bcf.s.s.01370.01373

SHEAR PLATE CONNECTION SUMMARY

Filler Beam profile: W21X111
Column profile: W14X257
Slope: 0.00 deg.
Skew: 90.00
Vertical Offset: 0.00 in.
Horizontal Offset: 0.00 in.
Span: 25.00 ft.
Reaction, V: 167.40 kips
Shear Capacity, Rn: 186.20 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: 4.75 in. x 15.00 in. x 0.75 in.
Configuration Geometry:
Welds at shear plate to support: 8/16 FILLET, 8/16 FILLET
Bolt: 5 rows x 1 column 1.00 in. Diameter A490N_TC bolts
Vertical spacing: 3.00 in.
Horizontal spacing: 3.00 in.
Shear plate edge setback = 0.75 in.
Beam centerline setback = 0.75 in.
Edge distance at vertical edge of plate: 2.00 in.
Edge distance at top edge of plate: 1.50 in.
Edge distance at bottom edge of plate: 1.50 in.
Edge distance at vertical edge of beam: 2.00 in.
Horizontal distance to first hole: 2.75 in.
Down distance from top of filler beam flange: 3.75 in.
Holes in beam web: STD diameter = 1.06 in.
Holes in shear plate: SSL diameter = 1.06 in., slot width = 1.31 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 = 1.38 in.
Angle = 0.00 deg.
C = 4.65
Using Table 7-1 to determine (phi)rn:
(phi)Rn = (phi)rn * C = 40.06 * 4.65 = 186.20 kips


Total Vertical Bolt Shear Capacity = 186.20 kips
186.20 kips >= Reaction V = 167.40 kips (OK)

BOLT BEARING AT BEAM AND SHEAR PLATE SIDE
Vertical Shear Only Load Case:
ICR cordinate relative to CG = (12.67, 0.00)
At Row 1, At Column 1:
Ribolt = 39.32 kips
Ri vector at Beam   = <16.83, 35.53>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 3.62 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 * 3.62 * (0.55/1) * 65.00 = 116.42 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 1.00 * (0.55/1) * 65.00 = 64.35 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(na, 116.42, 64.35) = 64.35 kips/bolt
Ri vector at Shear Plate   = <-16.83, -35.53>
Lcsshpl at Shear Plate spacing  = na
Lceshpl at Shear Plate edge    = 5.84 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 * 5.84 * 0.75 * 65.00 = 256.04 kips/bolt
(phi)Rndshpl on Shear Plate at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 1.00 * 0.75 * 65.00 = 87.75 kips/bolt
Shear Plate bearing capacity, (phi)Rnshpl = min((phi)Rnsshpl,(phi)Rneshpl,(phi)Rndshpl) = min(na, 256.04, 87.75) = 87.75 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(64.35, 87.75) = 64.35 kips/bolt
Bolt Shear Demand to Bearing ratio = 64.35 / 39.32 = 1.64

At Row 2, At Column 1:
Ribolt = 39.11 kips
Ri vector at Beam   = <9.01, 38.06>
Lcsbm at Beam spacing  = 1.94 in.
Lcebm at Beam edge    = 6.41 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.75 * 1.20 * 1.94 * (0.55/1) * 65.00 = 62.34 kips/bolt
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 6.41 * (0.55/1) * 65.00 = 206.10 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 1.00 * (0.55/1) * 65.00 = 64.35 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(62.34, 206.10, 64.35) = 62.34 kips/bolt
Ri vector at Shear Plate   = <-9.01, -38.06>
Lcsshpl at Shear Plate spacing  = 1.94 in.
Lceshpl at Shear Plate edge    = 10.24 in.
(phi)Rnsshpl at Shear Plate spacing = (phi) * hf1 * Lcs * t * Fu = 0.75 * 1.20 * 1.94 * 0.75 * 65.00 = 85.01 kips/bolt
(phi)Rneshpl at Shear Plate edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 10.24 * 0.75 * 65.00 = 449.49 kips/bolt
(phi)Rndshpl on Shear Plate at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 1.00 * 0.75 * 65.00 = 87.75 kips/bolt
Shear Plate bearing capacity, (phi)Rnshpl = min((phi)Rnsshpl,(phi)Rneshpl,(phi)Rndshpl) = min(85.01, 449.49, 87.75) = 85.01 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(62.34, 85.01) = 62.34 kips/bolt
Bolt Shear Demand to Bearing ratio = 62.34 / 39.11 = 1.59

At Row 3, At Column 1:
Ribolt = 39.03 kips
Ri vector at Beam   = <-0.00, 39.03>
Lcsbm at Beam spacing  = 1.94 in.
Lcebm at Beam edge    = 9.22 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.75 * 1.20 * 1.94 * (0.55/1) * 65.00 = 62.34 kips/bolt
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 9.22 * (0.55/1) * 65.00 = 296.62 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 1.00 * (0.55/1) * 65.00 = 64.35 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(62.34, 296.62, 64.35) = 62.34 kips/bolt
Ri vector at Shear Plate   = <0.00, -39.03>
Lcsshpl at Shear Plate spacing  = 1.94 in.
Lceshpl at Shear Plate edge    = 6.97 in.
(phi)Rnsshpl at Shear Plate spacing = (phi) * hf1 * Lcs * t * Fu = 0.75 * 1.20 * 1.94 * 0.75 * 65.00 = 85.01 kips/bolt
(phi)Rneshpl at Shear Plate edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 6.97 * 0.75 * 65.00 = 305.76 kips/bolt
(phi)Rndshpl on Shear Plate at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 1.00 * 0.75 * 65.00 = 87.75 kips/bolt
Shear Plate bearing capacity, (phi)Rnshpl = min((phi)Rnsshpl,(phi)Rneshpl,(phi)Rndshpl) = min(85.01, 305.76, 87.75) = 85.01 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(62.34, 85.01) = 62.34 kips/bolt
Bolt Shear Demand to Bearing ratio = 62.34 / 39.03 = 1.60

At Row 4, At Column 1:
Ribolt = 39.11 kips
Ri vector at Beam   = <-9.02, 38.06>
Lcsbm at Beam spacing  = 1.94 in.
Lcebm at Beam edge    = 8.15 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.75 * 1.20 * 1.94 * (0.55/1) * 65.00 = 62.34 kips/bolt
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 8.15 * (0.55/1) * 65.00 = 262.08 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 1.00 * (0.55/1) * 65.00 = 64.35 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(62.34, 262.08, 64.35) = 62.34 kips/bolt
Ri vector at Shear Plate   = <9.02, -38.06>
Lcsshpl at Shear Plate spacing  = 1.94 in.
Lceshpl at Shear Plate edge    = 4.08 in.
(phi)Rnsshpl at Shear Plate spacing = (phi) * hf1 * Lcs * t * Fu = 0.75 * 1.20 * 1.94 * 0.75 * 65.00 = 85.01 kips/bolt
(phi)Rneshpl at Shear Plate edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 4.08 * 0.75 * 65.00 = 178.95 kips/bolt
(phi)Rndshpl on Shear Plate at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 1.00 * 0.75 * 65.00 = 87.75 kips/bolt
Shear Plate bearing capacity, (phi)Rnshpl = min((phi)Rnsshpl,(phi)Rneshpl,(phi)Rndshpl) = min(85.01, 178.95, 87.75) = 85.01 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(62.34, 85.01) = 62.34 kips/bolt
Bolt Shear Demand to Bearing ratio = 62.34 / 39.11 = 1.59

At Row 5, At Column 1:
Ribolt = 39.32 kips
Ri vector at Beam   = <-16.83, 35.53>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 4.14 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 * 4.14 * (0.55/1) * 65.00 = 133.21 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 1.00 * (0.55/1) * 65.00 = 64.35 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(na, 133.21, 64.35) = 64.35 kips/bolt
Ri vector at Shear Plate   = <16.83, -35.53>
Lcsshpl at Shear Plate spacing  = na
Lceshpl at Shear Plate edge    = 1.07 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 * 1.07 * 0.75 * 65.00 = 47.03 kips/bolt
(phi)Rndshpl on Shear Plate at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 1.00 * 0.75 * 65.00 = 87.75 kips/bolt
Shear Plate bearing capacity, (phi)Rnshpl = min((phi)Rnsshpl,(phi)Rneshpl,(phi)Rndshpl) = min(na, 47.03, 87.75) = 47.03 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(64.35, 47.03) = 47.03 kips/bolt
Bolt Shear Demand to Bearing ratio = 47.03 / 39.32 = 1.20

Min Bolt Shear Demand to Bearing ratio Beam and Shear Plate for vertical shear only
 = min(1.00, 1.64, 1.59, 1.60, 1.59, 1.20) = 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 * 186.20 = 186.20 kips
Rbv = 186.20 kips >= Reaction V = 167.40 kips (OK)

Web Depth = d - [Top Cope Depth] - [Bottom Cope Depth] = 21.50 - 0.00 - 0.00 = 21.50 in.

Using AISC 14th Ed. Equation J4-3
Gross Area (Shear), Agross = [Web Depth] * tw = 21.50 * 0.55 = 11.83 in^2
Shear Yielding, (phi)Vny = (phi) * 0.6 * Fybeam * Agross = 1.00 * 0.6 * 50.00 * 11.83 = 354.75 kips

Using AISC 14th Ed. Equation J4-4
Net Area (Shear), Anet = ([Web Depth] - ([# rows] * [Diameter + 0.06])) * tw 
    = (21.50 - (5 * 1.12)) * 0.55 = 8.73 in^2
Shear Rupture, (phi)Vnu = (phi) * 0.6 * Fubeam * Anet = 0.75 * 0.6 * 65.00 * 8.73 = 255.40 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 = 0.75 * 15.00 = 11.25 in^2
Shear Yielding, (phi)Vny = (phi) * 0.6 * Fypl * Ag = 1.00 * 0.6 * 50.00 * 11.25 = 337.50 kips

337.50 kips >= Reaction V = 167.40 kips (OK)

Using AISC 14th Ed. Equation J4-4
Net Area, An = (15.00 - (5 * (1.06 + 1/16))) * 0.75 = 7.03 in^2
Shear Rupture, (phi)Vnu = (phi) * 0.6 * Fupl * An = 0.75 * 0.6 * 65.00 * 7.03 = 205.67 kips

205.67 kips >= Reaction V = 167.40 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 = (15.00 - 1.50) = 13.50 in.
Net Shear Length = 13.50 - (4.50 * (1.06 + 0.06)) = 8.44 in.
Gross Tension Length = (0.00 + 2.00) = 2.00 in.
Net Tension Length = 2.00 - (0.50 * (1.31 + 0.06)) = 1.31 in.
1. (phi) * [material thickness] * ((0.60 * Fupl* [net shear length]) + (Ubs * Fupl * [net tension length])) 
    = 0.75 * 0.75 * ((0.60 * 65.00 * 8.44) + (1.00 * 65.00 * 1.31)) = 233.09 kips
2. (phi) * [material thickness] * ((0.60 * Fypl * [gross shear length]) + (Ubs * Fupl * [net tension length])) 
    = 0.75 * 0.75 * ((0.60 * 50.00 * 13.50) + (1.00 * 65.00 * 1.31)) = 275.81 kips
Block Shear = 233.09 kips
233.09 kips >= Reaction V = 167.40 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 = 1.38 in.
Zgross = 42.19
Znet = 26.76
Mr = Vr * e = 167.40 * 1.38 = 230.18 kips-in
Mc = phi * Mn = phi * Fy * Zgross = 0.90 * 50.00 * 42.19 = 1898.44 kips-in
Vr = 167.40 kips
Vc = phi * Vn = phi * 0.60 * Fy * Ag = 1.00 * 0.60 * 50.00 * 11.25 = 337.50 kips
Interaction due to moment and shear, (Vr/Vc)^2 + (Mr/Mc)^2 <= 1.0
(Vr/Vc)^2 + (Mr/Mc)^2 = (167.40 / 337.50)^2 + (230.18 / 1898.44)^2 = 0.26 <= 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 = 15.00 in.
Shear Load per inch per weld, fv = R/Lv/2 = 167.40 / 15.00 / 2 = 5.58 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) = 5.58 / (0.75 * 1.86) = 4.01/16

Minimum fillet weld size : 
   At shear only load case = 0.25 in.
   per Table J2.4     = 0.25 in.
   5/8tp              = 0.47 in.
   user preference    = 0.25 in.

Dmax1 (using AISC 14th Ed. eqn 9-3)
 = tshpl * Fushpl / ( Fexx * C1 * 0.09)
 = 0.75 * 65.00 / ( 70.00 * 1.00 * 0.09 ) 
 = 7.88 
Dmax2 (using AISC 14th Ed. eqn 9-2)
 = tfcol * Fusupport / ( Fexx * C1 * 0.04 )
 = 1.89 * 65.00 / ( 70.00 * 1.00 * 0.04 ) 
 = 39.71 
Dmax3 = project max fillet weld = 12.00
Dmax=min(Dmax1, Dmax2, Dmax3) = min(7.88, 39.71, 12.00)
 = 7.88 

Use weld size
D1 = 8.00
D2 = 8.00

Weld Strength :

Vertical weld capacity during shear only load, phi * Rnv1 = 0.75 * 1.86 * 15.00 * (7.88 + 7.88) = 329.07 kips

329.07 kips >= Reaction V = 167.40 kips (OK)