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Calculation Cover Sheet and Design Check DocumentationSection: (Structural/MECS/Civil)

Number of pages Including Cover Sheet

Cecily Nolan

Tainter Gate design calculations and SAP model (excluding trunnion assembly)

Assigned Checker:

Additional Information: I reviewed the Plans, Specifications, and DDR as well.Chris Abela

Project Name:

Designer/Originator(of calculations):

Fargo Inlet Diversion Structure Date:

File Location:

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rmat

ion

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MVP ‐ Design Branch


Number of pages Including Cover

Sheet

Cheuk Wan

Tainter gate trunnion assembly design calculations and SAP model

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Additional Information: I reviewed the Plans, Specifications, and DDR as well.

Chris Abela

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Fargo Inlet Diversion Structure Date:

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Michele Louie

Tainter gate trunnion transition hub design calculations and SAP Model

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FMM Inlet Diversion Structure Date:

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CALCULATION COVER SHEET

Element: Friction Calculation for SAP2000 Model Iterations

Labor Code: 2686C1

Calculation Title: Friction and Misc. Calcs for SAP2000 Models & Load Cases

Total Number of Pages (including cover sheet): 120

Prepared by: Chris Abela PE Date: 2-22-2016

Checked by: Cecily Nolan PE Date: 2-22-2016

Design Basis/References/Assumptions: - ACI 318-14 -EM 1110-2-584 Design of Hydraulic Steel Structures -EM 1110-2-2702 Design of Spillway Tainter Gates - AISC 14th Ed.

Rev. No.

Description of Revision:

Prepared by:

Date:

Checked by:

Date:

Sheet Index:

1-2

3-13

14-26

26

27

28-29

Side Seal Calculation for SAP Models

Wire Rope Pressure for SAP2000 Models

Trunnion Friction Calculation for SAP2000 Models

Ice and Wave Impact Load Inputs

Trunnion Assembly Moment Couples for SAP2000 Model

Side Bumper Loads and Bumper Friction Force

FARGO DIVERSION INLET TAINTER ANALYSIS

Friction & Misc. Calcs for SAP 2000 Models Load Cases

Analysis By: Chris Abela PEDate:2/22/2016

Checked By: Cecily Nolan PEDate:2/22/2016

Side Seal Friction See ETL 1110-2-584

28'-6.3080"

El. 922 (H.1 H.2)

El. 925.7 (TOG)

El. 899.7 (BOG)

24'-9.0708"

Seal calculationsbased on 4313 or4314

1 of 29





Variables

E 900psi (Modulus of elasticity, per Seals Unlimited Catalog)

bs 12in (Unit length of seal, 12")

hs 1in (Thickness of seal between plates, see figure)

Ibs hs

3

121 in

4 (Moment of inertia of seal along axis of bending)

δps 0.25in (Preset of seal, assumed preset)

dex 2.25in (Width of seal exposed to upper pool hydrostatic pressure)

Ss

3 δps E I

dex3

1 ft

59.259lbf

ft (Force per unit length induced by presetting the seal ,ETL 1110-2-584, Eq. D-1, based on 3EI/h^3)

μs 0.75 (Coefficient of side seal friction, see EM 1110-2-2702, recommendation is 0.5,manufacturer recommendation is 1.0, value selected is based on the average of thetwo.)l0 342.31in (Total length of the side seal,)

l124.76ft

24.76ft

(See figure above, length of the side seal from the headwater to the bottom ofthe seal for H.1 & H.2)

hw22.3ft

22.3ft

γw 62.5pcf (Unit weight ofwater)

Fs μs Ss l0 μs γwdex

2

l1

hw

2

2.481

2.481

kip (ETL 1110-2-584, Eq. D-1, total side seal friction forceper side of gate)

SAPshl.width 6in (Shell Width in SAP)

Fs.sap

Fs

l0 SAPshl.width

173.95

173.95

psf (Input into SAP 2000 model to account for side sealfriction)

2 of 29





LC2b Rib and Skin Plate Wire Rope Pressure (Ice Impact), FactoredLoading Layout for LC2b Ice

28'-6.3080"

El. 922 (H.1 H.2)

El. 925.7 (TOG)

El. 899.7 (BOG)

25'-8.5116"

Wire Rope Loads

Qrp_pr 33kip Rope tension force from SAP2000, Equal Loading

Rgate 26ft Radius of gate

Wwire

Qrp_pr

Rgate 1.0 ft1.269 ksf Tributary wire rope pressure for SAP 2000 model, trib section consists of (2) 6in shell

elements

3 of 29





LC2b Rib and Skin Plate Wire Rope Pressure (Ice Impact), UnfactoredLoading Layout for LC2b Ice

28'-6.3080"

El. 922 (H.1 H.2)

El. 925.7 (TOG)

El. 899.7 (BOG)

25'-8.5116"

Wire Rope Loads



Wwire

Qrp_pr


elements

4 of 29





LC2b Rib and Skin Plate Wire Rope Pressure (Wave), FactoredLoading Layout for LC2b, Wave

28'-6.3080"

El. 922 (H.1 H.2)

El. 925.7 (TOG)

El. 899.7 (BOG)

25'-8.5116"

Wire Rope Loads



Wwire

Qrp_pr


elements

5 of 29





LC2b Rib and Skin Plate Wire Rope Pressure (Wave), UnfactoredLoading Layout for LC2b, Wave

28'-6.3080"

El. 922 (H.1 H.2)

El. 925.7 (TOG)

El. 899.7 (BOG)

25'-8.5116"

Wire Rope Loads



Wwire

Qrp_pr


elements

6 of 29





LC2c Rib and Skin Plate Wire Rope Pressure Factored

28'-6.3080"

El. 922 (H.1 H.2)

El. 925.7 (TOG)

El. 899.7 (BOG)

25'-8.5116"

Wire Rope Loads

Qrp_pr.lc2cF 54.04kip Rope tension force from SAP2000, Equal Loading


Wwire

Qrp_pr.lc2cF


elements

7 of 29





LC2c Rib and Skin Plate Wire Rope Pressure Unfactored

28'-6.3080"

El. 922 (H.1 H.2)

El. 925.7 (TOG)

El. 899.7 (BOG)

25'-8.5116"

Wire Rope Loads

Qrp_pr.lc2cU 44.1kip Rope tension force from SAP2000, Equal Loading


Wwire

Qrp_pr.lc2cU


elements

8 of 29





LC2d Rib and Skin Plate Wire Rope Pressure FactoredLoading Layout for LC2d, trial run

28'-6.3080"

El. 922 (H.1 H.2)

El. 925.7 (TOG)

El. 899.7 (BOG)

25'-8.5116"

Wire Rope Loads

Qrp_pr.lc2cF 45kip Rope tension force from SAP2000, Equal Loading


Wwire

Qrp_pr.lc2cF


elements

9 of 29





LC2d Rib and Skin Plate Wire Rope Pressure UnfactoredLoading Layout for LC2d, trial

28'-6.3080"

El. 922 (H.1 H.2)

El. 925.7 (TOG)

El. 899.7 (BOG)

25'-8.5116"

Wire Rope Loads

Qrp_pr.lc2cU 38kip Rope tension force from SAP2000, Equal Loading


Wwire

Qrp_pr.lc2cU


elements

10 of 29





LC3 Rib and Skin Plate Wire Rope Pressure FactoredLoading Layout for LC3

28'-6.3080"

El. 922 (H.1 H.2)

El. 925.7 (TOG)

El. 899.7 (BOG)

25'-8.5116"

Wire Rope Loads

Qrp_pr 180kip Rope tension force from SAP2000, single sideLoading


Wwire

Qrp_pr


elements

11 of 29





LC3 Rib and Skin Plate Wire Rope Pressure UnfactoredLoading Layout for LC3

28'-6.3080"

El. 922 (H.1 H.2)

El. 925.7 (TOG)

El. 899.7 (BOG)

25'-8.5116"

Wire Rope Loads

Qrp_pr 132kip Rope tension force from SAP2000, single side Loading


Wwire

Qrp_pr


elements

12 of 29





LC5 Rib and Skin Plate Wire Rope Pressure UnfactoredLoading Layout for LC3

28'-6.3080"

El. 922 (H.1 H.2)

El. 925.7 (TOG)

El. 899.7 (BOG)

25'-8.5116"

Wire Rope Loads

Qstl.tqe 2 Qrp_pr.lc2cU 225 % 171 kip Rope tension force from Stall Torque of Motor


Wwire

Qstl.tqe


elements

13 of 29





LC2b Trunnion Friction for H2 @ 922 & Ice Impact Load (Factored) See ETL 1110-2-584 p. 3-15

dpin 15.5in (Diameter of trunnion pin)

dhub 21in (Centerline diameter of hub)

μpin 0.3 (Coefficient of friction, see ETL 1110-2-584)

rp dpin 0.5 7.75 in (Moment arm from center of pin to contact surface between bushingand pin)

ru dhub 0.5 10.5 in (Moment arm from center of pin to center contact surface between hub andyolk plate)

R1.1 759kip (Resultant force from SAP in X direction)

R1.2 283kip (Resultant force from SAP in Z direction)

R1 R1.12

R1.22

810.043 kip (Resultant force in SAP XZ direction)

MFt.1 R1 μpin rp 156.946 kip ft (Moment acting on pin from SAP XZ forces)

R2 323kip (Resultant force from SAP in Ydirection)

MFt.2 R2 μpin ru 84.787 kip ft (Moment acting on pin from SAP Yforce)

14 of 29





MFt.tot MFt.1 MFt.2 241.733 kip ft (Friction moment to be inputted into SAP 2000model)

LC2b Trunnion Friction for H2 @ 922 & Ice Impact Load (Unfactored) See ETL 1110-2-584 p. 3-15








R1 R1.12

R1.22





15 of 29






LC2b Trunnion Friction for H2 @ 922 & Wave Loads Factored See ETL 1110-2-584 p. 3-15

dpin 15.5in (Diameter of trunnionpin)

dhub 21in (Centerline diameter ofhub)






R1 R1.12

R1.22





16 of 29






LC2b Trunnion Friction for H2 @ 922 & Wave Loads Unfactored See ETL 1110-2-584 p. 3-15








R1 R1.12

R1.22





17 of 29






LC2c Trunnion Friction for H2 @ 922 & Factored See ETL 1110-2-584 p. 3-15








R1 R1.12

R1.22





18 of 29





MFt.tot MFt.1 MFt.2 190.302 kip ft (Friction moment to be inputted into SAP 2000 model)

LC2c Trunnion Friction for H2 @ 922 & Unfactored See ETL 1110-2-584 p. 3-15



μpin 0.3 (Coefficient of friction, see ETL1110-2-584)





R1 R1.12

R1.22





19 of 29






LC2d Trunnion Friction for Trial Operation of Gate Factored See ETL 1110-2-584 p. 3-15






R1.1 15.3kip (Resultant force from SAP in X direction)

R1.2 8.8kip (Resultant force from SAP in Z direction)

R1 R1.12

R1.22





20 of 29






LC2d Trunnion Friction for for Trial Operation of Gate Unfactored See ETL 1110-2-584 p. 3-15



μpin 0.3 (Coefficient of friction, see ETL1110-2-584)




R1.2 7.3kip (Resultant force from SAP in Z direction)

R1 R1.12

R1.22



R2 3.5kip (Resultant force from SAP in Ydirection)


21 of 29






LC3 Trunnion Friction Left Side Factored See ETL 1110-2-584 p. 3-15








R1 R1.12

R1.22





22 of 29






LC3 Trunnion Friction Right Side Factored See ETL 1110-2-584 p. 3-15








R1 R1.12

R1.22



R2 223kip (Resultant force from SAP in Y direction)

MFt.2 R2 μpin ru 58.537 kip ft (Moment acting on pin from SAP Y force)

23 of 29






LC3 Trunnion Friction Left Side Unfactored See ETL 1110-2-584 p. 3-15




rp dpin 0.5 7.75 in (Moment arm from center of pin to contact surface between bushing and pin)

ru dhub 0.5 10.5 in (Moment arm from center of pin to center contact surface between hub and yolk plate)



R1 R1.12

R1.22





24 of 29






LC3 Trunnion Friction Right Side Unfactored See ETL 1110-2-584 p. 3-15








R1 R1.12

R1.22





25 of 29






Ice Impact Load

Iceim 5kip

ft ETL 1110-2-584, section D.2.4, Ice

SAP2000Ice

Iceim 6 in

ft2.5

kip

ft Note shells of skin plate on SAP2000 are spaced 6 inches apart

Icethk 2in Thickness of ice (assumed), provided by St. Paul PDT member (Kent Hokens)

Struttrib 12in Strut is a W12x106

Girdertrib 27in Girder is W27x161

SAP2000Ice.dead.strt γw Icethk Struttrib 10.417lbf

ft Loading on framing members

SAP2000Ice.dead.grdr γw Icethk Girdertrib 23.438lbf

ft Loading on framing members

Wave LoadsPDF provided by Kent regarding Wave loading pressure P.1, P.2,and P.3

26 of 29





Trunnion Assembly Moment Couples Loads UnfactoredBecause the trunnion assembly was modeled as a solid in SAP2000, joints within the model can only be assigned translational forcesand not rotational forces. Therefore, it is necessary to break the bending moment along the z-axis into force couples for both the leftand right side yoke plates. These force couples will be added into the model within the pin that is supported by the two yoke plates.

Fcpl.LC12.156kip ft

2.375ft0.908 kip

Fcpl.LC2.Ice83.58 kip ft

2.375ft35.192 kip All bending moment values were taken from the

Trunnion Assembly reaction table in the DDR(unfactored), which is derived from the SAP2000 Taintergate models. Please note that when applying theseloads into the SAP2000 model the values will need to bereversed in order to represent demands and notreactions.

Fcpl.LC325.86kip ft

2.375ft10.888 kip

Fcpl.LC531.09 kip ft

2.375ft13.091 kip

27 of 29





LC 3 Side Bumper Loads and Friction Calc. FactoredThis calculation determins the friction forces that will be applied to the contact points within the SAP2000 Model.

R.bpl

R.bprDyn.frc.l

Dyn.frc.r

Demands

Rbpr 258kip Max axial loading on bumber, LC3 andLC5

Rbpl 172kip

Frtn 0.15 Coefficient of friction between bumper and embed plate

Fvr Rbpr Frtn 38.7 kip Shear demand acting on bumper bolts from dynamic friction / drag rightside

Fvl Rbpl Frtn 25.8 kip Shear demand acting on bumper bolts from dynamic friction / drag leftside

Model was only able to converge with a friciton coefficient of 0.15 for the bumper. At higher friction values the wire rope exceeds thestall torque of the motor. Convergence of the model is within 5% of all iterated values, bumper, trunnion friction, and wire rope.

28 of 29





LC 3 Side Bumper Loads and Friction Calc. UnfactoredThis calculation determins the friction forces that will be applied to the contact points within the SAP2000 Model.

R.bpl

R.bprDyn.frc.l

Dyn.frc.r

Demands

Rbpr 164kip Max axial loading on bumber, LC3

Rbpl 98kip

Frtn 0.15 Coefficient of friction between bumper and embed plate

Fvr Rbpr Frtn 24.6 kip Shear demand acting on bumper bolts from dynamic friction / drag rightside


Model was only able to converge with a friciton coefficient of 0.15 for the bumper. At higher friction values the wire rope exceeds thestall torque of the motor. Convergence of the model is within 5% of all iterated values, bumper, trunnion friction, and wire rope.

29 of 29


Element: Strut Arm and Boundary Condition Verification

Labor Code: 2686C1

Calculation Title: Combined Axial and Bending Check in Strut Arm & Boundary Condition Check of 3D SAP Models





Rev. No.


Prepared by:

Date:

Checked by:

Date:

Sheet Index:

1-6

7

Strut Arm Verification Check

Wire Rope Pressure for SAP2000 Models

FARGO TAINTER GATE ANALYSIS

Combined Axial and Bending Check in Strut Arm & Boundary Condition Check of 3D SAP Models



Strut Arm Checks LC2b_Ice See ETL 1110-2-584

Top Strut Axial Force Capacity (W12X106)

Ag.s1 31.2in2

(Area of wide flange, AISC 14th Ed )

Fy 50ksi (Yield point, see Section II sec. 1.1 Steel shapes)

Ks1 1 (Effective length factor, AISC 13 th Ed, Based on Direct Analysis Method, K=1.0, see p. 16.1-196.)

Ls1y 0.5 20.99 ft (Maximum unbraced length of top strut in weak axis direction, coefficients from SAP)

Ls1z 20.99ft (Maximum unbraced length of top strut in strong axis direction, coefficients from SAP)

ry.s1 3.11in (Radius of gyration along weakaxis)

rz.s1 5.47in (Radius of gyration along strongaxis)

Es 29000ksi (Modulus of elasticity)

1 of 7





Iy 301in4

(Moment of inertia along weak axis)

Iz 933in4

(Moment of inertia along strongaxis)

ϕc 0.9 (Strength reduction factor, compression members, AISC 13th Ed. p. 16.1-32)

Fe.s1y

π2

Es

Ks1 Ls1y

ry.s1

2174.538 ksi

Fcr.s1y 0.658

Fy

Fe.s1y

Fy

Ks1 Ls1y

ry.s14.71

Es

Fyif

0.877 Fe.s1y otherwise

44.35 ksi

Pny Fcr.s1y Ag.s1 1383.731 kip (Axial load capacity along y axis)

Fe.s1z

π2

Es

Ks1 Ls1z

rz.s1

2134.985 ksi

Fcr.s1z 0.658

Fy

Fe.s1z

Fy

Ks1 Ls1z

rz.s14.71

Es

Fyif

0.877 Fe.s1z otherwise

42.819 ksi

Pnz Fcr.s1z Ag.s1 1335.96 kip (Axial load capacity along zaxis)

ϕPn min ϕc Pny ϕc Pnz 1202.364 kip

2 of 7





Top Strut Moment Capacity ( W12X106 )Lb.1y Ls1y (Unbraced length)

Lb.1z Ls1z (Unbraced length)

ry ry.s1 3.11 in (Radius ofgyration)

Lp.1 1.76 ryEs

Fy 10.985 ft (AISC 13th Ed. Eq.

F2-5)

rts 3.49in (AISC 13th Ed., ref. W12X96)

Jwf 6.85in4

(Torsinal constant,ref. W12X96)

ho 11.8in (Torsinal constant,ref. W12X96)

Cw 9410in6

(Torsinal constant,ref. W12X96)

cwf 1 (AISC 13th Ed. Eq.F2-8a)

Sz 131in3

(Section modulus, AISC 13th Ed. & AISC Shape database)

Sy 44.4in3

(Section modulus, AISC 13th Ed. & AISC Shape database)

Lr.1z 1.95 rtsEs

0.7 Fy

Jwf cwf

Sz ho 1 1 6.76

0.7 Fy Sz ho

Es Jwf cwf

2

46.663 ft (AISC 13th Ed. eq.F2-6)

Zz 147in3

(Plastic modulus, AISC 13th Ed. p. 3-17, ref. W12X96)

Zy 67.5in3

(Plastic modulus, AISC 13th Ed. p. 3-17, ref. W12X96)

ϕb 0.9 (Bending moment reduction factor, AISC 13th Ed. p. 16.1-16)

3 of 7





Compactness Check (Flange)

bf 6.1in (Width of flange)

tf 0.99in (Thicness of flange)

λ "Flange Compact"bf

tf0.38

Es

Fyif

"Flange Noncompact" 0.38Es

Fy

bf

tf 1.0

Es

Fyif

"See AISC" otherwise

"Flange Compact"

(AISC 13th Ed. p. 16.1-16 Case1)

Compactness Check (Web)

hw 9.125in (Height ofweb)

tw 0.61in (Thickness ofweb)

λ2 "Web Compact"hw

tw3.76

Es

Fyif

"Web Noncompact" 3.76Es

Fy

hw

tw 5.70

Es

Fyif

"See AISC" otherwise

"Web Compact"(AISC 13th Ed. p. 16.1-16 Case 9)

Find Controlling Moment Capacity Value (Weak Axis in bending) CHECK COMPACTNESS!

Mpy min Fy Zy 1.6 Fy Sy 281.25 kip ft (AISC 13th Ed. eq. F6-1)

Mny Mpy Mpy 0.7 Fy Sy

bf

tf0.38

Es

Fy

1.0Es

Fy0.38

Es

Fy

311.637 kip ft (AISC 13th Ed. eq. F6-2)

ϕMny min ϕb Mpy ϕb Mny 253.125 kip ft

4 of 7





Find Controlling Moment Capacity Value (Strong Axis in Bending)

Find C.b

Ma1z 31.70 kip ft (Moment value from SAP 2000 model, top strut @ quarter lengthof strut fromtrunnion pin)

Mb1z 30.60 kip ft (Moment value from SAP 2000 model, top strut @ half the total length of strut fromtrunnion pin)

Mc1z 19.79 kip ft (Moment value from SAP 2000 model, top strut @ three quarter length of strut fromtrunnion pin)

Mmax.z 32.95 kip ft (Maximum moment in strut armsection)

Rm 1.0 (AISC 13th Ed. p. 16.1-46, doubly symmetric member)

Cb.1z min 3.012.5 Mmax.z

2.5 Mmax.z 3 Ma1z 4 Mb1z 3 Mc1zRm

1.147

Mpz Fy Zz 612.5 kip ft

Mn1z Cb.1z Mpz Mpz 0.7 Fy Sz Lb.1z Lp.1

Lr.1z Lp.1

628.153 kip ft

Mr1z

Cb.1z π2

Es

Lb.1z

rts

21 0.078

Jwf cwf

Sz ho

Lb.1z

rts

2

Sz 1150.895 kip ft

ϕMnz ϕb Mpz Lb.1z Lp.1if

ϕb Mn1z Lp.1 Lb.1z Lr.1z Mn1z Mpzif

min ϕb Mr1z ϕb Mpz otherwise

551.25 kip ft

Top Strut Combine Axial and Moment Capacity Check (WF14x10 or 14WF74)Pr1 635.87kip (Axial force from SAP 2000 model, top strut left side facing

downstream)

Mry 108.47kip ft (Moment demand in y direction from SAP 2000 model, top strut left side facing downstream, Minor)

Mrz 53.41kip ft (Moment demand along z axis from SAP2000 model, top strut left side facing downstream, Major)

DCRPr1

ϕPn

8

9

Mry

ϕMny

Mrz

ϕMnz

Pr1

ϕPn0.2if

Pr1

2ϕPn

Mry

ϕMny

Mrz

ϕMnz

otherwise

0.9959

5 of 7





Hand Calc to SAP2000 Comparison

SAPDCR 0.953 (Results from SAP 2000 Interaction Equation)

DCR

SAPDCR1

4.5 % (Percent difference between hand method andSAP2000)

Check "OK"DCR

SAPDCR1

5%if

"Redesign" otherwise

"OK"

6 of 7





Reactions @ Boundary Conditions from Water Loading Verificaiton Calc.Gtwidth 50ft Overall gate sealing width

Gtheight 26ft Overall gate sealing height

γw 62.4pcf Unit weight of water

Ds 80.4 in Difference between the elvations of the center of curvature of skin plate and top seal

Di 231.6in Difference between the elevations of the center of curvature of skin plate and the sill

Dm 36in Difference between the elevations of the water level and the center of curvature of the skin plate

Rgt 26ft Radius of gate

H1 22.3ft Heighest estimated waterlevel

αs asinDs

Rgt

0.261

αi asinDi

Rgt

0.837

Fh.1 γw Gtwidth Gtheight H1

Gtheight

2

754.416 kip Hydrostatic horizontal force

Fv.1 γw Gtwidth Rgt Dm cos αs cos αi Rgt αi αs

2

Rgt sin αs cos αs sin αi cos αi

2

417.416 kip

Hydrostaticvertical forceFh.SAP 360kip 360kip 720 kip

LC1 from SAP2000 model,horizontal and vertical reactions Vertical Force Design of

Hydraulic Gates, p. 105 Eq.4.16

Fv.SAP 197kip 197kip 394 kip

Hand Calc to SAP2000 Comparison

Fh.1

Fh.SAP1

4.78 %

(Percent difference between hand method andSAP2000)Fv.1

Fv.SAP1

5.943 %

Percent difference is acceptable

7 of 7


Element: Stiffeners, Gusset Plates, Lifting Lug, Sill Beam, Reinf. Embed, Strut Arm Web Shear, Bumper Design

Labor Code: 2686C1

Calculation Title: Stiffener Eval. Chks. Lifting Lug, Brace Coonnection Eval., Gusset Pl Chks





Rev. No.


Prepared by:

Date:

Checked by:

Date:

Sheet Index:

1-4

5-7

8-14

15-19

20-22

23

24-28

29-31

Horizontal Girder Stiffener Plate Checks

Stiffener Design Check for Ribs Loaded with Wire Rope

Lifting Lug Design Checks

Downstream Truss Gusset Plate Connection Checks

Seal Beam Embed Anchor Check for Surcharge Loading

Strut Arm Web Shear Check W12x106

Bumper Design Checks

Headed Reinforcement Development Checks for Blockouts

FARGO TAINTER GATE CONNECTION AND MISC. COMP.

CHECKS

Stiffener Eval.Chks, Lifting Lug Eval.n, Brace Connection Eval., Gusset Pl Chks



Horizontal Girder Stiffener Plate Checks See ETL 1110-2-584

?

Stiffener Design Evaluation@ Strut Arm to Girder

Stiffener Design Evaluationfor Ribs Loaded with Wire Rope Pressure

Tainter Gate BumpterDesign Check

1 of 31


CHECKS




Stiffener Design Checks @ Strut Arm To Girder AISC 14th Ed. J10.8

2'-1.4400"

2.0000"

6.1400"P

1'-11.4400"

1'-2.1950"

Area: 34.6104 sq inPerimeter: 75.2600 inBounding box: X: -11.7200 -- 11.7200 in Y: -7.0150 -- 7.1750 inCentroid: X: 0.0000 in Y: 0.0800 inMoments of inertia: X: 239.7343 sq in sq in Y: 977.7432 sq in sq inProduct of inertia: XY: 0.0000 sq in sq inRadii of gyration: X: 2.6319 in Y: 5.3151 inPrincipal moments (sq in sq in) and X-Y directions about centroid: I: 239.5128 along [1.0000 0.0000] J: 977.7432 along [0.0000 1.0000]

Pstif.dmd.1 592kip Axial load demand from SAP2000 modelLC3Bending moment from strut arm acting with axial load, 12.9" is the spacingbetween the strut flanges to determine the force couple. Pstif.dmd.2

150kip ft

12.9in139.535 kip

Pstif.dmd Pstif.dmd.1 0.5 Pstif.dmd.2 435.535 kip Worst case axial load acting on bearing stiffener transferring strut armaxial and compression bending moment couple to girder. Please note thatthe axial load was split between the other stiffener. Column Stability Check

tstiff 1in Stiffener thickness

hstiff 6.14in Height of stiffener

twb.grdr 0.9375in Web thickness

Wh 23.625in Height ofweb

Ae 25 twb.grdr twb.grdr 2tstiff hstiff 34.253 in2

Effective area of column, see AISC 14th Ed. sectionJ10.8

KLef 0.75 Wh K=0.75, AISC 14th Ed. Section J10.8

Minimum radius of gyration (I.x/Area)^1/2,inertia provided above.rx

239.73in4

Ae2.646 in

2 of 31


CHECKS




Es 29000ksi Modulus of Elasticity

Fy.sec 50ksi Yield stress of section

ϕc 0.9 Strength reductionfactor

hstiff

tstiff0.59

Es

Fy.sec 1 Compactness check for single stiffener, AISC 14th Ed . Table B4.1a, Member is

Compact

Fe.grdr

π2

Es

KLef

rx

26380.573 ksi AISC 14th Ed. Eq.

E3-4

Fcr.grd 0.658

Fy.sec

Fe.grdr

Fy.sec

KLef

rx4.71

Es

Fy.secif

0.877 Fe.grdr otherwise

49.836 ksi AISC 14th Ed. Eq. E3-2

ϕc Fcr.grd Ae 1536.322 kip

Chk.1 "OK" ϕc Fcr.grd Ae Pstif.dmdif


"OK"

Weld Check

FE70 70ksi Assumed weld metal strength based on the performancespecifications

D8

16in Weld size to web plates

lwld KLef 2 2. in 13.719 in Effective length of weld subtracts out stiffenercopes

Rn.wld 0.6 FE702

2 D lwld 203.713 kip Single line weld strength

ϕwld 0.75 Fillet weld reductionfactor

4ϕwld Rn.wld 611.139 kip There are a total of 4 strips of weld, 2 per stiffener

Chk.2 "OK" 4ϕwld Rn.wld Pstif.dmdif


"OK"

3 of 31


CHECKS




Bearing Check

Apb 2 hstiff 2in tstiff 8.28 in2

Projected bearing area

Rn.pba 1.8 Fy.sec Apb 745.2 kip AISC 14th Ed. Eq. J7-1, 4 projected bearingareas

ϕba 0.75 AISC 14th Ed. Eq.J7-1

Chk.3 "OK" ϕba Rn.pba Pstif.dmdif


"OK"

4 of 31


CHECKS




Stiffener Design Check for Ribs Loaded with Wire Rope AISC 14th Ed. J10.8

2'-1.4400"

2.0000"

6.1400"P

1'-11.4400"

1'-2.1950"

Area: 34.6104 sq inPerimeter: 75.2600 inBounding box: X: -11.7200 -- 11.7200 in Y: -7.0150 -- 7.1750 inCentroid: X: 0.0000 in Y: 0.0800 inMoments of inertia: X: 239.7343 sq in sq in Y: 977.7432 sq in sq inProduct of inertia: XY: 0.0000 sq in sq inRadii of gyration: X: 2.6319 in Y: 5.3151 inPrincipal moments (sq in sq in) and X-Y directions about centroid: I: 239.5128 along [1.0000 0.0000] J: 977.7432 along [0.0000 1.0000]

Pstif.dmd 193.34kip Axial load demand from SAP2000 model LC2b (Ice)

Column Stability Check

tstiff 1in 1" Stiff

hstiff 6.14in Height of stiffener



Ae 25 twb.grdr twb.grdr 2tstiff hstiff 34.253 in2


KLef 0.75 Wh K=0.75, AISC 14th Ed. Section J10.8

rx239.73in

4

Ae2.646 in Minimum radius of gyration (I.x/Area)^1/2,




5 of 31


CHECKS




hstiff

tstiff0.59

Es

Fy.sec 1 Compactness check for single stiffener, AISC 14th Ed . Table B4.1a, Member is

Compact

Fe.grdr

π2

Es

KLef

rx

26380.573 ksi AISC 14th Ed. Eq. E3-4

Fcr.grd 0.658

Fy.sec

Fe.grdr

Fy.sec

KLef

rx4.71

Es

Fy.secif






"OK"

Weld Check


D8


lwld KLef 2 2. in 13.719 in Effective length of weld subtracts out stiffenercopes

Rn.wld 0.6 FE702

2 D lwld 203.713 kip Single line weld strength





"OK"

6 of 31


CHECKS




Bearing Check

Apb 2 hstiff 2in tstiff 8.28 in2

Projected bearingarea





"OK"

7 of 31


CHECKS




Lifting Bracket Design Checks AISC 14th Ed. J10.8

CALC. 5 (LIFTINGBRACKET/GATE

WELDAMENT)

Demands Factored stalled torque force of the motor, LC5 values perrecommendations of Mech. section in St. Paul MVPPbrk 1.2 200 kip 240 kip

***Please note that the lifting ears on the plans have been designed with a CJP weld. However, the weld calculations belowfor weld checks between the lifting ears and base plate have been performed assuming a partial pen weld with a reinforcingfillet. This calculations was performed to determine what the minimum weld size could be if a CJP was not used.***

8 of 31


CHECKS




Weld Check on Rectangular Lifting Plate Attached to Skin PlateNote: Based on the location of the bracket the force is parallel to the weld group and tangent to the skin plate. This calculationassumes that the only welds resisting the force are those parallel to the force. This is conservative.Ref: AISC 14th Ed. Table 8-4 p. 8-06

ϕw 0.75 Welding reduction value AISC 14th Ed. p.8-8

Cl 70ksi Assumes E70 Electrodes will be used for theweld

lw 24in 2 ft Assumed length ofweld

ex 9in Approximate eccentricty of force from weldgroup

aw

ex

lw0.375 Table 8-4 value, p.8-66 AISC 14th

Ed.

kw 0 Based on recommendations of AISC 14th Ed. p.8-66

Cw 2.66 Coefficient value from Table 8-4, based on a.w and k.w

Dmin

Pbrk

ϕw Cw Cl lw0.072 in Minimum required size of weld on either side of

the plate

Dreq max Dmin6

16in

0.375 in Required weld based on minimum strength value and minimum fillet weld size, seeTable J2.4

Use 3/8" Fillet weld all around plate section connected toskin plate

9 of 31


CHECKS




Weld Check on Lifting Plates Attached to Base Plate (Reinforcing Fillet)Note: Based on the location of the bracket the force is parallel to the weld group and tangent to the skin plate.Ref: AISC 14th Ed. Table 8-4 p. 8-06

ϕw 0.75 Welding reduction value AISC 14th Ed. p.8-8

Cl 70ksi Assumes E70 Electrodes will be used for theweld

lw 24in 2 ft Assumed length ofweld

ex 7in Approximate eccentricty of force from weldgroup

aw

ex

lw0.292 Table 8-4 value, p.8-66 AISC 14th

Ed.

kw 0 Based on recommendations of AISC 14th Ed. p.8-66

Cw 3.09 Coefficient value from Table 8-4, based on a.w and k.w

Dmin

Pbrk

ϕw Cw Cl lw0.062 in Minimum required size of weld on either side of

the plate

Dreq max Dmin6

16in

0.375 in Required weld based on minimum strength value and minimum fillet weld size, seeTable J2.4

Use 3/8" Fillet weld all around bracket plates attached to baseplate

10 of 31


CHECKS




Weld Check on Lifting Plates Attached to Base Plate (Partial Penetration Groove Weld)Note: Based on the location of the bracket the force is parallel to the weld group and tangent to the skin plate.Ref: AISC 14th Ed. Table 8-4 p. 8-06

dw lw 24 in Depth of weldgroup

Awp 1 dw 2881

ftin

2 Area of unit weld

group

Moment ofinertia of unitweld group

IS.wg

2 1 dw 3

122304 in

3

Demand

Rv

Pbrk

2Awp5

kip

in (Shear stress over weld)

Ml Pbrk 5 in 1200 kip in Bending moment @ base

Bending stress over weldRt

Ml

dw

2

IS.wg6.25

kip

in

Capacity Weld (Tension Portion) Capacity of 1/2" Groove weld, see AISC 14th Ed.Table J2.5,tension normal to weld axisΦRn.tgw 0.8 0.707 0.6 FE70 23.755 ksi

DRq.t

Rt

ΦRn.tgw0.263 in (Required weld size)

(Specified weld size)Dsel.t 0.375in

Chktension "OK" Dsel.t DRq.tif


"OK"

(Design check) Use 1/4" thk weld all around to handletension

Capacity Weld (Shear Portion)

ΦRn.vgw 0.75 0.707 0.6 FE70 22.271 ksi Capacity of 1/2" Groove weld, see AISC 14th Ed.Table J2.5,shear

DRq.v

Rv

ΦRn.vgw0.225 in (Required weld size)

Dsel.v 0.375in (Specified weld size)

Chkshear "OK" Dsel.v DRq.vif


"OK"(Design check) Use 1/4" thk weld all around to handle shear

Use 1/2" groove weld to handle both tension and shear components of stressdemands, meets minimum thickness requirements of Table J2.3 p. 16.1-110

11 of 31


CHECKS




Base Metal Check Along Lifting Plates (Tension) Note: Based on the location of the bracket the force is parallel to the two liftingplates.Ref: AISC 14th Ed. Φty 0.9 Tension strength reduction value

Fy.tab 50ksiAll steel related to the bracketdesgin shall be ASTM A709 Gr. 50Fu.tab 70ksi

Strength of Elements in Tension (Yielding Tab) Check

lst lw Length of lifting plates

tlftg.pl 2in Thickness of liftingplates

Ag.tab lst tlftg.pl 48 in2

Rn.fy Fy.tab Ag.tab 2400 kip (AISC 14th Ed. Equation J4-3)

ChkT.Yielding "OK" 2 Φty Rn.fy Rt

dw

2if


"OK"Tension check of lifting plates, (2) takes into accountboth plates

Strength of Elements in Tension (Rupture Tab) Check

Φtu 0.75 Tension strength reduction value

Anv Ag.tab Net area subject toshear

Rn.fu Fu.tab Anv 3360 kip (AISC 14th Ed. Equation J4-4)

ChkT.Rupture "OK" 2 Φtu Rn.fu Rt

dw

2if


"OK"Tension check of lifting plates, (2) takes into accountboth plates

12 of 31


CHECKS




Base Metal Check Along Lifting Plates (Shear) Note: Based on the location of the bracket the force is parallel to the two lifting plates.Ref: AISC 14th Ed.

Φsh.y 1 Shear strength reduction value

Φsh.r 0.75 Shear strength reduction value

Fy.tab 50ksiAll steel related to the bracketdesgin shall be ASTM A709 Gr. 50Fu.tab 70ksi

Strength of Elements in Shear (Yielding Shear Tab) Check

lst lw Length of lifting plates

tlftg.pl 2in Thickness of liftingplates

Ag.tab lst tlftg.pl 48 in2

Rn.fy 0.6 Fy.tab Ag.tab 1440 kip (AISC 14th Ed. Equation J4-3)

ChkV.Yielding "OK" 2 Φsh.y Rn.fy Pbrkif


"OK"Shear check of lifting plates, (2) takes into account bothplates

Strength of Elements in Shear (Rupture Shear Tab) Check


Rn.fu 0.6 Fu.tab Anv 2016 kip (AISC 14th Ed. Equation J4-4)

ChkV.Rupture "OK" 2 Φsh.r Rn.fu Pbrkif


"OK"Shear check of lifting plates, (2) takes into account bothplates

Bearing Check Within Lifting Plates Note: Based on the location of the bracket the force is parallel to the two liftingplates.Ref: AISC 14th Ed. Dpin 4.75in Pin hole diameter

Apbr Dpin tlftg.pl 9.5 in2

Projected bearing area of a singlelifting pl

ϕbrg 0.75 Bearing reductionvalue

Rn.brg 1.8 Apbr Fy.tab 855 kip AISC 14th Ed. Eq. J7-1

ChkBrg "OK" 2 ϕbrg Rn.brg Pbrkif


"OK"Bearing check ofthe two lifting

13 of 31


CHECKS




plates

Pin Connection Checks Tension and ShearNote: Based on the location of the bracket the force is parallel to the two lifting plates.Ref: AISC 14th Ed. Section D5.

Tension Strength of Pin Connected Elements

Φt 0.75 Reduction value for tension

beff 2 tlftg.pl 0.0625in 4.063 in Per AISC 14th Ed.

Pnt 2 tlftg.pl beff Fu.tab 1137.5 kip AISC 14th Ed. Eq.D5-1

Φt Pnt 853.125 kip

Chklg.T "OK" 2 Φt Pnt Pbrkif


"OK"

Shear Strength of Pin Connected Elements

Φv 0.75 Reduction value for shear

alg 3in3

16in 3.188 in Min edge distance parallel to

force

dpin 4.75in Diameter ofpin

Asf 2 tlftg.pl alg

dpin

2

22.25 in2

Pnv 0.6 Fu.tab Asf 934.5 kip AISC 14th Ed. Eq.D5-2

Φv Pnv 700.875 kip

Chklg.V "OK" 2 Φv Pnv Pbrkif


"OK"

Dimensional Requirements of Pin Connected Elements

Pwidth 4.25in dpin 4.25in 13.25 in Overal width of plate across centerlineof pin

Pwidth 2 beff dpin 1

apl 5.5in Lenght of plate parallel to loading and on bearing side ofpin hole

apl 1.33 beff 1

14 of 31


CHECKS




2"

214"

1'-8 716"

1'-112"

3'-7"

7 716"

2"

3/4"THKPL

R6.0000"

A.T.br

A.C.br

Downstream Truss Gusset Plate Connection Checks AISC 14th Ed. J10.8

AT.br 30.5kip Governing tension value from LC 3

AC.br 31.5kip Governing compression value from LC3

SB1 2in Spacing between bolts)

Ed.1 2in Minimum edge distance

Ed.2 2.51in Edge distance of bolt to leg

db.1 0.75in Diameter ofbolts

Shear in Bolts Check

Fnt 90ksi ASTM A325 bolts, AISC 14th Ed. Table J3.2

Fnv 54ksi ASTM A325 bolts, AISC 14th Ed. Table J3.2

msp.1 1 Number of shear planes

Φv.bolts 0.75 Reduction factor for bolts

Numbolts 3 Number of bolts in shear

Ab πdb.1

2

2

0.442 in2

Rn.bolts Numbolts Fnv msp.1 Ab 71.569 kip

Φv.bolts Rn.bolts 53.677 kip

ChkCon.1 "OK" Φv.bolts Rn.bolts max AT.br AC.br if


"OK"

15 of 31


CHECKS




Bearing Check (Angle Leg)

Lc 1.125in Clear distance,between two holes or edge of material

tw.angle 0.5in Thickness of member L5x5x1/2

Fu.Ang 65ksi Ultimate strength of bearingplate

Φbc 0.75 Reduction factor AISC 14th Ed. p. 16.1-111

Rn.bc 1.2 Lc tw.angle Fu.Ang 1.2 Lc tw.angle Fu.Ang 2.4 db.1 tw.angle Fu.Angif

2.4 db.1 tw.angle Fu.Ang otherwise

AISC 14th Ed. Eq.J3-6a

Φbc Rn.bc 32.906 kip For a single bolt, conservative

ChkCon.2 "OK" Φbc Rn.bc max AT.br AC.br if


"OK"

Block Shear Check (Angle Leg)

Lv.1 6in

Numbv 2.5 Number of bolt holes in shear

Numbt 0.5 Number of bolts holes in tension

Ubs.1 1.0 AISC 14th Ed. p.16.1-352

Fu.tab 70ksi

ttab 0.5in

Φbs 0.75

Anv Lv.1 Numbv db.1 0.125in ttab 1.906 in2

Ant Ed.2 Numbt db.1 0.125in ttab 1.036 in2

Agv Lv.1 ttab 3 in2

Rn.bs 0.6 Fu.tab Anv Ubs.1 Fu.tab Ant 0.6 Fu.tab Anv Ubs.1 Fu.tab Ant 0.6 Fu.tab Agv Ubs.1 Fu.tab Antif

0.6 Fu.tab Agv Ubs.1 Fu.tab Ant otherwise

Rn.bs 152.6 kip AISC 14th Ed. Equation J4-5

ChkCon.3 "OK" Φbs Rn.bs AT.brif


"OK"

16 of 31


CHECKS




Gusset Plate Buckling Check from R.c.max Loading

7 716"

A.C.br

1'-8.6495"

IDEALIZED GUSSETPLATE SECTION

11.4546"

Note the gusset plate was idealized as a rectangular section that has awidth of 11inches a length of 20.64in.

AC.br 31.5 kip Max compression load in brace members from SAP 2000 model forLC5

Kpl 1.2 Based on Steel tips 42

Lpl 20.64in Length of gussetplate

thkpl 1in Thickness of gussetplate

wpl 7.5in width of gusset plate

Φpl 0.9 Compression reduction factor AISC 14thEd.

Fy.pl 50ksi

ry.1

wpl thkpl3

12

thkpl wpl0.289 in

Fe.3

π2

Es

Kpl Lpl

ry.1

238.881 ksi (AISC 13th Ed. Equation E3-4)

Fcr.pl 0.658

Fy.pl

Fe.3

Fy.pl

Kpl Lpl

ry.14.71

Es

Fy.plif

0.877 Fe.3 otherwise

(AISC 13th Ed. Equation E3-2 & 3)

17 of 31


CHECKS




Fcr.pl 29.188 ksi

Pn.pl Fcr.pl thkpl wpl 218.914 kip

Φpl Pn.pl 197.022 kip

Chkpl "OK" Φpl Pn.pl AC.brif


"OK"

Gusset Plate Edge Buckling Check Ref. Steel Tips 42 Gusset Plate Checks

Lfg 11.45in Length of gusset plate edge between braces, see figure above

Chkpl "OK"Lfg

thkpl0.75

Es

Fy.plif


"OK"

18 of 31


CHECKS




Gusset Plate Tension Check from R.T.max Loading

7 716"

A.C.br

1'-8.6495"

IDEALIZED GUSSETPLATE SECTION

A.T.br

4.6110"

Yielding of Whitmore Section (

Asec 4.61in thkpl 4.61 in2

ϕt.pl 0.9

PWM Fy.pl Asec 230.5 kip AISC Eq. J4-1

ϕt.pl PWM 207.45 kip

Chkpl "OK" ϕt.pl PWM AT.brif


"OK"

Combined Loading Acting on Gusset Plate

***Negligible load was found in shear and bending on the gusset plates. The primary force seen is either tension orcompression. Combined loading was found to be ok by inspection.***

Design Checks For Smaller Gusset Plate

***Reviewer please note that the smaller gusset plate was not reviewed for brevity. It wos found to have smaller loads, but hasa similar thickness as the larger gusset plate. The design checks were found to be OK by inspection***

19 of 31


CHECKS




Sill Beam Embed Anchor Check for Surcharge Loading

2'-10.0000"

U.plft

FLOW

HRC HEADED BARS S.S.

Max water height H1 acting on gatesWtr.ht 22.3ft

Pr.wd 50ft Total width of opening

Unit weight of waterγw 62.4pcf

Uplft 1.3 1.7 γw Wtr.ht Pr.wd 2.83333ft( ) 435.661 kip Total uplift pressure acting on sill factored, EM 1110-2- 2104,Eq.3.2

20 of 31


CHECKS




Headed Reinforcement Development Checks

Barsz 6 (Bar size)

dstd 0.75in (Diameter of stud)

Area of #6 barAstd π

dstd

2

2( )

0.442 in2

Dhead 2.375in (Diameter of headed end)

Cvr 6in (Concrete cover)

Clrsp 5.25in (Clear spacing between bars)

Fy.rb 60ksi (ASTM A706, Gr. 60)

Fu.rb 95ksi (ASTM A706, Gr. 60)

Abrg πDhead

2

2

Astd 3.988 in2

(Bearing area of headed end)

ACI 318-08 Sec. 12.6.1 Checks

Chkhr.1 Fy.rb 60000psi 1

Chkhr.2 Barsz 11 1

Chkhr.3 Abrg 4 Astd 1 ****Note 1=True, 0=False***

Chkhr.4 Cvr 2 dstd 1

Chkhr.5 Clrsp 4 dstd 1

ldt max

0.016Fy.rb

psi

4000psi

psi

dstd 8 dstd 6in

11.384 in (Minimum development length of headed reinforcemet, ACI 318-08 Sec.12.6.2)

21 of 31


CHECKS




Tension Capacity Headed Reinforcement Appendix D equation

ϕt 0.8 ACI 318-08 Sec. D.4.5

Fu.ar min 1.9 Fy.rb Fu.rb 125ksi 95 ksi ACI 318-08, Sec. D.5.1.2

drb dstd 0.75 in Diameter of headed rebars

Arb πdrb

2

2

0.442 in2

Area of rebar

Nsa Arb Fu.ar 41.97 kip Tensile strength of a singleanchor

ϕt Nsa 33.576 kip

Arqd

Uplft

ϕt Nsa12.975 Minimum number of anchors

required

Apro 50 Number of anchorsprovided

Chk12 "OK" Apro Arqdif


"OK" Tension capacitycheck

Provide 3/4" d ia. headed reinf. bars S.S. @ 24" on center acrossthe sill

***Note transverse reinforcement is recommended to prevent splitting cracks at the head. ACI 318-08 R12.6 p. 212***

22 of 31


CHECKS




Strut Arm Web Shear Check W12x106 (LRFD) This calculation evaluates the remining shear capacity of the strut arm at the strut arm to transition hubconnection. Material Properties of Wide Flange Beam

Zx.ST 164in3

Sx.ST 145in3

Fy.ST 50ksi ASTM A709 Gr.50

Ix.ST 933in4

tw.ST 0.61in

dST 12.9in Overall depth ofsection

hw.ST dST 2 0.99 in( ) 2 2 in( ) 6.92 in Remaining length ofweb

Φv 0.9 AISC 13th Ed. Section G1

Shear Demand Acting on Web

Vu.wb max 12.78kip 12.20kip 3.89kip( ) 12.78 kip Controlling shear demand from SAP2000 (LC2b, LC3,LC5)

Shear Capacity of Wide Flange

Wv.ST 1hw.ST

tw.ST2.24

Es

Fy.STif

"See AISC 13th Ed. p.16.1-65" otherwise

1 (AISC 13th Ed. p. 16.1-65)

Aw.ST dST tw.ST 7.869 in2

Vn.ST 0.6 Fy.ST Aw.ST Wv.ST 236.07 kip

Φv Vn.ST 212.463 kip

Chkv.ST "OK" Φv Vn.ST Vu.wbif


"OK"

23 of 31


CHECKS




Bumper Design and Location ChecksThis calculation checks that the bumper can withstand the axial and shear forces applied during the Tainter Gate LC3, please note thatdue to the contact made with the pier and the assumption that the gate is being dragged open by one set of cables, LC3 should havean additional bending moment applied to the outside of the girders. This calculation also provides the SAP2000 input for the bendingmoment on the girders.

R.bpl

R.bprDyn.frc.l

Dyn.frc.r

Demands

Rbpr max 288kip 288kip( ) Max axial loading on bumber, LC3 andLC5

Rbpl 212kip

Frtn 0.15 Coefficient of friction between bumper and embedplate

Fv Rbpr Frtn 43.2 kip Shear demand acting on bumper bolts from dynamic friction / drag rightside


Bearing Stress in Bumper Checks

CIPy 15ksi Yield stress of CIP 151

CIPu 50ksi Ultimate compressivestress

BrgA 3.5in 12 in 42 in2

Bearing area of bumper

24 of 31


CHECKS




Brgstrs

Rbpr

BrgA6.857 ksi Bearing stress of bumper under load case 3

Chkbrg.strs "OK" CIPy Brgstrsif


"OK"

Shear Force in Bolts Check




Φv.bolts 0.75 Reduction factor for bolts


db.1 0.75in Boltdiameter

Ab πdb.1

2

2

0.442 in2


Φv.bolts Rn.bolts 107.354 kip

ChkShear "OK" Φv.bolts Rn.bolts Fvif


"OK"

Bearing Check


tw.pl 0.625in Thickness of base plate member connected to girder

Fu.pl 65ksi Ultimate strength of bearingplate

Φbc 0.75 Reduction factor AISC 13th Ed. p. 16.1-111(AISC 13th Ed. Eq. J3-6a)

Rn.bc 1.2 Lc tw.pl Fu.pl 1.2 Lc tw.pl Fu.pl 2.4 db.1 tw.pl Fu.plif

2.4 db.1 tw.pl Fu.pl otherwise

Φbc Rn.bc 54.844 kip For a single bolt, conservative

ChkBrg "OK" Φbc Rn.bc Numbolts Fvif


"OK"

25 of 31


CHECKS




Bumper Column Stability Check

516"

VT+MT

FCWTYP.

Pstif.dmd Rbpr 288 kip Axial load demand from SAP2000 modelLC5

tstiff 0.5in Stiff thickness

hstiff 5in Height of stiffener

twb.grdr 0in Web thickness

Wh 0in Height ofweb

Ae 25 twb.grdr twb.grdr 4tstiff3.5in 7in

2

10.5 in2

Effective area of column, see AISC 14th Ed. sectionJ10.8, average area of stiffener taken due to the taper.

KLef 0.75 5 in 0.313 ft

K=0.75, AISC 14th Ed. Section J10.8

26 of 31


CHECKS




ry

4hstiff tstiff

3

12

Ae0.141 in Minimum radius of gyration (I./Area)^1/2,




Fe.grdr

π2

Es

KLef

ry


Fcr.grd 0.658

Fy.sec

Fe.grdr

Fy.sec

KLef

rx4.71

Es

Fy.secif






"OK"

Weld Check


D4


lwld 7in 7in Effective length of weld

Rn.wld 0.6 FE702

2 D lwld 103.945 kip Single Fillet Weld strength, there are (8) 7in weld

lengths



Chk.2 "OK" 8ϕwld Rn.wld Fvif


"OK"

27 of 31


CHECKS




Bearing Check

Apb Ae 10.5 in2

Projected bearing area

Rn.pba 1.8 Fy.sec Ae 945 kip AISC 14th Ed. Eq. J7-1, 4 projected bearingareas




"OK"

28 of 31


CHECKS




Headed Reinforcement Development Checks (Side Seal Embed Anchors)

Barsz 6 (Bar size)


Area of #6 barAstd π

dstd

2

2( )

0.442 in2



Clrsp 5.25in (Clear spacing between bars)



Abrg πDhead

2

2

Astd 1.801 in2




Chkhr.2 Barsz 11 1




ldt max

0.016Fy.rb

psi

4000psi

psi

dstd 8 dstd 6in


29 of 31


CHECKS




Headed Reinforcement Development Checks (Concrete Block Outs S&T Reinf.)

Barsz 5 (Bar size)


Area of barAstd π

dstd

2

2( )

0.307 in2



Clrsp 4in (Clear spacing between bars)



Abrg 2in2

Astd 1.693 in2




Chkhr.2 Barsz 11 1




ldt max

0.016Fy.rb

psi

7000psi

psi

dstd 8 dstd 6in

7.171 in (Minimum development length of headed reinforcemet, ACI 318-08 Sec.12.6.2)Bar will be embedded in high stregnth grout and notconcrete

30 of 31


CHECKS




Headed Reinforcement Development Checks (Concrete Block Outs S&T Reinf.)

Barsz 4 (Bar size)


Area of barAstd π

dstd

2

2( )

0.196 in2



Clrsp 4in (Clear spacing between bars)



Abrg 2in2

Astd 1.804 in2




Chkhr.2 Barsz 11 1




ldt max

0.016Fy.rb

psi

4000psi

psi

dstd 8 dstd 6in


31 of 31


Element: Rib and Skin Plate Checks Labor Code: 2686C1

Calculation Title: Rib and Skin Plate Assembly Loads and Member Checks





Rev. No.


Prepared by:

Date:

Checked by:

Date:

Sheet Index:

1-11

12-15

16-19

20

Rib and Skin Plate Loads and Checks

Shear Flow Check for Built Up Section

Connection Check Between Rib and Horizontal Girder

Skin Plate Design Check

FARGO DIVERSION INLET TAINTER GATE

Rib and Skin Plate Assembly Loads and Member Checks


Checked By: Cecily Nolan PE Date:2/22/2016

Rib and Skin Plate Loads and Checks Gate Layout

16'-3.7300"

9'-4.2871"

2'-9.7422"

1 of 20





LC2b Rib and Skin Plate Wire Rope Pressure (Governs Typical Rib Design) Idealized Model of Skin Pl and Rib Assembly Loading (LC2b)

Wire Rope Loads

Qrp_pr 33kip Rope tension force from SAP2000, Equal Loading, wire rope load excluded for typical rib desgin


Wwire.2b

Qrp_pr

Rgate1.269 klf Tributary wire rope pressure for SAP 2000 model,

Ice Impact Load

Iceim 5kip

ft ETL 1110-2-584, section D.2.4, Ice

2 of 20





LC3 Rib and Skin Plate Wire Rope Pressure (May Govern Rib Supporting Wire Rope Loads)

Idealized Model of Skin Pl and Rib Assembly Loading (LC3)

Wire Rope Loads



Wwire.3

Qrp_pr


3 of 20





LC5 Rib and Skin Plate Wire Rope Pressure (May Govern Rib Supporting Wire Rope Loads)

Idealized Model of Skin Pl and Rib Assembly Loading (LC5)

Wire Rope Loads

Qstl.tqe 198.45kip Rope tension force from Stall Torque ofMotor


Wwire

Qstl.tqe


4 of 20





Rib and Skin Plate Water PressureLoading Layout for LC2b, LC3, LC5

16'-3.7300"

2'-9.7422"

El. 922 (H.1 H.2)

El. 925.7 (TOG)

El. 899.7 (BOG)

5'-7.1805"

Water Pressure Loads

Wht 24.72ft (Water heights based on arc length and not project performance criteria report.(conservative))

γw 62.5pcf

Trib1 18in (Tributary distance between ribs carrying wire rope loading and water pressure)

Trib2 24in (Tributary distance between ribs carrying water pressureonly)

Wpress.1 Wht γw Trib1 2.318 klf (Water pressure @ Bottom of gate un factored for Trib.1)

Wpress.2 Wht γw Trib2 3.09 klf (Water pressure @ Bottom of gate un factored forTrib.2)

***Note the SAP2000 hydrostatic loads are based on the idealized rib skin plate assembly being flat, this will create largerhydrostatic loads, but is conservative.***

5 of 20





Built Up Rib Skin Plate Capacity Verification Calculation for LC5 The purpose of this calculation is to verify that the DCR values shown in SAP are accurateand usable Moment Diagram for Load Case 5 (SAP 2000 Model) Trib_1 with Wire Pressure

Mmax.1 457 kip ft

6 of 20





Compaction Check of Built Up Sections W/ Bottom Flange in CompressionThe following calculation evaluates the cantilevered built up rib section at the top of the gate. This calc. is to confirm that SAP2000results may be used for evaluation. For this calc. the bottom flange is in compression and the skin plate is in tension.

bpl11.2

2in (Effective width)

tf.t 0.94in (Thickness of flange in Compession)

tf.b 1.125in (Thickness of flange in Tension)

Es 29000ksi (Modulus of elasticity ofsteel)

Fy.skn.pl 50ksi (Yield strength of skin plateASTM A709 Gr.50)

Fy.sec 50ksi (Yield strength of section ASTM A709Gr.50)

hw 8.09in Height of the web, overall heightshould match WT9X23

tw 0.59in (Thickness ofweb)

kc min 0.764

hw

tw

0.76 (AISC 13th Ed. p.16.1-18 footnote (a))

Ix 610.37in4

(Moment of inertia in xdirection)

ct 3.87in (Distance from centroid to top ofsection)

***Please Note: Cross section properties abovewere computed in AutoCAD***

cb 6.25in (Distance from centroid to bot of section)

(Compression section modulus ofsection)Sxc

Ix

cb97.659 in

3

Sxt

Ix

ct157.718 in

3 (Tension section modulus of

section)

(Section modulusratio)

Sxt

Sxc1.615

FL.t 0.7 Fy.sec Sxt

Sxc0.7if

maxFy.sec Sxt

Sxc0.5 Fy.sec

otherwise

35 ksi(AISC 13th Ed. p. 16.1-18 footnote(b))

7 of 20





Flange Compactness Check (Compression Flange)

λft

bpl

tf.t5.957

λp.ft 0.38Es

Fy.skn.pl 9.152

λr.ft 0.95kc Es

FL.t 23.839

Compactcheck.tf "Compact" λft λp.ftif

"Non-compact" λp.ft λft λr.ftif

"Slender" otherwise

"Compact"

AISC 13th Ed. Table B4.1, Flange limitingwidth thickness ratios, Case 2)

Web Compactness Check Top

λwt

cb tf.b

tw8.686

λr.wt 5.70Es

Fy.sec 137.274

Compactcheck.tw "Non-compact" λwt λr.wtif

"Slender" otherwise

"Non-compact"

AISC 14th Ed. Table B4.1, Web limitingwidth thickness ratios, Case 2)

8 of 20





Flexure Checks for Built Up Rib Plate

1. Compression Flange Yielding Check

Zx 119.70in3

Plastic Section Modulus, see SAP2000 properties for shape.

hc 5.31in 2 10.62 in 2 times distance from the centroid to inside face of compression flange

hp 8.22in 2 16.44 in 2 times distance from the PNA to inside face of compression flange

Mpc min Zx Fy.sec 1.6 Sxc Fy.sec 498.75 kip ft (Plastic moment, compressionside)

Myc Sxc Fy.sec 406.913 kip ft (Yielding moment, compressionside)

λp.wt min

hc

hp

Es

Fy.sec

0.54Mpc

Myc 0.09

2λr.wt

47.57

9 of 20





Rpc

Mpc

Myc

hc

twλp.wtif

minMpc

Myc

Mpc

Myc1

hc

twλp.wt

λr.wt λp.wt

Mpc

Myc

otherwise

1.226

(AISC 13th Ed. Eq. F4-9a,F4-9b)

Mn.1 Rpc Fy.sec Sxc 498.75 kip ft

2. Lateral Torsional Buckling

Lb 9.33ft (Unbraced length, top of gate)

Find Torsional Constant

Lskin.pl.trib 18in (Length of tributary skinplate)

ho hw

tf.t

2

tf.b

2 9.123 in (Distance between flange centroids)

Jsec1

3Lskin.pl.trib tf.b

3 hw tw

3 2bpl tf.t

3

12.198 in

4 (Torsional constant

estimate)

Asec 35.55in2

(Area of built up section)

rt

2bpl

12ho

hw tf.t tf.b

1

6

hc tw

2bpl tf.b

hw2

ho hw tf.t tf.b

3.305 in

(Radius of gyration, AISC 13th Ed.F4-10)

Lp 1.1 rtEs

Fy.sec 7.297 ft (AISC 13th Ed. Eq. F4-7)

Lr 1.95 rtEs

FL.t

Jsec

Sxc ho 1 1 6.76

FL.t

Es

Sxc ho

Jsec

2

74.117 ft (AISC 13th Ed. Eq.F4-8)

MA 27 kip ft (Moment at quarter point from SAP2000)

MB 97 kip ft (Moment at half point from SAP2000)

MC 245 kip ft (Moment at 3 quarter point from SAP2000)

Rm 1 (Singly symmetric members, 1.0, AISC 13th Ed. p.16.1-46)

10 of 20





Cb min12.5 Mmax.1

2.5 Mmax.1 3MA 4 MB 3 MCRm 3

2.434 (AISC 13th Ed. Eq.F1-1)

Fcr

Cb π2

Es

Lb

rt

21 0.078

Jsec

Sxc ho

Lb

rt

2

905.894 ksi (AISC 13th Ed. F4-5)

Mn.2 Mn.1 Lb Lpif

min Cb Rpc Myc Rpc Myc FL.t Sxc Lb Lp

Lr Lp

Rpc Myc

Lp Lb Lrif

min Fcr Sxc Rpc Myc otherwise

498.75 kip ft

(AISC 13th Ed.Eq. F4-2)

3. Compression Flange Local Buckling

Mn.3 Mn.1 λft λp.ftif

Rpc Myc Rpc Myc FL.t Sxc

hc

twλp.ft

λr.ft λp.ft

otherwise

498.75 kip ft

(AISC 13th Ed. Eq.F4-12)

4.Tension Flange Yielding

Sxt Sxc 1 (AISC 13th Ed. Section F4.4, 1=True, 0=False, if True the limit state of tension flange yielding does not apply)

Design Moment

ϕb 0.9 (AISC 13th Ed. Section F1, Flexural reductionfactor)

ϕMn ϕb min Mn.1 Mn.2 Mn.3 448.875 kip ft

ChkM "OK" ϕMn Mmax.1if


"OK"

Mmax.1

ϕMn1.018

SAP2000sec.dcr 1.018

Note : SAP2000 design check is Ok by inspection. SAP may be used for design checkpurposes for built up sections. Section is moderately overstressed. This is ok byinspection given the extreme load case.

11 of 20






12 of 20





Demand

Vmax 124kip Max shear, see load case 5 in SAP2000 for built up skin platesection

Askin.pl 1.125in 18 in 20.25 in2

Area of effective skinplate

ybar 3.87109in1.125in

2 3.309 in Distance from centroid of hatched section to neutral axis

Qv Askin.pl ybar 66.999 in3

First moment of area ofinterest

Ix 610.37 in4

Moment of inertia ofsection

tw 0.59 in Thickness ofweb

τmax

Vmax Qv

Ix13.611

kip

in Shear Flow

demand

Size Weld to Resist Shear Flow

FEXX 70ksi Electrodes strength

Dw.16

16in Size of fillet

weld

ϕw 0.75 AISC 14th Ed. reduction value

Rn.1 2 0.6 FEXX 0.707 Dw.1 22.27kip

in AISC 14th Ed. p.8-8

ϕw Rn.1 16.703kip

in

Minw4

16in AISC 14th Ed. p.16.1-96

Chkvf "OK" ϕw Rn.1 τmax Dw.1 Minwif


"OK"

Use a 3/8" min weld for web to skin plate

13 of 20






14 of 20





Demand

Vmax 124kip Max shear, see load case 5 in SAP2000 for built up skin platesection

Askin.pl 0.625in 18 in 11.25 in2

Area of effective skinplate

ybar 3.55859in Distance from centroid of hatched section to neutral axis

Qv Askin.pl ybar 40.034 in3

First moment of area ofinterest

Ix 610.37 in4

Moment of inertia ofsection

tw 0.59 in Thickness ofweb

τmax

Vmax Qv

Ix8.133

kip

in Shear Flow

demand

Size Weld to Resist Shear Flow


Dw.14

16in Size of fillet

weld


Rn.1 2 0.6 FEXX 0.707 Dw.1 14.847kip

in AISC 14th Ed. p.8-8

ϕw Rn.1 11.135kip

in

Minw4

16in AISC 14th Ed. p.16.1-96

Chkvf "OK" ϕw Rn.1 τmax Dw.1 Minwif


"OK"

Use a 1/4" min weld for web to skin plate

15 of 20





Connection Check Between Rib and Horizontal Girder

Upper Horizontal Girder to RibConnection

Lower Horizontal Girder to RibConnection

16 of 20





Demand

Maxf 193.34kip Max reaction force between rib and girder, see LC5 of RB_SKN_PL, SAP2000model

Capacity

This calculation check will make the assumption that the max force is in tension, and all four sides of the rib flange will be welded to thegirder to form a rectancular shape.

Size Weld to Resist Force


Dw.14

16in Size of fillet

weld


Rn.1 0.6 FEXX 0.707 Dw.1 2 6.06 in 2 14.02 in( ) 298.128 kip AISC 14th Ed. p.8-8

ϕw Rn.1 223.596 kip

Minw4

16in AISC 14th Ed. p.16.1-96

Chkgrf "OK" ϕw Rn.1 Maxf Dw.1 Minwif


"OK"

Use a 1/4" in all around weld between rib and girder

17 of 20





Stiffener Design Check for Ribs Loaded with Wire Rope AISC 14th Ed. J10.8

P

9.3750"

5.5600"

0.3750"

8.4250"

1.4713"

Area: 5.3250 sq inPerimeter: 29.8700 inBounding box: X: -2.7800 -- 2.7800 in Y: -4.6875 -- 4.6875 inCentroid: X: 0.0000 in Y: 0.0000 inMoments of inertia: X: 24.7421 sq in sq in Y: 5.4062 sq in sq inProduct of inertia: XY: 0.0000 sq in sq inRadii of gyration: X: 2.1556 in Y: 1.0076 inPrincipal moments (sq in sq in) and X-Y directions about centroid: I: 5.4062 along [0.0000 1.0000] J: 24.7421 along [-1.0000 0.0000]

Pstif.dmd 193.34kip Axial load demand from SAP2000 model LC2b (Ice)

Column Stability Check

tstiff 0.375in Stiffenerthickness

hstiff 1.47in Height ofstiffener



Ae 9.375in twb.grdr 2tstiff hstiff 4.478 in2


KLef Wh K=1.0 pin-pin

rx24.74in

4

Ae2.351 in Minimum radius of gyration (I.x/Area)^1/2,



18 of 20






Fe.grdr

π2

Es

KLef

rx

222280.351 ksi AISC 14th Ed. Eq. E3-4

Fcr.grd 0.658

Fy.sec

Fe.grdr

Fy.sec

KLef

rx4.71

Es

Fy.secif






"OK"

Weld Check


D6


lwld KLef 2 0.75 in 6.925 in Effective length of weld subtracts out stiffenercopes

Rn.wld 0.6 FE702

2 D lwld 77.123 kip Single 10" Weld strength, there are (4) 10" weld

lengths





"OK"

Bearing Check

Apb Ae Projected bearingarea





"OK"

19 of 20





Skin Plate Design Checks Demand Max von mises stress value from LC2b (taken along upper

horizontal girder), LC3 (taken along lower ribs), and LC5 (takenalong upper skin plate along wire pressure). Please note that forLC3 & LC5 localized yielding at the corners of the skin plate isexpected.. Bumpers or rollers will be designed to help preventexcessive damage to the skin plate at these locations.

Skinpl.vm max 39.7ksi 47.03ksi 39.91ksi( ) 47.03 ksi

Skin Plate Yield Limit State Capacity

Fy.pl 50ksi See ASTM A709 Gr. 50

ϕds 0.9 Designer selected reduction value

ϕds Fy.pl 45 ksi Design strength of skin plate, note alpha factor was included by increasing the load application of SAPmodels by 1/0.9

Chkskn.pl "OK" ϕds Fy.pl Skinpl.vmif


"Redesign"

Note : Please note that within the AISC 14th Ed. Sec. 9-4, a reduction value requirement is not listed or requiredfor use. However, a 0.9 reduction was taken, which is conservative. Because the skin plate is a continuous platelocalized yielding will under stress redistribution. The peak stress from LC3 was found to exceed the limitingstress value by 4.44%. This value is considered to be acceptalbe as the stress is not wide spread and the stressdoes not exceed the yield stress of the material.

20 of 20


Element: Trunnion Assembly Design Checks Labor Code: 2686C1

Calculation Title: Yoke Plate, Base Plate, Stiffener Plate, Key Plate, Chockfast Orange



Checked by: Cheuk Wan PE Date: 2-22-2016


Rev. No.


Prepared by:

Date:

Checked by:

Date:

Sheet Index:

1-6

7

8-9

10-11

12-14

15-16

17

18-20

21-23

Keeper Plate Design Checks (ASD)

Trunnion Assembly Design Checks (Demands from SAP Models)

Yoke Plate Bearing Strength Check

Yoke Plate Buckling Check

Trunnion Anchor Design Check

Bearing Base Plate Check

Chock Fast Orange Compressive Stress Check

Leveling Anchors Check Under Dead Load Conditions

SAP2000 Non Linear Area and Link Stiffness Inputs

FARGO TAINTER GATE TRUNNION ASSEMBLY DESIGN

CHECKS

Yoke Pl, Base Pl, Stiff. Pl, Key Pl, Chockfast Orange


Checked By: Cheuk Wan PEDate:5/3/2016

Trunnion Assembly Design Checks See ETL 1110-2-584

1 of 27


CHECKS




Keeper Plate Design Checks (ASD)This calculation sizes the keeper plate anchors and plate to withstand the trunnion frictionmoment, (Shear Couple)

TRN.M1'-8.5000"

1'

1.2500"2.5000"

6.5000"

1'-4.0000"

1.5000"

V.f

V.f

V.w

V.w

TRNM 1.33 169 kip ft See Tainter Gate Trunnion Friction Moment LC2b Factored

Lf 20.5in On center distance between bolts

Lw 16in Effective length of web

Vf

TRNM

Lf131.573 kip Shear force acting on a single row of bolts and through flange of

key pl w/ stress modifier

2 of 27


CHECKS




Shear Demand within Bolts (Elastiv Analysis Method AISC 14th Ed. p. 7-8)

2'-1.0000"

10.2500"

10.2500"

4.0000"

1

2

3

4

5

6

TRN.M

Bolt coordinates about centroidx1 4 in

y1 10.25in

x2 0in

y2 10.25in

x3 4in

y3 10.25in

x4 4 in

y4 10.25 in

x5 0in

y5 10.25 in

x6 4in

y6 10.25 in

Sumx x1 2 x2 2 x3 2 x4 2 x5 2 x6 2 64 in2

Sumy y1 2 y2 2 y3 2 y4 2 y5 2 y6 2 630.375 in2

3 of 27


CHECKS




Shear Forces in Bolts

Rx1 TRNM

y1

Sumx Sumy 39.815 kip

Ry1 TRNM

x1


R1.4 Rx12

Ry12

42.74 kip Shear demand within bolts 1 and 4

Rx2 TRNM

y2


Ry2 TRNM

x2

Sumx Sumy 0 kip

R2.5 Rx22

Ry22


Rx3 TRNM

y3


Ry3 TRNM

x3


R3.6 Rx32

Ry32


4 of 27


CHECKS




Shear and Moment Demand within Web Plate of Keeper Plate

w.ld

V.f

- -

V.max

w.ld

L.f

0.5*L

2.2500"0.1097 L.f

-

0.39 L.f

R.1

R.2

-

L.f

TRN.M

R.1

R.2

+

M.max+

-

wld Vf Lf1

0.39Lf 0.39 Lf

20.1097 Lf

0.39Lf 0.39 Lf

20.5Lf

42.165kip

in

Vmax wld 0.39 Lf Vf 205.534 kip

Mmax Vf 0.1097 Lf 0.5Vf

wld

Vf 41.764 kip ft

5 of 27


CHECKS









Ωv.bolts 2.00 Reduction factor for bolts


Ab πdb.1

2

2

1.485 in2


Rn.bolts

Ωv.bolts100.973 kip

ChkCon.1 "OK"Rn.bolts

Ωv.boltsmax R1.4 R2.5 R3.6 if


"OK"

Bearing Check (Keeper Pl)

Lc 1.25in (Clear distance,between two holes or edge of material)

tw.pl 1in Thickness of member

Fu.pl 135ksi Ultimate strength ASTM A693 Typ. 17-4 H1150

Ωbc 2 Reduction factor AISC 14th Ed. p. 16.1-127



(AISC 14th Ed. Eq. J3-10)

Rn.bc

Ωbc101.25 kip (For a single bolt, conservative)

ChkCon.2 "OK"Rn.bc

Ωbcmax R1.4 R2.5 R3.6 if


"OK"

6 of 27


CHECKS




Shear in Web Check

Ωsh.y 1.5 Shear strength reduction value

Ωsh.r 2 Shear strength reduction value

Fy.tab 105ksiUltimate strength ASTM A693 Typ. 17-4 H1150

Fu.tab 135ksi

Strength of Elements in Shear (Yielding Shear Tab) Check

lst 6.5in Length of shear

tlftg.pl tw.pl Thickness

Ag.tab lst tlftg.pl 6.5 in2

Rn.fy 0.6 Fy.tab Ag.tab 409.5 kip (AISC 14th Ed. Equation J4-3)

ChkV.Yielding "OK"Rn.fy

Ωsh.yVmaxif


"OK"

Strength of Elements in Shear (Rupture Shear Tab) Check


Rn.fu 0.6 Fu.tab Anv 526.5 kip (AISC 14th Ed. Equation J4-4)

ChkV.Rupture "OK"Rn.fu

Ωsh.rVmaxif


"OK"

7 of 27


CHECKS




Block Shear Check

1'

1.2500"2.5000"

6.5000"

1.5000"

V.f

Lv.1 12in

Numbv 2.5 (Number of bolt holes in shear)

Numbt 0.5 (Number of bolts holes in tension)

Ubs.1 1.0 (AISC 14th Ed. p.16.1-352)

Fu.tab 135 ksi

ttab tw.pl 1 in

Ωbv 2 Reduction factor AISC 14th Ed. p. 16.1-129

Ed.1 1.25in Minimum edgedistance

Ed.2 1.25in Edgedistance

Anv Lv.1 Numbv db.1 0.125in ttab 8.25 in2

Ant Ed.2 Numbt db.1 0.125in ttab 0.5 in2

Agv Lv.1 ttab 12 in2

Rn.bs 0.6 Fu.tab Anv Ubs.1 Fu.tab Ant 0.6 Fu.tab Anv

Ubs.1 Fu.tab Ant

0.6 Fu.tab Agv

Ubs.1 Fu.tab Ant

if

0.6 Fu.tab Agv Ubs.1 Fu.tab Ant otherwise

Rn.bs 735.75 kip (AISC 14th Ed. Equation J4-5)

ChkCon.3 "OK"Rn.bs

ΩbvVfif


"OK"

8 of 27


CHECKS




Moment Capacity of Key Plate

Es 29000ksi

Lb.pl Lw 16 in

tpl ttab 1 in

Zpl

tpl lst2

410.563 in

3

Spl

tpl lst2

67.042 in

3

Fy.pl Fy.tab 105 ksi

Cb 1.0

Ωpl 1.67

Mp.pl Fy.pl Zpl 92.422 kip ft

My.pl Fy.pl Spl 61.615 kip ft

Mn.pl min Mp.pl 1.6 My.pl Lb.pl lst

tpl2

0.08 Es

Fy.plif

min Mp.pl Cb 1.52 0.274Lb.pl lst

tpl2

Fy.pl

Es

Fy.pl Spl

0.08 Es

Fy.pl

Lb.pl lst

tpl2

1.9 Es

Fy.plif

min1.9 Es Cb

Lb.pl lst

tpl2

Spl Mp.pl

Lb.pl lst

tpl2

1.9 Es

Fy.plif

Mn.pl

Ωpl52.274 kip ft (Ref. AISC 14th Ed. Equation: (F11-1,2,3,4))

Chk1 "OK"Mn.pl

ΩplMmaxif


"OK"

9 of 27


CHECKS




Trunnion Assembly Design Checks (ASD) This calculation reviews the capacity of the trunnion yoke plates, trunnion base plate, andtrunnion stiffener plates.

Fy.yk.pl 70ksi ASTM A709 Gr.70

Fy.bs.pl 50ksi ASTM A709 Gr.50

Fy.stf.pl 50ksi ASTM A709 Gr.50

Ωpl 1.67

Trnmax.yk

Fy.yk.pl

Ωpl41.916 ksi

Trnmax.yk.sap max 31.57ksi 33.43ksi 31.49ksi( ) 33.43 ksi Max stress for LC2 (Ice), LC3,LC5

Chkyk Trnmax.yk Trnmax.yk.sap 1

DCRyk.pl

Trnmax.yk.sap

Trnmax.yk0.798

Note: Although the max allowable stress is exceeded, the values areacceptable. The stresses within th yoke plate are not widespread and wouldnot lead to total failure. In addition,LC5 is an extreme and rare load case. LC3can happen more frequently but has a DCR value of 1.07, which is ok byinspection. The most common load case, LC2 (Ice) does have a DCR value < 1(0.973). This will be documented in the DDR.

Trnmax.bs

Fy.bs.pl

Ωpl29.94 ksi

Max pressure found near base pl for LC5, note stresses at supportswere not consideredTrnmax.bs.sap 13.49ksi

Chkbs Trnmax.bs Trnmax.bs.sap 1

Trnmax.stf

Fy.stf.pl

Ωpl29.94 ksi

Max pressure found near stiffener pl for LC3, note stresses atsupports were not consideredTrnmax.stf.sap 14.68ksi

Chkyk Trnmax.stf Trnmax.stf.sap 1

10 of 27


CHECKS




Yoke Plate Bearing Strength Check

Unfactored Global X reactions from LC2a, and LC3 Models SAPTainter gate models unfactoredRx.ASD max 525kip 484kip( ) 525 kip

Unfactored Global Z reactions from LC2a, and LC3 Models SAPTainter gate models unfactoredRz.ASD max 202kip 268kip( ) 268 kip

RM.z.ASDmax 85kip ft 39kip ft( )

2ft 2.5in 2in41.633 kip

Ykpl.dmd Rx.ASD2

Rz.ASD2

RM.z.ASD 631.081 kip Resultant loading acting on Yoke plate from Pinreaciton

Stress modifier of 1.2 ETL 1110-2-584, Type Astructure, conservativeαsm 1.33

Ykpl.dmd.F

αsm Ykpl.dmd

2419.669 kip Yoke plate bearing stress loading / demand per yoke

plate Estimated projected bearing areaYkpl.w 2in Widht of yoke

plates

D1 15.5075in Diameter of yoke plate hole includingtolerances

D2 15.495in Diameter of pin includingtolerances

Diameter ratio factor from Roaks Formula book 7th Ed. Table 14.2 Cylinder in a Cylindrical sockKD

D1 D2

D1 D21.602 10

3 ft

11 of 27


CHECKS




Contact area of pin along yoke plate, refernce Roak Eq. 7th Ed. Table 14.2Cylinder in a Cylindrical socket bpl 2.15

Ykpl.dmd.F

Ykpl.w

KD

Es

25.357 in

Apb bpl Ykpl.w 50.713 in2

Fy.yk.pl 70 ksi Yield strength of yoke plate

Ωbrg 2 Bearing reduction value from AISC 14th Ed. Section J7 Bearing strength

Rbrg.yk.pl 1.8 Apb Fy.yk.pl 6389.84 kip AISC 14th Ed. Equ. J7-1

Rbrg.yk.pl

Ωbrg3194.92 kip

Chkyk.pl.brg "OK"Rbrg.yk.pl

ΩbrgYkpl.dmd.Fif


"OK"

12 of 27


CHECKS




Yoke Plate Buckling Check

Yk.pl.dmd.F

1'-2.0000"

1'-10.0000"

1'-3.5000"

Ykpl.dmd.F 419.669 kip Max compression load in yoke plate

Kpl 2.1 Based on Steel tips 42

Lpl 14in Laterally unbraced length of plate

thkpl 2in Thickness of plate in compression

wpl 15.5in effective width of plate in compression

Ωc 1.67 Compression reduction factor AISC 14thEd.

Fy.pl 70ksi Yield strength of compressin plate

13 of 27


CHECKS




ry.1

wpl thkpl3

12

thkpl wpl0.577 in

Fe.3

π2

Es

Kpl Lpl

ry.1

2110.378 ksi (AISC 13th Ed. Equation E3-4)

Fcr.pl 0.658

Fy.pl

Fe.3

Fy.pl

Kpl Lpl

ry.14.71

Es

Fy.plif

0.877 Fe.3 otherwise

(AISC 13th Ed. Equation E3-2 & 3)

Fcr.pl 53.681 ksi

Pn.pl Fcr.pl thkpl wpl 1.664 103

kip

Pn.pl

Ωc996.471 kip

Chkpl "OK"Pn.pl

ΩcYkpl.dmd.Fif


"OK"

14 of 27


CHECKS




Trunnion Anchor Design Checks (ASD) This calculation sizes the necessary anchors to support and connect the trunnion assemblyto the concrete girder.

MaxV.SAP 10.67kip Anchor reactions PF_LC3U


Fu.acr 90ksi ASTM A449 , 90ksi


2'-1012"

TYP.

3'-10"

914"

TYP.

2"TYP.

3'-6"

2"

TYP.

4"TYP.

11"

TYP.

1'1'-2"

TYP.

734"

TYP.

1014"

TYP.

8"TYP.

1'-112"

TYP.

DRILL & TAPTYP.

Fnv 0.45 Fu.acr 40.5 ksi AISC 14th Ed. Table J3.2


Ωv.bolts 2.00 Reduction factor forbolts

Numbolts 1 Number of bolts inshear

Ab πdb.1

2

2

2.405 in2


Rn.bolts

Ωv.bolts48.707 kip

Chkshr.blts "OK"Rn.bolts

Ωv.boltsMaxV.SAPif


"OK"

Slip Resistance of Base Plate with Pre-Tensioned Bolts (ASD, Service Loads)

Rcomp 988.63kip Compressive force within base plate joints from SAP2000 Model for LC3_U (ServiceCondition)Assumed coefficient of friction between concrete and steel based on EM 1110-2-2702 Eq. 5-2friction between steel and concreteμconc.stl 0.45

Ωslip 1.50 Assumed reduction factor based on slip critical connections AISC14th Ed.

Vrs 0.45 Rcomp 444.883 kip Equation based on EM 1110-2-2702 Eq. 5-2, but converted to ASD

Vu.slip 46kip 46 kip Total shear force acting on anchors for LC3u under service loadconditions

Chkbs.pl.slip "OK"Vrs

ΩslipVu.slipif


"OK"

15 of 27


CHECKS




Pretension of Bolts Check

Fprf 104.5kip Proof load of ASTM A449 anchor w/ 1.75"Dia.

Pretnsn 0.7 Fprf 73.15 kip Using AISC 14th Ed. Table J3.1, used 0.7*ProofLoad

16 of 27


CHECKS




Bending in Bolts Check (ASD)AISC 14th Ed. Section F11

MaxBdg 1.33 7.33 kip 6.25 in 5.078 kip ft Max bending on anchors from base plate bearing on anchors, based on LC2d_U*1.33

Ωb.acr 1.67 Bending reduction value

Zacr

db.13

60.893 in

3 Plastic section Modulus

Sacr

πdb.1

2

3

40.526 in

3 Elastic section

modulus

Fy.acr 0.8 Fu.acr 72 ksi Miimum yield strength for deformed ASTM A449bar

Mn.acr min Fy.acr Zacr 1.6 Fy.acr Sacr 5.051 kip ft AISC 14th Ed. Eq. F11-1

Numacrs.bnd 3 This assumption is based on the premise that not all the anchors take the load equally so only 3 will beconsidered effective.

Chkacr.bndg "OK"Numacrs.bnd Mn.acr

Ωb.acrMaxBdgif


"OK"

Bearing Check Keeper Plate Bolts Bearing on Yoke Plate (ASD)


tw.pl 2in Thickness of member

Fu.pl 85ksi Ultimate strength ASTM A709 Gr. 70W

Ωbrg 2.00 Reduction factor AISC 14th Ed. p. 16.1-127



AISC 14th Ed. Eq. J3-10

Rn.bc

Ωbrg293.25 kip For a single bolt, conservative

Chkbrg "OK"Rn.bc

ΩbrgVfif


"OK"

17 of 27


CHECKS




Bearing Base Plate Check (Cantilever Method) (ASD)

2'-1012"

TYP.

3'-10"

914"

TYP.

2"TYP.

3'-6"

2"

TYP.

4"TYP.

11"

TYP.

1'1'-2"

TYP.

734"

TYP.

1014"

TYP.

8"TYP.

1'-112"

TYP.

DRILL & TAPTYP.

Bplg 34.5in Width of base plate

bplg 30.5in Width of bearing member

dplg.1 42in Depth of bearing member

Nplg 46in Depth of base plate

Fy.pl 50ksi ASTM A709 Gr. 50

Ωc 1.67 AISC 14th Ed.compression reduction value

Rpl 524kip 1.33 Unfactored Load from LC2 Ice *Performance Factor or 1.33

plt 2.5in Thickness of bearing plate

Pp Fy.pl Bplg Nplg 79350 kip Compression StressCapacity

n2

Bplg 0.8 bplg 2

5.05 in

mpl2

Nplg 0.95 dplg.1 2

3.05 in AISC 14th Ed. Base Plate Design

n'2

dplg.1 bplg

48.948 in

Compression stress acting under the platefp

Rpl

Bplg Nplg0.439 ksi

X

4 dplg.1 bplg Ωc Rpl

Pp

dplg.1 bplg 2

4 dplg.1 bplg Ωc Rpl

Pp

dplg.1 bplg 21if


0.014 AISC 14th Ed. p.14-5

λpl 2X

1 1 X 2

X

1 1 X 1if

1 otherwise

0.12 AISC 14th Ed. p.14-5

lmax max n2 mpl2 λpl n'2 5.05 in

18 of 27


CHECKS




tmin lmax

3.33 Rpl Fy.pl Bplg Nplg

0.864 in AISC 14th Ed. Base Plate thickness check Eq.14-7b

Chkplg "OK" plt tminif


"OK"

Grout Allowable Bearing Check (LRFD)This calculation reviews the compressive strength of 7000psi non-shrink grout.

Pdmd 760kip 1.11 1.7 6 152 kip 2394 kip Max reaction + Post tensioned force of anchors (assumes load factor of 1.7 toconvert loading into LRFD)

Brg.area Bplg Nplg 6 Ab 1572.568 in2

Assumed effective bearing area of grout

fcg' 7000psi Assumed compressive strength of the grout

ϕbrg.grt 0.65 ACI 318-11, bearing reduction value Section 9.3.2.4

Rbrg 0.85 Brg.area fcg' 9356.781 kip ACI 318-11, Section10.14

ϕbrg.grt Rbrg 6081.908 kip

Chkgrt.brg "OK" ϕbrg.grt Rbrg Pdmdif


"OK"

19 of 27


CHECKS




Chock Fast Orange Compressive Stress Check This calculation reviews the compressive strength of Chock Fast Oragne, which will serveas a filler material between the yoke plates and pier, and the base plate and trunnion girder.

Areayk.pl.cc.ldg π 14in( )2

π 8in( )2

414.69 in2

Approxiamate Area of Yoke Plate bearing against chock fastoragne. This is conservative as it does not include entire yokeplate touching.

PrLc1208kip

Areayk.pl.cc.ldg0.502 ksi

PrLc2.ice224kip


PrLc.3216kip


PrLc5198kip


Pmax.LC11.33 304 kip


Pmax.LC2.ice1.33 321 kip


See support reactions (yaxis) unfactored loadsmultiplied by 1.33 stress modifier DDRPmax.LC3

1.33 304 kip


Pmax.LC51.33 237 kip


Allowable Compressive Strength from Chockfast OrangeTechnical Bulletin # 692DChofst.org 1200psi

Chkchk Chofst.org max Pmax.LC1 Pmax.LC2.ice Pmax.LC3 Pmax.LC5 1

20 of 27


CHECKS




Leveling Anchors Check Under Dead Load Conditions

3/16

NON-FCWTYP.

SIMPSON STRONG TIETITEN HD

TEMPORARYSCREW ANCHOR

3/4"Ø X 8 1/2"ZINC PLATED OR EQUAL

TYP. 934"

TYP.

9"

TYP.

412"

TYP.

312"

TYP.

112"

TYP.

312"

TYP.

BRACKET PL 1" THKASTM A36 TYP.

STIFF. PL. 3/4" THKASTM A36 TYP.

1/41/4

NON-FCWTYP.

SECTION

7"TYP.

1014"

***This section assumes that only 4 bolts along the bottom bracket are effective in taking the weight of the trunnionassembly, this should be conservative given that there are 12 bolts total***

VDmd.dead.ld 1.2 4.302 kip 5.162 kip Dead load has been factored by 1.2 to convert load into LRFD, loadrepresents weight of the trunnion assembly

Shear Demands on Screw Anchor

VJ22x 0lbf

VJ22y 0lbf

VJ22z VDmd.dead.ld 5.162 kip

21 of 27


CHECKS




ACI 318-08 Appendix D ShearChecks

Φt 0.70 ACI 318-08 Sec. D.4.5

Φs 0.65 ACI 318-08 Sec. D.4.5

Steel Strength of Anchor in Shear

dan 0.75in Diameter of anchor

nstd 4 Number of anchors acting in shear

Fy.ar 97ksi ICC ES Report ESR 2713

Fu.ar 110ksi ICC ES Report ESR 2713

futa min 1.9 Fy.acr 125ksi Fu.acr 90 ksi

Ase πdan

2

2

0.442 in2

Area of anchor)

Vsa 0.6nstd Ase futa 95.426 kip ACI 318-08 Eq. D-20

Φs Vsa 62.027 kip

Chkconn.13 "OK" Φs Vsa VJ22zif


"OK"

Concrete Breakout Strength of Anchor in Shear

heff 5in Effective depth of anchor

sp1 0in Spacing of studs vertically

sp2 0in Spacing of studs horizontally

λ 1.0 ACI 318-08 Sec. D.3.4 & 8.6.1

fc 4500psi Compressive strength of trunnion girder

ca1 4in Assumed edgedistance

cmin min 1.5 heff ca1 4 in

ca2 ca1

le heff Headed anchor with constant stiffness, ACI 318-08 Sec.D.6.2.2

s1 4.5in Spacing between bolts

22 of 27


CHECKS




AVco 4.5 ca1 2 72 in2

ACI 318-08 Eq. D-23

AVc 2 2 1.5 ca1 s1 heff 165 in2

Breakout area assuming that 2 sets of the bottom bolts resist theshear force

Vb 7le

dan

0.2

dan

in in

λfc

psi psi

cmin

in

1.5

in 4.755 kip ACI 318-08 Eq. D-24

ψec.V 1.0 ACI 318-08 Sec. D.6.2.5, negligible eccentricity acting onanchors

ψed.V 0.7 0.3ca2

1.5 ca1 0.9 ACI 318-08 Sec. D.6.2.6

ψc.V 1.0 ACI 318-08 Sec. D.6.2.7, cracked concrete without supplementaryreinforcement

ψh.V

1.5 ca1

heff1.095 ACI 318-08 Sec. D.6.2.8, h.eff < 1.5*c.a1

Vcb

AVc

AVcoψec.V ψed.V ψc.V ψh.V Vb 10.742 kip ACI 318-08 Eq. D-22

Φs Vcb 6.982 kip

Chka.cb "OK" Φs Vcb VJ22zif


"OK"

Shear Capacity of Anchors (Pryout)

kcp 2.0 ACI 318-08 Sec. D.6.3.1

kc 17 Post installedanchor

Nb kc λfc

psi

heff

in

1.5

1 lbf

heff 11inif

16 λfc

psi

heff

in

5

3

1 lbf

otherwise

12.75 kip

ACI 318-08 Eq. D-7 & D-8

Vcpg kcp Nb 25.5 kip ACI 318-08 RD.6.3

Φs Vcpg 16.575 kip

Chk14 "OK" Φs Vcpg VJ22zif


"OK"

23 of 27


CHECKS




SAP2000 Non-Linear Area & Link Stiffness Inputs High Precision Grout Pad

Bspl.area 1in2

Unit bearing area, SAP2000 area springs were assigned

Egrt 6000ksi Modulus of Elasticity for nonshrink grout, based on material Unisorb V-1, value isapproximate

Lgth.grt 5in

Kgrt

Egrt

Lgth.grt1200

kip

in in2

Area spring stiffness input

ChockFast Organe Pad

Brgcfo 1in2

Unit bearing area, SAP2000 area springs were assigned

CME 533ksi Chockfast Orange Modulus of Elasticity

Lgth.grt 0.5in

Kgrt

CME

Lgth.grt1066

kip

in in2

Area spring stiffness

input

Steel Pin Bearing

Brgara 1in 0.5 in 0.5 in2

Tributary area oflink

CM.pin 29000ksi Compression modulus for steel pin

Lgth.grt 0.5in

Kgrt

Brgara CM.pin

Lgth.grt29000

kip

in Link stiffness

input

Trunnion Anchor Bending Stiffness

Ibar

πdb.1

2

4

4

0.223 in4

Moment of Inertia for trunnion assemblyanchorage

Hbr 7.5in Height of anchor based on thickness of base plate +grout pad

Stf

3 Es Ibar

Hbr3

45.997kip

in Stiffness of anchors, assumed to act like a cantilever as the base plate

applies load

24 of 27


CHECKS




Stf.2 πdb.1

2

2

Es1

Hbr 9300.423

kip

in Axial stiffness of anchors

SAP2000 Loading Inputs

Pressure Acting on Yoke Plate from Hub Cross Canyon Loading

Hubbrg.area π 12.in( )2

π 8in( )2

251.327 in2

Bearing area of hubring

LC1b208kip

Hubbrg.area827.606 psi

LC2b.Ice225kip


Side pressure loads acting on Yokeplate

LC3216kip


LC5205kip


Friction Loading from Cross Canyon Load

Surfacearea.shll 0.5in 3 in 1.5 in2

Surface area of shell on solidface 1

Numshells.frtn.ld 150 Number of solids to be load from friction due to composite washer andSS ring

dhub 21in Centerline diameter ofhub

ru dhub 0.5 10.5 in Moment arm from center of pin to center contact surface between hub andyolk plate

μpin 0.3 Coefficient of friction, see ETL 1110-2-584

RLC2 194kip Resultant force from SAP in Y directionunfactored

MFt.LC2 RLC2 μpin ru 50.925 kip ft Moment acting on pin from SAP Yforce

Mprs.LC2.input

MFt.LC2

Surfacearea.shll Numshells.frtn.ld ru0.259 ksi Loading stress to be inputted into SAP

for LC2

RLC3.Lft 216kip Resultant force from SAP in Y direction unfactored

MFt.LC3.Lft RLC3.Lft μpin ru 56.7 kip ft Moment acting on pin from SAP Yforce

Mprs.LC3.input

MFt.LC3.Lft

Surfacearea.shll Numshells.frtn.ld ru0.288 ksi Loading stress to be inputted into SAP

for LC2

25 of 27


CHECKS




Keeper Plate Couple Pressure Loading on Yoke Plate

TRNM.LC.2 169kip ft See Tainter Gate Strut Arm Support Reaction table in DDR unfactored LC2b(Ice)

Lf 20.5in On center distance betweenbolts

Surfacearea.shll 0.5in 1 in 0.5 in2

Surface area of shell on solidface 1

Numshells.frtn.ld 12 Number of solids to be load from friction due to composite washer andSS ring

PK.pl.LC2

TRNM.LC.2

Lf Surfacearea.shll Numshells.frtn.ld16.488 ksi Pressure acting on solids from keeper plate

bolts

TRNM.LC.3 164kip ft See Tainter Gate Strut Arm Support Reaction table in DDR unfactored LC3 LS

Lf 20.5in On center distance betweenbolts

PK.pl.LC3

TRNM.LC.3

Lf Surfacearea.shll Numshells.frtn.ld16 ksi Pressure acting on solids from keeper plate

bolts

MZ Couple Loading

Spyk.pl 28.5in

Moment about Z axis in SAP for LC1Mz.LC1 4kip ft

Moment about Z axis in SAP for LC2Mz.LC2 59kip ft

Mz.LC3 19kip ft Moment about Z axis in SAP for LC3

Mz.LC5 9 kip ft Moment about Z axis in SAP for LC5

LC1.MZ

Mz.LC1

Spyk.pl1.684 kip

LC2.MZ

Mz.LC2

Spyk.pl24.842 kip SAP2000 Moment Couple

inpurt for MZ, loads shall beapplied as demands and notreactions in SAP, Left Joint +,Right Joint -

LC3.MZ

Mz.LC3

Spyk.pl8 kip

26 of 27


CHECKS




LC5.MZ

Mz.LC5

Spyk.pl3.789 kip

27 of 27


Element: Trunnion Hub Design Check Labor Code: 2686C1

Calculation Title: Trunnion Hub Thickness and Stress Check



Checked by: Michele Louie PE Date: 2-22-2016


Rev. No.


Prepared by:

Date:

Checked by:

Date:

Sheet Index:

1-4

Von Mises Combined Stress Analysis Design Che

FARGO TAINTER GATE DESIGN CHECKS

Trunnion Hub Thickness and Stress Check


Checked By: Michele Louie PEDate:2/22/2016

Trunnion Hub Design Checks See ETL 1110-2-584 & EM 1110-2-2702

1 of 4





Von Mises Combined Stress Analysis Design Checks

Demands based on LC2a Unfactored

Px 524kip Downstream force from SAP2000models

Py 224kip Thrust washer force from SAP2000models

Pz 202kip Vertical force from SAP2000Models

Mx 42kip ft Bending moment about the Xaxis

My 168kip ft Trunniuon Frictionmoment

Mz 59kip ft Bending moment about the Zaxis

Hub Design Inputs

thub 3.25in Thickness of hubring

Lcant 7in Approxiamate cantilever length of hub nearpier

Hb.w 26in Width ofhub

rinr 8.75in Inner radius ofhub

rotr rinr thub Outerdiameter

Es 29000ksi Modulus ofElasticity

cfbr 6.6875in Distance from neutral axis to extreme fiber

Fy.hub 36ksi ASTM A105 Forging

Atrib

π 2 rotr 2 2 rinr 2

40.5 105.931 in

2 Tributary

area

Ihub.trib 1144in4

Moment of inertia of half circle about weakaxis

Determine Distributed Load Behind Hub from Resultant Load P.x and P.z Marm.mz 1ft 2in Distance between flanges welded to

hub

Acnt

2 π rinr

227.489 in Half of the circumference around inner

diameter

Fcpl.mz

Mz

Marm.mz50.571 kip Component of force comple acting on left flange faceing downstream

2 of 4





Fcpl.mx

Mx

Marm.mz36 kip

Wxz

Px Fcpl.mz 2 Pz Fcpl.mx 2

Hb.w Acnt 125.303 ksf

Inner distributed pressure from P.xand P.z

Determine Bending Stress and Shear Stress at Point A from P.xMAxz Wxz Acnt Lcant Lcant 0.5 48.836 kip ft Bending moment at A from

P.x

Bending stress at A fromP.x

σbxz.1

MAxz cfbr

Ihub.trib3.426 ksi

VAxz Wxz Acnt Lcant 167.438 kip Shear at A fromP.x

Avxz 47.17in2

Effective area resisting shearforces

ybr.vxz 3.1875in Distance of shear resisting centroid to centroid ofsection

Ivxz 1144in4

Moment of inertia of entire section

σvx.1

VAxz Avxz ybr.vxz

Ivxz 2 thub3.386 ksi

3 of 4





Determine Axial Stress at Point from P.y

σay

Py

π rotr2

π rinr2

1.057 ksi

Determine Von Mises Stressσa1 σbxz.1 3.426 ksi Note: Under the worst case, the bending force at the extreme fiber will be

additive to the axial force heading in the same direction. These should beadded together.σa2 σay 1.057 ksi

σb 0kip

σab σvx.1 3.386 ksi

σVM σa1 σa2 2 σa1 σa2 σb σb2

3 σab2

7.381 ksi

ChkVM "OK" σVM 0.5 Fy.hubif


"OK"

4 of 4

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