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Seismic effects in secondary containments: Research needs
Nuclear Engineering and Design 50 (1978) 41-47 © North-Holland Publishing Company
SEISMIC EFFECTS IN SECONDARY CONTAINMENTS: RESEARCH NEEDS Peter GERGELY and Richard N. WHITE Cornell University, Ithaca, N. Y. 14853, USA, Department o f Structural Engineering
Received 16 January 1978 The purpose of this paper is to discuss the status of current and projected research on the behavior of nonprestressed secondary containment structures carrying combined pressurizationand seismic shear. Ongoing experimental research at Cornell Universityon specimens carrying combined biaxial tension and static cyclic shear is described. The remainder of the paper treats research needed to better predict the response of containments to seismiceffects and to serve as the basis for improved design methods for reinforced concrete containments.
1. Introduction The transfer of seismic membrane shear in rein. forced concrete secondary containment vessels subjected to simultaneous pressurization and seismic forces presents rather severe problems in design. The wall of the containment shell is cracked by internal pressure and is in a state of biaxial membrane tension. It must also resist substantial membrane shearing forces produced by the specified earthquake loading. These large cyclic shear forces must be transmitted across small cracks in the concrete by a combination of interface shear transfer on the cracked rough surfaces, by dowel forces in reinforcing bars normal to the cracks, and by tensile forces and dowel forces in reinforcing bars inclined to the crack direction. The basic behavior involved in this action is not sufficiently well understood at the present time. This necessitates the use of highly conservative and not always consistent design approaches that may well lead to more reinforcing than is really needed. The establishment of requirements for inclined reinforcing steel has been a particularly unsettled topic over the past decade. Cyclic shear transfer in biaxially tensioned reinforced concrete is a very complex phenomenon that gives rise to many difficult questions, including: (a) cracking patterns in the vessel prior to and during an earthquake. (b) effective shear stiffness of the heterogeneous combination of cracked concrete and multidirectional reinforcing steel. 41
(C) deformations associated with shear transfer at slightly open cracks. (d) axial, shear, and bending stresses in the reinforcement crossing the cracks. (e) possible degradation of the efficiency of the shear transfer mechanism (including bond degradation) as produced by the reversing characteristics of seismic load. (f) potential splitting effects in biaxially tensioned concrete from shear-induced dowel forces on large numbers of #18 reinforcing bars. (g) dependence of total shear capacity on reinforcing percentage and direction of bar placement (horizontal and meridional bars vs. inclined bars). (h) effect of cracks and degrading shear transfer properties on the dynamic response of secondary containments. In view of both the quantity and complexity of these questions, as well as their largely unknown degree of interaction, it is not surprising that research progress in membrane shear design methodologies has been rather slow. The situation has been further complicated by the fact that the very massiveness of containment wall construction (#18 bars and several feet of concrete) has prevented a direct extrapolation of earlier research on shear transfer in specimens reinforced with small bars. A clear understanding of all aspects of membrane shear transfer, in the special context of containment vessel walls (large reinforcing bars and biaxial tension), would lead to: (a) development of more rational design procedures
42
P. Gergely and R.N. White / Seismic efl?ets in secondary containments
that would provide the desired vessel strength and deformation resistance with a minimum of reinforcing steel. thus saving steel, reducing construction time, and reducing the extreme reinforcing bar congestion that often leads to difficulties in producing quality concrete in the containment. (b) improved dynamic analysis capabilities where nonlinear behavior introduced by the cracked concrete could be properly accounted for, including improved values of peak shear stress and the displacement history of the structure. (c) a logical, proven basis for more realistically assessing true safety margins in secondary containments. Shear transfer research aimed at containments and other thickwalled reinforced concrete structures began in 1969 at Cornell University under the sponsorship of Stone and Webster Engineering Corporation and several of its clients. This initial research and later studies sponsored by the National Science Foundation Division for Research Applied to National Needs (RANN) focused on the shear transfer mechanism in cracked concrete, on dowel behavior, on combined interface shear transfer and dowel action in specimens subjected to combined uniaxial tension and cyclic shear, and on incorporation of these experimentally determined behavior modes into dynamic analysis procedures. Several papers and a series of reports have been published on this research [1-4] and major findings are summarized in the first two parts of Paper J3/5 [5] of the 4th SMiRT Conference. The ongoing research program described in sect. 2 of this paper is a study of orthogonally reinforced concrete specimens subjected to combined biaxial tension and cyclic static shear. The study is being conducted under the combined sponsorship of the Nuclear Regulatory Commission and the National Science Foundation (RANN), with NRC being the chief contributor. Other ongoing and proposed research topics that are related directly to the research in biaxial tension plus shear are described in sect. 3. The paper concludes with brief comments on other important topics associated with containment design (sect. 4).
2. Behavior of reinforced concrete subjected to combined biaxial tension and cyclic shear The goal of this research is to determine the strength and stiffness of reinforced concrete sections carrying
combined biaxial tension and cyclic shear. The study, which began more than a year ago with the design and construction of special testing equipment, is mainly experimental in its initial stages. The tests will be supplemented by analysis after sufficient understanding of basic behavior is gained from the experiments. A number of specimen designs have been proposed by different researchers to physically model the behavior in the wall of a secondary containment vessel carrying combined pressurization and seismic shear forces. All feature the isolation of a square segment of wall, with forces applied at the boundary to introduce the required tensile forces in the reinforcement and shear forces in the concrete. Severe difficulties are met in applying shear loadings that produce proper shear stresses and at the same time do not interfere with the cracking behavior of the specimen. The specimen ideally should be several feet thick and be reinforced with #18 bars. Because of the great expense and the unknown difficulties involved in experiments on such a massive scale, it was decided to first pursue the research objectives with a pilot study on smaller specimens that were designed to have the same behavior as an actual containment wall. Thus the present investigation is regarded as a preliminary study for a larger-scale program. It would also be ideal to apply the shear dynamically to best simulate the earthquake effects, but again the expense and difficulties rule out dynamic loading in this first study on biaxially tensioned specimens. It is very unlikely that large-scale dynamic tests will ever be done because of the magnitude of forces involved (a 3-foot-thick specimen with shearing area of 15 square feet would require a force of +-864 kips to produce 400-psi shear stress), but it is feasible to undertake dynamic testing of specimens similar to those used here. The Cornell Research basic specimen is 6 in thick and is reinforced with one layer of #6 bars at 6-inch spacing in one direction (0 = 1.22%) and with two layers of #6 bars at 6-inch spacing in the other direction (p = 2.44%). The three layers of steel are located in the middle of the slab thickness. Concrete strength is about 3200 psi and Grade 60 reinforcement is used. Specimen geometry is defined in fig. 1a. The section has thickened corners through which the reversing shear loads are applied, as shown in fig. lb, by alternately pushing and pulling on the corners. Additional details on the equipment needed to implement the
P. Gergely and R.N. White /Seismic effects in secondary containments Ty
Tx'~"-'-
x
~ _ ~ L,.--~
Tx ~
_~
48" ONE #6AT 6" , SPACING
THICKENED I ~ ~ I ~ ~_I'=-~TW0"#'6AT6" CORNERREGIONS ' ~ '48"" "Ty" =} SPACING FORAPPLICATION 6" OF SHEARFORCES
a. DETAILSOF BIAXIAL SPECIMEN
TENSILECORNER LOAD%,
COMPRESSIVE CORNERLOAD
c. SHEARSTRESSES ALONG x = 0 COMPRESSIVE CORNERLOAD
TENSILECORNER LOAD
b. LOADING METHOD
Fig. 1. Specimen geometry and loading.
shear loading will be given subsequently. The region of interest is the central cruciform-shaped portion of the specimen. This region is 48 in. wide, giving a shearing area across the specimen of 288 in 2. Elastic shear stress distribution across the center of the specimen is shown in fig. lc. The entire specimen is precracked in two directions by applying tension to the bars with hydraulic rams that react against steel pipe frames built around the slab, fig. 2b. The bar stressing systems are independent in the two directions, and both are completely independent of the shear loading system in order to prevent undesired interaction. Thus biaxial tension of any specified level up to the yield strength of the reinforcement can be maintained during the application of cyclic shear. Extensive measurements are made in the central region of the specimen, inclu-
43
ding shear deformations, slip along the cracks, crack width changes, membrane stiffness, bar strains, and splitting effects. The specimen is loaded to failure in shear at the conclusion of each test. Fourteen experiments are scheduled for the first phase of the pilot study. Primary variables are level of tension in the reinforcement and shear stress history. Three duplicate tests are planned for each of three bar tension levels: 0, 0.6fy, and 0.9fy, where fy = yield stress. Specimens will be precracked by tensioning the bars to about 40 ksi. For the first two stress levels, the initial cyclic shear stress will be at -+125 psi for 10 cycles. The shear stress will then be increased in 50-psi increments (-+175, +225, etc.) with 10 cycles at each stress level until failure occurs. Specimens with 0.9fy bar tension will be cycled at lower stress levels because their ultimate shear strength is expected to be less than 100 psi. Three additional tests will be conducted with the beginning shear stress to be the average failure stress level determined from the three sets of duplicate tests described above. If the specimen withstands 20 cycles at this stress, the magnitude of applied shear will again be increased in increments of 50 psi, as described above. These tests will determine the effect of cycling at lower stress levels on the ulti. mate capacity in shear. The last two specimens will contain diagonal reinforcement inclined at 45 ° to the main reinforcement. The amount of steel and the shear stress history will be decided upon after the orthogo. nally reinforced specimens have been tested. Two specimens with bar tensions at 0.6fy have been tested, and a third is in progress (mid-July 1977) with bars stressed to 0.9[y. Preliminary results are given in ref. [5]. The experimental setup is functioning extremely well and specimens will be tested at the rate of about one every two weeks throughout the early fall of 1977. Initial results indicate that some changes may be made in the variables listed above. For example, the shear strength of a specimen with steel tensioned to 0.9fy is expected to be very low since there is little capacity left in the bars to equilibrate forces developed from shear. There is also need for tests to establish an interaction curve for combined biaxial tension and shear applied monotonically to failure. Four tests with bar tensions held at 0, 0.3fy, 0.6fy, and 0.9fy, while shear load is increased to failure, would establish this curve, which could then be used to assess the effects of cyclic
44
P. Ger,gely and R.N. White / Seismic effects in secondary containments
Fig. 2. Specimen configuration. shear load history on shear strength. Finally, three replications for each basic bar tension level may not be needed if two specimens show nearly identical results. Thus, the final testing program may well be
substantially different from that outlined above. A few additional words about the loading equipment are in order. The large prestressed concrete test frame, fig. 2a, has load capacities of +-150 kips at each
P. Gergely and R.N. White / Seismic effects in secondary containments
corner. Two double-acting 100-ton-capacity hydraulic rams are used to apply shear loads to the specimens, with two large tubular section load cells on opposite corners of the specimen. The linkage system conncecting the specimen corners to the rams and load cells is designed to transmit either tensile or compressive corner loads and at the same time be capable of permitting large shearing deformations in the specimen. Very heavy plates, high strength steel pins and rods, and heavy clevises were used in fabricating the corner connections. The combination of the specimen and its tubular frames and hydraulic rams (used in applying bar tensions) is free to deform without any undesired constraints. Peak shear stresses of 550 psi may be produced in the specimen with the rams pressurized to a load of 112 k, which is the maximum tension capacity of the rams. Each ram is controlled with separate electric hydraulic pumps, while the rams producing tension in the reinforcement are on two independent handoperated hydraulic pumps. It is evident that extremely heavy equipment is needed even in this pilot study on small specimens and that experiments on specimens with #18 reinforcing bars will involve extraordinarily massive loading devices and reaction systems.
3. Additional research needs associated with membrane seismic shear effects in secondary containment structures
The research program described in the previous section of this paper will provide considerable new insight into the basic problem of seismic membrane shear in nonprestressed secondary containments. Much work remains to be done, however, and it is nearly all in the realm of the behavior of reinforced concrete under repeated reversed loading. Some of the required experimental research can be conducted on the new equipment described above, and some must be done at a larger scale to study the special problems introduced by the use of #18 reinforcing bars. The most urgent problems are outlined here:
45
flexibility results from vertical cracking that allows some rotation of the concrete blocks bounded by cracks. A third factor is the diagonal cracking caused by seismic shear. The reduction of stiffness is an important research and design question. While experiments described in sect. 2 will provide considerable basic information on membrane stiffness after cracking and during shear cycling, the results cannot be extrapolated to predict behavior of actual containment walls without supporting experimental evidence on specimens with #18 reinforcing bars.
3.2. Maximum shear stress
There is considerable disagreement regarding the upper limit for shear capacity of reinforced concrete subjected to reversed cyclic loading. Estimates vary from about 4X/fc to about 8x/fc and higher where f~ = compressive strength of concrete. At these stresses, the concrete is normally cracked; in fact, in a containment wall, the cracks will be in two or more directions. As shown by experiments at the University of Washington [6-8], at Cornell University [ I--4] at Canterbury University in New Zealand [9], and elsewhere [I0], the shear strength increases with increasing steel percentages, but there has to be some upper limit at which deformations are still acceptable and undesirable effects (such as concrete splitting around the bars) do not predominate in terms of failure mode. The study of this very important design question is urgently needed. 3.3. Splitting effects o f large bars
Horizontal and vertical cracks in the shell are pro. duced by internal pressurization. Splitting tendencies in the concrete along both horizontal and vertical bars are created by the tension in these bars. Simultaneous earthquake action develops dowel shear forces in the bars. Experiments have indicated that the splitting tendency caused by large bars is greater than that by smaller bars, hence the initiation and propagation of splitting cracks for various axial and dowel force conditions needs further study.
3.1. Effective shear shiffness o f cracked shell 3.4. Biaxial tension effects
Horizontal and vertical cracking of the containment wall reduces its shear stiffness. Some of the deformation takes place as slip along horizontal cracks. Additional
The two-directional tension in the containment wall causes increased cracking of concrete and may affect
46
P. Gergelv and R.N. White / Seismic effi, cts in secondary containments
bond and dowel capacities, especially in the case of large bars. The following points need further investigation: the effect of biaxial tension on dowel splitting, on bond strength, on interface shear transfer, and on shear stiff ness degradation. The pilot program described in sect. 2 will answer these questions for specimens reinforced with small bars, but experiments with large bars are necessary to fully resolve the effects of biaxial tension on contai~anlents. 3.5. Design o f wall reinforcement A number of articles have been devoted to the design of reinforcement in containment walls [ 11-15]. The principal question is deciding when it is necessary to use diagonal bars to resist seismic shear. Designs for various combinations of sloping, horizontal, and vertical steel should be evaluated. Another important question is the "allowable strain in the reinforcement. What are realistic strain and stress limits in the orthogonal and inclined reinforcement? Can nonlinear analysis predict the expected strains in the steel? Additional experiments on specimens with various percentages of two-directional and four-directional reinforcement are being planned as a follow-up to the research described in sect. 2. 3.6. Effects o f high-frequency vibration All comprehensive studies to date on interface shear transfer have used quasi-static loading in which the frequency of the loading has not been a factor. It is known that vibration in any direction reduces friction forces. Since interface shear transfer involves friction, in addition to interlocking of the rough surfaces at the crack, the effect of vibration may have a significant effect on shear transfer behavior. 3. 7. Membrane seismic shear in prestressed containments Experiments are needed on specimens with lower steel percentages and much lower biaxial tensions (or perhaps even with biaxial compression) to study shear transfer in prestressed containments. The availability of the new research equipment described in Sect. 2 provides an opportunity to undertake this study at a modest cost.
3. 8. Performance o f construction/oints Most previous studies on construction joints have been concerned with walls having relatively small reinforcing bars, unidirectional loading, and without normal tension across the joint. Experiments are needed to study the effects of tension and various methods of sur. face preparation on the seismic shear transfer capacity of construction joints. One significant design question is the role of reinforcement near the joint on shear transfer behavior. 3. 9. Motion o f the shell Nonlinear dynamic analyses of tile cracked containment vessel may be required to more accurately evaluate the deformation of the vessel, tile distortion of the liner, and the motion of the structure. A few such analyses have already been performed [4,5], but several variables have not yet been examined in detail. Also, the nonlinear behavior of the vessel may result in response spectra at various elevations of the shell that are significantly different from those obtained in linear analyses. As results from the biaxially tensioned specimens become available, the corresponding stiffness of the cracked concrete will be embedded into tile dynamic analysis program developed by Smith [41. This development will allow accurate prediction of structural response at advanced stages of cracking.
4. Concluding remarks Research needs associated with seismic membrane shear effects in secondary containment structures have been outlined in this paper. Other shear-related problems requiring additional attention include: (a) Radial shear in the wall. The combination of radial shear and membrane stresses produces unusual demands on concrete and reinforcement near the base of a containment, and the proportioning of reinforcement for these effects needs further study. (b) Punching shear, The effects of biaxial tension on the punching shear strength of containment walls are not well understood. Experiments are in the planning stage for using the slab tensioning equipment described in sect. 2 in a program to establish punching strength as a function of steel percentage and level of biaxial tension.
P. Gergely and R.N. White /Seismic effects in secondary containments
It is evident that we still have much to learn about the behavior of reinforced concrete subjected to the complex stress histories encountered in the design of containment structures. However, substantial progress has been made in recent research and in improved analysis capabilities, and planned research activities will provide considerable new understanding. Improved containment design procedures that are less dependent on conservatism appear to be on the horizon.
Acknowledgments The research program described in sect. 2 is supported by the Nuclear Regulatory Commission (Site Safety Research Branch) and by the National Science Foundation (RANN Division); it is part of a broader investigation into the basic aspects of shear transfer in cracked reinforced concrete. Any opinions, findings, conclusions, or recommendations expressed herein are those of the authors and do not necessarily reflect the views of NSF or NRC. We express our thanks to Boris Browzin of NRC for his continuing help in formulating and implementing the research on biaxially tensioned specimens.
References [1 ] R.N. White and M.J. HoUey Jr., J. Structural Division, ASCE, (1972) p. 1835.
47
[2] J.P. Laible, R.N. White and P. Gergely, Reinforced Concrete Structures in Seismic Zones, ACI Special Publication SP-53 (1977) p. 203. [3] R. Jimenez, P. Perdikaris, P. Gergely and R.N. White, Proc. of the ASCE Specialty Conference on Structural Analysis, Madison, (1976) p. 457. [4] J.K. Smith, P. Gergely and R.N. White, Dept. Structural Engineering Report No. 368 (Cornell University, 1977). [5] R.N. White and P. Gergely, Paper J3/5, Transactions 4th Int. Conf. Structural Mechanics in Reactor Technology, August 1977. (Available from the authors). [6] A.H. Mattock, Shear in Reinforced Concrete, vol. 1, Special Publication SP-42 (American Concrete Institute Detroit, 1974). [7] A.H. Mattock and N.M. Hawkins, PCI Journal vol. 17, (1972). [8] A.H. Mattock, Report SM-74-4, Dept. Civil Engineering (University of Washington, Seattle, 1974). [9] T. Paulay, R. Park and M.H. Phillips, Shear in Reinforced Concrete, vol. 2, Special Publication SP-42 (American Concrete Institute, Detroit, 1974). [10] R.F. Mast, J. Structural Division, ASCE (1968). [11 ] D.F. Green and T.E. Johnson, Paper J3/4, Transactions 4th Int. Conf. Structural Mechanics in Reactor Technology, August 1977. [12] N. Duchon, ACI Journal (1972) p. 578. [13] S. Berg and I. Hoiand, Paper J3/6, Transactions, 4th Int. Conf. Structural Mechanics in Reactor Technology, August 1977. [14] T.S. Asiz and C.F. Reeves, Paper J3/3, Transactions, 4th Int. Conf. Structural Mechanics in Reactor Technology, August 1977. [15] A.L. Banerjee, K.A. Condon, R.A. Rettig and C.F. Reeves, Paper J 3/1, Transactions, 4th Int. Conf., Structural Mechanics in Reactor Technology, August 1977.
SEISMIC EFFECTS IN SECONDARY CONTAINMENTS: RESEARCH NEEDS Peter GERGELY and Richard N. WHITE Cornell University, Ithaca, N. Y. 14853, USA, Department o f Structural Engineering
Received 16 January 1978 The purpose of this paper is to discuss the status of current and projected research on the behavior of nonprestressed secondary containment structures carrying combined pressurizationand seismic shear. Ongoing experimental research at Cornell Universityon specimens carrying combined biaxial tension and static cyclic shear is described. The remainder of the paper treats research needed to better predict the response of containments to seismiceffects and to serve as the basis for improved design methods for reinforced concrete containments.
1. Introduction The transfer of seismic membrane shear in rein. forced concrete secondary containment vessels subjected to simultaneous pressurization and seismic forces presents rather severe problems in design. The wall of the containment shell is cracked by internal pressure and is in a state of biaxial membrane tension. It must also resist substantial membrane shearing forces produced by the specified earthquake loading. These large cyclic shear forces must be transmitted across small cracks in the concrete by a combination of interface shear transfer on the cracked rough surfaces, by dowel forces in reinforcing bars normal to the cracks, and by tensile forces and dowel forces in reinforcing bars inclined to the crack direction. The basic behavior involved in this action is not sufficiently well understood at the present time. This necessitates the use of highly conservative and not always consistent design approaches that may well lead to more reinforcing than is really needed. The establishment of requirements for inclined reinforcing steel has been a particularly unsettled topic over the past decade. Cyclic shear transfer in biaxially tensioned reinforced concrete is a very complex phenomenon that gives rise to many difficult questions, including: (a) cracking patterns in the vessel prior to and during an earthquake. (b) effective shear stiffness of the heterogeneous combination of cracked concrete and multidirectional reinforcing steel. 41
(C) deformations associated with shear transfer at slightly open cracks. (d) axial, shear, and bending stresses in the reinforcement crossing the cracks. (e) possible degradation of the efficiency of the shear transfer mechanism (including bond degradation) as produced by the reversing characteristics of seismic load. (f) potential splitting effects in biaxially tensioned concrete from shear-induced dowel forces on large numbers of #18 reinforcing bars. (g) dependence of total shear capacity on reinforcing percentage and direction of bar placement (horizontal and meridional bars vs. inclined bars). (h) effect of cracks and degrading shear transfer properties on the dynamic response of secondary containments. In view of both the quantity and complexity of these questions, as well as their largely unknown degree of interaction, it is not surprising that research progress in membrane shear design methodologies has been rather slow. The situation has been further complicated by the fact that the very massiveness of containment wall construction (#18 bars and several feet of concrete) has prevented a direct extrapolation of earlier research on shear transfer in specimens reinforced with small bars. A clear understanding of all aspects of membrane shear transfer, in the special context of containment vessel walls (large reinforcing bars and biaxial tension), would lead to: (a) development of more rational design procedures
42
P. Gergely and R.N. White / Seismic efl?ets in secondary containments
that would provide the desired vessel strength and deformation resistance with a minimum of reinforcing steel. thus saving steel, reducing construction time, and reducing the extreme reinforcing bar congestion that often leads to difficulties in producing quality concrete in the containment. (b) improved dynamic analysis capabilities where nonlinear behavior introduced by the cracked concrete could be properly accounted for, including improved values of peak shear stress and the displacement history of the structure. (c) a logical, proven basis for more realistically assessing true safety margins in secondary containments. Shear transfer research aimed at containments and other thickwalled reinforced concrete structures began in 1969 at Cornell University under the sponsorship of Stone and Webster Engineering Corporation and several of its clients. This initial research and later studies sponsored by the National Science Foundation Division for Research Applied to National Needs (RANN) focused on the shear transfer mechanism in cracked concrete, on dowel behavior, on combined interface shear transfer and dowel action in specimens subjected to combined uniaxial tension and cyclic shear, and on incorporation of these experimentally determined behavior modes into dynamic analysis procedures. Several papers and a series of reports have been published on this research [1-4] and major findings are summarized in the first two parts of Paper J3/5 [5] of the 4th SMiRT Conference. The ongoing research program described in sect. 2 of this paper is a study of orthogonally reinforced concrete specimens subjected to combined biaxial tension and cyclic static shear. The study is being conducted under the combined sponsorship of the Nuclear Regulatory Commission and the National Science Foundation (RANN), with NRC being the chief contributor. Other ongoing and proposed research topics that are related directly to the research in biaxial tension plus shear are described in sect. 3. The paper concludes with brief comments on other important topics associated with containment design (sect. 4).
2. Behavior of reinforced concrete subjected to combined biaxial tension and cyclic shear The goal of this research is to determine the strength and stiffness of reinforced concrete sections carrying
combined biaxial tension and cyclic shear. The study, which began more than a year ago with the design and construction of special testing equipment, is mainly experimental in its initial stages. The tests will be supplemented by analysis after sufficient understanding of basic behavior is gained from the experiments. A number of specimen designs have been proposed by different researchers to physically model the behavior in the wall of a secondary containment vessel carrying combined pressurization and seismic shear forces. All feature the isolation of a square segment of wall, with forces applied at the boundary to introduce the required tensile forces in the reinforcement and shear forces in the concrete. Severe difficulties are met in applying shear loadings that produce proper shear stresses and at the same time do not interfere with the cracking behavior of the specimen. The specimen ideally should be several feet thick and be reinforced with #18 bars. Because of the great expense and the unknown difficulties involved in experiments on such a massive scale, it was decided to first pursue the research objectives with a pilot study on smaller specimens that were designed to have the same behavior as an actual containment wall. Thus the present investigation is regarded as a preliminary study for a larger-scale program. It would also be ideal to apply the shear dynamically to best simulate the earthquake effects, but again the expense and difficulties rule out dynamic loading in this first study on biaxially tensioned specimens. It is very unlikely that large-scale dynamic tests will ever be done because of the magnitude of forces involved (a 3-foot-thick specimen with shearing area of 15 square feet would require a force of +-864 kips to produce 400-psi shear stress), but it is feasible to undertake dynamic testing of specimens similar to those used here. The Cornell Research basic specimen is 6 in thick and is reinforced with one layer of #6 bars at 6-inch spacing in one direction (0 = 1.22%) and with two layers of #6 bars at 6-inch spacing in the other direction (p = 2.44%). The three layers of steel are located in the middle of the slab thickness. Concrete strength is about 3200 psi and Grade 60 reinforcement is used. Specimen geometry is defined in fig. 1a. The section has thickened corners through which the reversing shear loads are applied, as shown in fig. lb, by alternately pushing and pulling on the corners. Additional details on the equipment needed to implement the
P. Gergely and R.N. White /Seismic effects in secondary containments Ty
Tx'~"-'-
x
~ _ ~ L,.--~
Tx ~
_~
48" ONE #6AT 6" , SPACING
THICKENED I ~ ~ I ~ ~_I'=-~TW0"#'6AT6" CORNERREGIONS ' ~ '48"" "Ty" =} SPACING FORAPPLICATION 6" OF SHEARFORCES
a. DETAILSOF BIAXIAL SPECIMEN
TENSILECORNER LOAD%,
COMPRESSIVE CORNERLOAD
c. SHEARSTRESSES ALONG x = 0 COMPRESSIVE CORNERLOAD
TENSILECORNER LOAD
b. LOADING METHOD
Fig. 1. Specimen geometry and loading.
shear loading will be given subsequently. The region of interest is the central cruciform-shaped portion of the specimen. This region is 48 in. wide, giving a shearing area across the specimen of 288 in 2. Elastic shear stress distribution across the center of the specimen is shown in fig. lc. The entire specimen is precracked in two directions by applying tension to the bars with hydraulic rams that react against steel pipe frames built around the slab, fig. 2b. The bar stressing systems are independent in the two directions, and both are completely independent of the shear loading system in order to prevent undesired interaction. Thus biaxial tension of any specified level up to the yield strength of the reinforcement can be maintained during the application of cyclic shear. Extensive measurements are made in the central region of the specimen, inclu-
43
ding shear deformations, slip along the cracks, crack width changes, membrane stiffness, bar strains, and splitting effects. The specimen is loaded to failure in shear at the conclusion of each test. Fourteen experiments are scheduled for the first phase of the pilot study. Primary variables are level of tension in the reinforcement and shear stress history. Three duplicate tests are planned for each of three bar tension levels: 0, 0.6fy, and 0.9fy, where fy = yield stress. Specimens will be precracked by tensioning the bars to about 40 ksi. For the first two stress levels, the initial cyclic shear stress will be at -+125 psi for 10 cycles. The shear stress will then be increased in 50-psi increments (-+175, +225, etc.) with 10 cycles at each stress level until failure occurs. Specimens with 0.9fy bar tension will be cycled at lower stress levels because their ultimate shear strength is expected to be less than 100 psi. Three additional tests will be conducted with the beginning shear stress to be the average failure stress level determined from the three sets of duplicate tests described above. If the specimen withstands 20 cycles at this stress, the magnitude of applied shear will again be increased in increments of 50 psi, as described above. These tests will determine the effect of cycling at lower stress levels on the ulti. mate capacity in shear. The last two specimens will contain diagonal reinforcement inclined at 45 ° to the main reinforcement. The amount of steel and the shear stress history will be decided upon after the orthogo. nally reinforced specimens have been tested. Two specimens with bar tensions at 0.6fy have been tested, and a third is in progress (mid-July 1977) with bars stressed to 0.9[y. Preliminary results are given in ref. [5]. The experimental setup is functioning extremely well and specimens will be tested at the rate of about one every two weeks throughout the early fall of 1977. Initial results indicate that some changes may be made in the variables listed above. For example, the shear strength of a specimen with steel tensioned to 0.9fy is expected to be very low since there is little capacity left in the bars to equilibrate forces developed from shear. There is also need for tests to establish an interaction curve for combined biaxial tension and shear applied monotonically to failure. Four tests with bar tensions held at 0, 0.3fy, 0.6fy, and 0.9fy, while shear load is increased to failure, would establish this curve, which could then be used to assess the effects of cyclic
44
P. Ger,gely and R.N. White / Seismic effects in secondary containments
Fig. 2. Specimen configuration. shear load history on shear strength. Finally, three replications for each basic bar tension level may not be needed if two specimens show nearly identical results. Thus, the final testing program may well be
substantially different from that outlined above. A few additional words about the loading equipment are in order. The large prestressed concrete test frame, fig. 2a, has load capacities of +-150 kips at each
P. Gergely and R.N. White / Seismic effects in secondary containments
corner. Two double-acting 100-ton-capacity hydraulic rams are used to apply shear loads to the specimens, with two large tubular section load cells on opposite corners of the specimen. The linkage system conncecting the specimen corners to the rams and load cells is designed to transmit either tensile or compressive corner loads and at the same time be capable of permitting large shearing deformations in the specimen. Very heavy plates, high strength steel pins and rods, and heavy clevises were used in fabricating the corner connections. The combination of the specimen and its tubular frames and hydraulic rams (used in applying bar tensions) is free to deform without any undesired constraints. Peak shear stresses of 550 psi may be produced in the specimen with the rams pressurized to a load of 112 k, which is the maximum tension capacity of the rams. Each ram is controlled with separate electric hydraulic pumps, while the rams producing tension in the reinforcement are on two independent handoperated hydraulic pumps. It is evident that extremely heavy equipment is needed even in this pilot study on small specimens and that experiments on specimens with #18 reinforcing bars will involve extraordinarily massive loading devices and reaction systems.
3. Additional research needs associated with membrane seismic shear effects in secondary containment structures
The research program described in the previous section of this paper will provide considerable new insight into the basic problem of seismic membrane shear in nonprestressed secondary containments. Much work remains to be done, however, and it is nearly all in the realm of the behavior of reinforced concrete under repeated reversed loading. Some of the required experimental research can be conducted on the new equipment described above, and some must be done at a larger scale to study the special problems introduced by the use of #18 reinforcing bars. The most urgent problems are outlined here:
45
flexibility results from vertical cracking that allows some rotation of the concrete blocks bounded by cracks. A third factor is the diagonal cracking caused by seismic shear. The reduction of stiffness is an important research and design question. While experiments described in sect. 2 will provide considerable basic information on membrane stiffness after cracking and during shear cycling, the results cannot be extrapolated to predict behavior of actual containment walls without supporting experimental evidence on specimens with #18 reinforcing bars.
3.2. Maximum shear stress
There is considerable disagreement regarding the upper limit for shear capacity of reinforced concrete subjected to reversed cyclic loading. Estimates vary from about 4X/fc to about 8x/fc and higher where f~ = compressive strength of concrete. At these stresses, the concrete is normally cracked; in fact, in a containment wall, the cracks will be in two or more directions. As shown by experiments at the University of Washington [6-8], at Cornell University [ I--4] at Canterbury University in New Zealand [9], and elsewhere [I0], the shear strength increases with increasing steel percentages, but there has to be some upper limit at which deformations are still acceptable and undesirable effects (such as concrete splitting around the bars) do not predominate in terms of failure mode. The study of this very important design question is urgently needed. 3.3. Splitting effects o f large bars
Horizontal and vertical cracks in the shell are pro. duced by internal pressurization. Splitting tendencies in the concrete along both horizontal and vertical bars are created by the tension in these bars. Simultaneous earthquake action develops dowel shear forces in the bars. Experiments have indicated that the splitting tendency caused by large bars is greater than that by smaller bars, hence the initiation and propagation of splitting cracks for various axial and dowel force conditions needs further study.
3.1. Effective shear shiffness o f cracked shell 3.4. Biaxial tension effects
Horizontal and vertical cracking of the containment wall reduces its shear stiffness. Some of the deformation takes place as slip along horizontal cracks. Additional
The two-directional tension in the containment wall causes increased cracking of concrete and may affect
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P. Gergelv and R.N. White / Seismic effi, cts in secondary containments
bond and dowel capacities, especially in the case of large bars. The following points need further investigation: the effect of biaxial tension on dowel splitting, on bond strength, on interface shear transfer, and on shear stiff ness degradation. The pilot program described in sect. 2 will answer these questions for specimens reinforced with small bars, but experiments with large bars are necessary to fully resolve the effects of biaxial tension on contai~anlents. 3.5. Design o f wall reinforcement A number of articles have been devoted to the design of reinforcement in containment walls [ 11-15]. The principal question is deciding when it is necessary to use diagonal bars to resist seismic shear. Designs for various combinations of sloping, horizontal, and vertical steel should be evaluated. Another important question is the "allowable strain in the reinforcement. What are realistic strain and stress limits in the orthogonal and inclined reinforcement? Can nonlinear analysis predict the expected strains in the steel? Additional experiments on specimens with various percentages of two-directional and four-directional reinforcement are being planned as a follow-up to the research described in sect. 2. 3.6. Effects o f high-frequency vibration All comprehensive studies to date on interface shear transfer have used quasi-static loading in which the frequency of the loading has not been a factor. It is known that vibration in any direction reduces friction forces. Since interface shear transfer involves friction, in addition to interlocking of the rough surfaces at the crack, the effect of vibration may have a significant effect on shear transfer behavior. 3. 7. Membrane seismic shear in prestressed containments Experiments are needed on specimens with lower steel percentages and much lower biaxial tensions (or perhaps even with biaxial compression) to study shear transfer in prestressed containments. The availability of the new research equipment described in Sect. 2 provides an opportunity to undertake this study at a modest cost.
3. 8. Performance o f construction/oints Most previous studies on construction joints have been concerned with walls having relatively small reinforcing bars, unidirectional loading, and without normal tension across the joint. Experiments are needed to study the effects of tension and various methods of sur. face preparation on the seismic shear transfer capacity of construction joints. One significant design question is the role of reinforcement near the joint on shear transfer behavior. 3. 9. Motion o f the shell Nonlinear dynamic analyses of tile cracked containment vessel may be required to more accurately evaluate the deformation of the vessel, tile distortion of the liner, and the motion of the structure. A few such analyses have already been performed [4,5], but several variables have not yet been examined in detail. Also, the nonlinear behavior of the vessel may result in response spectra at various elevations of the shell that are significantly different from those obtained in linear analyses. As results from the biaxially tensioned specimens become available, the corresponding stiffness of the cracked concrete will be embedded into tile dynamic analysis program developed by Smith [41. This development will allow accurate prediction of structural response at advanced stages of cracking.
4. Concluding remarks Research needs associated with seismic membrane shear effects in secondary containment structures have been outlined in this paper. Other shear-related problems requiring additional attention include: (a) Radial shear in the wall. The combination of radial shear and membrane stresses produces unusual demands on concrete and reinforcement near the base of a containment, and the proportioning of reinforcement for these effects needs further study. (b) Punching shear, The effects of biaxial tension on the punching shear strength of containment walls are not well understood. Experiments are in the planning stage for using the slab tensioning equipment described in sect. 2 in a program to establish punching strength as a function of steel percentage and level of biaxial tension.
P. Gergely and R.N. White /Seismic effects in secondary containments
It is evident that we still have much to learn about the behavior of reinforced concrete subjected to the complex stress histories encountered in the design of containment structures. However, substantial progress has been made in recent research and in improved analysis capabilities, and planned research activities will provide considerable new understanding. Improved containment design procedures that are less dependent on conservatism appear to be on the horizon.
Acknowledgments The research program described in sect. 2 is supported by the Nuclear Regulatory Commission (Site Safety Research Branch) and by the National Science Foundation (RANN Division); it is part of a broader investigation into the basic aspects of shear transfer in cracked reinforced concrete. Any opinions, findings, conclusions, or recommendations expressed herein are those of the authors and do not necessarily reflect the views of NSF or NRC. We express our thanks to Boris Browzin of NRC for his continuing help in formulating and implementing the research on biaxially tensioned specimens.
References [1 ] R.N. White and M.J. HoUey Jr., J. Structural Division, ASCE, (1972) p. 1835.
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[2] J.P. Laible, R.N. White and P. Gergely, Reinforced Concrete Structures in Seismic Zones, ACI Special Publication SP-53 (1977) p. 203. [3] R. Jimenez, P. Perdikaris, P. Gergely and R.N. White, Proc. of the ASCE Specialty Conference on Structural Analysis, Madison, (1976) p. 457. [4] J.K. Smith, P. Gergely and R.N. White, Dept. Structural Engineering Report No. 368 (Cornell University, 1977). [5] R.N. White and P. Gergely, Paper J3/5, Transactions 4th Int. Conf. Structural Mechanics in Reactor Technology, August 1977. (Available from the authors). [6] A.H. Mattock, Shear in Reinforced Concrete, vol. 1, Special Publication SP-42 (American Concrete Institute Detroit, 1974). [7] A.H. Mattock and N.M. Hawkins, PCI Journal vol. 17, (1972). [8] A.H. Mattock, Report SM-74-4, Dept. Civil Engineering (University of Washington, Seattle, 1974). [9] T. Paulay, R. Park and M.H. Phillips, Shear in Reinforced Concrete, vol. 2, Special Publication SP-42 (American Concrete Institute, Detroit, 1974). [10] R.F. Mast, J. Structural Division, ASCE (1968). [11 ] D.F. Green and T.E. Johnson, Paper J3/4, Transactions 4th Int. Conf. Structural Mechanics in Reactor Technology, August 1977. [12] N. Duchon, ACI Journal (1972) p. 578. [13] S. Berg and I. Hoiand, Paper J3/6, Transactions, 4th Int. Conf. Structural Mechanics in Reactor Technology, August 1977. [14] T.S. Asiz and C.F. Reeves, Paper J3/3, Transactions, 4th Int. Conf. Structural Mechanics in Reactor Technology, August 1977. [15] A.L. Banerjee, K.A. Condon, R.A. Rettig and C.F. Reeves, Paper J 3/1, Transactions, 4th Int. Conf., Structural Mechanics in Reactor Technology, August 1977.