bepl.s.s.00001.00003

SHEAR PLATE CONNECTION SUMMARY

Filler Beam profile: W14X43
Column profile: PL0.75X60X36
Slope: 0 deg.
Skew: 85
Vertical Offset: -11.6
Horizontal Offset: 0
Span: 5.3 ft.
Reaction, V: 12 kips
Shear Capacity, Rn: 18.3 kips
Design/Reference according to AISC 14th Ed. - ASD
Shear Plate: Extended Configuration
Beam material grade: A992
Support material grade: A572-GR.50
Plate material grade: A36
Weld grade: E70
Shear Plate Size: 5.250 in. x 8.500 in. x 0.375 in.
Plate Washer Size: 3 in. x 8.5 in. x 0.312 in.
Configuration Geometry:
Welds at shear plate to support: 4/16 FILLET, 5/16 FILLET
Bolt: 3 rows x 1 columns 0.75 in. Diameter A325N_TC bolts
Vertical spacing: 3 in.
Horizontal spacing: 3 in.
Shear plate edge setback = 1 in.
Beam centerline setback = 1.05 in.
Edge distance at vertical edge of plate: 2.25 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 = 0.812 in.
Holes in shear plate: LSL diameter = 0.812 in., slot width = 1.88 in.

BOLT STRENGTH BEAM SIDE:

Bolt Strength:
Using Instantaneous Center Of Rotation Method (AISC 7-1)
ex = 3.579 in.
Angle = 0.000 deg.
C = 1.534
Using Table 7-1 to determine (1/omega) * rn:
Rn = (1/omega) * rn * C = 11.93 * 1.53 = 18.30 kips

BOLT BEARING AT BEAM SIDE:
Vertical Shear Only Load Case:
ICR cordinate relative to CG = (1.16, 0.00)
At Row 1, At Column 1:
Ri1 = 11.71 kips
Ri vector at Beam   = <10.92, 4.22>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 7.91 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * na * (0.30/1) * 65.00 = na
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 7.91 * (0.30/1) * 65.00 = 94.07 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.30/1) * 65.00 = 17.84 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(na, 94.07, 17.84) = 17.84 kips/bolt
Ri vector at Shear Plate   = <-10.92, -4.22>
Lcsshpl at Shear Plate spacing  = na
Lceshpl at Shear Plate edge    = 2.21 in.
1/omegaRnsshpl at Shear Plate spacing = 1/omega * hf1 * Lcs * t * Fu = 0.50 * 1.00 * na * 0.38 * 58.00 = na
1/omegaRneshpl at Shear Plate edge = 1/omega * hf1 * Lce * t * Fu = 0.50 * 1.00 * 2.21 * 0.38 * 58.00 = 24.05 kips/bolt
1/omegaRndshpl on Shear Plate at Bolt Diameter   = 1/omega * hf2 * db * t * Fu = 0.50 * 2.00 * 0.75 * 0.38 * 58.00 = 16.31 kips/bolt
Shear Plate bearing capacity, 1/omegaRnshpl = min(1/omegaRnsshpl,1/omegaRneshpl,1/omegaRndshpl) = min(na, 24.05, 16.31) = 16.31 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(17.842, 16.312) = 16.31 kips/bolt
Bolt Shear Demand to Bearing ratio = 16.31 / 11.71 = 1.39

At Row 2, At Column 1:
Ri1 = 9.86 kips
Ri vector at Beam   = <-0.00, 9.86>
Lcsbm at Beam spacing  = 2.19 in.
Lcebm at Beam edge    = 5.59 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * 2.19 * (0.30/1) * 65.00 = 26.02 kips/bolt
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 5.59 * (0.30/1) * 65.00 = 66.54 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.30/1) * 65.00 = 17.84 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(26.02, 66.54, 17.84) = 17.84 kips/bolt
Ri vector at Shear Plate   = <0.00, -9.86>
Lcsshpl at Shear Plate spacing  = 2.19 in.
Lceshpl at Shear Plate edge    = 3.84 in.
1/omegaRnsshpl at Shear Plate spacing = 1/omega * hf1 * Lcs * t * Fu = 0.50 * 1.00 * 2.19 * 0.38 * 58.00 = 23.79 kips/bolt
1/omegaRneshpl at Shear Plate edge = 1/omega * hf1 * Lce * t * Fu = 0.50 * 1.00 * 3.84 * 0.38 * 58.00 = 41.80 kips/bolt
1/omegaRndshpl on Shear Plate at Bolt Diameter   = 1/omega * hf2 * db * t * Fu = 0.50 * 2.00 * 0.75 * 0.38 * 58.00 = 16.31 kips/bolt
Shear Plate bearing capacity, 1/omegaRnshpl = min(1/omegaRnsshpl,1/omegaRneshpl,1/omegaRndshpl) = min(23.79, 41.80, 16.31) = 16.31 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(17.842, 16.312) = 16.31 kips/bolt
Bolt Shear Demand to Bearing ratio = 16.31 / 9.86 = 1.66

At Row 3, At Column 1:
Ri1 = 11.71 kips
Ri vector at Beam   = <-10.92, 4.22>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 1.74 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * na * (0.30/1) * 65.00 = na
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 1.74 * (0.30/1) * 65.00 = 20.68 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.30/1) * 65.00 = 17.84 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(na, 20.68, 17.84) = 17.84 kips/bolt
Ri vector at Shear Plate   = <10.92, -4.22>
Lcsshpl at Shear Plate spacing  = na
Lceshpl at Shear Plate edge    = 1.41 in.
1/omegaRnsshpl at Shear Plate spacing = 1/omega * hf1 * Lcs * t * Fu = 0.50 * 1.00 * na * 0.38 * 58.00 = na
1/omegaRneshpl at Shear Plate edge = 1/omega * hf1 * Lce * t * Fu = 0.50 * 1.00 * 1.41 * 0.38 * 58.00 = 15.30 kips/bolt
1/omegaRndshpl on Shear Plate at Bolt Diameter   = 1/omega * hf2 * db * t * Fu = 0.50 * 2.00 * 0.75 * 0.38 * 58.00 = 16.31 kips/bolt
Shear Plate bearing capacity, 1/omegaRnshpl = min(1/omegaRnsshpl,1/omegaRneshpl,1/omegaRndshpl) = min(na, 15.30, 16.31) = 15.30 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(17.842, 15.304) = 15.30 kips/bolt
Bolt Shear Demand to Bearing ratio = 15.30 / 11.71 = 1.31

Min Bolt Shear Demand to Bearing ratio for vertical shear only = min(1.0, 1.39332, 1.6552, 1.3072) = 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 * 18.30 = 18.30 kips

Web Depth = d - [Top Cope Depth] - [Bottom Cope Depth] = 13.7 - 0 - 0 = 13.7 in.
Gross Area (Shear) = [Web Depth] * tw = 13.70 * 0.30 = 4.18 in^2
Net Shear Area (Shear) = ([Web Depth] - ([# rows] * [Diameter + 0.0625])) * tw 
    = (13.70 - (3 * 0.88)) * 0.30 = 3.38 in^2

Using Eq.J4-3:
Shear Yielding = (1/omega) * 0.6 * Fybeam * [Gross Area] = 0.67 * 0.6 * 50.00 * 4.18 = 83.57 kips

Using Eq.J4-4:
Shear Rupture = (1/omega) * 0.6 * Fubeam * [Net Area] = 0.50 * 0.6 * 65.00 * 3.38 = 65.87 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 *(0.81 + 1/16))) * 0.38 = 2.20 in^2

Using Eq.J4-3:
Shear Yielding = (1/omega) * 0.6 * Fypl * [Gross Area] = 0.67 * 0.6 * 36.00 * 3.19 = 45.90 kips

Using Eq.J4-4:
Shear Rupture = (1/omega) * 0.6 * Fupl * [Net Area] = 0.50 * 0.6 * 58.00 * 2.20 = 38.33 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 * (0.812 + 0.0625)) = 5.06 in.
Gross Tension Length = (0 + 2.25) = 2.25 in.
Net Tension Length = 2.25 - (0.5 * (1.88 + 0.0625)) = 1.28 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 * 5.06) + (1.00 * 58.00 * 1.28)) = 46.97 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 * 7.25) + (1.00 * 58.00 * 1.28)) = 43.30 kips
Block Shear = 43.30 kips

Flexural and Buckling Strength:

Eccentricity at first line of bolts, e = 3.58 in.
Zgross = 6.77 in^3
Znet   = 4.73 in^3
Sgross = 4.52 in^3
Snet   = 3.13 in^3

Using Eq. 9-4
Flexural Rupture = (1/omega) * Fu * Znet / e = 0.50 * 58.00 * 4.73 / 3.58 = 38.35 kips


Using Eq. 9-14 through 9-18, Fcr = Fy * Q
tw = 0.38 in.
ho = 8.50 in.
c = 3.02 in.
lambda = (ho * Fy ^ 0.5) / ( 10 * tw * ( 475.00 + 280.00 * (ho / c)^2 ) ^0.5 ) = 
 = 8.50 * 36.00^0.5 / (10 * 0.38 * (475.00 + 280.00 * (8.50/3.02)^2 )^0.5) = 0.26
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 * 4.52 / 3.58 = 27.25 kips

Interaction Check of Flexural Yielding, Per AISC 10-5: 
Eccentricity at CG of Bolt Group, e = 3.58 in.
Zgross = 6.77
Znet = 4.73
Mr = Vr * e = 12.00 * 3.58 = 42.95 kips-in
Mc = 1/omega * Mn = 1/omega * Fy * Zgross = 0.60 * 36.00 * 6.77 = 146.31 kips-in
Vr = 12.00 kips
Vc = 1/omega * Vn = 1/omega * 0.60 * Fy * Ag = 0.67 * 0.60 * 36.00 * 3.19 = 45.90 kips
Interaction due to moment and shear, (Vr/Vc)^2 + (Mr/Mc)^2 <= 1.0
(Vr/Vc)^2 + (Mr/Mc)^2 = (12.00 / 45.90)^2 + (42.95 / 146.31)^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 = 0.305 <= 0.4375 OK
Leh(plate) >= 2 * db = 2.25 >= 1.5 OK
Leh(bm) >= 2 * db = 2 >= 1.5 OK
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 = 12.000 / 8.500 / 2 = 0.706 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) = 0.706 / (0.500 * 1.856) = 0.761/16

Minimum fillet weld size : 
   At shear only load case = 0.05 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 9-2)
 = tembpl * Fuembpl / ( Fexx * C1 * 0.044 )
 = 0.750 * 65.000 / ( 70.000 * 1.000 * 0.044 ) 
 = 15.758 
Dmax3 = project max fillet weld = 12.000
Dmax=min(Dmax1, Dmax2, Dmax3) = min(3.515, 15.758, 12.000)
 = 3.515 

Dihedral Angle, DA       = 85.00 deg.
Gap on Obtuse Angle Side = 0.03 in.
Use weld size
Acute Side  D1 = 4.00
Obtuse Side D2 = 5.00

Weld Strength :
Vertical weld capacity during shear only load, 1/omega * Rnv1 = 0.50 * 1.86 * 8.50 * (3.52 + 3.52) = 55.46 kips
Check Effective Throat:
Acute Side Effect throat  = (D1/sin(DA)) * cos(DA/2) = (0.25/ sin( 85.00)) * cos( 42.50) = 0.19 in.
Obtuse Side Effect throat = ((D2/sin(DA)-tshpl/tan(DA))*sin((180-(180-DA))/2))= ((0.31 / sin(85.00) -0.38 / tan(85.00)) * sin((180 - (180 - 85.00)) / 2)) = 0.15 in.
Total Effective Throat    = 0.19 + 0.15 = 0.37 in.
Total Effective Throat of Square Case = D1 * 2^0.5 = 0.25 * 2^0.5 = 0.35 in.
0.35 in. <= 0.37 in. (OK)