bcf.s.s.01143.01143

SHEAR PLATE CONNECTION SUMMARY

Filler Beam profile: W12X14
Column profile: W14X257
Slope: 0.00 deg.
Skew: 90.00
Vertical Offset: 0.00
Horizontal Offset: 0.00
Span: 16.60 ft.
Reaction, V: 15.72 kips
Shear Capacity, Rn: 48.54 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 8.50 in. x 0.38 in.
Configuration Geometry:
Welds at shear plate to support: 4/16 FILLET, 4/16 FILLET
Bolt: 3 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.
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 = 2.71
Using Table 7-1 to determine (phi)rn:
(phi)Rn = (phi)rn * C = 17.89 * 2.71 = 48.57 kips


Total Vertical Bolt Shear Capacity = 48.57 kips
48.57 kips >= Reaction V = 15.72 kips (OK)

BOLT BEARING AT BEAM AND SHEAR PLATE SIDE
Vertical Shear Only Load Case:
ICR cordinate relative to CG = (5.77, 0.00)
At Row 1, At Column 1:
Ribolt = 17.56 kips
Ri vector at Beam   = <8.10, 15.58>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 2.97 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 * 2.97 * (0.20/1) * 65.00 = 34.80 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.75 * (0.20/1) * 65.00 = 17.55 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(na, 34.80, 17.55) = 17.55 kips/bolt
Ri vector at Shear Plate   = <-8.10, -15.58>
Lcsshpl at Shear Plate spacing  = na
Lceshpl at Shear Plate edge    = 3.88 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 * 3.88 * 0.38 * 65.00 = 85.13 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, 85.13, 32.91) = 32.91 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(17.55, 32.91) = 17.55 kips/bolt
Bolt Shear Demand to Bearing ratio = 17.55 / 17.56 = 1.00

At Row 2, At Column 1:
Ribolt = 17.41 kips
Ri vector at Beam   = <-0.00, 17.41>
Lcsbm at Beam spacing  = 2.19 in.
Lcebm at Beam edge    = 5.59 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.75 * 1.20 * 2.19 * (0.20/1) * 65.00 = 25.59 kips/bolt
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 5.59 * (0.20/1) * 65.00 = 65.45 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.75 * (0.20/1) * 65.00 = 17.55 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(25.59, 65.45, 17.55) = 17.55 kips/bolt
Ri vector at Shear Plate   = <0.00, -17.41>
Lcsshpl at Shear Plate spacing  = 2.19 in.
Lceshpl at Shear Plate edge    = 3.84 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 * 3.84 * 0.38 * 65.00 = 84.32 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, 84.32, 32.91) = 32.91 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(17.55, 32.91) = 17.55 kips/bolt
Bolt Shear Demand to Bearing ratio = 17.55 / 17.41 = 1.01

At Row 3, At Column 1:
Ribolt = 17.56 kips
Ri vector at Beam   = <-8.10, 15.58>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 2.85 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 * 2.85 * (0.20/1) * 65.00 = 33.31 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.75 * (0.20/1) * 65.00 = 17.55 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(na, 33.31, 17.55) = 17.55 kips/bolt
Ri vector at Shear Plate   = <8.10, -15.58>
Lcsshpl at Shear Plate spacing  = na
Lceshpl at Shear Plate edge    = 0.95 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 * 0.95 * 0.38 * 65.00 = 20.86 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, 20.86, 32.91) = 20.86 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(17.55, 20.86) = 17.55 kips/bolt
Bolt Shear Demand to Bearing ratio = 17.55 / 17.56 = 1.00

Min Bolt Shear Demand to Bearing ratio Beam and Shear Plate for vertical shear only
 = min(1.00, 1.00, 1.01, 1.00) = 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 * 48.57 = 48.54 kips
Rbv = 48.54 kips >= Reaction V = 15.72 kips (OK)

Web Depth = d - [Top Cope Depth] - [Bottom Cope Depth] = 11.90 - 0.00 - 0.00 = 11.90 in.

Using AISC 14th Ed. Equation J4-3
Gross Area (Shear), Agross = [Web Depth] * tw = 11.90 * 0.20 = 2.38 in^2
Shear Yielding, (phi)Vny = (phi) * 0.6 * Fybeam * Agross = 1.00 * 0.6 * 50.00 * 2.38 = 71.40 kips

Using AISC 14th Ed. Equation J4-4
Net Area (Shear), Anet = ([Web Depth] - ([# rows] * [Diameter + 0.06])) * tw 
    = (11.90 - (3 * 0.88)) * 0.20 = 1.86 in^2
Shear Rupture, (phi)Vnu = (phi) * 0.6 * Fubeam * Anet = 0.75 * 0.6 * 65.00 * 1.86 = 54.26 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 * 8.50 = 3.19 in^2
Shear Yielding, (phi)Vny = (phi) * 0.6 * Fypl * Ag = 1.00 * 0.6 * 50.00 * 3.19 = 95.62 kips

95.62 kips >= Reaction V = 15.72 kips (OK)

Using AISC 14th Ed. Equation J4-4
Net Area, An = (8.50 - (3 * (0.81 + 1/16))) * 0.38 = 2.20 in^2
Shear Rupture, (phi)Vnu = (phi) * 0.6 * Fupl * An = 0.75 * 0.6 * 65.00 * 2.20 = 64.44 kips

64.44 kips >= Reaction V = 15.72 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 = (8.50 - 1.25) = 7.25 in.
Net Shear Length = 7.25 - (2.50 * (0.81 + 0.06)) = 5.06 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 * 5.06) + (1.00 * 65.00 * 0.97)) = 73.24 kips
2. (phi) * [material thickness] * ((0.60 * Fypl * [gross shear length]) + (Ubs * Fupl * [net tension length])) 
    = 0.75 * 0.38 * ((0.60 * 50.00 * 7.25) + (1.00 * 65.00 * 0.97)) = 78.88 kips
Block Shear = 73.24 kips
73.24 kips >= Reaction V = 15.72 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 = 1.00 in.
Zgross = 6.77
Znet = 4.73
Mr = Vr * e = 15.72 * 1.00 = 15.72 kips-in
Mc = phi * Mn = phi * Fy * Zgross = 0.90 * 50.00 * 6.77 = 304.80 kips-in
Vr = 15.72 kips
Vc = phi * Vn = phi * 0.60 * Fy * Ag = 1.00 * 0.60 * 50.00 * 3.19 = 95.62 kips
Interaction due to moment and shear, (Vr/Vc)^2 + (Mr/Mc)^2 <= 1.0
(Vr/Vc)^2 + (Mr/Mc)^2 = (15.72 / 95.62)^2 + (15.72 / 304.80)^2 = 0.03 <= 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 = 8.50 in.
Shear Load per inch per weld, fv = R/Lv/2 = 15.72 / 8.50 / 2 = 0.92 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) = 0.92 / (0.75 * 1.86) = 0.66/16

Minimum fillet weld size : 
   At shear only load case = 0.04 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 )
 = 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(3.94, 39.71, 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 * 8.50 * (3.94 + 3.94) = 93.24 kips

93.24 kips >= Reaction V = 15.72 kips (OK)