bb.s.s.00018.00018

SHEAR PLATE CONNECTION SUMMARY

Filler Beam profile: W16X40
Support Girder profile: W21X50
Slope: 0 deg.
Skew: 90
Vertical Offset: 0
Horizontal Offset: 0
Span: 10 ft.
Reaction, V: 2 kips
Shear Capacity, Rn: 44.9 kips
Design/Reference according to AISC 14th Ed. - LRFD
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 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 column 0.875 in. Diameter A325N_TC bolts
Vertical spacing: 3 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 = 1.843
Using Table 7-1 to determine (phi)rn:
(phi)Rn = (phi)rn * C = 24.35 * 1.84 = 44.88 kips


Total Vertical Bolt Shear Capacity = 44.88 kips
44.88 kips >= 2.00 kips (OK)

BOLT BEARING AT BEAM AND SHEAR PLATE SIDE
Vertical Shear Only Load Case:
ICR cordinate relative to CG = (1.49, -0.00)
At Row 1, At Column 1:
Ribolt = 23.90 kips
Ri vector at Beam   = <22.70, 7.49>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 9.10 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.75 * 1.20 * na * (0.30/1) * 65.00 = na
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 9.10 * (0.30/1) * 65.00 = 162.45 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.88 * (0.30/1) * 65.00 = 31.23 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(na, 162.45, 31.23) = 31.23 kips/bolt
Ri vector at Shear Plate   = <-22.70, -7.49>
Lcsshpl at Shear Plate spacing  = na
Lceshpl at Shear Plate edge    = 5.07 in.
(phi)Rnsshpl at Shear Plate spacing = (phi) * hf1 * Lcs * t * Fu = 0.75 * 1.20 * na * 0.38 * 65.00 = na
(phi)Rneshpl at Shear Plate edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 5.07 * 0.38 * 65.00 = 111.18 kips/bolt
(phi)Rndshpl on Shear Plate at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.88 * 0.38 * 65.00 = 38.39 kips/bolt
Shear Plate bearing capacity, (phi)Rnshpl = min((phi)Rnsshpl,(phi)Rneshpl,(phi)Rndshpl) = min(na, 111.18, 38.39) = 38.39 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(31.225, 38.392) = 31.23 kips/bolt
Bolt Shear Demand to Bearing ratio = 31.23 / 23.90 = 1.31

At Row 2, At Column 1:
Ribolt = 21.24 kips
Ri vector at Beam   = <15.10, 14.95>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 8.06 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.75 * 1.20 * na * (0.30/1) * 65.00 = na
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 8.06 * (0.30/1) * 65.00 = 143.82 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.88 * (0.30/1) * 65.00 = 31.23 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(na, 143.82, 31.23) = 31.23 kips/bolt
Ri vector at Shear Plate   = <-15.10, -14.95>
Lcsshpl at Shear Plate spacing  = na
Lceshpl at Shear Plate edge    = 6.90 in.
(phi)Rnsshpl at Shear Plate spacing = (phi) * hf1 * Lcs * t * Fu = 0.75 * 1.20 * na * 0.38 * 65.00 = na
(phi)Rneshpl at Shear Plate edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 6.90 * 0.38 * 65.00 = 151.30 kips/bolt
(phi)Rndshpl on Shear Plate at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.88 * 0.38 * 65.00 = 38.39 kips/bolt
Shear Plate bearing capacity, (phi)Rnshpl = min((phi)Rnsshpl,(phi)Rneshpl,(phi)Rndshpl) = min(na, 151.30, 38.39) = 38.39 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(31.225, 38.392) = 31.23 kips/bolt
Bolt Shear Demand to Bearing ratio = 31.23 / 21.24 = 1.47

At Row 3, At Column 1:
Ribolt = 21.24 kips
Ri vector at Beam   = <-15.09, 14.95>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 1.99 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.75 * 1.20 * na * (0.30/1) * 65.00 = na
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 1.99 * (0.30/1) * 65.00 = 35.58 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.88 * (0.30/1) * 65.00 = 31.23 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(na, 35.58, 31.23) = 31.23 kips/bolt
Ri vector at Shear Plate   = <15.09, -14.95>
Lcsshpl at Shear Plate spacing  = na
Lceshpl at Shear Plate edge    = 1.80 in.
(phi)Rnsshpl at Shear Plate spacing = (phi) * hf1 * Lcs * t * Fu = 0.75 * 1.20 * na * 0.38 * 65.00 = na
(phi)Rneshpl at Shear Plate edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 1.80 * 0.38 * 65.00 = 39.42 kips/bolt
(phi)Rndshpl on Shear Plate at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.88 * 0.38 * 65.00 = 38.39 kips/bolt
Shear Plate bearing capacity, (phi)Rnshpl = min((phi)Rnsshpl,(phi)Rneshpl,(phi)Rndshpl) = min(na, 39.42, 38.39) = 38.39 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(31.225, 38.392) = 31.23 kips/bolt
Bolt Shear Demand to Bearing ratio = 31.23 / 21.24 = 1.47

At Row 4, At Column 1:
Ribolt = 23.90 kips
Ri vector at Beam   = <-22.70, 7.49>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 1.37 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.75 * 1.20 * na * (0.30/1) * 65.00 = na
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 1.37 * (0.30/1) * 65.00 = 24.52 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.88 * (0.30/1) * 65.00 = 31.23 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(na, 24.52, 31.23) = 24.52 kips/bolt
Ri vector at Shear Plate   = <22.70, -7.49>
Lcsshpl at Shear Plate spacing  = na
Lceshpl at Shear Plate edge    = 1.25 in.
(phi)Rnsshpl at Shear Plate spacing = (phi) * hf1 * Lcs * t * Fu = 0.75 * 1.20 * na * 0.38 * 65.00 = na
(phi)Rneshpl at Shear Plate edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 1.25 * 0.38 * 65.00 = 27.43 kips/bolt
(phi)Rndshpl on Shear Plate at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.88 * 0.38 * 65.00 = 38.39 kips/bolt
Shear Plate bearing capacity, (phi)Rnshpl = min((phi)Rnsshpl,(phi)Rneshpl,(phi)Rndshpl) = min(na, 27.43, 38.39) = 27.43 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(24.518, 27.434) = 24.52 kips/bolt
Bolt Shear Demand to Bearing ratio = 24.52 / 23.90 = 1.03

Min Bolt Shear Demand to Bearing ratio Beam and Shear Plate for vertical shear only
 = min(1.00, 1.31, 1.47, 1.47, 1.03) = 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 * 44.88 = 44.88 kips
Rbv = 44.88 kips >= Reaction V = 2.00 kips (OK)

Web Depth = d - [Top Cope Depth] - [Bottom Cope Depth] = 16 - 0 - 0 = 16 in.
Gross Area (Shear) = [Web Depth] * tw = 16.00 * 0.30 = 4.88 in^2
Net Shear Area (Shear) = ([Web Depth] - ([# rows] * [Diameter + 0.0625])) * tw 
    = (16.00 - (4 * 1.00)) * 0.30 = 3.66 in^2

Using Eq.J4-3:
Shear Yielding = (phi) * 0.6 * Fybeam * [Gross Area] = 1.00 * 0.6 * 50.00 * 4.88 = 146.40 kips

Using Eq.J4-4:
Shear Rupture = (phi) * 0.6 * Fubeam * [Net Area] = 0.75 * 0.6 * 65.00 * 3.66 = 107.06 kips


Block Shear

Using Eq.J4-5:
Block Shear = {(phi) * ((0.6 * Fu * Anv) + (Ubs * Fu * Ant))} <= {(phi) * ((0.6 * Fy * Agv) + (Ubs * Fu * Ant))}

Block Shear for Axial T/C is not required.

Gross Area = 0.38 * 11.50 = 4.31 in^2
Net Area = (11.50 - (4 *(0.94 + 1/16))) * 0.38 = 2.81 in^2

Using Eq.J4-3:
Shear Yielding = (phi) * 0.6 * Fypl * [Gross Area] = 1.00 * 0.6 * 50.00 * 4.31 = 129.38 kips

Using Eq.J4-4:
Shear Rupture = (phi) * 0.6 * Fupl * [Net Area] = 0.75 * 0.6 * 65.00 * 2.81 = 82.27 kips


Block Shear

Using Eq.J4-5:
Block Shear = {(phi) * ((0.6 * Fu * Anv) + (Ubs * Fu * Ant))} <= {(phi) * ((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 * (0.938 + 0.0625)) = 6.75 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. (phi) * [material thickness] * ((0.60 * Fupl* [net shear length]) + (Ubs * Fupl * [net tension length])) 
    = 0.75 * 0.38 * ((0.60 * 65.00 * 6.75) + (1.00 * 65.00 * 1.16)) = 95.18 kips
2. (phi) * [material thickness] * ((0.60 * Fypl * [gross shear length]) + (Ubs * Fupl * [net tension length])) 
    = 0.75 * 0.38 * ((0.60 * 50.00 * 10.25) + (1.00 * 65.00 * 1.16)) = 107.62 kips
Block Shear = 95.18 kips

95.18 kips >= Reaction V = 2.00 kips (OK)


Block Shear for Axial T/C is not required.

Flexural and Buckling Strength:

Eccentricity at first line of bolts, e = 5.57 in.
Zgross = 12.40 in^3
Znet   = 7.90 in^3
Sgross = 8.27 in^3
Snet   = 5.33 in^3

Using Eq. 9-4
Flexural Rupture = (phi) * Fu * Znet / e = 0.75 * 65.00 * 7.90 / 5.57 = 69.19 kips


Using Eq. 9-14 through 9-18, Fcr = Fy * Q
tw = 0.38 in.
ho = 11.50 in.
c = 5.38 in.
lambda = (ho * Fy ^ 0.5) / ( 10 * tw * ( 475.00 + 280.00 * (ho / c)^2 ) ^0.5 ) = 
 = 11.50 * 50.00^0.5 / (10 * 0.38 * (475.00 + 280.00 * (11.50/5.38)^2 )^0.5) = 0.52
When lambda <= 0.70, Q=1
Q = 1.00
Fcrmin =phi * Fcr = 0.90 * 50.00 * 1.00 = 45.00 ksi

Using Eq. 9-6
Buckling = Fcr * Sgross / e = 45.00 * 8.27 / 5.57 = 66.84 kips

Interaction Check of Flexural Yielding, Per AISC 10-5: 
Eccentricity at CG of Bolt Group, e = 5.57 in.
Zgross = 12.40
Znet = 7.90
Mr = Vr * e = 2.00 * 5.57 = 11.13 kips-in
Mc = phi * Mn = phi * Fy * Zgross = 0.90 * 50.00 * 12.40 = 557.93 kips-in
Vr = 2.00 kips
Vc = phi * Vn = phi * 0.60 * Fy * Ag = 1.00 * 0.60 * 50.00 * 4.31 = 129.38 kips
Interaction due to moment and shear, (Vr/Vc)^2 + (Mr/Mc)^2 <= 1.0
(Vr/Vc)^2 + (Mr/Mc)^2 = (2.00 / 129.38)^2 + (11.13 / 557.93)^2 = 0.00 <= 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 = 0.305 <= 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 = 11.500 in.
Shear Load per inch per weld, fv = R/Lv/2 = 2.000 / 11.500 / 2 = 0.087 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/ (phi * coeff) = 0.087 / (0.750 * 1.856) = 0.062/16

Minimum fillet weld size : 
   At shear only load case = 0.00 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, phi * Rnv1 = 0.75 * 1.86 * 11.50 * (3.94 + 3.94) = 126.14 kips

126.14 kips >= Reaction V = 2.00 kips (OK)