bb.s.s.00346.00346

SHEAR PLATE CONNECTION SUMMARY

Filler Beam profile: W10X12
Support Girder profile: W40X149
Slope: -2.47 deg.
Skew: 90
Vertical Offset: 0
Horizontal Offset: 0
Span: 5 ft.
Reaction, V: 10 kips
Shear Capacity, Rn: 11.5 kips
Design/Reference according to AISC 14th Ed. - ASD
Shear Plate: Extended Configuration
Beam material grade: A992
Support material grade: A992
Plate material grade: A36
Weld grade: E70
Shear Plate Size: 15.500 in. x 5.500 in. x 0.875 in.
Configuration Geometry:
Welds at shear plate to support: 9/16 FILLET, 9/16 FILLET
Bolt: 2 rows x 3 columns 0.75 in. Diameter A325N_TC bolts
Vertical spacing: 3 in.
Horizontal spacing: 3 in.
Shear plate edge setback = 6.06 in.
Beam centerline setback = 6.06 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 at top bolt: 1.65 in.
Edge distance at vertical edge of beam at bottom bolt: 1.78 in.
Horizontal distance to first hole: 8 in.
Down distance from top of filler beam flange: 3.25 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 = 11.315 in.
Angle = 0.000 deg.
C = 1.307
Using Table 7-1 to determine (1/omega) * rn:
Rn = (1/omega) * rn * C = 11.93 * 1.31 = 15.59 kips

BOLT BEARING AT BEAM SIDE:
Vertical Shear Only Load Case:
ICR cordinate relative to CG = (0.99, -0.00)
At Row 1, At Column 1:
Ri1 = 11.71 kips
Ri vector at Beam   = <4.12, 10.96>
Lcsbm at Beam spacing  = 3.12 in.
Lcebm at Beam edge    = 3.01 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * 3.12 * (0.19/1) * 65.00 = 23.09 kips/bolt
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 3.01 * (0.19/1) * 65.00 = 22.33 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.19/1) * 65.00 = 11.11 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(23.09, 22.33, 11.11) = 11.11 kips/bolt
Ri vector at Shear Plate   = <-4.12, -10.96>
Lcsshpl at Shear Plate spacing  = 3.05 in.
Lceshpl at Shear Plate edge    = 4.11 in.
1/omegaRnsshpl at Shear Plate spacing = 1/omega * hf1 * Lcs * t * Fu = 0.50 * 1.20 * 3.05 * 0.88 * 58.00 = 92.86 kips/bolt
1/omegaRneshpl at Shear Plate edge = 1/omega * hf1 * Lce * t * Fu = 0.50 * 1.20 * 4.11 * 0.88 * 58.00 = 125.04 kips/bolt
1/omegaRndshpl on Shear Plate at Bolt Diameter   = 1/omega * hf2 * db * t * Fu = 0.50 * 2.40 * 0.75 * 0.88 * 58.00 = 45.67 kips/bolt
Shear Plate bearing capacity, 1/omegaRnshpl = min(1/omegaRnsshpl,1/omegaRneshpl,1/omegaRndshpl) = min(92.86, 125.04, 45.67) = 45.67 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(11.115, 45.675) = 11.11 kips/bolt
Bolt Shear Demand to Bearing ratio = 11.11 / 11.71 = 0.95

At Row 1, At Column 2:
Ri1 = 10.27 kips
Ri vector at Beam   = <8.57, 5.66>
Lcsbm at Beam spacing  = 3.12 in.
Lcebm at Beam edge    = 4.91 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * 3.12 * (0.19/1) * 65.00 = 23.09 kips/bolt
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 4.91 * (0.19/1) * 65.00 = 36.41 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.19/1) * 65.00 = 11.11 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(23.09, 36.41, 11.11) = 11.11 kips/bolt
Ri vector at Shear Plate   = <-8.57, -5.66>
Lcsshpl at Shear Plate spacing  = 3.05 in.
Lceshpl at Shear Plate edge    = 7.11 in.
1/omegaRnsshpl at Shear Plate spacing = 1/omega * hf1 * Lcs * t * Fu = 0.50 * 1.20 * 3.05 * 0.88 * 58.00 = 92.86 kips/bolt
1/omegaRneshpl at Shear Plate edge = 1/omega * hf1 * Lce * t * Fu = 0.50 * 1.20 * 7.11 * 0.88 * 58.00 = 216.57 kips/bolt
1/omegaRndshpl on Shear Plate at Bolt Diameter   = 1/omega * hf2 * db * t * Fu = 0.50 * 2.40 * 0.75 * 0.88 * 58.00 = 45.67 kips/bolt
Shear Plate bearing capacity, 1/omegaRnshpl = min(1/omegaRnsshpl,1/omegaRneshpl,1/omegaRndshpl) = min(92.86, 216.57, 45.67) = 45.67 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(11.115, 45.675) = 11.11 kips/bolt
Bolt Shear Demand to Bearing ratio = 11.11 / 10.27 = 1.08

At Row 1, At Column 3:
Ri1 = 11.01 kips
Ri vector at Beam   = <6.59, -8.82>
Lcsbm at Beam spacing  = 3.12 in.
Lcebm at Beam edge    = 8.47 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * 3.12 * (0.19/1) * 65.00 = 23.09 kips/bolt
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 8.47 * (0.19/1) * 65.00 = 62.77 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.19/1) * 65.00 = 11.11 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(23.09, 62.77, 11.11) = 11.11 kips/bolt
Ri vector at Shear Plate   = <-6.59, 8.82>
Lcsshpl at Shear Plate spacing  = 3.05 in.
Lceshpl at Shear Plate edge    = 1.05 in.
1/omegaRnsshpl at Shear Plate spacing = 1/omega * hf1 * Lcs * t * Fu = 0.50 * 1.20 * 3.05 * 0.88 * 58.00 = 92.86 kips/bolt
1/omegaRneshpl at Shear Plate edge = 1/omega * hf1 * Lce * t * Fu = 0.50 * 1.20 * 1.05 * 0.88 * 58.00 = 32.06 kips/bolt
1/omegaRndshpl on Shear Plate at Bolt Diameter   = 1/omega * hf2 * db * t * Fu = 0.50 * 2.40 * 0.75 * 0.88 * 58.00 = 45.67 kips/bolt
Shear Plate bearing capacity, 1/omegaRnshpl = min(1/omegaRnsshpl,1/omegaRneshpl,1/omegaRndshpl) = min(92.86, 32.06, 45.67) = 32.06 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(11.115, 32.062) = 11.11 kips/bolt
Bolt Shear Demand to Bearing ratio = 11.11 / 11.01 = 1.01

At Row 2, At Column 1:
Ri1 = 11.71 kips
Ri vector at Beam   = <-4.12, 10.96>
Lcsbm at Beam spacing  = 3.12 in.
Lcebm at Beam edge    = 4.14 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * 3.12 * (0.19/1) * 65.00 = 23.09 kips/bolt
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 4.14 * (0.19/1) * 65.00 = 30.71 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.19/1) * 65.00 = 11.11 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(23.09, 30.71, 11.11) = 11.11 kips/bolt
Ri vector at Shear Plate   = <4.12, -10.96>
Lcsshpl at Shear Plate spacing  = 3.05 in.
Lceshpl at Shear Plate edge    = 0.90 in.
1/omegaRnsshpl at Shear Plate spacing = 1/omega * hf1 * Lcs * t * Fu = 0.50 * 1.20 * 3.05 * 0.88 * 58.00 = 92.86 kips/bolt
1/omegaRneshpl at Shear Plate edge = 1/omega * hf1 * Lce * t * Fu = 0.50 * 1.20 * 0.90 * 0.88 * 58.00 = 27.45 kips/bolt
1/omegaRndshpl on Shear Plate at Bolt Diameter   = 1/omega * hf2 * db * t * Fu = 0.50 * 2.40 * 0.75 * 0.88 * 58.00 = 45.67 kips/bolt
Shear Plate bearing capacity, 1/omegaRnshpl = min(1/omegaRnsshpl,1/omegaRneshpl,1/omegaRndshpl) = min(92.86, 27.45, 45.67) = 27.45 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(11.115, 27.447) = 11.11 kips/bolt
Bolt Shear Demand to Bearing ratio = 11.11 / 11.71 = 0.95

At Row 2, At Column 2:
Ri1 = 10.27 kips
Ri vector at Beam   = <-8.57, 5.66>
Lcsbm at Beam spacing  = 3.12 in.
Lcebm at Beam edge    = 5.17 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * 3.12 * (0.19/1) * 65.00 = 23.09 kips/bolt
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 5.17 * (0.19/1) * 65.00 = 38.30 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.19/1) * 65.00 = 11.11 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(23.09, 38.30, 11.11) = 11.11 kips/bolt
Ri vector at Shear Plate   = <8.57, -5.66>
Lcsshpl at Shear Plate spacing  = 3.05 in.
Lceshpl at Shear Plate edge    = 1.67 in.
1/omegaRnsshpl at Shear Plate spacing = 1/omega * hf1 * Lcs * t * Fu = 0.50 * 1.20 * 3.05 * 0.88 * 58.00 = 92.86 kips/bolt
1/omegaRneshpl at Shear Plate edge = 1/omega * hf1 * Lce * t * Fu = 0.50 * 1.20 * 1.67 * 0.88 * 58.00 = 50.82 kips/bolt
1/omegaRndshpl on Shear Plate at Bolt Diameter   = 1/omega * hf2 * db * t * Fu = 0.50 * 2.40 * 0.75 * 0.88 * 58.00 = 45.67 kips/bolt
Shear Plate bearing capacity, 1/omegaRnshpl = min(1/omegaRnsshpl,1/omegaRneshpl,1/omegaRndshpl) = min(92.86, 50.82, 45.67) = 45.67 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(11.115, 45.675) = 11.11 kips/bolt
Bolt Shear Demand to Bearing ratio = 11.11 / 10.27 = 1.08

At Row 2, At Column 3:
Ri1 = 11.01 kips
Ri vector at Beam   = <-6.59, -8.82>
Lcsbm at Beam spacing  = 3.12 in.
Lcebm at Beam edge    = 4.29 in.
1/omegaRnsbm at Beam spacing = 1/omega * hf1 * Lcs * (tw/# shear planes) * Fu = 0.50 * 1.20 * 3.12 * (0.19/1) * 65.00 = 23.09 kips/bolt
1/omegaRnebm at Beam edge = 1/omega * hf1 * Lce * (tw/# shear planes) * Fu = 0.50 * 1.20 * 4.29 * (0.19/1) * 65.00 = 31.79 kips/bolt
1/omegaRndbm on Beam at Bolt Diameter   = 1/omega * hf2 * db * (tw/# shear planes) * Fu = 0.50 * 2.40 * 0.75 * (0.19/1) * 65.00 = 11.11 kips/bolt
Beam bearing capacity, 1/omegaRnbm = min(1/omegaRnsbm,1/omegaRnebm,1/omegaRndbm) = min(23.09, 31.79, 11.11) = 11.11 kips/bolt
Ri vector at Shear Plate   = <6.59, 8.82>
Lcsshpl at Shear Plate spacing  = 3.05 in.
Lceshpl at Shear Plate edge    = 2.00 in.
1/omegaRnsshpl at Shear Plate spacing = 1/omega * hf1 * Lcs * t * Fu = 0.50 * 1.20 * 3.05 * 0.88 * 58.00 = 92.86 kips/bolt
1/omegaRneshpl at Shear Plate edge = 1/omega * hf1 * Lce * t * Fu = 0.50 * 1.20 * 2.00 * 0.88 * 58.00 = 60.91 kips/bolt
1/omegaRndshpl on Shear Plate at Bolt Diameter   = 1/omega * hf2 * db * t * Fu = 0.50 * 2.40 * 0.75 * 0.88 * 58.00 = 45.67 kips/bolt
Shear Plate bearing capacity, 1/omegaRnshpl = min(1/omegaRnsshpl,1/omegaRneshpl,1/omegaRndshpl) = min(92.86, 60.91, 45.67) = 45.67 kips/bolt
1/omegaRn = min(1/omegaRnbm, 1/omegaRnshpl) = min(11.115, 45.675) = 11.11 kips/bolt
Bolt Shear Demand to Bearing ratio = 11.11 / 11.01 = 1.01

Min Bolt Shear Demand to Bearing ratio for vertical shear only = min(1.0, 0.949382, 1.08242, 1.00944, 0.949382, 1.08242, 1.00944) = 0.95


Bearing Capacity at Beam and Shear Plate at Vertical Shear Load Only, Rbv1 = Min Bolt Shear Demand to Bearing Ratio * Bolt Shear = 0.95 * 15.59 = 14.80 kips

Web Depth = d - [Top Cope Depth] - [Bottom Cope Depth] = 9.87 - 0 - 0 = 9.87 in.
Gross Area (Shear) = [Web Depth] * tw = 9.87 * 0.19 = 1.88 in^2
Net Shear Area (Shear) = ([Web Depth] - ([# rows] * [Diameter + 0.0625])) * tw 
    = (9.87 - (2 * 0.88)) * 0.19 = 1.54 in^2

Using Eq.J4-3:
Shear Yielding = (1/omega) * 0.6 * Fybeam * [Gross Area] = 0.67 * 0.6 * 50.00 * 1.88 = 37.51 kips

Using Eq.J4-4:
Shear Rupture = (1/omega) * 0.6 * Fubeam * [Net Area] = 0.50 * 0.6 * 65.00 * 1.54 = 30.08 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 = 0.88 * 5.50 = 4.81 in^2
Net Area = (5.50 - (2 *(0.81 + 1/16))) * 0.88 = 3.28 in^2

Using Eq.J4-3:
Shear Yielding = (1/omega) * 0.6 * Fypl * [Gross Area] = 0.67 * 0.6 * 36.00 * 4.81 = 69.30 kips

Using Eq.J4-4:
Shear Rupture = (1/omega) * 0.6 * Fupl * [Net Area] = 0.50 * 0.6 * 58.00 * 3.28 = 57.09 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 = (6 + 1.5) = 7.50 in.
Net Tension Length = 7.5 - (2.5 * (1 + 0.0625)) = 4.84 in.
1. (1/omega) * [material thickness] * ((0.60 * Fupl* [net shear length]) + (Ubs * Fupl * [net tension length])) 
    = 0.50 * 0.88 * ((0.60 * 58.00 * 2.94) + (0.50 * 58.00 * 4.84)) = 106.18 kips
2. (1/omega) * [material thickness] * ((0.60 * Fypl * [gross shear length]) + (Ubs * Fupl * [net tension length])) 
    = 0.50 * 0.88 * ((0.60 * 36.00 * 4.25) + (0.50 * 58.00 * 4.84)) = 101.62 kips
Block Shear = 101.62 kips

Block 2 (Shear): 
Gross Shear Length = 2 * (5.5 - 1.25) = 8.50 in.
Net Shear Length = 2 * ( 4.25 - (1.5 * (0.812 + 0.0625)) ) = 5.88 in.
Gross Tension Length = (6 + 1.5) - 1.5 = 6.00 in.
Net Tension Length = 6 - 2 * (1 + 0.0625) = 3.88 in.
1. (1/omega) * [material thickness] * ((0.60 * Fupl* [net shear length]) + (Ubs * Fupl * [net tension length])) 
    = 0.50 * 0.88 * ((0.60 * 58.00 * 5.88) + (0.50 * 58.00 * 3.88)) = 138.61 kips
2. (1/omega) * [material thickness] * ((0.60 * Fypl * [gross shear length]) + (Ubs * Fupl * [net tension length])) 
    = 0.50 * 0.88 * ((0.60 * 36.00 * 8.50) + (0.50 * 58.00 * 3.88)) = 129.49 kips
Block Shear = 129.49 kips

Flexural and Buckling Strength:

Eccentricity at first line of bolts, e = 8.31 in.
Zgross = 6.62 in^3
Znet   = 4.32 in^3
Sgross = 4.41 in^3
Snet   = 3.16 in^3

Using Eq. 9-4
Flexural Rupture = (1/omega) * Fu * Znet / e = 0.50 * 58.00 * 4.32 / 8.31 = 15.07 kips


Using Eq. 9-14 through 9-18, Fcr = Fy * Q
tw = 0.88 in.
ho = 5.50 in.
c = 8.00 in.
lambda = (ho * Fy ^ 0.5) / ( 10 * tw * ( 475.00 + 280.00 * (ho / c)^2 ) ^0.5 ) = 
 = 5.50 * 36.00^0.5 / (10 * 0.88 * (475.00 + 280.00 * (5.50/8.00)^2 )^0.5) = 0.15
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 * 4.41 / 8.31 = 11.46 kips

Interaction Check of Flexural Yielding, Per AISC 10-5: 
Eccentricity at CG of Bolt Group, e = 11.31 in.
Zgross = 6.62
Znet = 4.32
Mr = Vr * e = 10.00 * 11.31 = 113.15 kips-in
Mc = 1/omega * Mn = 1/omega * Fy * Zgross = 0.60 * 36.00 * 6.62 = 142.93 kips-in
Vr = 10.00 kips
Vc = 1/omega * Vn = 1/omega * 0.60 * Fy * Ag = 0.67 * 0.60 * 36.00 * 4.81 = 69.30 kips
Interaction due to moment and shear, (Vr/Vc)^2 + (Mr/Mc)^2 <= 1.0
(Vr/Vc)^2 + (Mr/Mc)^2 = (10.00 / 69.30)^2 + (113.15 / 142.93)^2 = 0.65 <= 1  (OK)

Note: Mn <= 1.6My by inspection

MAXIMUM PLATE THICKNESS:
tmax = 6 * Mmax / (Fypl * d^2) Eq. 10-3
Mmax = (1/0.9) * Fv * Ab * C' Eq. 10-4
Mmax = (1/0.9) * 54 * 0.441786 * 15.7877 = 418.487 kips-in
tmax = 6 * 418.487 / (36 * 5.5^2) = 2.31 in.
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 = 10.000 / 5.500 / 2 = 0.909 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) = 0.909 / (0.500 * 1.856) = 0.980/16

Minimum fillet weld size : 
   At shear only load case = 0.06 in.
   per Table J2.4     = 0.25 in.
   5/8(tp)            = 0.55 in.
   user preference    = 0.25 in.

Dmax1 (using eqn 9-3)
 = tshpl * Fushpl / ( Fexx * C1 * 0.088)
 = 0.875 * 58.000 / ( 70.000 * 1.000 * 0.088 ) 
 = 8.202 
Dmax2 (using eqn 9-3)
 = twsupport * Fusupport / ( Fexx * C1 * 0.088 )
 = 0.630 * 65.000 / ( 70.000 * 1.000 * 0.088 ) 
 = 6.619 
Dmax3 = project max fillet weld = 12.000
Dmax=min(Dmax1, Dmax2, Dmax3) = min(8.202, 6.619, 12.000)
 = 6.619 

Use weld size
D1 = 9.00
D2 = 9.00

Weld Strength :
Vertical weld capacity during shear only load, 1/omega * Rnv1 = 0.50 * 1.86 * 5.50 * (6.62 + 6.62) = 67.57 kips