bhss.s.s.00009.00009

SHEAR PLATE CONNECTION SUMMARY

Filler Beam profile: W27X84
Column profile: HSS8X8X1/2
Slope: 0 deg.
Skew: 85
Vertical Offset: 0
Horizontal Offset: 0
Span: 5.02 ft.
Reaction, V: 55 kips
Shear Capacity, Rn: 67.1 kips
Design/Reference according to AISC 14th Ed. - ASD
Shear Plate: Conventional Configuration
Beam material grade: A992
Support material grade: A500-GR.B
Plate material grade: A36
Weld grade: E70
Shear Plate Size: 4.500 in. x 17.500 in. x 0.375 in.
Configuration Geometry:
Welds at shear plate to support: 4/16 FILLET, 5/16 FILLET
Bolt: 6 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: 1.5 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: SSL diameter = 0.812 in., slot width = 1 in.

BOLT STRENGTH BEAM SIDE:

Bolt Strength:
Using Instantaneous Center Of Rotation Method (AISC 7-1)
ex = 1.516 in.
Angle = 0.000 deg.
C = 5.624
Using Table 7-1 to determine (1/omega) * rn:
Rn = (1/omega) * rn * C = 11.93 * 5.62 = 67.08 kips

BOLT BEARING AT BEAM SIDE:
Vertical Shear Only Load Case:
ICR cordinate relative to CG = (16.78, 0.00)
At Row 1, At Column 1:
Ri1 = 11.71 kips
Ri vector at Beam   = <4.78, 10.69>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 2.88 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * na * (0.46/1) * 65.00 = na
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 2.88 * (0.46/1) * 65.00 = 51.66 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.46/1) * 65.00 = 26.91 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(na, 51.66, 26.91) = 26.91 kips/bolt
Ri vector at Shear Plate   = <-4.78, -10.69>
Lcsshpl at Shear Plate spacing  = na
Lceshpl at Shear Plate edge    = 6.91 in.
1/omegaRnsshpl at Shear Plate spacing = 1/omega * hf1 * Lcs * t * Fu = 0.50 * 1.20 * na * 0.38 * 58.00 = na
1/omegaRneshpl at Shear Plate edge = 1/omega * hf1 * Lce * t * Fu = 0.50 * 1.20 * 6.91 * 0.38 * 58.00 = 90.14 kips/bolt
1/omegaRndshpl on Shear Plate at Bolt Diameter   = 1/omega * hf2 * db * t * Fu = 0.50 * 2.40 * 0.75 * 0.38 * 58.00 = 19.57 kips/bolt
Shear Plate bearing capacity, 1/omegaRnshpl = min(1/omegaRnsshpl,1/omegaRneshpl,1/omegaRndshpl) = min(na, 90.14, 19.57) = 19.57 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(26.910, 19.575) = 19.57 kips/bolt
Bolt Shear Demand to Bearing ratio = 19.57 / 11.71 = 1.67

At Row 2, At Column 1:
Ri1 = 11.66 kips
Ri vector at Beam   = <3.02, 11.26>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 5.81 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * na * (0.46/1) * 65.00 = na
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 5.81 * (0.46/1) * 65.00 = 104.15 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.46/1) * 65.00 = 26.91 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(na, 104.15, 26.91) = 26.91 kips/bolt
Ri vector at Shear Plate   = <-3.02, -11.26>
Lcsshpl at Shear Plate spacing  = 2.19 in.
Lceshpl at Shear Plate edge    = 11.16 in.
1/omegaRnsshpl at Shear Plate spacing = 1/omega * hf1 * Lcs * t * Fu = 0.50 * 1.20 * 2.19 * 0.38 * 58.00 = 28.55 kips/bolt
1/omegaRneshpl at Shear Plate edge = 1/omega * hf1 * Lce * t * Fu = 0.50 * 1.20 * 11.16 * 0.38 * 58.00 = 145.67 kips/bolt
1/omegaRndshpl on Shear Plate at Bolt Diameter   = 1/omega * hf2 * db * t * Fu = 0.50 * 2.40 * 0.75 * 0.38 * 58.00 = 19.57 kips/bolt
Shear Plate bearing capacity, 1/omegaRnshpl = min(1/omegaRnsshpl,1/omegaRneshpl,1/omegaRndshpl) = min(28.55, 145.67, 19.57) = 19.57 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(26.910, 19.575) = 19.57 kips/bolt
Bolt Shear Demand to Bearing ratio = 19.57 / 11.66 = 1.68

At Row 3, At Column 1:
Ri1 = 11.63 kips
Ri vector at Beam   = <1.04, 11.59>
Lcsbm at Beam spacing  = 2.19 in.
Lcebm at Beam edge    = 8.63 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * 2.19 * (0.46/1) * 65.00 = 39.24 kips/bolt
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 8.63 * (0.46/1) * 65.00 = 154.82 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.46/1) * 65.00 = 26.91 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(39.24, 154.82, 26.91) = 26.91 kips/bolt
Ri vector at Shear Plate   = <-1.04, -11.59>
Lcsshpl at Shear Plate spacing  = 2.19 in.
Lceshpl at Shear Plate edge    = 9.88 in.
1/omegaRnsshpl at Shear Plate spacing = 1/omega * hf1 * Lcs * t * Fu = 0.50 * 1.20 * 2.19 * 0.38 * 58.00 = 28.55 kips/bolt
1/omegaRneshpl at Shear Plate edge = 1/omega * hf1 * Lce * t * Fu = 0.50 * 1.20 * 9.88 * 0.38 * 58.00 = 128.97 kips/bolt
1/omegaRndshpl on Shear Plate at Bolt Diameter   = 1/omega * hf2 * db * t * Fu = 0.50 * 2.40 * 0.75 * 0.38 * 58.00 = 19.57 kips/bolt
Shear Plate bearing capacity, 1/omegaRnshpl = min(1/omegaRnsshpl,1/omegaRneshpl,1/omegaRndshpl) = min(28.55, 128.97, 19.57) = 19.57 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(26.910, 19.575) = 19.57 kips/bolt
Bolt Shear Demand to Bearing ratio = 19.57 / 11.63 = 1.68

At Row 4, At Column 1:
Ri1 = 11.63 kips
Ri vector at Beam   = <-1.04, 11.59>
Lcsbm at Beam spacing  = 2.19 in.
Lcebm at Beam edge    = 11.64 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * 2.19 * (0.46/1) * 65.00 = 39.24 kips/bolt
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 11.64 * (0.46/1) * 65.00 = 208.85 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.46/1) * 65.00 = 26.91 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(39.24, 208.85, 26.91) = 26.91 kips/bolt
Ri vector at Shear Plate   = <1.04, -11.59>
Lcsshpl at Shear Plate spacing  = 2.19 in.
Lceshpl at Shear Plate edge    = 6.87 in.
1/omegaRnsshpl at Shear Plate spacing = 1/omega * hf1 * Lcs * t * Fu = 0.50 * 1.20 * 2.19 * 0.38 * 58.00 = 28.55 kips/bolt
1/omegaRneshpl at Shear Plate edge = 1/omega * hf1 * Lce * t * Fu = 0.50 * 1.20 * 6.87 * 0.38 * 58.00 = 89.67 kips/bolt
1/omegaRndshpl on Shear Plate at Bolt Diameter   = 1/omega * hf2 * db * t * Fu = 0.50 * 2.40 * 0.75 * 0.38 * 58.00 = 19.57 kips/bolt
Shear Plate bearing capacity, 1/omegaRnshpl = min(1/omegaRnsshpl,1/omegaRneshpl,1/omegaRndshpl) = min(28.55, 89.67, 19.57) = 19.57 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(26.910, 19.575) = 19.57 kips/bolt
Bolt Shear Demand to Bearing ratio = 19.57 / 11.63 = 1.68

At Row 5, At Column 1:
Ri1 = 11.66 kips
Ri vector at Beam   = <-3.02, 11.26>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 7.32 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * na * (0.46/1) * 65.00 = na
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 7.32 * (0.46/1) * 65.00 = 131.24 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.46/1) * 65.00 = 26.91 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(na, 131.24, 26.91) = 26.91 kips/bolt
Ri vector at Shear Plate   = <3.02, -11.26>
Lcsshpl at Shear Plate spacing  = 2.19 in.
Lceshpl at Shear Plate edge    = 3.98 in.
1/omegaRnsshpl at Shear Plate spacing = 1/omega * hf1 * Lcs * t * Fu = 0.50 * 1.20 * 2.19 * 0.38 * 58.00 = 28.55 kips/bolt
1/omegaRneshpl at Shear Plate edge = 1/omega * hf1 * Lce * t * Fu = 0.50 * 1.20 * 3.98 * 0.38 * 58.00 = 51.93 kips/bolt
1/omegaRndshpl on Shear Plate at Bolt Diameter   = 1/omega * hf2 * db * t * Fu = 0.50 * 2.40 * 0.75 * 0.38 * 58.00 = 19.57 kips/bolt
Shear Plate bearing capacity, 1/omegaRnshpl = min(1/omegaRnsshpl,1/omegaRneshpl,1/omegaRndshpl) = min(28.55, 51.93, 19.57) = 19.57 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(26.910, 19.575) = 19.57 kips/bolt
Bolt Shear Demand to Bearing ratio = 19.57 / 11.66 = 1.68

At Row 6, At Column 1:
Ri1 = 11.71 kips
Ri vector at Beam   = <-4.78, 10.69>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 4.50 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * na * (0.46/1) * 65.00 = na
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 4.50 * (0.46/1) * 65.00 = 80.65 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.46/1) * 65.00 = 26.91 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(na, 80.65, 26.91) = 26.91 kips/bolt
Ri vector at Shear Plate   = <4.78, -10.69>
Lcsshpl at Shear Plate spacing  = na
Lceshpl at Shear Plate edge    = 0.92 in.
1/omegaRnsshpl at Shear Plate spacing = 1/omega * hf1 * Lcs * t * Fu = 0.50 * 1.20 * na * 0.38 * 58.00 = na
1/omegaRneshpl at Shear Plate edge = 1/omega * hf1 * Lce * t * Fu = 0.50 * 1.20 * 0.92 * 0.38 * 58.00 = 12.06 kips/bolt
1/omegaRndshpl on Shear Plate at Bolt Diameter   = 1/omega * hf2 * db * t * Fu = 0.50 * 2.40 * 0.75 * 0.38 * 58.00 = 19.57 kips/bolt
Shear Plate bearing capacity, 1/omegaRnshpl = min(1/omegaRnsshpl,1/omegaRneshpl,1/omegaRndshpl) = min(na, 12.06, 19.57) = 12.06 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(26.910, 12.061) = 12.06 kips/bolt
Bolt Shear Demand to Bearing ratio = 12.06 / 11.71 = 1.03

Min Bolt Shear Demand to Bearing ratio for vertical shear only = min(1.0, 1.67199, 1.67852, 1.68249, 1.68249, 1.67852, 1.03015) = 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 * 67.08 = 67.08 kips

Web Depth = d - [Top Cope Depth] - [Bottom Cope Depth] = 26.7 - 0 - 0 = 26.7 in.
Gross Area (Shear) = [Web Depth] * tw = 26.70 * 0.46 = 12.28 in^2
Net Shear Area (Shear) = ([Web Depth] - ([# rows] * [Diameter + 0.0625])) * tw 
    = (26.70 - (6 * 0.88)) * 0.46 = 9.87 in^2

Using Eq.J4-3:
Shear Yielding = (1/omega) * 0.6 * Fybeam * [Gross Area] = 0.67 * 0.6 * 50.00 * 12.28 = 245.64 kips

Using Eq.J4-4:
Shear Rupture = (1/omega) * 0.6 * Fubeam * [Net Area] = 0.50 * 0.6 * 65.00 * 9.87 = 192.41 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 * 17.50 = 6.56 in^2
Net Area = (17.50 - (6 *(0.81 + 1/16))) * 0.38 = 4.59 in^2

Using Eq.J4-3:
Shear Yielding = (1/omega) * 0.6 * Fypl * [Gross Area] = 0.67 * 0.6 * 36.00 * 6.56 = 94.50 kips

Using Eq.J4-4:
Shear Rupture = (1/omega) * 0.6 * Fupl * [Net Area] = 0.50 * 0.6 * 58.00 * 4.59 = 79.93 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 = (17.5 - 1.25) = 16.25 in.
Net Shear Length = 16.2 - (5.5 * (0.812 + 0.0625)) = 11.44 in.
Gross Tension Length = (0 + 1.5) = 1.50 in.
Net Tension Length = 1.5 - (0.5 * (1 + 0.0625)) = 0.97 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 * 11.44) + (1.00 * 58.00 * 0.97)) = 85.16 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 * 16.25) + (1.00 * 58.00 * 0.97)) = 76.35 kips
Block Shear = 76.35 kips


Interaction Check of Flexural Yielding, Per AISC 10-5: 
Eccentricity due to Conventional Config. (e = a/2), e = 1.52 in.
Zgross = 28.71
Znet = 19.85
Mr = Vr * e = 55.00 * 1.52 = 83.40 kips-in
Mc = 1/omega * Mn = 1/omega * Fy * Zgross = 0.60 * 36.00 * 28.71 = 620.16 kips-in
Vr = 55.00 kips
Vc = 1/omega * Vn = 1/omega * 0.60 * Fy * Ag = 0.67 * 0.60 * 36.00 * 6.56 = 94.50 kips
Interaction due to moment and shear, (Vr/Vc)^2 + (Mr/Mc)^2 <= 1.0
(Vr/Vc)^2 + (Mr/Mc)^2 = (55.00 / 94.50)^2 + (83.40 / 620.16)^2 = 0.36 <= 1  (OK)

Note: Mn <= 1.6My by inspection

MAXIMUM PLATE THICKNESS:
No of columns = 1
12" < Distance cl top to cl bot bolts <= 33" (Equivalent depth of n = 6 to 12 at 3", AISC Table 10-9)
Slot shape = SSL
tw > (db/2) + (1/16) = 0.46 > 0.4375
tMax = (db/2) + (1/16) = 0.4375 in.
Maximum Plate Thickness is Not a Limiting Criteria.

Check Limits of Applicability Table K1.2A
Plate load angle:
   theta = 85.00 >= 30 deg (OK)
HSS wall slenderness:
   B/t or H/t  = 8 / 0.465 = 17.2043 <= 40 (OK)
   (B-3t)/t <= 1.40 * (E / Fy)^0.5 for loaded wall, for branch plate shear loading
   (8.00 - 3 * 0.47) / 0.47 = 14.20 <= 1.40 * (29000 / 46.00)^0.5 = 35.15 (OK)
Material Strength:
   Fy = 46.00 <= 52 ksi (OK)
Ductility: 
   Fy/Fu = 46.00 / 58.00 <= 0.80 (OK)

AISC K1-3, Plate Limit States and HSS Punching Shear : 
tpl <= thss * Fuhss/Fypl
0.38 <= 0.47 * 58.00 / 36.00 = 0.75 in. (OK)

WELD:

 Weld Requirements:

At shear only case: 
Weld Length for shear, Lv = 17.500 in.
Shear Load per inch per weld, fv = R/Lv/2 = 55.000 / 17.500 / 2 = 1.571 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) = 1.571 / (0.500 * 1.856) = 1.693/16

Minimum fillet weld size : 
   At shear only load case = 0.11 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)
 = thss * Fuhss / ( Fexx * C1 * 0.044 )
 = 0.465 * 58.000 / ( 70.000 * 1.000 * 0.044 ) 
 = 8.718 
Dmax3 = project max fillet weld = 12.000
Dmax=min(Dmax1, Dmax2, Dmax3) = min(3.515, 8.718, 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 * 17.50 * (3.52 + 3.52) = 114.19 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)