bb.s.s.01194.01357

SHEAR PLATE CONNECTION SUMMARY

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

Filler Beam profile: W21X50
Support Girder profile: W18X40
Slope: 0.00 deg.
Skew: 90.00
Vertical Offset: 0.00 in.
Horizontal Offset: 0.00 in.
Span: 45.00 ft.
Reaction, V: 36.67 kips
Shear Capacity, Rn: 52.64 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: 6.50 in. x 14.50 in. x 0.38 in.
Full Depth Shear Plate Detailing Height at Support: 16.75 in.
Full Depth Shear Plate Detailing Width at Support: 2.81 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: 5 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 = 3.38 in.
Beam centerline setback = 3.38 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: 2.31 in.
Edge distance at vertical edge of beam: 1.50 in.
Horizontal distance to first hole: 4.88 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 = 5.03 in.
Angle = 0.00 deg.
C = 2.94
Using Table 7-1 to determine (phi)rn:
(phi)Rn = (phi)rn * C = 17.89 * 2.94 = 52.64 kips


Total Vertical Bolt Shear Capacity = 52.64 kips
52.64 kips >= Reaction V = 36.67 kips (OK)

BOLT BEARING AT BEAM AND SHEAR PLATE SIDE
Vertical Shear Only Load Case:
ICR cordinate relative to CG = (2.76, -0.00)
At Row 1, At Column 1:
Ribolt = 17.56 kips
Ri vector at Beam   = <15.95, 7.35>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 6.76 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 * 6.76 * (0.38/1) * 65.00 = 150.36 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.75 * (0.38/1) * 65.00 = 33.35 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(na, 150.36, 33.35) = 33.35 kips/bolt
Ri vector at Shear Plate   = <-15.95, -7.35>
Lcsshpl at Shear Plate spacing  = na
Lceshpl at Shear Plate edge    = 4.82 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 * 4.82 * 0.38 * 65.00 = 105.67 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, 105.67, 32.91) = 32.91 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(33.35, 32.91) = 32.91 kips/bolt
Bolt Shear Demand to Bearing ratio = 32.91 / 17.56 = 1.87

At Row 2, At Column 1:
Ribolt = 16.65 kips
Ri vector at Beam   = <12.25, 11.28>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 8.45 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 * 8.45 * (0.38/1) * 65.00 = 187.82 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.75 * (0.38/1) * 65.00 = 33.35 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(na, 187.82, 33.35) = 33.35 kips/bolt
Ri vector at Shear Plate   = <-12.25, -11.28>
Lcsshpl at Shear Plate spacing  = na
Lceshpl at Shear Plate edge    = 6.03 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 * 6.03 * 0.38 * 65.00 = 132.26 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, 132.26, 32.91) = 32.91 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(33.35, 32.91) = 32.91 kips/bolt
Bolt Shear Demand to Bearing ratio = 32.91 / 16.65 = 1.98

At Row 3, At Column 1:
Ribolt = 15.37 kips
Ri vector at Beam   = <0.00, 15.37>
Lcsbm at Beam spacing  = 2.19 in.
Lcebm at Beam edge    = 8.59 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.75 * 1.20 * 2.19 * (0.38/1) * 65.00 = 48.63 kips/bolt
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 8.59 * (0.38/1) * 65.00 = 191.04 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.75 * (0.38/1) * 65.00 = 33.35 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(48.63, 191.04, 33.35) = 33.35 kips/bolt
Ri vector at Shear Plate   = <-0.00, -15.37>
Lcsshpl at Shear Plate spacing  = 2.19 in.
Lceshpl at Shear Plate edge    = 6.84 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 * 6.84 * 0.38 * 65.00 = 150.14 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, 150.14, 32.91) = 32.91 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(33.35, 32.91) = 32.91 kips/bolt
Bolt Shear Demand to Bearing ratio = 32.91 / 15.37 = 2.14

At Row 4, At Column 1:
Ribolt = 16.65 kips
Ri vector at Beam   = <-12.25, 11.28>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 1.63 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 * 1.63 * (0.38/1) * 65.00 = 36.31 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.75 * (0.38/1) * 65.00 = 33.35 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(na, 36.31, 33.35) = 33.35 kips/bolt
Ri vector at Shear Plate   = <12.25, -11.28>
Lcsshpl at Shear Plate spacing  = na
Lceshpl at Shear Plate edge    = 1.61 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 * 1.61 * 0.38 * 65.00 = 35.33 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, 35.33, 32.91) = 32.91 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(33.35, 32.91) = 32.91 kips/bolt
Bolt Shear Demand to Bearing ratio = 32.91 / 16.65 = 1.98

At Row 5, At Column 1:
Ribolt = 17.56 kips
Ri vector at Beam   = <-15.95, 7.35>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 1.25 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 * 1.25 * (0.38/1) * 65.00 = 27.68 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.75 * (0.38/1) * 65.00 = 33.35 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(na, 27.68, 33.35) = 27.68 kips/bolt
Ri vector at Shear Plate   = <15.95, -7.35>
Lcsshpl at Shear Plate spacing  = na
Lceshpl at Shear Plate edge    = 1.24 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 * 1.24 * 0.38 * 65.00 = 27.17 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, 27.17, 32.91) = 27.17 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(27.68, 27.17) = 27.17 kips/bolt
Bolt Shear Demand to Bearing ratio = 27.17 / 17.56 = 1.55

Min Bolt Shear Demand to Bearing ratio Beam and Shear Plate for vertical shear only
 = min(1.00, 1.87, 1.98, 2.14, 1.98, 1.55) = 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 * 52.64 = 52.64 kips
Rbv = 52.64 kips >= Reaction V = 36.67 kips (OK)

Web Depth = d - [Top Cope Depth] - [Bottom Cope Depth] = 20.80 - 0.00 - 0.00 = 20.80 in.

Using AISC 14th Ed. Equation J4-3
Gross Area (Shear), Agross = [Web Depth] * tw = 20.80 * 0.38 = 7.90 in^2
Shear Yielding, (phi)Vny = (phi) * 0.6 * Fybeam * Agross = 1.00 * 0.6 * 50.00 * 7.90 = 237.12 kips

Using AISC 14th Ed. Equation J4-4
Net Area (Shear), Anet = ([Web Depth] - ([# rows] * [Diameter + 0.06])) * tw 
    = (20.80 - (5 * 0.88)) * 0.38 = 6.24 in^2
Shear Rupture, (phi)Vnu = (phi) * 0.6 * Fubeam * Anet = 0.75 * 0.6 * 65.00 * 6.24 = 182.57 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 = 36.67 kips (OK)

Using AISC 14th Ed. Equation J4-4
Net Area, An = (14.50 - (5 * (0.81 + 1/16))) * 0.38 = 3.80 in^2
Shear Rupture, (phi)Vnu = (phi) * 0.6 * Fupl * An = 0.75 * 0.6 * 65.00 * 3.80 = 111.06 kips

111.06 kips >= Reaction V = 36.67 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 * (0.81 + 0.06)) = 9.31 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 * 9.31) + (1.00 * 65.00 * 1.09)) = 122.14 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 * 1.09)) = 131.80 kips
Block Shear = 122.14 kips
122.14 kips >= Reaction V = 36.67 kips (OK)

Block Shear for Axial T/C is not required.

Flexural and Buckling Strength:

Eccentricity at first line of bolts, e = 5.03 in.
Zgross = 19.71 in^3
Znet   = 13.73 in^3
Sgross = 13.14 in^3
Snet   = 9.07 in^3

Using AISC 14th Ed. Equation 9-4
Flexural Rupture = (phi) * Fu * Znet / e = 0.75 * 65.00 * 13.73 / 5.03 = 133.03 kips


Using AISC 14th Ed. Equation 9-14 through 9-18, Fcr = Fy * Q
tw = 0.38 in.
ho = 14.50 in.
c = 4.88 in.
lambda = (ho * Fy ^ 0.5) / ( 10 * tw * ( 475.00 + 280.00 * (ho / c)^2 ) ^0.5 ) = 
 = 14.50 * 50.00^0.5 / (10 * 0.38 * (475.00 + 280.00 * (14.50/4.88)^2 )^0.5) = 0.50
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 * 13.14 / 5.03 = 117.50 kips

Interaction Check of Flexural Yielding:
Using AISC 14th Ed. Equation 10-5
Eccentricity at CG of Bolt Group, e = 5.03 in.
Zgross = 19.71
Znet = 13.73
Mr = Vr * e = 36.67 * 5.03 = 184.54 kips-in
Mc = phi * Mn = phi * Fy * Zgross = 0.90 * 50.00 * 19.71 = 886.99 kips-in
Vr = 36.67 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 = (36.67 / 163.12)^2 + (184.54 / 886.99)^2 = 0.09 <= 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 = 0.38 <= 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 = 36.67 / 15.25 / 2 = 1.20 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) = 1.20 / (0.75 * 1.86) = 0.86/16

Minimum fillet weld size : 
   At shear only load case = 0.05 in.
   per Table J2.4     = 0.19 in.
   5/8tp              = 0.23 in.
   user preference    = 0.25 in.

Dmax1 (using AISC 14th Ed. eqn 9-3)
 = tshpl * Fushpl / ( Fexx * C1 * 0.09)
 = 0.38 * 65.00 / ( 70.00 * 1.00 * 0.09 ) 
 = 3.94 
Dmax2 (using AISC 14th Ed. eqn 9-3)
 = twbm * Fusupport / ( Fexx * C1 * 0.09 )
 = 0.32 * 65.00 / ( 70.00 * 1.00 * 0.09 ) 
 = 3.31 
Dmax3 = project max fillet weld = 12.00
Dmax=min(Dmax1, Dmax2, Dmax3) = min(3.94, 3.31, 12.00)
 = 3.31 

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 * (3.31 + 3.31) = 140.51 kips

140.51 kips >= Reaction V = 36.67 kips (OK)