bb.se.s.00001.00001

SHEAR PLATE CONNECTION SUMMARY

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

Filler Beam profile: W14X22
Support Girder profile: W21X50
Slope: 0.00 deg.
Skew: 90.00
Vertical Offset: 0.00 in.
Horizontal Offset: 0.00 in.
Span: 10.00 ft.
Reaction, V: 15.00 kips
Shear Capacity, Rn: 20.53 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: 7.62 in. x 9.00 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 1.00 in. Diameter A490N_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: 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: 5.62 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 14th Ed. Equation (7-1))
ex = 5.82 in.
Angle = 0.00 deg.
C = 1.00
Using Table 7-1 to determine (phi)rn:
(phi)Rn = (phi)rn * C = 40.06 * 1.00 = 39.96 kips


Total Vertical Bolt Shear Capacity = 39.96 kips
39.96 kips >= Reaction V = 15.00 kips (OK)

BOLT BEARING AT BEAM AND SHEAR PLATE SIDE
Vertical Shear Only Load Case:
ICR cordinate relative to CG = (0.54, -0.00)
At Row 1, At Column 1:
Ribolt = 39.32 kips
Ri vector at Beam   = <38.69, 7.00>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 16.31 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 * 16.31 * (0.23/1) * 65.00 = 219.47 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 1.00 * (0.23/1) * 65.00 = 26.91 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(na, 219.47, 26.91) = 26.91 kips/bolt
Ri vector at Shear Plate   = <-38.69, -7.00>
Lcsshpl at Shear Plate spacing  = na
Lceshpl at Shear Plate edge    = 5.05 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 * 5.05 * 0.38 * 65.00 = 110.78 kips/bolt
(phi)Rndshpl on Shear Plate at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 1.00 * 0.38 * 65.00 = 43.88 kips/bolt
Shear Plate bearing capacity, (phi)Rnshpl = min((phi)Rnsshpl,(phi)Rneshpl,(phi)Rndshpl) = min(na, 110.78, 43.88) = 43.88 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(26.91, 43.88) = 26.91 kips/bolt
Bolt Shear Demand to Bearing ratio = 26.91 / 39.32 = 0.68

At Row 2, At Column 1:
Ribolt = 25.95 kips
Ri vector at Beam   = <-0.00, 25.95>
Lcsbm at Beam spacing  = 1.94 in.
Lcebm at Beam edge    = 5.47 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.75 * 1.20 * 1.94 * (0.23/1) * 65.00 = 26.07 kips/bolt
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 5.47 * (0.23/1) * 65.00 = 73.58 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 1.00 * (0.23/1) * 65.00 = 26.91 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(26.07, 73.58, 26.91) = 26.07 kips/bolt
Ri vector at Shear Plate   = <0.00, -25.95>
Lcsshpl at Shear Plate spacing  = 1.94 in.
Lceshpl at Shear Plate edge    = 3.97 in.
(phi)Rnsshpl at Shear Plate spacing = (phi) * hf1 * Lcs * t * Fu = 0.75 * 1.20 * 1.94 * 0.38 * 65.00 = 42.50 kips/bolt
(phi)Rneshpl at Shear Plate edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 3.97 * 0.38 * 65.00 = 87.07 kips/bolt
(phi)Rndshpl on Shear Plate at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 1.00 * 0.38 * 65.00 = 43.88 kips/bolt
Shear Plate bearing capacity, (phi)Rnshpl = min((phi)Rnsshpl,(phi)Rneshpl,(phi)Rndshpl) = min(42.50, 87.07, 43.88) = 42.50 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(26.07, 42.50) = 26.07 kips/bolt
Bolt Shear Demand to Bearing ratio = 26.07 / 25.95 = 1.00

At Row 3, At Column 1:
Ribolt = 39.32 kips
Ri vector at Beam   = <-38.69, 7.00>
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 * (0.23/1) * 65.00 = 20.20 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 1.00 * (0.23/1) * 65.00 = 26.91 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(na, 20.20, 26.91) = 20.20 kips/bolt
Ri vector at Shear Plate   = <38.69, -7.00>
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 * 0.38 * 65.00 = 29.96 kips/bolt
(phi)Rndshpl on Shear Plate at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 1.00 * 0.38 * 65.00 = 43.88 kips/bolt
Shear Plate bearing capacity, (phi)Rnshpl = min((phi)Rnsshpl,(phi)Rneshpl,(phi)Rndshpl) = min(na, 29.96, 43.88) = 29.96 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(20.20, 29.96) = 20.20 kips/bolt
Bolt Shear Demand to Bearing ratio = 20.20 / 39.32 = 0.51

Min Bolt Shear Demand to Bearing ratio Beam and Shear Plate for vertical shear only
 = min(1.00, 0.68, 1.00, 0.51) = 0.51

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 = 0.51 * 39.96 = 20.53 kips
Rbv = 20.53 kips >= Reaction V = 15.00 kips (OK)

Web Depth = d - [Top Cope Depth] - [Bottom Cope Depth] = 13.70 - 0.00 - 0.00 = 13.70 in.

Using AISC 14th Ed. Equation J4-3
Gross Area (Shear), Agross = [Web Depth] * tw = 13.70 * 0.23 = 3.15 in^2
Shear Yielding, (phi)Vny = (phi) * 0.6 * Fybeam * Agross = 1.00 * 0.6 * 50.00 * 3.15 = 94.53 kips
94.53 kips >= Reaction V = 15.00 kips (OK)

Shear Rupture:
Using AISC 14th Ed. Equation J4-4
Net Area (Shear), Anet = ([Web Depth] - ([# rows] * [Diameter + 0.06])) * tw 
    = (13.70 - (3 * 1.12)) * 0.23 = 2.37 in^2
Shear Rupture, (phi)Vnu = (phi) * 0.6 * Fubeam * Anet = 0.75 * 0.6 * 65.00 * 2.37 = 69.46 kips
69.46 kips >= Reaction V = 15.00 kips (OK)


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 * 9.00 = 3.38 in^2
Shear Yielding, (phi)Vny = (phi) * 0.6 * Fypl * Ag = 1.00 * 0.6 * 50.00 * 3.38 = 101.25 kips
101.25 kips >= Reaction V = 15.00 kips (OK)

Shear Rupture:
Using AISC 14th Ed. Equation J4-4
Net Area, An = (9.00 - (3 * (1.06 + 1/16))) * 0.38 = 2.11 in^2
Shear Rupture, (phi)Vnu = (phi) * 0.6 * Fupl * An = 0.75 * 0.6 * 65.00 * 2.11 = 61.70 kips
61.70 kips >= Reaction V = 15.00 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 = (9.00 - 1.50) = 7.50 in.
Net Shear Length = 7.50 - (2.50 * (1.06 + 0.06)) = 4.69 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 * 0.38 * ((0.60 * 65.00 * 4.69) + (1.00 * 65.00 * 1.31)) = 75.41 kips
2. (phi) * [material thickness] * ((0.60 * Fypl * [gross shear length]) + (Ubs * Fupl * [net tension length])) 
    = 0.75 * 0.38 * ((0.60 * 50.00 * 7.50) + (1.00 * 65.00 * 1.31)) = 87.28 kips
Block Shear = 75.41 kips
75.41 kips >= Reaction V = 15.00 kips (OK)

Block Shear for Axial T/C is not required.

Flexural and Buckling Strength:

Eccentricity at first line of bolts, e = 5.82 in.
Zgross = 7.59 in^3
Znet   = 4.94 in^3
Sgross = 5.06 in^3
Snet   = 3.38 in^3

Using AISC 14th Ed. Equation 9-4
Flexural Rupture = (phi) * Fu * Znet / e = 0.75 * 65.00 * 4.94 / 5.82 = 41.45 kips


Using AISC 14th Ed. Equation 9-14 through 9-18, Fcr = Fy * Q
tw = 0.38 in.
ho = 9.00 in.
c = 5.62 in.
lambda = (ho * Fy ^ 0.5) / ( 10 * tw * ( 475.00 + 280.00 * (ho / c)^2 ) ^0.5 ) = 
 = 9.00 * 50.00^0.5 / (10 * 0.38 * (475.00 + 280.00 * (9.00/5.62)^2 )^0.5) = 0.49
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 * 5.06 / 5.82 = 39.18 kips

Interaction Check of Flexural Yielding:
Using AISC 14th Ed. Equation 10-5
Eccentricity at CG of Bolt Group, e = 5.82 in.
Zgross = 7.59
Znet = 4.94
Mr = Vr * e = 15.00 * 5.82 = 87.23 kips-in
Mc = phi * Mn = phi * Fy * Zgross = 0.90 * 50.00 * 7.59 = 341.72 kips-in
Vr = 15.00 kips
Vc = phi * Vn = phi * 0.60 * Fy * Ag = 1.00 * 0.60 * 50.00 * 3.38 = 101.25 kips
Interaction due to moment and shear, (Vr/Vc)^2 + (Mr/Mc)^2 <= 1.0
(Vr/Vc)^2 + (Mr/Mc)^2 = (15.00 / 101.25)^2 + (87.23 / 341.72)^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 <= 0.56 OK
tw  < = db/2 + 1/16 = 0.23 <= 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.

WELD:

 Weld Requirements:

At shear only case: 
Weld Length for shear, Lv = 9.00 in.
Shear Load per inch per weld, fv = R/Lv/2 = 15.00 / 9.00 / 2 = 0.83 kips/in/ weld 
theta = 0 deg.
cPhi  = 1.0 + 0.5 * sin(theta)^1.5 = 1.0 + 0.5 * sin(0.00)^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) = 0.83 / (0.75 * 1.86) = 0.60/16

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 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 )
 = 0.38 * 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 * 9.00 * (3.94 + 3.94) = 98.72 kips

98.72 kips >= Reaction V = 15.00 kips (OK)