bb.s.s.00051.00209

SHEAR PLATE CONNECTION SUMMARY

Filler Beam profile: W16X31
Support Girder profile: W21X55
Slope: 0 deg.
Skew: 74
Vertical Offset: -4.88
Horizontal Offset: 0.0415
Span: 29.5 ft.
Reaction, V: 20 kips
Shear Capacity, Rn: 29.3 kips
Design/Reference according to AISC 14th Ed. - ASD
Shear Plate: Conventional Configuration
Beam material grade: A992
Support material grade: A992
Plate material grade: A36
Weld grade: E70
Shear Plate Size: 4.500 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 columns 0.75 in. Diameter A325N_TC bolts
Vertical spacing: 3 in.
Horizontal spacing: 3 in.
Shear plate edge setback = 0.938 in.
Beam centerline setback = 1.08 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: 2.06 in.
Edge distance at bottom edge of beam: 5.9 in.
Bottom cope depth: 1 in.
Bottom cope length: 3.75 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 = 1.554 in.
Angle = 0.000 deg.
C = 2.454
Using Table 7-1 to determine (1/omega) * rn:
Rn = (1/omega) * rn * C = 11.93 * 2.45 = 29.27 kips

BOLT BEARING AT BEAM SIDE:
Vertical Shear Only Load Case:
ICR cordinate relative to CG = (3.53, 0.00)
At Row 1, At Column 1:
Ri1 = 11.71 kips
Ri vector at Beam   = <7.58, 8.92>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 3.53 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * na * (0.28/1) * 65.00 = na
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 3.53 * (0.28/1) * 65.00 = 37.86 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.28/1) * 65.00 = 16.09 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(na, 37.86, 16.09) = 16.09 kips/bolt
Ri vector at Shear Plate   = <-7.58, -8.92>
Lcsshpl at Shear Plate spacing  = na
Lceshpl at Shear Plate edge    = 4.10 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 * 4.10 * 0.38 * 58.00 = 53.51 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, 53.51, 19.57) = 19.57 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(16.087, 19.575) = 16.09 kips/bolt
Bolt Shear Demand to Bearing ratio = 16.09 / 11.71 = 1.37

At Row 2, At Column 1:
Ri1 = 11.43 kips
Ri vector at Beam   = <-0.00, 11.43>
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 * (0.28/1) * 65.00 = 23.46 kips/bolt
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 5.59 * (0.28/1) * 65.00 = 59.99 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.28/1) * 65.00 = 16.09 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(23.46, 59.99, 16.09) = 16.09 kips/bolt
Ri vector at Shear Plate   = <0.00, -11.43>
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 * 1.20 * 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 * 3.84 * 0.38 * 58.00 = 50.16 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, 50.16, 19.57) = 19.57 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(16.087, 19.575) = 16.09 kips/bolt
Bolt Shear Demand to Bearing ratio = 16.09 / 11.43 = 1.41

At Row 3, At Column 1:
Ri1 = 11.71 kips
Ri vector at Beam   = <-7.58, 8.92>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 2.78 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * na * (0.28/1) * 65.00 = na
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 2.78 * (0.28/1) * 65.00 = 29.80 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.28/1) * 65.00 = 16.09 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(na, 29.80, 16.09) = 16.09 kips/bolt
Ri vector at Shear Plate   = <7.58, -8.92>
Lcsshpl at Shear Plate spacing  = na
Lceshpl at Shear Plate edge    = 1.11 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 * 1.11 * 0.38 * 58.00 = 14.45 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, 14.45, 19.57) = 14.45 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(16.087, 14.449) = 14.45 kips/bolt
Bolt Shear Demand to Bearing ratio = 14.45 / 11.71 = 1.23

Min Bolt Shear Demand to Bearing ratio for vertical shear only = min(1.0, 1.37411, 1.40774, 1.23417) = 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 * 29.27 = 29.27 kips

Web Depth = d - [Top Cope Depth] - [Bottom Cope Depth] = 15.9 - 0 - 1 = 14.9 in.
Gross Area (Shear) = [Web Depth] * tw = 14.90 * 0.28 = 4.10 in^2
Net Shear Area (Shear) = ([Web Depth] - ([# rows] * [Diameter + 0.0625])) * tw 
    = (14.90 - (3 * 0.88)) * 0.28 = 3.38 in^2

Using Eq.J4-3:
Shear Yielding = (1/omega) * 0.6 * Fybeam * [Gross Area] = 0.67 * 0.6 * 50.00 * 4.10 = 81.95 kips

Using Eq.J4-4:
Shear Rupture = (1/omega) * 0.6 * Fubeam * [Net Area] = 0.50 * 0.6 * 65.00 * 3.38 = 65.82 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.


Flexure at Longest Cope (Bottom Cope Only at Section)
Eccentricity at Section, e = 4.94 in.
Fy = 50.00 ksi
Snet1 (bolt holes not applicable) = 15.22 in^3
Snet2 (bolt holes applicable) = 15.22 in^3
Znet = 27.12 in^3

Using Eq. 9-19
Flexural Yielding = (1/omega) * Fy * Snet1 / e = 0.60 * 50.00 * 15.22 / 4.94 = 92.51 kips

Using Eq. 9-4
Flexural Rupture = (1/omega) * Fu * Znet / e = 0.50 * 65.00 * 27.12 / 4.94 = 178.56 kips


Flexure at Furthest Bolt Line within Cope (Bottom Cope Only at Section)
Eccentricity at Section, e = 3.25 in.
Fy = 50.00 ksi
Snet1 (bolt holes not applicable) = 15.22 in^3
Snet2 (bolt holes applicable) = 14.47 in^3
Znet = 24.66 in^3

Using Eq. 9-19
Flexural Yielding = (1/omega) * Fy * Snet1 / e = 0.60 * 50.00 * 15.22 / 3.25 = 140.57 kips

Using Eq. 9-4
Flexural Rupture = (1/omega) * Fu * Znet / e = 0.50 * 65.00 * 24.66 / 3.25 = 246.67 kips


Section Bending Strength Calculations Summary:

   Coped Beam Flexure at Longest Cope (Bottom Cope Only at Section)
   Flexural Yielding : 92.51 >= 20.00 kips (OK)
   Flexural Rupture : 178.56 >= 20.00 kips (OK)

   Coped Beam Flexure at Furthest Bolt Line within Cope (Bottom Cope Only at Section)
   Flexural Yielding : 140.57 >= 20.00 kips (OK)
   Flexural Rupture : 246.67 >= 20.00 kips (OK)

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 + 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 * 5.06) + (1.00 * 58.00 * 0.97)) = 43.57 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 * 0.97)) = 39.90 kips
Block Shear = 39.90 kips


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 = 4.73
Mr = Vr * e = 20.00 * 1.55 = 31.08 kips-in
Mc = 1/omega * Mn = 1/omega * Fy * Zgross = 0.60 * 36.00 * 6.77 = 146.31 kips-in
Vr = 20.00 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 = (20.00 / 45.90)^2 + (31.08 / 146.31)^2 = 0.23 <= 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 = 20.000 / 8.500 / 2 = 1.176 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) = 1.176 / (0.500 * 1.856) = 1.268/16

Minimum fillet weld size : 
   At shear only load case = 0.08 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 9-3)
 = twsupport * Fusupport / ( Fexx * C1 * 0.088 )
 = 0.375 * 65.000 / ( 70.000 * 1.000 * 0.088 ) 
 = 3.940 
Dmax3 = project max fillet weld = 12.000
Dmax=min(Dmax1, Dmax2, Dmax3) = min(3.515, 3.940, 12.000)
 = 3.515 

Dihedral Angle, DA       = 74.00 deg.
Gap on Obtuse Angle Side = 0.10 in.
Use weld size
Acute Side  D1 = 4.00
Obtuse Side D2 = 6.00

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( 74.00)) * cos( 37.00) = 0.21 in.
Obtuse Side Effect throat = ((D2/sin(DA)-tshpl/tan(DA))*sin((180-(180-DA))/2))= ((0.38 / sin(74.00) -0.38 / tan(74.00)) * sin((180 - (180 - 74.00)) / 2)) = 0.17 in.
Total Effective Throat    = 0.21 + 0.17 = 0.38 in.
Total Effective Throat of Square Case = D1 * 2^0.5 = 0.25 * 2^0.5 = 0.35 in.
0.35 in. <= 0.38 in. (OK)