CA FTBR FSTR(2) Final Hydrology and Hydraulics Recommendations Report.pdf

Folsom South Trail Improvements Ph II

Trail and Pedestrian Bridge

Bureau of Reclamation (BOR)

Hydrology and Hydraulics

Recommendations Report

Federal Highway Administration

Central Federal Lands Highway Division

Prepared by

HDR Engineering, Inc.

January 3rd, 2020

Folsom South Trail Improvements Ph II 1 Central Federal Lands Highway

Trail and Pedestrian Bridge Hydrology and Hydraulics

1. Introduction

Project Description HDR is preparing a Project Delivery Plan for the Federal Highway Administration, Central Federal

Lands Highway Division (CFLHD) for proposed improvements to the Folsom South Trail within the Bureau of Reclamation (BOR) property in Sacramento County, CA. The scope of the proposed project includes design of a pedestrian bridge over Laguna Creek, minor drainage improvements, crack sealing, asphalt patching, surface treatment, fencing, open-air shelter, signing, pavement markings, and other miscellaneous items as requested by BOR.

The Folsom South Trail was originally a paved maintenance trail for BOR use. As the community developed and became more populated, bicyclists and pedestrians increased usage of the trail, and the BOR determined that the trail should become multi-use and open to the public. The trail begins at Hazel Avenue and traverses parallel to the Folsom South Canal approximately 13.5 miles south to near Sloughhouse Road. The first 5.5 miles of the road were patched and surfaced in CA FTBR Folsom South Trail (1), and pavement markings were placed along the length of the trail.

This report serves as the basis for hydrologic and hydraulic analysis for the proposed bridge and provides bridge scour calculations.

Project Location The proposed pedestrian bridge will cross Laguna Creek immediately west of the Folsom South

Canal in unincorporated Sacramento County on BOR land. The crossing is located southwest of the intersection of Jackson Road (State Highway 16) and Sunrise Boulevard (County Road E2) as shown on Figure 1.

Federal Emergency Management Agency (FEMA) has designated the special flood hazard area within the project site as a FEMA Zone AE, as determined by the Flood Insurance Rate Maps

(FIRM) #06067C0238J, effective date July, 19 2018, as shown in Appendix A. Floodplains designated Zone AE are areas subject to inundation by the 1-percent-annual-chance flood event determined by detailed methods and include Base Flood Elevations (BFEs). Sacramento County participates in the National Flood Insurance Program under the community identity 060262D.

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Figure 1. Project Location

Design Criteria

The Sacramento City/County Drainage Manual Volume 2: Hydrology Standards supplemented with Chapter 7 of the FLH "Project Development and Design Manual" (PDDM) are used as the basis to evaluate the proposed pedestrian bridge. Neither reference specifies design standards for a pedestrian bridge.

According to the criteria manuals, typical vehicular bridged waterways should be designed to the

50-year recurrence interval (2% annual exceedance probability [AEP]) for capacity with 2 feet of freeboard and the 100-year recurrence interval (1% AEP) for stability design. Since the proposed bridge will only be used for pedestrian traffic and is not critical infrastructure, it will be treated as a low-water crossing which should be designed to the 10-year recurrence interval (10% AEP) for capacity and the 25-year recurrence interval (4% AEP) for stability design.

The 100-year recurrence interval (1% AEP) was used as the design flood to evaluate floodplain encroachment with the 500-year recurrence interval (0.2% AEP) used to check overtopping.

There is no regulatory mapped floodway in the project vicinity so a Conditional Letter of Map

Revision (CLOMR) may not be required however, a floodplain permit must be obtained from

Sacramento County Department of Water Resources prior to any land disturbing activities.

There is the potential for rapid drawdown of Laguna Creek following flood events. Stream bank soils are more susceptible to failure during rapid drawdown of water levels due to the increase in soil pore water pressures. This condition can reduce the geotechnical design values for the proposed bridge abutments. The exact rate of drawdown is dependent on the receding limb of the storm hydrograph and is difficult to determine. Although unlikely, it is recommended that the extreme case of an abrupt drawdown from flood levels to base flow be assumed as a condition for design.

Folsom South Trail Improvements Ph II 3 Central Federal Lands Highway

2. Hydrology Flood Insurance Study (FIS) Number 06067CV001D was developed by FEMA for Sacramento

County, California, and incorporated areas. The FIS is a compilation and presentation of flood risk data for specific watercourses within the community and contains detailed flood elevation data in flood profiles and data tables. Table 10 in the FIS contains a summary of the hydrologic peak discharges developed and used to determine flood elevations. The proposed Folsom South

Trail pedestrian bridge is located approximately 1,000 feet downstream of the detailed FEMA model limits for Laguna Creek which is the crossing of Jackson Road (State Highway 16). The effective peak discharge values at the upstream study limits are presented in Table 1.

Table 1. FIS Peak Discharges for Laguna Creek at Sunrise Blvd

10% AEP (10-yr) 721 cfs

2% AEP (50-yr) 828 cfs 1% AEP (100-yr) 883 cfs

0.2% AEP (500-yr) 1,011 cfs

The FIS did not provide detail regarding how these peak discharges were calculated but listed that West Yost Associates provided the analysis used in the FIS in January of 2013. A copy of that report was not readily available however, since these effective peak discharge values were approved by FEMA, they will be used for this analysis.

To develop peak discharge values for the remaining events of interest, a power function was fit to the FIS values plotted against their annual exceedance probabilities and is shown in Figure 2.

Figure 2. FIS Peak Discharge Trendline

The remaining flows of interest are presented in using the power function trendline. Peak discharge values for the 2- and 5-year events may be overestimated slightly as the extrapolated

Folsom South Trail Improvements Ph II 4 Central Federal Lands Highway trendline shows a rather flat slope due to low variations in peak discharge values with respect to their recurrence interval.

Table 2. Calculated Peak Discharges from Trendline

50% AEP (2-yr) 628 cfs

20% AEP (5-yr) 680 cfs 4% AEP (25-yr) 782 cfs

0.5% AEP (200-yr) 937 cfs

In order to validate the peak discharges presented in and interpolated from the FIS, flows were also calculated using regression equations developed by the United States Geologic Survey

(USGS) in their Scientific Report 2012-5113 titled Methods for Determining Magnitude and

Frequency of Floods in California. USGS conducted a regional regression analysis using generalized least squares regression to develop a set of equations for estimating flows with 50-, 20-, 10-, 4-, 2-, 1-, 0.5-, and 0.2-percent AEP for ungaged basins in California that are outside of the southeastern desert region. According to the USGS report, flood-frequency estimates and basin characteristics for 630 streamgages were combined to form the final database used in the regional regression analysis. Five hydrologic regions were developed for the area of California outside of the desert region. This project is located in the Sierra Nevada region which has regression equations as functions of drainage area, mean basin elevation, and mean annual precipitation.

The tributary drainage area to the project site was delineated using 1-foot contours generated from a combination of USGS NED 1/3 arc-second 1 x 1 degree and 1/9 arc-second 15 x 15 minute

Digital Elevation Models (DEM). The higher resolution DEM was used where available, but did not cover the entirety of the drainage basin. The delineated drainage basin is shown in Figure 3.

The mean basin elevation was determined by clipping the blended USGS elevation DEMs and taking the average elevation of the resulting DEM. Similarly, the mean annual precipitation was determined by clipping the PRISM 1971-2000 Raster which has average annual precipitation depths at a 4 kilometer resolution. The calculated regression equation parameters are summarized in Table 3.

Table 3. Regression Equation Parameters

Drainage Area 8.49 square miles

Mean Basin Elevation 189.9 feet Mean Annual Precipitation 21.9 inches

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Figure 3. Drainage Basin for Laguna Creek at Folsom South Canal

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Table 4 shows the peak discharges calculated from the regression equations as well as the lower and upper bounds of the 90 percent confidence level. The FIS and interpolated flows are also included for reference. As the calculated peak discharges based on the FIS values are within the

90% confidence limits these values are being used for analysis.

Table 4. Regression Equation Flows

AEP Peak Discharge 90% Confidence

Lower Upper

Flows Used

50% 341 cfs 110 cfs 1,060 cfs 628 cfs

20% 787 cfs 327 cfs 1,894 cfs 680 cfs

10% 1,059 cfs 457 cfs 2,452 cfs 721 cfs

4% 1,324 cfs 566 cfs 3,097 cfs 782 cfs

2% 1,502 cfs 618 cfs 3,651 cfs 828 cfs

1% 1,653 cfs 648 cfs 4,216 cfs 883 cfs

0.5% 1,775 cfs 662 cfs 4,758 cfs 937 cfs

0.2% 1,911 cfs 660 cfs 5,536 cfs 1,011 cfs

The chosen values all fall within the 90% confidence level of the calculated regression equation flows but, with the exception of the 2-year recurrence interval, are all well below the predicted value from the regression equations. This is most likely explained by Blodgett Reservoir being within the drainage basin upstream of the project site. The hydrology in the FIS most likely accounts for the attenuation at this location which would explain the rather flat trendline slope.

3. Hydraulics A one-dimensional (1D) hydraulic model was developed using the Hydrologic Engineering Center

River Analysis System (HEC-RAS) step-backwater computer program, version 5.0.7. A 1D model was developed as a fixed-bed, subcritical regime with constant peak discharge. For this analysis, two models were developed:

• Existing Conditions

• Proposed Conditions: New Pedestrian Bridge

Model Parameters Existing conditions survey for the Bridge and channel cross sections was performed by Kjeldson, Sinnock & Neudeck, INC. (KSN) in August 2019. KSN surveyed 7 cross sections and developed a surface using additional spot elevations in the vicinity of the trail, creek, and canal. The USGS

1/9 arc-second 2009 15 x 15 minute DEM was used to cut 7 additional cross sections outside of the survey limits, 3 upstream and 4 downstream. An additional cross section was cut from the

KSN surface immediately downstream of the proposed bridge location. The furthest upstream

KSN cross section was extended and supplemented with DEM elevations for the overbanks. In total, the hydraulic model contains 15 cross sections along Laguna Creek as shown in Figure 4.

Folsom South Trail Improvements Ph II 7 Central Federal Lands Highway

Figure 4. HEC-RAS Cross Sections

Both the survey data and USGS DEM are in State Plane California II FIPS 0402 Feet, North

American Datum 1983 and all elevations are referenced to NAVD 88 (feet).

Surface roughness, represented by the Manning’s roughness coefficient, were assigned to the channels and banks of each cross section. Values were taken from Table 7-5 of Sacramento’s

Drainage Manual. A value of 0.048 was used for the channel since there is tall grass and vegetation, and a value of 0.06 was used for the banks since there is high grass, but also some shrubs, weeds, and scattered trees. These values fall into the ranges presented in Table 14 of the FIS. Photos from the site visit used to confirm the n-values selected are shown in Photo 1.

Photo 1. Existing Folsom South Trail at Laguna Creek

The downstream boundary condition of normal depth slope of 0.0024 was calculated based on channel bottom slopes in the vicinity of the downstream cross section.

The proposed condition model run adds the pedestrian bridge in between cross sections 1163 and 1137. The proposed bridge will be prefabricated steel and have a span of 90.0 feet supported by 3 foot wide concrete abutments at either side. The spacing between abutments will be 86.3 feet. The full 6 foot -5 inch distance between the top and bottom chord of the bridge was modeled as the bridge deck which excludes the gaps between support beams and the railing. The lowest elevation of the bottom chord will be 118.78 feet. The lowest exposed abutment elevation will be

Folsom South Trail Improvements Ph II 9 Central Federal Lands Highway

116.82 feet. The bridge will tie into the existing trail which is 8 feet wide. The modeled structure width is 9.3’ which accounts for the path and railing.

Model Results The results of the 1D HEC-RAS model show that flows for all analyzed events are contained within the main channel over Folsom South Canal and under the proposed bridge. There is over two and a half feet of freeboard between the low chord of the bridge and the 10%-AEP design flood elevation. The 500-year flood event is the only analyzed situation that encroaches upon the proposed abutments.

Table 5. Water Surface Elevation at Proposed Bridge

AEP Water Surface

Elevation

Freeboard

50% 116.02’ 2.76’

20% 116.16’ 2.62’

10% 116.27’ 2.51’

4% 116.43’ 2.35’

2% 116.54’ 2.24’

1% 116.67’ 2.11’

0.5% 116.79’ 1.99’

0.2% 116.95’ 1.83'

Due to the limited encroachment by the proposed bridge design, the model results show no increases in base flood elevation within the project area. Table 6 shows the 1% AEP water surface elevations for the existing and proposed conditions models as well as the approximated FEMA base flood elevations (BFE) taken from the FIS profile for each of the modeled cross sections.

Folsom South Trail Improvements Ph II 10 Central Federal Lands Highway

Table 6. 1% AEP Water Surface Elevations

Section Existing WSE Proposed WSE Difference Approximate

FEMA BFE

1830 118.18’ 118.18’ 0.00’ 117.6’

1650 117.93’ 117.93’ 0.00’ 117.6’

1505 117.25’ 117.25’ 0.00’ 117.5’

1377 116.92’ 116.92’ 0.00’ 117.3’

1286 116.77’ 116.77’ 0.00’ 117.1’

1212 116.70’ 116.70’ 0.00’ 117.0’

1163 116.68’ 116.68’ 0.00’ 116.9’

1153 Bridge 116.9’

1137 116.62’ 116.62’ 0.00’ 116.8’

1125 116.59’ 116.59’ 0.00’ 116.8’

1113 116.65’ 116.65’ 0.00’ 116.8’

1103 116.67’ 116.67’ 0.00’ 116.7’

1071 116.60’ 116.60’ 0.00’ 116.7’

1018 116.49’ 116.49’ 0.00’ 116.6’

923 116.36’ 116.36’ 0.00’ 116.4’

807 116.12’ 116.12’ 0.00’ 116.2’

639 115.87’ 115.87’ 0.00’ 116.0’

495 115.59’ 115.59’ 0.00’ 115.8’

317 115.18’ 115.18’ 0.00’ 115.7’

Scour A scour analysis was performed for Laguna Creek at the proposed Bridge location. The scour analysis is intended to inform the structural and countermeasure design of the crossing. Results from the HEC-RAS 1D model were used since flow stays within the channel banks for all of the evaluated storm events.

Methodologies presented in the FHWA Hydraulic Engineering Circular No. 18 Evaluation of Scour at Bridges (HEC-18) were used for scour analysis. Based on Table 2.1 from HEC-18 and the conditions of the Bridge, the 10-year event is used as the hydraulic design flood frequency and the 25-year event results are used as the scour design flood frequency.

At the project site, the following scour components were evaluated:

• Contraction Scour

• Abutment Scour

Long-Term Degradation was not estimated since the channel is restricted by its crossing over the

Folsom South Canal which limits potential degradation.

All scour calculations can be found in Appendix B.

Contraction Scour

Contraction scour represents short-term channel degradation caused by the contraction of flow area through a restricted bridge opening. Contraction scour was calculated using the following

Folsom South Trail Improvements Ph II 11 Central Federal Lands Highway

HEC-18 Contraction Scour approach. Contraction scour was calculated for the 10- and 25-year events. The calculation was performed using the clear-water condition since channel velocity was determined to be less than the critical velocity for both flood events.

Due to the limited encroachment by the proposed bridge, the calculated average equilibrium depth in the bridge section was less than the average existing depth in the bridge section before scour which means that there is no anticipated scour degradation due to contraction from the proposed bridge.

Abutment Scour

Abutment scour is used to determine bury depths for abutment foundations. Abutment scour was calculated using the Froehlich's Abutment Scour Equation as documented in HEC-18. Abutment scour was calculated for the 10- and 25-year events however, the proposed abutments do not reduce the floodplain top width when compared to the upstream cross section so the resulting calculated scour depths from Laguna Creek are zero. A rip rap pad surrounding the abutments should be provided as protection from localized surface runoff.

4. Conclusion The purpose of this report is to provide a channel hydraulic analysis and design of the proposed

Folsom South Trail pedestrian bridge over Laguna Creek, which includes: selection of hydrologic peak discharges, proposed design hydraulic modeling, flood profile and floodplain analysis, and scour analysis.

Based on the hydraulic analysis, the proposed bridge opening and abutments do not encroach on the design peak discharge and do not increase the 100-year floodplain base flood elevation.

The existing channel conveys all of the flood events analyzed without overtopping the channel banks. Since the proposed bridge does not contract or encroach the scour design flood event, there is limited potential for scour. In order to prevent erosion at the face of the abutments due to localized drainage a small area of riprap is recommended at the upstream and downstream abutments.

The conclusions and recommendations in this report are based on the conditions of the project site and the associated watershed at the time of this study. Any modifications to the site, man-made or natural, could alter the analysis, findings, and recommendations contained herein and could invalidate the analysis, findings, and recommendations. Site conditions, completion of upstream or downstream projects, upstream or downstream land use changes, climate changes, vegetation changes, maintenance practice changes, or other factors may change over time.

Additional analysis or updates may be required in the future as a result of these changes.

Folsom South Trail Improvements Ph II 12 Central Federal Lands Highway

5. References Federal Emergency Management Agency. Flood Insurance Study for Sacramento County.

California, and Incorporated Areas. Flood Insurance Study Number 06067CV001D.

Effective Date July 19, 2018.

Federal Highway Administration. 2009. Bridge Scour and Stream Instability Countermeasures:

Experience, Selection, and Design Guidance (Volume 2). Third Edition. Publication No.

FHWA-NHI-09-112. Hydraulic Engineering Circular No. 23.

Federal Highway Administration. 2012. Evaluating Scour at Bridges. Fifth Edition. Publication No.

FHWA-HIF-12-003. Hydraulic Engineering Circular No. 18.

Federal Lands Highway Division, "Project Development and Design Manual", Chapter 7

Hydrology and Hydraulics, December 2012.

United States Geologic Survey. Methods for Determining Magnitude and Frequency of Floods in

California, Based on Data through Water Year 2006. Scientific Investigation Report 2012-

5113.

Appendix A

FEMA FIRM

Appendix B Scour Calculations

S.O. No. 10164156

Subject: Folsom South Trail Improvements Ph II- Pedestrian Bridge

Scour Calculations

Computed by: JWM

Checked by: CM Sheet No. 1 of 5

It is assumed that long-term degradation or aggradation is considered minimal.

Use HEC-23 Eqn 14.1 & 14.2 to size RIPRAP at abutments

(Eq. 14.1 in HEC-23) where:

D50 = median stone diameter, ft (m)

V = V = characteristic average velocity in the contracted section, ft/s (m/s)

Ss = specific gravity of rock riprap g = gravitational acceleration, 32.2 ft/s2 (9.81 m/s2 ) y = depth of flow in the contracted bridge opening, ft (m)

K = 0.89 for a spill-through abutment 1.02 for a vertical wall abutment

Location V Ss y D50

Abutment (L) 1.6 2.65 2.2 0.05

Abutment (R) 1.9 2.65 0.5 0.07

1) U.S. Department of Transportation, Federal Highway Administration, Hydraulic Engineering Circular No. 18, Evaluation of Scour at Bridges, Fifth Edition, April 2012.

2) Federal Lands Highway Division, Project Development and Design Manual, Chapter 7 Hydrology and

Hydraulics, December 2012.

3) HDR Engineering Inc., Folsom South Trail Improvements Ph II Trail and Pedestrian Bridge Bureau of

Reclamation (BOR) Hydrology and Hydraulics Recommendations Report, November 2019.

Abutment Scour Rock Sizing for 500-Year Flood

Minimal rip rap protection required

INTRODUCTION

These sheets present the scour calculations for the porposed Folsom South Trail pedestrian bridge over Laguna Creek.

HEC-18

(1) is used to estimate the scour depths in accordance with FLHD Project Development and Design Manual, Chapter 7 (2)

. Hydraulic information is obtained from the proposed conditions HEC-RAS model, which was developed as part of the Project H&H Report (3)

. Scour depths are estimated for the 10-year and 25-year floods.

For Froude Numbers < 0.80, the recommended design equation for sizing rock riprap for spill-through and vertical wall abutments is in the form of the Isbash relationship

Due to the limited encroachment by the proposed bridge, the calculated average equilibrium depth in the bridge section was less than the average existing depth in the bridge section before scour which means that there is no anticipated scour degradation due to contraction from the proposed bridge.

In addition, the proposed abutments do not reduce the floodplain top width when compared to the upstream cross section so the resulting calculated scour depths from Laguna Creek are zero.

Bridge X-Sec Layout & Critical Velocity

Computed by: JWM

Checked by: CM Sheet No. 2 of 5

1. Upstream uncontracted cross section (XS output)

2. Internal bridge cross section (BR U or BR D in HEC-RAS output)

3. Upstream bounding cross section (XS output)

Calculate the critical velocity and compare to actual velocity to determine if live-bed or clear-water scour applies:

where:

Vc = Critical velocity above which bed material of size D and smaller will be transported (ft/s)

Ku = 11.17 (constant for english units)

D50 = Particle size in a mixture of which 50 percent are smaller (ft)

D50 (mm) = 0.5 Determination: Getotechnical Report (estimated based on soil type, no gradation provided)

D50 (in) = 0.10 Description: Very Dense Silty Gravel with Sand

If Vc > Vactual upstream of the contraction → Clear-Water Scour

Use uncontracted HEC-RAS cross section 1212 for the upstream data:

y

(ft)

Vc

(ft/s)

Vactual

(ft/s)

4.08 2.9 2.21

4.20 2.9 2.30

Since Vc > Vactual, calculate contraction scour using clear-water method.

BRIDGE X-SEC LAYOUT

Key

10-yr Clear-Water

25-yr Clear-Water

CRITICAL VELOCITY

(Eq. 6.1 in HEC-18)

Flood Event Scour Type

XS: 1212

XS: 1163

XS: 1153

Clear-Water Contraction Scour

Computed by: JWM

Checked by: CM Sheet No. 3 of 5

Use HEC-18 Eqns 6.4 and 6.5 to calculate clear-water contraction scour:

(Eq. 6.4 in HEC-18)

(Eq. 6.5 in HEC-18) where:

y2 = Average equilibrium depth in the contracted section after contraction scour (ft)

Ku = 0.0077 (constant for english units)

Q = Discharge through the bridge associated with width W (cfs) (from HEC-RAS XS-1153 BR)

Dm = Diameter of the smallest nontransportable particle (1.25 x D50) in contracted section (ft)

Dm = 0.01

W = Width of contracted section less pier widths (ft) = 86.0 yo = Average existing depth in the contracted section before scour (ft) yo = Total Flow Area between abutments / Width between abutments (W) (from HEC-RAS XS-1153 BR)

10-yr 25-yr

Flow area in contracted section (sq ft) = 326 340

Flow width in contracted section (ft) = 80 81 yo = 4.1 4.2

Q Bridge

(cfs) y2

(ft) yo

(ft) yS

(ft)

721 2.8 4.1 0.0

782 3.0 4.2 0.025-yr

10-yr

CLEAR-WATER CONTRACTION SCOUR

Flood Event

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Upstream Bridge Cross Section Computed by: JWM Checked by: CM Sheet No. 4 of 5

UPSTREAM BRIDGE XS

Abutment Scour Calculations Computed by: JWM Checked by: CM Sheet No. 5 of 5

Use HEC-18 Eqn 8.1 to check potential depth of scour to aid the design and placement of rock riprap and/or guide banks

(Eq. 8.1 in HEC-18) where:

K1 = Coefficient for abutment shape = 1.00 (from HEC-18 Table 8.1) K2 = Coefficient for angle of embankment to flow = (Ø/90)0.13

Ø < 90° if embankment points downstream Ø > 90° if embankment points upstream

L' = Length of active flow obstructed by the embankment (ft) Ae = Flow area of the approach cross section obstructed by the embankment (sf) Fr = Froude Number of approach flow upstream of the abutment = Ve /(gya)

1/2

Ve = Velocity at Embankment = Qe/Ae (ft/s) ya = Average depth of flow on the floodplain = Ae/L (ft) L = Length of embankment projected normal to the flow (ft) ys = Scour depth (ft)

Abut 1 Ø = 90 K2 Abut 1 = 1.00 (from HEC-18 Figure 8.5) Abut 2 Ø = 90 K2 Abut 2 = 1.00 (from HEC-18 Figure 8.5)

L' Ae Ve L ya Fr ys

0.0 0 2.2 10 0.0 12.32 0.0

0.0 0 1.6 10 0.0 8.97 0.0

L' Ae Ve L ya Fr ys

0.0 0 2.3 10 0.0 12.82 0.0

0.0 0 2.3 10 0.0 12.82 0.0

V e - Average overbank velocity from the detailed HEC-RAS output for Section 3326 L - Measured from HEC-RAS cross section on the upstream face of the bridge.

A e - Calculated from HEC-RAS cross section at the upstream face of the bridge - represents obstructed area.

ABUTMENT SCOUR (NOT USED)

Location Abutment Scour Summary Calcs for 10-Year Flood

Abutment (R) Abutment (L) Location

Abutment (R) Abutment (L) 𝑦 𝑦 = 2.27𝐾 𝐾

𝐿′ 𝑦

𝐹𝑟 . + 1