| Connection Number: |
bb.s.s.00346.01005 |
| |
| Main Calcs: |
SHEAR PLATE CONNECTION SUMMARY
Filler Beam profile: W8X10
Support Girder profile: W18X86
Slope: 0.00 deg.
Skew: 65.50
Vertical Offset: 0.00 in.
Horizontal Offset: 13.35 in.
Beam Length in Model: 6.35 ft.
Reaction, V: 6.00 kips
Shear Capacity, Rn: 15.32 kips
Design/Reference according to AISC 15th Ed. - LRFD
Shear Plate: Conventional Configuration
Beam material grade: A992
Support material grade: A992
Plate material grade: A572-GR.50
Weld grade: E70
Shear Plate Size: 4.12 in. x 5.25 in. x 0.25 in.
Configuration Geometry:
Welds at shear plate to support: 3/16 FILLET, 5/16 FILLET
Bolt: 2 rows x 1 column 0.88 in. Diameter F1852N_TC bolts
Vertical spacing: 3.00 in.
Horizontal spacing: 3.00 in.
Shear plate edge setback = 0.62 in.
Beam centerline setback = 0.78 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.
Edge distance at top edge of beam: 1.75 in.
Top cope depth: 1.25 in.
Top cope length: 6.00 in.
Horizontal distance to first hole: 2.38 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 Strength Calcs: |
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 = 1.22 in.
Angle = 0.00 deg.
C = 1.52
Using Table 7-1 to determine (phi)rn:
(phi)Rn = (phi)rn * C = 24.35 * 1.52 = 37.14 kips
Total Vertical Bolt Shear Capacity = 37.14 kips
37.14 kips >= Reaction V = 6.00 kips (OK) |
| Bolt Bearing Calcs: |
BOLT BEARING AT BEAM AND SHEAR PLATE SIDE
Vertical Shear Only Load Case:
ICR cordinate relative to CG = (1.85, 0.00)
At Row 1, At Column 1:
Ribolt = 23.90 kips
Ri vector at Beam = <0.63, 0.78>
Lcsbm at Beam spacing = na
Lcebm at Beam edge = 1.75 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 * 1.75 * (0.17/1) * 65.00 = 17.43 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(na, 17.43, 17.40) = 17.40 kips/bolt
Ri vector at Shear Plate = <-0.63, -0.78>
Lcsshpl at Shear Plate spacing = na
Lceshpl at Shear Plate edge = 3.13 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 * 3.13 * 0.25 * 65.00 = 45.74 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(na, 45.74, 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 2, At Column 1:
Ribolt = 23.90 kips
Ri vector at Beam = <-0.63, 0.78>
Lcsbm at Beam spacing = na
Lcebm at Beam edge = 2.28 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 * 2.28 * (0.17/1) * 65.00 = 22.66 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(na, 22.66, 17.40) = 17.40 kips/bolt
Ri vector at Shear Plate = <0.63, -0.78>
Lcsshpl at Shear Plate spacing = na
Lceshpl at Shear Plate edge = 0.80 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 * 0.80 * 0.25 * 65.00 = 11.77 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(na, 11.77, 25.59) = 11.77 kips/bolt
(phi)Rn = min((phi)Rnbm, (phi)Rnshpl) = min(17.40, 11.77) = 11.77 kips/bolt
Bolt Shear Demand to Bearing ratio = 11.77 / 23.90 = 0.49
Min Bolt Shear Demand to Bearing ratio Beam and Shear Plate for vertical shear only
= min(1.00, 0.73, 0.49) = 0.49
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 = 0.49 * 37.14 = 18.28 kips
Rbv = 18.28 kips >= Reaction V = 6.00 kips (OK) |
| Beam Strength Calcs: |
Web Depth = d - [Top Cope Depth] = 7.89 - 1.25 = 6.64 in.
Using AISC 15th Ed. Equation J4-3
Gross Area (Shear), Agross = [Web Depth] * tw = 6.64 * 0.17 = 1.13 in^2
Shear Yielding, (phi)Vny = (phi) * 0.6 * Fybeam * Agross = 1.00 * 0.6 * 50.00 * 1.13 = 33.86 kips
33.86 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
= (6.64 - 2 * (0.94 + 0.06)) * 0.17 = 0.79 in^2
Shear Rupture, (phi)Vnu = (phi) * 0.6 * Fubeam * Anet = 0.75 * 0.6 * 65.00 * 0.79 = 23.07 kips
23.07 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 Shear (1)
Gross Shear Length = [edge dist. at beam edge] + ([# rows - 1] * [spacing]) = 1.75 + (2 - 1) * 3.00 = 4.75 in.
Net Shear Length = Gross Shear Length - (# rows - 0.5) * (hole width + 0.06) = 4.75 - (2 - 0.5) * (0.94 + 0.06) = 3.25 in.
Gross Tension Length = [edge dist. at beam edge] + ([# cols - 1] * [spacing]) = 1.75 + (1 - 1) * 3.00 = 1.75 in.
Net Tension Length = Gross Tension Length - (# cols - 0.5) * (hole length + 0.06) = 1.75 - (1 - 0.5) * (0.94 + 0.06) = 1.25 in.
1. (phi) * [material thickness] * ((0.60 * Fubeam* [net shear length]) + (Ubs * Fubeam * [net tension length]))
= 0.75 * 0.17 * ((0.60 * 65.00 * 3.25) + (1.00 * 65.00 * 1.25)) = 26.52 kips
2. (phi) * [material thickness] * ((0.60 * Fybeam * [gross shear length]) + (Ubs * Fubeam * [net tension length]))
= 0.75 * 0.17 * ((0.60 * 50.00 * 4.75) + (1.00 * 65.00 * 1.25)) = 28.53 kips
Block Shear = 26.52 kips
Block Shear (1) Total = Block Shear (1) = 26.52 kips
26.52 kips >= Reaction V = 6.00 kips (OK)
Block Shear for Axial T/C is not required.
Buckling and Flexure at End of Cope
(Top Cope Only at Section - Using AISC 15th Ed. Equations 9-4 to 9-14, F11-1)
Eccentricity at Section, e = 6.95 in.
tw = 0.17 in.
d = 7.89 in.
dc = 1.25 in.
c = 6.00 in.
ho = d - [Top Cope Depth] = 7.89 - 1.25 = 6.64 in.
Fybeam = 50.00 ksi
Snet1 (bolt holes not applicable) = 1.92 in^3
Snet2 (bolt holes applicable) = 1.92 in^3
Znet1 (bolt holes not applicable) = 3.48 in^3
Znet2 (bolt holes applicable) = 3.48 in^3
Mp = Fybeam * Znet1 = 50.00 * 3.48 = 174.10 kips-in
My = Fybeam * Snet1 = 50.00 * 1.92 = 96.15 kips-in
c/ho = 6.00/6.64 = 0.90
when c/ho <= 1.0, k = 2.2*(ho/c)^1.65 = 2.2*(6.64/6.00)^1.65 = 2.60
c/d = 6.00/7.89 = 0.76
when c/d <= 1.0, f = 2*(c/d) = 2*(6.00/7.89) = 1.52
k1 = max(f*k,1.61) = max(1.52*2.60,1.61) = 3.96
web slenderness, lambda = ho/tw = 6.64/0.17 = 39.06
limiting slenderness for compact web, lambdap = 0.475 * (k1 * E / Fybeam)^0.5 = 0.475 * (3.96 * 29000 / 50.00)^0.5 = 22.75
When lambdap < lambda <= 2*lambdap, then Mn = Mp - (Mp - My) * (lambda/lambdap - 1)
= 174.10 - (174.10 - 96.15) * (39.06/22.75 - 1) = 118.22 kips-in
Flexural Local Buckling Reaction Capacity, (phi)Rn = (phi) * Mn / e = 0.90 * 118.22 / 6.95 = 15.32 kips
Flexural Yielding using AISC 15th Ed. Equation F11-1
Reaction Capacity, (phi)Rn = min((phi) * Mp / e, (phi) * 1.6 * Fybeam * Snet1 / e) =
= min(0.90 * 174.10 / 6.95, 0.90 * 1.6 * 50.00 * 1.92 / 6.95) = 19.93 kips
Flexural Rupture using AISC 15th Ed. Equation 9-4
Reaction Capacity, (phi)Rn = (phi)Mn / e = (phi) * Fubeam * Znet2 / e =
= 0.75 * 65.00 * 3.48 / 6.95 = 24.44 kips
Buckling and Flexure at Furthest Bolt Line within Cope
(Top Cope Only at Section - Using AISC 15th Ed. Equations 9-4 to 9-14, F11-1)
Eccentricity at Section, e = 2.70 in.
tw = 0.17 in.
d = 7.89 in.
dc = 1.25 in.
c = 6.00 in.
ho = d - [Top Cope Depth] = 7.89 - 1.25 = 6.64 in.
Fybeam = 50.00 ksi
Snet1 (bolt holes not applicable) = 1.92 in^3
Snet2 (bolt holes applicable) = 1.49 in^3
Znet1 (bolt holes not applicable) = 3.48 in^3
Znet2 (bolt holes applicable) = 2.52 in^3
Mp = Fybeam * Znet1 = 50.00 * 3.48 = 174.10 kips-in
My = Fybeam * Snet1 = 50.00 * 1.92 = 96.15 kips-in
c/ho = 6.00/6.64 = 0.90
when c/ho <= 1.0, k = 2.2*(ho/c)^1.65 = 2.2*(6.64/6.00)^1.65 = 2.60
c/d = 6.00/7.89 = 0.76
when c/d <= 1.0, f = 2*(c/d) = 2*(6.00/7.89) = 1.52
k1 = max(f*k,1.61) = max(1.52*2.60,1.61) = 3.96
web slenderness, lambda = ho/tw = 6.64/0.17 = 39.06
limiting slenderness for compact web, lambdap = 0.475 * (k1 * E / Fybeam)^0.5 = 0.475 * (3.96 * 29000 / 50.00)^0.5 = 22.75
When lambdap < lambda <= 2*lambdap, then Mn = Mp - (Mp - My) * (lambda/lambdap - 1)
= 174.10 - (174.10 - 96.15) * (39.06/22.75 - 1) = 118.22 kips-in
Flexural Local Buckling Reaction Capacity, (phi)Rn = (phi) * Mn / e = 0.90 * 118.22 / 2.70 = 39.47 kips
Flexural Yielding using AISC 15th Ed. Equation F11-1
Reaction Capacity, (phi)Rn = min((phi) * Mp / e, (phi) * 1.6 * Fybeam * Snet1 / e) =
= min(0.90 * 174.10 / 2.70, 0.90 * 1.6 * 50.00 * 1.92 / 2.70) = 51.36 kips
Flexural Rupture using AISC 15th Ed. Equation 9-4
Reaction Capacity, (phi)Rn = (phi)Mn / e = (phi) * Fubeam * Znet2 / e =
= 0.75 * 65.00 * 2.52 / 2.70 = 45.56 kips
Section Bending Strength Calculations Summary:
Buckling : 15.32 kips >= 6.00 kips (OK)
Flexural Yielding : 19.93 kips >= 6.00 kips (OK)
Flexural Rupture : 24.44 kips >= 6.00 kips (OK)
Buckling : 39.47 kips >= 6.00 kips (OK)
Flexural Yielding : 51.36 kips >= 6.00 kips (OK)
Flexural Rupture : 45.56 kips >= 6.00 kips (OK) |
| Shear Plate Calcs: |
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 = (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 * 0.25 * ((0.60 * 65.00 * 2.62) + (1.00 * 65.00 * 1.16)) = 33.29 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) + (1.00 * 65.00 * 1.16)) = 37.30 kips
Block Shear = 33.29 kips
33.29 kips >= Reaction V = 6.00 kips (OK)
Block Shear for Axial T/C is not required.
Check Flexural Yielding and Rupture:
Eccentricity due to Conventional Config. (e = a/2), e = 1.22 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 / 1.22, 0.90 * 1.6 * 50.00 * 1.15 / 1.22) = 63.75 kips
63.75 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 / 1.22 = 39.00 kips
39.00 kips >= 6.00 kips (OK)
Interaction Check of Flexural Yielding:
Using AISC 15th Ed. Equation 10-5
Eccentricity due to Conventional Config. (e = a/2), e = 1.22 in.
Sgross = 1.15 in^3
Zgross = 1.72 in^3
Mr = Vr * e = 6.00 * 1.22 = 7.30 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 + (7.30 / 77.52)^2 = 0.03
0.03 <= 1.00 (OK)
MAXIMUM PLATE THICKNESS:
No of columns = 1
Distance cl top to cl bot bolts <= 12" (Equivalent depth of n = 1 to 5 at 3", AISC 15th Ed. Table 10-9)
Slot shape = SSL
tmax = Unlimited
Maximum Plate Thickness is Not a Limiting Criteria. |
| Weld Calcs: |
Plate Thickness, tshpl = 0.25 in.
Skew = 65.50 deg.
Dihedral Angle, DA = Skew = 65.50 deg.
Gap on Obtuse Angle Side Without Shear Plate Bevel = 0.10 in., 0.19 in. >= 0.10 in. >= 0.06 in., account for gap in weld size
Weld Length for shear, Lv = 5.25 in.
Minimum weld sizes:
Acute Side Weld per Table J2.4 = 0.12 in.
Obtuse Side Weld per Table J2.4 = 0.12 in.
Per User Preference = 0.19 in.
Per 5/8*tshpl:
Required Effective Throat (Square Case), teff = 5/8 * tshpl * 2^0.5/2 = 0.62 * 0.25 * 2^0.5/2 = 0.11 in.
Required Acute Side Weld, treqa = (teff/cos(DA/2)) * sin(DA) = (0.11 / cos(65.50/2)) * sin(65.50) = 0.12 in.
Required Obtuse Side Weld, treqo = ((teff/sin(DA/2)) + tshpl/tan(DA)) * sin(DA) = ((0.11 / sin(65.50/2)) + 0.25/tan(65.50)) * sin(65.50) = 0.29 in.
Weld design size:
Acute Side Weld, D1 = max(Table J2.4 Min, User Pref Min, treqa) = max(0.12, 0.19, 0.12) = RoundUp(0.19) = 0.19 in., USE D1 = 3.00
Acute Side Effective Throat, teffa = ((D1/16)/sin(DA)) * cos(DA/2) = ((3.00/16) / sin(65.50)) * cos(65.50/2) = 0.17 in. >= 0.11 in. (OK)
Obtuse Side Weld, D2 = max(Table J2.4, User Pref Min, treqo) = max(0.12, 0.19, 0.29) = RoundUp(0.29) = 0.31 in., USE D2 = 5.00
(Weld size increased on obtuse side for gap at skew per AWS D1.1/D1.1M (2015, p.511, C-5.21.1))
Obtuse Side Effective throat, teffo = ((D2/16)/sin(DA) - tshpl/tan(DA)) * sin(DA/2)
= ((5.00/16)/sin(65.50) - 0.25/tan(65.50)) * sin(65.50/2) = 0.12 in. >= 0.11 in. (OK)
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
Maximum effective throat, tmax = 2.63/16 * 2^0.5/2 = 0.12 in.
Weld Strength:
Vertical weld capacity during shear only load:
theta = 0 deg.
cPhi = 1.0 + 0.5 * sin(theta)^1.5 = 1.0 + 0.5 * sin(0.00)^1.5 = 1.00
(phi) * Rnv1 = (phi) * 0.60 * Fexx * cPhi * C1 * Lv * (min(teffa, tmax) + min(teffo, tmax))
= 0.75 * 0.60 * 70.00 * 1.00 * 1.00 * 5.25 * (min(0.17,0.12) + min(0.12,0.12)) = 38.39 kips
38.39 kips >= Reaction V = 6.00 kips (OK) |
