bcw.s.s.02327.02327

SHEAR PLATE CONNECTION SUMMARY

NOTE: DESIGNED WITH MEMBERS CHOSEN ON ONLY ONE SIDE OF SUPPORT

Filler Beam profile: W18X40
Column profile: W14X257
Slope: 0.00 deg.
Skew: 90.00
Vertical Offset: 0.00 in.
Horizontal Offset: 0.00 in.
Span: 19.84 ft.
Reaction, V: 40.00 kips
Shear Capacity, Rn: 47.01 kips
Design/Reference according to AISC 14th Ed. - LRFD
Shear Plate: Extended Configuration
Beam material grade: A992
Support material grade: A992
Plate material grade: A572-GR.50
Weld grade: E70
Shear Plate Size: 12.00 in. x 15.00 in. x 0.50 in.
Configuration Geometry:
Welds at shear plate to support: 5/16 FILLET, 5/16 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 = 8.00 in.
Beam centerline setback = 8.00 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: 10.00 in.
Down distance from top of filler beam flange: 3.00 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 = 10.00 in.
Angle = 0.00 deg.
C = 1.66
Using Table 7-1 to determine (phi)rn:
(phi)Rn = (phi)rn * C = 40.06 * 1.66 = 66.68 kips


Total Vertical Bolt Shear Capacity = 66.68 kips
66.68 kips >= Reaction V = 40.00 kips (OK)

BOLT BEARING AT BEAM AND SHEAR PLATE SIDE
Vertical Shear Only Load Case:
ICR cordinate relative to CG = (1.14, -0.00)
At Row 1, At Column 1:
Ribolt = 39.32 kips
Ri vector at Beam   = <38.63, 7.31>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 15.60 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 * 15.60 * (0.32/1) * 65.00 = 287.42 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 1.00 * (0.32/1) * 65.00 = 36.86 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(na, 287.42, 36.86) = 36.86 kips/bolt
Ri vector at Shear Plate   = <-38.63, -7.31>
Lcsshpl at Shear Plate spacing  = na
Lceshpl at Shear Plate edge    = 9.51 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 * 9.51 * 0.50 * 65.00 = 278.17 kips/bolt
(phi)Rndshpl on Shear Plate at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 1.00 * 0.50 * 65.00 = 58.50 kips/bolt
Shear Plate bearing capacity, (phi)Rnshpl = min((phi)Rnsshpl,(phi)Rneshpl,(phi)Rndshpl) = min(na, 278.17, 58.50) = 58.50 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(36.86, 58.50) = 36.86 kips/bolt
Bolt Shear Demand to Bearing ratio = 36.86 / 39.32 = 0.94

At Row 2, At Column 1:
Ribolt = 36.21 kips
Ri vector at Beam   = <33.87, 12.82>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 16.41 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 * 16.41 * (0.32/1) * 65.00 = 302.46 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 1.00 * (0.32/1) * 65.00 = 36.86 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(na, 302.46, 36.86) = 36.86 kips/bolt
Ri vector at Shear Plate   = <-33.87, -12.82>
Lcsshpl at Shear Plate spacing  = na
Lceshpl at Shear Plate edge    = 9.99 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 * 9.99 * 0.50 * 65.00 = 292.25 kips/bolt
(phi)Rndshpl on Shear Plate at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 1.00 * 0.50 * 65.00 = 58.50 kips/bolt
Shear Plate bearing capacity, (phi)Rnshpl = min((phi)Rnsshpl,(phi)Rneshpl,(phi)Rndshpl) = min(na, 292.25, 58.50) = 58.50 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(36.86, 58.50) = 36.86 kips/bolt
Bolt Shear Demand to Bearing ratio = 36.86 / 36.21 = 1.02

At Row 3, At Column 1:
Ribolt = 26.40 kips
Ri vector at Beam   = <0.00, 26.40>
Lcsbm at Beam spacing  = 1.94 in.
Lcebm at Beam edge    = 8.47 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.75 * 1.20 * 1.94 * (0.32/1) * 65.00 = 35.70 kips/bolt
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 8.47 * (0.32/1) * 65.00 = 156.06 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 1.00 * (0.32/1) * 65.00 = 36.86 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(35.70, 156.06, 36.86) = 35.70 kips/bolt
Ri vector at Shear Plate   = <-0.00, -26.40>
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 * 0.50 * 65.00 = 56.67 kips/bolt
(phi)Rneshpl at Shear Plate edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 6.97 * 0.50 * 65.00 = 203.84 kips/bolt
(phi)Rndshpl on Shear Plate at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 1.00 * 0.50 * 65.00 = 58.50 kips/bolt
Shear Plate bearing capacity, (phi)Rnshpl = min((phi)Rnsshpl,(phi)Rneshpl,(phi)Rndshpl) = min(56.67, 203.84, 58.50) = 56.67 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(35.70, 56.67) = 35.70 kips/bolt
Bolt Shear Demand to Bearing ratio = 35.70 / 26.40 = 1.35

At Row 4, At Column 1:
Ribolt = 36.21 kips
Ri vector at Beam   = <-33.87, 12.82>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 1.61 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 * 1.61 * (0.32/1) * 65.00 = 29.62 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 1.00 * (0.32/1) * 65.00 = 36.86 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(na, 29.62, 36.86) = 29.62 kips/bolt
Ri vector at Shear Plate   = <33.87, -12.82>
Lcsshpl at Shear Plate spacing  = na
Lceshpl at Shear Plate edge    = 1.44 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 * 1.44 * 0.50 * 65.00 = 42.03 kips/bolt
(phi)Rndshpl on Shear Plate at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 1.00 * 0.50 * 65.00 = 58.50 kips/bolt
Shear Plate bearing capacity, (phi)Rnshpl = min((phi)Rnsshpl,(phi)Rneshpl,(phi)Rndshpl) = min(na, 42.03, 58.50) = 42.03 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(29.62, 42.03) = 29.62 kips/bolt
Bolt Shear Demand to Bearing ratio = 29.62 / 36.21 = 0.82

At Row 5, At Column 1:
Ribolt = 39.32 kips
Ri vector at Beam   = <-38.63, 7.31>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 1.50 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 * 1.50 * (0.32/1) * 65.00 = 27.72 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 1.00 * (0.32/1) * 65.00 = 36.86 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(na, 27.72, 36.86) = 27.72 kips/bolt
Ri vector at Shear Plate   = <38.63, -7.31>
Lcsshpl at Shear Plate spacing  = na
Lceshpl at Shear Plate edge    = 1.37 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 * 1.37 * 0.50 * 65.00 = 40.00 kips/bolt
(phi)Rndshpl on Shear Plate at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 1.00 * 0.50 * 65.00 = 58.50 kips/bolt
Shear Plate bearing capacity, (phi)Rnshpl = min((phi)Rnsshpl,(phi)Rneshpl,(phi)Rndshpl) = min(na, 40.00, 58.50) = 40.00 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(27.72, 40.00) = 27.72 kips/bolt
Bolt Shear Demand to Bearing ratio = 27.72 / 39.32 = 0.71

Min Bolt Shear Demand to Bearing ratio Beam and Shear Plate for vertical shear only
 = min(1.00, 0.94, 1.02, 1.35, 0.82, 0.71) = 0.71

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 = 0.71 * 66.68 = 47.01 kips
Rbv = 47.01 kips >= Reaction V = 40.00 kips (OK)

Web Depth = d - [Top Cope Depth] - [Bottom Cope Depth] = 17.90 - 0.00 - 0.00 = 17.90 in.

Using AISC 14th Ed. Equation J4-3
Gross Area (Shear), Agross = [Web Depth] * tw = 17.90 * 0.32 = 5.64 in^2
Shear Yielding, (phi)Vny = (phi) * 0.6 * Fybeam * Agross = 1.00 * 0.6 * 50.00 * 5.64 = 169.16 kips

Using AISC 14th Ed. Equation J4-4
Net Area (Shear), Anet = ([Web Depth] - ([# rows] * [Diameter + 0.06])) * tw 
    = (17.90 - (5 * 1.12)) * 0.32 = 3.87 in^2
Shear Rupture, (phi)Vnu = (phi) * 0.6 * Fubeam * Anet = 0.75 * 0.6 * 65.00 * 3.87 = 113.10 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 = 0.50 * 15.00 = 7.50 in^2
Shear Yielding, (phi)Vny = (phi) * 0.6 * Fypl * Ag = 1.00 * 0.6 * 50.00 * 7.50 = 225.00 kips

225.00 kips >= Reaction V = 40.00 kips (OK)

Using AISC 14th Ed. Equation J4-4
Net Area, An = (15.00 - (5 * (1.06 + 1/16))) * 0.50 = 4.69 in^2
Shear Rupture, (phi)Vnu = (phi) * 0.6 * Fupl * An = 0.75 * 0.6 * 65.00 * 4.69 = 137.11 kips

137.11 kips >= Reaction V = 40.00 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 = (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 * 0.50 * ((0.60 * 65.00 * 8.44) + (1.00 * 65.00 * 1.31)) = 155.39 kips
2. (phi) * [material thickness] * ((0.60 * Fypl * [gross shear length]) + (Ubs * Fupl * [net tension length])) 
    = 0.75 * 0.50 * ((0.60 * 50.00 * 13.50) + (1.00 * 65.00 * 1.31)) = 183.87 kips
Block Shear = 155.39 kips
155.39 kips >= Reaction V = 40.00 kips (OK)

Block Shear for Axial T/C is not required.

Flexural and Buckling Strength:

Eccentricity at first line of bolts, e = 10.00 in.
Zgross = 28.12 in^3
Znet   = 17.84 in^3
Sgross = 18.75 in^3
Snet   = 12.00 in^3

Using AISC 14th Ed. Equation 9-4
Flexural Rupture = (phi) * Fu * Znet / e = 0.75 * 65.00 * 17.84 / 10.00 = 86.98 kips


Using AISC 14th Ed. Equation 9-14 through 9-18, Fcr = Fy * Q
tw = 0.50 in.
ho = 15.00 in.
c = 10.00 in.
lambda = (ho * Fy ^ 0.5) / ( 10 * tw * ( 475.00 + 280.00 * (ho / c)^2 ) ^0.5 ) = 
 = 15.00 * 50.00^0.5 / (10 * 0.50 * (475.00 + 280.00 * (15.00/10.00)^2 )^0.5) = 0.64
When lambda <= 0.70, Q=1
Q = 1.00
Fcrmin =phi * Fcr = 0.90 * 50.00 * 1.00 = 45.00 ksi

Using AISC 14th Ed. Equation 9-6
Buckling = Fcr * Sgross / e = 45.00 * 18.75 / 10.00 = 84.38 kips

Interaction Check of Flexural Yielding:
Using AISC 14th Ed. Equation 10-5
Eccentricity at CG of Bolt Group, e = 10.00 in.
Zgross = 28.12
Znet = 17.84
Mr = Vr * e = 40.00 * 10.00 = 400.00 kips-in
Mc = phi * Mn = phi * Fy * Zgross = 0.90 * 50.00 * 28.12 = 1265.63 kips-in
Vr = 40.00 kips
Vc = phi * Vn = phi * 0.60 * Fy * Ag = 1.00 * 0.60 * 50.00 * 7.50 = 225.00 kips
Interaction due to moment and shear, (Vr/Vc)^2 + (Mr/Mc)^2 <= 1.0
(Vr/Vc)^2 + (Mr/Mc)^2 = (40.00 / 225.00)^2 + (400.00 / 1265.63)^2 = 0.13 <= 1  (OK)

Note: Mn <= 1.6My by inspection

MAXIMUM PLATE THICKNESS:
No of bolt columns = 1
tp  < = db/2 + 1/16 = 0.50 <= 0.56 OK
tw  < = db/2 + 1/16 = 0.32 <= 0.56 OK
Leh(plate) >= 2 * db = 2.00 >= 2.00 OK
Leh(bm) >= 2 * db = 2.00 >= 2.00 OK
Maximum Plate Thickness is Not a Limiting Criteria.

STABILIZER PLATE:

Available Strength to Resist Lateral Displacement:
Using AISC 14th Ed. Equation 10-6
phiRn = 1500.00  * 3.14159 * L * tp^3 / a^2 = 0.90 * 1500.00 * 3.14159 * 15.00 * 0.50^3 / 10.00^2 = 79.52 kips
Stabilizer Plate Not Required for lateral displacement

Torsional Strength:
Using AISC 14th Ed. Equation 10-8 and 10-7
Required, Mta or Mtu = Ru * (tw + tp) /2 = 40.00 * ((0.31 + 0.50) / 2) = 16.25 kips-in
Lateral Shear Strength of Shear Plate, Mtn (no slab) = [phiv*(0.6*Fyp)-(Ru/(L*tp))] *L*tp^2/2 =  ((1.00 * 0.6 * 50.00) - (40.00 / (15.00 * 0.50))) * 0.5 * 15.00 * 0.50^2 = 46.25 kips-in
Stabilizer Plate Not Required for torsional strength

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 = 40.00 / 15.00 / 2 = 1.33 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) = 1.33 / (0.75 * 1.86) = 0.96/16

Minimum fillet weld size : 
   At shear only load case = 0.06 in.
   per Table J2.4     = 0.19 in.
   5/8tp              = 0.31 in.
   user preference    = 0.25 in.

Dmax1 (using eqn 9-3)
 = tshpl * Fushpl / ( Fexx * C1 * 0.09)
 = 0.50 * 65.00 / ( 70.00 * 1.00 * 0.09 ) 
 = 5.25 
Dmax2 (using eqn 9-3)
 = twcol * Fusupport / ( Fexx * C1 * 0.09 )
 = 1.18 * 65.00 / ( 70.00 * 1.00 * 0.09 ) 
 = 12.40 
Dmax3 = project max fillet weld = 12.00
Dmax=min(Dmax1, Dmax2, Dmax3) = min(5.25, 12.40, 12.00)
 = 5.25 

Use weld size
D1 = 5.00
D2 = 5.00

Weld Strength :

Vertical weld capacity during shear only load, phi * Rnv1 = 0.75 * 1.86 * 15.00 * (5.00 + 5.00) = 208.82 kips

208.82 kips >= Reaction V = 40.00 kips (OK)