bb.s.s.01312.01331

SHEAR PLATE CONNECTION SUMMARY

Filler Beam profile: W16X36
Support Girder profile: W18X40
Slope: 0.00 deg.
Skew: 90.00
Vertical Offset: 0.00 in.
Horizontal Offset: 0.03 in.
Span: 24.05 ft.
Reaction, V: 39.91 kips
Shear Capacity, Rn: 67.13 kips
Design/Reference according to AISC 14th Ed. - LRFD
Shear Plate: Conventional Configuration
Beam material grade: A992
Support material grade: A992
Plate material grade: A572-GR.50
Weld grade: E70
Shear Plate Size: 3.50 in. x 11.50 in. x 0.38 in.
Configuration Geometry:
Welds at shear plate to support: 4/16 FILLET, 4/16 FILLET
Bolt: 4 rows x 1 column 0.75 in. Diameter A325N_TC bolts
Vertical spacing: 3.00 in.
Horizontal spacing: 3.00 in.
Shear plate edge setback = 0.50 in.
Beam centerline setback = 0.50 in.
Edge distance at vertical edge of plate: 1.50 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: 1.50 in.
Edge distance at top edge of beam: 2.00 in.
Top cope depth: 1.00 in.
Top cope length: 3.00 in.
Horizontal distance to first hole: 2.00 in.
Down distance from top of filler beam flange: 3.00 in.
Holes in beam web: STD diameter = 0.81 in.
Holes in shear plate: SSL diameter = 0.81 in., slot width = 1.00 in.

BOLT SHEAR CAPACITY AT BEAM AND SHEAR PLATE SIDE:
Bolt Shear Capacity at Shear Load Only:
Using Instantaneous Center Of Rotation Method (AISC 7-1)
ex = 1.00 in.
Angle = 0.00 deg.
C = 3.75
Using Table 7-1 to determine (phi)rn:
(phi)Rn = (phi)rn * C = 17.89 * 3.75 = 67.13 kips


Total Vertical Bolt Shear Capacity = 67.13 kips
67.13 kips >= Reaction V = 39.91 kips (OK)

BOLT BEARING AT BEAM AND SHEAR PLATE SIDE
Vertical Shear Only Load Case:
ICR cordinate relative to CG = (10.97, 0.00)
At Row 1, At Column 1:
Ribolt = 17.56 kips
Ri vector at Beam   = <6.66, 16.25>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 1.76 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = na
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 1.76 * (0.29/1) * 65.00 = 30.29 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.75 * (0.29/1) * 65.00 = 25.89 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(na, 30.29, 25.89) = 25.89 kips/bolt
Ri vector at Shear Plate   = <-6.66, -16.25>
Lcsshpl at Shear Plate spacing  = na
Lceshpl at Shear Plate edge    = 4.83 in.
(phi)Rnsshpl at Shear Plate spacing = (phi) * hf1 * Lcs * t * Fu = na
(phi)Rneshpl at Shear Plate edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 4.83 * 0.38 * 65.00 = 106.00 kips/bolt
(phi)Rndshpl on Shear Plate at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.75 * 0.38 * 65.00 = 32.91 kips/bolt
Shear Plate bearing capacity, (phi)Rnshpl = min((phi)Rnsshpl,(phi)Rneshpl,(phi)Rndshpl) = min(na, 106.00, 32.91) = 32.91 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(25.89, 32.91) = 25.89 kips/bolt
Bolt Shear Demand to Bearing ratio = 25.89 / 17.56 = 1.47

At Row 2, At Column 1:
Ribolt = 17.48 kips
Ri vector at Beam   = <2.37, 17.32>
Lcsbm at Beam spacing  = 2.19 in.
Lcebm at Beam edge    = 4.64 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.75 * 1.20 * 2.19 * (0.29/1) * 65.00 = 37.75 kips/bolt
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 4.64 * (0.29/1) * 65.00 = 80.08 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.75 * (0.29/1) * 65.00 = 25.89 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(37.75, 80.08, 25.89) = 25.89 kips/bolt
Ri vector at Shear Plate   = <-2.37, -17.32>
Lcsshpl at Shear Plate spacing  = 2.19 in.
Lceshpl at Shear Plate edge    = 6.91 in.
(phi)Rnsshpl at Shear Plate spacing = (phi) * hf1 * Lcs * t * Fu = 0.75 * 1.20 * 2.19 * 0.38 * 65.00 = 47.99 kips/bolt
(phi)Rneshpl at Shear Plate edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 6.91 * 0.38 * 65.00 = 151.53 kips/bolt
(phi)Rndshpl on Shear Plate at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.75 * 0.38 * 65.00 = 32.91 kips/bolt
Shear Plate bearing capacity, (phi)Rnshpl = min((phi)Rnsshpl,(phi)Rneshpl,(phi)Rndshpl) = min(47.99, 151.53, 32.91) = 32.91 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(25.89, 32.91) = 25.89 kips/bolt
Bolt Shear Demand to Bearing ratio = 25.89 / 17.48 = 1.48

At Row 3, At Column 1:
Ribolt = 17.48 kips
Ri vector at Beam   = <-2.37, 17.32>
Lcsbm at Beam spacing  = 2.19 in.
Lcebm at Beam edge    = 7.67 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.75 * 1.20 * 2.19 * (0.29/1) * 65.00 = 37.75 kips/bolt
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 7.67 * (0.29/1) * 65.00 = 132.34 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.75 * (0.29/1) * 65.00 = 25.89 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(37.75, 132.34, 25.89) = 25.89 kips/bolt
Ri vector at Shear Plate   = <2.37, -17.32>
Lcsshpl at Shear Plate spacing  = 2.19 in.
Lceshpl at Shear Plate edge    = 3.88 in.
(phi)Rnsshpl at Shear Plate spacing = (phi) * hf1 * Lcs * t * Fu = 0.75 * 1.20 * 2.19 * 0.38 * 65.00 = 47.99 kips/bolt
(phi)Rneshpl at Shear Plate edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 3.88 * 0.38 * 65.00 = 85.11 kips/bolt
(phi)Rndshpl on Shear Plate at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.75 * 0.38 * 65.00 = 32.91 kips/bolt
Shear Plate bearing capacity, (phi)Rnshpl = min((phi)Rnsshpl,(phi)Rneshpl,(phi)Rndshpl) = min(47.99, 85.11, 32.91) = 32.91 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(25.89, 32.91) = 25.89 kips/bolt
Bolt Shear Demand to Bearing ratio = 25.89 / 17.48 = 1.48

At Row 4, At Column 1:
Ribolt = 17.56 kips
Ri vector at Beam   = <-6.67, 16.25>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 3.55 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = na
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 3.55 * (0.29/1) * 65.00 = 61.19 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.75 * (0.29/1) * 65.00 = 25.89 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(na, 61.19, 25.89) = 25.89 kips/bolt
Ri vector at Shear Plate   = <6.67, -16.25>
Lcsshpl at Shear Plate spacing  = na
Lceshpl at Shear Plate edge    = 0.91 in.
(phi)Rnsshpl at Shear Plate spacing = (phi) * hf1 * Lcs * t * Fu = na
(phi)Rneshpl at Shear Plate edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 0.91 * 0.38 * 65.00 = 20.01 kips/bolt
(phi)Rndshpl on Shear Plate at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.75 * 0.38 * 65.00 = 32.91 kips/bolt
Shear Plate bearing capacity, (phi)Rnshpl = min((phi)Rnsshpl,(phi)Rneshpl,(phi)Rndshpl) = min(na, 20.01, 32.91) = 20.01 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(25.89, 20.01) = 20.01 kips/bolt
Bolt Shear Demand to Bearing ratio = 20.01 / 17.56 = 1.14

Min Bolt Shear Demand to Bearing ratio Beam and Shear Plate for vertical shear only
 = min(1.00, 1.47, 1.48, 1.48, 1.14) = 1.00

BEARING AT BEAM AND SHEAR PLATE SIDE SUMMARY:
Bearing Capacity at Vertical Shear Load Only, Rbv = Min Bolt Shear Demand to Bearing Ratio * Bolt Shear = 1.00 * 67.13 = 67.13 kips
Rbv = 67.13 kips >= Reaction V = 39.91 kips (OK)

Web Depth = d - [Top Cope Depth] - [Bottom Cope Depth] = 15.90 - 1.00 - 0.00 = 14.90 in.

Using AISC 14th Ed. Equation J4-3
Gross Area (Shear), Agross = [Web Depth] * tw = 14.90 * 0.29 = 4.40 in^2
Shear Yielding, (phi)Vny = (phi) * 0.6 * Fybeam * Agross = 1.00 * 0.6 * 50.00 * 4.40 = 131.87 kips

Using AISC 14th Ed. Equation J4-4
Net Area (Shear), Anet = ([Web Depth] - ([# rows] * [Diameter + 0.06])) * tw 
    = (14.90 - (4 * 0.88)) * 0.29 = 3.36 in^2
Shear Rupture, (phi)Vnu = (phi) * 0.6 * Fubeam * Anet = 0.75 * 0.6 * 65.00 * 3.36 = 98.37 kips


Check Vertical Block Shear

Using AISC 14th Ed. Equation J4-5
Block Shear = {(phi) * ((0.6 * Fu * Anv) + (Ubs * Fu * Ant))} <= {(phi) * ((0.6 * Fy * Agv) + (Ubs * Fu * Ant))}

Block Shear (1)
Gross Shear Length = [edge dist. at beam edge] + ([# rows - 1] * [spacing]) = 2.00 + 9.00 = 11.00 in.
Net Shear Length = Gross Shear Length - (# rows - 0.5) * (hole size + 0.06) = 11.00 - (4 - 0.5) * 0.88 = 7.94 in.
Gross Tension Length = [edge dist. at beam edge] + ([# cols - 1] * [spacing]) = 1.50 + (1 - 1) * 3.00 = 1.50 in.
Net Tension Length = Gross Tension Length - (# cols - 0.5) * (hole size + 0.06) = 1.50 - (1 - 0.5) * 0.88 = 1.06 in.
1. (phi) * [material thickness] * ((0.60 * Fubeam* [net shear length]) + (Ubs * Fubeam * [net tension length])) 
    = 0.75 * 0.29 * ((0.60 * 65.00 * 7.94) + (1.00 * 65.00 * 1.06)) = 83.77 kips
2. (phi) * [material thickness] * ((0.60 * Fybeam * [gross shear length]) + (Ubs * Fubeam * [net tension length])) 
    = 0.75 * 0.29 * ((0.60 * 50.00 * 11.00) + (1.00 * 65.00 * 1.06)) = 88.29 kips
Block Shear = 83.77 kips

Block Shear (1) Total = Block Shear (1) = 83.77 kips
83.77 kips >= Reaction V = 39.91 kips (OK)

Block Shear for Axial T/C is not required.

Buckling and Flexure at Longest Cope (Top Cope Only at Section)
Eccentricity at Section, e = 3.66 in.
If coped at top/bottom flange only and c <= 2d and dc <= d/2, use AISC 14th Ed. Equation 9-7, Fcr = 26210.00 * f * k * (tw/h1)^2 <= Fy

Using AISC Equations 9-7 through 9-11
tw = 0.29 in.
h1 = 10.31 in.
c = 3.00 in.
When c/h1<=1.0, k=2.2(h1/c)^1.65
k  = 2.20 * (10.31 / 3.00)^1.65 = 16.88
When c/d<=1.0, f=2c/d
f = 2 * (3.00 / 15.90) = 0.38
Fy = 50.00 ksi
Fcr = (phi) * 26210.00 * f * k * (tw/h1)^2 = 0.90 * 26210.00 * 0.38 * 16.88 * (0.29 / 10.31)^2 = 122.91 ksi
Fcrmin =phi * min(Fcr, Fy) = 45.00 ksi
Snet1 (bolt holes not applicable) = 16.72 in^3
Snet2 (bolt holes applicable) = 16.72 in^3
Znet1 (bolt holes not applicable) = 30.18 in^3
Znet2 (bolt holes applicable) = 30.18 in^3

Using AISC 14th Ed. Equation 9-6
Buckling = Fcr * Snet1 / e = 45.00 * 16.72 / 3.66 = 205.69 kips

Using AISC 14th Ed. Equation 9-19
Flexural Yielding = (phi) * Fy * Snet1 / e = 0.90 * 50.00 * 16.72 / 3.66 = 205.69 kips

Using AISC 14th Ed. Equation 9-4
Flexural Rupture = (phi) * Fu * Znet2 / e = 0.75 * 65.00 * 30.18 / 3.66 = 402.25 kips


Buckling and Flexure at Furthest Bolt Line within Cope (Top Cope Only at Section)
Eccentricity at Section, e = 2.16 in.
If coped at top/bottom flange only and c <= 2d and dc <= d/2, use AISC 14th Ed. Equation 9-7, Fcr = 26210.00 * f * k * (tw/h1)^2 <= Fy

Using AISC Equations 9-7 through 9-11
tw = 0.29 in.
h1 = 10.94 in.
c = 3.00 in.
When c/h1<=1.0, k=2.2(h1/c)^1.65
k  = 2.20 * (10.94 / 3.00)^1.65 = 18.61
When c/d<=1.0, f=2c/d
f = 2 * (3.00 / 15.90) = 0.38
Fy = 50.00 ksi
Fcr = (phi) * 26210.00 * f * k * (tw/h1)^2 = 0.90 * 26210.00 * 0.38 * 18.61 * (0.29 / 10.94)^2 = 120.38 ksi
Fcrmin =phi * min(Fcr, Fy) = 45.00 ksi
Snet1 (bolt holes not applicable) = 16.72 in^3
Snet2 (bolt holes applicable) = 13.09 in^3
Znet1 (bolt holes not applicable) = 30.18 in^3
Znet2 (bolt holes applicable) = 23.26 in^3

Using AISC 14th Ed. Equation 9-6
Buckling = Fcr * Snet1 / e = 45.00 * 16.72 / 2.16 = 348.70 kips

Using AISC 14th Ed. Equation 9-19
Flexural Yielding = (phi) * Fy * Snet1 / e = 0.90 * 50.00 * 16.72 / 2.16 = 348.70 kips

Using AISC 14th Ed. Equation 9-4
Flexural Rupture = (phi) * Fu * Znet2 / e = 0.75 * 65.00 * 23.26 / 2.16 = 525.49 kips


Section Bending Strength Calculations Summary:

   Coped Beam Buckling and Flexure at Longest Cope (Top Cope Only at Section)
   Buckling : 205.69 >= 39.91 kips (OK)
   Flexural Yielding : 205.69 >= 39.91 kips (OK)
   Flexural Rupture : 402.25 >= 39.91 kips (OK)

   Coped Beam Buckling and Flexure at Furthest Bolt Line within Cope (Top Cope Only at Section)
   Buckling : 348.70 >= 39.91 kips (OK)
   Flexural Yielding : 348.70 >= 39.91 kips (OK)
   Flexural Rupture : 525.49 >= 39.91 kips (OK)

Using AISC 14th Ed. Equation J4-3
Gross Area, Ag = 0.38 * 11.50 = 4.31 in^2
Shear Yielding, (phi)Vny = (phi) * 0.6 * Fypl * Ag = 1.00 * 0.6 * 50.00 * 4.31 = 129.38 kips

129.38 kips >= Reaction V = 39.91 kips (OK)

Using AISC 14th Ed. Equation J4-4
Net Area, An = (11.50 - (4 * (0.81 + 1/16))) * 0.38 = 3.00 in^2
Shear Rupture, (phi)Vnu = (phi) * 0.6 * Fupl * An = 0.75 * 0.6 * 65.00 * 3.00 = 87.75 kips

87.75 kips >= Reaction V = 39.91 kips (OK)


Check Vertical Block Shear

Using AISC 14th Ed. Equation J4-5
Block Shear = {(phi) * ((0.6 * Fu * Anv) + (Ubs * Fu * Ant))} <= {(phi) * ((0.6 * Fy * Agv) + (Ubs * Fu * Ant))}

Block 1 (Shear): 
Gross Shear Length = (11.50 - 1.25) = 10.25 in.
Net Shear Length = 10.25 - (3.50 * (0.81 + 0.06)) = 7.19 in.
Gross Tension Length = (0.00 + 1.50) = 1.50 in.
Net Tension Length = 1.50 - (0.50 * (1.00 + 0.06)) = 0.97 in.
1. (phi) * [material thickness] * ((0.60 * Fupl* [net shear length]) + (Ubs * Fupl * [net tension length])) 
    = 0.75 * 0.38 * ((0.60 * 65.00 * 7.19) + (1.00 * 65.00 * 0.97)) = 96.55 kips
2. (phi) * [material thickness] * ((0.60 * Fypl * [gross shear length]) + (Ubs * Fupl * [net tension length])) 
    = 0.75 * 0.38 * ((0.60 * 50.00 * 10.25) + (1.00 * 65.00 * 0.97)) = 104.20 kips
Block Shear = 96.55 kips
96.55 kips >= Reaction V = 39.91 kips (OK)

Block Shear for Axial T/C is not required.

Interaction Check of Flexural Yielding:
Using AISC 14th Ed. Equation 10-5
Eccentricity due to Conventional Config. (e = a/2), e = 1.00 in.
Zgross = 12.40
Znet = 8.46
Mr = Vr * e = 39.91 * 1.00 = 39.91 kips-in
Mc = phi * Mn = phi * Fy * Zgross = 0.90 * 50.00 * 12.40 = 557.93 kips-in
Vr = 39.91 kips
Vc = phi * Vn = phi * 0.60 * Fy * Ag = 1.00 * 0.60 * 50.00 * 4.31 = 129.38 kips
Interaction due to moment and shear, (Vr/Vc)^2 + (Mr/Mc)^2 <= 1.0
(Vr/Vc)^2 + (Mr/Mc)^2 = (39.91 / 129.38)^2 + (39.91 / 557.93)^2 = 0.10 <= 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 = 11.50 in.
Shear Load per inch per weld, fv = R/Lv/2 = 39.91 / 11.50 / 2 = 1.74 kips/in/ weld 
theta = 0 deg.
cPhi  = 1.0 + 0.5 * sin(0)^1.5 = 1.00
Weld Coefficient = 0.60 * 70.00 * 1.00 * 1.00 * (2^0.5/2)*(1/16) = 1.86
Required weld size, Dv = fv/ (phi * coeff) = 1.74 / (0.75 * 1.86) = 1.25/16

Minimum fillet weld size : 
   At shear only load case = 0.08 in.
   per Table J2.4     = 0.19 in.
   5/8tp              = 0.23 in.
   user preference    = 0.25 in.

Dmax1 (using AISC 14th Ed. eqn 9-3)
 = tshpl * Fushpl / ( Fexx * C1 * 0.09)
 = 0.38 * 65.00 / ( 70.00 * 1.00 * 0.09 ) 
 = 3.94 
Dmax2 (using AISC 14th Ed. eqn 9-3)
 = twbm * Fusupport / ( Fexx * C1 * 0.09 )
 = 0.32 * 65.00 / ( 70.00 * 1.00 * 0.09 ) 
 = 3.31 
Dmax3 = project max fillet weld = 12.00
Dmax=min(Dmax1, Dmax2, Dmax3) = min(3.94, 3.31, 12.00)
 = 3.31 

Use weld size
D1 = 4.00
D2 = 4.00

Weld Strength :

Vertical weld capacity during shear only load, phi * Rnv1 = 0.75 * 1.86 * 11.50 * (3.31 + 3.31) = 105.96 kips

105.96 kips >= Reaction V = 39.91 kips (OK)