1、 Serviceability of Concrete A Symposium Honoring Dr. Edward G. Nawy Editor Florian Barth Co-Editors Robert Frosch Hani Nassif Andrew Scanlon American Concrete Institute“ Advancing concrete knowledge SP-225 First printing, April 2005 DISCUSSION of individual papers in this symposium may be submitted
2、in accordance with general requirements of the AC1 Publication Policy to AC1 headquarters at the address given below. Closing date for submission of discussion is October 2005. All discussion approved by the Technical Activities Committee along with closing remarks by the authors will be published i
3、n the January-February 2006 issue of either AC1 Structural Journal or 42 1, Design of Reinforced Concrete Slabs; and 435, Deflection of Concrete Building Structures. The symposium and this special publication celebrate and honor the distinguished career of Dr. Nawy as an outstanding educator, commit
4、ted researcher, influential author, and professional engineer. The symposium consisted of three technical sessions with a total of 16 presentations. The symposium speakers and authors of articles in the volume consisted of friends, former students, and colleagues who traveled from around the world t
5、o join Dr. Nawy during this special tribute. Dr. Nawy is a distinguished professor in the Department of Civil and Environmental Engineering at Rutgers University, The State University of New Jersey. His commitment to engineering excellence during his nearly one-half century of service to the public
6、has earned him world-renowned recognition for his extensive work in the fields of reinforced and prestressed concrete, and particularly for addressing serviceability issues such as crack and deflection control. Not only has Dr. Nawy published over 175 technical papers during his career, he is also w
7、ell known for his concrete design textbooks. The “Nawy Books” are the first choice for the concrete engineering community, and his detailed approach and timely editing in response to continuous code changes has resulted in his textbooks being the preferred choice of educators, as well. This symposiu
8、m and special publication also recognized the outstanding contribution Dr. Nawy has made to the American Concrete Institute. He joinedAC1 in 1959, and is the founding chair ofACI Committee 224, Cracking. Dr. Nawy has essentially attended every committee meeting ofACI Committee 224 since its formatio
9、n in 1966, and is still an active contributor to the committee. He is an active member ofACI Committee 421, Design of Reinforced Concrete Slabs, and past chair and current member of committee 435, Deflection of Concrete Building Structures. He was the first chair of the AC1 Chapter Activities Commit
10、tee, where he helped implement key policies still used today. He is the recipient of numerous AC1 and other academic awards and is an AC1 Honorary Member. This special publication offers technical papers on aspects of concrete serviceability, with emphasis on concrete cracking and deflection for pre
11、stressed and non-prestressed members. iii Much of the effort of preparing this special publication was carried out by the technical session moderators, who deserve special thanks for their great support: Ted Krauthammer and Hani Nassif for Session No. 1; Debrethann Orsak and Andrew Scanlon for Sessi
12、on No. 2; and Robert Frosch and Harvey Haynes for Session No. 3. Of course, it goes without saying that this volume would not have been possible without the authors, the reviewers of the papers, and the continuous assistance of Todd R. Watson of AC1 staff in guiding the editors through the process.
13、The editors of this Special Publication would like to express their gratitude to Dr. Nawy for his guidance, sound advice, and friendship over the years, and to all those who contributed in making the symposium and dinner a memorable event for Dr. Nawy. Whether he is a mentor, teacher, colleague, or
14、friend, we all have learned to depend on Dr. Nawys achievements and on his dependable, hard-working character. Dr. Nawy has inspired us by displaying such exemplary conduct, outstanding dedication, and consummate technical knowledge throughout his many years of service to the engineering community a
15、nd ACI. Florian Barth FBA Inc. Structural Engineers Hayward, California December 2004 iv TABLE OF CONTENTS . Preface 111 SP-225-1: Theory of Elastic Analysis-Illusion and Superstition 1 by R. W. Furlong SP-225-2: Prescriptive or Performance Design for Fire? 13 by P. J. E. Sullivan SP-225-3: Performa
16、nce of Geopolymer Concrete Under Sulfate Exposure . 27 by S. E. Wallah, D. Hardjito, D. M. J. Sumajouw, and B. V. Rangan SP-225-4: Bacterial Concrete-A Concrete for the Future 37 by V. Ramakrishnan, R. K. Panchalan, and S. S. Bang SP-225-5: Analysis of 1-D Tension Stiffening with Discrete Cracks . 5
17、5 by D. Z. Yankelevsky and M. Jabareen SP-225-6: Deflection Control by Design 83 by A. Scanlon SP-225-7: Deflection Prediction and Cracking of Beams Prestressed with Unbonded Tendons . 93 by O. Ozkul, H. H. Nassif, and E Malhas SP-225-8: New Code Provisions for Long Term Deflection Calculations 1 19
18、 by R. H. Scott and A. W. Beeby SP-225-9: AC1 Code Deflection Requirements-Time for a Change? 133 by K. B. Bondy SP-225-10: Retrofitting and Repairing of Heavily Cracked Unbonded Post-Tensioned Structural Systems with Composite Materials 147 by P. R. Chakrabarti SP-225-11: Epoxy Coated Reinforcement
19、 and Crack Control 163 by D. T. Blackman and R. J. Frosch SP-225-12: Crack Width Prediction for Ledges in Inverted T Bent Caps . 179 by R. R. H. Zhu and T. T. C. Hsu SP-225-13: Assessment of Crack Width Prediction Methods for Post-Tensioned Beams 197 by A. Schokker, J. West, E. Villari, J. Breen, an
20、d M. Kreger V SP-225-14: Crack Control in Pnst-Tensioned One-way Slab Systems 21 3 by E V. Ulloa, S. R. Witthoft, and R. W. Poston SP-225-15: Time-Dependent Cracking and Crack Control in Reinforced Concrete Structures . 223 by R. I. Gilbert vi SP-225- 1 Theory of Elastic Analysis- Illusion and Super
21、stition by R. W. Furlong Synopsis: Building Codes have specified for the purpose of design, that “Theory of Elastic Frames ” be used for analyses of indeterminate structures. Sophisticated computer software has been developed based on the condition of elastic response to loading. Designers rely on c
22、omputed results from such analyses as if those results were perfect and reliable evaluations of structural behavior. The influence of assumptions regarding accepted simplifications, member stiffnesses, load definitions and frame connectivity is addressed. Reliability from elastic analyses is reveale
23、d as an illusion, and less sophisticated alternate analytic requirements are suggested. Kevwords: analysis; frame analysis; structural design 1 2 Furlong Richard W. Furlong, P.E., Ph.D. Honorary Member ASCE Emeritus Professor of Civil Engineering The University of Texas at Austin Introduction where
24、the right hand side (RHS) is the moment of resistance of the steel, the uniform load is W and g is the load factor. As the temperature of the steel increases during a fire, its yield stress reduces by a factor say Y and therefore and substituting (la) into (lb) we have This means that cover is not t
25、he only criterion for fire resistance. We can also vary the amount of positive steel reinforcing bars (Y) or the lever arm (depth) or alter the load factor. This gives the designer more latitude with his choice of materials to improve fire resistance. The approach is also more rational and its expon
26、ents (*39f0) called it as such. The trade off between various design factors to achieve a required fire resistance becomes even more important when we have a more practical structural member such as a continuous beam. A uniformly loaded continuous reinforced concrete beam subjected to a fire will no
27、w be investigated. In this instance we have: Mc + Ms = gWL8 (before heating) Serviceability of Concrete 17 Where Mc is the moment of resistance at the centre Ms is the moment of resistance at the supports g is the load factor against collapse. The effect of fire is to reduce the moment of resistance
28、 at the centre to Mct and the resistance at the support may reduce to Mst. For the member to survive the following condition has to apply: Mct + MSt WL8 or (Mc + Ms)/g At normal temperatures one can equate Mc to the moment of resistance provided by the positive steel reinforcement, since it is desir
29、able that the steel rather than the concrete should govern failure, to ensure ductility at the ultimate limit state. Thus: M, = As fy la As the temperature of the steel increases, the yield stress reduces to Yfy and hence: MCt = Y Mc (4) (5) and substituting equations (5) in (3) and defining r as MJ
30、M, which is a measure of the restraint or continuity at the support at normal temperature, we have, gY 1 -r(gMst/Ms- 1) (6) Note as the fire is assumed to be below the beam the top steel is not affected by the fire Mst = Ms and MstIMc = r (7) Substituting (7) into equation (6) gives gY 1 -r(g- 1) (8
31、) i.e. Failure cannot occur if left hand side LHS is greater than the RHS (Note when the beam is simply supported r = O and hence: gY1 (9) as in equation IC for the simply supported case.) 18 Sullivan Hence the fire resistance of a member is increased by increasing the value of the LHS or by decreas
32、ing the RHS of inequality (9). Therefore when the ends of the beams have a fixity equal to 1 and, if the load factor g or = 2, the RHS becomes O or negative. The LHS is therefore always greater than the RHS and the fire resistance becomes theoretically infinite. With this rational approach the desig
33、ner has available to him a wider choice of action to achieve a given fire resistance and a greater flexibility in the options he has for improvement, economy and safety in design. He can improve the fire resistance of the member by: a) Increasing the area of reinforcement at the support (or value of
34、 r). b) 1. Giving a greater protective cover to the bottom steel and/or 2. Changing the type or area of reinforcement andlor 3. Increase the lever arm (depth) 4. Reduce the intensity of the fire if this warrants it. c) Increasing the load factor g These results illustrate the link between applied lo
35、ading, fire intensity and the necessity for good detailing in determining fire resistance. If tabulated values recommended in Building/Structural Standards are selected, then the designer has little option in exercising his ingenuity to improve the fire resistance of his structure. Shortcomings The
36、above examples only deal with flcxure but other members subjected to other stress regimes can also be considered in a similar fashion. Greater difficulty may be encountered, where the member is designed for failure of the concrete to occur in compression. However a simplified method of design for fi
37、re exposed concrete columns due to Hertz (I3) has been included in reference 3 and the Danish code of practice DS411. The author considers effects of fires on various faces of the column and deals with eccentrically loaded columns with cracked and un-cracked cross sections. As in normal design it ha
38、s been assumed in the continuous beam example that full moment redistribution can take place and although this frequently happens, errors in detailing can reduce this ductility. The method results in a particular application of the Upper Bound Theorem of Plasticity where an estimate of the collapse
39、load is made on the basis of an assumed collapse mechanism (see figure 1). The theorem requires the material to exhibit perfect plasticity and it is this property, which allows the separation of kinematic and static variables and enables conditions at collapse to be considered without reference to t
40、he previous history of loading and deformation. The conventional ultimate load method for beams is applicable only where the span to depth ratio does not make shear the limiting criterion for collapse, but fire design on the Serviceability of Concrete 19 basis of limiting shear or compression has no
41、t yet been attempted. Comparison of the prescriptive and this “analytical“ method of fire design can be found in a 1978 publication of the Institution of Structural Engineers (London). An example of a slab supported on edge beams for a prescriptive 2-hour fire resistance can in reality have an addit
42、ional 112 hour fire resistance, when the nominal steel appropriately anchored over the slab and beam is taken into account. It is because of the reservations in the above paragraph, that a complete structural analysis has particular appeal for a highly indeterminate structure. Analytical procedure I
43、n attempts to model more closely the behaviour of reinforced concrete elements, a number of research workers have developed computer programs capable of detailed analysis using finite elements (I4, I5,l6) and finite strip methods (17) to simulate deflections, cracking and ultimate failure of reinfor
44、ced beams, columns and portal frames. Although, in all cases approximations have had to be made in dealing with the mechanical and thermal properties of concrete, close correlation has been achieved with the behaviour of reinforced concrete beams tests in a standard furnace (I8, 19, 209 *, 22). A nu
45、mber of programs are available, some of which have been developed by software houses and others by research establishments and are capable of performing thermal and/or structural analysis. Department of the UK Environment Reports provide a list of some of these programs and a summary paper (22) publ
46、ished which includes 14 such programs developed in the USA and Europe. One of the U.K. software houses which markets a well-structured program Lusas, originating from Imperial College, has had a module developed dedicated to fire design (19, 2o ). Another program Sosmef (2) developed at the City Uni
47、versity is a structural code capable of analysing structural steeUreinforced concrete elements using a finite difference formulation for compatibility of curvature with increase of temperature and deterioration of the material. Temperature distribution is derived from a Swedish based program and is
48、at the front end of the program. Both these programs are written in Fortran and Ansis and can be used on a P.C. Most of the above programs do not take moisture into account, but a number of other programs have included this effect (23, 242 253 26, 27). A technique novel to Civil Engineering but comm
49、only used in Physical Science, discretises the domain by random lattice modelling using Voronoi Tesselation (28). This has the advantage that irregular shaped elements can follow more closely the shape of aggregates and/or gel particles. Stress is then determined together with the possible fracture associated with heat and moisture movement within the concrete. Cracking is modelled using energy balance relations within the framework of non-linear fracture mechanics. The modelling of heat flow, moisture flow, and fracture are objective with respe
