bb.s.s.00009.00009

SHEAR PLATE CONNECTION SUMMARY

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

Filler Beam profile: W16X40
Support Girder profile: W18X50
Slope: 0.00 deg.
Skew: 90.00
Vertical Offset: 0.00
Horizontal Offset: 0.00
Span: 2.00 ft.
Reaction, V: 20.00 kips
Shear Capacity, Rn: 31.83 kips
Design/Reference according to AISC 14th Ed. - LRFD
Full Depth Shear Plate: Extended Configuration
Beam material grade: A992
Support material grade: A992
Plate material grade: A572-GR.50
Weld grade: E70
Shear Plate Design Size: 7.25 in. x 11.50 in. x 0.38 in.
Full Depth Shear Plate Detailing Height at Support: 16.75 in.
Full Depth Shear Plate Detailing Width at Support: 3.56 in.
Configuration Geometry:
Welds at shear plate to support: 4/16 FILLET, 4/16 FILLET
at girder flange: 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 = 4.12 in.
Beam centerline setback = 4.12 in.
Edge distance at vertical edge of plate: 1.62 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: 5.62 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 = 5.80 in.
Angle = 0.00 deg.
C = 1.78
Using Table 7-1 to determine (phi)rn:
(phi)Rn = (phi)rn * C = 17.89 * 1.78 = 31.83 kips


Total Vertical Bolt Shear Capacity = 31.83 kips
31.83 kips >= Reaction V = 20.00 kips (OK)

BOLT BEARING AT BEAM AND SHEAR PLATE SIDE
Vertical Shear Only Load Case:
ICR cordinate relative to CG = (1.41, -0.00)
At Row 1, At Column 1:
Ribolt = 17.56 kips
Ri vector at Beam   = <16.76, 5.26>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 9.61 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 * 9.61 * (0.30/1) * 65.00 = 171.44 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.75 * (0.30/1) * 65.00 = 26.76 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(na, 171.44, 26.76) = 26.76 kips/bolt
Ri vector at Shear Plate   = <-16.76, -5.26>
Lcsshpl at Shear Plate spacing  = na
Lceshpl at Shear Plate edge    = 5.37 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 * 5.37 * 0.38 * 65.00 = 117.84 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, 117.84, 32.91) = 32.91 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(26.76, 32.91) = 26.76 kips/bolt
Bolt Shear Demand to Bearing ratio = 26.76 / 17.56 = 1.52

At Row 2, At Column 1:
Ribolt = 15.54 kips
Ri vector at Beam   = <11.31, 10.65>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 8.35 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 * 8.35 * (0.30/1) * 65.00 = 148.92 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.75 * (0.30/1) * 65.00 = 26.76 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(na, 148.92, 26.76) = 26.76 kips/bolt
Ri vector at Shear Plate   = <-11.31, -10.65>
Lcsshpl at Shear Plate spacing  = na
Lceshpl at Shear Plate edge    = 7.13 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 * 7.13 * 0.38 * 65.00 = 156.49 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, 156.49, 32.91) = 32.91 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(26.76, 32.91) = 26.76 kips/bolt
Bolt Shear Demand to Bearing ratio = 26.76 / 15.54 = 1.72

At Row 3, At Column 1:
Ribolt = 15.54 kips
Ri vector at Beam   = <-11.30, 10.66>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 1.66 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 * 1.66 * (0.30/1) * 65.00 = 29.54 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.75 * (0.30/1) * 65.00 = 26.76 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(na, 29.54, 26.76) = 26.76 kips/bolt
Ri vector at Shear Plate   = <11.30, -10.66>
Lcsshpl at Shear Plate spacing  = na
Lceshpl at Shear Plate edge    = 1.64 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 * 1.64 * 0.38 * 65.00 = 36.00 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, 36.00, 32.91) = 32.91 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(26.76, 32.91) = 26.76 kips/bolt
Bolt Shear Demand to Bearing ratio = 26.76 / 15.54 = 1.72

At Row 4, At Column 1:
Ribolt = 17.56 kips
Ri vector at Beam   = <-16.75, 5.26>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 1.17 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 * 1.17 * (0.30/1) * 65.00 = 20.81 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.75 * (0.30/1) * 65.00 = 26.76 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(na, 20.81, 26.76) = 20.81 kips/bolt
Ri vector at Shear Plate   = <16.75, -5.26>
Lcsshpl at Shear Plate spacing  = na
Lceshpl at Shear Plate edge    = 1.18 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 * 1.18 * 0.38 * 65.00 = 25.87 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, 25.87, 32.91) = 25.87 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(20.81, 25.87) = 20.81 kips/bolt
Bolt Shear Demand to Bearing ratio = 20.81 / 17.56 = 1.18

Min Bolt Shear Demand to Bearing ratio Beam and Shear Plate for vertical shear only
 = min(1.00, 1.52, 1.72, 1.72, 1.18) = 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 * 31.83 = 31.83 kips
Rbv = 31.83 kips >= Reaction V = 20.00 kips (OK)

Web Depth = d - [Top Cope Depth] - [Bottom Cope Depth] = 16.00 - 0.00 - 0.00 = 16.00 in.

Using AISC 14th Ed. Equation J4-3
Gross Area (Shear), Agross = [Web Depth] * tw = 16.00 * 0.30 = 4.88 in^2
Shear Yielding, (phi)Vny = (phi) * 0.6 * Fybeam * Agross = 1.00 * 0.6 * 50.00 * 4.88 = 146.40 kips

Using AISC 14th Ed. Equation J4-4
Net Area (Shear), Anet = ([Web Depth] - ([# rows] * [Diameter + 0.06])) * tw 
    = (16.00 - (4 * 0.88)) * 0.30 = 3.81 in^2
Shear Rupture, (phi)Vnu = (phi) * 0.6 * Fubeam * Anet = 0.75 * 0.6 * 65.00 * 3.81 = 111.52 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 * 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 = 20.00 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 = 20.00 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 = (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 + 1.62) = 1.62 in.
Net Tension Length = 1.62 - (0.50 * (1.00 + 0.06)) = 1.09 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 * 1.09)) = 98.84 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 * 1.09)) = 106.48 kips
Block Shear = 98.84 kips
98.84 kips >= Reaction V = 20.00 kips (OK)

Block Shear for Axial T/C is not required.

Flexural and Buckling Strength:

Eccentricity at first line of bolts, e = 5.80 in.
Zgross = 12.40 in^3
Znet   = 8.46 in^3
Sgross = 8.27 in^3
Snet   = 5.70 in^3

Using AISC 14th Ed. Equation 9-4
Flexural Rupture = (phi) * Fu * Znet / e = 0.75 * 65.00 * 8.46 / 5.80 = 71.09 kips


Using AISC 14th Ed. Equation 9-14 through 9-18, Fcr = Fy * Q
tw = 0.38 in.
ho = 11.50 in.
c = 5.62 in.
lambda = (ho * Fy ^ 0.5) / ( 10 * tw * ( 475.00 + 280.00 * (ho / c)^2 ) ^0.5 ) = 
 = 11.50 * 50.00^0.5 / (10 * 0.38 * (475.00 + 280.00 * (11.50/5.62)^2 )^0.5) = 0.53
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 * 8.27 / 5.80 = 64.10 kips

Interaction Check of Flexural Yielding, Per AISC 10-5: 
Eccentricity at CG of Bolt Group, e = 5.80 in.
Zgross = 12.40
Znet = 8.46
Mr = Vr * e = 20.00 * 5.80 = 116.05 kips-in
Mc = phi * Mn = phi * Fy * Zgross = 0.90 * 50.00 * 12.40 = 557.93 kips-in
Vr = 20.00 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 = (20.00 / 129.38)^2 + (116.05 / 557.93)^2 = 0.07 <= 1  (OK)

Note: Mn <= 1.6My by inspection

MAXIMUM PLATE THICKNESS:
No of bolt columns = 1
tp  < = db/2 + 1/16 = 0.38 <= 0.44 OK
tw  < = db/2 + 1/16 = 0.30 <= 0.44 OK
Leh(plate) >= 2 * db = 1.62 >= 1.50 OK
Leh(bm) >= 2 * db = 1.50 >= 1.50 OK
Maximum Plate Thickness is Not a Limiting Criteria.

WELD:

 Weld Requirements:

At shear only case: 
Weld Length for shear, Lv = 15.25 in.
Shear Load per inch per weld, fv = R/Lv/2 = 20.00 / 15.25 / 2 = 0.66 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) = 0.66 / (0.75 * 1.86) = 0.47/16

Minimum fillet weld size : 
   At shear only load case = 0.03 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 9-3)
 = twsupport * Fusupport / ( Fexx * C1 * 0.09 )
 = 0.35 * 65.00 / ( 70.00 * 1.00 * 0.09 ) 
 = 3.73 
Dmax3 = project max fillet weld = 12.00
Dmax=min(Dmax1, Dmax2, Dmax3) = min(3.94, 3.73, 12.00)
 = 3.73 

Use weld size
D1 = 4.00
D2 = 4.00

Weld Strength :

Vertical weld capacity during shear only load, phi * Rnv1 = 0.75 * 1.86 * 15.25 * (3.73 + 3.73) = 158.36 kips

158.36 kips >= Reaction V = 20.00 kips (OK)