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Investigation of transfer bond in pretensioned prestresses concrete members by an original method Taylor, Peter Ridgway 1962

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INVESTIGATION OF TRANSFER BOND IN PRETENSIONED PRESTRESSED CONCRETE MEMBERS BY AN ORIGINAL METHOD b y PETER RIDGWAY TAYLOR B.Sc. ( C i v i l Engineering), University of Birmingham, i 9 6 0 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR/THE DEGREE OF MASTER OF APPLIED SCIENCE i n the Department of CIVIL ENGINEERING We accept t h i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA June, 1 9 6 2 In presenting t h i s thesis i n p a r t i a l f u l f i l m e n t of the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the Library s h a l l make i t f r e e l y available for reference and study* I further agree that permission for extensive copying of t h i s thesis for scholarly purposes may be granted by the Head of my Department or by his representatives. It i s understood that copying or publication of t h i s thesis for f i n a n c i a l gain s h a l l not be allowed without my written permission. Department of C i v i l Engineering The University of B r i t i s h Columbia, Vancouver 8, Canada. Date June. 1962.  i i ABSTRACT A simple method i s presented, suitable for the r e p e t i t i v e testing necessary to investigate f u l l y the bond ch a r a c t e r i s t i c s i n the anchorage zones of pretensioned pre-stressed members. Conditions i n one anchorage zone of a member are simulated, the central zone of constant stress being re-placed by a r i g i d s t e e l frame.. Loads i n the wire on either side of the specimen are measured by load c e l l s incorporating s t r a i n gauges. The experimental series comprised t h i r t y spe-cimens, of which f i v e were prestressed with bright wire. Seventeen specimens were prestressed with rusted wire and the remainder were cast with rusted wire under zero prestress. The results show the superior anchorage char-A a c t e r i s t i c s of rusted wire over bright wire and the exponential nature of the load pickup of the wire i n the anchorage zone. A r e l a t i o n i s suggested between end p u l l i n at the free end and ultimate load anchored. A short description of an i n -vestigation of the relaxation behaviour of prestress wires i s appended to the thesis. V ACKNOWLEDGEMENT The author wishes to express h i s thanks to his adviser, Professor S.L. Lipson, for his valuable sugges-tions and guidance. It was a pleasure to work under h i s super-v i s i o n . The author also expresses his indebtedness to the st a f f of the C i v i l Engineering workshop for t h e i r help, and to Mr. B. Ferman of Superior Concrete Ltd. who gave every assistance. Part of t h i s work extended into the summer of 1961 and was sponsored for three months by the National Research Council of Canada. Their f i n a n c i a l assistance was greatly appreciated. June, 1962 Vancouver, B r i t i s h Columbia i i i TABLE OF CONTENTS CHAPTER PAGE 1 INTRODUCTION 1 D e f i n i t i o n of Transfer Bond 1 Quantities Influencing Bond . . . . . . . . 1 Discussion of Previous Work . . . . . . . 3 Purpose of t h i s Investigation 8 1 1 DESCRIPTION OF THE EXPERIMENTAL METHOD . . . . 1 0 Mix Design . 1 3 Experimental Series 1 ^ 1 1 1 EXPERIMENTAL RESULTS AND CONCLUSIONS . . . . . 1 7 Table of Results 1 9 Observations from Experimental Results . . 2 1 Conclusions 2 3 APPENDIX 1 The Theory of Bond Anchorage 2 6 APPENDIX 2 Specifications of Materials and Apparatus Used 2 9 APPENDIX 3 Observations on the Relaxation Character-i s t i c s of Prestress Wire 3 2 BIBLIOGRAPHY 3 9 i v TABLE OF FIGURES FIGURE PAGE 1 Stress Transfer D i s t r i b u t i o n f o r Clean and Lubricated 0 . 2 7 6 i n . dia. Wire 6 2 Stress Transfer D i s t r i b u t i o n for Clean and Rusted 0 . 1 6 2 i n . dia. Wire 6 3 Theoretical Stress Transfer D i s t r i b u t i o n for 0 . 2 7 6 i n dia. Wire 6 h Details of Test Frame 1 2 5 Load Transfer D i s t r i b u t i o n for Smooth 0 . 2 7 6 i n . d i a . Wire 2 0 6 Load Transfer D i s t r i b u t i o n f o r Rusted O . 2 7 6 i n . d i a. Wire 2 0 7 Load Transfer D i s t r i b u t i o n for Untensioned Rusted 0 . 2 7 6 i n . dia. wire 2 0 8 Load Strain Curve f o r 0 . 2 7 6 i n . d i a . Wire 3 1 9 Individual and Combined Aggregate Gradings 3 1 1 0 Relaxation Curves f o r 0 . 2 7 6 i n . d i a . Wire 3 3 1 1 Relaxation Curves for Heated Wire 3 7 1 CHAPTER 1 INTRODUCTION D e f i n i t i o n of transfer bond. Concrete members are usually reinforced i n the tension zone by the in c l u s i o n of s t e e l reinforcement. In pretensioned prestressed concrete members the s t e e l i s tensioned before pouring the concrete and then released when the l a t t e r attains s u f f i c i e n t strength. The s t e e l , on release, tends to return to i t s o r i g i n a l length, but i s re-strained by the concrete, which i n turn i s compressed. The transfer of force between the two materials i s by means of bond at the interface. This bond i s referred to as prestre transfer bond and i s present from the ends of the members t the beginning of a region i n which the s t e e l tension i s con stanfc. The i n t e r v a l , at each end of the member, over which the transfer bond acts i s c a l l e d the transfer length or anchorage length. Quantities influencing bond. Quantities influencing bond may be divided into two categories, the adhesive and the f r i c t i o n a l , a l -though the d i s t i n c t i o n i s la r g e l y one of convention. Ad-hesion i s a loose term to describe an i n i t i a l resistance to s l i p , that i s , a resistance that i s present only when s l i p i s very small. Of the theories advanced to explain 2 i t , micro-mechanical locking appears to be the most reason-able. This postulates that the resistance to s l i p i s given by the sheer strength of the f i n e p a r t i c l e s of concrete that have been forced into micro-indentations i n the surface of the reinforcement. When a s l i p comparable with the size of the micro-indentations takes place the adhesive r e s i s -tance disappears. F r i c t i o n a l resistance: This may be assessed by multiplying the r a d i a l pressure by the appropriate c o e f f i -cient. Some c o e f f i c i e n t s given by Armstrong 1 show the i n -fluence of grease and rust on the surface. Mechanical locking: This i s a phenomenon similar to the micro-mechanical locking described previously except that the indentations are deliberate and of the same order of magnitude as the diameter of the wire. Dilatancy: This e f f e c t , investigated by Jenkyn , i s a resistance to s l i p a r i s i n g from the wedging action of the f i n e p a r t i c l e s produced aft e r an i n i t i a l s l i p has taken place. Wedge action: This i s a f r i c t i o n a l resistance r e s u l t i n g from the setting up of r a d i a l strains due to Poisson's e f f e c t i n locations where the longitudinal s t r a i n i s changing. The length of concrete section required to anchor the force i n a wire, by means of some or a l l of the above e f f e c t s , i s a function of many i n t e r r e l a t e d v a r i a b l e s . The following investigation i s an e f f o r t to determine the 3 anchorage length and the d i s t r i b u t i o n of bond forces for one size of prestress. wire, w^o surface conditions are included. Discussion of previous work. Previous work on prestress transfer bond, notably by Evans and Robinson^ and Janney1*", has consisted mainly of highly instrumented tests on r e l a t i v e l y few speci-mens. Evans evolved a very successful x-ray technique using platinum f o i l markers, which show a high x-ray absorption, embedded at intervals i n the prestress wire and protruding into the concrete. S l i p between the wire and concrete sheared off the f o i l at the interface, leaving two pieces of f o i l , marking the extent of s l i p which were r e a d i l y v i s i b l e on x-ray photographs taken through the specimen. The changes i n length between markers, accurately measured from the x-ray photographs, permitted Evans to calculate s t e e l s t r a i n s , and hence stresses, d i r e c t l y . Bond stresses were obtained from the gradient of the s t e e l stress d i s t r i b u t i o n curve. Evans' results indicated that the pickup of s t e e l s t r a i n may be approximated, by an expression originated by Marshall5 £ s s £ s o ( 1 - e ) where: £ s = true s t e e l s t r a i n C s o = maximum retained s t e e l s t r a i n a = a constant for the p a r t i c u l a r wire x = distance from the free end d = wire diameter Furthermore the end s l i p or p u l l i n of the wire may he related d i r e c t l y to the transmission length by the following expression L = k . go_ Cis where: g Q = end s l i p L = transmission length d s - s t e e l s t r a i n immediately before transfer k = a constant for the p a r t i c u l a r wire Qualitative observations also indicated that the concrete strength had a large e f f e c t on transmission length and that the l a t t e r also increased with time, p a r t i -c u l a r l y i n the case of smooth bright wires. Furthermore rusted wires were found to have superior bond characteris-t i c s to bright wire and that the c h a r a c t e r i s t i c s of twisted strand were superior to either of these. l+ The experimental procedure adopted by Janney was more conventional than that of Evans, s t r a i n gauges were fi x e d to the single prestress wire and to the outer surface of the concrete prism surrounding the wire. Before preten-sioning each wire was f i t t e d with two SB. h gauges. In each case one waterproof gauge was placed at the midpoint of the prism. Twenty s i x SR. h gauges were placed along the sides of the prism after moist curing was complete. Just 5 before the pretension was released readings were taken on a l l gauges. The tension on the s t e e l was released and again a l l gauges were read. These data established the pretension i n the s t e e l just prior to release, the tension retained i n the s t e e l at the centre of the specimen after release, and the d i s t r i b u t i o n of prestress. The s t e e l stress d i s t r i b u t i o n s were derived from s t r a i n measurements on the concrete surface. This pro-cedure i s only j u s t i f i e d i f , at a l l points along the prism, the stress i n concrete i s uniform over the whole cross section. At any point the t o t a l compression i n the concrete must equal the s t e e l tension at that point, however the concrete s t r a i n measured at the surface does not necessarily correspond to the concrete s t r a i n at the centre of the prism. It can be seen that Janney's method i s less d i r e c t than that of Evans and also retains some basic assump-tions that are open to question. Janney's re s u l t s may be summarized i n three curves, Figures 1 , 2 and 3« Some d i s t r i -butions of s t e e l stresses, as derived from strains on the s t e e l and on the surface of the concrete prisms are given i n Figures 1 and 2 . It i s seen that the length which must be embedded i n order to transmit the prestress f u l l y to the concrete increases i n proportion to the wire diameter. The length of embedment i n each case i s approximately one hun-dred diameters. The cross section of a l l prisms was h sq. ins. and a l l s t e e l was pretensioned to 1 2 0 , 0 0 0 p . s . i . Con-sequently the prestress force imposed upon each specimen, 6 . I n i t i a l - Stress 0 1 0 2 0 Stress Transfer. D i s t r i -b u t i o n f o r Clean a n d L u b r i c a t e d 0 : 2 7 6 i n . d i a . Wire 3 0 Inches' from- free- end. Stress Transfer D i s t r i -bution f o r Clean and Rusted 0 . 1 6 2 in.- d i a . •Wire 0 1 0 2 0 3 0 Inches from free end Theoretical Stress Transfer D i s t r i b u -• t i o n f o r 0 . 2 7 6 i n . dia . Wire 0 1 0 2 0 3 0 Inches frpm free end 7 and the r e s u l t i n g concrete s t r a i n , were greater as the wire diameter increased. Figure 1 gives the comparison of the stress transfer for a clean and rusted wire. The rusted wire de-veloped the f u l l transfer of prestress more quickly and nearer to the free end than did the clean wire. The compar-ison of clean and lubricated wires, given i n Figure 2 shows a more marked spread. It seems reasonable to assume that this marked difference i n behaviour between clean and l u b r i -cated wires arises c h i e f l y from a reduction i n the c o e f f i -cient of f r i c t i o n bond between concrete and s t e e l . , Janney attempts to j u s t i f y this l a s t assump-ti o n further by saying that of the three f a c t o r s , adhesion, mechanical locking and f r i c t i o n , which may contribute to bond only the l a t t e r i s important i n the zones of s l i p of a member prestressed with smooth wires. On t h i s basis Janney made an e l a s t i c analysis of the transfer, similar to those made e a r l i e r by Mains , Evans, Marshall and others. As the tension i s released and a wire starts to s l i p back into the concrete, the diameter increases i n proportion to the reduction i n tension. This swelling i s r e s i s t e d by the concrete surrounding the wire. In t h i s respect the concrete i s assumed to act as an e l a s t i c thick walled cylinder. Thus the wire exerts a r a d i a l pressure on the concrete and the f r i c t i o n a l bond force i s assumed to be proportional to this pressure and to the c o e f f i c i e n t of f r i c t i o n between the st e e l and surrounding concrete. When such assumptions are introduced into the 8 equations of equilibrium and compatibility an exponential re l a t i o n s h i p between wire tension and length from the free end results l o g e T Q - T = - 2L0 . / i 8 where s T Q s i n i t i a l wire tension T = tension aft e r release L = length from free end 0 = c o e f f i c i e n t of f r i c t i o n between s t e e l and concrete r = wire radius j X Q i j x s = Poisson r a t i o s s t e e l and concrete n = modular r a t i o Such an expression was plotted by the present author f o r 0.276 inch diameter wires. The curves, shown i n Figure 3> resemble experimental curves 1 and 2. Janney concludes that the assumption that the transfer of stress i s effected mainly by f r i c t i o n i s v a l i d , but points out that for the pretensions used i n practice the concrete i s stressed well into the p l a s t i c domain i n the v i c i n i t y of the wire. Purpose of t h i s investigation. It can be seen from the preceeding discussion that previous workers i n t h i s f i e l d have reached substantial agreement as to the general nature of the bond and bond curve. There i s also some agreement i n th e i r transmission lengths. However, the extensive instrumentation used by 9 these workers has prevented them carrying out the broader testing programme necessary to confirm and u t i l i z e t h e i r findings. Furthermore t h e i r r e s u l t s were obtained using i d e a l test specimens which bore only l i m i t e d resemblance to materials and mixes used i n construction practice. The purpose of t h i s investigation i s to put forward a simple method for the determination of transmission length, whereby large numbers of specimens of r e a l i s t i c dim-ensions and material s p e c i f i c a t i o n s may be rapi d l y tested, without the use of elaborate instrumentation. It was recognized at the s t a r t that bond charac t e r i s t i c s are affected by, i f not dependent upon, many var-ia b l e s . Test series were therefore c a r r i e d out with a l l var-iables but one constant throughout, i n an e f f o r t to ascertain the e f f e c t of that variable alone. CHAPTER 11 DESCRIPTION OF THE EXPERIMENTAL METHOD The basic idea of the experimental method adopted i s to cast only a single anchorage zone of a pre-stressed concrete beam, the i n t e r i o r zone of constant s t r a i n being replaced by a r i g i d frame through which the prestress wire passes. Several variations on this idea were considered, the frame had to be of f a i r l y heavy section to ensure r i g i d -i t y and minimize compressive s t r a i n s . F i n a l l y i t was decided to use 7 i n . by 2 i n . channels. The frame i s shown i n Figure h. The two end diaphragms and the centre d i a -phragm were also short lengths of 7 i n . by 2 i n . channel, welded to the longitudinal channels. S t i f f e n e r s were welded inside the web, at the t h i r d points of these diaphragms. A plywood base was f i t t e d to carry the wooden forms, and wooden skids were attached to ease movement of the frame when necessary. Prestressing a wire demanded a method which, i n addition to a capacity of 20 kips, possessed a s e n s i t i v i t y of a few pounds and minimum creep c h a r a c t e r i s t i c s under load. I n i t i a l l y a hydraulic system was designed with c o l l a r s running on a threaded ram. However l a t e r experience proved that the more simple screw jack arrangement shown i n Figure was 11 f u l l y s a t i s f a c t o r y . The jack was turned by a lever about four feet long and ran on a s p e c i a l l y machined plate, bolted to the diaphragm. A robust, simple, but highly sensitive method was needed to measure tension and changes i n tension i n the wire. The conditions encountered i n pouring concrete meant that any apparatus used had to withstand moisture, possibly steam curing and also heavy v i b r a t i o n . "Load c e l l s " made by the Baldwin Lima Hamilton Company were claimed to withstand these conditions. They consist of a round s o l i d s t e e l rod carrying s t r a i n gauges. This rod, the dummy gauge and ne-cessary c i r c u i t r y are sealed inside a c y l i n d r i c a l s t e e l case. F a c i l i t i e s are provided f o r loading i n tension or compression. In practice the load c e l l s were altogether s a t i s f a c t o r y i n both degree of accuracy and robustness. C a l i -bration showed that the load s t r a i n reading c h a r a c t e r i s t i c s are very nearly l i n e a r up to f u l l load. Readings remained very consistent through seven months of testing and zero d r i f t was n e g l i g i b l e . Since, i n general, the stress i n the wire on either side of the specimen, see Figure was not the same, i t was necessary to use two load c e l l s . They were each connected to the prestress wire by commercial wire grips, housed i n screw couplings. Similar screw couplings at the other end of each load c e l l housed grips for the wire strand used to connect the c e l l s to the screw jacks. 12 Yoke Prevents Rotation of,Upper Part of Jack Jack Base Plate W,ire Gr,ip Toke ,Rotor j V Wooden Base ah!d Skids 11-1/2-ins . End View FIGURE' ht DETAILS OF TEST FRAME 1 1 Screw Jack Rotor Lbad C e l l 1 Prestress 1 Wire Concrete Specimen 7 .in. x 2 in-. Channel Section' Diaphragm Load C e l l 2 -,Wire Strand -Wire Grip /Plan 1 1 3 The two load c e l l s frequently had to be read i n quick succession on the single s t r a i n i n d icator. This necessitated a switching unit of some kind. Commercial knife switches proved to have a v a r i a t i o n of contact r e s i s -tance of the same order as the change i n gauge resistance. This problem was solved by mounting four two-way mercury switches i n a watertight plexiglass box. The r e s u l t s ob-tained with t h i s unit showed no v a r i a t i o n due to contact resistance. The wires used i n the tests were normal com-mercial prestress wires of Japanese manufacture. Two sur-face conditions were tested, clean bright wire as delivered from the maker and wire s l i g h t l y rusted a f t e r outside stor-age. The l a t t e r condition i s that normally used i n practice, some manufacturers of prestressed concrete products even induce rusting deliberately by exposing wire to the weather and spraying with water. Some creep of the wire at high tension had been anticipated, on testing however, some un-usual c h a r a c t e r i s t i c s emerged. These are f u l l y covered i n Appendix 3 . Creep was minimized i n the test series by applying a f i v e percent overstress for about one minute during pre-stressing. Five hours were allowed between prestressing and pouring the concrete to permit creep, which would otherwise have had a harmful e f f e c t on bond. Mix Design. In an e f f o r t to conform as cl o s e l y as possible to commercial practice, as stated i n Chapter 1 , i t was de-cided to use the same mix as Superior Concrete Ltd., who at that time were producing pretensioned prestressed beams. Unfortunately the mix proved too s t i f f f o r the small drum mixer available. Only minor modifications to the mix and mixer however, were necessary to produce a r e a l i s t i c mix of the required strength. The mix proportions and aggregate sp e c i f i c a t i o n s are shown i n Appendix 2 . Vibration was es-s e n t i a l for such a dense mix and r e s t r i c t e d section. It was o r i g i n a l l y thought that steam curing would be necessary to permit testing to be car r i e d out at about M>8 hours aft e r pouring. In fa c t the f i r s t specimen was steam cured at the plant of Superior Concrete Ltd. , The cylinder strength attained at 2h- hours after steam curing was i n excess of 6 , 2 0 0 p . s . i . Laboratory tests on the modi-f i e d mix yielded cylinder strengths i n excess of 6 , 1 0 0 p . s . i . a f t e r ^ 8 hours of moist curing. On t h i s evidence i t was de-cided that steam curing was not ess e n t i a l to a t t a i n the strengths required ( i . e . M-,500 to 5 , 0 0 0 p.s.i.) at hQ hours. Experimental Series. Thirty experiments were carried out over a period of six months. After a few i n i t i a l t r i a l s an experi-mental cycle was evolved which was used for twenty f i v e of the experiments. The:"cycle covered h7 hours and enabled two. specimens to be conveniently cast i n one week. The wire was tenstoned between the previously o i l e d forms and then l e f t 1 5 for f i v e hours, i n which time the majority of the primary creep took place. The weighing and batching were started after four hours, i n time to pour the specimen and control cylinder at time f i v e hours. These were immediately covered with damp hessian, which was sprayed continuously for about f o r t y hours. The cylinder was temporarily removed for capping at about f i v e hours after pouring. At forty-two hours aft e r pouring the forms were stripped and d i a l gauges were fix e d i n the v i c i n i t y of the ends of the specimen to record any s l i p i n the wire. The gauges were attached by magnets to the frame and bore against c o l l a r s , r i g i d l y attached to the wire. I n i t i a l readings were taken of the gauges and load i n the wire on each side of the specimen. The load i n the wire on the free side of the specimen was reduced by increments, both gauges and c e l l s being read at each incre-ment. If the specimen was of s u f f i c i e n t length to anchor the whole prestress then the load i n the wire could be reduced to zero at the free end, without su b s t a n t i a l l y reducing the load i n the wire at the f a r side of the speci-men. In t h i s case the load on the tensioned side of the specimen was increased u n t i l bond f a i l u r e occured. Ideally the length of specimen could be reduced u n t i l any small i n -crease of t h i s sort would cause bond f a i l u r e . The length of the specimen would then be equal to the anchorage length f o r the p a r t i c u l a r wire, concrete and prestress force used. Experiments were carried out on 0.276 i n . diameter wire 1 6 under two loading conditions and two surface conditions. The cross-section of the specimen was maintained at h i n . by h- i n . , with a single c e n t r a l l y positioned prestress wire. Specimen lengths varied from 6 inches to +7 inches. CHAPTER 111 EXPERIMENTAL RESULTS AND CONCLUSIONS The experimental series was designed to eva-luate the e f f e c t of a single variable at a time. To t h i s end conditions were maintained constant for each test and change was made only i n the single variable under i n v e s t i -gation. Bright wire, as delivered from the manufacturer, was used i n the i n i t i a l t e s t s , but unfortunately further supplies could not be obtained and the remaining tests were carried out with rusted wire. This l a t t e r condition was exactly as used by the l o c a l manufacturers of prestressed products. None of the wire surfaces were cleaned since t h i s i s r a r e l y done i n practice and would lead to a r t i f i c i a l r e -s u l t s . The f i r s t f i v e experiments comprised specimens ofrarying length, prestressed with bright wire. Seventeen of the remaining twenty-five tests were specimens of various lengths, prestressed with rusted wire. The rest of the spe-cimens were cast with rusted wire under zero prestress. The re s u l t s are tabulated i n Table 1. A s i x inch diameter control cylinder was cast with every batch and cured under the same conditions as the specimen. The c y l i n -der was crushed, at the time of testing the specimen, at a rate of 0 . 0 5 inches per minute i n the two hundred ton Baldwin 1 8 testing machine. The cylinder crushing strengths are tabu-lated i n Column 2 of Table 1 . Columns 3 to 6 are s e l f ex-planatory. Column 7 shows the maximum recorded difference i n load, as indicated by the load c e l l s , i n the wire on either side of the specimen. Column 8 shows the wire move-ment at the free end immediately before f i r s t s l i p . This i s the time when the maximum load, tabulated i n Column 7 ? i s sustained by the specimen. The wire movement at the free end at this stage represents the " p u l l i n " or "end s l i p on release of the pretension" for the anchorage of the load tabulated i n Column 7 . Column 8 i s incomplete because the d i a l gauges were removed at loads i n excess of 1 1 , 0 0 0 pounds to protect them from damage i n sudden f a i l u r e s . Column 9 shows the load remaining i n the wire on the " t i g h t " end of the specimen, when the load i n the wire at the "free" end has been reduced to zero. I f zero s l i p has occured at detension, then the tension remaining on the " t i g h t " side, as indicated i n Column 9 ? i s about 9 , 0 0 0 l b s . A lower figure than t h i s indicates that some s l i p has already taken place. Column 9 has no meaning for the untensioned speci-mens since they were only intended to furnish comparative data on the force anchored by pretensioned and untensioned wires. Column 1 0 shows the wire movement recorded on the d i a l gauge at the "free" end when the wire tension at that end has been reduced to zero. Column 1 1 shows the wire movement at the tensioned end for the same condition. Col-umn 1 2 notes the type of f a i l u r e . m. 19. TABLE- 1 ( 1 ) Speci-men 1 2 3 4 5 6 7 8 9 1 0 1 1 1 2 1 3 14 1 5 1 6 1 7 1 8 1 9 2 0 2 1 2 2 2? 24 2 5 2 6 2 7 2 8 2 9 3 0 ( 2 ) Cylinder Strength p . s . i . 5,400 5 , 6 0 0 5,470 5 , 6 0 0 5,\io 4 , 940 h\k60 4 , 2 2 0 Jf,35o 4 ,350 ^, 270 4,870 4 , 2 9 0 ^ , 1 0 0 4,840 4 , 6 5 0 4,400 3 , 3 2 0 3 , 3 2 0 ^ , 2 2 0 If, 3 5 0 ^ , 3 5 0 3 , 9 6 0 3 , 9 6 0 3 , 3 8 0 3 , 3 8 0 3 , 3 8 0 3 , 8 9 0 2,7-80 ( 3 ) (4) ( 5 ) ( 6 ) ( 7 ) Time of Surface Maximum Length Curing Condi- Load Con- Anchored inches hours tions di t i o n s pounds 47 8 Bright Tension 1 1 , 0 0 0 3 6 if 8 II »i 9 , 5 5 0 3 0 48 ' II; II 1 2 , 3 5 0 24 ?s II ii 3 , 8 5 0 3 3 48 Bright II 9 , 2 0 0 3 0 42 Rusted it 1 2 , 8 5 0 2 0 42 it it 1 0 , 6 5 0 1 7 42 II ii 7 , 5 0 0 1 8 ii It: it* 6 , 5 0 0 1 9 it II II 6 , 2 0 0 2 2 it II it 6 , 6 9 5 2 5 ii 11 it 9 , 6 0 0 2 5 » tl ii 1 0 , 1 0 0 2 3 ti tl II 6 , 7 0 0 2 7 it It ti 8,^+75 2 7 it Rusted it 1 1 , 5 0 0 3 5 it Bright II 4 , 7 5 o 1 5 it Rusted it 1 1 , 1 2 0 1 0 » it Tension 7 , ^ 5 0 2 5 it II Untension 1 0 , 0 0 0 1 8 it II « 9 , 0 0 0 1 9 ti; it II 8 , 3 0 0 2 2 ti tt n 9 , 1 0 0 6 II II Tension 3 , 8 5 0 6 ti ti Untension 2 , 5 5 0 1 1 . 5 1+2 it n 3 , 9 5 0 14 it ti Tension 1 0 , 1 5 0 1 5 II II Untension 1 0 , 4 5 0 2 1 ti it Tension 1 1 , 9 0 0 1 1 ti II it 5 , 7 5 0 ( 8 ) Free End P u l l i n at Maximum Load Ins. x 1 0 1 1 0 . 7 2 1 5 . 3 100 .5 107 .5 78.0 80 .2 137.1 141.0 2 9 . 5 52.0 3 9 . 2 9 8~4 1 0 1 . 7 ( 9 ) Load at Detension pounds 8 , 6 5 0 9 , 0 0 0 8 , 9 5 0 1 , 8 0 0 9 , 1 0 0 8 , 9 1 0 8 , 9 5 0 3 , 0 5 0 ^ , 1 5 0 2 , 9 5 0 3 , 5 7 5 9 , 2 5 0 9 , 2 0 0 3 , ^ 5 0 4 ,950 9 , 2 0 0 3 , 5 0 0 9 , 2 0 0 3 , 2 2 5 1 , 6 5 0 9 , 1 0 0 8 , 8 5 0 ( 1 0 ) Free End P u l l i n at Detension Ins. x 1 0 9 ^ . 7 2 5 0 . 0 2 0 0.0 1 0 2 . 0 82.2 2 0 3 . 5 178.0 2 1 5 . 0 170.0 120.0 1 0 9 . 5 1 3 8 . 0 204 .5 11*+. 2 2 5 0.0 7 1 . 5 147 .5 1 7 5 . 0 7 1 . 5 7 5 . 2 - 3 ( 1 1 ) Tensioned End P u l l i n at Detension Ins. x 1 Q - 3 2 . 9 1 1 6 . 0 7 . 5 2 . 1 4 . 1 ' 9 9 . 0 64 .7 8 8 . 3 84 .0 8 . 0 4 . 0 8 1 . 0 5 7 . 5 5 . 6 7 7 . 0 4 . 8 8 5 . 5 8 3 . 0 4 T 0 5T2 ( 1 2 ) Type of Fai l u r e Slow Slow Slow Slow Slow Sudden Slow Slow Slow Slow Slow Sudden Sudden Slow Slow Sudden Slow Sudden Slow Sudden Sudden Slow Slow Slow Slow S l o w Sudden Sudden Sudden Slow Specimen 3 0 was not instrumented, the concrete strength was too low. '4f% 20 1 0 8 6-Load i n wires kips FIGURE 5: • Load Transfer D i s t r i b u t i o n for Smooth 0 . 2 7 6 i n . d i a . Wire 1 0 20 ' Distance"from free end: inches 0 * 0 1 0 2 0 Distance from free end: inches 2 1 The results are shown graphically i n Figures 5} 6 and 7 ? which are curves of load anchored, versus length from the free end for p a r t i c u l a r wire conditions. Where s l i p took place before the load in the wire at the free end had been reduced to zero, the maximum difference anchored was plotted. In the absence of s l i p the load anchored aft e r the tension at the "free end" had been reduced to zero was plotted. Observations from experimental r e s u l t s . Comparisons of Figures 5? 6 and 7 shows that bright wire attains the same, anchored load i n a considerably longer length than rusted wire. It w i l l also be noticed from Table 1 that no sudden f a i l u r e s occured with bright wire, the f a i l u r e was always of the slow type with the wire s l i d i n g through the concrete at s t e a d i l y decreasing load. There i s i n s u f f i c i e n t data i n the short specimen region for bright wires to indicate whether the b u i l d up of load there d i f f e r s from the b u i l d up i n the case of rusty wires. Com-parison of Figures 6 and 7 shows that a rusted tensioned wire anchors force fa s t e r than an i d e n t i c a l untensioned wire. The difference i s p a r t i c u l a r l y marked i n the 6 inch speci-mens. The pretensioned specimen anchors a maximum load of 3 , 8 5 0 l b s . while the untensioned specimen only anchors 2 , 5 5 0 l b s . The force anchored versus length plot for rusty untensioned wire i s substantially l i n e a r . • The same 22 plot for pretensioned rusted wire would be more nearly ex-ponential. A t h e o r e t i c a l curve, given below and derived i n Appendix 1 , i s shown against the experimental points i n Figure 6 . l o g e T Q - T = - 2L0 . ^ T Q r 1 - J L 8 / ( 1 /y.G)n where: T Q = i n i t i a l wire tension T = tension af t e r release L = length from free end 0 = c o e f f i c i e n t of f r i c t i o n between s t e e l and concrete Poisson r a t i o s s t e e l and concrete r = wire radius n -= modular r a t i o The assumed values used i n Figure 6 were: ^ s - 0 . 3 0 n = 1 0 s 0 . 1 5 0 = 0 . ^ The concrete cylinder strengths show a steady drop throughout the experimental s e r i e s . The same mix was used for specimens 2 to 3 0 and i d e n t i c a l curing conditions were used for specimens 6 to 3 0 . Any small v a r i a t i o n s i n experimental technique would, i t i s thought, give r i s e to a more random d i s t r i b u t i o n of concrete strengths. The d e f i -n i t e downward trend can only be attributed to deterioration of the cement under storage i n the laboratory. The r e s u l t s as a whole show some scatter when 2 3 plotted. This i s not unusual i n the testing of concrete, where re l a t i o n s are less exact than i n completely homogeneous materials. This scatter was anticipated and every e f f o r t was made to keep conditions p e r f e c t l y constant. The mixing and curing processes were standardized after the i n i t i a l t r i a l s and remained unchanged throughout the s e r i e s . Vib-r a t i o n was o r i g i n a l l y continued u n t i l the mix appeared to have reached maximum density, l a t e i n the series a f i x e d time of v i b r a t i o n was used. The load i n the wire retained a f t e r relase of the pretension i s shown i n Column 9 of Table 1 . It w i l l be observed that t h i s load only attains about ninety percent of the i n i t i a l prestress of 1 0 , 0 0 0 l b s . , even when the pre-stress i s apparently f u l l y anchored. The reduction i s pa r t l y due to relaxation of the wire, (see Appendix 2 ) , but mainly due to e l a s t i c flexure of the diaphragm under the compressive prestress load i n the concrete. This d e f l e c t i o n i s analogous to the e l a s t i c shortening of the central zone of a prestressed concrete member, which causes a sim i l a r reduction i n retained load i n the prestress wire. The magnitude of the reduction i n the apparatus used was quite large, but the high i n i t i a l stress used led to a retained stress, a f t e r detension, of 6 5 percent of ultimate. Use of a stronger section for the diaphragm would rais e t h i s figure further. Conclusions. The close agreement between the t h e o r e t i c a l curve and observed data, shown i n Figure 6 , indicates that 2h the assumptions made i n the derivation of the former are v a l i d . The derivation i s shown i n Appendix 1, i t assumes that the bond i s due to f r i c t i o n , the Poisson ef f e c t i n the wire i s included. Calculation by t h i s e l a s t i c theory of the stresses i n the v i c i n i t y of the wire-concrete interface show that p l a s t i c conditions p r e v a i l . This would reduce the r a d i a l and hence the f r i c t i o n forces acting. However the e l a s t i c theory also takes no account of the a x i a l stress i n the concrete, t h i s l a t t e r would tend to increase the r a d i a l pressure due to Poisson 1s e f f e c t i n the concrete. The fore-going conclusions are strengthened by the difference of be-haviour of tensioned and untensioned specimens. The former are able to anchor a higher load i n the short specimens, although the anchored loads become equal at a specimen length of twenty inches or more. This extra anchorage capacity i s due to the approximately constant contribution.of the Poisson e f f e c t , not present i n the untensioned specimens. This e f f e c t i s r e l a t i v e l y large i n the short specimens, decreasing i n r e l a t i v e importance as the length increases. The fact that rust improves the bond charac-t e r i s t i c s agrees with the foregoing, since the c o e f f i c i e n t of f r i c t i o n between rusted wire and concrete i s higher than that between bright wire and concrete. The modes of f a i l u r e , tabulated i n column 12 of Table 1, show that no bright wires were subject to sudden f a i l u r e , but that ten out of twelve of the rusted wires anchoring the highest ultimate loads f a i l e d suddenly. Also the specimens exhibiting unusually high ultimate anchored 2 5 loads, notably specimens 18, 27 and 28, a l l f a i l e d suddenly. This indicates that there i s sometimes present i n the bond between rusted wire and concrete an addit i o n a l adhesive com-ponent, which contributes to anchorage u n t i l some micro-slip occurs. The adhesion i s then broken. F r i c t i o n alone i s unable to anchor the load and rapid bond f a i l u r e takes place without warning. The confirmation and expansion of e a r l i e r ideas of anchorage show that this simple method of testing can indeed provide the r e p e t i t i v e test data necessary before the laws governing bond can become accepted i n practice. APPENDIX 1 THE THEORY OF BOND ANCHORAGE.. Notation: d = wire diameter r = wire radius 1 = distance from free end f s = t e n s i l e stress i n wire at any point f s e = i n i t i a l t e n s i l e stress i n wire = Poisson's r a t i o s t e e l = Poisson's r a t i o concrete E s a modulus of e l a s t i c i t y s t e e l E c = modulus of e l a s t i c i t y concrete c r r = r a d i a l stress at interface a t = tangential stress at interface 0 = c o e f f i c i e n t of f r i c t i o n , s t e e l to concrete U - "bond stress T Q = i n i t i a l wire tension T = wire tension a f t e r release If a wire i s free to expand, a reduction i n tension at any point from f se to f w i l l cause an increase s of radius i n the wire. A rs /is < fse - fs> 2 7 Thick walled cylinder theory gives the radial deformation in the concrete: A r e = - r aT ( 1 / ^ c ) E c for small wire diameters. Similarly: and or hence: A r s = r o ^ ( 1 -M- s) A r s - A r c = r c r s ( f s e - f s ) E P Es 1 "^s ' 1 ^ , E< E, = i i s j £ s e _ l _ £ s l _ _ 1 " f s ^  i i j i > V E s E, The bond stress at any point is equal to the slope of the stress transfer curve multiplied by r / 2 U = df£ 6L r 2 If the load is entirely transmitted by friction: or U = 00, dL = r . df< 2 28 Substituting for o"r, integrating and using the boundary condition f s = G at h = 0, l o g e f s e ~ f s = ~ <&Y~ •se 1 / ( 1 / > ^ C ) E £ E or, l o g e Tp_JL_T =-20/-sL  1 - ^ 3 / ( 1 / ^ ^ X T 0 r E, APPENDIX 2 SPECIFICATIONS OF MATERIALS AND APPARATUS USED Wire; The wire supplied was s p e c i f i e d as 0 . 2 7 6 i n . diameter and conforming to ASTM sp e c i f i c a t i o n s A * + 2 1 - 5 9 T Type WA. Breaking load 1*+. 5 - 1 ^ . 6 kip Tensile strength k . s . i . Y i e l d 2 1 5 k . s . i . Elongation i n 1 0 i n . 5.5% Tensile tests were carried out on two speci-mens of wire, one carrying a Cambridge extensometer and the other two a x i a l l y mounted etched f o i l s t r a i n gauges. The measured spe c i f i c a t i o n s were as follows! S p e c i f i c a t i o n S t r a i n Gauges Exstensometer Breaking load - kip 1 ^ . 5 7 1 ^ . 3 9 Tensile strength - k . s . i . 2>+1+ . 2k0 Y i e l d - k . s . i . 2 1 8 2 0 6 I n i t i a l tangent modulus - k . s . i . 2 9 , 0 0 0 2 7 . 7 0 0 The stress s t r a i n curve derived from the readings of one s t r a i n gauge i s shown i n Figure 8 . The 1 0 0 ton Olsen testing machine was used . for these t e s t s . 3 0 Aggregate: The re s u l t s of a sieve analysis of the aggre-gate i s shown below: PERCENTAGE RETAINED  Sieve No. 1 " Aggregate 3 / 8 " Aggregate Sand Combined 1 " 1 . 0 O A 1 / 2 " 6 2 . 6 0 2 5 . 6 3 / 8 " 8 8 . h 1 . 3 3 6 A No. h 9 8 . 8 9 2 . 9 0 5 6 . 9 No. 8 1 0 0 . 0 9 8 . 3 1 2 . 8 6 3 . 5 No. lh 9 9 . 2 2 6 . 5 6 9 A No. 3 0 9 9 . 8 5 7 . 7 8 2 . 5 No. 5 0 1 0 0 . 0 8 0 . 7 92.O No. 1 0 0 9 ^ . 9 9 7 . 9 No. 2 0 0 9 9 . 0 9 9 . 6 The combination of aggregates used i n the mix i s shown i n the r i g h t hand column. The gradings are plotted i n Figure 9 , the combined gradings being shown as dotted. The aggre-gate cement r a t i o used i n the mix was * f . l l and the water cement r a t i o was 0.*+3» Type 3 cement was used throughout. 3 1 Loads 1 kips W .12 1 0 8 6 .2 0 / / / /_ o FIGURE 8 : Load-Strain'Curve for 0 . 2 7 6 i n . d i a . Wire T 2 ~ l b -2 t r S t r a i n x 1 0 -1 0 0 8 0 60-H o 2 0 ' 0 , 2 0 0 1 0 0 '50 3 0 Ik t. Pa s s i ng j A / / / / / / / A / / 1 8 h 3 / 8 1 / 2 1 U.S. (Standard Sie.vesL,_ FIGURE 9 s Individual and Combined Aggre^atei Gradings APPENDIX 3 OBSERVATIONS ON THE RELAXATION CHARACTERISTICS OF PRESTRESS WIRE Introductions Preliminary tests to determine the optimum mixing and curing conditions included one specimen which was cast and steam cured at a commercial plant. Immediately prior to detension, when the specimen was thoroughly cooled, i t was noticed that the wire had l o s t about 10% of i t s pre-tension. Some relaxation was anticipated under the i n i t i a l pretension, but a figure of 5% i s the generally accepted value. It was considered possible that heating caused an increase of relaxation and to c l a r i f y t h i s point a few ex-periments were carried out i n which tensioned wires were surrounded by a water bath. These i n i t i a l tests p a r t i a l l y confirmed the idea that the amount and rate of relaxation were affected by temperature. A further eight tests were then conducted using a thermostatically controlled o i l bath. The results of these tests and the conclusions drawn from them are included i n this appendix. Theory of relaxation: Relaxation i s the decrease of stress i n a material held at constant s t r a i n . The problems posed by relaxation are by no means recent. The development of the 33 3* whole technique of prestressed concrete was hampered "by the f a i l u r e of the contemporary stressing s t e e l to maintain the necessary stress at constant s t r a i n . The advent of cold drawn, heat treated high t e n s i l e steels has reduced, but not eliminated, the problem. The stress time or relaxation curve f o r the high t e n s i l e s t e e l wire used for prestressirig the specimens i s shown in Figure 10. It can be seen that p r a c t i c a l l y a l l of the loss i s attained i n the f i r s t twenty hours after tensioning. This loss can be reduced i f the wire i s subjected to a small p l a s t i c extension. This extension e f f e c t i v e l y raises the proportional l i m i t of the wire. The technique i s widely used i n practice. The wire i s given a small overstress at ten-sioning, which i s maintained for a few minutes before being reduced to the required i n i t i a l tension. The relaxation curve for a wire which was subject to an i n i t i a l overstress of 5% i s shown in Figure 10. It can be seen that the stress loss i s considerably reduced. E f f o r t s have been made to formulate expressions connecting the variables governing relaxation. These ex-pressions are somewhat empirical and moreover are usually appropriate to conditions of high temperatures and stresses that are low by comparison with those used i n prestressing. These are the conditions where creep normally becomes a problem. It i s accepted that, at least i n the i n i t i a l 3 5 stages, loss of stress varies exponentially with time. An expression of the form: E E where: & = stress in wire E a Young1s modulus for wire Cq, = creep strain c 0 = i n i t i a l stress in wire. Now i f 6 C = Kt m(e^ S - 1 ) , as suggested by Soderberg?, where K, m and s are constants and e is the base of natural logar-ithms, then the expression: c y - c y 0 = - K t ^ C e 0 7 8 - 1) E predicts the stress at time t in a specimen under steady temperature conditions, the constants being adjusted to suit the particular conditions. It is generally accepted that the rate of creep increases in some manner with temperature, but l i t t l e work has been done in this field. Experimental, series: Experience with the steam cured specimen suggested that at the high working stress the rate and amount of creep may be sensitive to heating. Eight experiments were made in which identical wires were stressed and then subjected to various temperatures, times of application of 3 6 heat and durations of heating. The i n i t i a l tension was 1 0 kips i n a l l cases except specimen 1 where the i n i t i a l tension was 9 » 8 5 kips. The results are shown graphically i n Figure 1 1 . A l l specimens show a steady logarithmic rate of relaxation at constant temperature. The portions of the curves i n red ink indicate the time for which the wire was maintained at the temperature shown. Experimental observations: Specimens 1 and 2 did not receive any i n i t i a l overstress and consequently show, at any time prior to heating, a greater creep loss than specimens H , 5 and 8 , which did r e -ceive i n i t i a l overstress. The d i s p a r i t y between curves laand 2 i s due to the low i n i t i a l tension of specimen 1 , as noted i n the previous paragraph. Specimens H , 5 , 6 , 7 and 8 a l l received a 5% i n i t i a l overstress and were then heated at 220°F f o r varying periods at various times, as shown i n Figure 1 1 . Specimens 1 and 2 were heated at successively higher temperatures with periods of cooling i n between. The constant temperature regions of a l l curves show a remark-able l i n e a r i t y indicating that the relaxation time r e l a t i o n i s primarily exponential, at least i n the period ( 0 to 1 0 0 hours) of primary creep. The v a r i a t i o n between specimens of the t o t a l amount of tension l o s t through creep i s small. There i s a s u b s t a n t i a l l y constant loss of 8 5 0 l b . at 1 0 0 hours. No increase i n relaxation i s caused by increase i n duration of heating, the loss at a p a r t i c u l a r temperature takes place very quickly. Specimens 1 and 2 show that the 37 Load i n wire: kips 10.0 . , — Time: Hours After Tensioning FIGURE 1 1 . R E L A X A T j o K CURVES FOR HEATED WIRES 38 amount of creep i s proportional to the curing temperature. Comparison of specimens h and 6 shows that the time aft e r release at which heating occurs has no eff e c t on the loss due to that heating. Conclusions; Normally the rate of primary creep i n ten-sioned prestress wires i s exponential, the t o t a l creep loss at 100 hours a f t e r tensioning i s about h to 5% of the i n i -t i a l pretension. The application of the sort of temperatures encountered i n steam curing, f o r one hour or more, causes a sharp drop i n tension, amounting to h or 5% of the i n i t i a l pretension. This loss i s not recovered. The application of this heat at any stage of primary creep w i l l have the same r e s u l t . The amount of relaxation increases i n some manner with temperature, i . e . curing at 210°F w i l l induce a greater loss than curing at 180°F. The losses due to heating occur i n addition to the normal creep l o s s , which seems to remain unaffected, although these re s u l t s do not indicate whether ultimately the t o t a l creeps, with or without heating, are equal. The present author was unable to f i n d any references to previous work i n t h i s f i e l d . The losses may be a p e c u l i a r i t y of the p a r t i c u l a r s t e e l used, but they attain s i g n i f i c a n t proportions and warrant consideration i n design. BIBLIOGRAPHY: 1 . Armstrong, W.E.., "Bond in Prestressed Concrete," Journal of Institution of Civil Engineers, Vol. 3 3 , November, 2 . Jenkyn, C.F., "The Pressure Exerted by G r anular Material}' an Application of the Principles of Dilatency," Proceedings of the Roval Society of London. Vol. 1 3 1 5 1 9 3 1 . 3 . Evans, R.H. and Robinson, G., "Bond Stresses in Prest-ressed Concrete from X-ray Photographs," Proceedings  Institution of Civil Engineers. Pt. 1 , Vol. 4-, No. 2 , March, 1 9 5 5 . Janney, J.R., "Nature of Bond in Pretensioned Prestressed Concrete," Journal of the American Concrete Institute. Vol..25 , No. 9 , May, 1 9 5 ^ . 5 . Marshall, G., "End Anchorage and Bond Stress in Prest-ressed Concrete," Magazine of Concrete Research. Vol. 1 . 6. Mains, R.M., "Measurement of the Distribution of Tensile and Bond Stresses Along Reinforcing Bars," Journal  of the American Concrete Institute. November, 1 9 5 1 , Vol. 2 3 . 7. Soderberg, C.R., "The Interpretation of Creep Tests for Machine Design," Transactions American Society of  Mechanical Engineers. 58. 733-7^3. 1936. '. 

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