bb.s.s.01160.01160

SHEAR PLATE CONNECTION SUMMARY

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

Filler Beam profile: W18X40
Support Girder profile: W21X50
Slope: 0.00 deg.
Skew: 90.00
Vertical Offset: 0.00 in.
Horizontal Offset: 0.00 in.
Span: 2.49 ft.
Reaction, V: 2.00 kips
Shear Capacity, Rn: 50.65 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: 6.62 in. x 14.50 in. x 0.38 in.
Configuration Geometry:
Welds at shear plate to support: 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 = 3.62 in.
Beam centerline setback = 3.62 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: 5.12 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 = 5.32 in.
Angle = 0.00 deg.
C = 2.83
Using Table 7-1 to determine (phi)rn:
(phi)Rn = (phi)rn * C = 17.89 * 2.83 = 50.65 kips


Total Vertical Bolt Shear Capacity = 50.65 kips
50.65 kips >= Reaction V = 2.00 kips (OK)

BOLT BEARING AT BEAM AND SHEAR PLATE SIDE
Vertical Shear Only Load Case:
ICR cordinate relative to CG = (2.58, 0.00)
At Row 1, At Column 1:
Ribolt = 17.56 kips
Ri vector at Beam   = <16.14, 6.93>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 7.19 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 * 7.19 * (0.32/1) * 65.00 = 132.58 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.75 * (0.32/1) * 65.00 = 27.64 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(na, 132.58, 27.64) = 27.64 kips/bolt
Ri vector at Shear Plate   = <-16.14, -6.93>
Lcsshpl at Shear Plate spacing  = na
Lceshpl at Shear Plate edge    = 5.03 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 * 5.03 * 0.38 * 65.00 = 110.43 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, 110.43, 32.91) = 32.91 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(27.64, 32.91) = 27.64 kips/bolt
Bolt Shear Demand to Bearing ratio = 27.64 / 17.56 = 1.57

At Row 2, At Column 1:
Ribolt = 16.60 kips
Ri vector at Beam   = <12.59, 10.82>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 8.80 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 * 8.80 * (0.32/1) * 65.00 = 162.18 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.75 * (0.32/1) * 65.00 = 27.64 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(na, 162.18, 27.64) = 27.64 kips/bolt
Ri vector at Shear Plate   = <-12.59, -10.82>
Lcsshpl at Shear Plate spacing  = na
Lceshpl at Shear Plate edge    = 6.13 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 * 6.13 * 0.38 * 65.00 = 134.56 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, 134.56, 32.91) = 32.91 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(27.64, 32.91) = 27.64 kips/bolt
Bolt Shear Demand to Bearing ratio = 27.64 / 16.60 = 1.67

At Row 3, At Column 1:
Ribolt = 15.15 kips
Ri vector at Beam   = <-0.00, 15.15>
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 * (0.32/1) * 65.00 = 40.31 kips/bolt
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 8.59 * (0.32/1) * 65.00 = 158.37 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.75 * (0.32/1) * 65.00 = 27.64 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(40.31, 158.37, 27.64) = 27.64 kips/bolt
Ri vector at Shear Plate   = <0.00, -15.15>
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(27.64, 32.91) = 27.64 kips/bolt
Bolt Shear Demand to Bearing ratio = 27.64 / 15.15 = 1.82

At Row 4, At Column 1:
Ribolt = 16.60 kips
Ri vector at Beam   = <-12.59, 10.82>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 1.57 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 * 1.57 * (0.32/1) * 65.00 = 28.96 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.75 * (0.32/1) * 65.00 = 27.64 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(na, 28.96, 27.64) = 27.64 kips/bolt
Ri vector at Shear Plate   = <12.59, -10.82>
Lcsshpl at Shear Plate spacing  = na
Lceshpl at Shear Plate edge    = 1.35 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 * 1.35 * 0.38 * 65.00 = 29.71 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, 29.71, 32.91) = 29.71 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(27.64, 29.71) = 27.64 kips/bolt
Bolt Shear Demand to Bearing ratio = 27.64 / 16.60 = 1.67

At Row 5, At Column 1:
Ribolt = 17.56 kips
Ri vector at Beam   = <-16.14, 6.93>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 1.23 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 * 1.23 * (0.32/1) * 65.00 = 22.60 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.75 * (0.32/1) * 65.00 = 27.64 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(na, 22.60, 27.64) = 22.60 kips/bolt
Ri vector at Shear Plate   = <16.14, -6.93>
Lcsshpl at Shear Plate spacing  = na
Lceshpl at Shear Plate edge    = 1.09 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 * 1.09 * 0.38 * 65.00 = 23.88 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, 23.88, 32.91) = 23.88 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(22.60, 23.88) = 22.60 kips/bolt
Bolt Shear Demand to Bearing ratio = 22.60 / 17.56 = 1.29

Min Bolt Shear Demand to Bearing ratio Beam and Shear Plate for vertical shear only
 = min(1.00, 1.57, 1.67, 1.82, 1.67, 1.29) = 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 * 50.65 = 50.65 kips
Rbv = 50.65 kips >= Reaction V = 2.00 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 * 0.88)) * 0.32 = 4.26 in^2
Shear Rupture, (phi)Vnu = (phi) * 0.6 * Fubeam * Anet = 0.75 * 0.6 * 65.00 * 4.26 = 124.62 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 = 2.00 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 = 2.00 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 = (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 + 1.50) = 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 * 9.31) + (1.00 * 65.00 * 0.97)) = 119.86 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 * 0.97)) = 129.51 kips
Block Shear = 119.86 kips
119.86 kips >= Reaction V = 2.00 kips (OK)

Block Shear for Axial T/C is not required.

Flexural and Buckling Strength:

Eccentricity at first line of bolts, e = 5.32 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 / 5.32 = 125.96 kips


Using AISC 14th Ed. Equation 9-14 through 9-18, Fcr = Fy * Q
tw = 0.38 in.
ho = 14.50 in.
c = 5.12 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 * (14.50/5.12)^2 )^0.5) = 0.52
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 / 5.32 = 111.26 kips

Interaction Check of Flexural Yielding, Per AISC 10-5: 
Eccentricity at CG of Bolt Group, e = 5.32 in.
Zgross = 19.71
Znet = 13.73
Mr = Vr * e = 2.00 * 5.32 = 10.63 kips-in
Mc = phi * Mn = phi * Fy * Zgross = 0.90 * 50.00 * 19.71 = 886.99 kips-in
Vr = 2.00 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 = (2.00 / 163.12)^2 + (10.63 / 886.99)^2 = 0.00 <= 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 = 0.32 <= 0.44 OK
Leh(plate) >= 2 * db = 1.50 >= 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 = 14.50 in.
Shear Load per inch per weld, fv = R/Lv/2 = 2.00 / 14.50 / 2 = 0.07 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) = 0.07 / (0.75 * 1.86) = 0.05/16

Minimum fillet weld size : 
   At shear only load case = 0.00 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 )
 = 0.38 * 65.00 / ( 70.00 * 1.00 * 0.09 ) 
 = 3.99 
Dmax3 = project max fillet weld = 12.00
Dmax=min(Dmax1, Dmax2, Dmax3) = min(3.94, 3.99, 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 * 14.50 * (3.94 + 3.94) = 159.05 kips

159.05 kips >= Reaction V = 2.00 kips (OK)