bb.se.s.00010.00129

SHEAR PLATE CONNECTION SUMMARY

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

Filler Beam profile: W18X55
Support Girder profile: W18X55
Slope: 0.00 deg.
Skew: 90.00
Vertical Offset: 0.00 in.
Horizontal Offset: 0.00 in.
Beam Length in Model: 6.42 ft.
Reaction, V: 45.00 kips
Shear Capacity, Rn: 53.33 kips
Design/Reference according to AISC 15th 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: 7.50 in. x 14.25 in. x 0.38 in.
Configuration Geometry:
Welds at shear plate to support: 4/16 FILLET, 4/16 FILLET
Bolt: 4 rows x 1 column 0.88 in. Diameter F1852N_TC bolts
Vertical spacing: 4.00 in.
Horizontal spacing: 3.00 in.
Shear plate edge setback = 4.00 in.
Beam centerline setback = 4.00 in.
Edge distance at vertical edge of plate: 1.75 in.
Edge distance at top edge of plate: 1.12 in.
Edge distance at bottom edge of plate: 1.12 in.
Edge distance at vertical edge of beam: 1.75 in.
Horizontal distance to first hole: 5.75 in.
Down distance from top of filler beam flange: 3.00 in.
Holes in beam web: STD diameter = 0.94 in.
Holes in shear plate: SSL slot width = 0.94 in., slot length = 1.12 in.

BOLT SHEAR CAPACITY AT BEAM AND SHEAR PLATE SIDE:
Bolt Shear Capacity at Shear Load Only:
Using Instantaneous Center Of Rotation Method (AISC 15th Ed. Equation (7-1))
ex = 5.95 in.
Angle = 0.00 deg.
C = 2.19
Using Table 7-1 to determine (phi)rn:
(phi)Rn = (phi)rn * C = 24.35 * 2.19 = 53.33 kips


Total Vertical Bolt Shear Capacity = 53.33 kips
53.33 kips >= Reaction V = 45.00 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 = 23.90 kips
Ri vector at Beam   = <0.92, 0.39>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 7.10 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 * 7.10 * (0.39/1) * 65.00 = 161.88 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.88 * (0.39/1) * 65.00 = 39.93 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(na, 161.88, 39.93) = 39.93 kips/bolt
Ri vector at Shear Plate   = <-0.92, -0.39>
Lcsshpl at Shear Plate spacing  = na
Lceshpl at Shear Plate edge    = 5.61 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 * 5.61 * 0.38 * 65.00 = 123.13 kips/bolt
(phi)Rndshpl on Shear Plate at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.88 * 0.38 * 65.00 = 38.39 kips/bolt
Shear Plate bearing capacity, (phi)Rnshpl = min((phi)Rnsshpl,(phi)Rneshpl,(phi)Rndshpl) = min(na, 123.13, 38.39) = 38.39 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(39.93, 38.39) = 38.39 kips/bolt
Bolt Shear Demand to Bearing ratio = 38.39 / 23.90 = 1.61

At Row 2, At Column 1:
Ribolt = 21.79 kips
Ri vector at Beam   = <0.61, 0.79>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 8.36 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 * 8.36 * (0.39/1) * 65.00 = 190.67 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.88 * (0.39/1) * 65.00 = 39.93 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(na, 190.67, 39.93) = 39.93 kips/bolt
Ri vector at Shear Plate   = <-0.61, -0.79>
Lcsshpl at Shear Plate spacing  = na
Lceshpl at Shear Plate edge    = 8.75 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 * 8.75 * 0.38 * 65.00 = 192.01 kips/bolt
(phi)Rndshpl on Shear Plate at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.88 * 0.38 * 65.00 = 38.39 kips/bolt
Shear Plate bearing capacity, (phi)Rnshpl = min((phi)Rnsshpl,(phi)Rneshpl,(phi)Rndshpl) = min(na, 192.01, 38.39) = 38.39 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(39.93, 38.39) = 38.39 kips/bolt
Bolt Shear Demand to Bearing ratio = 38.39 / 21.79 = 1.76

At Row 3, At Column 1:
Ribolt = 21.79 kips
Ri vector at Beam   = <-0.61, 0.79>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 2.36 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 * 2.36 * (0.39/1) * 65.00 = 53.75 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.88 * (0.39/1) * 65.00 = 39.93 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(na, 53.75, 39.93) = 39.93 kips/bolt
Ri vector at Shear Plate   = <0.61, -0.79>
Lcsshpl at Shear Plate spacing  = na
Lceshpl at Shear Plate edge    = 2.22 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 * 2.22 * 0.38 * 65.00 = 48.77 kips/bolt
(phi)Rndshpl on Shear Plate at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.88 * 0.38 * 65.00 = 38.39 kips/bolt
Shear Plate bearing capacity, (phi)Rnshpl = min((phi)Rnsshpl,(phi)Rneshpl,(phi)Rndshpl) = min(na, 48.77, 38.39) = 38.39 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(39.93, 38.39) = 38.39 kips/bolt
Bolt Shear Demand to Bearing ratio = 38.39 / 21.79 = 1.76

At Row 4, At Column 1:
Ribolt = 23.90 kips
Ri vector at Beam   = <-0.92, 0.39>
Lcsbm at Beam spacing  = na
Lcebm at Beam edge    = 1.40 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 * 1.40 * (0.39/1) * 65.00 = 32.05 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.88 * (0.39/1) * 65.00 = 39.93 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(na, 32.05, 39.93) = 32.05 kips/bolt
Ri vector at Shear Plate   = <0.92, -0.39>
Lcsshpl at Shear Plate spacing  = na
Lceshpl at Shear Plate edge    = 1.26 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 * 1.26 * 0.38 * 65.00 = 27.61 kips/bolt
(phi)Rndshpl on Shear Plate at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.88 * 0.38 * 65.00 = 38.39 kips/bolt
Shear Plate bearing capacity, (phi)Rnshpl = min((phi)Rnsshpl,(phi)Rneshpl,(phi)Rndshpl) = min(na, 27.61, 38.39) = 27.61 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(32.05, 27.61) = 27.61 kips/bolt
Bolt Shear Demand to Bearing ratio = 27.61 / 23.90 = 1.16

Min Bolt Shear Demand to Bearing ratio Beam and Shear Plate for vertical shear only
 = min(1.00, 1.61, 1.76, 1.76, 1.16) = 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 * 53.33 = 53.33 kips
Rbv = 53.33 kips >= Reaction V = 45.00 kips (OK)

Web Depth = d = 18.10 in.

Using AISC 15th Ed. Equation J4-3
Gross Area (Shear), Agross = [Web Depth] * tw = 18.10 * 0.39 = 7.06 in^2
Shear Yielding, (phi)Vny = (phi) * 0.6 * Fybeam * Agross = 1.00 * 0.6 * 50.00 * 7.06 = 211.77 kips
211.77 kips >= Reaction V = 45.00 kips (OK)

Shear Rupture:
Using AISC 15th Ed. Equation J4-4
Net Area (Shear), Anet = ([Web Depth] - [# rows] * (hole width + 0.06)) * tw 
    = (18.10 - 4 * (0.94 + 0.06)) * 0.39 = 5.50 in^2
Shear Rupture, (phi)Vnu = (phi) * 0.6 * Fubeam * Anet = 0.75 * 0.6 * 65.00 * 5.50 = 160.85 kips
160.85 kips >= Reaction V = 45.00 kips (OK)


Check Horizontal Block Shear

Using AISC 15th 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 15th Ed. Equation J4-3
Gross Area, Ag = 0.38 * 14.25 = 5.34 in^2
Shear Yielding, (phi)Vny = (phi) * 0.6 * Fypl * Ag = 1.00 * 0.6 * 50.00 * 5.34 = 160.31 kips
160.31 kips >= Reaction V = 45.00 kips (OK)

Shear Rupture:
Using AISC 15th Ed. Equation J4-4
Net Area, An = (14.25 - (4 * (0.94 + 0.06))) * 0.38 = 3.84 in^2
Shear Rupture, (phi)Vnu = (phi) * 0.6 * Fupl * An = 0.75 * 0.6 * 65.00 * 3.84 = 112.43 kips
112.43 kips >= Reaction V = 45.00 kips (OK)


Check Vertical Block Shear

Using AISC 15th 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 = (14.25 - 1.12) = 13.12 in.
Net Shear Length = 13.12 - (4 - 0.5) * (0.94 + 0.06) = 9.62 in.
Gross Tension Length = (0.00 + 1.75) = 1.75 in.
Net Tension Length = 1.75 - (1 - 0.5) * (1.12 + 0.06) = 1.16 in.
1. (phi) * [material thickness] * ((0.60 * Fupl* [net shear length]) + (Ubs * Fupl * [net tension length])) 
    = 0.75 * 0.38 * ((0.60 * 65.00 * 9.62) + (1.00 * 65.00 * 1.16)) = 126.72 kips
2. (phi) * [material thickness] * ((0.60 * Fypl * [gross shear length]) + (Ubs * Fupl * [net tension length])) 
    = 0.75 * 0.38 * ((0.60 * 50.00 * 13.12) + (1.00 * 65.00 * 1.16)) = 131.88 kips
Block Shear = 126.72 kips
126.72 kips >= Reaction V = 45.00 kips (OK)

Block Shear for Axial T/C is not required.

Check Flexural Yielding and Rupture:

Eccentricity at first line of bolts, e = 5.95 in.
Zgross = 19.04 in^3
Znet   = 13.04 in^3
Sgross = 12.69 in^3
Snet   = 8.46 in^3
Fypl = 50.00 ksi
Fupl = 65.00 ksi
Mp = Fypl * Zgross = 50.00 * 19.04 = 951.86 kips-in
My = Fypl * Sgross = 50.00 * 12.69 = 634.57 kips-in

Flexural Yielding using AISC 15th Ed. Equation F11-1
Reaction Capacity, (phi)Rn = min((phi) * Mp / e, (phi) * 1.6 * Fypl * Sgross / e) = 
 = min(0.90 * 951.86 / 5.95, 0.90 * 1.6 * 50.00 * 12.69 / 5.95) = 144.10 kips
144.10 kips >= 45.00 kips (OK)

Flexural Rupture using AISC 15th Ed. Equation 9-4
Reaction Capacity, (phi)Rn = (phi)Mn / e = (phi) * Fupl * Znet / e = 
 = 0.75 * 65.00 * 13.04 / 5.95 = 106.91 kips
106.91 kips >= 45.00 kips (OK)

Flexural and Buckling Strength:

Lateral Torsional Buckling using AISC 15th Ed. Equations 9-15 to 9-16, F11-1 to F11-4
t = tshpl = 0.38 in.
d = hshpl = 14.25 in.
drect = hshpl = 14.25 in.
dc = down distance (per AISC Example II.A-19B) = 3.00 in.
Lb = horizontal distance to first hole = 5.75 in.
Fypl = 50.00 ksi
Cb = max((3 + ln(Lb / d)) * (1 - dc / d), 1.84) = 
 = max((3 + ln(5.75 / 14.25)) * (1 - 3.00 / 14.25), 1.84) = 1.84
Lb * drect / t^2 = 5.75 * 14.25 / 0.38^2 = 582.67
0.08 * E / Fypl = 0.08 * 29000 / 50.00 = 46.40
1.9 * E / Fypl = 1.9 * 29000 / 50.00 = 1102.00
For case when 0.08 * E / Fypl < Lb * drect / t^2 <= 1.9 * E / Fypl
Mn = min(Cb * (1.52 - 0.274 * (Lb * drect / t^2) * Fypl / E) * My, Mp)
 = min(1.84 * (1.52 - 0.274 * (5.75 * 14.25 / 0.38^2) * 50.00 / 29000) * 634.57, 951.86)
 = min(1453.37, 951.86) = 951.86 kips-in

Flexural Local Buckling Reaction Capacity, (phi)Rn = (phi) * Mn / e = 0.90 * 951.86 / 5.95 = 144.10 kips
144.10 kips >= 45.00 kips (OK)

Interaction Check of Flexural Yielding:
Using AISC 15th Ed. Equation 10-5
Eccentricity at first line of bolts, e = 5.95 in.
Sgross = 12.69 in^3
Zgross = 19.04 in^3
Mr = Vr * e = 45.00 * 5.95 = 267.53 kips-in
Mc = phi * Mn = min(phi * Fypl * Zgross, phi * 1.6 * Fypl * Sgross) = 
 = min(0.90 * 50.00 * 19.04, 0.90 * 1.6 * 50.00 * 12.69) = 856.67 kips-in
Vr = 45.00 kips
Vc = phi * Vn = phi * 0.60 * Fypl * Ag = 1.00 * 0.60 * 50.00 * 5.34 = 160.31 kips
Interaction due to moment and shear, (Vr/Vc)^2 + (Mr/Mc)^2 <= 1.0
(Vr/Vc)^2 + (Mr/Mc)^2 = (45.00 / 160.31)^2 + (267.53 / 856.67)^2 = 0.18
0.18 <= 1.00 (OK)

LATERAL-TORSIONAL STABILITY:

Available Strength to Resist Lateral Displacement:
Using Eq. 6, Thornton and Fortney 2011 Engineering Journal
(phi)Rn = 1500.00 * 3.14 * L * tp^3 / a^2 = 0.90 * 1500.00 * 3.14 * 14.25 * 0.38^3 / 5.75^2 = 96.40 kips
96.40 kips >= Reaction V = 45.00 kips (OK)

Torsional Strength:
Using Eq. 10 and Eq. 16, Thornton and Fortney 2011 Engineering Journal
Required, Mtu = Ru * (tw + tp) / 2 = 45.00 * ((0.38 + 0.38) / 2) = 16.88 kips-in
Lateral Shear Strength of Shear Plate, Mtn (no slab) = [(phiv) * (0.6 * Fyp) - (Ru / (L * tp))] * L * tp^2 / 2 = 
= [(1.00) * (0.6 * 50.00) - (45.00 / (14.25 * 0.38))] * 14.25 * 0.38^2 / 2 = 21.62 kips-in
21.62 kips-in >= Mtu = 16.88 kips-in (OK)

MAXIMUM PLATE THICKNESS:
No of bolt columns = 1
tp  < = db/2 + 0.06 = 0.38 <= 0.50 OK
tw  < = db/2 + 0.06 = 0.39 <= 0.50 OK
Leh(plate) >= 2 * db = 1.75 >= 1.75 OK
Leh(bm) >= 2 * db = 1.75 >= 1.75 OK
Maximum Plate Thickness is Not a Limiting Criteria.

WELD:

 Weld Requirements:

At shear only case: 
Weld Length for shear, Lv = 14.25 in.
Shear Load per inch per weld, fv = R/Lv/2 = 45.00 / 14.25 / 2 = 1.58 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) = 1.58 / (0.75 * 1.86) = 1.13/16

Minimum fillet weld size : 
   At shear only load case = 0.07 in.
   per Table J2.4          = 0.19 in.
   5/8tp                   = 0.23 in.
   user preference         = 0.19 in.

Dmax1 (using AISC 15th 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 15th Ed. eqn 9-3)
 = twbm * Fusupport / ( Fexx * C1 * 0.09 )
 = 0.39 * 65.00 / ( 70.00 * 1.00 * 0.09 ) 
 = 4.10 
Dmax3 = project max fillet weld = 16.00
Dmax=min(Dmax1, Dmax2, Dmax3) = min(3.94, 4.10, 16.00)
 = 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 * 14.25 * (3.94 + 3.94) = 156.31 kips

156.31 kips >= Reaction V = 45.00 kips (OK)