post-tensioned reinforced concrete as applied to the construction of ships

7/27/2019 POST-TENSIONED REINFORCED CONCRETE AS APPLIED TO THE CONSTRUCTION OF SHIPS

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POST-TENSIONED REINFORCED CONCRETEAS APPLIED TO

THE CONSTRUCTION OF SHIPS

James Daniel Ertner


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OUATE SCHOOtFORNU 93940


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POST-TENSIONED REINFORCED CONCRETEAS APPLIED TO

THE CONSTRUCTION OP SHIPSby

JAMES DANIEL ERTNERB.S., Wheaton College (Illinois)

1968

SUBMITTED IN PARTIAL FULFILLMENTOF THE REQUIREMENTS FOR THEDEGREE OF OCEAN ENGINEER

AND THEDEGREE OF MASTER OF SCIENCE IN

NAVAL ARCHITECTURE AND MARINE ENGINEERINGat the

MASSACHUSETTS INSTITUTE OF TECHNOLOGY


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NAVAL POST^"ONTEREY. ( dPOST-TENSIONED REINFORCED CONCRETEAS APPLIED TOTHE CONSTRUCTION OF SHIPS

byJames Daniel Ertner

Submitted to the Department of Ocean Engineering onMay 9, 1975, in partial fulfillment of the requirements forthe degree of Ocean Engineer and the degree of Master ofScience in Naval Architecture and Marine Engineering.ABSTRACT

Post-tensioned reinforced concrete is a material whichintegrates the advantages of concrete, steel, reinforcedconcrete, and prestressed concrete. Unlike ferro-cement(which has been limited to small boats), post-tensionedreinforced concrete has the potential for being applied tothe construction of larger ships, such as liquifiednatural gas tankers. An investigation of its engineeringproperties, permissible stresses under loading, designconsiderations (cracking, corrosion, concrete cover thick-ness, etc.), and its flexural behavior, all lead to theapplication of post-tensioned reinforced concrete to atanker midship section. The key parameters in the designof such a midship section (excluding the principal shipdimensions) are: concrete cover thickness, diameter ofordinary reinforcing rods, total area of ordinary rein-forcing steel, diameter of post-tensioning tendons, totalarea of post-tensioning steel, strength of the respectivesteels and the concrete, and modular ratio. The threeparameters with the greatest impact on section properties(i.e., moment of inertia and section modulus) are modularratio, overall steel area, and concrete area. -The effecton moment of inertia (determined with the aid of acomputer program) of varying these parameters is pre-sented graphically. One particularly significant con-clusion is that, for a constant moment of inertia, theweight of a midship section can be reduced by increasingthe modular ratio while decreasing the steel area and/orthe concrete area; furthermore, the steel stress increasesconsiderably, whereas the concrete tensile stress (thecritical stress in post-tensioned reinforced concretestructures) is virtually unaffected.

Thesis Supervisor: J. Harvey EvansTitle: Professor of Naval Architecture


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ACKNOWLEDGEMENT

For originally suggesting the thesis topic, for al-ways being enthusiastically willing to discuss its pro-gress, for freely offering professional advice, and formaking the year's work a pleasurable experience, I want toheartily and gratefully thank Professor J, Harvey Evans.Appreciation is also due Mr. Keatinge Keays, Adminis-tration Officer of the Ocean Engineering Department, forgranting me use of his computer program.

The excellent typing is the handiwork of my dearwife, Jenny, for which I express a loving thanks. Andeven though my beautiful daughter, Gail, is too young tounderstand what this is all about, she neverthelessdeserves congratulations for being such a well-behavedbaby, and thereby indirectly helping me with rny thesis.

Last, but certainly not least, a sincere note ofgratitude is extended to the United States Navy, withoutwhose sponsorship my three-year course of study at M.I.T.would not have been possible.


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TABLE OP CONTENTSPage

Title Page -jAbstract 2Acknowledgement


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5Page

E, Material Selection Economic Aspects 551

.

Steel 552. Concrete 61

F. Selection of Concrete Mix for a Ship 64CHAPTER III: DESIGN CONSIDERATIONS 69

A. Cracking of Concrete 691

.

Fracture Mechanics 702. Application of Fracture Mechanics 73to Concrete3. Application of Fracture Mechanicsto Reinforced Concrete 754. Cracking as a Design Factor 77

B. Corrosion and Concrete 94C Cover of Concrete 101D. Spacing of Rods 105E. Cost Considerations 109

CHAPTER IV: FLEXURAL ANALYSIS OF CONCRETE BEAMS 112A. Bending of Reinforced Concrete Members 112

1 . Reinforced Concrete Beam BendingAnalysis 113

2. Applications 1183. Use of Codes in Reinforced ConcreteBending 120

B. Bending of Prestressed Concrete Members 1281 . Flexural Analysis of Prestressed

Concrete 1282. Use of Codes in Prestressed ConcreteBending 134


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C. Bending of Post-Tensioned ReinforcedConcrete Members1

.

Synthesis of Reinforced andPrestressed Concrete2. Calculation of Section Properties3. Applications

CHAPTER V: APPLICATION TO THE DESIGN OP A TANKERMIDSHIP SECTIONA. Calculation of Section Modulus

1

.

Post-Tensioned Reinforced ConcreteBeam2. Computerized Extension to a TankerMidship Section

B. Effect on Tanker Midship Section Modulusof Varying Key Parameters1

.

Selection of Parameter Range of Values2. Application of Computer Program

C. Results and Conclusions1

.

Treatment of Cover Thickness2. Effect of Varying Depth and Breadth3. Effect of Five Key Parameters4. Effect of the Three Primary Parameters5. Minimum Y/eight Considerations

D. Stress DiagramE. Recommendations

APPENDICESA. Conversion Table

Page

135

138140144

147148149

151

153154156161161163164I 70184186193197197


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7Page

B. Effect on Beam Depth of VaryingModular Ratio 198C. Effect on Beam Depth of Varying SteelStress 200D. Effect on Beam Weight of Varying Depth 202E. Analytical Expression for MinimumWeight of Beam 204F. Effect on Stress and Section Modulus ofVarying Beam Depth 207G-. Effect on Stress and Section Modulus ofVarying Steel Area and Distribution 211H. Determination of Post-Tensioning Steel Area 214I. Determination of Nonprestressed andPrestressed Steel Area 219J. Modified Computer Program to Calculate theSection Modulus of a Post-Tensioned Rein-forced Concrete Ship 222K. Effect on Moment of Inertia of VaryingPrimary Parameters 227L. Minimum Weight Considerations 230

REFERENCES 232


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8LIST OP TABLES

Table Page1

.

Types and Strengths of Portland Cement 472. Aggregates Commonly Used in Concrete 50

(a) Weight of Aggregates(b) Strength of Aggregates

3. Aggregate-Cement Ratio (By Weight) Requiredto Give Four Degrees of Workability withDifferent Gradings for Rounded 3/4 inchAggregate 534. Size and Weight of Ordinary Reinforcing Bars 565. Cost of Steel Used for Post-Tensioning 60Tendons6. Average Cost of Aggregates 637. Constants for Use in Determination ofRequired Area of Nonprestressed Rein-

forcement (Equation 19) 828. Allowable Tensile Stresses for Class 2Post-Tensioned Members 869. Allowable Tensile Stresses for Class 3Post-Tensioned Members 88

10. Factors to be Multiplied by Allowable TensileStresses in Table 9 8811. Stress in Post-Tensioning Tendons forDetermination of Ultimate Moment(Equation 57) 13612. Calculation of Neutral Axis Location andMoment of Inertia for Example in Figure 12 15213. Possible Combinations of the Five KeyParameters 16614. Computer Results of the Thirty- two Combi-nations of Five Key Parameters (for n = 7) 168


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Table Page15. Effect on Total Stress of Varying ModularRatio 191F1 . Effect on Stress and Section Modulus ofVarying Beam Depth 210G1 . Effect on Stress and Section Modulus ofVarying Steel Area and Distribution 213


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10LIST OP FIGURES

Figure Page1

.

Typical Stress-Strain Curves for ConcreteReinforcement 26

2. Typical Stress-Strain Curves for PrestressingSteels 273. Typical Stress-Strain Curve for Concrete 294. Tangent and Secant Concrete Moduli ofElasticity 305. Permissible Tensile Stress in Concrete 396. Relation Between Concrete CompressiveStrength and Water-Cement Ratio 457. Rectangular Reinforced Concrete Beam 1 18. Rectangular Reinforced Concrete Beam(ACI Code) 1239. Rectangular Beam with Both Tension and

Compression Reinforcement 12510. Determination of Stresses 131(a) Plain Concrete Beam

(b) Prestressed Concrete Beam11. Post-Tensioned Reinforced Concrete Beam 14212. Post-Tensioned Reinforced Concrete Beamwith Both Tension and Compression Rein-

forcement 15013. Post-Tensioned Reinforced Concrete Rectan-gular Midship Section 15714. Moment of Inertia vs. Modular Ratio (forconstant concrete area) 17315. Moment of Inertia vs. Modular Ratio (forconstant steel area) 17516. Moment of Inertia vs. Concrete Area (forconstant modular ratio) 176


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11

Figure17. Moment of Inertia vs. Concrete Area (forconstant steel area)18. Moment of Inertia vs. Steel Area (forconstant concrete area)19. Moment of Inertia vs. Steel Area (forconstant modular ratio)20. Effect on Moment of Inertia of IncreasingModular Ratio and Decreasing Concrete Area21. Effect on Moment of Inertia of IncreasingModular Ratio and Decreasing Steel Area22. Effect on Moment of Inertia of IncreasingConcrete Area and Decreasing Steel Area23. Stress Diagram for a Post-Tensioned Rein-forced Concrete Tanker Midship Section

Page

177

178

179

181

182

183

192


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12NOMENCLATURE

A cross-sectional areaA area of concreteA^ equivalent concrete area = A~ - A + nA CTec^ - & o sAg gross sectional area of concreteA_._ area of prestressed reinforcementpsA s area of nonprestressed tension reinforcementA' area of nonprestressed compression reinforcementaQr distance from surface to nearest reinforcing "barb breadthC total compressive force in concretec distance from neutral axis to extreme fiber;depth of notch; half the initial crack lengthcm, minimum concrete cover thickness to reinforcementmmD reinforcement rod diameterd depth of beam from top to center of tensionreinforcementd' depth from top of beam to center of compressionreinforcementd overall depth of beamEc Young 1 s modulus of elasticity for concreteEg Young's modulus of elasticity for steele strain; eccentricityf bending stressesfc concrete stress at service loadsf specified compressive strength of concrete


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13fpk tensile stress in prestressing tendon at failuref stress in prestressing steel at design loadsf ultimate strength of prestressing steelf modulus of rupture of concretef Q stress in tension reinforcement at service loadsf

'

stress in compression steel at service loadsfy yield strength of nonprestressed tensionreinforcementf ' yield strength of nonprestressed compressiony reinforcementG strain energy release rateh overall depth of reinforced concrete beam;net depth of "beam with notch = d - ch maximum diameter of aggregateaggI moment of inertiaj ratio of moment arm of C-T couple to depthK stress intensity factork ratio of location of neutral axis to depthM bending momentn modular ratio = Es/^cP applied loadp percentage of nonprestressed tension steel

=. A s/bdp 1 percentage of nonprestressed compression steel= A^/bdp percentage of prestressed reinforcement = A /bdpcf pounds per cubic footpsi pounds per squared inch


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14q prestressing steel reinforcement ratio = P-n^^/fAq f alternative prestressing steel reinforcementratio = P^f^/f

'

^p ps' cR ratio of distances from the neutral axis to thetension face and to the reinforcement centroidr radius from crack tip to any pointS section modulus = i/c; specific surface energyT total tensile force; surface energyU elastic strain energyu Poisson's ratioW unit weight of concretewmax maximum crack widthx distance from surface to neutral axisz moment arm = jd

f density; radius of curvature of crack tip**" applied stressc critical stress for failuren nominal stress at the notch root(J> capacity reduction factor


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15CHAPTER I

INTRODUCTION

The application of concrete to ship constructionaffords two immediate advantages in times of risingmaterial prices and rapidly diminishing natural resources,namely, low relative cost and general availability.The raw materials for making cement and aggregates areessentially limitless, since practically all of theearth* s crust can be used, assuming that the energyrequirements for such production can be met. Further,concrete is the one construction material the engineercan personally formulate, within limits, to meet specificindividual job requirements of durability and strength.The prospect of applying concrete to ship design andconstruction thus offers a potential benefit which meritsserious consideration.

A. Historical Perspective

1 . Ferro-cement . The first floating structuresmade of Portland cement mortar, the forerunner of today'sferro-cement type of construction, were the ten-foot longreinforced mortar rowboats built in the late 1840's byJ.L. Lambot in France (1). The mortar hulls were rein-forced with wire fabric and iron grid. Until 1967, atwhich time it was transferred to a French museum, one of


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16these "boats was still afloat in a pond on Lambot's estate.

Present-day ferro-cement construction was developedby the Italian architect P.L. Nervi (2). In 1946, Nervibuilt his largest ferro-cement vessel; with a displace-ment of 165 tons, the hull was nearly 1-1/2 inches thickand reinforcement consisted of three layers of 1/4 inchround steel bars at 4 inch centers and eight layers ofwire fabric. After eight years of sea service, thevessel required no maintenance - unfortunately, it waswrecked on a rocky coast during a storm in 1959.

Ferro-cement is currently receiving widespreadattention from the United States Navy (3, 4, 5, 6, 7),individuals (8, 9), and professional societies (10). Infact, the Society of Naval Architects and Marine Engineershas formed a committee whose technical objective is thedevelopment and standardization of ferro-cement for marinepurposes. Hov/ever, the applicability of the afore-mentioned references has been limited to small boats,primarily due to the limited tensile strength of suchstructures. It is, thus, unlikely that ferro-cementconstruction will ever be practical for large ships (say,longer than 200 feet).

2. Reinforced Concrete . One solution to thisproblem is reinforced concrete. As opposed to ferro-cement which is formed in relatively thin layers on the


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17order of 1 to 1-1/2 inches, ordinary reinforced concreteis typically cast in sections approaching 6 inches andmore. Whereas ferro- cement contains thin rods and/orwire mesh, reinforced concrete is reinforced with thickersteel bars . Tensile cracking is considered negligibleand structures are designed so that all design tensileloads are carried by the bars, the concrete being used tocarry compression loads.

The first large reinforced concrete ocean-going shipproduced in the United States v/as the "Faith"; constructedin 1917, this vessel displaced 3,427 tons and had a hullthickness varying from 4 to 4-1/2 inches. The U.S.Shipping Board Emergency Fleet Corporation programconstructed twelve concrete ships for V/orld War I use(six of them were tankers); ranging in length from 260 to434 feet, the hulls of these ships incorporated steelreinforcing bars ranging from 3/8 to 1-3/8 inches indiameter; hull thicknesses varied from 4 to 6 inches.The average compressive strength of the concrete was4,000 pounds per squared inch (psi) at age 28 days.Crushed lightweight (expanded clay) aggregate was utilizedin the 120 pounds per cubic foot (pcf) concrete (11).It is apropos to note that drill cores extracted about1953 from the hull of the wrecked "Selma" , one of thesetwelve ships, revealed no corrosion of reinforcing steelafter 35 years of exposure to seawater.


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18During World War II, the U.S. Maritime Commission

constructed a total of 104 concrete hulls: 24 of theseere for self-propelled dry cargo ships each 350 feet

long; the remainder were for seagoing oil barges, with acargo capacity of 5,000 to 7,000 tons. The concrete in

of these vessels incorporated lightweight aggregate(maximum size =1/2 inch) and modified portland cement(ASTM Type II). Minimum compressive strength required

age 28 days was 5,000 psi; hull thicknesses ranged4 to 6-1/2 inches (12).

Fundamentals and Problem DefinitionBefore progressing any further, it is fitting that a

key terms be identified. Ferro-cement , suffice it tois characterized by a thin wire mesh of the chickenvariety covered by mortar that, in general, can be

pplied with a trowel. Its application has been limitedsmall boats. Reinforced concrete , on the other hand,concrete containing steel bar reinforcement, and, like

erro-cement, is designed on the assumption that the twoact together in resisting forces (13).on its own, is a material which is relatively

in tension; steel reinforcing rods are thereforein that part of a beam subject to tensile strain,

the lower layer in a simply supported beam. (Aidealized as a beam on a 1.1 (L) *^ wave, experiences


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19alternating loads in a seaway, and thus requiresreinforcing rods at both deck and keel). Standard text-books on reinforced concrete (14, 15) present thefundamental characteristics, and traditional strength ofmaterials texts include sections on the bending analysisof reinforced concrete beams (16, 17). The concreteships constructed during World Wars I and II were of thismaterial.

Prestressed concrete is reinforced concrete in whichthere have been introduced internal stresses of suchmagnitude and distribution that the stresses resultingfrom loads are counteracted to a desired degree (13).Two principal methods of prestressing are post-tensioningand pre-tensioning, in which tendons embodied in theconcrete are tensioned after the concrete has hardenedand before the concrete is placed, respectively.

Post-tensioned prestressed concrete incorporatesthe use of tensioned tendons in preformed voids or ductsthroughout the length of the member. The tendons arestressed by hydraulic jacks and anchored after theconcrete has developed a specified strength (generallyafter about 14 to 28 days). As a final operation, theducts or voids are pressure grouted to protect the tendonsagainst corrosion and also to provide bond between thetendon and the concrete.

One of the main advantages of prestressing is that it


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20tends to minimize tensile cracking in the concrete. Thisis accomplished by means of the "prestress", namely, thecompression induced in the concrete by the externalpressure (tension) applied to the tendons. Thus, underconditions of superimposed loading, the normal tendencyfor tensile stress to develop only goes towards nullifyingthe artificial compressive prestress.

Resulting advantages are that the concrete is incompression, high prestress tends to increase durabilityof the concrete, impact resistance is good, and fatigue

is high. Prestressed concrete textbooks (18,19, 20, 21) cover the various engineering properties,specifically as applied to land-based structures. The

of prestressed concrete to ships is a recentand is sparsely represented in the literature

(22, 23, 24).A significant point must be made at this juncture.

on reinforced concrete (a binary system con-isting of concrete + reinforcing rods) and prestressed

(a binary system consisting of concrete + rein-rods that have been post- or pre-tensioned) are

available. However, a survey of the literaturenot reveal any references dealing strictly with

a_s well as prestressed concrete. I will thusfor purposes of this thesis, a tertiary system

of the "union" of the above two binary "sets",


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21and will call it "prestressed (or, post-tensioned) rein-forced concrete". Therefore:

Post-Tensioned Reinforced Concrete =Concrete+Reinforcing Rods

+Post-Tensioned TendonsThe purpose of this thesis is thus to investigate

the feasibility of applying post-tensioned reinforcedconcrete to the construction of ships.


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22CHAPTER II

POST-TENSIONED REINFORCED CONCRETE

Despite the fact that the ocean-going concrete shipsand barges of Chapter I were structurally sound, furtherdevelopment was apparently undesirable because conven-tionally reinforced thick concrete hulls are heavier thancomparatively thin steel hulls. Furthermore, even ifno immediate structural degradation or leakage resulted,tensile cracking in a ship operating in a seaway(experiencing large hogging and sagging bending moments)would act to pump salt water into the structure and ontothe bars, causing corrosion. This in turn requires alarger cover of cement to prevent tensile cracks fromreaching the reinforcing bars, contributing further tosize and weight of the structure.

The weight of the hull thus seems to be the mostdamaging drawback in using concrete for large ships.The alternating loads in a seaway present difficulties inutilizing concrete properties. However, numerousadvantages indicate that consideration of this materialas applied to the construction of ships should not beneglected.

A. Preliminary ArgumentsSome of these advantages of prestressed concrete


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23include: economy of construction vis-a-vis steelstructures; high prestress tends to increase durabilityof the concrete; low maintenance (e.g., no drydocking dueto concrete durability); sparkproof, fire resistant, andextremely advantageous for transporting flammable orexplosive cargo. Prestressed concrete has high fatiguestrength, due chiefly to the small stress variations inthe prestressing steel; prestressing improves ability forenergy absorption under impact loads. Prestressedconcrete has a favorable mode of failure under accidentor over-stress conditions, such as grounding, collision,and explosion it develops localized cracks or disrup-tion, but does not rip or tear as metals do; if a shiphull is damaged, repairs are rapid and relativelyinexpensive (chip away cracked areas, apply bondingcompound to the contact surface, and pour a concretepatch). Prestressed concrete is virtually corrosionresistant, and is less likely than many other structuralmaterials to exhibit brittle fracture at low temperatures.A favorable result of corrosion resistance is that rustingwould be precluded in the cargo compartments: furtherramifications would be minimization of cargo contaminationand no expensive gas freeing procedures incidental to hotwork or chipping of rusted steel hulls. Anotheradvantage of prestressed concrete is that thermal conduc-tivity is only one-sixth that of steel hulls, thereby


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24holding condensation in cargo holds to a minimum.

The weight disadvantage of concrete ships previously-alluded to might be overcome by resorting to post-tensioned reinforced concrete hulls. Prestressedconcrete usually employs high-strength materials andtherefore requires less of them for the same load, whichresults in lighter members. The small steel area (dueto the use of high-strength steel) warrants thinnermembers which are also more flexible than conventionallyreinforced concrete members. Furthermore, prestressingis intended to minimize the formation of tension cracksunder working loads. V/ith this reduction of (or hope-fully, lack of) cracking, the entire cross-sectionremains effective for stress; a smaller required sectionnormally results.

Any weight disadvantage would be further allayed ifpost-tensioned reinforced concrete were used in theconstruction of ships designed to carry a typically lightcargo, e.g., a liquified natural gas (LNG) tanker. Notonly would the light cargo counteract the heavier(compared to steel) concrete hull, but the concrete hullwould also preclude (or at least greatly minimize) thetaking on of ballast upon off-loading the cargo. Thepreceding discussion of the corrosion resistant advantageof prestressed concrete, as well as cracking minimization,are both also particularly applicable to tankers. Thus,


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25there seems to be ample evidence to justify furtherinvestigation into the applicability of post-tensionedreinforced concrete to large ship construction.

B. Engineering PropertiesBefore the load-carrying behavior of post-tensioned

reinforced concrete attains meaning, the basic physicalproperties of concrete and steel (both prestressing andnonprestressed) must be understood.

Prestressed concrete combines the best properties ofconcrete and steel. Concrete is capable of resistingrelatively high compressive stresses, although its tensilestrength is only 10 to 15 percent of its compressivestrength. On the other hand, steel is strong in tension.Prestressing combines these two materials in the mostefficient manner: by stretching the steel before it isbonded to the concrete, compressive forces are placed inthe concrete; and if the steel and the resultant compres-sive portion are located in the ship hull area wheretensile forces occur under loading, these materials willbe utilized most efficiently.

1. Steel . Turning briefly first to steel, as itis the more familiar material (at least to naval archi-tects), the stress-strain relationship deserves attention.Figures 1 and 2 portray typical stress-strain curves forseveral steels, There are three basic differences


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26

CuVLO\na

OVU

WlRF-s

ZOO !

/ .-ALLOY STEEL B/1R (-fx ^?0 K


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27

300

WIRE (E^ c/.5xl0 psi)a.ILoenQ (/JQ>

Ov3\s\

co\ft in CL

fcH

cl> H?O M Mf^ COr o 525W

* fcH3- - H4- HipqMCOCOMO So

-4

ill

hoc: CL


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40the typical concrete compressive strength range of 4,500to 10,000 psi. Notice that the curve representingequation (9) is rather conservative (as compared with theother curves) in the range indicated.D. Material Selection Theoretical Aspects

One of the first chronological steps in consideringthe feasibility of applying post-tensioned reinforcedconcrete to ship construction is that of materialselection. Preliminary decisions to be made include thedetermination of the composition of all components in thetertiary system, namely: the type of steel for reinforcingrods, the type of steel for post-tensioned tendons, andthe type of concrete. (Steel has been traditionallyused as reinforcement rather than other materials, suchas aluminum or titanium, for the simple reason ofeconomics, namely, cost and availability. Some mate-rials, particularly copper and aluminum, have beenavoided because of the possibility of electrolyticcorrosion and hydrogen embrittlement.

The material selection process, appearing in thisand the following section, will be divided into twoaspects theoretical and economic. A preliminaryselection v/ill be made solely on technical considerations;and after the economic factors are weighed, a finaldecision will be made: either supporting or revising the


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41

original choice.

1 Steel . Alternatives to choose from are:(a) low carbon, or mild, steel, with a tensile yieldstrength (f ) of about 32,000 psi; (b) high-tensile-strength (HTS) steel, with a yield strength of about50,000 psi; (c) HY-80, with a minimum tensile yieldstrength of 80,000 psi; (d) HY-100; and (e) HY-130 andother higher strength steels.

Material selection is basically a trade-off study,to determine which of various material characteristicsare most suitable. Some of the more important propertiesmaterials must possess and which merit considerationare (28): strength-to-weight ratio, fracture toughness,fatigue strength, corrosion resistance, ease of fabri-cation, weldability, durability, maintainability, generalavailability, and cost.

In dealing with concrete ships, the weight factordeserves paramount attention, since the inherent disad-vantage of concrete vessels is low deadweight-displacementratio due to notoriously heavy structure. Thus,selection of a high strength steel (e.g., HY-80) would belogical, since steel cross-sectional area, and henceweight, decreases as steel yield strength increases.( Higher strength steels, such as HY-100 and above, areeliminated at this preliminary stage from further


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42consideration due to high cost, fabrication and/or joiningproblems, low ductility, relatively low fatigue life, andpoor corrosion resistance (29)). This choice (HY-80) ismore appropriate for the post-tensioned tendons than thereinforcing rods, as the purpose of the tendons is toinduce compression in the concrete; furthermore, thegreater the tensile strength of the tendon, the greaterlevel of prestress (post-tensioning) can be applied(although this is also a function of the number oftendons)

.

This last statement implies that perhaps the higherstrength steels (HY-100 and above) should not have beenso hastily discarded, since more than 80,000 psi prestressmay be desirous. Hence, final judgment will be deferreduntil the next section.

In addition to weight, cost certainly deserves tobe a prime consideration. Cost reduction can be bestapplied to the selection of steel for reinforcing rods,since the largest (in total-number-of-rods sense) steelcomponent in a post-tensioned reinforced concrete sectionis the reinforcement. Thus, in order to reduce cost,reinforcing rods should be composed of a lesser strengthsteel (e.g., mild steel). This, too, is a logicaldecision for another reason: since the reinforcement willbe in compression (due to the post-tensioned tendonsinducing compression in the concrete and hence in the


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43reinforcing rods), a high tensile strength will not berequired to reduce tension in the concrete; under loadingconditions, any tendency for tensile stress to developwill merely negate the applied prestress.

2 Concrete . The selection of concrete entailsthe consideration of factors somewhat different from thosein choosing steel. Several of the properties listedpreviously are all inherent advantages of concrete:corrosion resistant, ease of fabrication, maintainability,availability, and low cost. Obviously, considerationof only these factors would be somewhat limited.

Other factors, integral aspects in the selection ofconcrete, are: type and size of aggregate, porosity,density, compressive strength, and water-cement ratio.

Concrete is a heterogeneous mixture of sand, gravel,cement and water, plus air, salts, fine inert materials,and other additives or admixtures which modify thecharacteristics of concrete. In brief, concrete forreinforced concrete consists of aggregate bonded togetherin a paste made from portland cement and water. Theaggregate occupies roughly three-quarters of the entirevolume of an average concrete; the remaining one-quarteris filled with cement paste and air voids (27).

It may be said that the properties of concrete arestudied primarily for the purpose of mix design.


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44Mix design can "be defined as the process of selectingsuitable ingredients of concrete and determining theirrelative quantities with the object of producing aseconomically as possible concrete of certain minimumproperties, notably strength and durability (31).

There are several methods of mix design, althoughin principle they are all basically similar. Thetraditional British method is summarized below (32):(1) To satisfy a specified compressive strength anddurability, a value of water-cement ratio is chosen,from data given, for the appropriate age and type ofPortland cement (see Figure 6),(2) The level of workability of the concrete requiredis chosen, being based primarily on the degree of mixwetness desired,(3) Tables are provided relating aggregate-cement ratio,workability, and water-cement ratio for aggregates ofdifferent particle shape and maximum particle size.Therefore, knowing the available aggregates and havingfixed the workability and water-cement ratio, theaggregate-cement ratio can be selected.

Referring to step (1), factors which affect compres-sive strength are water-cement ratio, cement type,aggregate type, and aggregate-cement ratio. Figure 6 (31)shov/s the relation between compressive strength andwater-cement ratio for different cement types at various


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45

13,000

^ / 0,000-5:

f-V)Ui>

u

8ooo 3

*

r 3 D/1Y50.3 a* 0.5 o.b on o.% o.f /.o /./ /.a

FIGURE 6RELATION BETWEEN CONCRETE COMPRESSIVE STRENGTHAND WATER- CEMENT RATIO


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46ages. In essence, a lower water-cement ratio yields agreater compressive strength, and a Type III portlandcement attains its strength sooner than ordinary Type I.(Note: The ratio of water to cement is expressed in U.S.gallons of water per 94-pound sack of cement.) Table 1gives the five types of portland cement, as well astheir approximate relative strengths, with normal port-land cement used as the basis for comparison (33). TheAmerican Concrete Institute (ACl) specifies (13) thatwhen concrete made with normal weight aggregate isintended to be watertight, it must have a maximum water-cement ratio of 0.48 for exposure to fresh water and0.44 for exposure to sea water.

Aggregates, the next consideration enumerated above,should be selected with regard to the following (14):(a) strength (a strong aggregate, e.g., granite, makesfor a strong concrete); (b) size (must be small enoughto be worked in between and around all reinforcements);(c) particle shape (rounded aggregates require thesmallest water-cement ratio); (d) surface texture (arough surface gives a stronger concrete); (e) grading;and (f) cost.

Another consideration in selecting concrete is thewater-cement ratio. The quantity of v/ater relative tothat of the cement is the most important item in deter-mining concrete strength. In general, the lower the


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47^^ CO^ ^p pfctO c O o in o inPi o o o r o\ CDa> e v * rJh-p mGO

MQ>P>>EH.o aS o LTl o in in6s u Hi UEH P COOP4 0)T~

Pq > COw o CO >.Hi CO as o o o o inpq CO CD xi o CO >^J -P^ H -P Pitj Pi W) P I aJCO CD aJ Pi aJ CD PW H H CD CD CD P COPM 0) as H -P S S H & P 1 h coEH PJ a! Pi ^d t*0 CO H


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48water-cement ratio, the greater the strength and water-tightness. Also, low permeability (low porosity or highwater-tightness) is associated with high strength andhigh resistance to weathering. Thus, the three factorsof strength, porosity, ana water-cement ratio are inter-related.

Density, another property for consideration, dependson the grading, 3hape and maximum size of the aggregates,as well as the water-cement ratio. Actually, the sizeand grading of aggregates have an important influence onthe water-cement ratio itself. So, in fact, all thefactors mentioned so far are interrelated.

In reinforced concrete, the maximum size of aggre-gate that can be used is governed by the width of thesection and, as just mentioned, the spacing of thereinforcement. With this proviso, it has generally beenconsidered desirable to use as large a maximum size ofaggregate as possible. However, it has been demonstrated(31) that the improvement in concrete properties with anincrease in aggregate size does not extend beyond about1-1/2 inches. Above the 1-1/2 inch maximum size, thegain in strength due to the reduced water requirement isoffset by the detrimental effects of lower bond area andof discontinuities introduced by the very large particles.Therefore, from the point of view of strength, there isno advantage in using aggregate with a maximum size


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49greater than about 1-1/2 inch. Table 2(a) presents thegeneral range in unit weight of common natural aggre-gates (27), while Table 2(b) summarizes the basicaggregates and their approximate 28-day compressivestrength (3).

For a given water-cement ratio, the higher theaggregate-cement ratio the higher the compressive strengthtends to be, for mixes of the same aggregate type. Thus,a leaner mix will give a higher strength than a rich one.

So far only the requirements for the concrete to besatisfactory in the hardened state have been considered-- step (1). However, properties when being handled andplaced are equally important; one essential at this stageis a satisfactory workability step (2).The workability that is considered desirable dependson two factors. The first of these is the size of thesection to be concreted and the amount and spacing ofreinforcement; the second is the method of compactionused (e.g., for very low workability too dry a mix intensive vibration is required, since it cannot besufficiently worked by hand; for high workability -- toowet a mix vibration should not be used, as segregationmay result)

.

The most important influences affecting workabilityare water content of the mix, aggregate properties, andcement content. For given materials and proportions,


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50

TABLE 2AGGREGATES COMMONLY USED IN CONCRETE

(a) Weight of AggregatesMaterial Unit Weight (pcf)sand 95 to 115gravel: 3/4 inch 99 to 107

1-1/2 inch 104 to 112crushedstone: 3/4 inch 95 to 103

1-1/2 inch 100 to 108

(b) Strength of AggregatesMaximum 28-dayAggregate Concrete Compressivetype Density (pcf) Strength (psi)

lightweight 100 8,000-10,000sand and gravelor crushed stone 150 12,000-15,000heavy aggregates 200-300 9,000-11,000


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51

the workability increases with increase in water contentper cubic yard of concrete. If the water content andthe other mix proportions are fixed, workability isgoverned by the maximum size of aggregate, its grading,shape and texture. As the aggregate size decreases,more water must be added to maintain workability , andthe corresponding aggregate-cement ratio increases.As an aggregate progresses in shape from angular toirregular to rounded, the aggregate-cement ratio alsoincreases. Grading refers not only to the percentageof sand, but also to the overall range of particlesizes; in general, an increase in sand content at thelow end of the workability range may cause a more notice-able drop in workability than at the higher end of therange. The final influence on workability, cementcontent, is negligible and may be ignored for normalmixes (v/hen cement content is less than 24 lb/ft ) ; invery rich mixes, however, (richer than 28 lb of cementper cubic foot of concrete), there is an apparent dropin workability (32).

It must be noted that predicting the influence ofmix proportions on workability requires care, since ofthe three factors, namely, water-cement ratio, aggregate-cement ratio, and water content, only two are independent.For instance, if the aggregate-cement ratio is reduced,but the water-cement ratio is kept constant, the water


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52content increases, and consequently the workability alsoincreases. If, on the other hand, the water content iskept constant when the aggregate-cement ratio is reduced,then the water-cement ratio decreases but workabilityis not seriously affected.

All the factors considered up to now, includingwater-cement ratio, v/ill determine between them theaggregate-cement ratio of the mix -- step (3). Thechoice of the aggregate-cement ratio is made either onthe personal experience of the mix designer or alterna-tively from charts and tables prepared from comprehensivelaboratory tests. The latter course is frequentlyfollowed, use being made of tables of Road Note No. 4 (32);these tables are reproduced in reference (31). As anexample, Table 3 presents the aggregate-cement ratio (byweight) required to give four degrees of workability withdifferent gradings of rounded, 3/4 inch aggregates. Asthe grading number increases frorn 1 to 4 the aggregategrading varies from coarse to fine. Knowing the water-cement ratio and the aggregate-cement ratio, there islittle difficulty in determining the proportions ofcement, water, and aggregate the major components ofconcrete.

One other consideration, endemic to concrete ships,is the minimization of weight. So overriding was thisfactor in the World War II concrete ship program that


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53LfN tO t- 00 LfN t-CNJ tO "3" "3" LfN VD

EH vo m irv to T- COM tOJ-3 A CNJ to


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54heavy aggregates (200 to 300 pcf) and natural sand andgravel aggregates (150 pcf) were not even considered.Lightweight aggregates (110 pcf) were used solely tolighten the hull structure, despite its disadvantages.

Some of the disadvantages of lightweight aggregateconcrete just alluded to are: lightweight aggregates arerelatively weak (27), and tensile strength is lower thanordinary weight concrete in inany cases (15); lightweightaggregates are more costly, they present greater diffi-culty in handling, mixing, and controlling the concretemixes, and they are more porous (12). All concretesmade with lightweight aggregate exhibit a higher moisturemovement than is the case v/ith normal weight concrete.Many lightweight aggregates are angular and have a roughsurface, producing harsh mixes and hence decreasingworkability. If lightweight aggregate is to "be used inreinforced concrete, a greater cover will be requiredthan if ordinary aggregates were employed (31). Creepand drying shrinkage (the latter a cause of cracking) arelikely to be perhaps twice the magnitude of that of compa-rable normal concrete (32). It is, thus, doubtfulwhether the weight advantage of lightweight aggregateoutweighs all the disadvantages enumerated here.Furthermore, even a 33-1/3 percent savings in weight byusing 100 pcf vice 150 pcf aggregates would be nullifiedby a corresponding increase in cover thickness from say,


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551-1/2 to 2 inches. (The figures are arbitrary, but theyemphasize the point.)

Thus, a preliminary selection of concrete wouldindicate usage of an ordinary weight (150 pcf) aggregate,Type III portland cement for its high-early-strength,and a low (about 0.45) water-cement ratio.

The definition of mix design given at the beginningof this section stressed two points: that the concreteis to have certain specified minimum properties, and thatit is to be produced as economically as possible. Thefollowing section will consider the economic aspects ofmaterial selection.

E Material Selection Economic AspectsHaving arrived at a quasi-theoretical determination

of material selection, it is necessary to approach thesubject from a practical standpoint. In other words,what materials are physically available (i.e., "off-the-shelf")? And which are the optimum economically-speaking?

1 Steel . In general, the price of reinforcingsteel depends upon the quantity in pounds purchased, thesize of the bars, and the number of bends and hooks.The base price is the price per 100 pounds of reinforcingbars. The size of the bars available for ordinary steelreinforcement are indicated in Table 4 (34-).


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56

TAELE 4

SIZE AND WEIGHT OF ORDINARY REINFORCING BARS

Bar number Diameter_ (in) Area (in ) Weight (lb/ft)3 3/8 0.110 0.3764 1/2 0,196 0.6685 5/8 0.307 1.0436 3/4 0.442 1.5027 7/8 0.601 2.0448 1 0.785 2.6709 1-1/3 1.000 3.400

10 1-1/4 1.2656 4.30011 1-3/8 1.5625 5.31014 1-3/4 2.405 8.18018 2-1/4 3.976 13.520


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57It is trivial, yet significant, to point out that

steel reinforcing bars cost more per unit weight thanstructural steel (due to fabrication and formation).For example, a 20-cities 1 average cost of structuralsteel (average 3 mills) in September 1974 was $10.80 perhundredweight (cwt); the cost of reinforcing bars per cwtat the same time was $18.83. To indicate the effect ofinflation, the percentage change of these two prices fromSeptember 1973 was + 27.1 and + 84.4, respectively (35).

As a comparison with 1974 prices in Europe (36), thesame reinforcing steel bars cost 179 Pounds per metricton in England (vice 110 Pounds in 1973), and845 Deutschemarks per metric ton in West Germany (vice700 Deutschemarks in 1973). With the latest exchangerates of 2.55 Deutschemarks per U.S. Dollar and0.425 Pounds per U.S. Dollar, these figures translateinto $421 per metric ton in England and $331 per metricton in West Germany; or, compared with the 1974 U.S.price of $18.83 per cwt, the English cost is $19.10 percwt and the West German cost is only $15 per cwt.Interestingly, the U.S., English and West German pricesper cwt in 1973 were 310.21, $11.74, and $12.43, respec-tively.

The $18.83 per cwt average quotation is for ASTMA-615 Grade 40 reinforcing bars, with a minimum order of20 to 25 tons. The price varies from a low of $14.50 in


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58Los Angeles to a high of $25 in Pittsburgh (Boston is$21); a 6 percent sales tax in California andPennsylvania is not included.

Extra orders (i.e., over the minimum) average$0.87 per cwt for bar size numbers 6 through 11, $1.10per cwt for number 5, $2 per cwt for number 4, and $2,70per cwt for number 3 Charges for extra orders ofdifferent quality bars are: $0.38 per cwt for A-615Grade 60, and $1.13 per cwt for A-615 Grade 75 (37).The three grades in which reinforcing bars are commer-cially available (40, 60, and 75) have minimum yieldstrengths of 40,000 psi, 60,000 psi and 75,000 psi,respectively. Reinforcing bars of Grades 40 and 60 areavailable in all bar sizes shown in Table 4, whereasGrade 75 comes only in size numbers 11, 14 and 18 (38).

It thus appears from available price quotationsthat, in practice, only one grade of steel is used forreinforcing bars in the majority of cases. This isbuttressed by the fact that the 1971 ACI Code is intendedspecifically for the use of standard Grade 60 reinforce-ment (f = 36ksi), although provision is also made forsthe use of Grades 40 and 75 (39). The latter areavailable under the reference ASTM specifications, upto a maximum limit of 80 ksi yield strength, except forprestressing steels.

The price differential for the different available


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59grades of reinforcing steel is actually not verysignificant. Taking A-615 Grade 60 as the standard,its cost is $18.83 + SO. 38 = $19.21 per cwt. The mostexpensive commercial reinforcement, A-615 Grade 75, costs$19. 96 per cwt, or just 3.9 percent more than Grade 60.The least expensive commercial reinforcement, A-615Grade 40, costs $18.83 per cwt, or only 1.9 percent lessthan Grade 60. Hence, varying the grade of steelreinforcing bars will not have a tremendous economiceffect.

A significant conclusion, for steel reinforcingbars, is that the greatest price differential is not forthe various qualities of steel, but rather for the sizeof the bars. Hence, the selection of mild steel (Grade40) is a valid and logical choice for reinforcing steel,confirming the preceding section.

For post-tensioned tendons, the three types ofsteel used are bars, strands, and wires. Bars varyfrom 3/4 inch to 1-3/8 inch diameter; indeed, the leadingimporter (40) of prestressed concrete strand and wiresells post-tensioned steel bars in four sizes: 18 mm(0.71 in), 24 mm, 27 mm, and 33 mm (1.3 in). Tendonswith up to 168 wires are available. Table 5 summarizesthe costs, both material and labor, of various tendonsavailable for post-tensioning (41). Labor cost consistsof preparation and placing cables, stressing cables, and


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60

inWHiPQwhere c . = the minimum cover to the tension steel.

A more complex expression is propounded by theBritish, and is valid provided the strain in the tensionreinforcement is limited to 0.8f /E . A simplified ver-sion of this formula gives a crack width with anacceptably small chance of being exceeded (26):

"max = 'acrem/ (1 + 2 < aCr " min )/(d " X,) (23)where e = the average strain at the point in question,m Another researcher (65) has derived an expressionfor the average crack v/idth. It has been shown that ifthe maximum width is taken as twice the average, theprobability is only about 0.01 that the calculated maxi-mum will be exceeded. Thus, for plain round bars:

wW o V = 4a yf /< d - x )E ( 24 >max cr s swhere y = d - x, and other terms are as defined earlier.


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92Equation (23) is similar to equation (24), but

slightly less conservative; i.e., equation (23) corre-sponds to a slightly higher probability of any givencrack exceeding the width calculated for it.

It can be seen from equation (24) that there are twobasic ways of controlling crack widths: (a) using lowworking stresses for the main steel, and (b) distributingthe bars so that a is kept to a minimum. The formeralternative is generally uneconomical, and the lattershould be adopted. .For a given area of steel, the useof smaller diameter bars increases the maximum permissiblebar stress for a fixed crack width (65).

An interesting exercise is to calculate the maximumcrack width, for a given member, from the five precedingequations and compare the results. Suppose a cross-sectional area is configured as follows:

~r

ft-

SO lOOnro

- - o-0Io o

Q

5oo5'7? rnrn

_^*k

Considering that the widest cracks are at the bottomcorners of the beam and referring to the sketch, it canbe observed that: dQ = 575 mm; d = 500 mm; x = 225 mm;


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93y = dQ - x = 350 ram; acr = 50^2* - 12.5 = 58.2 ram;cmin = 50 " 12,5 = 37#5 mm; R = 225/150 = 1.5;6A = (300)(150) - 6t(25) 2/4 = 42,055 mm2 , orA = 7,009 mm2 . Letting fg = 213 N/mm2 (30,885 psi) ande g = 0.0013, and assuming that em = e s (since concretestrain is small compared to steel strain), substitutioninto equations (20-24) yields:

eauation wmax(20) 0.3mm(21) 0.3mm(22) 0.26mm(23) 0,197mm(24) 0.31mm

Equation (23), a simplified version of the Britishformula, appears to be the best for design purposes.

V/hile many expressions for maximum crack v/idth havebeen proposed, few investigators have agreed on even thesignificance of fundamental variables. Recent investi-gations in the United States have indicated that barspacing (54) and concrete area about the reinforcing bars(56) have important influences on crack spacing and v/idth,v/hile bar size and reinforcement percentage are consideredsignificant in Europe (62). Another American (66)considers steel stress as the most important variableaffecting crack v/idth, with other major factors including


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94the number of bars and the cover thickness.

Another difficulty is the large variation of crackwidths. It has been shown (67) that the range of crackwidth within the same specimen, because of variation incrack spacing, can be as high as 50 percent. Thus,the prediction of an absolute maximum width is notpossible.

It is in this perspective that post-tensioned rein-forced concrete becomes a viable and attractive option.V/ith a combination of reinforcing rods and post-tensioning tendons, a greater amount of tensile stressescan be encountered before any net tension in the concreteresults, and therefore before there arise any tendenciesto crack.B. Corrosion and Concrete

The paramount incentive of precluding (or at leastminimizing) crack formation in concrete is to preventcorrosion of the underlying steel rods. (Of course,in the words of that trite expression, there are twosides to the proverbial coin. One investigator (68) hastheorized that cracks are generally not as important afactor in the corrosion mechanism as commonly believed;he offers evidence that cracks at the concrete surfacenarrower than 0.2 mm (0.008 inch) will not necessarilylead to serious corrosion.)


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95The two categories of rods in a post-tensioned rein-

forced concrete system are inhibited from corroding indissimilar fashion. Reinforcing rods are protected by a"sufficient" cover of concrete (see next section)* Thetendons, on the other hand, are protected by grouting:after the steel tendons have been post-tensioned andanchored, the ducts which contain the tendons are filledcompletely with grout j this protects the steel againstcorrosion and prevents any free water in the ducts fromfreezing with consequent expansion and cracking; thegrout also enables proper bond to be developed, and thisreduces deformation under conditions of over-loading.

Corrosion has traditionally been a prime designfactor when new materials are considered for marineapplications. Such has been the case for aluminum-magnesium alloys, titanium alloys, and glass reinforcedplastics. In this sense, concrete thus becomes an idealcandidate for a marine structural (i.e., ship) material.Its corrosion resistant attributes have already beenmentioned in the first section of Chapter II, Accruedmonetary benefits also occur: lower maintenance and life-cycle costs result from the virtual absence of corrosion.For example, drydocking time and costs would be practi-cally eliminated as constant scraping, chipping, andpainting for both appearance and function would no longerbe necessary. It has even been demonstrated that


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96concrete ship hulls exhibit reduced fouling frombarnacles. Furthermore, tests on the World War II con-crete ships confirmed what had been experienced with theWorld War I vessels, namely, that dense, strong concreteis immune to attack or disintegration by seawater (12).As a result, no paint, either anti-fouling or protective,need be applied to the hull underbody; this obviouslyalso reduces lifecycle costs.

In the case of ordinary reinforced concrete, sea-water used in the mixing process with cement is believedto increase the risk of corrosion of the reinforcement,although there is no experimental evidence that the useof seawater in mixing leads to attack on the reinforcingsteel. The danger appears to be greater in tropicalclimates. In practice, however, it is generally consid-ered inadvisable to use seawater for mixing unless thisis unavoidable. On the other hand, in prestressed con-crete the use of seawater is definitely not permitted,since the small cross-section of the tendon means thatthe effects of corrosion are relatively more serious (31).

In the case of a concrete ship, the concrete in thesplash zone, subjected to alternating wetting and drying,is severely attacked; permanently immersed concrete,however, is attacked least. In addition to the seawateritself, there is ample oxygen for corrosion of the rein-forcement. Chlorides may be deposited by evaporation in


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97permeable concrete and lead to salt-cell electrolyticcorrosion. In some cases the action of seawater on con-crete in the splash zone is accompanied by the destructiveagencies of frost, wave impact and abrasion, and allthese tend to aggravate the damage of the concrete.

Concrete for prestressed structural elements thatare to be exposed to freezing and thawing in a moistcondition should contain entrained air. Air-entrainingcements are designated as Types IA, IIA, and IIIA, andcorrespond to Types I, II and III. Air entrainment canalso be obtained by adding a suitable admixture to theconcrete during the mixing process. In Western Norway,up to 8 percent entrained air is used with success incombatting the combination of freeze-thaw and marineenvironment ( 43 )

.

The mechanism of corrosion in reinforced concretedoes not neatly fall into one of the standard categoriesof corrosion: uniform attack, pitting, dezincificationand parting, intergranular corrosion, or stress corrosioncracking (69). Rather, the deleterious effects beginas the seawater evaporates, creating concentrated solu-tions of magnesium sulfate which usually attack most ofthe constituents of the hardened cement paste matrix inthe concrete. The sodium chloride concentrations promotecorrosion of the steel reinforcement. The alkalies(sodium and potassium) present in the concentrated


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98solutions may react with the aggregate in the concrete.The reaction "between calcium hydroxide crystals, formedin the hydration of portland cement, and the magnesiumsulfate (from the seawater) results in the formation ofcalcium sulfate and magnesium hydroxide. The insolubleproducts of this reaction occupy a greater volume than dothe calcium hydroxide crystals that are replaced; conse-quently, these products are the cause of disruptiveforces which are evidenced by cracking of the concretecover over the steel and subsequent spalling (70).

In reinforced concrete, the absorption of salt estab-lishes anodic and cathodic areas; the resultingelectrolytic action leads to an accumulation of thecorrosion products on the steel with a consequent ruptureof the surrounding concrete, so that the effects of sea-water are more severe on reinforced concrete than onplain concrete.

In the case of prestressed concrete, it is essentialthat tendons be protected from substantial corrosion.Corrosion may affect the ductility of the tendons or maysimply reduce the cross-section of tendons and thusreduce both the prestress and the ultimate strength.Corrosion may also reduce the fatigue strength.

To minimize these problems, the concrete must incor-porate a sulfate-resistant portland cement (ASTM Type Vor Type II) and the steel reinforcement must be covered


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100by increasing its resistance to the effects of the sul-fates present in seawater.

There remain a couple other considerations whendealing with corrosion of post-tensioned reinforced con-crete. Stress corrosion cracking is an extremely rarephenomenon but, unfortunately, the occurrence of the word"stress" in both stress corrosion and prestress has ledto unwarranted fear and trepidation. Stress corrosionis usually associated v/ith minute traces of chlorides orsulfides occurring in a humid atmosphere.

Hydorgen embrittlement , while extremely serious,also appears to be rare. The International Federationof Prestressing (F.I. P.) Commission on Durability warnsagainst the use of dissimilar materials, other than steel,in prestressed concrete, because of the possibility ofelectrolytic corrosion and hydrogen embrittlement. Alu-minum and copper are particularly to be avoided.

Another consideration, attributable exclusively topost-tensioned construction, is that the anchorages mustbe protected from corrosion. The wires at the anchoragesare under higher stress than anywhere else. This matteris especially important when high-capacity tendons areused. When the anchorage is seated in a pocket, and theencasement consists of filling the pocket with epoxy con-crete flush with the ends, performance should be excellent,with no cracking, rust-staining, or other evidence of


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101corrosion (43).

In an attempt to establish serviceability criteriato the design and construction of prestressed concretevessels, it has been suggested (23) that the following beadhered to, most of which have already been mentioned.For corrosion protection, there should be: (1) rigidwatertight ducts; (2) grouted tendons; (3) maximum water-cement ratio = 0,45; (4) recessed anchorages, with pocketsfilled v/ith epoxy mortar; (5) strict limitations onchloride and sulfide contents in concrete mix; and (6) acertain minimum cover of concrete. The latter pointlogically brings us to the next section.

C Cover of ConcreteThe section on corrosion is a natural transition

between the design factors of cracking and cover of con-crete. Cracking must be minimized to preclude corrosionof the steel rods; and one way to guard against suchcorrosion is by having an adequate concrete cover overthe rods. This "sufficient" cover has been qualitativelyalluded to several times, and it now remains to attach toit some quantitative relevance.

A few general design considerations should be lookedat first. The optimum cover of concrete must be enoughto prevent seawater from seeping through any surface ten-sile cracks and attacking corrosively the reinforcement;


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103Oxygen is necessary to the corrosion mechanism; a

thicker cover minimizes the movement of oxygen to thesteel surface. In seawater, chloride ion movement isalso inhibited by thicker covers.

The cover should properly be related to the densityand cement content. The exact relationships have notbeen thoroughly established, so arbitrary values areusually used as guides or standards. Thicker coversmake it possible to achieve better compaction, fewervoids, and less permeability (43)*

Recommended thicknesses of concrete cover tend torange rather widely. At one end of the spectrum arethe reinforced concrete ships of World War II: specifi-cations called for the outer layer of steel to have aminimum concrete coverage of 3/4 inches for those portionsof the shell in contact with the water, and 1/2 inchcoverage elsewhere (12). On the other hand, the"adequate amount" of watertight concrete referred to inthe last section is 3 inches (70). As stated though,increasing the concrete cover results in considerablecost increases; thus, Gerwick (71) considers a 2-inchcover adequate in marine structures. However, Gerwickhas recently altered his figures (23) such that the mini-mum cover over tendon ducts should be 2 inches, but theminimum cover over mild reinforcing steel need only be1-1/2 inches.


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104The American Concrete Institute (13) specifies that

the minimum concrete cover over reinforcing bars and post-tensioned tendons shall he 1-1/2 inches for membersexposed to earth or weather. If tensile stresses exceed6(f') , cover must be increased 50 percent. No spe-cific coverage is given for "corrosive atmospheres orsevere exposure conditions" (i.e., seawater) other thanthat the amount of concrete protection "shall be suitablyincreased.

The British Standards Institution (26) is a littlemore specific on this last point. They claim that theconcrete cover to both ordinary reinforcement and post-tensioning tendons will generally be governed by consider-ations of durability and fire resistance. For post-tensioning systems in particular, a dense concrete coveris recommended. The nominal cover should always be atleast equal to the diameter of the bar. Specifically,the nominal cover for "very severe" conditions of expo-sure (i.e., seav/ater) is 60 mm (2.36 inches) for concreteof grade 40, and 50 mm (1.97 inches) for concrete ofgrades 50 and over.

The fire resistance of reinforced concrete and pre-stressed concrete is dependent primarily on the protectiveconcrete cover of the steel. For ordinary reinforcedconcrete beams, the fire rating improves from 1 to 4hours as the concrete cover increases from 3/4 inch to


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1051-1/2 inches (27). Prestressed concrete requires athicker cover for a given fire rating since prestressingsteel, which is usually cold-drawn to increase itsstrength, is weakened more by high temperatures thanordinary reinforcement steel is. Excluding fire resist-ance, however, the required cover for prestressed concreteis less than that for nonprestressed concrete (39).

The CEB Code (62) actually recommends a maximum(vice minimum) permissible distance between reinforcementand concrete surface. This amount is 4 cm (1.57 inches),and is remarkably close to Gerwick's 1-1/2 inches recom-mended cover over mild reinforcing steel. Similarly,the BSI nominal cover of 50 mm (1.97 inches) is almostidentical to Gerwick's 2 inches cover over ducts.Another reference (39) indicates that beyond about2 inches, increases in cover do not provide proportionalincreases in protection against penetration of seawater.Thus, it seems that Gerwick's recommendations may bereasonable.D< Spacing of Rods

As indicated in the section on cracking, reinforcingbar spacing has an important influence on crack width.It has been shown (63) that because of the reinforcement,which prevents concentrations of tensile strain (if thereinforcement is "suitably spaced"), cracks will remain


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106very small on the order of 0.01 mm. An adequatedefinition of "suitably spaced", however, remains to beseen.

Intuitively, reinforcement rods must be spaced farenough apart to allow maneuvering room for the largestaggregate. The American Concrete Institute (13) speci-fies that the maximum size of the aggregate shall not belarger than three-fourths of the minimum clear spacingbetween individual reinforcing bars or post-tensioningducts. As to what this minimum spacing is, it is alsospecified that the clear distance between parallel rein-forcing bars in a layer shall be not less than the nominaldiameter of the bars, nor 1 inch. Where parallel rein-forcement is placed in two or more layers, the bars inthe upper layers are to be placed directly above those inthe bottom layer, with the clear distance between layersnot less than 1 inch.

The British Code (26) requires that the horizontaldistance between bars should not be less than h + 5 mm,a&gwhere Yl~ is the maximum size of the coarse aggregate.aggFor two or more rows, the vertical distance between barsshould be not less than 2/3h . Thus, for a 1-1/2 inchaggregate, the British regulation coincides with itsAmerican counterpart regarding distance between layers.

The CEB Code (62), recommendations for an inter-national code of practice, suggests that the free distance


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107between two neighboring bars in the same plane must beequal at least to: (a) 1 cm; (b) the diameter of thethicker bar; or (c) 1.2 times the maximum size of theaggregate.

The British Code also specifies the minimum area ofreinforcement. The area of tension reinforcement in abeam should not be less than 0.15 percent of bd whenusing high yield reinforcement, or 0.25 percent of bdwhen mild steel reinforcement is used, where b = thebreadth of the section and d = the effective depth.

Bar size and reinforcement percentage, factors con-sidered significant in Europe, give rise to the termsunder-reinforced and over-reinforced. An under-reinforced cross-section is one in which ultimate failureis characterized by large deflections and cracking on thetensile face. An over-reinforced cross-section is onewhere ultimate failure is characterized by cracking ofthe compressive side and rapid collapse; there are noknown flexural failures in this over-reinforced mode (7).

The size, number, and spacing of reinforcing barsand post-tensioning tendons should be such that crackingof the concrete would precede failure of the beam (26).This requirement will be satisfied for under-reinforcedbeams where failure would be due to fracture of thetendons, if the percentage of reinforcement, calculatedon an area equal to bd, is not less than 0.25. For


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108over-reinforced beams, where failure would be due tocrushing of the concrete, the maximum number and size oftendons will be governed by strain compatibility consider-ations.

An equation for the maximum diameter (mm) of mildsteel reinforcement has been proposed (63), and is depen-dent upon the effective percentage of reinforcement(p - A /bd), tensile stress in the steel (f in kg/cm2 ),o Sand k -- a factor which is dependent on the consequencesof cracking. This equation is:

maximum diameter = kp/f (10 + p) (25)swhere k has the value 150,000 or 100,000 or 50,000depending on whether the effects of the crack are slight,undesirable, or very serious, respectively. The percent-age, p, should not be less than 2 percent. A possiblesynthesis with the section on cracking is to use equation(19) to solve for the required area of reinforcement,A. and then use that result to find the percentage ofsreinforcement, p, for use in equation (25).

There is no requirement for minimum dia.meters ofreinforcing bars. Diameters which are too small, however,should not be used in an attempt to reduce the opening ofcracks because of the risks of corrosion (low cover pro-tection) .

All these empirical rules can be considered onlyas indicative, however; and the distribution of the


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109reinforcement, both as regards position and diameter, isprimarily a question of good judgment.

E. Cost ConsiderationsThe economic and durable properties required of

marine structural materials are (8): low cost, easy tofabricate and handle, easy to repair, low maintenancerequirement, high resistance to corrosion, waterproof,and high fire resistance, As has been previously stated,post-tensioned reinforced concrete possesses most ofthese properties. What remains to be demonstrated iswhether such a concrete ship-as-a-whole is economicallyfeasible and comparable to a steel ship.

The economic advantage that post-tensioned reinforcedconcrete ships would have over steel ships, particularlyregarding maintenance costs, has already been mentioned.Periodic maintenance drydocking for steel ships, thoughvery expensive in terms of labor and material, is alsocostly from the standpoint of revenue loss due to thehulls being out of service during drydocking.

The first economic comparison between concrete andsteel ships was undoubtedly that done on the World War IIreinforced concrete ship program. Unfortunately, theconstruction cost was higher than had originally beenestimated; this was due, in part, to (12): lack of back-ground knowledge and experience; the thin shell (to save


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110weight) with many closely spaced reinforcing "bars wasdifficult to form and presented many concrete pouringproblems; the use of lightweight aggregates introducedproblems already well-documented; shipyard facilities andequipment were inadequate; and labor costs ran high.

A recent comparison has been made between prestressedconcrete tankers and steel tankers having the same cargocapacity (22 ) This study corrected the invalidity ofthe World War II study, in that the latter compared steeltankers to concrete tankers with only one-half the capac-ity of its steel counterpart. The more current reportpresents an economical evaluation of the total cost(building cost and operating expenses) of the two tankers.

Before discussing the results, two diametricallyopposed facts of prestressed concrete should be under-stood. On one end of the spectrum, prestressed concretehas resulted in substantial economies in marine structures;these economies are due to two causes (43): greaterstructural efficiency and economies in production. Onthe other hand, prestressed concrete requires more hard-ware, e.g., end anchorages and ducting. Including allthese extra costs, prestressed concrete is approximatelythree times more expensive than reinforced concrete (63).

The study just alluded to (22) concludes that thebuilding cost of concrete tankers is about 90 percent ofthe building cost of steel tankers with corresponding


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111speed, draft, and cargo capacity. Furthermore, the lifeof a concrete ship will probably exceed the 20 yearsassumed for a steel ship, consequently decreasing itsannual cost. Therefore, it appears that prestressed con-crete tankers may be competitive with steel tankers.

It, thus, follows that post-tensioned reinforcedconcrete ships are also competitive with steel ships, ifnot more so, This is apparent since fewer of the moreexpensive prestressing tendons are used, the balanceconsisting of less expensive ordinary reinforcing bars.


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112CHAPTER IV

FLEXURAL ANALYSIS OP CONCRETE BEAMS

As a prelude to Chapter V, it is necessary to under-stand the mechanics of flexural analysis as applied toconcrete members, or, in other words, the bending behaviorof concrete beams. This is particularly important whenone realizes that a ship has traditionally been analyt-ically approximated in a gross sense as a simplebeam. The principles of bending analysis apropos ofsimple reinforced concrete beams will first be considered;they will then be extended to the bending of prestressedconcrete beams. Finally, a synthesis of the two caseswill be made in an attempt to examine the bending ofpost-tensioned reinforced concrete beams.

A Bending of Reinforced Concrete MembersIn a homogeneous elastic beam subjected to a bending

moment (M), one can calculate the bending stresses (f)from:

f = Mc/I (26)v/here c is the distance from the face in question to theneutral axis, and I is the moment of inertia. Theextreme fiber on one face carries compression, while theopposite face carries tension. If the beam is rectan-gular (or of any shape symmetrical about the centroidal


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113axis), the maximum tensile stress equals the maximumcompressive stress. In concrete construction, it is noteconomical to accept the low tensile strength of plainconcrete as a limit on beam strength (15). It is gener-ally more economical to make up a beam with compressivebending stresses carried by concrete and tensile bendingstresses carried entirely by steel reinforcing bars.

1 . Reinforced Concrete Beam Bending Analysis .Certain general assumptions must be made prior to analy-sis of reinforced concrete beam bending (72): (a) Thetensile load is carried by the reinforcement alone,(b) Perfect adhesion exists between reinforcement andsurrounding concrete; in other words, the reinforcingmaterial must be properly bonded to the concrete so thatthe beam acts as a single unit. (c) Sections which areplane before bending remain so during bending. (d) Thestress-strain diagram of concrete, v/hen compressed, is inreality not a straight line but a curve. However, forpurposes of design calculation, Hooke's law is assumed tobe valid, or, strain is proportional to stress. (e) Asa result of assumptions (c) and (d), the stress distri-bution follows the linear law.

At this time, only the bending stresses in reinforcedconcrete beams will be considered and the discussion willbe limited to "simple reinforced rectangular beams,"


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1Ui.e., beams having reinforcement only on the tension sideof the neutral axis. Since such beams are composed oftwo materials having different moduli of elasticity, thesimple bending formula (equation 26) is not applicable,because the neutral axis does not pa

post-tensioned reinforced concrete as applied to the construction of ships

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