bb.se.s.00090.00121

SHEAR PLATE CONNECTION SUMMARY

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

Filler Beam profile: W8X10
Support Girder profile: W18X86
Slope: 0.00 deg.
Skew: 90.00
Vertical Offset: 0.00 in.
Horizontal Offset: 0.00 in.
Beam Length in Model: 8.88 ft.
Reaction, V: 6.00 kips
Shear Capacity, Rn: 6.13 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: 12.25 in. x 5.25 in. x 0.25 in.
Configuration Geometry:
Welds at shear plate to support: 3/16 FILLET, 3/16 FILLET
Bolt: 2 rows x 2 columns 0.88 in. Diameter F1852N_TC bolts
Vertical spacing: 3.00 in.
Horizontal spacing: 3.00 in.
Shear plate edge setback = 5.75 in.
Beam centerline setback = 5.75 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: 7.50 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 = 9.24 in.
Angle = 0.00 deg.
C = 0.84
Using Table 7-1 to determine (phi)rn:
(phi)Rn = (phi)rn * C = 24.35 * 0.84 = 20.53 kips


Total Vertical Bolt Shear Capacity = 20.53 kips
20.53 kips >= Reaction V = 6.00 kips (OK)

BOLT BEARING AT BEAM AND SHEAR PLATE SIDE
Vertical Shear Only Load Case:
ICR cordinate relative to CG = (0.79, -0.00)
At Row 1, At Column 1:
Ribolt = 23.90 kips
Ri vector at Beam   = <0.55, 0.84>
Lcsbm at Beam spacing  = 2.87 in.
Lcebm at Beam edge    = 3.09 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.75 * 1.20 * 2.87 * (0.17/1) * 65.00 = 28.57 kips/bolt
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 3.09 * (0.17/1) * 65.00 = 30.72 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.88 * (0.17/1) * 65.00 = 17.40 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(28.57, 30.72, 17.40) = 17.40 kips/bolt
Ri vector at Shear Plate   = <-0.55, -0.84>
Lcsshpl at Shear Plate spacing  = 2.81 in.
Lceshpl at Shear Plate edge    = 4.34 in.
(phi)Rnsshpl at Shear Plate spacing = (phi) * hf1 * Lcs * t * Fu = 0.75 * 1.20 * 2.81 * 0.25 * 65.00 = 41.04 kips/bolt
(phi)Rneshpl at Shear Plate edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 4.34 * 0.25 * 65.00 = 63.42 kips/bolt
(phi)Rndshpl on Shear Plate at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.88 * 0.25 * 65.00 = 25.59 kips/bolt
Shear Plate bearing capacity, (phi)Rnshpl = min((phi)Rnsshpl,(phi)Rneshpl,(phi)Rndshpl) = min(41.04, 63.42, 25.59) = 25.59 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(17.40, 25.59) = 17.40 kips/bolt
Bolt Shear Demand to Bearing ratio = 17.40 / 23.90 = 0.73

At Row 1, At Column 2:
Ribolt = 22.61 kips
Ri vector at Beam   = <0.90, -0.43>
Lcsbm at Beam spacing  = 2.87 in.
Lcebm at Beam edge    = 10.87 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.75 * 1.20 * 2.87 * (0.17/1) * 65.00 = 28.57 kips/bolt
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 10.87 * (0.17/1) * 65.00 = 108.13 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.88 * (0.17/1) * 65.00 = 17.40 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(28.57, 108.13, 17.40) = 17.40 kips/bolt
Ri vector at Shear Plate   = <-0.90, 0.43>
Lcsshpl at Shear Plate spacing  = 2.81 in.
Lceshpl at Shear Plate edge    = 1.96 in.
(phi)Rnsshpl at Shear Plate spacing = (phi) * hf1 * Lcs * t * Fu = 0.75 * 1.20 * 2.81 * 0.25 * 65.00 = 41.04 kips/bolt
(phi)Rneshpl at Shear Plate edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 1.96 * 0.25 * 65.00 = 28.65 kips/bolt
(phi)Rndshpl on Shear Plate at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.88 * 0.25 * 65.00 = 25.59 kips/bolt
Shear Plate bearing capacity, (phi)Rnshpl = min((phi)Rnsshpl,(phi)Rneshpl,(phi)Rndshpl) = min(41.04, 28.65, 25.59) = 25.59 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(17.40, 25.59) = 17.40 kips/bolt
Bolt Shear Demand to Bearing ratio = 17.40 / 22.61 = 0.77

At Row 2, At Column 1:
Ribolt = 23.90 kips
Ri vector at Beam   = <-0.55, 0.84>
Lcsbm at Beam spacing  = 2.87 in.
Lcebm at Beam edge    = 2.69 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.75 * 1.20 * 2.87 * (0.17/1) * 65.00 = 28.57 kips/bolt
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 2.69 * (0.17/1) * 65.00 = 26.75 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.88 * (0.17/1) * 65.00 = 17.40 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(28.57, 26.75, 17.40) = 17.40 kips/bolt
Ri vector at Shear Plate   = <0.55, -0.84>
Lcsshpl at Shear Plate spacing  = 2.81 in.
Lceshpl at Shear Plate edge    = 0.75 in.
(phi)Rnsshpl at Shear Plate spacing = (phi) * hf1 * Lcs * t * Fu = 0.75 * 1.20 * 2.81 * 0.25 * 65.00 = 41.04 kips/bolt
(phi)Rneshpl at Shear Plate edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 0.75 * 0.25 * 65.00 = 10.93 kips/bolt
(phi)Rndshpl on Shear Plate at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.88 * 0.25 * 65.00 = 25.59 kips/bolt
Shear Plate bearing capacity, (phi)Rnshpl = min((phi)Rnsshpl,(phi)Rneshpl,(phi)Rndshpl) = min(41.04, 10.93, 25.59) = 10.93 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(17.40, 10.93) = 10.93 kips/bolt
Bolt Shear Demand to Bearing ratio = 10.93 / 23.90 = 0.46

At Row 2, At Column 2:
Ribolt = 22.61 kips
Ri vector at Beam   = <-0.90, -0.43>
Lcsbm at Beam spacing  = 2.87 in.
Lcebm at Beam edge    = 3.89 in.
(phi)Rnsbm at Beam spacing = (phi) * hf1 * Lcs * (tw/# shear planes) * Fu = 0.75 * 1.20 * 2.87 * (0.17/1) * 65.00 = 28.57 kips/bolt
(phi)Rnebm at Beam edge = (phi) * hf1 * Lce * (tw/# shear planes) * Fu = 0.75 * 1.20 * 3.89 * (0.17/1) * 65.00 = 38.73 kips/bolt
(phi)Rndbm on Beam at Bolt Diameter   = (phi) * hf2 * db * (tw/# shear planes) * Fu = 0.75 * 2.40 * 0.88 * (0.17/1) * 65.00 = 17.40 kips/bolt
Beam bearing capacity, (phi)Rnbm = min((phi)Rnsbm,(phi)Rnebm,(phi)Rndbm) = min(28.57, 38.73, 17.40) = 17.40 kips/bolt
Ri vector at Shear Plate   = <0.90, 0.43>
Lcsshpl at Shear Plate spacing  = 2.81 in.
Lceshpl at Shear Plate edge    = 1.28 in.
(phi)Rnsshpl at Shear Plate spacing = (phi) * hf1 * Lcs * t * Fu = 0.75 * 1.20 * 2.81 * 0.25 * 65.00 = 41.04 kips/bolt
(phi)Rneshpl at Shear Plate edge = (phi) * hf1 * Lce * t * Fu = 0.75 * 1.20 * 1.28 * 0.25 * 65.00 = 18.73 kips/bolt
(phi)Rndshpl on Shear Plate at Bolt Diameter   = (phi) * hf2 * db * t * Fu = 0.75 * 2.40 * 0.88 * 0.25 * 65.00 = 25.59 kips/bolt
Shear Plate bearing capacity, (phi)Rnshpl = min((phi)Rnsshpl,(phi)Rneshpl,(phi)Rndshpl) = min(41.04, 18.73, 25.59) = 18.73 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(17.40, 18.73) = 17.40 kips/bolt
Bolt Shear Demand to Bearing ratio = 17.40 / 22.61 = 0.77

Min Bolt Shear Demand to Bearing ratio Beam and Shear Plate for vertical shear only
 = min(1.00, 0.73, 0.77, 0.46, 0.77) = 0.46

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 = 0.46 * 20.53 = 9.39 kips
Rbv = 9.39 kips >= Reaction V = 6.00 kips (OK)

Web Depth = d = 7.89 in.

Using AISC 15th Ed. Equation J4-3
Gross Area (Shear), Agross = [Web Depth] * tw = 7.89 * 0.17 = 1.34 in^2
Shear Yielding, (phi)Vny = (phi) * 0.6 * Fybeam * Agross = 1.00 * 0.6 * 50.00 * 1.34 = 40.24 kips
40.24 kips >= Reaction V = 6.00 kips (OK)

Shear Rupture:
Using AISC 15th Ed. Equation J4-4
Net Area (Shear), Anet = ([Web Depth] - [# rows] * (hole width + 0.06)) * tw 
    = (7.89 - 2 * (0.94 + 0.06)) * 0.17 = 1.00 in^2
Shear Rupture, (phi)Vnu = (phi) * 0.6 * Fubeam * Anet = 0.75 * 0.6 * 65.00 * 1.00 = 29.29 kips
29.29 kips >= Reaction V = 6.00 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 = 0.25 * 5.25 = 1.31 in^2
Shear Yielding, (phi)Vny = (phi) * 0.6 * Fypl * Ag = 1.00 * 0.6 * 50.00 * 1.31 = 39.38 kips
39.38 kips >= Reaction V = 6.00 kips (OK)

Shear Rupture:
Using AISC 15th Ed. Equation J4-4
Net Area, An = (5.25 - (2 * (0.94 + 0.06))) * 0.25 = 0.81 in^2
Shear Rupture, (phi)Vnu = (phi) * 0.6 * Fupl * An = 0.75 * 0.6 * 65.00 * 0.81 = 23.77 kips
23.77 kips >= Reaction V = 6.00 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 = (5.25 - 1.12) = 4.12 in.
Net Shear Length = 4.12 - (2 - 0.5) * (0.94 + 0.06) = 2.62 in.
Gross Tension Length = (3.00 + 1.75) = 4.75 in.
Net Tension Length = 4.75 - (2 - 0.5) * (1.12 + 0.06) = 2.97 in.
1. (phi) * [material thickness] * ((0.60 * Fupl* [net shear length]) + (Ubs * Fupl * [net tension length])) 
    = 0.75 * 0.25 * ((0.60 * 65.00 * 2.62) + (0.50 * 65.00 * 2.97)) = 37.29 kips
2. (phi) * [material thickness] * ((0.60 * Fypl * [gross shear length]) + (Ubs * Fupl * [net tension length])) 
    = 0.75 * 0.25 * ((0.60 * 50.00 * 4.12) + (0.50 * 65.00 * 2.97)) = 41.29 kips
Block Shear = 37.29 kips

Block 2 (Shear): 
Gross Shear Length = 2 * (5.25 - 1.12) = 8.25 in.
Net Shear Length = 2 * ( 4.12 - (2 - 0.5) * (0.94 + 0.06) ) = 5.25 in.
Gross Tension Length = (3.00 + 1.75) - 1.75 = 3.00 in.
Net Tension Length = 3.00 - (2 - 1) * (1.12 + 0.06) = 1.81 in.
1. (phi) * [material thickness] * ((0.60 * Fupl* [net shear length]) + (Ubs * Fupl * [net tension length])) 
    = 0.75 * 0.25 * ((0.60 * 65.00 * 5.25) + (0.50 * 65.00 * 1.81)) = 49.44 kips
2. (phi) * [material thickness] * ((0.60 * Fypl * [gross shear length]) + (Ubs * Fupl * [net tension length])) 
    = 0.75 * 0.25 * ((0.60 * 50.00 * 8.25) + (0.50 * 65.00 * 1.81)) = 57.45 kips
Block Shear = 49.44 kips

Block Shear Total = min(Block Shear (1), Block Shear (2)) = min(37.29,49.44) = 37.29
37.29 kips >= Reaction V = 6.00 kips (OK)

Block Shear for Axial T/C is not required.

Check Flexural Yielding and Rupture:

Eccentricity at first line of bolts, e = 7.74 in.
Zgross = 1.72 in^3
Znet   = 0.97 in^3
Sgross = 1.15 in^3
Snet   = 0.70 in^3
Fypl = 50.00 ksi
Fupl = 65.00 ksi
Mp = Fypl * Zgross = 50.00 * 1.72 = 86.13 kips-in
My = Fypl * Sgross = 50.00 * 1.15 = 57.42 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 * 86.13 / 7.74, 0.90 * 1.6 * 50.00 * 1.15 / 7.74) = 10.02 kips
10.02 kips >= 6.00 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 * 0.97 / 7.74 = 6.13 kips
6.13 kips >= 6.00 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 = 0.25 in.
d = hshpl = 5.25 in.
drect = hshpl = 5.25 in.
dc = down distance (per AISC Example II.A-19B) = 3.00 in.
Lb = horizontal distance to first hole = 7.50 in.
Fypl = 50.00 ksi
Cb = max((3 + ln(Lb / d)) * (1 - dc / d), 1.84) = 
 = max((3 + ln(7.50 / 5.25)) * (1 - 3.00 / 5.25), 1.84) = 1.84
Lb * drect / t^2 = 7.50 * 5.25 / 0.25^2 = 630.00
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 * (7.50 * 5.25 / 0.25^2) * 50.00 / 29000) * 57.42, 86.13)
 = min(129.15, 86.13) = 86.13 kips-in

Flexural Local Buckling Reaction Capacity, (phi)Rn = (phi) * Mn / e = 0.90 * 86.13 / 7.74 = 10.02 kips
10.02 kips >= 6.00 kips (OK)

Interaction Check of Flexural Yielding:
Using AISC 15th Ed. Equation 10-5
Eccentricity at first line of bolts, e = 7.74 in.
Sgross = 1.15 in^3
Zgross = 1.72 in^3
Mr = Vr * e = 6.00 * 7.74 = 46.44 kips-in
Mc = phi * Mn = min(phi * Fypl * Zgross, phi * 1.6 * Fypl * Sgross) = 
 = min(0.90 * 50.00 * 1.72, 0.90 * 1.6 * 50.00 * 1.15) = 77.52 kips-in
Vr = 6.00 kips
Vc = phi * Vn = phi * 0.60 * Fypl * Ag = 1.00 * 0.60 * 50.00 * 1.31 = 39.38 kips
Interaction due to moment and shear, (Vr/Vc)^2 + (Mr/Mc)^2 <= 1.0
(Vr/Vc)^2 + (Mr/Mc)^2 = (6.00 / 39.38)^2 + (46.44 / 77.52)^2 = 0.38
0.38 <= 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 * 5.25 * 0.25^3 / 7.50^2 = 6.19 kips
6.19 kips >= Reaction V = 6.00 kips (OK)

Torsional Strength:
Using Eq. 10 and Eq. 16, Thornton and Fortney 2011 Engineering Journal
Required, Mtu = Ru * (tw + tp) / 2 = 6.00 * ((0.19 + 0.25) / 2) = 1.31 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) - (6.00 / (5.25 * 0.25))] * 5.25 * 0.25^2 / 2 = 4.17 kips-in
4.17 kips-in >= Mtu = 1.31 kips-in (OK)

MAXIMUM PLATE THICKNESS:
No of bolt columns = 2
tp  < = db/2 + 0.06 = 0.25 <= 0.50 OK
tw  < = db/2 + 0.06 = 0.17 <= 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 = 5.25 in.
Shear Load per inch per weld, fv = R/Lv/2 = 6.00 / 5.25 / 2 = 0.57 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) = 0.57 / (0.75 * 1.86) = 0.41/16

Minimum fillet weld size : 
   At shear only load case = 0.03 in.
   per Table J2.4          = 0.12 in.
   5/8tp                   = 0.16 in.
   user preference         = 0.19 in.

Dmax1 (using AISC 15th Ed. eqn 9-3)
 = tshpl * Fushpl / ( Fexx * C1 * 0.09)
 = 0.25 * 65.00 / ( 70.00 * 1.00 * 0.09 ) 
 = 2.63 
Dmax2 (using AISC 15th Ed. eqn 9-3)
 = twbm * Fusupport / ( Fexx * C1 * 0.09 )
 = 0.48 * 65.00 / ( 70.00 * 1.00 * 0.09 ) 
 = 5.04 
Dmax3 = project max fillet weld = 16.00
Dmax=min(Dmax1, Dmax2, Dmax3) = min(2.63, 5.04, 16.00)
 = 2.63 

Use weld size
D1 = 3.00
D2 = 3.00

Weld Strength :

Vertical weld capacity during shear only load, phi * Rnv1 = 0.75 * 1.86 * 5.25 * (2.63 + 2.63) = 38.39 kips

38.39 kips >= Reaction V = 6.00 kips (OK)