RESTRAINT CRACKS AND THEIR MITIGATION IN UNBONDED POST-TENSIONED BUILDING STRUCTURES BY BIJAN O. AALAMI PN tke) 1 RO aU LaRESTRAINT CRACKS AND THEIR MITIGATION IN UNBONDED POST-TENSIONED BUILDING STRUCTURES By Bijan O. Aalami’, and Florian G. Barth? Synopsis: Based on extensive observations and a survey of the performance of unbonded post-tensioned buildings, the paper presenis a categorization of the common cracks in beams and slabs. The principal causes of crack formation due to restraining effects of supporting structures are discussed in detail. Current methods of crack formation control are presented and evaluated. The consequences of cracks on serviceability and strength of post- tensioned buildings are reviewed. Recommendations are made for crack mitigation and maintenance of buildings which are post-tensioned with unbonded tendons. Presented at the 1986 ACI Convention Baltimore, Maryland November 9-14 Printed by ACI as SP-113, 1989Copyright © 1988 vy ‘American Conerete institute All tights reserved. This book or any part thereof may not be reproduced in any form without the written permission of the ‘American Concrete Institut. Printed in USA ‘Although the Post-Tensioning Institute does its bast to insure that any advice, recommendation or information it may give Is accurate, no liability or esponsibility of any kind (including liability for negligence) is accepted in this respect by the Institut, its servants or agents.‘Bijan O. Aalami Ph.D, SE, is the principal consultant to Bijan, Florian & Associates, Inc. Dr. Aalami also serves as professor of Civil Engineering at San Francisco State University. He is the author of the internationally used ADAPT Post-tensioning software system and a member of ACI/ASCE committees 423 and 421 ‘Florian G. Barth is President of Bijan, Florian Associates, Inc. (BFL), a structural consulting firm in Mountain View, California, specializing in design of post- tensioned structures. He serves on the Technical Advisory Board of PTI. He holds a master’s degree in structural engineering and is a registered engineer. INTRODUCTION Most concrete structures develop cracks for one reason or another. In most cases, cracks do not impair the expected performance of the structure. Some cracks, on the other hand, may be detrimental by leading to excessive deflections, exposure to corrosive environment, and possibly strength reduction. Cracks may also be aesthetically unacceptable. Undesirable cracks should be avoided by design, and if they occur, should be identified and neutralized. It is important to recognize which cracks are unwanted and should be treated, and what method of repair is best suited. Preventive measures against crack formation are an essential component of the process of design, construction and maintenance. Richardson [1] has presented a comprehensive overview of different crack types in reinforced concrete structures, their causes and effects,and has concluded with a lucid crack categorization flow chart. ACI Committee 362 State-of-the Art Report on Parking Structures [2] reviews the cracking problems of parking structures and their rehabilitation. Hom and Kost [3], and Ojha [4] report on crack formation, evaluation and repair of a specific parking structure. For box girder bridges Podoiny [5] has presented a detailed account on the causes of cracks and their retrofit procedures. For the purposes of the present work the causes of crack formation are categorized as follows: (@) Inadequate design, such as insufficient reinforcement; deficient detailing: and, poor workmanship.(i) Restrained volume changes which include: shrinkage; ‘creep; elastic shortening; and, temperature. This paper is limited in scope to the treatment of cracks of the second category (ii), namely shrinkage, creep, elastic shortening and temperature, as they occur in post- tensioned members and the supporting structural elements. These cracks are commonly referred to as “restraining cracks." Further, the work is directed primarily to the application of unbonded post- tensioning in commercial buildings, with specific references to parking structures and subterranean structures. A subterranean structure is one in which one or several post-tensioned concrete decks partially or totally below grade are topped with a superstructure built of wood, concrete or steel construction, The architectural outline of the post-tensioned lower levels is generally different from the upper levels as they commonly serve different functions. The lower concrete levels may be for parking or commercial retail, the upper levels for residential or office occupancy. This type of structure is widely used in California metroplexes where high land cost prohibits the provision of off-site parking. ‘The study reported herein is the outcome of design, review and observation on over three hundred post-tensioned structures between 1982 and 1987. The work is subdivided into (1) crack causes and types, (2) crack mitigation measures, (3) structural evaluation of cracks, and (4) repair of cracks; the work concludes with (5) remarks and recommendations. 1. CRACK CAUSES AND TYPES ‘Three factors, when combined, lead to restraint cracks in post-tensioned slabs. First, post-tensioned slabs tend to shorten. Second, walls and columns restrain free movement of a slab. Third, the tension developed in slab due to restraint exceeds the slab’s tensile capacity. Factors causing shortening of slab are: A- SHRINKAGE OF CONCRETE B- CREEP IN CONCRETE DUE TO PRECOMPRESSION C- ELASTIC SHORTENING DUE TO PRECOMPRESSION D- FALL IN TEMPERATURE For a typical parking structure in Southern California with 70 percent ambient humidity and a moderate temperature variation of 40°F, the contributions of theCONTRIBUTION OF DIFFERENT FACTORS TO TYPICAL, SLAB SHORTENING * DESCRIPTION PERCENTAGE SHRINKAGE * For a parking structure In southern California pe 200 ft. { ‘SHORTENING 0.8 in. ) 100 ft. tl _S 16 in <— LONG-TERM SHORTENING OF A TYPICAL SLAB, IF FREE TO MOVE SLAB THICKNESS 8 inch PRECOMPRESSION 150 psi CONCRETE STRENGTH 4000 psi CONCRETE SHRINKAGE 450 micro-strain Figure 1.1 “3above factors to slab shortening are as given in Table 1.1. It is noteworthy that two-thirds of slab shortening is typically due to shrinkage of concrete. Axial creep and elastic shortening, which are the only direct consequences of post-tensioning, precipitate about one-sixth of total shortening. In order to appreciate the magnitude of shortenings which are likely to occur in a post-tensioned slab consider the example shown in Figure 1.1. For the 200x100 ft slab shown, the shortenings - if free to take place - are estimated at 0.8 in. per 100 ftof slab length, Obviously, this shortening cannot materialize in most cases, since the slabs are commonly tied to supporting structural elements. The interaction of, slab with its restraining structural elements is the crucial factor in the formation of cracks. Assume that the wall and column supports fully inhibit the shortening of the slab. For the example given in Figure 1.1 the following situation would arise: Hypothetical shortening tension. - approx +1000 psi Precompression due to post-tensioning . 150 ps Net hypothetical tension .. + 850 psi As the calculated hypothetical tension of 850 psi exceeds the slab’s tensile capacity of approximately 250 psi, cracks would occur. One method of releasing the tension generated in the slab is to allow the slab to move and shorten. Referring to the breakdown of shortenings in Table 1.1, observe that only 18% of the calculated shortening is due to post-tensioning. ‘The balance is common to non-prestressed as well as post-tensioned slabs. A similar calculation for the hypothetical tension in a non-prestressed concrete slab having the same parameters as in Figure 1.1 would indicate a calculated tension of 830 psi, due to shortening effects. This shows that there is little difference between post-tensioned and non-prestressed slabs as far as crack initiation is concerned. However, crack propagation is fundamentally different between the two types. Prominent characteristics of cracks in unbonded post-tensioned slabs as compared. to the regular reinforced concrete are: (Cracks are lesser in number. Instead of a multitude of hairline cracks fewer cracks form. (ii) Cracks are generally wider. They are spaced farther apart and generally extend deeper into the slab. In regular reinforced concrete the spacing between cracks is of the order of slab depth, whereas in post-tensioned slabs it is more related to the span length and the overall dimensions of the slabs. In most cases crack spacing is more than one quarter of the shorter slab span.CREEP/SHRINKAGE STRENGTH /SHRINKAGE ‘CRACKS ‘CRACKS: 5 \ +, o le ca WH | * + POST-TENSIONED REINFORCED CONCRETE SLAB SLAB REFLECTED CEILING VIEW OF SLABS Figure 1.2 VIEW OF REFLECTED CEILING SHOWING CRACKS IN PT SLAB (VILLAGE SERRAMONTE, CA) Figure 1.3 “5(iii) Cracks are normally longer and continuous. Continuous cracks may extend over one span and beyond. In non-prestressed concrete cracks are generally shorter in length. (iv) Cracks commonly do not coincide with locations of maximum moments. Restraining cracks do not necessarily develop at bottom of mid-span or top of supports where the bending moments are maximum. (v)__ Cracks occur at axially weak locations. Axially weak regions are typically found at construction joints; pour strips; cold joints; paths with reduced cross-sectional area ; paths with fewer bars across the line of potential cracking; at discontinuities in slab; and finally, where precompression is reduced either due to termination of tendons or friction iosses in them. Figure 12 compares typical crack patterns on the soffit of an interior panel of a two-way slab construction, For the regular reinforced concrete structure the shrinkage cracks are shown coinciding with the locations of maximum tension. ‘Unbonded post-tensioned slabs generally exhibit a poorer cracking performance on account of lesser bonded reinforcement which mobilizes the concrete in the immediate vicinity of a crack. Hence, a series of large slab segments separated by wide cracks rather than well distributed small cracks are produced unless either the unbonded post-tensioning is accompanied by a sufficient non-prestressed reinforcement or in-plane restraining actions are present which result in a similar improvement of the crack distribution. In the following, the common cracks in SLABS, COLUMNS and WALLS are reviewed. 1.1 SLAB CRACKS SLAB CRACKS are grouped into OVERALL and LOCALIZED cracks. A Overall Slab Cracks ‘The primary causes of overall cracks are: (i) POOR LAYOUT OF SUPPORTing structural elements and the manner in which the slab is tied to them, and (fi) IRREGULARITIES IN SLAB GEOMETRY. @ Figures 1.3 and 1.4 show crack formation in two out of many similar slab conditions investigated by the authors. The examples are representative of many slabs having similar crack formation. The slabs are post-tensioned in both directions and designed as a two-way system according to Chapter 18 of ACI 318. TheVIEW OF REFLECTED CEILING SHOWING CRACKS IN PT SLAB (VILLAGE SERRAMONTE, CA) Figure 1.4 r- TENDON -F L m2 et, = oa = CONCRETE COMPRESSION = TENDON TEXSION (a) SLAB FREE 10 MOVE (fe ‘SLAB = bay r= een sh. DIVERSION OF — [= COMPRESSION : I WALL 10 WALL a CONCRETE COMPRESSION < TENDON TENSION (b) SLAB RESTRAINED AGAINST MOVEMENT DIVERSION OF PT FORCE TO WALLS Figure 1.5 7CRACKS SoG Pr Pr fee PASSIVE RESISTANCE, OF SOIL CRACK FORMATION IN SLAB ON GRADE DUE TO RESISTANCE BEHIND CROSS BEAMS Figure 1.6 SLAB (a) (0) () IRREGULAR SLAB PLANS SHOWING CRACK FORMATION Figure 1.7 ~8-CRACKS AT SLAB CORNERS WHICH ARE TIED TO CORNER WALLS Figure 1.8 CRACK FORMATION AT CORNER OF INTERIOR OPENINGS Figure 1.9 ~9-precompression provided by the tendons in the longitudinal direction is, in both cases, dissipated into the supporting walls, since the primary transverse cracks extend across the entire width of the slab and through its thickness. In the two cases exemplified the prime cause of the cracks is the restraining effects of the perimeter walls. In a slab which is free to move, such as is illustrated in Figure 1.5 (a), the tendon force (F) is balanced by the precompression developed in the slab. If the slab ‘movement is restrained through walls or columns, such as the walls in Figure 1.5 (b), a part of the tendon force F is diverted to the supporting elements. One other common example of overall cracking in slabs is the case of slab on grade with cross beams as shown in Figure 1.6. The resistance provided by cross beams against slab movement results in a reduction or elimination of post-tensioning forces in the slab and leads to crack formation when concrete’s tensile capacity is exhausted. (ii) The second major source of overall slab cracks is the IRREGULARITIES IN SLAB GEOMETRY. Typical examples of irregularities occurring in slabs are shown in Figure 1.7, If not properly detailed, the discontinuities at the reentrant comers invariably lead to cracks which may extend as far as a quarter to one-third of the shorter width at the location of crack. B- Localized Slab Cracks Figures 1.8 and 1.9 are examples of localized cracks in post-tensioned slabs. The cracks shown normally initiate within the first few days after concrete is placed and before the application of post-tensioning. 1.2 COLUMN CRACKS SHORT COLUMNS at split levels in parking structures, as illustrated in Figure 1.10, can develop severe cracks and spalling of concrete due to the shortening of the parking decks immediately above and below. The same figure shows a release detail with a central dowel for prevention of such cracks. For simplicity the stirrups in the short column are not shown. Columns tied to half-height walls as shown in Figure 1.11 (a) develop similar cracks to the short columns described in Figure 1.10. The crack formation is especially severe in beam-slab floor constructions. Provision of full-height or hatf-height joints between the walls and the columns, illustrated in Figure 1.11 (b), are effective methods of mitigating such cracks. End columns of slabs 150 ft or more in length are particularly susceptible to cracks of the type illustrated in Figure 1.12. -10-SLAB SHORT COLUMN Urennow se] HELEISE E ko PT FORCE ~ + CENTRAL DOWEL, COLUMN FF LE Csi RIGIDLY CONNECTED COLUMN: RELEASE COLUMN CRACKING IN SHORT COLUMN AT SPLIT LEVEL OF PARKING STRUCTURE Figure 1.10 SLAB— CRACKS cout SLAB 1 C MOVEMENT piREction < += = COLUMN WAL =a PARTIAL HEIGHT No sont (a) SIDE VIEW OF COLUMN (b) FRONT VIEW TIED TO WALL WALL-COLUMN RELEASE Figure 1.11 -u-cow PT SAB yoveuent ei \ st conn N= N TT CRACKS IN END COLUMNS OF LONG BUILDINGS Figure 1,12 “™ SHEAR WALL iTS. SHORTENNG OF sup [| | || UePeR Levets a il ct ieee i rc ro Ty pstaess || | | Locanions PLAZA J ']) oisteess ar LEVEL lowes: counan LOCATIONS OF POTENTIAL DISTRESS DUE TO SHORTENING OF POST-TENSIONED SLABS IN MULTISTORY BUILDINGS Figure 1.13 2s'-DA ae 1 al PT SLAB ile +- 1/2" INCH NEOPRENE dl | oom, 24" DIA. COLUMN US RELEASE DETAIL. EDGE COLUMNS OF SUNNYVALE SHOPPING CENTER, SUNNYVALE, CA Figure 1.14 “1‘The moment generated in the column due to this displacement should be accounted for in the design of such columns. Multistory towers extending above rigid plaza levels, as illustrated in Figure 1.13, generate potential distress locations at the junction of the tower to the plaza level, ‘Typically the shortening at the plaza level is less than the upper levels due to the restraints of the footings and the grade beams which are not commonly post- tensioned. The same figure identifies the lowest level column of the tower over the footing as another distress location with a great likelihood of crack formation. Architecturally sized thick columns are another source of distress. Figure 1.14 illustrates details developed for such columns and employed successfully on several projects. 1.3 WALL CRACKS Wall cracks may also be grouped into overall and local categories. Figure 1.15 illustrates the most common crack formation due to overall behavior of walls tied to post-tensioned slabs. The diagonal tension cracks shown form at the ends of the walls due to the movement of the slab and extend over a region having a length of approximately one to two wall heights from the wall end. Such cracks can be reduced or eliminated by design as is discussed in section 2.4 (iii) of this paper. Local distresses in walls occur at tips of inadequately reinforced masonry or concrete walls as shown in Figure 1.16, at the corners of openings, and over the height of ‘masonry columns located at the corners of slabs where the slab movement is most, severe. Such distress locations need to be identified during the design phase and structural drawings detailed to withstand the anticipated movement prepared. It is observed that, regardless of whether a column or wall supports an unbonded or a non-prestressed slab the restraints exerted by the slab on the supporting member precipitates the same consequences. The same principles of crack mitigation should be applied to the supporting members of both types of slab construction. 2. CRACK MITIGATION The principal techniques of crack mitigation are: 2.1 PLANNING THE LAYOUT OF RESTRAINING MEMBERS ‘The most effective method of restraint crack prevention is a good selection of walls and columns locations during the architectural planning of the building. The equal number and length of walls may be positioned such as to reduce the tendency of iesDIRECTION OF SLAB MOVEMENT END OF —4 a WALL T+ SLAB }~ WALL Kh tr Fooring — CRACKS CRACKS IN WALL DUE 10 SLAB MOVEMENT Figure 1.15 SUP JOINT PT SLAB ‘SLAB — = VovEMENT ' TJ \ oirtzeron I a ONO ALL jp pemnorceuanr AT CORNER SPALLING OF CONCRETE MASONRY UNITS (CMU) AT SLIP JOINTS AND RECOMMENDED ADDED REINFORCEMENT Figure 1.16 -15-: COLUMN y (a) FAVORABLE ARRANGEMENT OF RESTRAINING WALLS (b) UNFAVORABLE ARRANGEMENT OF RESTRAINING WALLS PLANNING IN LAYOUT OF SHEAR WALLS TO MITIGATE SLAB CRACK Figure 2.1 -16-crack formation by allowing the slab to move freely toward a planned point of zero movement (2.1a). Figure 2.1(b) shows examples of unfavorably arranged walls and layouts in which the walls impede the free movement and thus create conditions conducive to crack formation. 2.2 STRUCTURAL SEPARATION Slabs of irregular geometry in plan are particularly susceptible to cracking, Figure 2.2 (a) shows a small slab area appended to a larger rectangular shaped region. The structural separation shown in the figure between the two post-tensioned slabs consists of a physical gap between the slabs equal to 0.5 to 1 in. For the particular example shown, itis advisable to continue the slab separation through the supporting walls. ‘The major difference between such structural separations and the expansion Joints lies in that the structural separation discussed herein loses its significance after a period of two to three months during which time the bulk of the slab shortening takes place. The structural separation need not be designed to remain serviceable during the lifetime of the structure. An expansion joint which has been designed to accommodaté~temperature induced movements must be detailed to remain operational during the in-service life of the structure. Smaller areas separated by openings or irregular slab geometries, such as the appendix shown in the top right corner of Figure 2.2 (b) cannot generally follow the overall pattern of shortening of the entire slab area. ‘Their connection to the main slab is mostly over short lengths. Stairwells, elevator shafts and other walls impart substantial restraint against free movement of small slab areas. Moreover, for most cases, it is neither economical nor practical to effectively post-tension small slab areas less than 20 feet in length. ‘The authors’ practice has been to provide a separation between the two slab areas and construct the detached smaller region as. a non-prestressed slab. The structural separation for such conditions need not extend through the supporting walls. Typically, the separation is achieved by placing styrofoam sheets 0.5 to 0.75 in. thick vertically between the two slabs. 23 CLOSURE STRIPS, JOINTS AND FAVORABLE POUR SEQUENCING A CLOSURE STRIP, also referred to as a pour strip, is a temporary separation of approximately 30 to 36 in. between two regions of slab which will be constructed and post-tensioned separately. Each region is allowed to independently undergo its shortening. After a period of typically 30 to 60 days, the gap between the two post- tensioned slab regions - the closure strip - is closed by placing and consolidating non-shrink concrete. The reinforcement which extends from the concrete slab on each side into the closure strip provides for the continuity of the slab over the strip ueAPPENDIX ‘USE REINFORCED CONCRETE c SHEAR WALL | prsup | STRUCTURAL ‘SEPARATION SEPARATION BETWEEN LARGE. AREAS FORMING AN IRREGULAR SHAPE Figure SEPARATION SEPARATION BETWEEN A LARGE AREA AND A SMALL APPENDIX CONSTRUCTION JOINT WITH NO STRESSING CONSTRUCTION JOINT WITH INTERMEDIATE STRESSING CLOSURE STRIP DETAILS OF SLAB JOINTS Figure 2.3 -18-‘The width of a closure strip is determined by the net distance required to position a stressing jack between the two sides of the strip and conclude the stressing operation, The reinforcement across the closure strip is designed on the basis of actions (moments and shears) occurring at the location of the strip when the entire slab is combined into a continuum. Between two adjacent supports, the preferred location of a closure strip is, for regular conditions, at quarter span where the moments are typically small. Other considerations, however, may dictate the location of closure strip. The position of the closure strip in relation to the entire slab is discussed at the end of this section. For corrosion protection, it is emphasized that as a good practice the stressing ends of the tendons terminating in the closure strip should be cut, sealed and grouted in the same manner as at free edges. The time necessary to keep a closure strip open is determined by the extent of shortening deemed necessary before the two slab regions are tied together. A number of building officials engaged in plan check of post-tensioned slabs use, from experience, 0.25 in. as the hypothetical displacement which can be accommodated in a post-tensioned structure without significant impairment to its serviceability. For example, the closure concrete should be placed at a time when the remaining calculated displacement of the slabs at each side of the strip is 0.25 in. Obviously, once the two slab regions are tied through the closure strip, the displacement referred to cannot take place. It is recognized that this is an empirical procedure backed by the satisfactory performance of closure strips in place. Section 2.4 discusses a direct method for estimating the closing time of a pour strip. CONSTRUCTION JOINTS are joints at predetermined locations in the slab between two concrete placements. The joints provide a planned temporary break between two slab regions for the purpose of crack control and construction operations. They are also used to subdivide a larger slab area into constructionally manageable sizes. A construction joint as shown in Figure 2.3 differs from a cold joint in that, (i) its location is determined by design as opposed to the location at which a concrete batch is finished, and (ii) there is a time gap of commonly three to seven days between the placement of first pour and the second pour. This time gap is applicable to joints which are designed for crack control. Construction joints may or may not have intermediate stressing, Intermediate stressing of tendons is carried out for long tendons where friction losses are appreciable. From the performance experience of post-tensioned slabs, the following guidelines for the provision of CLOSURE STRIPS or STRUCTURAL SEPARATIONS are developed and pursued by the authors in their designs: (i) If the slab length is less than 250 feet, no closure strip or structural separations are necessary, unless the supporting walls are unfavorably placed. 19+(ii) If the slab length is longer than 250 feet, but less than 375 feet, provide one centrally located closure strip. (iii) If the slab length is longer than 375 feet, provide a structural separation. 2.4 RELEASED CONNECTIONS Released connections are effective means of crack mitigation when favorable layout of supporting structural elements or provision of construction separations and closure strips cannot be fully implemented. Released connections are those in which a joint is detailed and constructed such as to permit a limited movement of the slab relative to its support. Released connections may be used in conjunction with closure strips and structural joints. Released connections with successful results are now common practice for post-tensioned slab construction in California. Released ‘connections are grouped into: WALL/SLAB release, SLAB/COLUMN release, SLAB JOINTS and WALL JOINTS. () WALL/SLAB RELEASE Figure 2.4 shows several types of wall/slab connections commonly used. To facilitate slippage, a slip material is normally provided at the interface of wall and slab. For simplicity in presentation, the connections shown are for the end walls and a terminating roof slab, but these are equally applicable with appropriate modifications for interior walls and intermediate slabs. Connection type (a) with no ties between the slab and its supporting wall is the most effective release joint, but its application is restricted by the fact that walls, in many cases, in addition to gravity loading must be designed to transfer shear forces at their interface to the slabs. Moreover, the stability of the walls due to lateral loads may become a governing consideration. Such releases, where possible, are employed at the corners of the slab areas. The maximum length of a "NO TIE" release is recommended to be limited to the height of the respective wall. ‘A permanent release with a dowel encased in a compressible material is shown in part (b) of the figure. The dowel is provided to impede catastrophic movements of the wall such as in the event of an earthquake. This permanent release detail is used more frequently than the no-tie connection. However, it is more costly and requires greater care during construction. A temporary release as shown in Figures 2.4 (d) and 2.5 is one in which the slab is initially constructed released from the wall. After the shortening of the slab has taken place to the extent that the balance is considered acceptable, the joint is fixed by grouting the pockets (Figure 2.4-d), or dry packing the space between the wall -20-SLIP MATERIAL | BR fr Dow Wal A (2) NO TIE (b) PERMANENT RELBASE (c) FULL TIE a LATER COMPRESSIBLE. MATERIAL a (4) TEMPORARY RELEASE (e) NON-IOAD BEARING SLAB TYPICAL DETAILS OF DIFFERENT WALL/SLAB CONNECTION TYPES Figure 2.4 COMPRESSIBLE BLOCKOUT. REMOVE AND FILL WITH GROUT AFTER Pr fea SLAB SHORTENING tt sur fi sont CONCRETE 4 AAsONRY -] UNIT SlaB DOWEL TEMPORARY RELEASE OVER MASONRY WALL Figure 2.5 ~21-and the slab (Figure 2.5). The detail shown in Figure 2.5 does not have the disadvantage of detail 2.4 (d), where construction over the wall must accommodate the grouting operation of the release. It should be noted that in the in-service condition the dowel shown for the non-load bearing wall detail of Figure 2.4 (e) does not provide lateral constraint. The wall should be designed to withstand the wind/seismic or other lateral loads without a connection at the top. The performance of a release joint is greatly dependent on the workmanship and the selection of slip material. A smooth trowel finish is commonly specified for the top of the wall. In practice most walls inspected are found to have a surface roughness at the slip interface of 0.5 in. or more. Two layers of 15-Ib building paper are used by many engineers as slip material. The effectiveness of the slip materials depends primarily on the smoothness of the finished surface at the top of the wall. ‘The wet concrete of the slab has the tendency to force the paper or the felt into the uneven wall top yielding an undesirable interlocked connection. Tempered wood particle board, which is a stiff and strong material with a smooth finished surface, is superior to building paper or felt. ‘The minimum material thickness used is one layer of 1/8 in. between the two surfaces. For critical conditions up to two layers 1/4 in. each may be used. High density plastic elastomeric strips, such as neoprene, are also used as slip material. Due to their high cost the use of elastomeric materials is primarily limited to smaller areas such as between the columns and slab or columns and footings. ‘The use of elastomeric materials is particularly recommended where the connection is expected to undergo appreciable rotation in addition to relative displacements in plane of the slip joint. (i) SLAB/COLUMN RELEASE Columns may either be designed to withstand the anticipated forces conducive to lateral displacements between their ends without sign of distress, or may be released to accommodate relative displacements of slab to column at the joints. The latter option, where applicable, leads to a superior slab performance. Several considerations must be reviewed in arriving at a satisfactory solution. Maximum displacements are typically at the end columns as shown in Figure 2.6. A detail providing rotational release at the base of the column, as shown in the same figure, may prove adequate. Where columns are excessively bulky, as may be required for architectural reasons, it becomes necessary to provide a detail which would accommodate displacements in addition to rotation. ‘The detail shown in Figure 2.7 has been used successfully on several projects.SHEAR WALL PT SLAB COLUMN. 3S HINGED Pa Ivf |/ CONSTRUCTION sup = = NEOPRENE, as “PAD A so on ei me sl ass ES oe uals ELEVATION DETAIL OF HINGE CONSTRUCTION HINGED CONSTRUCTION AT BASE OF END COLUMNS Figure 2.6 7 k _’ NEOPRENE PAD Figure 2.7 =23-PLAN SHOWING SLAB JOINTS ISOLATING REGIONS OF POTENTIAL DISTRESS Figure 2.8 -24-(ii) SLAB JOINTS Slab joints are separations provided in the slab between regions which are critical in accommodating the anticipated rotations or displacements, but are neither strong. enough to resist the forces generated, nor flexible enough to articulate it without distress. Slab strips over the walls or between openings as shown in Figure 2.8 are typical examples. A slab joint is a joint in the slab only and does not extend through the supporting structure. (v) WALL JOINTS ‘Wall joints are vertical separations between adjacent walls in order to enable the walls to accommodate displacements of slabs/beams supported by walls. Wall joints are very effective in mitigating cracks in slabs/beams as well as ctacks in the supporting walls themselves. Figure 2.9 (a) shows the plan of a rectangular slab resting on perimeter walls and interior columns. The columns are not shown for clarity. ‘The wall joints (WJ) provided at the corners of the slab extend through the entire height of the walls. They afford the end walls movement toward the center of the slab without being impeded by the longitudinal walls. Such wall joints perform best when accompanied by a slip joint between the slab and cross walls as. shown in Figure 2.10. The detail shows joints with no ties at the corners, thus allowing the wall shown at left to follow the movement of the slab to the right without interference of the cross wall shown in elevation. The size of the gap is estimated at 0.75 in. for every 100 feet of slab movement to be accommodated by the wall. Wall joints need not in all cases extend through the entire height of a wall down to the lower level. ™ EXAMPLES OF RELEASED SLABS Figure 2.9 is an example of a slab in which a central closure strip, wall/slab releases and wall joints are used in combination for optimum performance. Part (a) of the figure shows the location of wall joints. Part (b) indicates the wall/slab releases employed. Alternative applications of closure strips are shown in Figure 2.11 for a slab in which. the shear wall layout is unfavorable toward the unrestrained movement of slab. (¥) REMARKS ON RELEASES The estimate of expected shortening of a post-tensioned structural member and the determination of the time lapse prior to grouting or concreting a temporary release joint are two critical considerations in the planning of release joints. =25-WL a n caasuee 5 W Ws (a) PLAN SHOWING WALL JOINTS(WJ) AND CLOSURE STRIP ABOVE a PERMANENT (b) PLAN SHOWING ARRANGEMENT OF DEFFERENT WALL/SLAB CONNECTIONS Figure 2.9 | SLIP JOINT ELEVATION OF CORNER WALL SHOWING WALL JOINT Figure 2,10 26‘The unrestrained shortening of a post-tensioned member can be estimated on the basis of data given in PCI handbook (6]. Figure 2.12 is composed from data in the same reference and applies to post-tensioned slabs of regular construction. It relates the amount of creep and shrinkage shortening to the age of concrete. Referring to Table 1.1, it is concluded that these are the primary parameters which need to be considered in the estimation of time lapse for release joints. Neither elastic shortening, which takes place only during the stressing operation, nor the ‘movements due to temperature variations are time-dependent parameters in the context of Figure 2.12. Tis important to note that implementation of releases in slabs/beams and the supporting structures improve the serviceability of the slab/beam at the cost of reducing the strength reserve of the entire structure against collapse under catastrophic loadings. Each release eliminates a redundancy in the structure which could possibly be considered as a structural reserve against failure. Such redundancies, although recognized, are not always accounted for in design, and are not called upon in the planned life cycle of a structure. 25 ADDITION/IMPROVED LAYOUT OF MILD REINFORCEMENT In addition to a well planned layout of shear walls and supporting structures and provision of releases, it is necessary to place additional mild reinforcement at locations of potential distress to mitigate crack formation. Figures 2.13 through 2.15 illustrate examples of typical cases. Figure 2.13 shows reinforcement added next to non-released exterior walls. Due to design shear transfer requirements between a slab and its supporting wall, it might not always be feasible to provide sufficient release details to prevent all cracks. The reinforcement shown in Figure 2.13 is found to be highly effective for such conditions. ‘The steel is placed parallel to the wall over a width equal to approximately 10 feet normal to the wall. The steel area is determined as 0.0015 times the cross-sectional area of the slab over one-third of the transverse span. The bars are spaced alternatively at top and bottom at approximately 1.5 times the slab thickness. Note that this is not a code requirement, but a practice found to yield satisfactory results in the elimination of potential restraint cracks. 2.6 ADDITION/IMPROVED LAYOUT OF TENDONS Figures 2.16 and 2.17 show two conditions where wall restraints can lead to significant losses of precompression in the central region of the slab and consequently formation of cracks. In addition to other measures, such as releases, -27-‘SHEAR Wauls 290 ft. an _| (a) PLAN OF SLAB WITH FOUR CORNER SHEAR WALLS FF % CO, i A cuosure J € CLOSURE ‘STRIPS STRIP < (b) ALTERNATIVE PLANS FOR PLACEMENT OF CLOSURE STRIPS Figure 2.11 =28-1008 EXTRACTED FROM PCI DESIGN HANDBOOK “0 SHORTENING ET ‘day 37 1 0 30 50 100 200 tyr PERCENTAGE OF FINAL SHRINKAGE AND CREEP Dye 2 yrs. TIME SCALE ESTIMATE.OF CREEP AND SHRINKAGE SHORTENING FOR TYPICAL POST-TENSIONED SLABS Figure 2.12 \— SHRINKAGE/ — WALL CREEP REBAR CRACK MITIGATION REBAR NEXT TO SHEAR WALLS Figure 2.13 29+(a) INTERIOR SHEAR WALL Np mee a = = (b) EXTERIOR SHEAR WALL CRACK MITIGATING REBAR NEXT TO SHEAR WALLS Figure 2.14 |— SLAB REINFORCEMENT AT SLAB CORNERS Figure 2.15 -30-as described in the preceding sections, itis helpful to lay out the tendons so as to deposit additional compression in regions where losses are expected to be highest. Dead ending and overlapping of tendons as illustrated in Figures 2.16 and 2.17 can serve this purpose. Detailing of strand layout around discontinuities and openings are also of importance. Figure 2.18 illustrates two arrangements for tendon layout at an interior opening. ‘The detail on the right shows the common practice where the sides of the opening are pulled apart. Cracks at the corners of such openings are not uncommon. The detail on the left demonstrates an alternative tendon layout, whereby the opening is provided with an additional precompression ring to counteract crack precipitating stresses at the corners. 2.7 INCOMPLETE OR POOR IMPLEMENTATION OF CRACK MITIGATION MEASURES MAY LEAD TO UNSUCCESSFUL RESULTS. Crack mitigation schemes must be well designed, and more importantly, clearly detailed and followed closely through the construction phase for successful results. ‘The following shows three examples where the incomplete implementation of crack prevention steps led to distress. Figures 2.19 and 2.20 show the schematic and picture of a slab and wall construction in which the slab and the soffit of a wide shallow beam were shown with a slip detail, but no gap or compressive material was provided between the side of the beam’and the masonry wall. ‘The resulting concentration of forces generated at this, point led to the cracking of the wall as shown in the picture resulting in a gap at the opposite side of the beam, If the length of a slip joint is not adequate, a condition such as displayed in Figures 221 and 2.22 may result. In these figures the diagonal cracks which normally precipitate at the ends of the wall occurred at the tip of the slip joint. The cracks developed are obviously lesser in number and intensity compared to a no-slip condition, but were not totally eliminated due to deficient slip joint design. A slip joint will function properly as long as movement can be accommodated without significant obstructions, Schematic 2.23 shows a beam resting on a wall and an end column with a slip surface detail at the interfaces of the beam/wall and the beam/column. The column dowels extending into the beam led to spalling of concrete at the end of the beam as pictured in Figure 2.24, which shows the end view of the beam. The dowels should either not cross the slip joint, or if they do, they should be detailed with articulation as illustrated in Figure 2.4 (b), in which the dowel is surrounded by a compressible blockout. -31-TENDON ARRANGEMENT TO COMPENSATE RESTRAINING EFFECTS OF TRANSVERSE WALLS Figure 2.16 TENDON ARRANGEMENT FOR MITIGATING CRACKS IN CENTRAL SPANS Figure 2.17 -32-Ceavoon Ccexon CRACK INHIBITING LAYOUT CRACK PROMOTING LAYOUT ~ ARRANGEMENT OF TENDONS AT OPENING Figure 2.18 -33-RESISTANCE (Cove 70 Key sur dow i Tt < sus SLAB/BEAM MOVEMENT {-— CONCRETE MLL ‘MASONRY unt CRACK PROVIDE RECOMMENDED COUPEE CRACK FORMATION AT SLIP JOINT WHERE BEAM STEM KEYS INTO WALL Figure 2.19 Figure 2, 34WALL sup — JOINT DIRECTION OF SLAB MOVEMENT > SLAB t C POOTING ‘~ CRACKS CRACKS AT END OF SLIP JOINTS Figure 2.21 Figure 2.22 =35-BEAM MOVEMENT > r— REBAR BEAM CRACKS : 4 +— SUP JOINT 7% coLUMN VW Y i SA~ TALL “No GaP INCORRECT IMPLEMENTATION OF SLIP JOINT Figure 2.23 Figure 2.24 =36-2.8 COMMON FIELD SHORTCOMINGS IN IMPLEMENTATION OF CRACK MITIGATION MEASURES No release design will perform satisfactorily when incorrectly constructed. Figure 2.25 shows several examples of common shortcomings in construction. ‘The most common problem is that the top of the wall is not always leveled with a smooth trowel finish, resulting in the slab interlocking with the undulation at top of wall. Dowels from the wall, detailed to be encompassed in compressible material, are wrongly used as a support to which the reinforcement from the slab is tied. “The wires used to tie the reinforcements fully exhaust the compressibility capacity of the lockout material Where blockouts are achieved through corrugated tubing, the tubing may not be properly centered over the dowel, thus restricting the slippage along the joint. Figure 2.26 shows the wall penetrating into the slab and thereby impeding its unrestricted movement transverse to the wall. Obviously, the slip joint shown cannot function for displacements normal to the wall, 29 EXAMPLES OF SUCCESSFUL IMPLEMENTATION OF CRACK MITIGATION PROCEDURES There are many gratifying examples where a release provision in construction demonstrates its effectiveness by actual movements between the post-tensioned structural member and its supports together with absence of cracks in critical regions. Figures 227 and 2.28 demonstrate two such examples where relative movements of 0.75 to 1 in. across the slip joint has led to the release of forces conducive to crack formation, 3. STRUCTURAL EVALUATION OF CRACKS The first step in the treatment of cracks is their structural evaluation, Cracked regions must be appraised against code requirements of SERVICEABILITY and STRENGTH. SERVICEABILITY when applied to a typical post-tensioned structure consists of checks for (i) deflections under working conditions, (ii) exposure to corrosive elements and durability, and (iii) for certain geographical locations, freeze-thaw damage. STRENGTH requirements ensure that the affected structural members maintain a minimum factor of safety against collapse. e315MIRE WRAPPING SLAB COMPRESSIBLE REINFORCEMENT | MATERIAL SLAB += t COMPERSSIBLE SUP _j Ly MATERIAL JOINT on , WALL Zz RELEASE CORRUGATED | A WALL DOWEL © TUBE (a) ELEVATION - SLAB REINFORCEMENT — (b) PLAN ~ WRONG OFF-CENTER AT LEFT IS WRONGLY TIED TO PLACEMENT OF BLOCKOUT RELEASE DOWEL TUBING INCORRECT EXECUTION OF SLAB/WALL RELEASE BLOCKOUTS Figure 2.25 SLAB SLIP PAD C (is “ot + WALL PENETRATES CONCRETE CONCRETE | INTO SLAB ow WAL INCORRECT IMPLEMENTATION OF SLIP JOINT IN LOAD BEARING WALL Figure 2.26 -38-Figure 2.28 -39-Prior to a detailed discussion on the evaluation steps, it is helpful to review the functions of post-tensioning in a post-tensioned member, with particular reference to consequences of cracking. 3.1 CONTRIBUTIONS OF POST-TENSIONING IN SLABS For the purpose of evaluating the consequences of cracks, the contributions of post- tensioning are grouped into (i) providing uplift, (i) subscribing to the ultimate strength of the section, and (iii) providing precompression. ()__ UPLIFTiis the force exerted by the tendon on a member due to the former's curvature. Figure 3.1 shows the schematics of a model selected to illustrate the uplift in slabs. Part (a) of the figure shows the slab resting freely on two rigid abutments. The UNBONDED tendon is stressed and anchored behind the rigid supports. Since there is an open gap between the rigid abutments and the slab, it is clear that the slab does not experience precompression, Part (b) of the figure shows the free body diagram of the resulting forces acting on the slab if the strand is considered removed from its sheathing. These forces, which are referred to as UPLIFT, are functions of: A- FORCE IN TENDON B- PROFILE (SHAPE) OF TENDON ‘The width and position of the gaps, which are intended to model cracking, do not affect the uplift forces, even if gaps are at mid-span. As long as the distance between the rigid bulkheads is maintained, the tendon force remains unaffected by the size and number of cracks (gaps). As cracks in slabs do not significantly affect the tendon force and its profile, it is concluded that the UPLIFT CHARACTERISTICS OF A Post-TENSIONED SLAB ARE NOT IMPAIRED BY CRACKING. Gi) _Atultimate strength, the tensile force available to resist the design moment will be less, by the amount of post-tensioning force that is diverted to the restraining supports. As aresult, the nominal moment of the section will be less. For common construction, however, the reduction in ultimate strength is not considered to be substantial. (iil) _ PRECOMPRESSION is the average force in slab due to post-tensioning, At locations of cracks, particularly if cracks extend through the thickness of slab, the precompression is partially or fully lost. Besides uplift and strength, major rounds for specifying a minimum precompression inthe design of post-tensioned labs are: A- MITIGATE CRACKING B- REDUCE DEFLECTIONS C- IMPART TWO-WAY ACTIONS IN TWO-WAY SLAB SYSTEMS D- IMPROVE PUNCHING SHEAR PERFORMANCE A+ Cracking by itself is not a prime issue, provided the consequences of cracking do not render the performance of the slab unsatisfactory. Since the present work A442. -43-im (a) SECTION (b) FORCE RESULTANTS C= COMPRESSION FORCE DUE 10 CONCRETE Fe= COMPRESSION FORCE DUE TO COMPRESSIVE STEEL. (IF AVAILABLE) j= TENSILE FORCE DUE 10 TENSION STEEL p= TENSILE FORCE DUE 10 POST-TENSIONING ILLUSTRATION OF FORCE COMPONENTS CONTRIBUTING TO THE ULTIMATE STRENGTH OF A SECTION Figure 3.3 4drests on the premise that cracks have formed, the following discussion places emphasis on consequences of cracks, with the objective of evaluating the significance of cracks formed. B- Most post-tensioned slabs are designed assuming little or no cracking of concrete for in-service conditions. As a result, the gross moment of inertia based on the full cross-section of the slab is considered in deflection calculations. A cracked section means a local decrease in the flexural stiffness of the slab. As only a few cracks develop in any given span of a post-tensioned concrete slab, its overall stiffness is not affected to the same degree that non-prestressed concrete would be. In a conventional concrete slab, formation of a multiple of closely spaced hairline cracks results in a widespread reduction of slab stiffness. However, a wider crack typical of post-tensioned concrete undergoes a greater rotation at the cracked surface. The other major factor in deflection of a slab is the amount of uplift provided by post-tensioning, As illustrated in the preceding sections cracking does not reduce the uplift From over 100 cracked post-tensioned slabs surveyed, none exhibited deflections beyond permissible code values, provided that their designs met or exceeded the minimum recommended ACI-318 recommendations. It is concluded that the margin of safety against excessive deflections in the ACI code is such that post-tensioned slabs complying with its recommendation commonly can accommodate restraint cracks and the resulting local loss of precompression without undergoing unacceptable deflections C- Biaxial precompression imparts two-way action. A concrete slab, when compressed in two perpendicular directions, behaves essentially as a homogeneous plate in resisting the applied loading. Moments and shear forces develop in both directions. Reduction or loss in precompression, when leading to crack formation, changes the biaxial load carrying characteristics of the slab. The biaxial action referred to herein is a serviceability consideration, since for ultimate strength the collapse characteristics of slabs are primarily affected by the location and details of reinforcing, and the slab geometry. When evaluating a cracked slab, consequences of cracking on the slab’s biaxial load carrying characteristics should be viewed with its in-service performance in mind, Ifa slab is not exhibiting excessive deformations and other signs of distress, such as local spalling of concrete, or multiple hair cracks attributable to local undereapacity, it is indicative that the slab’s serviceability is not impaired. It can be concluded that the anticipated role of the biaxial compression is fulfilled. D- Axial compression increases the punching shear capacity of slab/columa regions. ‘The small vertical component of tension in tendons is another contributory factor. Constraints may lead to the reduction of precompression at a column region, but the vertical component of tendon forces remains unaffected. 45+3.2 SUMMARY OF STRUCTURAL EVALUATION AND RECOMMENDATIONS From the observations and evaluations made on post-tensioned slabs constructed in California and the foregoing arguments, the following conclusions are made in relation to restraint cracks: i) RESTRAINT CRACKS GENERALLY DO NOT IMPAIR THE. STRENGTH OF SLABS i) RESTRAINTCRACKS DO NOTCOMMONLY LEAD TO EXCESSIVE, DEFLECTIONS iii) CRACKS INCREASE EXPOSURE TO CORROSION iv) MOSTRESTRAINT CRACKS DONOT OCCUR ATSTRUCTURALLY CRITICAL LOCATIONS In terms of recommendations: v) SEAL OFF CRACKS OF EXCESSIVE WIDTH (greater than 0.01 in.), PARTICULARLY WHERE CORROSIONAND DURABILITY ARE IMPORTANT CONSIDERATIONS 4, REPAIR OF CRACKS 4.1 OBJECTIVES OF CRACK REPAIR ‘The repair on the structures with restraint cracks which were surveyed by the authors served the following purposes: i) _ Tn most cases repair was conducted as a precautionary measure to cut off exposure of reinforcements and post-tensioning to weather and moisture. In some cases it was performed to stop leakage. i) Tt was rarely necessary to carry out repairs in order to restore structural, strength. ') Occasionally repairs were conducted for aesthetic reasons. 4.2 WHICH CRACKS TO REPAIR i) Cracks which are determined to be of structural significance should be repaired regardless of width and location. Most such cracks are due to poor design, deficient detailing or bad workmanship. ii) Cracks which affect the serviceability of a structure, such as deflection and local distress, may be left unrepaired if the diminished serviceability is acceptable and the repair is not cost effective. -46-iil) Under normal congitions of service, shorteomings due to deterioration may be encountered if cracks exceed 0.01 in. in width. Such cracks should be sealed to prevent the intrusion of moisture and possible oxidization, loss of steel area, and possible spalling {7}. jv) _ Cracks in structures exposed to especially adverse conditions should be sealed, even if they are less than 0.01 in. in width, Also, cracks which show rust stain should be sealed. 4.3 WHEN TO REPAIR Restraint cracks are best repaired after the shrinkage and creep shortenings are essentially complete. Generally, a lapse of time between one-and-one-half to two years is adequate, after which cracks may be repaired. A time delay in sealing of Eracks is only justifiable if corrosion considerations permit. 4.4 HOWTO REPAIR ‘There are numerous reports on methods of sealing cracks in reinforced concrete structures, The most common and effective procedure is the injection of an epoxy fesin compound under pressure into the cracks in order to fillin the crack voids. For details consult the manufacturers’ literature. i) For cracks which are “non-working.” that is to say they no longer move, the ‘best method of sealing is to inject the cracks with an epoxy resin of low viscosity. ‘This is done in such a manner that the cracks filled with the resin and the concrete on each side is reunited by "gluing" action of the resin. Another method is to rout a groove along the crack throughout its entire length and fill the groove with an epoxy compound, The latter scheme is not recommended in highly corrosive environment. ii) Cracks which are ‘working’, i. open and close as a result of Loads, temperature, ete. cannot normally be successfully sealed with epoxy compounds, but runt be sealed with flexible sealant that can withstand the movements to which the cracks are subjected. 5. GENERAL CONCLUSIONS AND RECOMMENDATIONS Crack formation in post-tensioned slabs, beams and their supporting elements, due to constraint against free movement is reviewed. The influences of cracks on serviceability and strength of post-tensioned structural members are discussed -47-Methods to inhibit crack formation are pointed out. From the study of cracks in post-tensioned structures a number of general conclusions are formulated: j) Shortening cracks (cracks due to constraint against free movement of slab) are frequent in post-tensioned slabs supported on walls and stiff columns. ii) Shortening cracks can be reduced significantly through crack mitigation measures, The principal crack reduction procedures are: A) _ Planning for layout of constraints B) Structural separations C) Closure strips, joints and favorable pour sequencing D) _ Released connections E) _Addition/improved layout of mild reinforcement F) Addition improved layout of tendons In regards to the implementation of crack mitigation procedures the following guideline is recommended: > For small and simple slab geometries (10,000 square feet or less) supported on regular size columns, design the slab to withstand the forces generated by shortening. It is not generally cost effective to implement crack mitigation measures. > For slabs with substantial restraint it is necessary to implement crack mitigation measures. iii) Most shortening cracks are not structurally significant iv) ‘The most common impairment of shortening cracks is exposure of reinforcement and post-tensioning to corrosive elements; aesthetics and leakage are the next common considerations. y) __ For slabs with significant support restraints, such as perimeter walls, it is Gitentimes necessary to conduct a one-time maintenance routine to repair shortening cracks. ‘Add notes on the structural drawings indicating that: A- Shortening cracks are likely to occur B_ Shortening cracks do not normally impair the structural integrity of slabs C- Slabs should have a one-time crack maintenance operation, which consists of: > Inspecting and evaluating slabs and supporting members two years after construction » Determining cracks to be repaired >» Repairing cracks -48-vii) _ Describe the details. of crack maintenance scheme on the structural drawings, ensuring that the following items are accounted for: ‘The maintenance program consists of: a) _ Give an estimate of the total length of anticipated cracks requiring repair. For the structures surveyed by the authors in California, the length can conservatively be estimated at 0.009 feet of cracks per sq/ft of slab area. ‘This value is for slabs up to three levels above the foundation. For slabs at higher levels of multi-story buildings the value is commonly less. b)__ State who should reserve funds for the one-time maintenance program, which is to take place one-and-one-half to two-years after the completion of construction. It is important to clarify whether it is the owner, or the contractor who would fund the work. ¢) __ Estimate funds to be allocated for the maintenance program. A first estimate for California is $8.-$10. per lineal foot of crack, or 7 cents per sq/ft of slab area. EES REFERENCES 1. Richardson, M.G. "Cracking in Reinforced Concrete Buildings’, Concrete International, January 1987, pp 21-23. 2. ACI Committee 362, "State-of-the-Art Report on Parking Structures, ACI 362R-85, ACI Journal, July-August 1985, pp 544-578. 3. Hom,$. and Kost, G., "Investigation and Repair of Post-Tensioned Concrete Slabs - A Case Study", Concrete International, July 1983, pp 44-49. 4. Ojha, S., "Rehabilitation of a Parking Structure’, Concrete International, April 1986, pp 24-28. 5. Podolny, Jr. W., "The Cause of Cracking in Post-Tensioned Concrete Box Girder Bridges and Retrofit Procedures", PC Journal, March-April 1986, pp 82-139. 6. PCI, "PCI Design Handbook for Precast Prestressed Concrete’, Illinois, 1978 7. Libby, J. R., "Modern Prestressed Concrete’, Book, Van Nostrand Reinhold, New York, 1977. = 49PTI COMPANY MEMBERS LAA PP ‘Amsysco, Inc. 740 Racquet Club Drive ‘Addison, IL 60101 (312) 628-6969 Cable Concrete Structures, Inc. 2825 Breckenridge Bivd., Ste. 125 Duluth, GA 30136 (404) 921-5500 Canadian BBR (1980), Inc. P.O. Box 37, 3450 Midland Avenue Agincourt, Ontario MIS 3BR CANADA (416) 291-1618 Con-Force Structures, Limited Post-Tensioning Division P.O, Box 1650 4300 50th Avenue, S.E. Calgary, Alberta T2P 2L7 CANADA (403) 272-3191 Continental Concrete Structures, Inc. P.O. Box 734 1400 Union Hill Road, S.W. Alpharetta, GA 30201 (404) 475-1700 Dywidag Systems International USA, Inc. & Canada, Ltd. Corporate Office 301 Marmon Drive Lemont, IL 60439 (312) 739-1100 ry ati POST-TENSIONING esl INSTITUTE “Teleshone (602) 87 FAX: (602) 670-7541, Florida Stee! Corporation 1919 Tennessee Avenue P.O. Box 1882 Knoxville, TN 37801 (615) 546-5472 Freyssinet Company, Inc. 2919 Interstate Street Charlotte, NC 28208 (704) 394-9222 Lang Tendons incorporated 143 N, Newark Road ‘Toughkenamon, PA 19374 (218) 268-2201 Linden Post-Tensioning Corporation P.O. Box 1032 Tucker, GA 30085 (404) 491-3790 Post-Tensioned Structures Inc. 540 West 83rd Street Hialeah, FL 33014 (808) 822-6316 VSL Canada Ltd. 318 Arvin Avenue Stoney Creek Ontario L8E 22 CANADA (416) 364-1908 VSL Corporation Corporate Office 401 Albright Way Los Gatos, CA 95030 (408) 866-677ati POST-TENSIONING 2SF institute