bcf.s.s.00510.00510

SHEAR PLATE CONNECTION SUMMARY

Filler Beam profile: W12X19
Column profile: W14X120
Slope: 0 deg.
Skew: 74.8
Vertical Offset: 0
Horizontal Offset: 0
Span: 11.1 ft.
Reaction, V: 25 kips
Shear Capacity, Rn: 37.5 kips
Design/Reference according to AISC 14th Ed. - ASD
Shear Plate: Conventional Configuration
Beam material grade: A992
Support material grade: A992
Plate material grade: A572-GR.50
Weld grade: E70
Shear Plate Size: 4.750 in. x 8.500 in. x 0.375 in.
Configuration Geometry:
Welds at shear plate to support: 4/16 FILLET, 6/16 FILLET
Bolt: 3 rows x 1 column 0.875 in. Diameter A325N_TC bolts
Vertical spacing: 3 in.
Horizontal spacing: 3 in.
Shear plate edge setback = 1 in.
Beam centerline setback = 1.14 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: 2 in.
Horizontal distance to first hole: 3 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 = 1.551 in.
Angle = 0.000 deg.
C = 2.455
Using Table 7-1 to determine (1/omega)rn:
(1/omega)Rn = (1/omega)rn * C = 16.24 * 2.45 = 39.85 kips


Total Vertical Bolt Shear Capacity = 39.85 kips
39.85 kips >= 25.00 kips (OK)

BOLT BEARING AT BEAM AND SHEAR PLATE SIDE
Vertical Shear Only Load Case:
ICR cordinate relative to CG = (3.53, 0.00)
At Row 1, At Column 1:
Ribolt = 15.94 kips
Ri vector at Beam   = <10.31, 12.15>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 3.47 in.
(1/omega)Rnsbm at Beam spacing = (1/omega) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * na * (0.23/1) * 65.00 = na
(1/omega)Rnebm at Beam edge = (1/omega) * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 3.47 * (0.23/1) * 65.00 = 31.76 kips/bolt
(1/omega)Rndbm on Beam at Bolt Diameter   = (1/omega) * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.88 * (0.23/1) * 65.00 = 16.04 kips/bolt
Beam bearing capacity, (1/omega)Rnbm = min((1/omega)Rnsbm,(1/omega)Rnebm,(1/omega)Rndbm) = min(na, 31.76, 16.04) = 16.04 kips/bolt
Ri vector at Shear Plate   = <-10.31, -12.15>
Lcsshpl at Shear Plate spacing  = na
Lceshpl at Shear Plate edge    = 4.02 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 * 4.02 * 0.38 * 65.00 = 58.82 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, 58.82, 25.59) = 25.59 kips/bolt
(1/omega)Rn = min((1/omega)Rnbm, (1/omega)Rnshpl) = min(16.039, 25.594) = 16.04 kips/bolt
Bolt Shear Demand to Bearing ratio = 16.04 / 15.94 = 1.01

At Row 2, At Column 1:
Ribolt = 15.56 kips
Ri vector at Beam   = <-0.00, 15.56>
Lcsbm at Beam spacing  = 2.06 in.
Lcebm at Beam edge    = 5.53 in.
(1/omega)Rnsbm at Beam spacing = (1/omega) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * 2.06 * (0.23/1) * 65.00 = 18.90 kips/bolt
(1/omega)Rnebm at Beam edge = (1/omega) * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 5.53 * (0.23/1) * 65.00 = 50.69 kips/bolt
(1/omega)Rndbm on Beam at Bolt Diameter   = (1/omega) * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.88 * (0.23/1) * 65.00 = 16.04 kips/bolt
Beam bearing capacity, (1/omega)Rnbm = min((1/omega)Rnsbm,(1/omega)Rnebm,(1/omega)Rndbm) = min(18.90, 50.69, 16.04) = 16.04 kips/bolt
Ri vector at Shear Plate   = <0.00, -15.56>
Lcsshpl at Shear Plate spacing  = 2.06 in.
Lceshpl at Shear Plate edge    = 3.78 in.
(1/omega)Rnsshpl at Shear Plate spacing = (1/omega) * hf1 * Lcs * t * Fu = 0.50 * 1.20 * 2.06 * 0.38 * 65.00 = 30.16 kips/bolt
(1/omega)Rneshpl at Shear Plate edge = (1/omega) * hf1 * Lce * t * Fu = 0.50 * 1.20 * 3.78 * 0.38 * 65.00 = 55.30 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(30.16, 55.30, 25.59) = 25.59 kips/bolt
(1/omega)Rn = min((1/omega)Rnbm, (1/omega)Rnshpl) = min(16.039, 25.594) = 16.04 kips/bolt
Bolt Shear Demand to Bearing ratio = 16.04 / 15.56 = 1.03

At Row 3, At Column 1:
Ribolt = 15.94 kips
Ri vector at Beam   = <-10.31, 12.15>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 2.62 in.
(1/omega)Rnsbm at Beam spacing = (1/omega) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * na * (0.23/1) * 65.00 = na
(1/omega)Rnebm at Beam edge = (1/omega) * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 2.62 * (0.23/1) * 65.00 = 24.02 kips/bolt
(1/omega)Rndbm on Beam at Bolt Diameter   = (1/omega) * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.88 * (0.23/1) * 65.00 = 16.04 kips/bolt
Beam bearing capacity, (1/omega)Rnbm = min((1/omega)Rnsbm,(1/omega)Rnebm,(1/omega)Rndbm) = min(na, 24.02, 16.04) = 16.04 kips/bolt
Ri vector at Shear Plate   = <10.31, -12.15>
Lcsshpl at Shear Plate spacing  = na
Lceshpl at Shear Plate edge    = 1.02 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 * 1.02 * 0.38 * 65.00 = 14.99 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, 14.99, 25.59) = 14.99 kips/bolt
(1/omega)Rn = min((1/omega)Rnbm, (1/omega)Rnshpl) = min(16.039, 14.989) = 14.99 kips/bolt
Bolt Shear Demand to Bearing ratio = 14.99 / 15.94 = 0.94

Min Bolt Shear Demand to Bearing ratio Beam and Shear Plate for vertical shear only
 = min(1.00, 1.01, 1.03, 0.94) = 0.94

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 = 0.94 * 39.85 = 37.49 kips
Rbv = 37.49 kips >= V = 25.00 kips (OK)

Web Depth = d - [Top Cope Depth] - [Bottom Cope Depth] = 12.2 - 0 - 0 = 12.2 in.
Gross Area (Shear) = [Web Depth] * tw = 12.20 * 0.23 = 2.87 in^2
Net Shear Area (Shear) = ([Web Depth] - ([# rows] * [Diameter + 0.0625])) * tw 
    = (12.20 - (3 * 1.00)) * 0.23 = 2.16 in^2

Using Eq.J4-3:
Shear Yielding = (1/omega) * 0.6 * Fybeam * [Gross Area] = 0.67 * 0.6 * 50.00 * 2.87 = 57.34 kips

Using Eq.J4-4:
Shear Rupture = (1/omega) * 0.6 * Fubeam * [Net Area] = 0.50 * 0.6 * 65.00 * 2.16 = 42.16 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 * 8.50 = 3.19 in^2
Net Area = (8.50 - (3 *(0.94 + 1/16))) * 0.38 = 2.06 in^2

Using Eq.J4-3:
Shear Yielding = (1/omega) * 0.6 * Fypl * [Gross Area] = 0.67 * 0.6 * 50.00 * 3.19 = 63.75 kips

Using Eq.J4-4:
Shear Rupture = (1/omega) * 0.6 * Fupl * [Net Area] = 0.50 * 0.6 * 65.00 * 2.06 = 40.22 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 = (8.5 - 1.25) = 7.25 in.
Net Shear Length = 7.25 - (2.5 * (0.938 + 0.0625)) = 4.75 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 * 0.38 * ((0.60 * 65.00 * 4.75) + (1.00 * 65.00 * 1.16)) = 48.83 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 * 7.25) + (1.00 * 65.00 * 1.16)) = 54.87 kips
Block Shear = 48.83 kips

48.83 kips >= Vbm = 25.00 kips (OK)


Interaction Check of Flexural Yielding, Per AISC 10-5: 
Eccentricity due to Conventional Config. (e = a/2), e = 1.55 in.
Zgross = 6.77
Znet = 4.43
Mr = Vr * e = 25.00 * 1.55 = 38.77 kips-in
Mc = 1/omega * Mn = 1/omega * Fy * Zgross = 0.60 * 50.00 * 6.77 = 203.20 kips-in
Vr = 25.00 kips
Vc = 1/omega * Vn = 1/omega * 0.60 * Fy * Ag = 0.67 * 0.60 * 50.00 * 3.19 = 63.75 kips
Interaction due to moment and shear, (Vr/Vc)^2 + (Mr/Mc)^2 <= 1.0
(Vr/Vc)^2 + (Mr/Mc)^2 = (25.00 / 63.75)^2 + (38.77 / 203.20)^2 = 0.19 <= 1  (OK)

Note: Mn <= 1.6My by inspection

MAXIMUM PLATE THICKNESS:
No of columns = 1
Distance cl top to cl bot bolts <= 12" (Equivalent depth of n = 1 to 5 at 3", AISC Table 10-9)
Slot shape = SSL
tmax = Unlimited
Maximum Plate Thickness is Not a Limiting Criteria.

WELD:

 Weld Requirements:

At shear only case: 
Weld Length for shear, Lv = 8.500 in.
Shear Load per inch per weld, fv = R/Lv/2 = 25.000 / 8.500 / 2 = 1.471 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) = 1.471 / (0.500 * 1.856) = 1.585/16

Minimum fillet weld size : 
   At shear only load case = 0.10 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 9-2)
 = tfsupport * Fusupport / ( Fexx * C1 * 0.044 )
 = 0.940 * 65.000 / ( 70.000 * 1.000 * 0.044 ) 
 = 19.751 
Dmax3 = project max fillet weld = 12.000
Dmax=min(Dmax1, Dmax2, Dmax3) = min(3.940, 19.751, 12.000)
 = 3.940 

Dihedral Angle, DA = 74.80 deg.
Gap on Obtuse Angle Side if No Bevel = 0.10 in.
Use weld size
Acute Side  D1 = 4.00
Obtuse Side D2 = 6.00 (weld size increased on obtuse side for gap at skew per AWS D1.1/D1.1M (2015, p.511, C-5.21.1))

Weld Strength :

Vertical weld capacity during shear only load, 1/omega * Rnv1 = 0.50 * 1.86 * 8.50 * (3.94 + 3.94) = 62.16 kips

62.16 kips >= Vbm = 25.00 kips (OK)

Check Effective Throat:
Acute Side Effect throat  = (D1/sin(DA)) * cos(DA/2) = (0.25/ sin( 74.80)) * cos( 37.40) = 0.21 in.
Obtuse Side Effect throat = (D2/sin(DA)-tshpl/tan(DA))*sin(DA/2) = (0.38 / sin(74.80) - 0.38 / tan(74.80)) * sin(74.80 / 2) = 0.17 in.
Total Effective Throat    = 0.21 + 0.17 = 0.38 in.
Total Effective Throat of Square Case = 5/8tp * 2^0.5 = 0.23 * 2^0.5 = 0.33 in.
0.38 >= 0.33 (OK)