.38 * 58.00 = 13.63 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, 13.63, 19.57) = 13.63 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(12.591, 13.633) = 12.59 kips/bolt
Bolt Shear Demand to Bearing ratio = 12.59 / 11.71 = 1.08

Min Bolt Shear Demand to Bearing ratio for vertical shear only = min(1.0, 1.24919, 1.41683, 1.41699, 1.07545) = 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 * 20.64 = 20.64 kips

Web Depth = d - [Top Cope Depth] - [Bottom Cope Depth] = 15.7 - 0 - 0 = 15.7 in.
Gross Area (Shear) = [Web Depth] * tw = 15.70 * 0.25 = 3.92 in^2
Net Shear Area (Shear) = ([Web Depth] - ([# rows] * [Diameter + 0.0625])) * tw 
    = (15.70 - (4 * 0.88)) * 0.25 = 3.05 in^2

Using Eq.J4-3:
Shear Yielding = (1/omega) * 0.6 * Fybeam * [Gross Area] = 0.67 * 0.6 * 50.00 * 3.92 = 78.50 kips

Using Eq.J4-4:
Shear Rupture = (1/omega) * 0.6 * Fubeam * [Net Area] = 0.50 * 0.6 * 65.00 * 3.05 = 59.47 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 Shear not required.

Gross Area = 0.38 * 11.50 = 4.31 in^2
Net Area = (11.50 - (4 *(0.81 + 1/16))) * 0.38 = 3.00 in^2

Using Eq.J4-3:
Shear Yielding = (1/omega) * 0.6 * Fypl * [Gross Area] = 0.67 * 0.6 * 36.00 * 4.31 = 62.10 kips

Using Eq.J4-4:
Shear Rupture = (1/omega) * 0.6 * Fupl * [Net Area] = 0.50 * 0.6 * 58.00 * 3.00 = 52.20 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 = (11.5 - 1.25) = 10.25 in.
Net Shear Length = 10.2 - (3.5 * (0.812 + 0.0625)) = 7.19 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 * 7.19) + (1.00 * 58.00 * 0.97)) = 57.43 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 * 10.25) + (1.00 * 58.00 * 0.97)) = 52.05 kips
Block Shear = 52.05 kips

Flexural and Buckling Strength:

Eccentricity at first line of bolts, e = 6.00 in.
Zgross = 12.40 in^3
Znet   = 8.46 in^3
Sgross = 8.27 in^3
Snet   = 5.70 in^3

Using Eq. 9-4
Flexural Rupture = (1/omega) * Fu * Znet / e = 0.50 * 58.00 * 8.46 / 6.00 = 40.89 kips


Using Eq. 9-14 through 9-18, Fcr = Fy * Q
tw = 0.38 in.
ho = 11.50 in.
c = 6.00 in.
lambda = (ho * Fy ^ 0.5) / ( 10 * tw * ( 475.00 + 280.00 * (ho / c)^2 ) ^0.5 ) = 
 = 11.50 * 36.00^0.5 / (10 * 0.38 * (475.00 + 280.00 * (11.50/6.00)^2 )^0.5) = 0.47
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 * 8.27 / 6.00 = 29.76 kips

Interaction Check of Flexural Yielding, Per AISC 10-5: 
Eccentricity at CG of Bolt Group, e = 6.00 in.
Zgross = 12.40
Znet = 8.46
Mr = Vr * e = 14.00 * 6.00 = 84.00 kips-in
Mc = 1/omega * Mn = 1/omega * Fy * Zgross = 0.60 * 36.00 * 12.40 = 267.81 kips-in
Vr = 14.00 kips
Vc = 1/omega * Vn = 1/omega * 0.60 * Fy * Ag = 0.67 * 0.60 * 36.00 * 4.31 = 62.10 kips
Interaction due to moment and shear, (Vr/Vc)^2 + (Mr/Mc)^2 <= 1.0
(Vr/Vc)^2 + (Mr/Mc)^2 = (14.00 / 62.10)^2 + (84.00 / 267.81)^2 = 0.15 <= 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 = 0.25 <= 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 * 11.50 * 0.38^3 / 6.00^2 = 47.63 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 = 14.00 * ((0.25 + 0.38) / 2) = 4.38 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) - (14.00 / (11.50 * 0.38))) * 0.5 * 11.50 * 0.38^2 = 9.02 kips-in
Stabilizer Plate Not Required for torsional strength

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 = 14.000 / 11.500 / 2 = 0.609 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) = 0.609 / (0.500 * 1.856) = 0.656/16

Minimum fillet weld size : 
   At shear only load case = 0.04 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 )
 = 0.305 * 65.000 / ( 70.000 * 1.000 * 0.088 ) 
 = 3.204 
Dmax3 = project max fillet weld = 12.000
Dmax=min(Dmax1, Dmax2, Dmax3) = min(3.515, 3.204, 12.000)
 = 3.204 

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 * 11.50 * (3.20 + 3.20) = 68.40 kips