bcw.s.s.01954.01954

SHEAR PLATE CONNECTION SUMMARY

Filler Beam profile: W21X50
Column profile: W14X132
Slope: 0 deg.
Skew: 90
Vertical Offset: 0
Horizontal Offset: 0
Span: 19.9 ft.
Reaction, V: 30 kips
Shear Capacity, Rn: 32.9 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: 11.125 in. x 16.500 in. x 0.500 in.
Configuration Geometry:
Welds at shear plate to support: 5/16 FILLET, 5/16 FILLET
Bolt: 5 rows x 1 column 0.875 in. Diameter A325N_TC bolts
Vertical spacing: 3.5 in.
Horizontal spacing: 3 in.
Shear plate edge setback = 7.62 in.
Beam centerline setback = 7.62 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: 9.38 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 = 9.375 in.
Angle = 0.000 deg.
C = 2.028
Using Table 7-1 to determine (1/omega)rn:
(1/omega)Rn = (1/omega)rn * C = 16.24 * 2.03 = 32.93 kips


Total Vertical Bolt Shear Capacity = 32.93 kips
32.93 kips >= 30.00 kips (OK)

BOLT BEARING AT BEAM AND SHEAR PLATE SIDE
Vertical Shear Only Load Case:
ICR cordinate relative to CG = (1.76, -0.00)
At Row 1, At Column 1:
Ribolt = 15.94 kips
Ri vector at Beam   = <15.45, 3.89>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 11.81 in.
(1/omega)Rnsbm at Beam spacing = (1/omega) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * na * (0.38/1) * 65.00 = na
(1/omega)Rnebm at Beam edge = (1/omega) * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 11.81 * (0.38/1) * 65.00 = 175.08 kips/bolt
(1/omega)Rndbm on Beam at Bolt Diameter   = (1/omega) * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.88 * (0.38/1) * 65.00 = 25.94 kips/bolt
Beam bearing capacity, (1/omega)Rnbm = min((1/omega)Rnsbm,(1/omega)Rnebm,(1/omega)Rndbm) = min(na, 175.08, 25.94) = 25.94 kips/bolt
Ri vector at Shear Plate   = <-15.45, -3.89>
Lcsshpl at Shear Plate spacing  = na
Lceshpl at Shear Plate edge    = 9.09 in.
(1/omega)Rnsshpl at Shear Plate spacing = (1/omega) * hf1 * Lcs * t * Fu = 0.50 * 1.20 * na * 0.50 * 65.00 = na
(1/omega)Rneshpl at Shear Plate edge = (1/omega) * hf1 * Lce * t * Fu = 0.50 * 1.20 * 9.09 * 0.50 * 65.00 = 177.21 kips/bolt
(1/omega)Rndshpl on Shear Plate at Bolt Diameter   = (1/omega) * hf2 * db * t * Fu = 0.50 * 2.40 * 0.88 * 0.50 * 65.00 = 34.12 kips/bolt
Shear Plate bearing capacity, (1/omega)Rnshpl = min((1/omega)Rnsshpl,(1/omega)Rneshpl,(1/omega)Rndshpl) = min(na, 177.21, 34.12) = 34.12 kips/bolt
(1/omega)Rn = min((1/omega)Rnbm, (1/omega)Rnshpl) = min(25.935, 34.125) = 25.94 kips/bolt
Bolt Shear Demand to Bearing ratio = 25.94 / 15.94 = 1.63

At Row 2, At Column 1:
Ribolt = 14.77 kips
Ri vector at Beam   = <13.19, 6.65>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 13.98 in.
(1/omega)Rnsbm at Beam spacing = (1/omega) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * na * (0.38/1) * 65.00 = na
(1/omega)Rnebm at Beam edge = (1/omega) * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 13.98 * (0.38/1) * 65.00 = 207.17 kips/bolt
(1/omega)Rndbm on Beam at Bolt Diameter   = (1/omega) * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.88 * (0.38/1) * 65.00 = 25.94 kips/bolt
Beam bearing capacity, (1/omega)Rnbm = min((1/omega)Rnsbm,(1/omega)Rnebm,(1/omega)Rndbm) = min(na, 207.17, 25.94) = 25.94 kips/bolt
Ri vector at Shear Plate   = <-13.19, -6.65>
Lcsshpl at Shear Plate spacing  = na
Lceshpl at Shear Plate edge    = 9.87 in.
(1/omega)Rnsshpl at Shear Plate spacing = (1/omega) * hf1 * Lcs * t * Fu = 0.50 * 1.20 * na * 0.50 * 65.00 = na
(1/omega)Rneshpl at Shear Plate edge = (1/omega) * hf1 * Lce * t * Fu = 0.50 * 1.20 * 9.87 * 0.50 * 65.00 = 192.42 kips/bolt
(1/omega)Rndshpl on Shear Plate at Bolt Diameter   = (1/omega) * hf2 * db * t * Fu = 0.50 * 2.40 * 0.88 * 0.50 * 65.00 = 34.12 kips/bolt
Shear Plate bearing capacity, (1/omega)Rnshpl = min((1/omega)Rnsshpl,(1/omega)Rneshpl,(1/omega)Rndshpl) = min(na, 192.42, 34.12) = 34.12 kips/bolt
(1/omega)Rn = min((1/omega)Rnbm, (1/omega)Rnshpl) = min(25.935, 34.125) = 25.94 kips/bolt
Bolt Shear Demand to Bearing ratio = 25.94 / 14.77 = 1.76

At Row 3, At Column 1:
Ribolt = 11.85 kips
Ri vector at Beam   = <0.00, 11.85>
Lcsbm at Beam spacing  = 2.56 in.
Lcebm at Beam edge    = 9.53 in.
(1/omega)Rnsbm at Beam spacing = (1/omega) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * 2.56 * (0.38/1) * 65.00 = 37.98 kips/bolt
(1/omega)Rnebm at Beam edge = (1/omega) * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 9.53 * (0.38/1) * 65.00 = 141.25 kips/bolt
(1/omega)Rndbm on Beam at Bolt Diameter   = (1/omega) * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.88 * (0.38/1) * 65.00 = 25.94 kips/bolt
Beam bearing capacity, (1/omega)Rnbm = min((1/omega)Rnsbm,(1/omega)Rnebm,(1/omega)Rndbm) = min(37.98, 141.25, 25.94) = 25.94 kips/bolt
Ri vector at Shear Plate   = <-0.00, -11.85>
Lcsshpl at Shear Plate spacing  = 2.56 in.
Lceshpl at Shear Plate edge    = 7.78 in.
(1/omega)Rnsshpl at Shear Plate spacing = (1/omega) * hf1 * Lcs * t * Fu = 0.50 * 1.20 * 2.56 * 0.50 * 65.00 = 49.97 kips/bolt
(1/omega)Rneshpl at Shear Plate edge = (1/omega) * hf1 * Lce * t * Fu = 0.50 * 1.20 * 7.78 * 0.50 * 65.00 = 151.73 kips/bolt
(1/omega)Rndshpl on Shear Plate at Bolt Diameter   = (1/omega) * hf2 * db * t * Fu = 0.50 * 2.40 * 0.88 * 0.50 * 65.00 = 34.12 kips/bolt
Shear Plate bearing capacity, (1/omega)Rnshpl = min((1/omega)Rnsshpl,(1/omega)Rneshpl,(1/omega)Rndshpl) = min(49.97, 151.73, 34.12) = 34.12 kips/bolt
(1/omega)Rn = min((1/omega)Rnbm, (1/omega)Rnshpl) = min(25.935, 34.125) = 25.94 kips/bolt
Bolt Shear Demand to Bearing ratio = 25.94 / 11.85 = 2.19

At Row 4, At Column 1:
Ribolt = 14.77 kips
Ri vector at Beam   = <-13.19, 6.65>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 1.49 in.
(1/omega)Rnsbm at Beam spacing = (1/omega) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * na * (0.38/1) * 65.00 = na
(1/omega)Rnebm at Beam edge = (1/omega) * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 1.49 * (0.38/1) * 65.00 = 22.09 kips/bolt
(1/omega)Rndbm on Beam at Bolt Diameter   = (1/omega) * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.88 * (0.38/1) * 65.00 = 25.94 kips/bolt
Beam bearing capacity, (1/omega)Rnbm = min((1/omega)Rnsbm,(1/omega)Rnebm,(1/omega)Rndbm) = min(na, 22.09, 25.94) = 22.09 kips/bolt
Ri vector at Shear Plate   = <13.19, -6.65>
Lcsshpl at Shear Plate spacing  = na
Lceshpl at Shear Plate edge    = 1.33 in.
(1/omega)Rnsshpl at Shear Plate spacing = (1/omega) * hf1 * Lcs * t * Fu = 0.50 * 1.20 * na * 0.50 * 65.00 = na
(1/omega)Rneshpl at Shear Plate edge = (1/omega) * hf1 * Lce * t * Fu = 0.50 * 1.20 * 1.33 * 0.50 * 65.00 = 25.93 kips/bolt
(1/omega)Rndshpl on Shear Plate at Bolt Diameter   = (1/omega) * hf2 * db * t * Fu = 0.50 * 2.40 * 0.88 * 0.50 * 65.00 = 34.12 kips/bolt
Shear Plate bearing capacity, (1/omega)Rnshpl = min((1/omega)Rnsshpl,(1/omega)Rneshpl,(1/omega)Rndshpl) = min(na, 25.93, 34.12) = 25.93 kips/bolt
(1/omega)Rn = min((1/omega)Rnbm, (1/omega)Rnshpl) = min(22.094, 25.930) = 22.09 kips/bolt
Bolt Shear Demand to Bearing ratio = 22.09 / 14.77 = 1.50

At Row 5, At Column 1:
Ribolt = 15.94 kips
Ri vector at Beam   = <-15.45, 3.89>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 1.34 in.
(1/omega)Rnsbm at Beam spacing = (1/omega) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * na * (0.38/1) * 65.00 = na
(1/omega)Rnebm at Beam edge = (1/omega) * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 1.34 * (0.38/1) * 65.00 = 19.80 kips/bolt
(1/omega)Rndbm on Beam at Bolt Diameter   = (1/omega) * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.88 * (0.38/1) * 65.00 = 25.94 kips/bolt
Beam bearing capacity, (1/omega)Rnbm = min((1/omega)Rnsbm,(1/omega)Rnebm,(1/omega)Rndbm) = min(na, 19.80, 25.94) = 19.80 kips/bolt
Ri vector at Shear Plate   = <15.45, -3.89>
Lcsshpl at Shear Plate spacing  = na
Lceshpl at Shear Plate edge    = 1.22 in.
(1/omega)Rnsshpl at Shear Plate spacing = (1/omega) * hf1 * Lcs * t * Fu = 0.50 * 1.20 * na * 0.50 * 65.00 = na
(1/omega)Rneshpl at Shear Plate edge = (1/omega) * hf1 * Lce * t * Fu = 0.50 * 1.20 * 1.22 * 0.50 * 65.00 = 23.88 kips/bolt
(1/omega)Rndshpl on Shear Plate at Bolt Diameter   = (1/omega) * hf2 * db * t * Fu = 0.50 * 2.40 * 0.88 * 0.50 * 65.00 = 34.12 kips/bolt
Shear Plate bearing capacity, (1/omega)Rnshpl = min((1/omega)Rnsshpl,(1/omega)Rneshpl,(1/omega)Rndshpl) = min(na, 23.88, 34.12) = 23.88 kips/bolt
(1/omega)Rn = min((1/omega)Rnbm, (1/omega)Rnshpl) = min(19.798, 23.880) = 19.80 kips/bolt
Bolt Shear Demand to Bearing ratio = 19.80 / 15.94 = 1.24

Min Bolt Shear Demand to Bearing ratio Beam and Shear Plate for vertical shear only
 = min(1.00, 1.63, 1.76, 2.19, 1.50, 1.24) = 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 * 32.93 = 32.93 kips
Rbv = 32.93 kips >= V = 30.00 kips (OK)

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 - (5 * 1.00)) * 0.38 = 6.00 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 * 6.00 = 117.08 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 * 16.50 = 8.25 in^2
Net Area = (16.50 - (5 *(0.94 + 1/16))) * 0.50 = 5.75 in^2

Using Eq.J4-3:
Shear Yielding = (1/omega) * 0.6 * Fypl * [Gross Area] = 0.67 * 0.6 * 50.00 * 8.25 = 165.00 kips

Using Eq.J4-4:
Shear Rupture = (1/omega) * 0.6 * Fupl * [Net Area] = 0.50 * 0.6 * 65.00 * 5.75 = 112.12 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 = (16.5 - 1.25) = 15.25 in.
Net Shear Length = 15.2 - (4.5 * (0.938 + 0.0625)) = 10.75 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 * 0.50 * ((0.60 * 65.00 * 10.75) + (1.00 * 65.00 * 1.16)) = 123.60 kips
2. (1/omega) * [material thickness] * ((0.60 * Fypl * [gross shear length]) + (Ubs * Fupl * [net tension length])) 
    = 0.50 * 0.50 * ((0.60 * 50.00 * 15.25) + (1.00 * 65.00 * 1.16)) = 133.16 kips
Block Shear = 123.60 kips

123.60 kips >= Reaction V = 30.00 kips (OK)

Flexural and Buckling Strength:

Eccentricity at first line of bolts, e = 9.38 in.
Zgross = 34.03 in^3
Znet   = 23.41 in^3
Sgross = 22.69 in^3
Snet   = 15.26 in^3

Using Eq. 9-4
Flexural Rupture = (1/omega) * Fu * Znet / e = 0.50 * 65.00 * 23.41 / 9.38 = 81.14 kips


Using Eq. 9-14 through 9-18, Fcr = Fy * Q
tw = 0.50 in.
ho = 16.50 in.
c = 9.38 in.
lambda = (ho * Fy ^ 0.5) / ( 10 * tw * ( 475.00 + 280.00 * (ho / c)^2 ) ^0.5 ) = 
 = 16.50 * 50.00^0.5 / (10 * 0.50 * (475.00 + 280.00 * (16.50/9.38)^2 )^0.5) = 0.64
When lambda <= 0.70, Q=1
Q = 1.00
Fcrmin =1/omega * Fcr = 0.60 * 50.00 * 1.00 = 30.00 ksi

Using Eq. 9-6
Buckling = Fcr * Sgross / e = 30.00 * 22.69 / 9.38 = 72.60 kips

Interaction Check of Flexural Yielding, Per AISC 10-5: 
Eccentricity at CG of Bolt Group, e = 9.38 in.
Zgross = 34.03
Znet = 23.41
Mr = Vr * e = 30.00 * 9.38 = 281.25 kips-in
Mc = 1/omega * Mn = 1/omega * Fy * Zgross = 0.60 * 50.00 * 34.03 = 1020.94 kips-in
Vr = 30.00 kips
Vc = 1/omega * Vn = 1/omega * 0.60 * Fy * Ag = 0.67 * 0.60 * 50.00 * 8.25 = 165.00 kips
Interaction due to moment and shear, (Vr/Vc)^2 + (Mr/Mc)^2 <= 1.0
(Vr/Vc)^2 + (Mr/Mc)^2 = (30.00 / 165.00)^2 + (281.25 / 1020.94)^2 = 0.11 <= 1  (OK)

Note: Mn <= 1.6My by inspection

MAXIMUM PLATE THICKNESS:
No of bolt columns = 1
tp  < = db/2 + 1/16 = 0.5 <= 0.5 OK
tw  < = db/2 + 1/16 = 0.38 <= 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 * 16.50 * 0.50^3 / 9.38^2 = 66.35 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 + 0.50) / 2) = 13.12 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) - (30.00 / (16.50 * 0.50))) * 0.5 * 16.50 * 0.50^2 = 33.75 kips-in
Stabilizer Plate Not Required for torsional strength

WELD:

 Weld Requirements:

At shear only case: 
Weld Length for shear, Lv = 16.500 in.
Shear Load per inch per weld, fv = R/Lv/2 = 30.000 / 16.500 / 2 = 0.909 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) = 0.909 / (0.500 * 1.856) = 0.980/16

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

Dmax1 (using eqn 9-3)
 = tshpl * Fushpl / ( Fexx * C1 * 0.088)
 = 0.500 * 65.000 / ( 70.000 * 1.000 * 0.088 ) 
 = 5.253 
Dmax2 (using eqn 9-3)
 = twsupport * Fusupport / ( Fexx * C1 * 0.088 )
 = 0.645 * 65.000 / ( 70.000 * 1.000 * 0.088 ) 
 = 6.776 
Dmax3 = project max fillet weld = 12.000
Dmax=min(Dmax1, Dmax2, Dmax3) = min(5.253, 6.776, 12.000)
 = 5.253 

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 * 16.50 * (5.00 + 5.00) = 153.13 kips

153.13 kips >= Vbm = 30.00 kips (OK)