bb.s.s.00131.00289

SHEAR PLATE CONNECTION SUMMARY

Filler Beam profile: W12X19
Support Girder profile: W18X40
Slope: 0 deg.
Support Slope: 0.641 deg.
Skew: 90
Vertical Offset: -7.08
Horizontal Offset: 0
Span: 20 ft.
Reaction, V: 14 kips
Shear Capacity, Rn: 16.6 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 5.500 in. x 0.375 in.
Configuration Geometry:
Welds at shear plate to support: 4/16 FILLET, 4/16 FILLET
Bolt: 2 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 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.
Edge distance at bottom edge of beam: 3.7 in.
Bottom cope depth: 2.5 in.
Bottom cope length: 2.5 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 = 1.500 in.
Angle = 0.000 deg.
C = 1.388
Using Table 7-1 to determine (1/omega) * rn:
Rn = (1/omega) * rn * C = 11.93 * 1.39 = 16.56 kips

BOLT BEARING AT BEAM SIDE:
Vertical Shear Only Load Case:
ICR cordinate relative to CG = (1.50, -0.00)
At Row 1, At Column 1:
Ri1 = 11.71 kips
Ri vector at Beam   = <8.28, 8.28>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 3.84 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * na * (0.23/1) * 65.00 = na
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 3.84 * (0.23/1) * 65.00 = 35.16 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.23/1) * 65.00 = 13.75 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(na, 35.16, 13.75) = 13.75 kips/bolt
Ri vector at Shear Plate   = <-8.28, -8.28>
Lcsshpl at Shear Plate spacing  = na
Lceshpl at Shear Plate edge    = 3.67 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 * 3.67 * 0.38 * 58.00 = 47.86 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, 47.86, 19.57) = 19.57 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(13.747, 19.575) = 13.75 kips/bolt
Bolt Shear Demand to Bearing ratio = 13.75 / 11.71 = 1.17

At Row 2, At Column 1:
Ri1 = 11.71 kips
Ri vector at Beam   = <-8.28, 8.28>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 2.42 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * na * (0.23/1) * 65.00 = na
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 2.42 * (0.23/1) * 65.00 = 22.20 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.23/1) * 65.00 = 13.75 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(na, 22.20, 13.75) = 13.75 kips/bolt
Ri vector at Shear Plate   = <8.28, -8.28>
Lcsshpl at Shear Plate spacing  = na
Lceshpl at Shear Plate edge    = 1.19 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 * 1.19 * 0.38 * 58.00 = 15.57 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, 15.57, 19.57) = 15.57 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(13.747, 15.573) = 13.75 kips/bolt
Bolt Shear Demand to Bearing ratio = 13.75 / 11.71 = 1.17

Min Bolt Shear Demand to Bearing ratio for vertical shear only = min(1.0, 1.17424, 1.17424) = 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 * 16.56 = 16.56 kips

Web Depth = d - [Top Cope Depth] - [Bottom Cope Depth] = 12.2 - 0 - 2.5 = 9.7 in.
Gross Area (Shear) = [Web Depth] * tw = 9.70 * 0.23 = 2.28 in^2
Net Shear Area (Shear) = ([Web Depth] - ([# rows] * [Diameter + 0.0625])) * tw 
    = (9.70 - (2 * 0.88)) * 0.23 = 1.87 in^2

Using Eq.J4-3:
Shear Yielding = (1/omega) * 0.6 * Fybeam * [Gross Area] = 0.67 * 0.6 * 50.00 * 2.28 = 45.59 kips

Using Eq.J4-4:
Shear Rupture = (1/omega) * 0.6 * Fubeam * [Net Area] = 0.50 * 0.6 * 65.00 * 1.87 = 36.43 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 = 3.66 in.
Fy = 50.00 ksi
Snet1 (bolt holes not applicable) = 5.51 in^3
Snet2 (bolt holes applicable) = 5.51 in^3
Znet = 9.85 in^3

Using Eq. 9-19
Flexural Yielding = (1/omega) * Fy * Snet1 / e = 0.60 * 50.00 * 5.51 / 3.66 = 45.18 kips

Using Eq. 9-4
Flexural Rupture = (1/omega) * Fu * Znet / e = 0.50 * 65.00 * 9.85 / 3.66 = 87.50 kips


Flexure at Furthest Bolt Line within Cope (Bottom Cope Only at Section)
Eccentricity at Section, e = 3.16 in.
Fy = 50.00 ksi
Snet1 (bolt holes not applicable) = 5.51 in^3
Snet2 (bolt holes applicable) = 5.10 in^3
Znet = 8.66 in^3

Using Eq. 9-19
Flexural Yielding = (1/omega) * Fy * Snet1 / e = 0.60 * 50.00 * 5.51 / 3.16 = 52.34 kips

Using Eq. 9-4
Flexural Rupture = (1/omega) * Fu * Znet / e = 0.50 * 65.00 * 8.66 / 3.16 = 89.09 kips


Section Bending Strength Calculations Summary:

   Coped Beam Flexure at Longest Cope (Bottom Cope Only at Section)
   Flexural Yielding : 45.18 >= 14.00 kips (OK)
   Flexural Rupture : 87.50 >= 14.00 kips (OK)

   Coped Beam Flexure at Furthest Bolt Line within Cope (Bottom Cope Only at Section)
   Flexural Yielding : 52.34 >= 14.00 kips (OK)
   Flexural Rupture : 89.09 >= 14.00 kips (OK)

Gross Area = 0.38 * 5.50 = 2.06 in^2
Net Area = (5.50 - (2 *(0.81 + 1/16))) * 0.38 = 1.41 in^2

Using Eq.J4-3:
Shear Yielding = (1/omega) * 0.6 * Fypl * [Gross Area] = 0.67 * 0.6 * 36.00 * 2.06 = 29.70 kips

Using Eq.J4-4:
Shear Rupture = (1/omega) * 0.6 * Fupl * [Net Area] = 0.50 * 0.6 * 58.00 * 1.41 = 24.47 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 = (5.5 - 1.25) = 4.25 in.
Net Shear Length = 4.25 - (1.5 * (0.812 + 0.0625)) = 2.94 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 * 2.94) + (1.00 * 58.00 * 0.97)) = 29.70 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 * 4.25) + (1.00 * 58.00 * 0.97)) = 27.75 kips
Block Shear = 27.75 kips


Interaction Check of Flexural Yielding, Per AISC 10-5: 
Eccentricity due to Conventional Config. (e = a/2), e = 1.50 in.
Zgross = 2.84
Znet = 1.85
Mr = Vr * e = 14.00 * 1.50 = 21.00 kips-in
Mc = 1/omega * Mn = 1/omega * Fy * Zgross = 0.60 * 36.00 * 2.84 = 61.26 kips-in
Vr = 14.00 kips
Vc = 1/omega * Vn = 1/omega * 0.60 * Fy * Ag = 0.67 * 0.60 * 36.00 * 2.06 = 29.70 kips
Interaction due to moment and shear, (Vr/Vc)^2 + (Mr/Mc)^2 <= 1.0
(Vr/Vc)^2 + (Mr/Mc)^2 = (14.00 / 29.70)^2 + (21.00 / 61.26)^2 = 0.34 <= 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 = 5.500 in.
Shear Load per inch per weld, fv = R/Lv/2 = 14.000 / 5.500 / 2 = 1.273 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) = 1.273 / (0.500 * 1.856) = 1.371/16

Minimum fillet weld size : 
   At shear only load case = 0.09 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 )
 = 0.315 * 65.000 / ( 70.000 * 1.000 * 0.088 ) 
 = 3.309 
Dmax3 = project max fillet weld = 12.000
Dmax=min(Dmax1, Dmax2, Dmax3) = min(3.515, 3.309, 12.000)
 = 3.309 

Use weld size
D1 = 4.00
D2 = 4.00

Weld Strength :
Vertical weld capacity during shear only load, 1/omega * Rnv1 = 0.50 * 1.86 * 5.50 * (3.31 + 3.31) = 33.78 kips