97-6an1

Report No. TR 97-6

© 1997 Gas Machinery Research Council

TECHNICAL REPORTCOMPRESSOR ANCHOR BOLT DESIGN

By

P. J. PantermuehlA. J. Smalley

Mechanical and Fluids Engineering DivisionSouthwest Research Institute

December 1997

This document contains information resulting from a cooperative researcheffort. The contents hereof are only intended to be guidelines for the subjectmatter to which the document pertains. Neither Southern Gas Associationnor the Gas Machinery Research Council make any warranty orrepresentation, express or implied, with respect to the accuracy,completeness or usefulness of the information contained in this document,including, without limitation, implied warranties of merchantability andfitness for a particular purpose, or that the use of any method, suggestion,technology, information or guidelines disclosed herein may not infringe onrights owned or claimed by others. In no event will Southern GasAssociation or the Gas Machinery Research Council be liable for anydamages, including, without limitation, liability arising out of contract,negligence, strict liability, environmental or tort, warranty or copyrightinfringement, or any incidental or consequential damage arising out of theuse of this Report. The user assumes any liability with respect to anymethods, suggestions, technology, guidelines or other informationcontained herein and releases Southern Gas Association and the GasMachinery Research Council from any and all damage, loss or injury havingto do with use of any such methods, suggestions, technology, guidelines orother such information.

This document may contain references to product(s) which may assist inachieving one or more guidelines as may be set forth herein. Suchreferences are not intended to constitute endorsement or criticism of anysuch product(s) by the Gas Machinery Research Council or SouthwestResearch Institute. Any attempted use of this Report, or its contents, byanyone, as an endorsement or criticism of any such product(s) is expresslyprohibited. Neither this Report or its contents may be used for anyadvertising purposes whatsoever.

GMRC PURPOSE

The Gas Machinery Research Council provides member companies and industry with thebenefits of an applied research and technology program directed toward improvingreliability and cost effectiveness of the design, construction, and operation of mechanicaland fluid systems.

For additional copies of this report, please contact:

Marsha ShortDirector, Member Services

Gas Machinery Research Council3030 LBJ Freeway, Suite 1300, L.B. 60

Dallas, TX 75234Telephone (972) 620-4024

FAX (972) 620-8518

BOARDO F

DIRECTORS

RESEARCHADVISORY

COMMITTEE

SGA GMRCSTAFF

Winston A. Johnson, II, ChairmanEl Paso Natural Gas Co.

John P. Platt, Jr., ChairmanAmoco Corp.

Larry Everett, CAEPresident

Jack W. Hotzel, Vice ChairmanDuke Energy Corp.

Barry G. SelkeWilliams Natural Gas Co.

Marsha ShortDirector,Operating & MemberServices

Bruce L. Hopper, TreasurerChevron Research & Technology Co.

Sam Clowney Tennessee Gas Pipeline Co.

John W. Fulton, SecretaryExxon Research & Engineering Co.

Hans MathewsTennessee Gas Pipeline Co.

Larry Everett, CAESouthern Gas Association/GMRC

Greg PhillippiAriel Corp.

Frank SimsCooper Energy Services

Steve EnglishLone Star Pipeline Co.

Rick CraigEnron Gas Pipeline Group

K. Frederick Wrenn, Jr.Columbia Gas Transmission

John P. Platt, Jr.Amoco Corporation

Larry RogersPeerless Mfg. Co.

Don CrusanColumbia Gas Transmission Corp.

F. Douglas StoverPMC/Beta Limited Partnership

Orin Flanigan, Director EmeritusAdobe Enterprises

Walter J. TuymerHoerbiger Corp. of America

SGA Board of Directors &Transmission Sec. Com. Liaisons

Terrance L. McGillColumbia Gulf Trans. Co.

Dick EimersSolar Turbines

Michael P. WhelanGas Research Institute

ii

EXECUTIVE SUMMARY

This report presents information on selection and design of anchor bolt installations in concrete

foundations for reciprocating compressors. The report uses finite element analysis of a preloaded

anchor bolt and immediately surrounding concrete. The model includes the compressor base,

chock, soleplate, epoxy grout layer, bolt termination, and nearby rebar. It investigates both

termination geometry, bolt length, the use of rebar, and the difference between linear and nonlinear

treatment of the concrete. It shows the benefits of a termination with axial extent of at least 1.5 bolt

diameters, and diameter equal to 3 or 4 bolt diameters. It makes clear the desirability of long

anchor bolts, and quantifies the compression of the stack (base, chock, soleplate, grout, concrete)

which accompanies bolt stretch. It shows that, while rebar stops cracks growing, it does not

inhibit cracks starting under high local tensile stress. Lengthening the anchor bolt moves the

region of high tensile stress and potential local cracking down into the block, and away from

dynamically varying stress, away from oil sources, and for bolt termination in the mat, out of

sight!

The report analyses the effects of grout layer compression. The report shows that epoxy chocks of

the three materials tested and documented in another GMRC report (TR 97-5) will not creep

sufficiently for concern; however, it shows an epoxy grout layer can creep more than an epoxy

chock, and how layer thickness and anchor bolt length combine to influence the associated creep

loss of bolt tension. It further shows how an increase in epoxy grout layer temperature after bolt

tightening can reduce bolt tension as a result of reduced material compression modulus;

retightening anchor bolts at operating temperature can reduce the influence of this problem.

iii

TABLE OF CONTENTS

Page

LIST OF TABLES ii i

LIST OF FIGURES i v

1 . INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

2 . SUMMARY. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

3 . FINITE ELEMENT MODELING APPROACH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

4 . RESULTS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1 6

4.1 PARAMETRIC STUDIES OF TERMINATION PLATE GEOMETRY .... . . . . . . . . . . . . . . . . . . . . . . . . . . . 164.2 EFFECTS OF REBAR ..... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174.3 NONLINEAR MODEL..... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174.4 LINEAR ANALYSES VERSUS NONLINEAR ANALYSES.... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

5 . INFLUENCE OF BOLT LENGTH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3 5

6 . INFLUENCE OF CHOCK AND GROUT PARAMETERS . . . . . . . . . . . . . . . . . . .4 3

6.1 INFLUENCE OF TEMPERATURE ON CHOCK AND GROUT COMPRESSION.... . . . . . . . . . . . . . . . . . . 466.2 10,000 HOUR CREEP RATIO ..... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

iv

LIST OF TABLES

Page

Table 3-1. Finite Element Model Parametric Variables..... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7Table 4-1. Concrete Block Stress Vs. Termination Plate Geometry and Bolt

Preload - Principal Stress (S1), Vertical Component Stress (Sy)... . . . . . . . . . . . . . . . . . 19Table 4-2. Summary of Concrete Tensile Stresses Vs. Plate Diameter and

Thickness (Initial Anchor Bolt Preload - 1500 Microstrain; t = PlateThickness)...... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

Table 4-3. Summary of Concrete Compressive Stresses Vs. Plate Diameter andThickness (Initial Anchor Bolt Preload - 1500 Microstrain; t = PlateThickness)...... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

Table 4-4. Concrete Tensile Stresses With and Without Rebar (Initial AnchorBolt Preload - 1500 Microstrain; t = 1.5").... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

Table 4-5. Concrete Compressive Stresses With and Without Rebar (InitialAnchor Bolt Preload - 1500 Microstrain; t = 1.5")... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

Table 4-6. Nonlinear Analyses With and Without Rebar (Case 7 With 1%Rebar, Case 8 Without Rebar); (Termination Plate = 3" Thick, 6"Diameter, Initial Bolt Strain = 1500 Microstrain)... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

Table 4-7. Linear Analyses Vs. Nonlinear Analyses (Case 6A Linear; Case 7Nonlinear); (Termination Plate = 3" Thick, 6" Diameter, Initial BoltStrain = 1500 Microstrain).... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

Table 5-1. Concrete Tensile Stresses Vs. Anchor Bolt Length (Initial AnchorBolt Preload - 1500 Microstrain); (Plate Thickness = 3"; PlateDiameter = 6")..... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

Table 5-2. Stack Deflection Vs. Bolt Length..... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37Table 6-1. Geometry and Material Properties for Figure 6-4.... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

v

LIST OF FIGURES

Page

Figure 3-1. Schematic of Configuration Modeled..... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11Figure 3-2. Model - Anchor Bolt, Nut, Termination Plate..... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12Figure 3-3. Model - Isometric of Block with Rebar.... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13Figure 3-4. Model - Cross Section of Block..... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14Figure 3-5. Model - Anchor Bolt, Chock, Rail, Grout, Rebar.... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15Figure 4-1. S1 Stress (Total) - Case 1A..... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22Figure 4-2. Sy Stress (Total) - Case 1A..... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23Figure 4-3. UY Deflection (Total) - Case 1A..... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24Figure 4-4. S1 Stress (Concrete) - Case 1A..... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25Figure 4-5. Stress (Concrete) - Case 1A..... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26Figure 4-6. UY Deflection (Concrete) - Case 1A..... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27Figure 4-7. Sy Stress (Anchor Bolt) - Case 1A..... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28Figure 4-8. Concrete Tensile Stress Near Bolt Termination Vs. Termination

Plate Diameter and Thickness (Initial Anchor Bolt Preload - 1500Microstrain)..... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

Figure 4-9. Concrete Compressive Stresses at Bolt Termination Vs. PlateTermination Diameter (Initial Anchor Bolt Preload - 1500Microstrain)..... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

Figure 4-10. Comparison of Concrete Tensile Stresses Near Bolt Termination(With and Without Rebar) Vs. Termination Plate Diameter;Termination Plate Thickness = 1.5"; Initial Bolt Strain = 1500Microstrain)..... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

Figure 4-11. Comparison of Compressive Stresses (With and Without Rebar).. . . . . . . . . . . . . . . . . . 32Figure 4-12. Extent of Cracking with Rebar.... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33Figure 4-13. Extent of Cracking with No Rebar.... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34Figure 5-1. Tensile Concrete Stress at Termination as a Function of Bolt Length... . . . . . . . . . . . . 38Figure 5-2. Compressive Concrete Stress at Termination as a Function of

Anchor Bolt Length..... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39Figure 5-3. Maximum Local Concrete Stress as a Function of Distance Up From

the Bottom of the Bolt Termination at a Wide Range of Bolt Lengths... . . . . . . . . . . . . 40Figure 5-4. Maximum Local Stress as a Function of Radial Distance from the

Bolt Centerline (Starting at the Outer Limit of the Termination Plate).. . . . . . . . . . . . . . 41Figure 5-5. Stack Compression Vs. Bolt Length - Anchor Bolt Tension.... . . . . . . . . . . . . . . . . . . . . . 42Figure 6-1. Epoxy Chock Compression Vs. Chock Width (1000 psi

Compressive Pressure).... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49Figure 6-2. Shape Factor Vs. Ratio of Side Width to Chock Thickness.... . . . . . . . . . . . . . . . . . . . . . . 50Figure 6-3. Epoxy Chock Compression Vs. Young's Modulus (2"x12"x12")

Chock with 1000 psi Surface Load..... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51Figure 6-4. Loss in Bolt Tension (% as a Function of Bolt Length, Bolt Yield

Strength = 105,000 psi)... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52Figure 6-5. Grout Layer Compression and Percent Loss in Bolt Tension with

Increase from 70 to 130°F at 1 Hour and No Bolt Retightening; BoltLength = 48"; Steel Chock; Grout Layer = 4.5" Thick.... . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

1

1. INTRODUCTION

A number of industries make essential or critical use of reciprocating compressors for services

which include natural gas, hydrogen, carbon dioxide, and ethylene. The reciprocating pistons and

rotating crankshaft produce significant gas and inertia forces. While the compressor frame partially

supports these forces, the foundation adds needed structural rigidity, and a significant fraction of

the individual cylinder forces must be transmitted horizontally through the compressor mounting

system to the foundation.

This requirement demands significant attention to the mounting system. For the mounting system

to achieve high rigidity and long term integrity, the anchor bolt must impose sufficient downwards

force at the mounting interface to resist (through Coulomb friction) the highest expected horizontal

loads. Previous GMRC research has made clear that mounting systems must sustain horizontal

forces based on local forces for individual cylinders (as opposed to forces inferred from global

shaking forces and moments). In general, this demands higher bolt tensions than typical past

practice.

The anchor bolt compresses a “stack” consisting of:

• A thick flange at the base of the compressor frame.

• A mounting chock of steel, epoxy, or composite material.

• A steel soleplate.

• A layer of foundation grout.

• Several feet of concrete.

This “stack” under goes stresses and deformations as a result of the anchor bolt tension.

Past GMRC research has addressed various aspects of load generation, load transmission,

mounting system characteristics and foundation integrity, including the anchor bolts. The studies

have included finite element analysis of an entire concrete foundation, including anchor bolts and

their interaction with the concrete. These past investigations have made clear the potential for

tensile stresses and cracking at the anchor bolt termination point, the presence of significant

compressive stresses in the concrete around the anchor bolt, and a number of positive reasons for

moving the anchor bolt termination far down in the concrete block (to reduce sensitivity to creep,

2

and to separate it from areas of high dynamic stress and oil leakage). Past investigations indicate

that, for these foundations, while rebar resists propagation of cracks through the concrete, it does

not significantly control the initial formation of these cracks.

Because previous research considered the compressor and foundation as a structural system, a lack

of fine detail in the model inhibited focused analysis of mounting system integrity and structural

response near the anchor bolt. The present investigation seeks to address this limitation by

modeling a single tie-down (which incorporates the “stack” listed above), to help investigate how

the following influence relevant stresses and deflections:

• Preload (bolt tension)

• Bolt Termination Details

• Mounting System Details

• Concrete Characteristics

• Rebar

• Bolt Length

• Chock/Grout Moduli

The majority of studies reported here have used the ANSYS Finite Element program, and

incorporate the above features with enough surrounding concrete to eliminate sensitivity to

boundary conditions, and with sufficient detail to allow meaningful investigation of the above

parameters. The report presents modeling details, typical overall graphic distributions of stress and

deflected shape, together with graphical displays showing how critical stresses and deflections

vary with influential loading, geometry, and material properties.

3

2. SUMMARY

In summary, this report shows the following:

• High tensile stress tends to induce cracking in the concrete around the bolt termination point.

• These tensile stresses in the concrete near the bolt termination attenuate rapidly with distance

above the termination.

• They also attenuate rapidly with horizontal distance from the termination.

• A termination 1.5 bolt diameters thick beneficially reduces tensile stresses in the concrete for a

relatively small termination diameter.

• A termination plate diameter of 3 or 4 bolt diameters reduces local tensile stresses in the

concrete.

• At the same time, increasing termination plate diameter pushes the location of high tensile

stresses further from the bolt centerline -- potentially joining with other sources of tensile

stress, and moving them closer to the outer surface of the concrete block; hence, there exists a

tradeoff on termination plate diameter.

• Rebar density does not significantly influence the tendency for cracks to occur at the

termination point.

• Lengthening the anchor bolt does not significantly affect the magnitude of local tensile stresses

in the concrete at the end of the anchor bolt, but moves them further from other sources of high

stress, and from sources of oil.

• Lengthening anchor bolts also beneficially reduces the ratio of chock and grout compression to

anchor bolt extension for a given preload. Reducing this ratio reduces sensitivity to creep.

• Decreasing Young’s Modulus of the epoxy material (corresponding to increasing compliance)

or thickening the foundation grout layer increases the ratio of chock and grout compression to

anchor bolt extension, and thereby increases the desirability of a long anchor bolt.

• For the three epoxy chock materials tested (in a separate study), loaded to 1,000 psi or less,

creep deflection in a year should be less than 2.5 mils for the chocks alone.

• Anchor bolts at least 48 inches long coupled with a grout layer 4.5 inches thick or less are

needed to keep creep loss in bolt tension below 5 percent in a year; even longer anchor bolts are

desirable to minimize grout creep effects.

4

• The combination of bolt geometry, grout and chock parameters, preload, gas loads and inertia

loads make for a complex system; an independent analysis using the methods described in this

report should be considered for any reciprocating compressor installation which will use epoxy

chocks or an epoxy grout layer.

• Heating the epoxy by running the engine after bolt tightening under cold conditions can induce

an immediate increase in compression of the epoxy, and a loss in anchor bolt tension.

• Operator's should retighten the anchor bolts at operating temperature to correct for this loss in

tension due to heating.

• Foundation grout layers can contribute more to creep loss of anchor bolt tension than epoxy

chocks.

5

3. FINITE ELEMENT MODELING APPROACH

ANSYS 5.3 was used to construct a parametric finite element model of a compressor foundation

in the vicinity of the anchor bolt with a termination plate embedded in the concrete. Figure 3-1

shows a schematic of the configuration modeled which includes bolt, compressor base, chock,

soleplate, grout, concrete, and bolt termination. The model utilizes ANSYS Link8 3D spar element

for the anchor bolt, which has the capability for bolt preload, expressed as initial bolt strain

(change in length divided by the zero strain length). The Link8 spar (which simulated a 2 inch

diameter bolt in this model) is connected at the bottom to a 3D element Solid45 termination plate,

and at the top to a Solid45 nut (Figure 3-2). The anchor bolt nut bears on a thick section of foot

pad representing the compressor base. Included in the model below the nut are portions of epoxy

chock, rail or soleplate, epoxy grout, and concrete foundation (Figure 3-3 isometric view, and

Figure 3-4 cross-sectional view). The concrete foundation was modeled using Solid45 elements

for the linear model, and Solid65 elements for the nonlinear model. In both cases, rebar was

modeled, as shown in Figure 3-5, using Link8 spars (representing number 7 rebar) interlaced in

the mesh (instead of the “smeared” rebar technique previously used in the Solid65 elements). The

boundary conditions include displacement constraints in all directions at the base of the concrete

block, and displacement constraints along the axis of the foot pad and rail to simulate continuity

beyond the domain of the model.

As mentioned, initial strain was input into the Link8 anchor bolt element causing a tensile preload

that pulls up on the termination plate embedded in the concrete and down on the nut, compressing

the elements in between. The termination plate, as modeled, has no connectivity to the concrete,

except on its top surface, and is unbonded to the concrete on its sides and under surface. The

results clearly show deformation of the termination plate, strongly indicating that this lack of

bonding occurs; if the sides and underneath surface of the plate were initially bonded to the

concrete, loading would immediately distort and deform the plate and break these bonds.

Several model variations were run. Linear analysis (Solid45 element) shows the effect of local

tensile stresses which would be present around the termination plate, but does not allow for

sequential cracking of concrete. Nonlinear analyses (Solid65 element) shows the “after” effects on

those stresses, where cracking of the concrete is predicted in the area by the analyses. The benefits

of linear analyses include speed of execution and indication of severity in terms of predicted tensile

stress level. The nonlinear runs indicate severity by the extent of cracking, which is less precise

and takes longer to execute, but provides a confirmation of observations from the linear runs. The

6

model was run both with and without rebar. The analyses included initial bolt strains of 500,

1000, and 1500 micro-inches per inch of length. In the solution, the anchor bolt strain fell to about

78 percent of its initial value due to deformation of the stacked layer of mixed components. For the

initial preload strain of 1500 microstrain, the final strain in the bolt was around 1200 microstrain,

indicating a bolt preload of about 36,000 psi, a typical value for high strength bolts in compressor

installations. In addition to anchor bolt preload, the analyses also included a 100 psi pressure load

on the chock, to approximate the percentage of compressor weight on the portion of block being

modeled.

Parameter studies included variations in initial anchor bolt strain, anchor bolt length, termination

plate thickness and diameter, epoxy chock size, and Young's Modulus of the epoxy chock, as

listed in Table 3-1. Table 3-2 lists all of the case studies. Cases 1 through 6 involved linear

analyses with no rebar and with 1% rebar (1% of the volume of concrete). Cases 7 and 8 are

nonlinear analyses comparing no rebar and 1% rebar. The cases labeled “Chock 1” to “Chock 7”

involved variation in chock size and modulus of elasticity. The cases labeled “Chock 8A” to

“Chock 8D” involved variation of modulus of elasticity of a 12 inch square chock block with a

1000 psi surface load.

7

Table 3-1. Finite Element Model Parametric Variables

1. Anchor Bolt Initial Strain

2. Anchor Bolt Diameter, Length

3. Termination Plate Thickness, Diameter

4. Chock, Rail, and Block Dimensions

5. Chock Young's Modulus

6. Rebar Presence and Density

7. Concrete Tensile Strength and Cracking Stress

8

Table 3-2. List of Case Studies

ITEM CASE

NO.

DESCRIPTION

1 1A Linear (no rebar), Plate Thickness (1.5), Diameter (6.0), Initial Strain

(500 microstrain)

2 1B Linear (no rebar), Plate Thickness (1.5), Diameter (6.0), Initial Strain

(1000 microstrain)

3 1C Linear (no rebar), Plate Thickness (1.5), Diameter (6.0), Initial Strain

(1500 microstrain)

4 1D Linear (no rebar), Plate Thickness (1.5), Diameter (4.5), Initial Strain

(500 microstrain)

5 1E Linear (no rebar), Plate Thickness (1.5), Diameter (4.5), Initial Strain

(1000 microstrain)

6 1F Linear (no rebar), Plate Thickness (1.5), Diameter (4.5), Initial Strain

(1500 microstrain)


(500 microstrain)


(1000 microstrain)


(1500 microstrain)


(500 microstrain)


(1000 microstrain)


(1500 microstrain)


(1500 microstrain)


(1500 microstrain)


(1500 microstrain)

9


(Continued)

ITEM CASE

NO.

DESCRIPTION

16 4D Linear (no rebar), Plate Thickness (3.0), Diameter (4.5), Initial Strain

(1500 microstrain)

17 5A Linear (1% rebar), Plate Thickness (1.5), Diameter (4.5), Initial Strain

(1500 microstrain)

18 5B Linear (1% rebar), Plate Thickness (1.5), Diameter (6.0), Initial Strain

(1500 microstrain)

19 5C Linear (1% rebar), Plate Thickness (1.5), Diameter (8.0), Initial Strain

(1500 microstrain)

20 5D Linear (1% rebar), Plate Thickness (1.5), Diameter (10.0), Initial Strain

(1500 microstrain)

21 6A Linear (1% rebar), Plate Thickness ( 3.0"), Diameter (6.0"), Initial

Strain (1500 microstrain), Bolt Depth (18")

22 6B Linear (1% rebar), Plate Thickness (3.0"), Diameter (6.0"), Initial Strain

(1500 microstrain), Bolt Depth (24")

23 6C Linear (1% rebar), Plate Thickness (3.0"), Diameter (6.0"), Initial Strain


24 6D Linear (1% rebar), Plate Thickness (3.0"), Diameter (6.0"), Initial Strain


25 6E Linear (1% rebar), Plate Thickness (3.0"), Diameter (6.0"), Initial Strain


26 7 Nonlinear (1% rebar), Plate Thickness (3.0"), Diameter (6.0"), Strain


27 8 Nonlinear (no rebar), Plate Thickness (3.0"), Diameter (6.0"), Strain


28 Chock 1 Chock Size (2" x 4"x 4"), E=1E6


30 Chock 3 Chock Size (2" x 12" x 12"), E=1E6

10


(Continued)

ITEM CASE

NO.

DESCRIPTION



33 Chock 6 Chock Size (2" x 0.5" x 0.5"), E=1E6


35 Chock 8A Chock Size (2" x 2" x 2"), E=2E5

36 Chock 8B Chock Size (2" x 12" x 12"), E=5E5

37 Chock 8C Chock Size (2" x 12" x 12"), E=1E6

38 Chock 8D Chock Size (2"x 12" x 12"), E=5E6

11

NUT

COMPBASE

CHOCK

RAIL

GROUT

RELIEF

FOUNDATION

DISCRETEREBAR

BOLT PRELOADIN TENSION

NUT/PLATE

MAT

Y4

Y3

Y2Y1

Y3

PAD THK

NUT THK

VARDIMVARDIM

VARDIM

Figure 3-1. Schematic of Configuration Modeled

12

Figure 3-2. Model - Anchor Bolt, Nut, Termination Plate

13

Figure 3-3. Model - Isometric of Block with Rebar

14

Figure 3-4. Model - Cross Section of Block

15

Figure 3-5. Model - Anchor Bolt, Chock, Rail, Grout, Rebar

16

4. RESULTS

Direct results from the analyses consist of graphical representations of stress and deflection

distribution in the concrete block and various independent components, with minimum and

maximum stresses or deflections printed on each, as presented in Figures 4-1 through 4-7.

Figures 4-1 through 4-3 show stresses and deflections for the total block and assembly, and

Figures 4-4 through 4-6 show stresses and deflections for the concrete only. Figure 4-7 shows

stresses in the anchor bolt. Additional data printed out in the string of output plots (not shown in

the examples) included individual component stresses and deflections for the epoxy chock, the

epoxy grout, and the rails, and anchor bolt final strain. Data from the output plots is transferred to

spreadsheets for analysis and display of trends.

After compression of the stacked components, the initial strain in the anchor bolt reduced to levels

around 78 percent of the initial values. Deformation of the components and termination plate is

evident in Figures 4-1 through 4-7.

4. 1 PARAMETRIC STUDIES OF TERMINATION PLATE GEOMETRY

Table 4-1 summarizes the concrete stresses and bolt strains for the variations in termination plate

geometry (Cases 1 through 5) in which plate thickness, diameter, and initial bolt strain were

varied. Cases 1 through 4 were run with no rebar. Cases 5A to 5D were run with 1 percent rebar.

The tensile stresses in Table 4-1 are summarized in Table 4-2, and the compressive stresses are

summarized in Table 4-3, for the different plate diameters (concrete with no rebar, and constant

initial bolt strain of 1500 microstrain). Figure 4-8 presents concrete tensile stresses as a function

of plate diameter, and Figure 4-9 presents concrete compressive stresses as a function of plate

diameter; in these figures, S1 is maximum principal stress, and Sy is the component stress in the

vertical direction (Y). Tensile stresses clearly roll off with increasing plate diameter, although the

trend is more gradual for a 3 inch thick plate (1.5 bolt diameters), compared to a 1.5 inch thick

plate (0.75 bolt diameters). High tensile stresses in the concrete surrounding the termination plate

appear to result from the top edge of the plate pulling upward on the concrete elements, which are

restrained through other concrete elements attached to the foundation base. As the plate outer edge

moves outwards, increased bending of the plate over its radius appears to reduce its tensile

influence in the concrete near its outer edge. The disadvantage of extending the termination plate is

to move high tensile stresses further from the bolt, where they could cause cracks which join up

17

with cracks from other locations, or penetrate the block outer surface. A “cross-over” point occurs

in Figure 4-8 at around 8 inches diameter (4 bolt diameter), where tensile stresses are equivalent

for both the 1.5 and 3.0 inch thick plates. Figure 4-9 shows compressive stresses (Sy) are higher

(more compressive) for the thinner plate. Above 8 inches (four times bolt diameter), termination

diameter does not appear to influence compressive stresses.

4. 2 EFFECTS OF REBAR

Tables 4-4 and 4-5 compare the tensile and compressive stresses for cases without rebar (1F, 1C,

2C, and 3C) to Cases with 1 percent rebar (Cases 5A to 5D). These cases were run with a 1.5-

inch thick termination plate and initial bolt strain of 1500 microstrain. The data is plotted in

Figures 4-10 and 4-11, which indicate rebar has very little influence on stresses predicted by linear

analysis. The tensile stresses surrounding the termination plate are very localized and tend to

decay rapidly before extending to areas where rebar could control stresses.

4. 3 NONLINEAR M ODEL

Cases 7 and 8 are nonlinear analyses that show differences in stresses where cracking is predicted

in the concrete in the vicinity of the termination plate. In these analyses, the model adjusts the

stresses after cracking. The cases were run using a termination plate 3 inches thick, 6 inches in

diameter, an anchor bolt depth of 18 inches (25 inches total length), and an initial bolt strain of

1500 microstrain. Case 7 was run with 1 percent rebar, and Case 8 was run with no rebar. Table

4-6 compares stresses for the two runs, and indicates little significant difference in maximum

tensile or compressive stresses. The prediction of cracked elements for the two cases is displayed

in Figures 4-12 and 4-13. The cracked elements are identified by the light colored elements near

the bolt termination. The two plots are essentially identical, confirming the limited influence of

rebar on crack initiation.

4. 4 LINEAR ANALYSES VERSUS NONLINEAR ANALYSES

Table 4-7 compares stresses calculated by linear analyses (Case 6A) against stresses calculated by

the nonlinear method (Case 7). The nonlinear analysis solves the problem repeatedly, adjusting the

extent of cracking until the loads can be carried by uncracked elements. Both were performed with

18

plates 3 inches thick, and of 6-inch diameter; and 18-inch depth anchor bolts with 1500 microstrain

initial bolt strain. Tensile stresses fall substantially in the nonlinear model, reflecting the inability

of the concrete to sustain tension above about 290 psi. As a result of the reduced tensile strength,

elements under compression pick up more of the load with resultant increases in maximum

compressive stresses for the nonlinear case with cracking.

19

Table 4-1. Concrete Block Stress Vs. Termination Plate Geometry and Bolt

Preload - Principal Stress (S1), Vertical Component Stress (Sy)

Case Plate Dia. Plate Thk Final Compressive Strs Tensile StrsN o . (inches) (inches) Bolt Strn S 1 S y S 1 S y1D 4.5 1.5 389 -42 -899 404 3951E 4.5 1.5 788 -70 -1798 842 8251F 4.5 1.5 1187 -96 -2698 1280 12541A 6 1.5 387 -41 -925 341 3361B 6 1.5 783 -70 -1852 720 7091C 6 1.5 1179 -100 -2779 1098 10822A 8 1.5 384 -39 -965 260 2582B 8 1.5 776 -66 -1934 563 5592C 8 1.5 1169 -93 -2903 867 8603A 10 1.5 383 -33 -946 177 1773B 10 1.5 775 -55 -1898 408 4063C 10 1.5 1168 -78 -2850 638 6364D 4.5 3 1199 -263 -2360 1094 10454A 6 3 1212 -172 -1947 1000 9564B 8 3 1219 -85 -1806 875 8404C 10 3 1223 -73 -1768 732 7085A 4.5 1.5 1193 -111 -2673 1230 12095B 6 1.5 1184 -113 -2762 1073 10515C 8 1.5 1174 -108 -2892 869 8565D 10 1.5 1172 -95 -2838 646 638

Cases 1-4: No Rebar Case 5: 1% Rebar

Table 4-2. Summary of Concrete Tensile Stresses Vs. Plate Diameter and

Thickness (Initial Anchor Bolt Preload - 1500 Microstrain; t = Plate Thickness)

Case Plate Tensile Stress (psi)N o . Dia. S 1 S y S 1 S y

(inches) t=1.5" t=1.5" t=3" t=3"1F,4D 4.5 1280 1254 1094 10451C,4A 6 1098 1082 1000 9562C,4B 8 867 860 875 8403C,4C 10 638 636 732 708

20

Table 4-3. Summary of Concrete Compressive Stresses Vs. Plate Diameter and

Thickness (Initial Anchor Bolt Preload - 1500 Microstrain; t = Plate Thickness)

Case Plate Compressive Stress (psi)N o . Dia. S 1 S y S 1 S y

(inches) t=1.5" t=1.5" t=3" t=3"1F,4D 4.5 -96 -2698 -263 -23601C,4A 6 -100 -2779 -172 -19472C,4B 8 -93 -2903 -85 -18063C,4C 10 -78 -2850 -73 -1768

Table 4-4. Concrete Tensile Stresses With and Without Rebar (Initial Anchor

Bolt Preload - 1500 Microstrain; t = 1.5")

Case Plate Tensile Stress (psi)N o . Dia. S 1 S y S 1 S y

(inches) (w/o Rebar) (w/o Rebar) (1% Rebar) (1% Rebar)1F,5A 4.5 1280 1254 1230 12091C,5B 6 1098 1082 1073 10512C,5C 8 867 860 869 8563C,5D 10 638 636 646 638

Table 4-5. Concrete Compressive Stresses With and Without Rebar (Initial

Anchor Bolt Preload - 1500 Microstrain; t = 1.5")

Case Plate Compressive Stress (psi)N o . Dia. S 1 S y S 1 S y

(inches) (w/o Rebar) (w/o Rebar) (1% Rebar) (1% Rebar)1F,5A 4.5 -96 -2698 -111 -26731C,5B 6 -100 -2779 -113 -27622C,5C 8 -93 -2903 -108 -28923C,5D 10 -78 -2850 -95 -2838

21

Table 4-6. Nonlinear Analyses With and Without Rebar (Case 7 With 1% Rebar,

Case 8 Without Rebar); (Termination Plate = 3" Thick, 6" Diameter, Initial Bolt

Strain = 1500 Microstrain)

Case Rebar Final Compressive Stress Tensile StressN o . Strain S 1 S y S 1 S y

7 1% 1192 -409 -2160 289 1038 None 1187 -417 -2181 277 122

Table 4-7. Linear Analyses Vs. Nonlinear Analyses (Case 6A Linear; Case 7

Nonlinear); (Termination Plate = 3" Thick, 6" Diameter, Initial Bolt Strain = 1500

Microstrain)

Maximum MaximumCase Final Compressive Stress Tensile StressN o . Strain S 1 S y S 1 S y

Case 6A 1217 -160 -1925 1001 942Case 7 1187 -409 -2160 289 103

22

Figure 4-1. S1 Stress (Total) - Case 1A

23

Figure 4-2. Sy Stress (Total) - Case 1A

24

Figure 4-3. UY Deflection (Total) - Case 1A

25

Figure 4-4. S1 Stress (Concrete) - Case 1A

26

Figure 4-5. Stress (Concrete) - Case 1A

27

Figure 4-6. UY Deflection (Concrete) - Case 1A

28

Figure 4-7. Sy Stress (Anchor Bolt) - Case 1A

29

600

700

800

900

1000

1100

1200

1300

4.5 6 8 1 0Plate Dia.

Str

ess

(p

si)

S1(1.5)Sy(1.5)S1(3.0)Sy(3.0)

1 .5

3

Figure 4-8. Concrete Tensile Stress Near Bolt Termination Vs. Termination Plate

Diameter and Thickness (Initial Anchor Bolt Preload - 1500 Microstrain)

1.5 Inch Thickness Termination Plate

3 Inch Thick Termination Plate

Termination Plate Diameter, Inch

30

-3000

-2500

-2000

-1500

-1000

-500

0

4 .5 6 8 1 0Plate Dia.

Str

ess

(p

si)

S1(1.5)Sy(1.5)S1(3.0)Sy(3.0)

Figure 4-9. Concrete Compressive Stresses at Bolt Termination Vs. Plate

Termination Diameter (Initial Anchor Bolt Preload - 1500 Microstrain)

Plate Diameter, Inch

31

0

200

400

600

800

1000

1200

1400

4.5 6 8 1 0

Plate Dia.

Str

ess

(p

si)

S1(1.5)Sy(1.5)

S1(rbar)Sy(rbar)

Figure 4-10. Comparison of Concrete Tensile Stresses Near Bolt Termination

(With and Without Rebar) Vs. Termination Plate Diameter; Termination Plate

Thickness = 1.5"; Initial Bolt Strain = 1500 Microstrain)


32

-3000

-2500

-2000

-1500

-1000

-500

04 .5 6 8 1 0

Plate Dia.

Str

ess

(p

si)

S1(1.5)Sy(1.5)S1(rbar)Sy(rbar)

Figure 4-11. Comparison of Compressive Stresses (With and Without Rebar)


33

Figure 4-12. Extent of Cracking with Rebar

34

Figure 4-13. Extent of Cracking with No Rebar

35

5. INFLUENCE OF BOLT LENGTH

As previously discussed, a long anchor bolt reduces sensitivity to creep; it also moves the point of

termination away from locations of high stress induced by horizontal shaking forces (which tend to

concentrate near the top of the block) and away from the leaking oil. In considering these desirable

features, the study has also looked for any hidden technical or performance disadvantage of long

anchor bolts -- in particular, how does length (and thereby depth of the termination) influence local

stresses at the termination, and the total amount of compression of the “stack” (concrete, grout,

soleplate, chock, frame base)? Table 5-1 summarizes results of length investigations. Figure 5-1

shows that concrete tensile stress increases slightly with increasing bolt length, but only by 20

percent for a factor of five increase in bolt length from 25 to 120 inches. Figure 5-2 shows that

concrete compressive stress decreases by about 20 percent between a 25-inch and a 120-inch bolt

length. Figure 5-3 plots maximum tensile stress in the concrete as a function of distance up from

the bottom of the bolt termination for a 6-inch diameter plate; it shows how the tensile stress peaks

then reduces rapidly with this distance -- to zero at 3 or 3.5 inches. The shape and extent of the

tensile stress region shows little dependence on bolt length; this tensile stress region simply occurs

in the concrete wherever the bolt ends. Figure 5-4 shows how rapidly maximum tensile stress

reduces with radial distance, starting at the radius of the plate (3 inches), falling to zero within 6.5

inches of the bolt/plate axis. Thus each termination creates a small localized region of high stress

in the surrounding concrete. The scale of this region is such that rebar affects it little. The local

high stresses will tend to cause local cracking, and using a long anchor bolt to move the

termination point as low as possible in the block has the benefit of moving this “hot spot” away

from where it can cause trouble. Moving the termination right into the mat under the foundation

block ensures that any cracks developed are unlikely to grow to the extent where they become

visible and unsightly or contribute to any deterioration of installation strength.

Since the anchor bolt stretch tends to increase in direct proportion to length, it is worth reviewing

whether the compression of the “stack” also increases significantly with anchor bolt length. Table

5-2 summarizes stack compression resistance. Figure 5-5 shows how “stack” compression (based

on finite element analysis) increases as a function of anchor bolt length under 120,000 lb anchor

bolt tension. Figure 5-5 shows that the total compression increases gradually with anchor bolt

length from 7.5 mils at 25 inches bolt length to about 11.5 mils for the longest anchor bolt (120

inches) considered in this parametric investigation. The corresponding anchor bolt stretch is

36

approximately 1.3 mils per inch or 156 mils for the longest anchor bolt considered. With an

anchor bolt length of 72 inches or more, the ratio of bolt stretch to stack compression approaches

10:1 -- a desirable target.

37

Table 5-1. Concrete Tensile Stresses Vs. Anchor Bolt Length (Initial Anchor

Bolt Preload - 1500 Microstrain); (Plate Thickness = 3"; Plate Diameter = 6")

Case Bolt Len Final Bolt Tensile Strs Compressive Strs Stack DeflN o . ( in. ) Strn S 1 S y S 1 S y (mils)6A 25 1217 1001 942 -160 -1925 7.46B 31 1254 1055 997 -92 -1618 7.96C 37 1282 1088 1032 -79 -1405 8.26D 43 1306 1138 1088 -62 -1240 8.66F 80 1375 1183 1123 -85 -1628 10.16G 120 1405 1202 1142 -76 -1503 11.5

Table 5-2. Stack Deflection Vs. Bolt Length

Case Bolt StackN o . Len(in.) Defl(mils)

- 0 06A 25 7.46B 31 7.96C 37 8.26D 43 8.66F 80 10.16G 120 11.5

38

0

200

400

600

800

1000

1200

1400

0 2 0 4 0 6 0 8 0 100 120

Bolt Length

Te

nsi

le

Str

ess

, p

si

S1Sy

Figure 5-1. Tensile Concrete Stress at Termination as a Function of Bolt Length

39

-2000

-1800

-1600

-1400

-1200

-1000

-800

-600

-400

-200

00 2 0 4 0 6 0 8 0 100 120

S1Sy

Figure 5-2. Compressive Concrete Stress at Termination as a Function of Anchor

Bolt Length

40

-600

-400

-200

0

200

400

600

800

1000

1200

1400

0 2 4 6 8 10 12 14

Vertical Position (inches)

Str

ess

Sy

(psi

) 120"depth73"depth36"depth18"depth

Figure 5-3. Maximum Local Concrete Stress as a Function of Distance Up From

the Bottom of the Bolt Termination at a Wide Range of Bolt Lengths

41

-200

0

200

400

600

800

1000

1200

0 2 4 6 8 10 12

Horizontal Position (inches)

Str

ess

Sy

(psi

) 18"depth36"depth73"depth120"depth

Figure 5-4. Maximum Local Stress as a Function of Radial Distance from the

Bolt Centerline (Starting at the Outer Limit of the Termination Plate)

42

0

2

4

6

8

1 0

1 2

0 2 0 4 0 6 0 8 0 100 120

Anchor Bolt Length (in.)

De

fle

ctio

n

(mils

)

Figure 5-5. Stack Compression Vs. Bolt Length - Anchor Bolt Tension

43

6. INFLUENCE OF CHOCK AND GROUT PARAMETERS

Finite element results show that an epoxy chock deflects with sufficient uniformity over its extent

in the horizontal plane that its compressive deflection characteristics can be modeled with one

dimensional analysis. Provided it has uniform thickness, the grout layer at the top of the block

may be similarly analyzed. Of interest is how much the chock and grout layer compress under

load, how chock and grout geometry and material properties influence the deflection, and the role

that time and temperature may play in this deflection.

An appealing approach to calculating deflection of a thin layer under normal compressive load over

its surface is to treat it as a short, broad “column”. The stiffness of a slender elastic column, Kcol

under a vertical load is:

Kcol = E A / h [6-1]

where:

E = Young’s Modulus.

A = compressed area.

H = the height of the column.

The material in a slender column is free to deform at right angles to the applied load. Poisson’s

ratio quantifies this deformation, but does not enter into the formula for column stiffness.

When the column goes from slender to broad, the material near the middle has less freedom to

deform horizontally, because the partially incompressible material further out constrains it. Thus, a

chock has a higher stiffness than the above formula would give, specifically:

Klayer = F1 Eeff A / h [6-2]

where:

Klayer = the stiffness of the chock or loaded layer of foundation grout.

Eeff = the effective material Young’s Modulus (inverse of creep compliance for the time of

interest).

44

A = the loaded area.

h = the thickness of the chock or layer.

F1 = a shape factor (typically between 1 and 2 for the configuration and materials under

consideration).

Figure 6-1 plots compression of a 2-inch thick square chock as a function of the length of one side,

loaded at 1000 psi, as predicted by finite element analysis, for a material with Young’s Modulus of

one million and a Poisson’s ration of 0.4. The figure shows that deflection falls by a factor close

to 2 over the range of side length considered. This side length goes from “slender” (one-quarter of

the chock thickness) to “broad” (twelve times the chock thickness). This implies an epoxy chock

generally has a higher stiffness than that based on a simple column model, for a given value of

effective Young’s Modulus. From this data, a 12-inch square chock with thickness of 2 inches

and an effective modulus of one million psi has a stiffness of over 1 x 108 lbs/inch. Figure 6-2

replots the deflection data non-dimensionally as stiffening “shape” factor (F1) versus the ratio of

side length to chock thickness. This shape factor approaches 1.75 for typical chock dimensions.

Figure 6-3 shows how compression of a 12-inch by 12-inch square chock, loaded to 1000 psi, 2

inches thick, varies with effective Young’s Modulus in the range 0.2 x 106 to 5 x 106 psi. The

deflection varies inversely with Young’s Modulus, with a range of 0.2 mils to 5.5 mils.

A GMRC supported test program to determine time and temperature deflection characteristics of

epoxy materials provided by three suppliers has shown that effective Young’s Modulus for chock

materials ranges from about 106 to 2.5 x 106 psi (accounting for creep) for loading periods of 104

hours and nominal temperatures up to 120°F. The tests used a pressure loading 200 psi. For

higher loadings to 1000 psi, some nonlinearity is observed, which may cut the effective modulus

in half. The shape factor effect discussed above adds 50 percent or more to the stiffness of typical

chock geometries. Thus, we expect chock deflections to lie below 2.5 mils for most combinations

of material, geometry, and loading for temperatures up to 120°F, even after creep has occurred

over one year. Review of higher temperature results indicates little increase in this deflection even

up to 140°F. Based on these observations, any bolt stretch greater than 50 mils will not likely

deflect the chock more than about 5 percent of the bolt stretch, even after a year of creep for the

tested chock materials for operation at temperatures up to 140°F. The chock grouts tested tend to

incur an initial deflection after one hour, which exceeds the additional creep deflection over the next

year, indicating that the contribution of chock creep alone will generally be significantly less than 5

percent.

45

The above discussion addresses deflection and creep specifically for chock materials. The majority

of installations use additional epoxy material on the top of the concrete and under any soleplates or

rails -- another loaded layer of material subject to deformation and creep. Test data shows

foundation grouts tend to creep more than chock grouts, so foundation design should ensure that

foundation grouts do not introduce significant creep loss of bolt tension that the chock itself

avoids. This is accomplished by keeping the thickness of all grout layers subject to anchor bolt

loading below a few inches (6-inch suggested maximum), by maximizing the length of anchor

bolts, and by checking the anchor bolt tension with a frequency that ensures acceptably low tension

loss over the period between checks. The potential for foundation grout creep must be considered

with steel chocks just as with epoxy or composite chocks.

Figure 6-4 shows percentage loss in bolt tension due to creep as a function of anchor bolt length

and grout layer thickness. Table 6-1 lists the geometry and material properties selected for Figure

6-4.

Some quantities in Table 6-1 deserve discussion or further definition. A high strength bolt material

has been chosen with a yield of 105,000 psi (ASTM A-193). The chock thickness chosen is 2

inches -- a relatively high value for an epoxy chock. The initial bolt tension (40 percent of yield)

and chock area combine to give a pressure loading of 585 psi (bolt tension = 75,000 lbs). The

chock modulus and grout modulus, each 1.5 million lb/in2, are reasonable median values for

materials tested at an accelerated test time of 10,000 hours. The creep tests actually generated

values for compliance, and effective Young’s Modulus is the inverse of compliance selected at the

longest time of interest (one year -- ~10,000 hours is suggested). In addition to the bolt tension, a

per chock load of 10,000 lbs has been added in the analysis to account for the compressor’s

weight. The 10,000 hour creep ratio is the ratio of compliance at 10,000 hours to compliance at

one hour for constant temperature. Again, these are representative values, slightly on the high side

of the median test values. There is quite a spread in both values, as tested, and providing a

comprehensive set of curves to address all ranges of material properties and geometry is not

attempted here. Application of the available data for specific selections of these parameters is

straightforward enough that it should be considered for any new or repaired compressor; Figure 6-

4 should be treated as a broad guideline and representative of the sort of analysis which should be

specifically undertaken for each installation to help ensure integrity, particularly with higher loads,

higher temperatures, thicker grout layers, or shorter bolts.

46

Figure 6-4 confirms the desirability of thin grout layers and long anchor bolts. It shows that for

the specific parameters of this analysis a bolt length of at least 48 inches coupled with a grout layer

no thicker than 4.5 inches are needed to keep the creep loss in bolt tension below 5 percent at

110°F.

In all results presented in Figure 6-4, the contribution of chock creep was 10 percent or less of the

total loss in bolt tension; thus foundation grout creep dominates even when it is acceptably low.

6. 1 INFLUENCE OF TEMPERATURE ON CHOCK AND GROUT COMPRESSION

By the nature of epoxy materials, the passage of time causes an increase in compression of an

epoxy layer under compressive load; an increase in temperature also causes an increase in

compression. A bolt tightened at a temperature of 70°F or below will immediately experience some

loss in tension when heated to 110°F because of the temperature dependent Young’s Modulus of

epoxy. While the analysis of grout creep presented in Figure 6-4 was for 110°F, and the results

presented included the effect of bolt loosening for temperatures up to 110°F, it is recommended that

any anchor bolt be retightened at operating temperature. It is further important to note that

interpretations of the preceding examples may become less conservative when the operating

temperature exceeds 110°F, and that retightening at operating temperature becomes even more

significant if that operating temperature exceeds 110°F. Figure 6-5 presents a plot of chock

compression and anchor bolt tension versus time for a combination of anchor bolt, chock and

foundation grout, where the bolt is tightened at 70°F, then heated to 130°F, and operated at that

temperature for 10,000 hours continuously. The step increase in compression and loss of bolt

tension as a result of the step increase in temperature are apparent, and emphasize the need for bolt

retightening at operating temperature.

6. 2 10,000 HOUR CREEP RATIO

This quantity referred to in the preceding sections of this report, provides a measure of the relative

contributions of “initial deflection,” and creep to the deflection after about one year:

RC10K = 104A [6-3]

47

Where we define RC10K as the deflection under-load (or compliance) after 10,000 hours divided by

the deflection under load after one hour. We find that for the three chock grouts tested, the 10,000

hour creep ratio lies between 1.18 and 1.63 at 110°F, and between 1.06 and 1.34 at 140°F. For

the three foundation grouts tested, it lies between 1.6 and 6.67 at 110°F, and between 1.37 and

3.53 at 140°F.

Since all chock epoxies tested exhibit RC10K values of less than 2 at all temperatures between 110°Fand 140°F, it can be inferred that for these chock materials, the initial deflection contributes more

than the creep resulting from the passage of one year provided the bolt is tightened hot . Some of

the foundation grouts exhibit RC10K values greater than two, and in this case, creep contributes

more than the initial deflection.

Even though the relative contribution of creep to lateral deflection appears to fall with increasing

temperature, the total deflection under load increases with temperature because temperature

“softens” the material and at 140°F, the effective Young's Modulus may fall as low as one-third the

values in Table 6-1.

48

Table 6-1. Geometry and Material Properties for Figure 6-4

Bolt Length, inches 60

Bolt Diameter, inches 1.5

Initial Bolt Stress, % of Yield 40

Bolt Modulus, psi 2.80E+07

Bolt Yield Stress, psi 105,000

Chock Thickness, inches 2

Chock Area, inch squared 144

Grout Thickness, inches 3

Time Dep. Chock Compliance, inch squared/lb 0.667E-6

Time Dep. Grout Compliance, inch squared/lb 0.667E-6

Chock Modulus, psi 1.5E+6

Grout Modulus, psi 1.5E+6

Compressor Weight Per Bolt, lb 10,000

10,000 Hour Chock Creep Ratio 1.3

10,000 Hour Grout Creep Ratio 3

Time in Hours at which Compliance Values Apply 10,000

49

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0 4 8 12 16 20 24

Side, Inches

Def

lect

ion,

Mils

Figure 6-1. Epoxy Chock Compression Vs. Chock Width (1000 psi Compressive

Pressure)

50

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0 2 4 6 8 10 12

Width/Height Ratio

F1

Figure 6-2. Shape Factor Vs. Ratio of Side Width to Chock Thickness

51

0

1

2

3

4

5

6

0.00E+00 1.00E+06 2.00E+06 3.00E+06 4.00E+06 5.00E+06

Young's Modulus

Def

lect

ion,

Mils

Figure 6-3. Epoxy Chock Compression Vs. Young's Modulus (2"x12"x12")

Chock with 1000 psi Surface Load

52

0

2

4

6

8

1 0

1 2

1 4

0 2 0 4 0 6 0 8 0 100 120

Bolt Length, Inches

Lo

ss i

n B

olt

Te

nsi

on

, % 3 Inch Grout

4.5 Inch Grout6 Inch Grout

Figure 6-4. Loss in Bolt Tension (% as a Function of Bolt Length, Bolt Yield

Strength = 105,000 psi)

53

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

0 .1 1 1 0 100 1000 10000

Time in Hours

Co

mp

ress

ion

in

Mils

& P

erc

en

t L

oss

in

Bo

lt T

en

sio

n

Compression

T Loss %

Figure 6-5. Grout Layer Compression and Percent Loss in Bolt Tension with

Increase from 70 to 130°F at 1 Hour and No Bolt Retightening; Bolt Length =

48"; Steel Chock; Grout Layer = 4.5" Thick

97-6an1

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