bcf.s.s.01038.01038

SHEAR PLATE CONNECTION SUMMARY

Filler Beam profile: W21X68
Column profile: W14X342
Slope: 0.00 deg.
Skew: 90.00
Vertical Offset: 0.00
Horizontal Offset: 0.00
Span: 21.12 ft.
Reaction, V: 45.00 kips
Shear Capacity, Rn: 88.48 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: 4.00 in. x 14.50 in. x 0.38 in.
Configuration Geometry:
Welds at shear plate to support: 4/16 FILLET, 4/16 FILLET
Bolt: 5 rows x 1 column 0.88 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: 1.75 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: 1.75 in.
Horizontal distance to first hole: 2.25 in.
Down distance from top of filler beam flange: 3.00 in.
Holes in beam web: STD diameter = 0.94 in.
Holes in shear plate: SSL diameter = 0.94 in., slot width = 1.12 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 = 1.12 in.
Angle = 0.00 deg.
C = 4.73
Using Table 7-1 to determine (phi)rn:
(phi)Rn = (phi)rn * C = 24.35 * 4.73 = 115.21 kips


Total Vertical Bolt Shear Capacity = 115.21 kips
115.21 kips >= Reaction V = 45.00 kips (OK)

BOLT BEARING AT BEAM AND SHEAR PLATE SIDE
Vertical Shear Only Load Case:
ICR cordinate relative to CG = (15.64, 0.00)
At Row 1, At Column 1:
Ribolt = 23.90 kips
Ri vector at Beam   = <8.56, 22.32>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 2.74 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 * 2.74 * (0.43/1) * 65.00 = 69.04 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.88 * (0.43/1) * 65.00 = 44.02 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(na, 69.04, 44.02) = 44.02 kips/bolt
Ri vector at Shear Plate   = <-8.56, -22.32>
Lcsshpl at Shear Plate spacing  = na
Lceshpl at Shear Plate edge    = 5.78 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 * 5.78 * 0.38 * 65.00 = 126.76 kips/bolt
(phi)Rndshpl on Shear Plate at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.88 * 0.38 * 65.00 = 38.39 kips/bolt
Shear Plate bearing capacity, (phi)Rnshpl = min((phi)Rnsshpl,(phi)Rneshpl,(phi)Rndshpl) = min(na, 126.76, 38.39) = 38.39 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(44.02, 38.39) = 38.39 kips/bolt
Bolt Shear Demand to Bearing ratio = 38.39 / 23.90 = 1.61

At Row 2, At Column 1:
Ribolt = 23.82 kips
Ri vector at Beam   = <4.49, 23.39>
Lcsbm at Beam spacing  = 2.06 in.
Lcebm at Beam edge    = 5.64 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.75 * 1.20 * 2.06 * (0.43/1) * 65.00 = 51.88 kips/bolt
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 5.64 * (0.43/1) * 65.00 = 141.90 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.88 * (0.43/1) * 65.00 = 44.02 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(51.88, 141.90, 44.02) = 44.02 kips/bolt
Ri vector at Shear Plate   = <-4.49, -23.39>
Lcsshpl at Shear Plate spacing  = 2.06 in.
Lceshpl at Shear Plate edge    = 9.96 in.
(phi)Rnsshpl at Shear Plate spacing = (phi) * hf1 * Lcs * t * Fu = 0.75 * 1.20 * 2.06 * 0.38 * 65.00 = 45.25 kips/bolt
(phi)Rneshpl at Shear Plate edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 9.96 * 0.38 * 65.00 = 218.50 kips/bolt
(phi)Rndshpl on Shear Plate at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.88 * 0.38 * 65.00 = 38.39 kips/bolt
Shear Plate bearing capacity, (phi)Rnshpl = min((phi)Rnsshpl,(phi)Rneshpl,(phi)Rndshpl) = min(45.25, 218.50, 38.39) = 38.39 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(44.02, 38.39) = 38.39 kips/bolt
Bolt Shear Demand to Bearing ratio = 38.39 / 23.82 = 1.61

At Row 3, At Column 1:
Ribolt = 23.79 kips
Ri vector at Beam   = <-0.00, 23.79>
Lcsbm at Beam spacing  = 2.06 in.
Lcebm at Beam edge    = 8.53 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.75 * 1.20 * 2.06 * (0.43/1) * 65.00 = 51.88 kips/bolt
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 8.53 * (0.43/1) * 65.00 = 214.61 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.88 * (0.43/1) * 65.00 = 44.02 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(51.88, 214.61, 44.02) = 44.02 kips/bolt
Ri vector at Shear Plate   = <0.00, -23.79>
Lcsshpl at Shear Plate spacing  = 2.06 in.
Lceshpl at Shear Plate edge    = 6.78 in.
(phi)Rnsshpl at Shear Plate spacing = (phi) * hf1 * Lcs * t * Fu = 0.75 * 1.20 * 2.06 * 0.38 * 65.00 = 45.25 kips/bolt
(phi)Rneshpl at Shear Plate edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 6.78 * 0.38 * 65.00 = 148.77 kips/bolt
(phi)Rndshpl on Shear Plate at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.88 * 0.38 * 65.00 = 38.39 kips/bolt
Shear Plate bearing capacity, (phi)Rnshpl = min((phi)Rnsshpl,(phi)Rneshpl,(phi)Rndshpl) = min(45.25, 148.77, 38.39) = 38.39 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(44.02, 38.39) = 38.39 kips/bolt
Bolt Shear Demand to Bearing ratio = 38.39 / 23.79 = 1.61

At Row 4, At Column 1:
Ribolt = 23.82 kips
Ri vector at Beam   = <-4.49, 23.39>
Lcsbm at Beam spacing  = 2.06 in.
Lcebm at Beam edge    = 8.82 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.75 * 1.20 * 2.06 * (0.43/1) * 65.00 = 51.88 kips/bolt
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 8.82 * (0.43/1) * 65.00 = 221.83 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.88 * (0.43/1) * 65.00 = 44.02 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(51.88, 221.83, 44.02) = 44.02 kips/bolt
Ri vector at Shear Plate   = <4.49, -23.39>
Lcsshpl at Shear Plate spacing  = 2.06 in.
Lceshpl at Shear Plate edge    = 3.85 in.
(phi)Rnsshpl at Shear Plate spacing = (phi) * hf1 * Lcs * t * Fu = 0.75 * 1.20 * 2.06 * 0.38 * 65.00 = 45.25 kips/bolt
(phi)Rneshpl at Shear Plate edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 3.85 * 0.38 * 65.00 = 84.47 kips/bolt
(phi)Rndshpl on Shear Plate at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.88 * 0.38 * 65.00 = 38.39 kips/bolt
Shear Plate bearing capacity, (phi)Rnshpl = min((phi)Rnsshpl,(phi)Rneshpl,(phi)Rndshpl) = min(45.25, 84.47, 38.39) = 38.39 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(44.02, 38.39) = 38.39 kips/bolt
Bolt Shear Demand to Bearing ratio = 38.39 / 23.82 = 1.61

At Row 5, At Column 1:
Ribolt = 23.90 kips
Ri vector at Beam   = <-8.56, 22.32>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 4.42 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 * 4.42 * (0.43/1) * 65.00 = 111.09 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.88 * (0.43/1) * 65.00 = 44.02 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(na, 111.09, 44.02) = 44.02 kips/bolt
Ri vector at Shear Plate   = <8.56, -22.32>
Lcsshpl at Shear Plate spacing  = na
Lceshpl at Shear Plate edge    = 0.84 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 * 0.84 * 0.38 * 65.00 = 18.36 kips/bolt
(phi)Rndshpl on Shear Plate at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.88 * 0.38 * 65.00 = 38.39 kips/bolt
Shear Plate bearing capacity, (phi)Rnshpl = min((phi)Rnsshpl,(phi)Rneshpl,(phi)Rndshpl) = min(na, 18.36, 38.39) = 18.36 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(44.02, 18.36) = 18.36 kips/bolt
Bolt Shear Demand to Bearing ratio = 18.36 / 23.90 = 0.77

Min Bolt Shear Demand to Bearing ratio Beam and Shear Plate for vertical shear only
 = min(1.00, 1.61, 1.61, 1.61, 1.61, 0.77) = 0.77

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 = 0.77 * 115.21 = 88.48 kips
Rbv = 88.48 kips >= Reaction V = 45.00 kips (OK)

Web Depth = d - [Top Cope Depth] - [Bottom Cope Depth] = 21.10 - 0.00 - 0.00 = 21.10 in.

Using AISC 14th Ed. Equation J4-3
Gross Area (Shear), Agross = [Web Depth] * tw = 21.10 * 0.43 = 9.07 in^2
Shear Yielding, (phi)Vny = (phi) * 0.6 * Fybeam * Agross = 1.00 * 0.6 * 50.00 * 9.07 = 272.19 kips

Using AISC 14th Ed. Equation J4-4
Net Area (Shear), Anet = ([Web Depth] - ([# rows] * [Diameter + 0.06])) * tw 
    = (21.10 - (5 * 1.00)) * 0.43 = 6.92 in^2
Shear Rupture, (phi)Vnu = (phi) * 0.6 * Fubeam * Anet = 0.75 * 0.6 * 65.00 * 6.92 = 202.50 kips


Check Horizontal 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 for Axial T/C is not required.

Using AISC 14th Ed. Equation J4-3
Gross Area, Ag = 0.38 * 14.50 = 5.44 in^2
Shear Yielding, (phi)Vny = (phi) * 0.6 * Fypl * Ag = 1.00 * 0.6 * 50.00 * 5.44 = 163.12 kips

163.12 kips >= Reaction V = 45.00 kips (OK)

Using AISC 14th Ed. Equation J4-4
Net Area, An = (14.50 - (5 * (0.94 + 1/16))) * 0.38 = 3.56 in^2
Shear Rupture, (phi)Vnu = (phi) * 0.6 * Fupl * An = 0.75 * 0.6 * 65.00 * 3.56 = 104.21 kips

104.21 kips >= Reaction V = 45.00 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 = (14.50 - 1.25) = 13.25 in.
Net Shear Length = 13.25 - (4.50 * (0.94 + 0.06)) = 8.75 in.
Gross Tension Length = (0.00 + 1.75) = 1.75 in.
Net Tension Length = 1.75 - (0.50 * (1.12 + 0.06)) = 1.16 in.
1. (phi) * [material thickness] * ((0.60 * Fupl* [net shear length]) + (Ubs * Fupl * [net tension length])) 
    = 0.75 * 0.38 * ((0.60 * 65.00 * 8.75) + (1.00 * 65.00 * 1.16)) = 117.12 kips
2. (phi) * [material thickness] * ((0.60 * Fypl * [gross shear length]) + (Ubs * Fupl * [net tension length])) 
    = 0.75 * 0.38 * ((0.60 * 50.00 * 13.25) + (1.00 * 65.00 * 1.16)) = 132.94 kips
Block Shear = 117.12 kips
117.12 kips >= Reaction V = 45.00 kips (OK)

Block Shear for Axial T/C is not required.

Interaction Check of Flexural Yielding, Per AISC 10-5: 
Eccentricity due to Conventional Config. (e = a/2), e = 1.12 in.
Zgross = 19.71
Znet = 12.87
Mr = Vr * e = 45.00 * 1.12 = 50.62 kips-in
Mc = phi * Mn = phi * Fy * Zgross = 0.90 * 50.00 * 19.71 = 886.99 kips-in
Vr = 45.00 kips
Vc = phi * Vn = phi * 0.60 * Fy * Ag = 1.00 * 0.60 * 50.00 * 5.44 = 163.12 kips
Interaction due to moment and shear, (Vr/Vc)^2 + (Mr/Mc)^2 <= 1.0
(Vr/Vc)^2 + (Mr/Mc)^2 = (45.00 / 163.12)^2 + (50.62 / 886.99)^2 = 0.08 <= 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 = 14.50 in.
Shear Load per inch per weld, fv = R/Lv/2 = 45.00 / 14.50 / 2 = 1.55 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) = 1.55 / (0.75 * 1.86) = 1.11/16

Minimum fillet weld size : 
   At shear only load case = 0.07 in.
   per Table J2.4     = 0.19 in.
   5/8tp              = 0.23 in.
   user preference    = 0.25 in.

Dmax1 (using eqn 9-3)
 = tshpl * Fushpl / ( Fexx * C1 * 0.09)
 = 0.38 * 65.00 / ( 70.00 * 1.00 * 0.09 ) 
 = 3.94 
Dmax2 (using eqn 9-2)
 = tfsupport * Fusupport / ( Fexx * C1 * 0.04 )
 = 2.47 * 65.00 / ( 70.00 * 1.00 * 0.04 ) 
 = 51.90 
Dmax3 = project max fillet weld = 12.00
Dmax=min(Dmax1, Dmax2, Dmax3) = min(3.94, 51.90, 12.00)
 = 3.94 

Use weld size
D1 = 4.00
D2 = 4.00

Weld Strength :

Vertical weld capacity during shear only load, phi * Rnv1 = 0.75 * 1.86 * 14.50 * (3.94 + 3.94) = 159.05 kips

159.05 kips >= Reaction V = 45.00 kips (OK)