UNITED STATES DEPARTMENT OF AGRICULTURE 

Rural Development Utilities Programs 

RUS BULLETIN 1724E-205 

RD-GD-2017-86

SUBJECT: Design Guide: Preliminary Embedment Depths for Concrete and Steel Poles

TO: All Electric BmTowers 

EFFECTIVE DATE: Date of Approval 

EXPIRATION DATE: Seven years from effective date 

OFFICE OF PRIMARY INTEREST: Engineering Standards Branch; Office ofPolicy, 

Outreach, and Standards

. PREVIOUS INSTRUCTIONS: None

FILING INSTRUCTIONS: This bulletin updates Bulletin l 724E-205, "Design Guide: 

Embedment Depths for Concrete and Steel Poles", issued August 1995. 

AVAILABILITY: This bulletin can be accessed via the internet at 

http://www.rd.usda.gov/publications/regulations-guidelines/bulletins/electric

Christopher A. McLean 

Assistant Administrator, 

Electric Program 

Date 

PURPOSE: This bulletin provides engineering information concerning selection of preliminary 

embedment depths, along with final embedment design criteria, for steel and concrete 

transmission poles subject to large ove1iurning moments. 

Disclaimer: The contents of this guidance document does not have the force and effect of law and is 

not meant to bind the public in any way. This document is intended only to provide clarity to the 

public regarding existing requirements under the law or agency policies.
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CONTRIBUTORS: Current and former members of the Transmission Subcommittee of the 

Transmission and Distribution (T&D) Engineering Committee of the National Rural Electric 

Cooperative Association (NRECA).

Current members: 

Beadle, Bob, North Carolina EMC, Raleigh, NC

Beckett, Thomas, Enercon, Kennesaw, GA

Bertelsen, James, Dairyland Power Cooperative, La Crosse, WI

Caldwell, Art, Georgia Transmission Corporation, Tucker, GA

Harvey, Garry, East Kentucky Power Cooperative, Winchester, KY

Johnson, Wilson, USDA, Rural Utilities Service, Washington, DC

Kahanek, Bil, McCord Engineering, Inc., College Station, TX

McAndrew, Jeremy, South Mississippi Electric Power Assoc., Hattiesburg, MS

Metro, Patti, National Rural Electric Cooperative Association, Arlington, VA

Nicholson, Norris, USDA, Rural Development Utilities Program, Washington, DC 

Nordin, Bryan, Tri-State Generation & Transmission Association, Inc., Denver, CO

Ruggeri, Erik, Power Engineers, Hailey, ID

Shambrock, Aaron, South Central Power Company, Lancaster, OH

Twitty, John, PowerSouth Energy Cooperative, Andalusia, AL

Woodruff, Paul, Great River Energy, Maple Grove, MN
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TABLE OF CONTENTS

CHAPTER PAGE

1 INTRODUCTION ......................................................................................................5

2 DISCUSSION OF DESIGN METHODS...................................................................5

3 EMBEDMENT CHARTS ........................................................................................10

4 SUGGESTED PROCEDURE FOR USING THE CHARTS AND DETERMINING 

EMBEDMENT DEPTHS.........................................................................................21

5 POLE ANALYSIS AND FOUNDATION DESIGN EXAMPLES .........................22

EXHIBITS

A - REFERENCES

B - BACKGROUND INFORMATION, EMBEDMENT CALCULATION OVERVIEW 

TABLE, ABSTRACT OF HANSEN METHOD

C - SOIL PROPERTIES CORRELATION

D - CONVERSION TABLE

INDEX:

 DESIGN, SYSTEM: Embedment Depths for Concrete and Steel Poles

 POLES: Embedment Depths

ABBREVIATIONS

ACSR Aluminum Conductor Steel Reinforced

MPH Miles Per Hour

NESC National Electrical Safety Code

OHGW Overhead Ground Wire

RBS Rated Breaking Strength

RUS Rural Utilities Service

LF Load Factor

SF Strength Factor

ASTM ASTM International
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SYMBOLS

Symbol Term Units

C Cohesion psi, ksf

K Subgrade modulus at bottom of pole nhD, psi

Kc

D Earth pressure coefficient for cohesion

Kc

D Earth pressure coefficient for overburden 

pressure

d Diameter of the pole in, ft

D Depth ft

Dd Depth of dry soil ft

De Embedment depth of pole ft

Ds Depth of submerged soil from water table to 

pole butt ft

Dr Depth from groundline to point of rotation of 

a rigid pile ft

M Moment ft-kips, ft-lb, in-lb

n Blow counts Blows/ft

nh Constant of horizontal subgrade modulus lb/in3

P Horizontal force lb, kips

pD

Resultant pressure per unit front area on the 

embedded pole psf

q Effective overburden pressure

Yg Deflection at the groundline in, ft

q Unit weight of the soil pcf

q' Submerged unit weight of the soil pcf

φ Internal friction angle Radians, degrees
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1 INTRODUCTION

a Purpose. Increasing use of steel and concrete poles has necessitated a more 

definitive method of determining pole embedment depths. The primary purpose of 

this bulletin is to furnish engineering information concerning preliminary selection 

of embedment depths for steel and concrete poles in different types of soils. The 

information in this bulletin may be used to approximate embedment depths for cost 

estimates, to make preliminary selection of embedment depths, and to verify or 

check selection of embedment depths based on other or more exact methods.

Computer design programs can be used for determining embedment depths for 

steel and concrete poles. Such programs may provide a more efficient selection 

of embedment depths, particularly for stratified soils, in preliminary design and 

their use should be considered in any final design.

b Scope. The engineering information in this bulletin is for use in preliminary 

selection of embedment depths for steel and concrete transmission poles 

sustaining relatively large overturning moments. The Rural Utilities Service 

(RUS) reviewed several methods of evaluating and approximating embedment 

depth requirements. As a result of this review, embedment charts have been 

developed for nine typical soil types. Sample calculations illustrating the use of 

these charts and illustrating the use of design methods for those occasions when 

the charts cannot be used, are also provided.

Since the RUS program is national in scope, it is necessary that designs be 

adaptable to various conditions and local requirements. In the design and 

selection of embedment depths the engineer should consider soil conditions, 

performance of existing embedded pole lines, local environmental conditions, and 

other pertinent factors, such as foundation movement and duration of loads.

A comparison of several techniques for determining embedment depths, 

groundline deflection and rotation were made. A brief discussion comparing the 

different design methods is included in Appendix B. As a result of this study, the 

Hansen method was selected for developing the embedment charts.

2 DISCUSSION OF DESIGN METHODS

a Lateral Resistance Using the Hansen Method. The advantage of the Hansen 

method is that it provides for foundation design and embedment evaluation in 

stratified soils. This may be an important consideration for soil formations with a 

relatively poor layer near the ground surface since the analysis permits utilization 

of the greater strength of the deeper soils without overstating the strength of the 

surface soils.
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The following method of analysis was developed by Brinch Hansen and presented 

in the article, "The Ultimate Resistance of Rigid Piles Against Transversal 

Forces," Bulletin No. 12, The Danish Geotechnical Institute, Copenhagen, 1961.

A prerequisite to using the Hansen method to compute the ultimate lateral 

resistance is a knowledge of the different types and depths of soils underlying the 

site. The density q, submerged density q', angle of internal friction, φ, and 

cohesion "C" for each major soil type must be determined, preferably by 

subsurface soil investigations and soil lab tests. For preliminary embedment depth 

selections, these values can be estimated. The depth to the ground water table 

must be known if it is located above the bottom of the footing. In this event, the 

submerged weight of the soil can have a significant effect on the embedment 

depth. Water table depths can be estimated for preliminary design but, for final 

design, should be more accurately determined through the subsurface soil 

investigation process (ASTM D1586).

Figure 1

The resultant (passive minus active) pressure per unit front area on the embedded 

pole (pD) at an arbitrary depth "D" is given by:

pD = qKqD + CKcD Eq. 1
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where:

q = qDd + q'Ds

(effective overburden pressure)

q,q' = Dry and submerged density of the soil

Dd = Depth of dry soil C = Cohesion of soil

Ds = Depth of submerged soil from water 

table to pole butt

(d)(pD) = Pressure per unit length of pile

KqD = See figure 2 Dr = depth to point of rotation of a rigid pile 

(See figure 5)

KcD = See figure 3

 

The general procedure to compute the embedment depth De is as follows given 

that the moment (M), horizontal load (P), diameter of the pole (d), and soil 

properties are known.

Earth pressure coefficients for overburden 

pressure

Figure 2

Earth pressure coefficient for cohesion

Figure 3
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Figure 4

Compute embedment depth, De 

(1) Compute Do, the depth to point of zero shear and maximum moment. This 

can be done by equating the total earth pressure above this point to the force 

P.

(2) Compute Mmax by taking moments of all forces acting above this point.

(3) Assume De

(4) Assume Dr. For the first trial, try Dr = 0.75 De for granular soils and Dr = 

0.6 De for clay soils.

(5) Compute the algebraic sum of all lateral earth forces below the point of 

zero shear. This should be equal to zero. If not, adjust Dr so that it will 

be.

(6) Calculate moments of all forces acting below the point of zero shear. This 

should be equal to Mmax computed in Step 2. If not, start with Step 3 again 

by assuming a new De.

b Deflection Using Davisson's Method. Groundline deflections can be estimated 

based on a method developed by Davisson and Prakash in an article titled, "A 

Review of Soil-Pole Behavior," published in the Highway Research Record, 

Number 39. The equations are valid for loads in the range of 1/3 to 1/2 of the 

ultimate load. At higher load levels, the load deflection relationship becomes 

nonlinear.
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Although it is not possible to compute the deflections near the range of the 

ultimate loads, Broms1 states that maximum resistance is in general reached when 

the deflection at the ground surface is approximately equal to 20 percent of the 

diameter of the pile. The working loads, particularly for non-iced conductors, 

should be in the range of the load-deflection curves so that the preceding 

equations are valid.

No deflection limits are recommended. Each design case will have to be evaluated 

for the particular structure by itself and in relation to the other structures in the 

line.

Figure 5

(P and M are less than 1/2 the ultimate loads.)

For clay soils:

Yg = [2.15PDr/De] / [KDe((1.87 Dr/De) - 1)] Eq. 2

Dr/De = [(M/(PDe)) + .683] / [(1.87 M/(PDe)) +1] Eq. 3

For granular soils:

Yg = [3PDr/De] / [nhDe

2

((1.5 Dr/De) - 1)] Eq. 4

Dr/De = [(M/(PDe)) + .750] / [(1.5 M/(PDe)) + 1] Eq. 5

Values of K for clays

Cohesion (lb/ft2) K psi

1000 - 2000 700

2000 - 4000 1400 >4000 2800

Values nh for granular soils

nh (lb/in3)

 Dry Submerged

Loose 9.4 5.3

Medium 28 19

Dense 75 45
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3 EMBEDMENT CHARTS. 

Nine charts have been developed which show embedment depths for pole diameters 

ranging from 1.0 to 4.0 feet. Ultimate moments at groundline range from 0 to 2000 ftkips.

Because of the sensitivity of embedment depths to groundline moments and relative 

insensitivity of embedment depth to ground shears, the embedment charts were 

developed based on a horizontal load on the pole of 20 kips. In general, the degree of 

conservatism of the 20 kip load is greatest for very small groundline moments, and 

diminishes to a negligible value for a groundline moment of 300 ft-kips.

The nine embedment charts have been developed for nine soil types. These soil types 

and characteristics are shown in Table 1. Submergence significantly influences the 

strength of the sand foundations because they are weight-dependent. Submergence does 

not influence the strength of the clay foundations because they are not weight dependent.

Most soils are neither a pure sand nor a pure clay and may often be multilayer. In 

making preliminary selection of embedment depths, the user of these charts should 

select the predominant soil type based on the best available soils information. For 

example, if the soil type is a submerged silty sand, embedment depths estimated with 

these charts should be based on a submerged sand.

The designer should assume that the top 1 to 2 feet of soil provide little or no strength. 

When using these charts or when using computer programs, this assumption may be a 

consideration by the designer.

Table 1

Soil Parameters Typical

Chart SOIL/TYPE γ, C, φ, blow count No: & DESCRIPTION: Kip/CFt Kip/SqFt Degrees Values ("n") ------------------------------------------------------------------------------------------------------------------- 1-DDS DENSE DRY SAND 0.14 0.0 41 >30

2-DSS DENSE SUBMERGED SAND 0.085 0.0 41 >30

3-MDS MEDIUM DRY SAND 0.12 0.0 33 10-30

4-MSS MEDIUM SUBMERGED SAND 0.065 0.0 33 10-30

5-LDS LOOSE DRY SAND 0.095 0.0 28 0-10

6-LSS LOOSE SUBMERGED SAND 0.055 0.0 28 0-10

7-SSC STIFF SATURATED CLAY 0.14 2.0 0.0 >8

8-MSC MEDIUM SATURATED CLAY 0.12 0.75 0.0 4-8

9-SOSC SOFT SATURATED CLAY 0.10 0.25 0.0 0-4
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When using the embedment charts the following are applicable:

a Moment values shown on the charts represent an ultimate capacity for 

embedment depths. Overturning moments should include structural loads 

multiplied by appropriate load factors. Strength reduction factors should be 

applied to the allowable moments. See RUS Bulletin 1724E-200, Section 13.

b Charts are based on a horizontal load of 20 kips acting at an equivalent load 

height for a given moment and are slightly conservative for horizontal loads 

less than 20 kips. For horizontal loads greater than 20 kips but less than 40 

kips, the charts are marginal but are adequate for use. For horizontal loads 

greater than 40 kips or for stratified soils, embedment depths should be 

determined by the Hansen formulae instead of the charts.

c Recommended minimum embedment depth is three times either the pole 

diameter or pole's lateral dimension at the groundline. It is also recommended 

that the ratio of embedment depth to the pole diameter or pole's lateral 

dimension at groundline not exceed 10.
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4 SUGGESTED PROCEDURE FOR USING THE CHARTS AND DETERMINING 

EMBEDMENT DEPTHS

a Define Pole Dimensions and Loading Positions. The user should first 

specify/tabulate the following: pole heights and dimensional data (above ground), 

wire or insulator attachment points and heights, and pole diameters at top and 

groundline (given or estimated).

b Specify Design Data, Load Cases/Conditions, Criteria and Requirements. For a 

given pole type, the user should name or designate the structure, define data on 

the vertical, horizontal spans, and maximum design line angle (if any), and 

tabulate design load cases or combinations being considered. At a minimum, 

NESC District loading extreme load cases as indicated in Chapter 11 of RUS 

Bulletin 1724E-200 should be used to determine structure loads. Other more 

extreme load cases should be included if necessary when considering local 

conditions.

For each load case, the following should be specified: (a) design wind pressures 

on wires and pole; (b) radial ice thickness/type on wires and conductors; (c) 

groundwire and conductor design tensions; and (d) required Load Factors (LF) for 

vertical, transverse and longitudinal loads, including separate load factors for 

components due to wire tensions, wind-on-wires and structure.

c Calculate Forces and Moments at Groundline. Section 13, RUS Bulletin 1724E200 provides the methodology for determining forces and moments at the 

groundline. For each load case compute and combine forces and moments due to: 

transverse wind acting on conductors, wires and pole; pole moments due to 

vertical loads acting on lateral pole deflection (P-delta effect) and nonsymmetrical 

vertical conductor wire loads (two arms vs. one arm on each side of the pole); and 

any additional transverse or longitudinal loads from wire tension components 

caused by line angle or unbalanced/deadending conditions. Each load component 

is applied with its required LF as specified in the design criteria. From all the 

design cases, the maximum induced groundline moment, Mg, and maximum 

horizontal shear force should be determined.

d Determine Subsurface Soil Type and Condition. For preliminary design, the 

engineer may wish to estimate the soil type and condition (dry vs. saturated). 

For tangent structures, it may be sufficient to only list locations where there is 

similar soil. However, site investigation and soil testing is recommended at poles 

subject to long duration, high lateral loads and overturning moments.

During construction when the holes are augured for the poles, soil type and 

condition should be monitored. If the soil conditions during excavation and 

construction are different than the assumed conditions, alternatives may need to 

be considered in order to provide adequate overturning moment capacity.
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e Select a Chart for the Soil and Determine Embedment Depth. In many instances, 

the engineer will be able to select an embedment chart which most clearly 

represents the soil and the state of the soil at the pole location. Occasionally, two 

charts may be used to bracket and average the required embedment depth.

Once the chart has been selected for the soil and the maximum induced 

groundline moment (includes overload factors) at groundline has been calculated, 

the embedment depth is determined in the chart for a given or estimated pole 

diameter at groundline.

5 POLE ANALYSIS AND FOUNDATION DESIGN EXAMPLES

a Example 1, Steel Pole Preliminary Embedment Design Using The Embedment 

Charts. For the TUS-1 steel pole structure and loading conditions given below, 

determine if 10 percent of height plus 2 feet is an adequate embedment depth. 

Assume medium-dense, dry sand is the soil.

(1) General information:

Line voltage: 138 kV/69 kV Double Circuit

Design by: RUS Engineers

Structure type: TUS-1 Steel Pole

Geometry of the structure and location of loads:

Distance from Pole Top, Ft.

OHGW 0.25

COND-1 7.50

COND-2 17.50

COND-3 27.50

COND-69-1 7.50

COND-69-2 17.50

COND-69-3 27.50

Underbuild-NONE 97.00

At Gd.Line-assumed 97.00

Pole-End 110.00

Overall pole length is 110 feet. The above dimensions assume 13.0 foot 

embedment depth for the steel pole using the standard rule for wood poles of 10 

percent pole length plus 2 feet. Assume top of the pole has a 12 inch diameter, 

and the groundline diameter is 30 inches.
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(2) Load Factors (LFs) used in this example:

For NESC Light, Medium or Heavy Loading District Loads

Vertical 1.50 Wind on Pole 2.50

Transverse wind 2.50 Transverse Line Angle 1.65

Longitudinal Loads 1.65

For Extreme Wind Loads 1.10

(3) Conductor and OHGW Data:

 OHGW: 3/8" HSS

 R.B.S. - 10,800 lb.

 138 kV Conductor: Drake (795 26/7 ACSR)

 R.B.S. - 31,500 lb.

 69 kV Conductor: Linnet (336-4 26/7 ACSR)

 R.B.S. - 14,100 lb.

Ruling Span - 550 ft.

Vertical Span - 700 ft.

Horizontal Span - 750 ft.

Line Angle - 10 degrees

(4) Load Cases:

Load Case A: NESC Medium District Loads with an Unbalanced Longitudinal

Load of 1,600 lb. at the Top Conductor (1.65 LF applied)

Load Case B: 100 Mph Extreme Wind Load

(1.1 LF applied)

(5) Loading Information (summary):

NESC Medium Loading Data

Transverse Vertical

Cond.Tension (kips) lb/ft. lb/ft.

Drake - 138 kV 7.91 .536 1.516

Linnet- 69 kV 4.15 .407 .765

OHGW - 3/8 HSS 2.56 .287 .463

Extreme Wind Loading Data (26 psf)

Transverse Vertical

Cond.Tension (kips) lb/ft. lb/ft.

Drake - 138 kV 8.54 2.4007 1.0940

Linnet- 69 kV 4.72 1.5622 .4630

OHGW - 3/8 HSS 1.23 .7800 .2730
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(6) Calculate forces and moments at the groundline:

NESC Medium District Loading

Load due to Load due to Total Transv. Moment Ultimate

Wind on Wire Line Angle Load W/LF Arm Moments

(kips) (kips) (kips) (feet) (ft kips)

OHGW .22 .45 1.27 96.75 123

COND-1 .40 1.38 3.28 89.50 294

COND-2 .40 1.38 3.28 79.50 261

COND-3 .40 1.38 3.28 69.50 228

COND-69-1 .31 .72 1.96 89.50 175

COND-69-2 .31 .72 1.96 79.50 156

COND-69-3 .31 .72 1.96 69.50 136

GROUNDLNE 0.0

 Totals for Wire Loads 16.99 1373

 Wind on the Pole 1.70 71

 Moments due to unbalanced vertical load 

 (Negligible if crossarms are all the same length) 0

Additional moment due to deflection (Approximated) 140

Total Transverse Shear and

Moments at Groundline 18.69 1584

For the unbalanced longitudinal load - the shear is 1.6 kips and the longitudinal 

moment is 236.3 ft-kips (1.6 kips @ top cond, 89.5 ft. moment arm, 1.65 LF)

TOTAL RESULTANT GROUNDLINE MOMENT = 1600 ft kips

Extreme Wind Loading

Similar calculations are performed for the extreme wind load.

TOTAL GROUNDLINE MOMENT = 1560 ft-kips

Conclusions: The NESC Medium Loading case with a longitudinal load controls 

design.

(7) Select Embedment Chart and Determine Embedment Depth

 Required

Embedment Depth

Medium dry sand, Chart 3, dia. of 2.5 ft. 18 ft.

Dense dry sand, Chart 1, dia. of 2.5 ft. 13 ft.

Average sand Med/Dense dry material, use 15 ft, or 

10 percent of pole height plus 4 ft.

For identical data and medium/dense submerged sand, the charts indicate a

required embedment depth of 22 ft. 
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b Example 2: For a single circuit, medium-angle 90 ft. steel pole, the maximum 

ultimate groundline moment has been determined to be 580 ft-kips.

For a pole groundline diameter of 2.0 ft. and a medium dry sand material the 

required embedment depth is 14.5 ft. (use 15 ft.).

c Example 3: For a prestressed concrete pole, determine the embedment depth. 

The concrete pole is designed so that the cracking moment is not exceeded by a

6,000 lb. load applied 2 feet from the top and the ultimate strength is not exceeded 

by a 12,000 lb. load applied 2 feet from the top.

In order to achieve the same ultimate strength for the foundation as the pole, the 

embedment depth is selected to sustain an ultimate load of 12 kips.

Characteristics of the pole follow:

height: 80 ft.

taper: .165 in/ft. of height

assumed embedded depth: 10% + 4 feet in dense dry sand

groundline diameter: 24.5" (use 24")

ult. groundline moment: 792 ft-kip (based on 12k x 66 ft.)

The chart for dense dry sand shows a required embedment of 11.9 feet for a 2 ft. 

diameter foundation to resist 792 ft-kips of overturning moment at groundline. 

This approximates the 12.0 foot embedment depth obtained from the 10 percent 

of pole length plus 4.0 feet originally estimated.

d Example 4: For the pole in example 3, calculate the deflection and rotation at the 

groundline for the working loads.

Since the working load is less than one half of the ultimate load, equations 2 to 5 

are valid.

Given: Horizontal working load, P = 5.0 kips

 Embedment depth D = 12.0 ft.

 Groundline working moment M = 5 x 66 = 330 ft-kips

 Dense dry sand nh = 75 lb/in3 or 129 kcf

(1) Calculations using Davisson's formulae for sandy soil:

 Dr = Depth to point of rotation, ft

Dr/De = [(M/PDe) + .750]/[(1.5 M/PDe) + 1]

 = [330/(5x12)) + 0.75]/[(1.5 x 330)/(5x12)) + 1]

Dr/De = .676
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(2) Groundline deflection, and rotation:

Yg = [3PDr/De]/[nhDe

2

((1.5 Dr/De) - 1)]

 = 3(5) (.676)/[(129)(12)2(1.5 x .676 - 1)]

 = 0.039 ft.

 = 0.47 in.

Dr = (Dr/De) x De

 = 0.676 x 12 = 8.112

 θ = Yg /Dr = 0.039/8.112

 = 0.00481 Radian = 0.00481 x 57.3 degrees

 = 0.28 degrees

(3) Estimated pole deflections at groundline: 

 Horizontal deflection = 0.5 inch (approximate)

 Rotation about vertical axis = 0.28 degree (approximate)

These deflections are assumed to be reasonable because the loads are in the range 

between 1/3 and 1/2 of the ultimate load and, as such, the load deflection 

relationship is linear.
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Exhibit A

Page 1

References

1. Broms, B.B., "Lateral Resistance of Piles in Cohesive Soils," Journal of Soil Mechanics 

and Foundations Division, ASCE, March 1964, pp 27-63.

2. Broms, B.B. "Lateral Resistance of Piles in Cohesionless Soils," Journal of Soil 

Mechanics and Foundation Division, ASCE, May 1964, pp 123-156.

3. Broms, B.B., "Design of Laterally Loaded Piles," Journal of Soil Mechanics and 

Foundations Division, ASCE, May 1965, pp 79-99.

4. Czerniak, E., "Resistance to Overturning of Single, Short Pile," Journal of Structural 

Division, ASCE, March 1957.

5. Davisson, M.T. and Prakash, Shanisher, "A Review of Soil Pole Behavior," Highway 

Research Board No. 39, 1963.

6. Hansen, J.B., "Ultimate Resistance of Rigid Piles Against Transversal Forces," The 

Danish Geotechnical Institute, Bulletin No. 12, 1961.

7. Naik, T.R. and Peyrot, Alain, "Analysis and Design of Laterally-Loaded Piles and 

Corrosions in a Layered Soil System," Professors at University of Wisconsin -

Milwaukee, 1980.
Bulletin 1724E-205

Exhibit A

Page 2

THIS PAGE IS 

INTENTIONALLY 

BLANK
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Exhibit B

Page 1

TABLE OF CONTENTS

Comparison of Design Methods ..............................................................................2

Embedment Calculations Overview Table ..............................................................3

Abstract of Hansen Method .....................................................................................5
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Exhibit B

Page 2

COMPARISON OF DESIGN METHODS

Comparisons were made of embedment requirements, groundline deflection and foundation 

rotation for tubular steel and concrete transmission poles, using various analytical techniques. 

The techniques used to evaluate and tabulate embedment depths are the Broms method, the 

Hansen method, and the method found in RUS Bulletin 1724E-200, "Design Manual for High 

Voltage Transmission Lines." The “Embedment Calculations Overview Table” which follows is 

a condensed tabulation of representative calculations for these three methods in nine soil types 

for steel and concrete poles. The horizontal loads in the table are 5, 35, and 50 kips applied at 

heights of 30, 60, and 90 feet, respectively. The Davisson method is used to evaluate groundline 

deflection and rotation for all embedment techniques. The method by Naik & Peyrot was 

compared to Broms and Hansen for one case.

Inspection of calculations shows very good correlation between the embedments required by the 

Hansen method and the Broms method, with the Hansen method being generally more 

conservative of the two. The RUS method for wood poles is in reasonable agreement with the 

other methods in good soils but is marginal in poor soils. The one sample calculation made 

using the Naik method is in agreement with Hansen and Broms.

In comparing the different methods, several general conclusions can be reached. Inspection of 

the calculations reveals that there is generally a slight reduction in the embedment depths 

associated with an increase in embedment diameter. The data also shows that there is a 

substantial increase in groundline rotations with a relatively small decrease in embedment depths 

resulting from doubling the embedment diameter. Capacity and rotation are affected more by the 

embedment depth rather than the diameter of the embedded pole.

The calculations also show the comparative insensitivity of the required embedment to 

groundline shear. For the range of shears from 10 kips to 40 kips, the required embedments 

based on the Hansen method, varied from 18 feet to 20 feet in medium sand and from 27.8 to 

30.9 feet in medium clay. In medium sand and medium clay respectively, the depths required for 

10 kips shear are 

96.6 percent and 94.9 percent of the depths required for 25 kips, and the depths required for 40 

kips shear are 103 percent and 105.5 percent of the depths required for 25 kips shear.

The comparison of various methods of evaluating embedment requirements resulted in using the 

Hansen method in developing the embedment charts in this bulletin.
Bulletin 1724E-205

Exhibit B

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EMBEDMENT CALCULATIONS OVERVIEW TABLE

 POLE

 S = Steel HANSEN________ BROMS__________ REA______ 

 C = Concrete LOAD HEIGHT DIA. DEPTH ROT. bL DEPTH ROT. L DEPTH ROT.

 Soil Type (KIPS) (FT) (FT) (FT) (DEG.) (FT) (DEG.) (FT) (DEG.)

Dense Dry Sand S 5.0 30.0 1.01 8.19 0.63 2.87 8.25 0.61 2.89 6.55 1.49

 C 5.0 30.0 1.52 7.52 0.87 1.77 7.13 1.07 1.68 6.55 1.49

 S 35.0 60.0 2.43 15.19 0.73 2.63 14.71 0.83 2.55 13.24 1.25

 C 35.0 60.0 3.65 13.93 1.03 1.62 12.74 1.45 1.49 13.24 1.25

 S 50.0 90.0 3.14 18.03 0.77 2.55 17.17 0.93 2.43 16.17 1.17

 C 50.0 90.0 4.71 16.45 1.10 1.57 14.89 1.62 1.42 16.17 1.17

Dense Submerged S 5.0 30.0 1.01 9.53 0.58 3.01 9.88 0.51 3.12 6.55 2.48

Sand C 5.0 30.0 1.52 8.83 0.78 1.88 8.53 0.89 1.81 6.55 2.48

 S 35.0 60.0 2.43 17.84 0.66 2.79 17.60 0.69 2.75 13.24 2.08

 C 35.0 60.0 3.65 16.34 0.92 1.72 15.21 1.22 1.60 13.24 2.08

 S 50.0 90.0 3.14 21.02 0.71 2.69 20.48 0.78 2.62 16.17 1.96

 C 50.0 90.0 4.71 19.34 0.97 1.66 17.75 1.36 1.53 16.17 1.96

Medium Dry S 5.0 30.0 1.01 10.87 0.57 3.13 9.90 0.81 2.85 7.91 1.92

Sand C 5.0 30.0 1.52 9.87 0.82 1.91 8.95 1.43 1.65 7.91 1.92

 S 35.0 60.0 2.43 20.10 0.67 2.86 17.63 1.11 2.51 15.99 1.61

 C 35.0 60.0 3.65 18.29 0.96 1.75 15.24 1.94 1.46 15.99 1.61

 S 50.0 90.0 3.14 23.62 0.72 2.74 20.52 1.25 2.38 19.51 1.51

 C 50.0 90.0 4.71 21.59 1.02 1.69 17.78 2.17 1.39 19.51 1.51

Medium Submerged S 5.0 30.0 1.01 13.20 0.40 3.51 12.39 0.51 3.29 7.91 2.83

Sand C 5.0 30.0 1.52 12.11 0.56 2.17 10.67 0.90 1.91 7.91 2.83

 S 35.0 60.0 2.43 24.47 0.47 3.22 22.03 0.70 2.90 15.99 2.38

 C 35.0 60.0 3.65 22.44 0.65 1.99 19.01 1.23 1.68 15.99 2.38

 S 50.0 90.0 3.14 28.76 0.50 3.09 25.56 0.79 2.75 19.51 2.23

 C 50.0 90.0 4.71 26.30 0.71 1.90 22.10 1.38 1.60 19.51 2.23

Loose Dry Sand S 5.0 30.0 1.01 13.61 0.72 3.14 11.61 1.32 2.68 9.56 2.77

 C 5.0 30.0 1.52 12.34 1.05 1.92 10.01 2.33 1.56 9.56 2.77

 S 35.0 60.0 2.43 24.95 0.88 2.85 20.65 1.81 2.36 19.33 2.33

 C 35.0 60.0 3.65 22.55 1.29 1.74 17.83 3.17 1.37 19.33 2.33

 S 50.0 90.0 3.14 29.24 0.95 2.73 23.99 2.04 2.24 23.56 2.18

 C 50.0 90.0 4.71 26.56 1.38 1.67 20.75 3.57 1.30 23.56 2.18

Loose Submerged S 5.0 30.0 1.01 16.37 0.64 3.38 14.21 1.09 2.93 9.56 4.89

Sand C 5.0 30.0 1.52 14.80 0.93 2.05 12.22 1.91 1.70 9.56 4.89

 S 35.0 60.0 2.43 29.87 0.79 3.05 25.24 1.49 2.58 19.33 4.10

 C 35.0 60.0 3.65 27.06 1.14 1.86 21.75 2.61 1.49 19.22 4.10

 S 50.0 90.0 3.14 35.02 0.84 2.92 29.21 1.69 2.44 23.56 3.84

 C 50.0 90.0 4.71 31.74 1.23 1.78 25.23 2.95 1.42 23.56 3.84
Bulletin 1724E-205

Exhibit B

Page 4

EMBEDMENT CALCULATIONS OVERVIEW TABLE

(Cont.)

 POLE

 S = Steel HANSEN________ BROMS__________ REA______ 

 C = Concrete LOAD HEIGHT DIA. DEPTH ROT. bL DEPTH ROT. L DEPTH ROT.

 Soil Type (KIPS) (FT) (FT) (FT) (DEG.) (FT) (DEG.) (FT) (DEG.)

Stiff Saturated S 5.0 30.0 1.01 7.72 0.77 2.76 7.69 0.78 2.74 6.55 1.24

Clay C 5.0 30.0 1.52 6.59 1.22 1.43 7.33 0.90 1.59 6.55 1.24

 S 35.0 60.0 2.43 18.72 0.78 2.78 18.75 0.77 2.78 13.24 2.10

 C 35.0 60.0 3.65 16.01 1.21 1.45 17.84 0.89 1.61 13.24 2.10

 S 50.0 90.0 3.14 23.89 0.78 2.75 23.95 0.78 2.75 16.17 2.43

 C 50.0 90.0 4.71 20.46 1.22 1.43 22.81 0.89 1.60 16.17 2.43

Medium Saturated S 5.0 30.0 1.01 12.53 0.39 3.76 11.91 0.45 3.58 7.91 1.44

Clay C 5.0 30.0 1.52 10.60 0.62 1.94 10.73 0.60 1.96 7.91 1.44

 S 35.0 60.0 2.43 30.72 0.38 3.83 29.26 0.44 3.65 15.99 2.44

 C 35.0 60.0 3.65 25.92 0.62 1.97 26.29 0.59 2.00 15.99 2.44

 S 50.0 90.0 3.14 38.89 0.39 3.76 37.16 0.44 3.59 19.51 2.81

 C 50.0 90.0 4.71 32.84 0.63 1.94 33.45 0.60 1.97 19.51 2.81

Soft Saturated S 5.0 30.0 1.01 22.29 0.16 5.63 20.65 0.19 5.21 9.56 1.67

Clay C 5.0 30.0 1.52 18.50 0.26 2.85 17.65 0.30 1.72 9.56 1.67

 S 35.0 60.0 2.43 55.70 0.15 5.84 51.37 0.19 5.38 19.33 2.83

 C 35.0 60.0 3.65 45.89 0.25 2.93 43.68 0.29 2.79 19.33 2.83

 S 50.0 90.0 3.14 69.73 0.16 5.67 64.54 0.19 5.25 23.56 3.26

 C 50.0 90.0 4.71 57.72 0.26 2.86 55.11 0.30 2.73 23.56 3.26
Bulletin 1724E-205

Exhibit B

Page 5

ABSTRACT OF HANSEN METHOD

P = Transverse Load in kips

H = Load height above grade in ft.

d = diameter of foundation in ft.

D = arbitrary depth below ground

q = effective overburden pressure at depth in ksf

pD = resultant (passive minus active) pressure per 

unit frontal area of foundation in ksf

ф = soil friction angle in degrees

C = cohesion

γ = unit weight above ground water table in pcf

γ' = unit weight below ground water table in pcf

Hansen Formulas

( 1) Kq

° = e[.5π + (π/180)ф]tanф cosфtan(45°+.5ф) - e-[.5π-(π/180)фtanф] cosфtan(45° + .5ф)

( 2) Kc° = [e[.5π+(π/180)фtanф] cosфtan(45° + .5ф)-1]cot ф

( 3) A = 1.58 + 4.09 tan4 ф

( 4) B = [eπtanфtan2

(45 + .5 ф)-1]cot ф

( 5) Ko = 1-sin ф

( 6) Kc∞ = (A)(B)

( 7) Kq∞ = (A)(B) Kotan ф

( 8) aq = [Kq

°

/( Kq∞- Kq

°

)][Kosin ф /sin(45 + .5 ф)]

( 9) ac = [Kc°/( Kc∞- Kc°)][2sin(45 + .5 ф)]

(10) Kq

D = [Kq

° - Kq∞ (aq)(D/d)]/[1+(aq)(D/d)]

(11) Kc

D = [Kc° + Kc∞ (ac)(D/d)]/[1 + ac(D/d)]

(12) q = γDd + γ'Ds
Bulletin 1724E-205

Exhibit B

Page 6

(13) pD = qKq

D + CKcD

SAMPLE CALCULATIONS: HANSEN METHOD 

Medium Dry Sand

Medium Dry Sand: γ = 0.120 kcf, ф = 33°, C = nh = 48.4 kcf

Working Lateral Load, P = 17.5 kips

Height of P Acting Above Ground = 60.0 ft.

Use Overload Factor = 2.0

Ultimate Lateral Load = 17.5 x 2.0 = 35.0 kips

Ultimate Moment at Ground Line = 35 x 60 = 2100.0 k-ft.

A1 = .5π + (фπ/180) = 2.14675498

A2 = .5π - (фπ/180) = 0.99483767

e(A1)tan ф = 4.03142127 

-e-(A2)tan ф = -0.52410924

tan(45 + ф/2) = 184177089

tan(45 - ф/2) = 0.54295570

1) Kq

° = 5.98843176

2) Kc°= 8.04901376

3) A = 2.30743260

4) B = 28.63831029

5) Ko = 0.45536097

6) Kc∞ = 89.15529677

7) Kq∞ = 26.36454713

8) aq = 0.08293881

9) ac = 0.17442819
Bulletin 1724E-205

Exhibit B

Page 7

SAMPLE CALCULATIONS: HANSEN METHOD (Cont.) - Medium Dry Sand
Bulletin 1724E-205

Exhibit B

Page 8

SAMPLE CALCULATIONS: HANSEN METHOD (Cont.) - Medium Dry Sand

Point of Zero Shear

9.84y + 0.25(16.537 - 9.84)y2 = 35 - 4.252 - 14.092

y2 + 5.877y - 9.948 = 0

y = 1.372

Zero Shear Distance from Ground = 4.0 + 1.372 = 5.372'

Soil Load Ordinate at Point of Zero Shear:

9.84 + 1.372(16.537- 9.84)/2.0 = 14.434

Moment at Point of Zero Shear:

35 x 65.372 - 4.252(2/3 + 3.372)-4.252(1 + 1.372)2 - 5.588(2/3 + 1.372) - 9.840 (1.372/2)2 + 

4.594/6) x (1.3722 = 2228.58 kip-ft.

*ARM tabulated above are distance from centroid to point of zero shear. Moments M are 

about point of zero shear.
Bulletin 1724E-205

Exhibit B

Page 9

SAMPLE CALCULATIONS: HANSEN METHOD (Cont.) - Medium Dry Sand

The summation of soil pressures below the point of zero shear must be equal to zero. The 

summation of moments of the soil pressures below the point of zero shear, about the point of 

zero shear, must equal the moment in the pole at the point of zero shear (2228.58 kip-ft. in this 

case).

ZONE AREA MOMENT ΣA ΣM

5-6 9.725 3.122 9.725 3.122

6-8 40.702 68.827 50.427 71.949

8-10 56.746 208.655 107.173 280.604

10-1 74.253 420.940 181.426 701.544

12-14 93.015 712.774 274.441 1414.318

14-16 112.861 1090.011 387.302 2504.329

16-18 133.651 1557.569 520.953 4061.898

18-20 155.267 2119.705 676.220 6181.603

20-22 177.610 2779.419 853.830 8961.022

First Trial: Depth = 20' (to bottom of zone 18-20)

as total area is 676.220, point of rotation (where ΣA - 338.11) is in zone 14-16, at 

about (338110 - 274.441)/112.861 = 0.564 of zone depth. 

Say M1 = 1414.318 + 0.564 x 1090.011 = 2029.233 

Say M2 = 6181.603 - 2029.233 = 4152.370 

M2 - M1 = 2123.137 <2228.580. So 20.0' is not enough.

Second Trial: Depth = 20.2' 

Ordinate = 83.134 + 0.2(94.476 - 83.134)/2 = 84.268

Area of zone 20-21, A = (83.134 + 84.268) x 0.5 x 0.2 = 16.740

ARM = 14.728, M = 246.550

 ΣA = 692.96, ΣM = 6428.153

Point rotation, where ΣA =0.5 x 692.960=346.480 is in zone 14-16. 

51.343y + 0.25(61.518 - 51.343) y2 = 346.480 - 274.441, 

 y = 1.317

Ordinate = 51.343 + 1.317 (61.518 - 51.343)/2 = 58.043

ARM = 9.300, A = 72.031, M = 669.881,

 ΣM = 2084.199

 M1 = 2084.199

 M2 = 6428.153 - 2084.199 = 4343.954

 M2 - M1 = 2259.76 > 2228.58 so 20.2 is slightly too deep
Bulletin 1724E-205

Exhibit B

Page 10

SAMPLE CALCULATIONS: HANSEN METHOD (Cont.) - Medium Dry Sand

For Rotation and Deflection of the Pole, Assume an Embedment Depth of 20.10 feet

 nh = 48.4 kcf, E - 30000 x 144 = 4,320,000 ksf

 I = πR3t = πd3t/8

 when d = 72t, I = πd4/576

 say EI = (4320.000)(2.434π/576) = 821554.0 k-ft.2

 1/T = (nh/EI)1/5 = (48.4/821554)1/5 = 0.143

 β = De/T = (20.10)(0.143) = 2.8743

 Dr/De = [(60/20.1) + 0.75]/[1.5(60/20.1) + 1] = 0.682

Working Load, P = 17.5k

Yg = (3 x 17.5 x 0.682)/[48.4 x (20.1)2

{(1.5 x 0.682)-1}]

 = 0.0796 ft. = 0.96 in.

 Rotation = Yg/Dr = 0.0796/(0.682 x 20.1) = 0.00581 rad.

 = 0.33 degrees

NOTE: Had this problem been solved using the chart for medium dry sand, the embedment 

depth of a 2.4 ft. pier for 60 ft. x 35 kips = 2100 kip-feet is about 19.5 ft.

This illustrates the order of magnitude of the error in using the 20 kip charts for a load of 

35 kips. The amount of error is negligible.
Bulletin 1724E-205

Exhibit B

Page 11

SAMPLE CALCULATIONS: HANSEN METHOD - STRATIFIED SOILS

Soil Parameters: Soft Dry Clay, Depth = 0-4'

 Medium Dry Sand, Depth = 4'-10'

 Medium Dry Clay, Depth = 10'-16'

Working Lateral Load, P = 17.5 kips

Height of P Acting Above Ground = 60.0 ft.

Use Overload Factor = 2.0

Ultimate Lateral Load = 17.5 x 2.0 = 35.0 kips

Ultimate Moment at Ground Line = 35 x 60 = 2100 k-ft.

Dry Soft Clay: 

γ = 0.100 kcf, ф = 0.001°, c = 0.25ksf, K - 100 ksf

(following parameters can be applied both to soft and medium clay)

A1 = (π/2) + (πф/180) = 1.570813780

A2 = (π/2) - (πф/180) = 1.570778874

 e(A1) tan ф = 1.000027416

 -e-(A2) tan ф = 0.999972585

tan (45 + ф /2) = 1.000017453

tan (45 - ф /2) = 0.999982547

1) Kq

° = 0.00089737

2) Kc

°

 = 2.570804331

3) A = 1.580000000

4) B = 5.141780549

5) Ko = 0.999982547

6) Kc∞ = 8.124025125

7) Kq∞ = 0.000141788

8) aq

° = 0.000042552

9) ac

°

 = 0.654700797

Note 1: ф is revised from 0° to .001° to keep Hansen's coefficients for Kc

° and Nc from 

disappearing.
Bulletin 1724E-205

Exhibit B

Page 12

SAMPLE CALCULATIONS: HANSEN METHOD - STRATIFIED SOILS

Medium Dry Sand: γ= 0.120 kcf, ф = 33° , c = 0, nh = 48.4 kcf

A1 = (π/2) + (πф/180) = 2.146754980

A2 = (π/2) - (πф /180) = 0.994837674

 e(A1) tan ф = 4.031421265

 -e-(A2) tan ф = 0.524109242

tan (45 + ф /2) = 1.841770886

tan (45 - ф /2) = 0.542955700

1) Kq

° = 5.988431762

2) Kc

°

 = 8.049013758

3) A = 2.307432595

4) B = 38.63831030

5) Ko = 0.455360965

6) Kc∞ = 89.15529660

7) Kq∞ = 26.36454679

8) aq

°

 = 0.082938806

9) ac

° = 0.174428189
Bulletin 1724E-205

Exhibit B

Page 13

SAMPLE CALCULATIONS: HANSEN METHOD - STRATIFIED SOILS

Medium Dry Sand: γ = 0.085 kcf, ф = 41° , c = 0, nh = 77.8 kcf

A1 = ( π/2) + (πф/180) = 2.286381320

A2 = ( π/2) - (πф/180) = 0.855211334

 e(A1) tan ф = 7.297420715

 -e-(A2)tan ф = -0.475483133

tan (45 + ф /2) = 2.194299731

tan (45 - ф /2) = 0.455726256

1) Kq

°

 = 11.92142133

2) Kc

°

 = 12.75178716

3) A = 3.915476618

4) B = 83.85828093

5) Ko = 0.343940971

6) Kc∞ = 328.3451382

7) Kq∞ = 98.16972110

8) aq

°

 = 0.034275312

9) ac

°

 = 0.073535342
Bulletin 1724E-205

Exhibit B

Page 14

SAMPLE CALCULATIONS: HANSEN METHOD - STRATIFIED SOILS

Pole is steel and pole ground line diameter = 1.0 (M).333

B = 1.0(35k x 60' x 12"/')

.333 = 29.22 inc. = 2.43 ft.
Bulletin 1724E-205

Exhibit B

Page 15

SAMPLE CALCULATIONS: HANSEN METHOD - STRATIFIED SOILS
Bulletin 1724E-205

Exhibit B

Page 16

SAMPLE CALCULATIONS: HANSEN METHOD - STRATIFIED SOILS

Moment at Point of Zero Shear

35k (60 + 6.103) - 1.56176(.5)(5.853) - 1⁄2 (.5)(.40052)(5.770)

 - 1.96228(.5)(5.353) - 1⁄2 (.5)(.31552)(5.270)

 - 2.27780(.5)(4.853) - 1⁄2 (.5)(.25498)(4.770)

 - 2.53278(.5)(4.353) - 1⁄2 (.5)(.21033)(4.270)

 - 2.74311(.5)(3.853) - 1⁄2 (.5)(.17648)(3.770)

 - 2.91959(.5)(3.353) - 1⁄2 (.5)(.15018)(3.270)

 - 3.06977(.5)(2.853) - 1⁄2 (.5)(11259)(2.270)

 - 8.19900(2)(1.103) - 1⁄2 (2)(6.50063)(.770)

 - 14.69963(.103)(.103/2) - 1⁄2(.103)(.38383)(.103/3)

 = 2249.285 k-ft.

The summation of soil pressures below the point of zero shear must equal zero. The summation 

of moments of the soil pressures below the point of zero shear, about the point of zero shear, 

must equal the moment in the pole at the point of zero shear.

ZONE AREA MOMENT ∑ AREA ∑ MOMENT

6.1-8 35.31713 35.61782 35.31713 35.61782

8-10 52.56068 155.01826 87.87781 190.63608

10-12 24.48217 120.00533 112.35998 310.64141

12-14 25.10098 173.21138 137.46096 483.85279

14-16 25.58625 227.71254 163.04721 711.56533

16-18 267.83475 2924.99470 430.88196 3636.56003

18-20 307.20874 3968.78323 738.09070 7605.34326

20-22 348.39998 5197.11908 1086.49068 12802.46234

22-24 391.29230 6618.94456 1477.78298 19421.40690

24-26 435.77915 8242.45415 1913.56213 27633.86105

26-28 481.76280 10075.17423 2395.32493 37739.03528

28-30 529.15328 12124.02668 2924.47821 49863.06196
Bulletin 1724E-205

Exhibit B

Page 17

SAMPLE CALCULATIONS: HANSEN METHOD - STRATIFIED SOILS

First Trial: Depth = 20'

As total area is 738.09070, point of rotation where 1⁄2 ΣA = 369.04535 is in zone 16-18, at 

 about (369.04535-163.04721)/267.83475 = 0.76912 of zone depth.

Say M1 = 71156533 + .76912(2924.99470) = 2961.24902

 M2 = 7605.34326 - 2961.24902 = 4644.09424

 M2 - M1 = 1682.84522 < 2249.285, too shallow.

Second Trial: Depth = 22'

As total area is 1086.49068, point of rotation where 1⁄2 Σ = 543.24534 is in zone 18-20, at 

 about (543.24534-430.88196)/307.20874 = 0.36576 of zone depth.

Say M1 = 3636.56003 + .36576(3968.78323) = 5088.16554

 M2 = 12,802.46234 - 5088.16554 = 7714.29681

 M2 - M1 = 2626.13127 > 2249.285, too deep.

Third Trial: Depth = 21.2'

Ordinate = 163.68261 + 1⁄2 (1.2)(18471737 - 163.68261) = 176.30347

 zone 20'-21.1'

 Area = 163.68261(1.2) + 1⁄2 (1.2)(176.30347 - 163.68261) = 203.99165

 Moment = 163.68261(1.2)(14.497) + 1⁄2 (1.2)(12.62086)(14.697) = 2958.78143

 ΣA = 738.09070 + 203.99165 = 942.08235

 ΣM = 7605.34326 + 2958.78143 = 10,564.12469

Point of rotation where 1⁄2 ΣA = 471.04117 is in zone 18-20

143.52613 y + 1⁄4 (163.68261 - 143.52612) y2 = 471.04117 - 430.88196

y = .27711

Ordinate = 143.52613 + 1⁄2(0.27711)(20.15648) = 146.31889

 Moment = 143.52613(.27711)(12.036) + 1⁄2(.27711)(2.79276)(12.082)

 = 483.37716

ΣM = M1 = 3636.56003 + 483.37716 = 4119.93719

 M2 = 10,564.12469 - 4119.93719 = 6444.18750

 M2 - M1 = 2324.25031 > 2249.285, too deep.
Bulletin 1724E-205

Exhibit B

Page 18

SAMPLE CALCULATIONS: HANSEN METHOD - STRATIFIED SOILS

Fourth Trial: Depth = 21.1'

Ordinate = 163.68261 + 1⁄2 (1.1)(184.71737 - 163.68261) = 175.25173

zone 10-21.1

 Area = 163.68261 + 1⁄2 (1.1)(175.25173 - 163.68261) = 186.41389

Moment = 163.68261(1.1)(14.447) + 1⁄2(1.1)(11.569)(14.630) = 2694.28586

 ΣA = 738.09070 + 186.41389 = 924.50459

 ΣM = 7605.34326 + 2694.28586 = 10,299.62912

Point of rotation where 1⁄2 ΣA = 462.25229 is in zone 18-20

143.52613 y + 1⁄4 (163.68261 - 143.52613) y2 = 462.25229 - 430.88196

y = 0.21692

Ordinate = 143.52613 + 1⁄2 (0.21692)(20.15648) = 145.71227

Moment = 143.52613(2.692)(2.005) + 1⁄2 (.21692)(2.18614)(12.042) = 376.61510

ΣM = M1 = 3656.56003 + 376.61510 = 4033.17513

 M2 = 10,299.62912 - 4033.17513 = 6266.45399

 M2 - M1 = 2233.27886 <2249.285, too shallow.

Say Depth between 21.1 to 21.2
Bulletin 1724E-205

Exhibit C

Page 1
Bulletin 1724E-205

Exhibit D

Page 1

Selected SI-Metric Conversions and Other Conversions

AREA

 To Convert From To Multiply by 

circular mil (cmil) square meter (m2) 5.067075 E-10

square centimeter (cm2) square meter (m2) *1.000 E-04

square foot (ft2) square meter (m2) *9.290304 E-02

square inch (in2) square meter (m2) *6.451600 E-04

square kilometer (km2) square meter (m2) *1.000 E+06

square mile (mi2) square meter (m2) 2.589988 E+06

FORCE

 To Convert From To Multiply by 

kilogram force(kgf) newton (N) *9.806650

kip newton (N) 4.448222 E+03

pound force (lbf) newton (N) 4.448222

FORCE PER LENGTH

 To Convert From To Multiply by 

kilogram force per newton per meter (N/m) *9.806650

meter (kgf/m)

pound per foot (lb/ft) newton per meter (N/m) 1.459390 E+01

DENSITY

 To Convert From To Multiply by 

pound per cubic inch kilogram per cubic 2.767990 E+04

(lb/in3) meter (kg/m3)

pound per cubic foot kilogram per cubic 1.601846 E+01

(lb/ft3) meter (kg/m3)

LENGTH

 To Convert From To Multiply by 

foot (ft) meter (m) 3.048 E-01

inch (in) meter (m) *2.540 E-02

kilometer (km) meter (m) *1.000 E+03

mile (mi) meter (m) *1.609344 E+03
Bulletin 1724E-205

Exhibit D

Page 2

LOAD CONCENTRATION

 To Convert From To Multiply by 

pound per square kilogram per square 7.030696 E+02

inch (lb/in2) meter (kg/m2)

pound per square kilogram per square 4.882428

foot (lb/ft2) meter (kg/m2)

ton per square kilogram per square 9.071847 E+02

foot (ton/ft2) meter (kg/m2)

MASS

 To Convert From To Multiply by 

pound (avoirdupois)(lb) kilogram (kg) 4.534924 E-01

PRESSURE

 To Convert From To Multiply by 

kip per square inch pascal (Pa) 6.894757 E+06

(kip/in2) 

kip per square foot pascal (Pa) 4.788026 E+04

(kip/ft2)

newton per square pascal (Pa) *1.000

meter (N/m2)

pound per square pascal (Pa) 4.788026 E+01

foot (lb/ft2)

pound per square pascal (Pa) 6.894757 E+03

inch (lb/in2)

BENDING MOMENT

 To Convert From To Multiply by 

kilogram force meter (kgf-m) newton meter (N-m) *9.806650

kip-foot (kip-ft) newton meter (N-m) 1.355818 E+03

pound-foot (lb-ft) newton meter (N-m) 1.355818

DEGREE/RADIANS

 To Convert From To Multiply by

degree radians π/180

radians degrees 57.3

*Exact Conversion
Bulletin 1724E-205

Exhibit D

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