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MANN.STEPHANIE.MARIE.1612765444

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11/18/2025

Watson, MN Chippewa Low Flow Gate Machinery Replacement

Peter Allen, PE

09/23/2025

MVP

X:\PROJECTS\O&M\Chippewa_Diversion_Projects_2023\02 Engineering\Low Flow Gate Machinery Replacement

Chippewa Diversion Low Flow Gate Machinery Calculations

13, plus 1 Cover Sheet, plus 1 QC Cover Sheet, for 15 total

Stephanie M. Mann, Mechanical Engineer, PE

Daniel D. Anderson, Mechanical Engineer

CALCULATION COVER SHEET

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Chippewa Low Flow Gate 43BCB3

Chippewa Diversion Low Flow Gate Machinery Calculations

15 total

Daniel D. Anderson, Mechanical Engineer 10/08/2025

Stephanie M. Mann, Mechanical Engineer, PE 09/23/2025

A.1 Signed QA-QC Cover Sheet A.2 Calculation Cover Sheet (Table of Contents) A.3 - A.15 Gate Machinery Calculations

- EM 1110-2-2610 Mechanical and Electrical Design for Lock and Dam Operating Equipment, 03/18/2025

- AWWA C560-21 Cast-Iron Slide Gates, 01/01/2022

- ASME B1.5 ACME Screw Threads, 1997, R 2024

- ASTM A276/276M Stainless Steel Bars and Shapes, 2023

- Fundamentals of Machine Component Design, Juvinall & Marshek, 2017, 6th Edition

Chippewa Diversion Low Flow Gate Machinery Calculations

Table of Contents

1. Introduction

2. References

3. Gate Unseating Force Discussion

4. Defined Constants

5. Gate Unseating Force Calculations

6. Stem Criteria and Max Allowable Force Calculations

7. Summary Appendix

1. Introduction

The Chippewa Diversion low flow gate machinery needs to be replaced due to a non-functioning multi-turn actuator and bent stem. The original 4' x 4' cast iron slide gate and gate thrust nut will remain. A new electric motor multi-turn actuator (operator), pedestal, non-rotating stem, and stem guides are to be purchased and installed by the Government.

These calculations determine the limiting loads used in sizing the actuator/motor assembly.

The relevant values are the working load required to unseat the gate at maximum head, the rated load of the actuator based on the rated torque of the motor, and the extreme load based on the locked rotor torque of the motor. The limiting component of this system is the stem, whose size and material will remain as 2.000" diameter stainless steel.

The 4' x 4' Chippewa Low Flow gate is the same size and model of cast iron gate as the Lac qui Parle (LQP) low flow gates. All these structures were built at the same time by the Works Progress Administration. During the 1986 Rehabilitation and Gate Motorization project, the Lac qui Parle dam and Chippewa Diversion gates were motorized. LQP has six 6' x 8' gates and three 4' x 4' gates. The government purchased electric motor actuators for all these gates on the same contract. However, the machinery sizing calculations were based on 25' and 10' heads at LQP and Chippewa, respectively. It was decided to use the same 5 HP motor for the 4' x 4' gates at both locations even though the lift requirement for the low flow gate was less than half of that required at LQP due to a much lower hydrostatic pressure friction force. So, the low flow actuator was greatly oversized, but the actuator torque switches were set to match the conditions.

Around Nov 14, 2023, the stem of the Chippewa low flow gate buckled while being used to drive the gate closed. The actuator was operated in a non-standard manner that bypassed the closing torque switch. The oversized motor/actuator was rated 3.2 times the required torque, easily capable of exceeding the buckling rating of the stem. This point is made to validate the stem having been designed with a proper diameter of 2.000 inches.

The original stem is a two-piece design joined with a bronze coupling for ease of shipment, according to the Rodney Hunt catalog. Recent gate modernizations at LQP included stem segments up to 252" long. The stem length for this application will be no more than 210", so shipping this length is not a concern.

On-site measurements were taken to validate the original Works Progress Administration lb ft ft ft ft ft lb lb ft in in ft lb ft lb lb lb lb lb lb lb in ft ft ft ft ft ft ft ft ft psi ksi ksi π in in π kip kip kip kip kip kip kip kip kip kip kip lb lb kip kip

(WPA) drawing. One notable difference was found. The upper surface of the water control structure, where the pedestal is mounted, has a a hole in the concrete where the stem passes through. This hole is offset from original design by 2.5 inches and explains the very short edge distance of the anchor bolts. It's suspected that the result of this offset is a stem that is at a slight angle from vertical. This cannot be determined until new bulkheads are built and the structure dewatered. The Government project design team had an informed discussion on this issue. Though recommended in a future project, moving the hole to its proper location is beyond the scope of this supply contract. This arrangement has worked for nine decades, so risk is low. The problem of the anchor bolts being too close to the edge will be solved by designing a pedestal base plate with relocated anchoring points and will be fabricated by the Government.

Other measurements taken showed consistency with the WPA drawing. Assumptions had to be made on where the bottom end of the stem is located since we cannot dewater the structure until bulkheads are fabricated. The stem ends in a region between the center horizontal rib of the gate and the rib above it. A reasonable and conservative assumption is to place the bottom of the stem at the center rib for measuring total length and put the fixed point used in the Euler buckling formula at 6" above the center rib.

2. References

American Society of Mechanical Engineers

ASME B1.5 1997, R 2024 ACME Screw Threads

American Society for Testing and Materials

ASTM A276/276M 2023 Stainless Steel Bars and Shapes

American Water Works Association

AWWA C560-21 01/01/2022 Cast-Iron Slide Gates

Textbooks

Fundamentals of Machine Component Design, Juvinall & Marshek, 2017, 6th Edition

US Army Corps of Engineers

EM 1110-2-2610 03/18/2025 Mechanical and Electrical Design for Lock and Dam Operating Equipment

3. Gate Unseating Force Discussion

The lifting force for slide gates is calculated for two conditions; the unseating force and sustained effort force. Of these, the unseating force is considerably higher. The unseating force includes the effort to pull the gate from its wedges and is where the friction caused by hydrostatic pressure is at the greatest. The guide spec for Section 35 20 16.54 Slide Gates lb ft ft ft ft ft lb lb ft in in ft lb ft lb lb lb lb lb lb lb in ft ft ft ft ft ft ft ft ft psi ksi ksi π in in π kip kip kip kip kip kip kip kip kip kip kip lb lb kip g g and Actuators paragraph 2.3.1 reads, "Gate actuation forces must follow the requirements as shown in Appendix A of AWWA C560 ...", which contains the opening (unseating) force formula. However, the formulas written into the spec are slightly different than given in AWWA C560. Additionally, the original Rodney Hunt catalog contains yet another formula and tables for evaluating the lifting force. All three versions of the unseating formulas are calculated in this document.

During the 1986 Rehabilitation and Gate Motorization, a lifting force of 8200 lb. was used for motor/actuator sizing. It was based on a 10 foot head. There is no documentation of how this value was derived. However, this value was applied to result in nearly four decades of service and will be used to compare to the calculated values.

Formula from AWWA C560 Appendix A

Two formulas are given in this appendix; one for the unseating force, F , and the other for sustained effort of the actuator, F1. Per the appendix, F1 is "significant only on large gates and higher heads". Our 4' x 4' gate is small, so we're only interested in the unseating force of F.

AWWA C560, App A, pg. 21

Formulas from Specification Section 35 20 16.54

Two formulas are given; one for the unseating force Fu and the other for sustained effort Fn .

Again, we're only interested in the unseating force Fu .

lb ft ft ft ft ft lb lb ft in in ft lb ft lb lb lb lb lb lb lb in ft ft ft ft ft ft ft ft ft psi ksi ksi π in in π kip kip kip kip kip kip kip kip kip kip kip lb lb kip

Specification Section 35 20 16.54

Formula from Rodney Hunt Catalog

The catalog gives the force required to open a sluice gate (unseating force) as:

FRH = F(water) + F(wedge) + F(weight)

Rodney Hunt Catalog 267R pg. 22

Gate Unseating Thrust per 1986 Rehabilitation

The table below shows values that U.S. Army Corps of Engineers (USACE) provided to Portersville Teledyne for sizing the motors. The Unseating Thrust at the Chippewa Low Flow lb ft ft ft ft ft lb lb ft in in ft lb ft lb lb lb lb lb lb lb in ft ft ft ft ft ft ft ft ft psi ksi ksi π in in π kip kip kip kip kip kip kip kip kip kip kip lb lb kip

Gate is given in the last column of row H as 8200 lb.

Portersville Teledyne Motor Sizing Specifications

4. Defined Constants

Density of Water

The density of water shown above in both formulas is:

≔ρ 62.4 ―― lb ft 3

Friction

Friction for the AWWA C560 calculation is:

≔f 0.35

Friction for the guide spec formula is:

≔fu 0.6

The friction factor for the Rodney Hunt formula is given a subscript to differentiate it from the AWWA C560 friction factor.

≔fRH 0.35

Area

The gate area (disc opening area) is:

≔A =⋅4 ft 4 ft 16 ft 2

Design Head

A 10' head was used in calculating the unseating force during the 1986 actuator supply contract. The gate centerline elevation is EL 937.0. The head elevation is EL 947.0. The top ft lb lb ft in in ft lb ft lb lb lb lb lb lb lb in ft ft ft ft ft ft ft ft ft psi ksi ksi π in in π kip kip kip kip kip kip kip kip kip kip kip lb lb kip lb ft ft ft ft g surface of the control structure is 950.0. See Works Progress Administration drawing "WPA Sheet LC-4 Details of Low Water Control Works Chippewa River" in the appendix. Thus, the 10' head is the case where the water surface elevation is 3' below the top of the low flow structure, i.e. 3' below the surface where a maintenance worker would stand while using the actuator. This is a reasonable elevation above which the gate would certainly have already been positioned to fully open.

≔H 10 ft

Gate Weight

The weight for a 48" x 48" cast iron gate is given in Rodney Hunt Catalog 267R on page 22:

≔P1 1150 lb

≔Wg =P1 1150 lb

Stem Weight

Stem weight is given in pounds per lineal foot. The exact stem length cannot be determined until a dewatering can be accomplished. The total stem length is conservatively calculated as the sum of the length from the center of the lift nut at EL 953.0 ft to the middle rib of the gate at EL 937.0 ft (just below the thrust nut), a 12" section from the center of the stem nut to the top of the actuator (conservative estimate), and an additional 6" for the contractor to affix a temporary connection for shop testing. This sacrificial section will be removed at a later ft in in ft lb ft lb lb lb lb lb lb lb in ft ft ft ft ft ft ft ft ft psi ksi ksi π in in π kip kip kip kip kip kip kip kip kip kip kip lb lb kip lb ft ft ft ft ft lb lb g date when the bottom of the stem is cut and threaded to match field conditions.

Total stem length:

≔l =++(( -953.0 937.0)) ft 12 in 6 in 17.5 ft

The weight per lineal foot of the steel 2-inch diameter gate stem is given in Rodney Hunt Catalog 267R on page 18:

≔P2 =⋅10.66 ― lb ft l 187 lb

≔Ws =P2 187 lb

5. Gate Unseating Force Calculations

The AWWA C560 and Rodney Hunt formulas are equivalent.

AWWA C560 Formula:

≔FC560 =++⋅⋅⋅ρ f A H 1.5 P1 P2 5406 lb

Guide Spec Formula:

≔Fu =+⋅⋅⋅ρ H A fu (( +Wg Ws)) 7327 lb

Rodney Hunt Formula:

≔FRH =++⋅⋅⋅H ρ A fRH ⋅0.5 Wg (( +Wg Ws)) 5406 lb

1986 Rehab Unseating Thrust:

≔F1986 8200 lb lb in ft ft ft ft ft ft ft ft ft psi ksi ksi π in in π kip kip kip kip kip kip kip kip kip kip kip lb lb kip lb ft ft ft ft ft lb lb ft in in ft lb ft lb lb lb lb lb lb

The conservative working load (unseating force) is the maximum of these four values:

Working load used in specifications≔Fworking =max⎛⎝ ,,,FC560 Fu FRH F1986⎞⎠ 8200 lb

6. Stem Criteria and Max Allowable Force Calculations

Stem calculations include checking for ultimate tensile strength, yield strength, and buckling.

These calculations are intended to verify that the 2.000" stem diameter design from the 1930s meets the factors of safety under the current standards. It's possible to use a larger diameter stem for this gate, but that's an option to be avoided. Increasing the stem diameter would mean modifying or replacing the thrust nut. Although the thread size of the current thrust nut is unverified, we do know that the nominal size is 2.000". The threads-per-inch of the thrust nut will be verified at the next dewatering, after which the bottom of the stem will have matching threads machined into it.

Stem Diameter and Radius

The current gate stem is 2.000" in diameter with 2.000-3-ACME threads at the top and into the coupling. The thread size at the bottom into the gate thrust nut will remain unknown until bulkheads are fabricated and the water control structure dewatered. When the thread size of the thrust nut and an accurate total length of the stem are determined, the bottom of the stem will cut to length and threaded.

The top end of the new stem will have threads of the double-lead ACME type and meet the requirements of ASME B1.5 with thread designation 2.000-0.25P-0.50L-ACME-2G-LH.

For 2" nominal size threads, the minor diameter is 1.750" (ASME B1.5, Table 2). The minor diameter will be used in calculations.

Thread minor diameter≔d 1.750 in

Stem Segment Lengths

The stem consists of three segments held between four fixed-type supports. A fourth segment above the lift nut is not under load and does not need to be checked for strength. The lengths of the three segments under load must be determined to check for critical load in buckling.

The supports from the top down are: lift nut, upper stem guide, lower stem guide, and gate thrust nut. The calculation for critical load in buckling is determined for the longest length of stem between supports. The length of segments between supports is taken from the original WPA drawing Sheet LC4, reproduced in Fig. A1 in the Appendix, and is determined as follows:

1.

2.

3.

The topmost support is where the stem is threaded into the stem nut at the actuator, which will be specified as 36" above the upper surface of the water control structure.

This puts the elevation of this support at EL 953.0.

The upper stem guide will be wall-mounted under the cantilevered section of the control structure at EL 948.0. This section of stem, between the lift nut and upper stem guide, is designated l1 .

The lower stem guide will be floor-mounted to the top of the horizontal surface at EL ft ft ft ft ft ft ft ft ft psi ksi ksi π in in π kip kip kip kip kip kip kip kip kip kip kip lb lb kip lb ft ft ft ft ft lb lb ft in in ft lb ft lb lb lb lb lb lb lb in

4.

g

944.0. The section between upper and lower stem guides is designated l2 .

The bottommost support is where the stem threads into the thrust nut. Images from the Rodney Hunt catalog, a picture from a previous PI, and a GoPro video taken onsite show that a reasonable assumption is that the top of the thrust nut is no less than 6" above the center rib of the gate and puts it at EL 937.5. This segment below the lower stem guide is designated length l3 .

≔l1 =-953.0 ft 948.0 ft 5 ft

≔l2 =-948.0 ft 944.0 ft 4 ft

Longest segment - for buckling calculation≔l3 =-944.0 ft 937.5 ft 6.5 ft

Changing the elevation of the upper stem guide did not change the selection of the length of the longest segment that was

Stem Properties

Modulus of Elasticity

The minimum modulus of elasticity for 304 and 316 stainless steel can be found here:

https://www.theworldmaterial.com/type-304-grade-stainless-steel/ https://www.theworldmaterial.com/316-stainless-steel/ https://shop.machinemfg.com/comprehensive-guide-to-aisi-304-stainless-steel-properties/ https://mechanical-engineering.com/316-stainless-steel-properties/

≔E ⋅28 106 psi

Ultimate Tensile Strength

The minimum ultimate tensile strength for cold-finished, annealed 304 and 316 stainless steel is given in Table 2 ASTM A276/A276M.

≔Su 75 ksi

Yield Strength

The minimum yield strength for cold-finished, annealed 304 and 316 stainless steel is given in Table 2 ASTM A276/A276M.

≔Sy 30 ksi

End-restraint Condition

"The critical buckling load shall be determined by using the Euler column formula, where end-constraint condition C = 2." (AWWA C560, para 4.4.11.2)

Fixed-fixed end condition≔C 2 π in in π kip kip kip kip kip kip kip kip kip kip kip lb lb kip lb ft ft ft ft ft lb lb ft in in ft lb ft lb lb lb lb lb lb lb in ft ft ft ft ft ft ft ft ft psi ksi ksi

Stem Area

Stem cross-sectional area≔Astem =⋅π ― d2

2.405 in 2

Radius of Gyration

The radius of gyration is r= which, for a circle, reduces to d/4 (Juvinall & Marshek, I

A

2017, App B-1a).

Radius of gyration≔r =― d

0.438 in

Length/Radius of Gyration Ratio (Slenderness Ratio)

For stem guide spacing, AWWA C560 requires, "The length/radius of gyration ratio (l/r) shall not be greater than 200." The l/r ratio also informs us of whether to use the Euler or JB Johnson bucking formula. The JB Johnson formula is intended for short column, that are commonly regarded as those having le/r less than 10 (Juvinall & Marshek, 2017, para 5.12). The effective length, le , for C=2 is one-half of l .

Okay, less than 200≔lrRatio =― l3 r 178.286

Greater than 10 - use Euler column bucking formula≔leffrRatio =―― l3

2 r 89.143

Factors of Safety

The following factors of safety will be used in calculations that follow. Each place they're used will be accompanied by references to corresponding sections in EM 2610 and AWWA C560.

≔FoS1.25 1.25

≔FoS2 2

≔FoS3 3

≔FoS5 5

Motor/Actuator Rating Definitions

AWWA C560 defines the terms "rated load" and "extreme load". EM 2610 uses similar π kip kip kip kip kip kip kip kip kip kip kip lb lb kip lb ft ft ft ft ft lb lb ft in in ft lb ft lb lb lb lb lb lb lb in ft ft ft ft ft ft ft ft ft psi ksi ksi π in in terminology. To be clear, equivalent terms are grouped together.

Rated load: The thrust produced by the rated starting torque of the actuator. The equivalent terms in EM 2610 are "maximum working load" and "maximum normal full load".

Extreme load: The thrust produced by the rated stall (locked rotor) torque of the actuator.

The equivalent terms in EM 2610 are "overload" and "stall load".

Buckling Criteria

The Euler Column Formula (EM 2610, para 9-12 and C560, para 4.4.11.2) is:

* Euler Column formula: P = C EA (r/l )2, where P = critical buckling compressive load π2 on stem, C = end-restraint conditions, E = modulus of elasticity, l = length or span between supports, r = radius of gyration, and A = area of stem.

≔Pcrit =⋅⋅⋅C π2 E Astem r l3

41.824 kip

"Components that might fail in buckling compression should be designed for a minimum factor of safety of 3, using the Euler or J.B. Johnson formulas, as appropriate." (EM 2610, para 2-1 c.)

"The factor of safety must be applied to the maximum working load on the member and the critical buckling load." (EM 2610, para 2-1 c. (1))

≔Pbuckle.rated =―― Pcrit

FoS3

13.941 kip

Max allowable rated load for buckling criteria

In compression, the stem shall be designed for a critical buckling load caused by 1.25 times the extreme load of the actuator. (AWWA C560, para 4.4.11.2)

Max allowable extreme load for buckling criteria≔Pbuckle.extreme =――― Pcrit

FoS1.25

33.459 kip

Yield Strength Criteria

≔Pyield =⋅Sy Astem 72.158 kip

"Each operating stem shall be designed for the thrust produced by the rated load of the actuator with ... a minimum safety factor of 2 with regard to the yield strength of the material used." (AWWA C560, para 4.4.11.2)

Max allowable rated load - yield criteria≔Pyield.rated =―― Pyield

FoS2

36.079 kip kip kip kip kip kip kip lb lb kip lb ft ft ft ft ft lb lb ft in in ft lb ft lb lb lb lb lb lb lb in ft ft ft ft ft ft ft ft ft psi ksi ksi π in in π kip kip kip kip kip

"The stem shall also be designed for the thrust produced by the extreme load of the actuator with ... a minimum safety factor of 1.25 with regard to the yield strength of the material used."

Max allowable extreme load - yield criteria≔Pyield.extreme =――― Pyield

FoS1.25

57.727 kip

Ultimate Tensile Strength Criteria

≔Pultimate =⋅Su Astem 180.396 kip

"Each operating stem shall be designed for the thrust produced by the rated load of the actuator with a minimum safety factor of 5 with regard to the ultimate tensile strength ...

of the material used" (AWWA C560, para 4.4.11.2)

Max allowable rated load - ultimate criteria≔Pultimate.rated =――― Pultimate

FoS5

36.079 kip

"The stem shall also be designed for the thrust produced by the extreme load of the actuator with a minimum safety factor of 2 with regard to the ultimate tensile strength ...

of the material used." (AWWA C560, para 4.4.11.2)

Max allowable extreme load - ultimate criteria≔Pultimate.extreme =――― Pultimate

FoS2

90.198 kip

Max Allowable Load Ratings

The maximum allowable rated load and extreme load produced by the motor/actuator assembly are the minima of the criteria buckling, yield strength, and ultimate strength in both loading conditions.

The maximum allowable load rating of the motor/actuator assembly, based on the motor rated torque, is:

≔Fmax.rated =min ⎛⎝ ,,Pbuckle.rated Pyield.rated Pultimate.rated⎞⎠ 13.9 kip

The maximum allowable extreme load of the motor/actuator assembly, based on the motor locked rotor torque, is:

≔Fmax.extreme =min ⎛⎝ ,,Pbuckle.extreme Pyield.extreme Pultimate.extreme⎞⎠ 33.5 kip

7. Summary

The criteria to be used in the specifications are presented here.

lb lb kip lb ft ft ft ft ft lb lb ft in in ft lb ft lb lb lb lb lb lb lb in ft ft ft ft ft ft ft ft ft psi ksi ksi π in in π kip kip kip kip kip kip kip kip kip kip kip

Gate Weight

Weight of existing cast iron gate, excluding stem.

=Wg 1150 lb

Working Load

This value is the minimum required load for unseating the existing cast-iron slide gate. The specifications require the Contractor to choose an actuator with a specified percentage of minimum reserve capacity.

=Fworking 8200 lb

Max Rated Load

This value is the maximum allowable rated load of the motor/actuator assembly. Buckling of the 2" nominal diameter stem is the determining criteria.

=Fmax.rated 13.9 kip

Max Extreme Load

This value is the maximum allowable extreme load of the motor/actuator assembly. Buckling of the 2" nominal diameter stem is the determining criteria.

=Fmax.extreme 33.5 kip

Force Transmitted to the Pedestal

This value will be determined by the Contractor once they select the an actuator. The actual extreme load produced by the chosen actuator, based on the locked rotor torque of its motor, will be used as the load for which the Contractor chooses or designs the pedestal with factors of safety as given in EM 2610 para 2.1.b and 2.1.b (1).

Lateral Load on Stem Guides

This value will be determined by the Contractor once they select the an actuator. The actual rated load produced by the chosen actuator, based on the rated torque of its motor, will be used as the load for which the Contractor chooses stem guides. The minimum lateral load rating of the stem guides will be specified to be 2% of the rated load.

- End of Calculations -