bb.s.s.01001.01001

SHEAR PLATE CONNECTION SUMMARY

Filler Beam profile: W21X50
Support Girder profile: W21X50
Slope: 0 deg.
Skew: 90
Vertical Offset: 0
Horizontal Offset: 0
Span: 45 ft.
Reaction, V: 33 kips
Shear Capacity, Rn: 33.8 kips
Design/Reference according to AISC 14th Ed. - ASD
Shear Plate: Extended Configuration
Beam material grade: A992
Support material grade: A992
Plate material grade: A572-GR.50
Weld grade: E70
Shear Plate Size: 7.125 in. x 13.000 in. x 0.375 in.
Configuration Geometry:
Welds at shear plate to support: 4/16 FILLET, 4/16 FILLET
Bolt: 4 rows x 1 column 0.875 in. Diameter A325N_TC bolts
Vertical spacing: 3.5 in.
Horizontal spacing: 3 in.
Shear plate edge setback = 3.62 in.
Beam centerline setback = 3.62 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: 5.38 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 = 5.565 in.
Angle = 0.000 deg.
C = 2.081
Using Table 7-1 to determine (1/omega)rn:
(1/omega)Rn = (1/omega)rn * C = 16.24 * 2.08 = 33.79 kips


Total Vertical Bolt Shear Capacity = 33.79 kips
33.79 kips >= 33.00 kips (OK)

BOLT BEARING AT BEAM AND SHEAR PLATE SIDE
Vertical Shear Only Load Case:
ICR cordinate relative to CG = (2.08, 0.00)
At Row 1, At Column 1:
Ribolt = 15.94 kips
Ri vector at Beam   = <14.82, 5.87>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 7.68 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 * 7.68 * (0.38/1) * 65.00 = 113.78 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, 113.78, 25.94) = 25.94 kips/bolt
Ri vector at Shear Plate   = <-14.82, -5.87>
Lcsshpl at Shear Plate spacing  = na
Lceshpl at Shear Plate edge    = 5.18 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 * 5.18 * 0.38 * 65.00 = 75.70 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, 75.70, 25.59) = 25.59 kips/bolt
(1/omega)Rn = min((1/omega)Rnbm, (1/omega)Rnshpl) = min(25.935, 25.594) = 25.59 kips/bolt
Bolt Shear Demand to Bearing ratio = 25.59 / 15.94 = 1.61

At Row 2, At Column 1:
Ribolt = 14.41 kips
Ri vector at Beam   = <9.28, 11.03>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 8.03 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 * 8.03 * (0.38/1) * 65.00 = 118.95 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, 118.95, 25.94) = 25.94 kips/bolt
Ri vector at Shear Plate   = <-9.28, -11.03>
Lcsshpl at Shear Plate spacing  = na
Lceshpl at Shear Plate edge    = 7.74 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 * 7.74 * 0.38 * 65.00 = 113.13 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, 113.13, 25.59) = 25.59 kips/bolt
(1/omega)Rn = min((1/omega)Rnbm, (1/omega)Rnshpl) = min(25.935, 25.594) = 25.59 kips/bolt
Bolt Shear Demand to Bearing ratio = 25.59 / 14.41 = 1.78

At Row 3, At Column 1:
Ribolt = 14.41 kips
Ri vector at Beam   = <-9.28, 11.03>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 2.25 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 * 2.25 * (0.38/1) * 65.00 = 33.33 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, 33.33, 25.94) = 25.94 kips/bolt
Ri vector at Shear Plate   = <9.28, -11.03>
Lcsshpl at Shear Plate spacing  = na
Lceshpl at Shear Plate edge    = 2.11 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 * 2.11 * 0.38 * 65.00 = 30.79 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, 30.79, 25.59) = 25.59 kips/bolt
(1/omega)Rn = min((1/omega)Rnbm, (1/omega)Rnshpl) = min(25.935, 25.594) = 25.59 kips/bolt
Bolt Shear Demand to Bearing ratio = 25.59 / 14.41 = 1.78

At Row 4, At Column 1:
Ribolt = 15.94 kips
Ri vector at Beam   = <-14.82, 5.87>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 1.41 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 * 1.41 * (0.38/1) * 65.00 = 20.95 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, 20.95, 25.94) = 20.95 kips/bolt
Ri vector at Shear Plate   = <14.82, -5.87>
Lcsshpl at Shear Plate spacing  = na
Lceshpl at Shear Plate edge    = 1.28 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 * 1.28 * 0.38 * 65.00 = 18.68 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, 18.68, 25.59) = 18.68 kips/bolt
(1/omega)Rn = min((1/omega)Rnbm, (1/omega)Rnshpl) = min(20.948, 18.680) = 18.68 kips/bolt
Bolt Shear Demand to Bearing ratio = 18.68 / 15.94 = 1.17

Min Bolt Shear Demand to Bearing ratio Beam and Shear Plate for vertical shear only
 = min(1.00, 1.61, 1.78, 1.78, 1.17) = 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 * 33.79 = 33.79 kips
Rbv = 33.79 kips >= V = 33.00 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 - (4 * 1.00)) * 0.38 = 6.38 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 * 6.38 = 124.49 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 * 13.00 = 4.88 in^2
Net Area = (13.00 - (4 *(0.94 + 1/16))) * 0.38 = 3.38 in^2

Using Eq.J4-3:
Shear Yielding = (1/omega) * 0.6 * Fypl * [Gross Area] = 0.67 * 0.6 * 50.00 * 4.88 = 97.50 kips

Using Eq.J4-4:
Shear Rupture = (1/omega) * 0.6 * Fupl * [Net Area] = 0.50 * 0.6 * 65.00 * 3.38 = 65.81 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 = (13 - 1.25) = 11.75 in.
Net Shear Length = 11.8 - (3.5 * (0.938 + 0.0625)) = 8.25 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 * 8.25) + (1.00 * 65.00 * 1.16)) = 74.42 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 * 11.75) + (1.00 * 65.00 * 1.16)) = 80.19 kips
Block Shear = 74.42 kips

74.42 kips >= Reaction V = 33.00 kips (OK)

Flexural and Buckling Strength:

Eccentricity at first line of bolts, e = 5.57 in.
Zgross = 15.84 in^3
Znet   = 10.59 in^3
Sgross = 10.56 in^3
Snet   = 7.03 in^3

Using Eq. 9-4
Flexural Rupture = (1/omega) * Fu * Znet / e = 0.50 * 65.00 * 10.59 / 5.57 = 61.87 kips


Using Eq. 9-14 through 9-18, Fcr = Fy * Q
tw = 0.38 in.
ho = 13.00 in.
c = 5.38 in.
lambda = (ho * Fy ^ 0.5) / ( 10 * tw * ( 475.00 + 280.00 * (ho / c)^2 ) ^0.5 ) = 
 = 13.00 * 50.00^0.5 / (10 * 0.38 * (475.00 + 280.00 * (13.00/5.38)^2 )^0.5) = 0.53
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 * 10.56 / 5.57 = 56.94 kips

Interaction Check of Flexural Yielding, Per AISC 10-5: 
Eccentricity at CG of Bolt Group, e = 5.57 in.
Zgross = 15.84
Znet = 10.59
Mr = Vr * e = 33.00 * 5.57 = 183.65 kips-in
Mc = 1/omega * Mn = 1/omega * Fy * Zgross = 0.60 * 50.00 * 15.84 = 475.31 kips-in
Vr = 33.00 kips
Vc = 1/omega * Vn = 1/omega * 0.60 * Fy * Ag = 0.67 * 0.60 * 50.00 * 4.88 = 97.50 kips
Interaction due to moment and shear, (Vr/Vc)^2 + (Mr/Mc)^2 <= 1.0
(Vr/Vc)^2 + (Mr/Mc)^2 = (33.00 / 97.50)^2 + (183.65 / 475.31)^2 = 0.26 <= 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 = 0.38 <= 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.

WELD:

 Weld Requirements:

At shear only case: 
Weld Length for shear, Lv = 13.000 in.
Shear Load per inch per weld, fv = R/Lv/2 = 33.000 / 13.000 / 2 = 1.269 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) = 1.269 / (0.500 * 1.856) = 1.368/16

Minimum fillet weld size : 
   At shear only load case = 0.09 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 )
 = 0.380 * 65.000 / ( 70.000 * 1.000 * 0.088 ) 
 = 3.992 
Dmax3 = project max fillet weld = 12.000
Dmax=min(Dmax1, Dmax2, Dmax3) = min(3.940, 3.992, 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 * 13.00 * (3.94 + 3.94) = 95.06 kips

95.06 kips >= Vbm = 33.00 kips (OK)