ML20198Q147
| ML20198Q147 | |
| Person / Time | |
|---|---|
| Site: | 05200003 |
| Issue date: | 01/13/1998 |
| From: | Joseph Sebrosky NRC (Affiliation Not Assigned) |
| To: | NRC (Affiliation Not Assigned) |
| References | |
| NUDOCS 9801220353 | |
| Download: ML20198Q147 (78) | |
Text
{{#Wiki_filter:- - _ - _ _ _ _ _ _ _ _ - - _ _ - _ - _ _ _ - _ - - - - - - - _ - - - _ - - - - - - - - - - - - - - 31~003 4 ! g f..g\ UNITED t' \TES I NUCLEAR REGULATOHY COMMISSION WASHINGTON o.C. see6 Hoot
% January 13, 1998 APPLICANT: Westinghouse Electric Corporation PROJECT: AP600
SUBJECT:
SUMMARY
OF AP600 MEETING TO CISCUSS THE NUCLEAR ISLAND BASE-MAT DESIGN The subject meeting was held on November 4,1997, in the Rockville offices of the Westing-house Electric Corporation. Attachment 1 is a list of the participants. Attachment 2 contains the handouts provided by Westinghouse during the meeting The purpose of the meeting was to discuss analyses contained in an October 17,1997, letter from Westinghouse concoming the AP600 Nuclear Island Basemat design. The two major issues that were discussed were the configuration of the shear stirrups and the shear capacity of deep slabs. Confiauration of the shear stirruos: The staff's position on the configuration C the shear stirrups was discussed in an August 29, 1997, letter to Westinghouse title .1 "Two Major issues Resulting from the Structural Design Review of the Westinghouse AP600 advanced Reactor Design." The staff stated in this letter that "According to Chapter 21 of the ACI 318 95 Code, stirrups used as shear reinforcement have to be provided with a 135 degree hook at both the top and bottom faces of the foundation mat. However, only stirrups (90 degree hook et the bottom face and 135 degree hook at the top face) were provided by Westinghouse for resisting shear." in their letter of October 17,1997, Westinghouse proposed using shear ties with anchor heads. During the meeting Westinghouse stated that anchor head ties provide performance equivalent to 135 degree hooks and are easier to construct. Westinghouse noted that the ACI 318-95 commentary accepts the use of headed bars. Westinghouse also distributed Attachment 3 during the meetir7 which contains additionalinformation on the subject. The staff Indicated that, based on a preliminary review, Westinghouse's proposal seemed to be an acceptable approach for resolving this issue. The staff stated that it would have the safety evaluation report written on the subject by the end of November, and any open items on the subject would be forwarded to Westinghou:e at that time. The staff noted that one potential ogen item concemed documenting the use of the anchor head ties in the standard safety analysis report (SSAR), Sheer caoacity of deep slobs: The staff and Westinghouse's positions on the issue are documented in the August 29,1907, and October 17,1997, letters respectively. The issue revolves around the interpretation of l American Concrete institute (ACl) codes. The staff believes that according to the ratio of span to If depth, the nuclear island foundation mat should be classified as deep flexural members and be l 9901220353 990113 PDR A ADOCK 05200003 PDR
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-2 January 13, 1998 designed for the requirements for deep flexural members in accordance with American Concrete institute ACI codes 318-89 and 318-95. Although the ACI 318 code does not apply to nuclear power plants, the staff believes that the nuclear code (ACI 349) will adopt the more stringent requirements currently found in the non nuclear code.
To resolve the issue Westinghouse stated that it established an independent technical expert team to establish a course of action, determine the acceptance criteria, and to review the final results. Westinghouse stated that the AP600 basemat design is in accordance with ACI 349-85 Section 11.11 for slabs. In an attempt to resolve the issue, Westinghouse evaluated a portion of the basemat (critical bay K L) against the requirements for deep flexural members. Westing-house stated that this critical bay met the ACI 318-95 requirements for deep flexural members. Westinghouse's assertion was based on the following: strength and equilibrium analyses performed in accordance with paragraph 11.8.3 of ACl 318 95, non linear cracking analyses, and review of test data which Westinghouse believed demonstrated that the shear capacity of a continuous beam is similar to that of a simply supported beam. Westinghouse presented the results of the strength and equilibrium analyses and the non-linear cracking analyses. During the discussion of the strength and equilibrium analyses Westinghouse referred to Figure 3.8.5-3 found in attachment 2. The figure shows the areas that would receive shear tvinforcement in the basemat based on Westinghouse's latest analyses. The staff questioned why the most northeastem panel did not receive shear reinforcement. Westinghouse took an action to get back to the staff on this issue. Based on the staff's preliminary review, it expressed reservations about Westinghouse's approach on this issue. Although the staff stated that the basemat design is feasible, it believes additional shear reinforcement is required. The staff noted that ACI 318-95 Section 11.8 for deep flexural members requires that a minimum amount of shear reinforce ment be used throughout the basemat. Westinghouse's proposelincluded shear reinforcement only in areas demonstrated it need the reinforcement based on its analyses. The staff was also concemed that no analyses were done for areas other than entical bay K L. The staff did not agree with Westinghouse's position that other areas of the basemat were bounded by the analyses performed for critical bay K-L. A draft of this meeting summary was provided to Westinghouse to allow them the opportunity to comment on the summary prior to issuance. original signed by-Joseph M. Sebrosky, Project Manager Standardization Project Directorate Division of Reactor Program Management Office of Nuclear Reactor Regulation Docket No. 52-003 DISTRIBUTION: See next page Attachmenta: As stated cc w/atts: See next page DOCUMENT NAME: AANOV_BSMT. SUM To receive a copy of this document, Indicate in the box: C" = Copy without attachment / enclosure *E" = Copy with attachment / enclosure *N" = No copy _ OFFICE PM:PDST:DRPM ECF g l D:PDST:DRPM l NAME JMSebrosky:sgd# W Trl.ne4hf./ TRQuaM DATE 011/3 98 t/ 01//$ /98 01/ 6/98Wh l OFFICIAL RECORD COPY
l ( DISTRIBUTION w/ attachments: Docket File PUBLIC PDST R/F TKenyon BHuffman JSebrosky DScaletti JNWilson DISTRIBUTION w/o attachrngnty SCollins/FMiraglia,0-12 G18 BSheron,0-12 G18 RZimmerman,012 G18 JRoe DMatthews TQuay WDean,0-18 E15 ACRS (11) JMoore,015 B18 TCheng,0 7 H15 GBagchl,0 7 H15
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Westinghouse Electric Corporation Docket No. 52 003 cc: Mr. Nicholas J. Uparulo, Manager Mr. Frank A. Ross Nuclear Safety and Regulatory Analysis U.S. Department of Energy, NE 42 Nuclear and Advanced Technology Division Office of LWR Safety and Technology Westinghouse Electric Corporation 19901 Germantown Road P.O. Box 355 Germantown. MD 20874 Pittsburgh, PA 15230 Mr. Russ Bell Mr. B. A. McIntyre Senior Project Manager, Programs Advanced Plant Safety & Ucensing Nuclear Energy Institute Westinghouse Electric Corporation 1776 i Street, NW Energy Systemt Business Unit Suite 300 Box 355 Washington, DC 20006 3706 Pittsburgh, PA 15230 Ms. Lynn Connor Ms. Cindy L. Haag Doc Search Associates Advanced Plant Safety & Licensing Post Office Box 34 Westinghouse Electric Corporation Cabin John, MD 20618 Ersrgy Systems Business Unit Box 355 Dr. Craig D. Sawyer, Manager Pittsburgh, PA 15230 Advanced Reactor Programs GE Nuclear Energy Mr. M. D. Beaumont 175 Curtner Avenue, MC 754 Nuclear and Advanced Technology Division San Jose, CA 95125 Westinghouse Electric Corporation One Montrose Metro Mr. Robert H. Buchholz 11921 Rockville Pike GE Nuclear Energy Suite 350 175 Curtner Avenue, MC 781 Rockville, MD 20852 San Jose, CA 95125 Mr. Sterling Franks Barton Z. Cowan, Esq. U.S. Department of Energy Eckert Seamans Cherin & Mellott NE 50 600 Grant Street 42nd Floor 19901 Germantown Road Pittsburgh, PA 15219 Germantown, MD 20874 Mr. Ed Rodwell, Manager Mr. Charles Thompson, Nuclear Engineer PWR Design Certification AP600 Certification Electric Power Research Instituto NE 50 3412 Hillview Avenue 19901 Germantown Road Palo Alto, CA 94303 Germantown, MD 20874 Mr. Robert Maiers, P.E. Pennsylvania Department of Environmental Prote:. tion Bureau of Radiation Protection Rachel Carson State Office Building P.O. Box 8469 Harrisburg, PA 17105-8469
AP600 U.JETING TO DISCUSS THE NUCLEAR ISLAND BASEMAT DESIGN MEETING ATTENDEES NOVEMBER 4,1997 NAME ORGANIZATION DON LINDGREN WESTINGHOU" E RICHARD ORR WESTINGHOUSE RAO MANDAVA WESTINGHOUSE BRIAN MCINTYRE WESTINGHOUSE ARIDANAY DANAY ENGINEERS LTD (WEST-lNGHOUSE CONSULTANT) WILLIAM WHITE BECHTEL CORPORATION (WEST. INGHOUSE CONSULTANT) NOEL DUDLEY* ACRS JACK STROSNIDER* NRR/CE GOUTAM BAGCHI NRR/DE/ECGB TOM CHENG NRR/DE/ECGB GUNNAR HARSTEAD NRC CONSULTANT TED QUAY
- NRR/DRPM/PDST JOE SEBROSKY NRR/DRPM/PDST
*PART TIME t
Attachmer.t 1
Nuclear Island Basemat .' Meeting Agenda November 4,1997 Introduction M c I n t y r e Basemat issues and overview of response R. Orr i Shar capacity of deep slabs Configuration of shear stirrups Design of bay K- L R. Orr Nonlinear analyses A.Danay Strut and tie analyses A.Danay I Results of NRC review G.Bagchi $ Discussion ! Conclusions / schedule for staff decision {
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Open items on Nuclear Island Basemat - Westinghouse letter, dated October 17,1997, addressed 7 issues raised during the structural meetings in August,1997:
. Shear capacity of deep slabs -:
. Configuration of shear stirrups e
. Soil stiffness variation in alternate spans
. Post 72 hour design change
. Construction induced loads
. Effect of shear wall stiffness on basemat
. Design margins t
Shear capacity of deep slabs .' SSAR coinmits to ACI 349-85 including Regulatory Guide 1.142 positions. The AP600 basemat design is in accordance with ACI 349-85 section 11.11 for slabs whereas the staff believe that section 11.8 for deep flexural members should be applied. Westinghouse review shows that design also meets the ACI 349-85 requirements for deep flexural members. I Effect of alternate assumptions of structural element type on shear reinforcement required by AC6' 349-85 for bay K - L Type of structural Code Location of Factored shear Concrete Shear element equation critical section force design reinforcement V. kips / ft strength required
$V, kips /ft sq.in/sq.ft Slab 11-3* "d" 117.8 86.1 0.10*
Simply supported deep beam 11-29 015 In 161.4 145.4 0.06 Continuous deep beam 11-29 0.151 161.4 258.4 i None The shear reinforcement is designed to 349-85, equation 11-3. Reinforcement of 0.18 sq.in. per sq.ft. is provided. _._.m..
I Shear capacity of deep slabs 1 NRC staff identified during August meeting that provisions of future ACI 349 code may be more stringent than in the 1985 edition. NRC staff have not reviewed or endorsed ACI 318~95. ACI 349-85 is based on ACI 318-83 and will be updated to parallel ACI 318-95. Provisions for shear in continuous deep flexural members have been revised in ACI 318-95. u
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- i Shear capacity of deep slabs l
Westinghouse has evaluated provisions of ACI 318-95 for a critical bay. L Design also meets the ACI 318-95 requirements for deep flexural members. 1
- Review of test data shows that shear capacity of a continuous beam is similar to that of a simply supported beam
. Strength and equilibrium analyses were performed in accordance with paragraph 11.8.3 of ACI 318-95, e in addition non-linear cracking analyses were performed.
Review of test data and results of both sets of new analyses demonstrate that the basemat can withstand the design loads. Design performed to the slab provisions of ACl 349-85 also satisfies other code criteria suggested by NT :?.
Confiauration of shear stirrups i Review conducted of extensive data on shear reinforcement in slabs including stirrups with 90*,135" and 180* hooks as well as ties with anchor heads. 135" hooks at each end are not constructable in a mat. l Mat does not experience reversible loads. Code provision of 21.3.3 (which requires 135" hooks for flexural frames) is not applicable. Anchor head ties provide performance equivalent to 135 degree hooks and are easier to construct. ACI 318 commentary accepts use of headed bars. 90* hooks have been changed to anchor heads. Where shear reinforcement is required, it has been extended throughout the span. L
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Desian of Bay K - L . I Designed as a one way slab with clear span of 23' 6" between the walls on column lines K and L. Slab is continuous with the adjacent slabs to the east and west. , Critical loading is the bearing pressure on the underside of the slab due to dead and seismic loads. The basemat is designed for the maximum
- bearing pressure of 16.25 ksf at one corner of the bay from the analyses on uniform soil springs.
l The design moments ar.d shears are increased by 20 percent to accommodate the nonuniform sites. Equivalent design pressure equals l l 19.5 ksf. i Negative moments are redistributed as permitted by ACI 349. Top and bottom reinforcement in the east- west direction of span are # 14 at 10" centers. Shear reinforcement is # 7 at 20" x 24" centers. A
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Presentation to NRC on Westinghouse AP600 Program Nonlinear analyses of the Nuclear Island basemat November 4,1997 Washington, D.C. Prepared by: Dr. Ari Danay, P. Eng Principal For: Westinghouse Electric Corporation Nuclear Technology Division h' Myf" Wa"" m e m *.,7_ M
i GENERAL METHODOLOGY
- 1. The Modified Compression Field Theory provides a unified, ;
rational approach to the analysis of reinforced concrete components under generalin-plan conditions. Extensive corroborative testing has shown that the theory is able to accurately model the response of structural concrete even under : extensive cracking and rebar yield conditions.
- 2. TRIX97 is a finite element computer program which incorporates the state-of-the-art formulations of the Modified Compression Field Theory. The program is capable of simulating in great detail the response ofin-plane reinforced
- concrete structures, including cracking patterns, rebar yielding, concrete distress regions, and failure. Its accuracy has been thoroughly examined and confirmed by modeling " benchmark" tests reported in literature.
- 3. Considerable insight into the flow of forces in disturbed regions L can be gained by the use of simple strut and tie models.
- 4. The results of the TRIX97 analyses indicate that (a) no shear
- failure in the K-L bay will occur before flexural yield, (b) a limit state condition with a rebar capacity reduction coefficient ,
4 of 0.9 is reached in flexure at about 20 Ksf, and (c ) failure may occur at about 32 Ksf. .
- 5. The results of the strut and tie analysis similarly indicate that L (a) no shear failure in the K-L bay will occur before flexural yield, and, (b) a limit state condition with a concrete capacity reduction coefficient of 0.85 and rebar capacity reduction coefficient of 0.9 is reached in flexur: at about 20.7 Ksf.
- 6. The load capacity of the basemat slab is actually higher than indicated by the TRIX97 analyses due to the neglect of the confining action of the in-plane resistance of the slab and of the load re-distribution in the post-cracking regime as a result of-the flexibility of the elastic foundation.
+- - - e
I MODIFIED COMPRESSION FIELD THEORY
- The Modified Compression Field Theory provides 3 a unified, rational approach to the analysis of structural concrete elements under general in-plane stress conditions.
- Cracked reinforced concrete is treated as a nonlinear elastic orthotropic material based on a smeared, rotating crack assumption.
- Formulations satisfying equilibrium and compatibility conditions are developed, and new constitutive relations for the component materials are defined.
- The theory is incorporated into several analytical .
algorithms.
- Procedures have been developed for the analysis of membrane structures, beams, plane frames, plates and shells, and three-dimensional solids.
- Extensive corroborative testing has shown the theory to be able to model accurately the response
.of structural concrete.
MODIF ED
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[- G}O 2PRESSIO FIELD V4 pi s q THEORY
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FINITE ELEMENT FORMULATIONS
. The MCFR was incorporated into nonlinear finite element analysis algorithms, for membrane structures, using several alternative approaches.
- Adeghe [4] introduced the model's constitutive relations into the standard program ADINA.
- Stevens et al [3] developed program FIERCM, a nonlinear algorithm based on a tangent stiffness solution procedure and utilizing high-order quadratic strain elements.
. Cook and Mitchell [5] developed program FIELDS, also a nonlinear finite element algorithm based on a tangent stiffness scheme.
. Lastly, a secant-stiffness based algorithm was used by Vecchio [6,7] in developing program TRIX.
. In the secant-stiffness formulation, finite elements were developed such as to completely represent the formulations of the MCFR. By incorporating these elements into a iterative linear elastic procedure, nonlinear analysis capability was achieved.
. The resulting procedure demonstrated good numerical stability and good convergence characteristics.
. TRIX analyses pertaining to strength, stiffness, cracking patterns, reinforcement stresses, concrete distress regions, and failure modes predicted response with good accuracy [ 6,7, 8,9]
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. q 4 'l m ADEGHE, L. and DANAY, A., 'The Effect of Post cracking Constitutive Models on Crack dj Propagation and Ultimate Capacity of Reinforced Concrete Containments", Trans of the
,'y O ::j lith Int. Conf. of Structural Mechanics in Reactor Technotorv, Vol. H, Paper H09 /6. Tokyo, 1-w.3 s japan, August 1991. ,.
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TRIX REFERENCES
- 1. Vecchio, FJ., and Chan, C.C.L., " Reinforced Concrete Membrane Elements with Perforations", ASCE Journal of Structural Engineering, V.116, No. 9, Sept 1990.
- 2. Vecchio, F.J., and Nieto, M., " Shear-Friction Tests on Reinforced Concrete Panels", ACI Str.J., Sept 1990. ,
- 3. Stevens, N.J., Uzumeri, S.M., and Collins, M.P.,
" Analytical Modeling of Reinforced Concrete Subjected to Monotonic and Reversed Loadings", Publ.No. 87-1, Dept.
of Civil Engineering, Univ. of Toronto, Jan 1987.
- 4. Adeghe, L.N., "A Finite Element Model for Studying Reinforced Concrete Detailing Problems", Ph.D. Thesis, University of Toronto,1986,264 pp.
- 5. Cook, W.D., and Mitchell, D., " Studies of Disturbed Regions near Discontinuities in Reinforced Concrete Members", ACI Str. Jrnl, V. 85, No. 2, Mar - Apr 1988, pp 206-216.
- 6. Vecchio, F.J., " Nonlinear Finite Element Analysis of .
Reinforced Concrete Membranes", ACI Str.Jrnl, V. 86, No.1, Jan - Feb 1989, pp 26-35.
- 7. Vecchio, F.J., " Reinforced Concrete Membrane Element Formulations", ASCE Journal of Structural Engineering, V.116, No. 3, March 1990, pp 730-750.
- 8. Vecchio, F.J., and Collins, M.P., " Predicting the Response of Reinforced Concrete Beams Subjected to Shear Using Modified Compression Field Theory", ACI Structural Journal, V. 85, No. 3, May - June 1988, pp 258-268.
- 9. Vecchio, F.J . " Analyses based on the Modified Compression Field Theory", IABSE Colloquitun, Stuttgart 1991, pp 321-326.
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TRIX UDL MODEL Bottom rebar stress (average between cracks) at 20 Ksf fs 1 Stress If: 1.00 300:0 250:0 200:0 150:0 2 ' 100:0 . 50:0 ; 0:0 150D05Q.01950.0 2J50[37b0.0 46b0.0 5550.0 6450.0 8250.0 735k.
-50:0 Distance (mm)
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TRIX UDL MODEL Bottom rebar stress (at cracks) at 20 Ksf fs 1 Stress (crack) If: 1.00 350:0 300:0 250:0 200:0 g 150:0 2 100:0 50:0 0:0 - - - k 1I50 D 5 37d0.0 4650.0 5550.0 64N0.0 7
-50:0 Distance (mm)
Data Maximum: 352.300 MPa Simple Average: 82.235 MPa Data Minimum:-84.900 MPa
TRIX USL MODEL First stirrup from support, stress at cracks at 20 Ksf fs 1 Stress (crack) If: 1.00 ; 1525.0 - 1325.0 - 1125.0 -- E E
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-___-________-__-_-_---N-'=--
TRIX UDL MODEL t P Midspan dispiacement 50 7 40 / ai 30 ! ' g / / + fixed Y' 20 / / + 3 spans
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$ 200 w , /a f
100 10 15 20 25 30 Pressure Ksf 1
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lf(e :: f a .'{m& d, h:. kN,$u c Walraven (1981>1 Walraven, Joost C.. " Fundamental Analysis of Aggregate Interlock," /ournolof the Structurol M l, yl} ,y Division AJCE. Vol. '107. No. STil. Nov.1981, pp. 2245-2270.
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, 35 g y,2m -5 3 30 'E g M ___
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TRIX MODEL WITH SUBGRADE SPRINGS 0.9 " support movement bottom rebar stress fs 1 Stress (crack) If: 0.75 360:0 300:0 240:0 g 180:0 s . 120:0 60:0 0:D-)Db 150.0 Q.019 0.0 28 0.0'3750.0 4650.0 55b0.0 64h0.0 735h
-60:0 N
Distance (mm) Deta Maximum: 418.500 MPa Simple Average: 100.197 MPa Data Minimum:-101.700 MPs
w . . Bay K-L Mid-span displacement , 50 A p 40 E :
~ 30 o TRIX subgrade niodel l
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l' A Ad[ 0 0 10 20 30 40 Pressure (Ksf)
O Bottom rebar stress at support . 2^ U timate stress fu=551 Mpa (80 Ksi) 550 - -- 500 A
^
450 -
,-Yield stress f y=413 Mpa (60 Ksi) 5 7 400
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$$250 g 200 A 150 4 100 0 10 20 30 40 Pressure (Ksf)
- -- --________.__m _ _ _ . _ _ _ _ _ _ _ _ _ _ _ _ _ . _ _ _ _ _ _ _ _ _ _ _ __ _ _ _ _ _ _ _ _ _ _ _ _ _ __
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- - - - - - - _ - _ _ - __ _m _. _ . _ _ _ . ._.___.___________...m________ _ . . _ _ . _ _ . _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ ,_ _ _ _ _ _ _ _ _ __ _ _ _ _ _ _ _ _ _ ___
Strut and tie method e Considerable insight into the flow of forces in disturbed regions can be gained by the use of simple strut and tie models. Cracked reinforced concrete carries load principally by compressive stresses in the concrete and tensile stresses in the reinforcement.
- After significant cracking has occurred, the principal compressive stress trajectories in the concrete tend towards straight linec and hence can be approximated by straight compressive struts. The internal flow of forces in disturbed regions can be modeled using concrete compressive struts to represent the concrete in uniaxial compression, tension ties to model the principal reinforcement and nodal zones which represent the regions of concrete subjected to multidirectional stresses where the struts and the ties meet. .
- A comprehensive study of elastic stress fields in disturbed regions and the way in which these elastic stress flows can be represented by detailed strut and tie models, is given by Schlaich, Schafer and Jennewein [2]
and discussed by Rogowski and al [3] and Collins and Mitchell [4].
- Marti [5] has pointed out the importance of considering the actual dimensions of the compressive struts and tension ties in formulating the strut and tie models 4
-___------___._..m_ ____.________ _ _ _ _ _ _ _ _ _ _ _ , _ _ _ _
i STRUT AND TIE REFERENCES 1 Morsch, E., " Concrete-Steel Construction", McGraw-Hill Book Company, New York, 1909,368 pp. (English translation by E.P. Goodrich, from third edition of Der Eisenbetonbau,first edition,1902.) 2 Schlaich, J., Schafer, K., and Jennewein, M., "Towards a Consistent Design of Reinforced Concrete Structures," PCIJournal, Vol. 32, No. 3, May-June 1987, pp. ?4-150. 3 Rogowsky, D.M., and MacGregor, J.G., " Design of Reinforced Concrete Deep Beams," Concrete International, Aug.1986, pp. 49-57. 4 Collins, M.P. and Mitchell, M., " Prestressed Concrete Structures", Prentice-Hall inc.,1991. 5 Marti, P., " Basic Tools of Reinforced Concrete Beam Design," ACI Joornal, Vol. 82, No.1, Jan.-Feb.1985, pp. 46-56.
# e .e '
I . STRT T-AND-TIE l i l l . l MODELS {1 },. - Un nodalzone n,gg 4 g
'5 eq w o
/ o / ~
k ,;W,i M 3 i i b i ,., .. , . hpb;p o , i,y',I2 < f eman 's,':,', l' g ;w;w%ngy Gji a *.* '..ls *
'dyb
,,,, 6 ' /,2y,.
IM, u^ , e, '* 0.75 4i* a %. ,,',\,b L pB, ~G. .
^"
/
,gl I-Gydy'Wl11);Q, 1 _<
,1 t
'N'CIIV' tension tie anchorage k develop tension- area a '
T [%,yd N, tie iorce over et this length fc,
- s hmu = 0.8 + 170q A9 (a) Flow of forces W s;o.85/l
.. W truss node hh
. ; sg ,.
o
. "y / ,
, ,. ,............y, ,
/
'.'s,
. 's p /// 's,
's, 4 / // \s'. strut p)j j // ', .
compression r ,. / .
~,
c, , S -
/
d 7 j s .- hij o p o ( i tension-tie
$ . force g
d (c) Truss model 9 y.i CSA Committec A23.3 Design ofConcreteStructuresforBuildings,CAN3 A23.3
- dian Standards Association, Rexdale, Canada, 1984,281 pp.
' Collins, M.P., and Mitchell, D., " A Rational Approach to Shear Design - The 198 Code Provisions," AC/ Journal, Vol. 83, No. 6 Nov.-Dec.1986, pp. 925-933.
STRUT AND TIE ANALYSIS STEPS e In a disturbed region, the first step is to sketch the flow of forces in the region and locate the nodal zones. The nodal zones must be made large enough to ensure that the nodal zone stresses remain below permissible limits: 0.85pcfc in node region bounded by compressive struts and bearing area, 0.75pcfc in node region anchoring only one tension tie, and 0.6 c fc in node region anchoring more than one tension tie
. Forces in the struts and the ties of the truss due to
, factored loads can be found from statics.
- Calculate required area of tension-tie reinforcement, l
using a strength reduction factor for axial tension such as p, = 0.90.
. The tension-tie reinforcement must be anchored so that it can transfer the required tension to the nodal zone of the truss. Typically such a requirement is a length of 12 diameters of the rebar.
I
- . , . - - ,-a- ,- .,-n --
i STRUT AND TIE ANALYSIS STEPS 1
- The dimensions of tne strut must be large enough to ensure that the calculated compressive force in the strut does not exceed cAcu/cu., where pc is the strength reduction factor for axial compression, Acu, is the effective crosssectional area of the strut, and feu is the j effective compressive strength of the concrete.
- The value of Acu is calculated by considering both the available concrete area and the anchorage conditions at the ends of the strut, such as 12 times the diameter of the t
rebars.
- The value o'rfeu is computed from I
l
#" " 0.8 + 70Em s 0.85[c li where cm is calculated from 2
c,, = c+(c+ 0.002) cot g and 6, is the smallest angle between the compressive strut and the adjoining tensile ties and e is the tensile strain in L the tensile tie inclined at 6 to the compressive strut. i
- - - - - - - . m .ae, - r y-m-,
i STRUT-AND-TIE n, ,: MODELS _ r . . - . . 4. j 3 lfi s . jpll x,
, :j ,, cc:-
k N- - +[ a _ _y~ $ MhfaD ......m.........._,.... ,
,.,, . . .. .....m(........,_,.....
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- g. n p'ffg 0.2f) -
- r. -
-- ^
4m b.vid i Km ) 1 ce io mm) {'47 i / I il < h {l I\\*V ., 3d V
- h. V V '
fj'q3 V 0.15 - li.3s40 psi t.r., MPs) -
' ]
%dI*s ma n. egg . 3/4 in (19 mm) j d.212 m (638 mm)
;;Ql'4 e.61in (155 mm) 3
- r. , ands
@ A, .3 63 m8 (,,7 7 mm8 )
0.10 - h4 ,y ,3 3 , ,,, g 3,, y,,3 b M o si m ' el k't g 0.05 -
- ors .74 76
,, o .3 o e6 , , ,
( ' l@y q p!,, strut and lie model sectional model C . d 0 0 1 2 3 4 5 6 7 {d. a/d g .
)}L Predicted and obses ved strengths of a series of reinforced concrete beams tested by Kani. ,
c . . STRUT AND TIE MODEL Disturbed regions Undkiurbed zone Disiurbed zone Undhiurbed y (Strut Lee model) Dh c fl4@l0 { 41920"
, N M ei c\' \ 135t. N j
~ - ~~ ' '
/
, m)h gui .s4
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'r i Ft1 c
'gr E 33.s4$ l
, 33' S' , 7' n, _ -
5.75' e r \@t -
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% I2.4 50
\
0 e e r STRUT AND TIE MODEL _{ m_, !!b*k _7 151. [ JIe_' w h
- # eye; ep h,-
s x s eo 5.
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3 6
<5 . . .
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o . , STRUT AND TIE MODEL Forces equilibrium Tx. Geo. s . b n
@f gn4 .. .
? Y . IC77 y _ 47.7' NO' S geo,s- 22s.s cus .47.7e AB A v
A 4 Taa.:2.57.l Ak T4 T Taiutg7; A Qs E
* # 67 1
%f C1.9 T,t .$7 - 74.1ces6t+ 4# %
u 2C0. 5 5 a
. m.,cacs n 2/
L ~'h-J4 %:AO
,. j< ..
17' G 75o3 Tu. 24.5- St twsn.7
= rezi E Fig. 4.21 Strut and tie calculations for Nodes IL,2L and 3L
STRUT AND TIE MODEL rine g46.3 5' Tee,214 3 I #8 9 n @ g Ti. $9 ~, 4 3' ~TRAe 2AG.S~ lOt. levs 757
- ,,22e2 1
% )
ne 22a.1 2
+ 'y
' N w.g2c2 M ~rsa
~g L
'a GlA* % Q A r 5 TSRe 22f.2=ll3.3066l4 t, = r74.o ,
To u TsR r s74o <3 nc ga y . .
%sv g 1 T44= rM.o.
#M S co47 7
% = 5 5.5 w
T4 R 85.5 i si. g rs
% Q Rg Kys J khh, y Tv. sa r .. isi s 4 354
% Y k' k%g 4 3r.2 '%j Fig. 4.22 Strut and tie calcu!ations for Nodes IR,2R,3R and 4R t
l 1 STRUT AND TIE MODEL Bottom nodes calculations Table 3.2 Strul and tie snodel: stress calculations for bottom of slab Strut Angle force Stress Force in tie at mode (T) Average Principal Compr. Relative e F /=g4 3 Left Right Asg. strela strain Strength stress
, . . T,_ t, a f.
(t*21") d4 s + (a + 0002) cot' # , [e [ 02 + 170s,f, (deg.) (Kips) (Kst) (Kips) (Kips) (Kips) gog$f, (Kst) fit 47.7 2259 0 636 48 4 2005 124 5 0 00101 0 00350 2 866 0253 fn 61 4 76 4 01II 2005 2371 218 8 0 00178 0 00290 3 094 0 067 ft 79 7 51.1 0 108 23? 1 246 3 241.) 0 00196 0 00209 3 400 0 036
- f. 90 33 5 0 070 246 3 246 3 2463 0 00:00 0 00200 3 400 0 023 fei 79 7 101 1 0 214 246 3 2282 237 2 0 00193 0 00206 3 400 0 072 fm 61 4 113 3 0 269 228 2 174 0 208.1 0 00163 0 00271 3.171 0 097 f>a 47.7 134 5 0 379 174 0 83 5 1287 0 00104 0 00357 2 844 0 152 f.a 38 2 2089 0 704 83.5 151.5 34 0 0 00027 0 00251 3.262 0 247 Ci 42 $ 48 0 0 161 33.5 151.5 34 0 0 00027 0 00179 3.321 0 048 Cs 54 0 401 0 118 83 5 151.5 34 0 000027 0 00064 3.400 0 035 Ci 70 0 34 5 0 087 83.5 151 5 34 0 000027 000004 3 400 0.026 E(+/4R C2 +C3) + Cl
=0 356
o , , STRUT AND TIE MODEL Top node calculations Table 3.1 Strut and tie model: stress calculations for top of slab Strut l Angle Forte Stress Fortes at top node Average Principal Compt. Strength Relative e F /*6 L4ft Right strain strain f stress
~
(t=24) 7 To a * [a 02+ 70s s + (c + 0002) cot' # ' (concrete) (rebar) r s l! (deg.) (Kips) (Kips) (Kips) N 5025f, [a (gel) g,;) fit 47 7 225 9 0 636 .48 4 80 7 0 00035 0 002.10 3 400 0 200 fs 61 4 76 4 0 181 48 4 80 7 0 00035 0 00105 *400 0 053 fit 79 7 $11 0 108 484 80 7 0 00035 0 0004) 3 400 0 032 f, 90 33 5 0 070 -48 4 80 7 0 00035 0 00335 3.400 0 020 fie 79 7 101.1 0 214 .48 4 80.7 0 00035 0 00043 3 400 0 063 fut 61 4 113 3 0 269 .48 4 80 7 0 00035 0 00105 3 400 0 079 fin 47.7 134 5 0 379 -48 4 80 7 0 00035 0 00235 3 400 0 111 f4a 38 2 208 9 0 704 .48 4 80 7 0 00035 0 00415 2 654 0 265
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[.g Lw\-)*S' b. = = AN = M'.m <a ' C *k*m a6'n 3.*!~ 2 . '.3n ~Q 4.N.'j'd> "IF,,ic - J #~ ~' bhN;,$hh,k N..E .J^w .w d f5 h he m- E E M d d -
, ___: = = = - 4 . , HRC 100 series HRC 200 sc. ries T Headed Bars are manufactured by a friction forging process, under strict quality control to ensure a zero slip connection between head and bar that exceeds the actual tentile strength of A706 reinforcement bar. Head sizes are in accordance with ASTM A970 97 to transfer the full rebar force into multi axial stresses in the concrete beneath the head without crushing the concrete or bending the head. Concentrated Anchorage of the Rebar Force
- ,_ a - - .-
i $
//
1\ - a u y Not enough developmentlength? fi Solve it with Headed Reinforcement fg 1i fi - , gg- ' 1\ j t f.t L- . 147ith T-Headed Bars the reinforcement It is possible to save considerable can beplaced exactly at the desired construction costs, because the concentrated anchorage can minimize location and thefullrebarforce anchored close to the structure's surface. member sizes. e.g. reduced concrete depth,formtvork and excavatingfor footings. In Strut T e modeling the concentrated anchorage optimizes the truss analogy, since it is utilizing more of the concrete section and clearly defl 2es the nodes.T Headed Bars have proven to be more efficient than conventional reinforcement, particularly in disturbed strain regions such as anchorage and transition zc nes. As there is no bond length, hook, or crossing bar required to develop the reinforcemen't; larger diameter and/or higher strength bars may be used. In addition the failure mode of the stirrup is limited by crushing under the bend, hence stirrup bars typically develop only 70 percent of yield at failure.
l 4*s , 1 ( Typical Applications m , c-pene,h e a b q p ql
. M ..
v
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" ARC Standard & High Performance T-Headed Bars
, TYPE 110 TYPE 130 , c y I'~ ~ F-' c_[ l 4 j_s w -9j ~ " rlll::l:
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' llll ..M l
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TYPE 120 TYPE 140 E E E ~'
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loIl *L l l o _l *l I ol TYPE 210 TYPE 230 g -ir > , , n .r 1 ..,,,n , , 61 - a 7,, 1,,
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l TYF E 720 TYPE 240 A , b , , , , , , , , , , , , , , , ,
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*t - cworaan itwin sonen too a 200 ene amene o wseu nom 17 sea N cmeo nbect v creve a*as ncace ASTM 706 sfon*xd ASTM 206 Mr%c f' '
A ssenens d i8 C D 8 7 8 * - sor Do A sswom es lacr Do Sao h:h neh # noe sensse l$ae tryn mm rlmee nonsar neh neh ech nch Nh neh neh neh neh nch_
- - - - ~
es a62s 031 1e600 pesoo lsto sse 199 so 109 250 t.25 625 2 00 500 d6 Giso 0 44 3s200 ld19 19.1 2et 114 156 3 00 I so 150 22s 62s 3 00 1.52 612 23e Cs6_ 26400 fr oers C60 secoo 48000lr22 222 387 1Ss 213 e 00 150 rso 2so .a2s 3 50 1.13 62s 2 ??do_6L re__ s.ow C19 traco espoo lo2s asa sto 204 2eo e 00 2 00 .ers 3 00 150 s 00 t.97 .ser ? 25 0 s3 To I.tse 1.w eoooo exoo!r29 2e r ses 2se oss s 00 2oo .ers 3 rs iso a so 22r .rso 3 so.p69
*Io I.210 t.27 16200 1016001r32 323 er9 328 450 s vo 2so 1 00 3 so .ers s 00 2 52 .e12 400 0 rs a11 1.A rc t.se 93sw tpaexto3e 35 e r006 402 ss* 6 ao eco I.00 s ao rco s so 2 16 s.00 toso iose se1 199 7.so 3 00 1.25 s 00 1.2s 62s 3 60 1 25 s 32 1 25 94 f.693 2.2% 13s000 leoooo!#43 43o 14s2 aue rper sw <oao wwn sr er.3 aser son us2a - - - - -
ers < ar o.so nouso Headed Reinforcement Corp 11200 Condor Avenue
- Fountain Valley, CA 9270R Ph: (714) 557-1455 a Fax: (714) 557-4460
- urms2iFrM M Er i
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[ -i --
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Reduced Congestion and the case of placing Headed Reinforcement will improve construct-ability and speed up the project. The concrete also benefits because adequate space for pouring and vibrating will give better concrete consolidation.
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f~ Q Y.N A *** Anchorage without utilization ofbond improves robustness at overload and accidental , conditions. If spalling of concrete cover occurs-from f.e. fir: or seismic loading-the heads still proside full anchorage without cover. STIFF ANCHORAGE - DUCTILE MEMBER Head size and the ultimately rigid head to-bar ' connetion of HRC's products significantly
~
increases the reinforcement's confining effect. The
- passive confinement of Headed Reinforcement -
b-results in enhanced concrete compressive strength ',v ' .'/ and ductility. The stixf anchorr.ge reduces the [/ /,/ width of shear cracks, resulting in improved aggregate interlock, which incretses the concrete's 8
!~
/ /
/
shear capacity. The Canadian Code (CSA A23.3 94) is acknowledging this by allowing a 50% increase in [ ., .. ('.;',../ / factored shear stresc resistance of concrete ,v., and " " * " " ' " ' -
- 33% increase in factored shear stress allowed when
- using Headed Reinforcement instead of conventional stirrups.
__ _ ------_-- ----_ -- - - - - - - - - - - - - - - - - - - - - - - - --- --- - -~}}