INCREASING PRIMARY CONTAINMENT CAPABILITIES OF LIQUID-METAL FAST BREEDER REACTOR PLANTS BY THE USE OF PRESTRESSED CONCRETE

Transcription

1 Seiden sticker, R. W., Marchertas, A. H., and Baiant, Z.P. (1980). "Increasing primary cntainment capabilities f liquid-metal fast breeder reactr plants by the use f prestressed cncrete.» Nuclear Technlgy, 51, INCREASING PRIMARY CONTAINMENT CAPABILITIES OF LIQUID-METAL FAST BREEDER REACTOR PLANTS BY THE USE OF PRESTRESSED CONCRETE RALPH W. SEIDENSTICKER and ALGIRDAS H. MARCHERTAS Argnne Natinal Labratry, Engineering Mechanics Prgram Reactr Analysis and Safety Divisin, Argnne, Illinis ZDENEK P. BAZANT Nrthestern University Evanstn, Illinis Received January 28, 1980 Accepted fr Publicatin May 22, 1980 The Argnne Natinal Labratry develped cmputer prgram DYNAPCON fr the transient analysis f a prestressed cncrete reactr vessel (PCRV) fr liquid-metal fast breeder reactr (LMFBR) primary cntainment is applied t a reference design cncept representative f large, pl-type LMFBR reactr plants. Estimates f the energy absrptin capability f a PCR V primary cntainment vessel are prvided t assist in the establishment f the engineering feasibility f such a design cncept. The reference design analyed utilies existing cncrete stnlctures already in place fr bilgical shielding and cmpnent supprt. The very large energy absrptin capability is achieved thrugh the use f fairly large amunts f prestressing steel and mild steel reinfrcement ithin these cncrete matrices. Energy surces used range frm 2720 t MW-s. Even fr the largest energy surce, the maximum cmputed strain in the prestressing tendn anyhere in the structure is -2.3%, hich is still bel the strain assciated ith the minimum ultimate stress levels fr mst prestressing steels. These results are very encuraging and shuld prvide sufficient incentive t mre firmly establish the feasibility f this cncept f using a PCR V fr primary cntainment. INTROOUCTION Marchertas and Belytschk I have described the develpment f a cmputer prgram fr use in analying the behavir f a prestressed cncrete reactr vessel (PCRV) under transient lading cnditins. The purpse f this paper is t describe the results f applying that cmputer prgram t a full-sied liquid-metal fast breeder reactr (LMFBR) plant t btain an estimate f the energy absrptin capability f the primary cntainment f that plant in resisting the effects f a large, hypthetical cre disruptive accident (HCDA). Such estimates are f value in establishing the feasibility f using a PCR V fr LMFBR primary cntainment. Ultimately, feasibility f a PCR V fr such use rests n the basis that it prvides much greater energy absrptin than steel NUCLEAR TECHNOLOGY VOL. 51 MID DEC.1980 reactr vessels currently in use, and that it can ecnmically prvide sufficient capability fr absrbing the effects f even the mst severe HCDA scenaris cnsidered. Althugh rk is still under ay, preliminary results reprted in this' paper are, indeed, very encuraging. DESCRIPTION OF PRIMARY CONTAINMENT DESIGN The cnfiguratin used fr the PCRV in this applicatin study as chsen t clsely resemble (physically) the basic structure used fr bilgical shielding in typical pl-type LMFBR plants. The purpse f this as t see if sufficiently large increases in energy absrptin capability culd be 443

2 Seidensticker et ai. INCREASING CAPABILITIES BY PRESTRESSED CONCRETE btained by merely prestressing and reinfrcing the cncrete already needed fr radiatin shielding and supprt f cmpnents. Then, if the energy absrptin capability is sufficiently large, e can state that use f the PCRV ill prbably have a negligible effect n the verall sie f the secndary cntainment structure. The PCRV design cnfiguratin selected is shn in Fig. 1. Essential dimensins, such as inside diameter, verall height, tp clsure head thickness, and radial bilgical shield all thickness, ere chsen t be fairly representative f large, pl-type LMFBR plants, such as the French Super-Phenix and recent U.S. designs resulting frm an Electric Per Research Institute spnsred prgram fr pl-type LMFBR design studies. The design f bth the prestressing steel system and mild steel reinfrcement as based primarily n btaining as much steel as practical ithin the physical limitatins f the cncrete vessel. The amunt f steel is by n means ptimal additinal rk is under ay and changes in the amunt shn are likely. It is expected, hever, that such changes ill tend t reduce the amunt f steel and, perhaps, sme redistributin f the prestressing tendns. The basic philsphy emplyed in selecting bth the prestressing steel and the mild steel reinfrcing as as flls: I. Use as much mild steel reinfrcement as practical in additin t prestressing steel. Actually, fr the present design, there is much mre mild steel than prestressing steel. The percentage f mild steel t cncrete used in the current design is 4%, in bth the vertical and hrintal (hp) directins. 2. Use a smaller value fr the stress level in the prestressing steel than nrmally used in the design f prestressed cncrete cntainment vessels. The design analyed in this paper uses an effective (net) prestress level f 50% f the ultimate strength f the prestressing steel versus the value f 70% minus prestress lsses nrmally used. The benefit f this reductin is t permit the prestressing steel t absrb mre energy in its elastic range f behavir. 3. Use heavy crss-all mild steel ties that shuld greatly reduce the cracking f cncrete. The perceqtage f crss-all steel ties used in this analysis as 2.77%. This is desired t assure that the cncrete underges a three-dimensinal cnfining pressure that tends t increase its ductility, delay crack frmatin, and increase the absrptin f the energy. 4. Additinal strength culd still be derived, if necessary, by (a) increasing the percentage f mild steel reinfrcement t, say, 6%, and (b) reducing the effective prestress level t -30% f the ultimate strength f the prestressing steel (the structure might 444 then be called the "partially prestressed" cncrete vessel). As shn in Fig. 1, a separate steel vessel (r tank) carrying the primary sdium is suspended frm the tp clsure head, and a gas gap f -0.3 m exists beteen this steel vessel and the inner surface f the PCRV. First f all, it shuld be nted that n energy is assumed t be absrbed by this suspended steel vessel keeping the calculatins n the safe side. Fr the greatly simplified design shn here, the steel vessel merely acts t establish a barrier fr the liquid sdium. Further rk is required t establish mre realistic design cnfiguratins, including the use f sme type f insulatin n the inner liner f the PCRV. DESCRIPTION OF ANALYTICAL MODEL AND APPROACH The analytical mdeling f the PCRV respnse as dne by means f t cdes, ICECO (Ref. 2) and DYNAPCON (Ref. 3). The HCDA reactr cre expansin as mdeled by the hydrdynamics cde lceco, prviding the internal pressure lading n the inside alls f the PCR V mdel. The analytical ICECO mdel invlved simplifying gemetry assumptins that influenced the pressure histry results. First,. the utside bundaries (PeR V alls) ere taken t be ideally rigid. This is cnsidered t be a gd assumptin in vie f the facts that the true PCRV displa!?ements are really quite small and that n gas space is cnsidered in calculatins beteen the steel vessel and the PCRV all. Neglecting the gas space may be verly cnservative, since it culd accunt fr a significant reductin f pressure n the alls f the PCRV. Furthermre, the cre supprt structure and the cre barrel are taken as being cmpletely rigid. The assumptin f a rigid cre supprt structure seems reasnable, taking int cnsideratin the large mass f the structure and the relatively shrt time f cre expansin. The rigid-cre-barrel assumptin as made ith the intentin f simplifying the analytical slutin and als yielding a cnservative lading n the PCRV due t slug impact f sdium n the tp slab. The errr caused by this assumptin is small fr the reference HCDA case, but culd becme appreciable fr the larger energy cases. Future rk ill include the use f a flexible cre barrel t assess its effects n magnitude and lcatin f maximum strains in the prestressing steel. Fr cmputatins, the analytical ICECO mdel as assumed t have a flat bttm. This is a departure frm the design shn in Fig. I and as dne t simplify the ICECO mdeling. This mdificatin shuld nt greatly affect the results f the ICECO lad predictins, especially as far as the lading n NUCLEAR TECHNOLOGY VOL. 51 MID DEC.1980

3 R > ::0 r;l (") ::c t"" < r VI :: 9 -a ()O t en,10m II SEAL RING A T 1.5 m m T<:"""......F ' IUm Fig LAYERS Of TENDONS EACH LAYER: 12 BANDS Of 3 TENDONS EACH I A THREE DIMENSIONAL GRID OF MILD STEEL SOfT fiber THERMAL INSULATION I CENTRAL PlUGr r-.<-- EXTRA TIES Reinfrcement and prestressing details f the bilgical shielding. LS for WOUND /nntnr WIRES SECTION SOfT fiber THERMAL INSULATION THREE IMENSIONAL GRID OF MILD STEEL ROWS Of TENDONS A-A Ul <» s: <» e!,.. <»... (") Cl (")? ttl Ul Ul ttl t:j (")

4 Seidensticker et al. INCREASING CAP ABIUTIES BY PRESTRESSED CONCRETE the cver and the upper part f the cylinder are cncerned. It can playa significant part, hever, if the gas vlume shn in Fig. I ere made available t accmmdate cre expansin. Three runs ere made ith the ICECO mdel using different HCDA energies in the cre. The first ne, cnsidered t be the reference case, had a surce tenn equivalent t 2720 MW-s, based n expansin f the fuel vapr t I atm. This same surce as used in an Argnne Natinal Labratry (ANL) study f pl-type reactrs t evaluate the energy absrptin capability f the stainless-steel sdium vessels cmprising the primary cntainment fr systems included in the pl study reprt. 4 The pressure-vlume relatinship is shn in Fig. 2, hich as reprduced frm this reference. Here, V F is the fmal vlume and V is the current vlume f the cre. Fr the ther t runs, called cases A and B, the pressures ere dubled and quadrupled, respectively, ith everything else being the same. The energy cntent assciated ith case A as 5440 MW-s and that assciated ith case B as MW-s. Histries f the pressures fr these three runs ere extended beynd the time f slug impact and ere stred n penn anent recrd fr subsequent use ith the PCRV mdel. The reinfrced bilgical shielding (r the PCRV) as mdeled by the cde DYNAPCON. In this versin f the cde, cncrete is represented by a linearly elastic material here the cracking criterin is based n maximn stress; aggregate interlck is als apprximated in a simplified manner. The cmpnents f the simplified axisymmetric PCRV mdel, tgether ith the descriptin f the analytical mdel, are shn in Fig. 3. The material prperties used fr mdeling are given in Table I, hile the equivalent prestressing values are listed in Table II. The plug as assumed t be a cmpsite structure and t be attached t the general bdy f the PCRV at the upper right cmer (ne nde nly). N cracking as pennitted in the plug. The PCR V analytical mdel is first prepared fr internal lading by prestressing it t the specificatins given in Table II. This is accmplished by the dynamic relaxatin prcedure, 1 here nly elastic material behavir is cnsidered and cncrete cracking is nt alled. The plug des nt participate in this prestressing peratin. The PCRV mdel is retained as a penn anent recrd, hich becmes the initial state f the mdel befre the internal lading frm an HCDA is applied. Befre calculating the respnse f the PCRV due t internal dynamic lading, e first jin the plug t the general reinfrced/prestressed structure. Then the cmbined mdel f the structure is subjected t the previusly derived pressure histry. Here, cracking is pennitted, accrding t the strain-rate dependence described in Ref. I. The strain-rate dependence f reinfrcing steel is als taken int accunt. Viscus TABLE I Material Prperties Used in the PCRV Mdel Cncrete Cmpressive strength Tensile strength Elastic mdulus Pissn's rati Density Prestressing tendns Yield strength Elastic mdulus Reinfrcement Yield pint Elastic mdulus Plug material Elastic mdulus Pissn's rati Density 51.7 MPa 3.58 MPa 33 GPa kg/m MPa 200GPa 400 MPa 200 GPa 50GPa kg/m TOTAL ENERGY TO 1 atm = 2720 MW s a: :;:) a: Q. 8 TABLE II Equivalent Prestressing f PCRV Mdel Type f Prestressing Lcatin Radial Axial Circumferential Fig Pressure vlume relatinship fr the reference case. Bttm slab F= 26.3 MN/m - -- p = 3.87 MPa h = 3.18 em --- h = 6.7 em Tp slab F= 26.3 MN/m --- p = 7.75 MPa h=3.l8em --- h = em Cylinder --- F=9.71MN/m p = 3.87 MPa --- h = 1.17 em h=6.7 em NUCLEAR TECHNOLOGY VOL. 51 MID DEC.1980

5 Seidensticker et ai. INCREASING CAPABILITIES BY PRESTRESSED CONCRETE L ""'" ""'" f"'" """ i"" , I""" "'"... "'"... "'" "'" "'"... ["""'::"""...," r": f' f' f' ',,- [\1\[\f\[\ "-... "-.""... "- r":!""::!"":: f"'.: 1\1\ 1\1\-[\ f' f' '''- I"'-... [\1\ 1\1'\ 1\- r":.///// "'" ' '/ ////////////,/,:: 1\[\ 1\['\ [\- iiiir- VERTICAL PRESTRESS '" '" "- '" I'\. I'\. "'''' -. '" '" "-... "- '" I... "::S... '\.'",,'\.,,- I\f\ \1\ \ \ PLUG I\f\ \1\ \ I\f\ \1\1\ I\f\ I\I\, I 0.64 cm THICK LINER I\f\ f\ i\f\ 1\1\ r\ 1\1\ 1\1\ r\ 1\1\ f\\ f\f\1\ f\\ 1\f\1\ en en f\1\ I\\I\ a:: I I- en 1\1\ 1\f\1\ a:: Q.. 1\1\ 1\\1\ <C f\1\ 1\1\1\ I- STEEL REINFORCEMENT: 1\1\ N\I\ a:: AXIAL AND CYLINDRICAL RADIAL r\1\ 1\ f\ 1\ u. :E TOP SLAB AND :::::> 4.0% 2.77% CYLINDER 1\1\ 1\1\1\ u a:: I BOTTOM SLAB 3.0% 2.08% f\\ I\f\ 1\ u f\\ I\f\ 1\ f\1\ I\f\ 1\ 1\1\ 1\\ 1\ f\1\ 1\\ f\ 1\1\ 1\1\ 1\ "-... "- "- "-... "- "-1\1\ I\f\ [\ - 'RADIAL PRESTRESS.. -- Fig. 3. Discretiatin and prestressing f the PCRV mdel. NUCLEAR TECHNOLOGY VOL. 51 MID DEC

6 Seidensticker et al. INCREASING CAP ABIUTIES BY PRESTRESSED CONCRETE damping in the numerical simulatins is used t the minimum; hever, it is increased hen extensive cracking ccurs, hich makes the cntinuatin f the slutin difficult. Nte that the bjective ithis analytical slutin as t mnitr the behavir f the steel tendns, the main lad-carrying members f the structure. This bjective necessitated carrying the slutin thrugh the largest pressure peaks f the lading s that the tendns uld be stressed t their maximum values. It turned ut that slutins ere necessary far beynd the pint after extensive cncrete cracking had taken place. These situatins necessitated increases in viscus damping and the reductin f the time step. DISCUSSION OF RESULTS The prgress f the simulatin f cracking thrugh the alls f the PCRV mdel is quite interesting. Figures 4 and 5 depict the sequence f cracking fr cases A and B, respectively. Nte that the plug is nt alled t underg any cracking; it serves slely as a member transmitting lad t the main PCRVbdy. It is bserved that fr case A, extensive cracking is first initiated ith the slug impact, hich begins at s. After the impact, radial cracks prpagate als thrugh the cylinder alls starting frm the tp f the vessel Fr case B, circumferential stresses in the vessel cause radial cracks bel the cre befre the slug impact starting at s. Slug impact causes circumferential cracks at the tp cver and the tp f the cylinder all. Additinal radial cracks appear in the cylinder all after slug impact. Because the cracking sequences are different fr the t cases, it can be seen that the maximum strains and stresses in the PCRV mdel vary ith lcatin and time. The lcatin f maximum radial displacement f the cylindrical all, fr example, uld depend n the lading case cnsidered. Fr all f the PCRV mdel runs, the strains f the tendns ere mnitred. A cntinuus recrd f strain values fr the tp and bttm layer f the tp slab and the inner and uter layers f the vertical all tendns ere mnitred. In additin, the circumferential strain f the simulated ire rap miday beteen the tp and bttm slabs as recrded. The abslute maximum recrded strain values fr the radial tendns in the tp slab, the axial tendns f the cylindrical all, and the circumferential prestressed ire indings ere detennined and are pltted in Fig. 6. Cmbined ith the respective maximum strain values fr all the three runs, the curves prvide us infnnatin n the trend f maximum strain as a functin f the energy cntent f the HCDA. There appears t be a certain degree f uncertainty regarding the shape f the 448 curves, like that f the circumferential ire strain at the midpint f the cylindrical all. It is nt clear at this pint, especially keeping in mind the different cracking sequences in Figs. 4 and 5, that an inflectin in the relatinship is all that unreasnable. Mre detailed studies may reveal the anser. The fact that the maximum strain values are acceptable is, hever, the significant result f the study. Fr the imaginary HCDA surce f MW-s (case B), the maximum strain is 2.3%. The maximum ultimate static strain values fr these tendns quted in the literature range frm 3 t 6%. Fr dynamic cnditins, as the PCRV mdeling, this range uld prbably be higher. T put the range f HCDA energies in perspective, e shuld refer t sme typical values used in present designs. The maximum HCDA reference case fr the Clinch River Breeder Reactr (CRBR) is 661 MW-s (Ref. 5), hile that fr the French Super-Phenix is 800 MW-s (Ref. 6). Fr such energy magnitudes, the maximum strains in the tendns frm Fig. 6 uld hardly be nticeable. It appears that under the mst cnservative cnditins, the HCDA energy culd easily be increased t MW-s t reach a maximum strain f 3% in the tendns. This crrespnds t mre than 16 times the HCDA surce used fr Super-Phenix. Nte that althugh the prestressing steel cables are nt taxed t their ultimate capacity, cracking in the PCRV can be quite extensive, bth in the extent f cracking and the crack pening sies. Failure f the liner f the vessel thus becmes the bject f interest as far as leak-tightness is cncerned. This must be kept in mind in safety evaluatins f the PCRV. CONCLUSIONS Preliminary calculatins, based n rather cnservative assumptins, indicate very large energy absrptin ptential using a PCRV fr LMFBR primary cntainment. This ptential is achieved by the intrductin f large amunts f prestressing steel, bth tendns and und-ire, and large quantities f mild steel reinfrcement int that physical space already devted t cncrete bilgical shield used in a typical pl-type LMFBR. The maximum steel tendn strains at any pint are -2.3% fr an energy surce level f MW-s. This energy surce f MW,.s is times larger than the maximum reference case f 660 MW-s fr the CRBR, and times larger than the reference design basis f 800 MW-s fr the French Super-Phenix. Clearly, certain questins remain t be ansered mre fully befre it can be stated that ecnmic engineering feasibility has been finnly established. The cnstitutive equatins fr the cncrete must be develped further t include an imprved understanding f the strain-rate dependence f the cncrete NUCLEAR TECHNOLOGY VOL. Sl MID DEC.1980

7 Seidensticlcer et al. INCREASING CAP ABIUTIES BY PRESTRESSED CONCRETE * RADIAL CRACK I CRACK IN THE r PLANE..";:4 +--t.+-""... j:::: l..t:'1::;"''. :..:......,.+..::d 1:::t:;: t Fig. 4. Cracking sequence f PCRV mdel under case A lading. NUCLEAR TECHNOLOGY VOL. 51 MID-DEC

8 Seidensticker et ai. INCREASINP CAPABILITIES BY PRESTRESSED CONCRETE *" RADIAL CRACK I CRACK IN THE r- PLANE 0.08 s 0.07 s I <t Fig. 5. t = 0.01 s Cracking sequence f PCRV mdel under case B lading. 450 NUCLEAR TECHNOLOGY VOL. 51 MID DEC.1980

9 Seidensticker et at. INCREASING CAPABILITIES BY PRESTRESSED CONCRETE , ,...-,..., 2.5 <C a: t; 5 en en a: 4 t; a: e:.3 <C a:: t; 2 X «== Fig ?/l. 1.5 «a:: t; 1.0 == 0.5 CYLINDRICAL WALL (VERTICAL) HCDA CORE ENERGY, MW s Variatin f maximum strain in prestressing tendn ith HCDA energy cntent. behavir. The design cnfiguratin used in this paper is admittedly greatly simplified, particularly ith regard t the details f the PCRV liner and insulatin f the liner and cncrete. An analysis must be made assuming a flexible cre barrel versus a rigid ne. In spite f these limitatins, hever, preliminary feasibility seems assured. Clearly, very large energy absrptin capability is achievable ith reasnable amunts f prestressing and mild steel reinfrcements. Cupling this ith the ell-established safe behavir in failure mdes fr PCRVs seems t prvide strng incentives fr carrying thrugh the remaining rk t establish a sund engineering basis fr this cncept. This paper cncerns the ultimate strength capacity f the PCRV. Leak-tightness f the PCRV, can, hever, be f equal imprtance t the safety f the LMFBR design. The safety aspect f PCRV, invlving X «fine pints f cncrete cracking as ell as the degradatin f cncrete under severe envirnmental cnditins, ill be the subject f subsequent studies. ACKNOWLEDGMENTS The authrs acknledge the encuragement and advice f S. H. Fistedis h frmulated the cncept f PCRV fr primary cntainment and initiated the riginal rk in this area. We are indebted t individual members f the Engineering Mechanics Prgram fr valuable suggestins during the study and in revieing the paper. The rk reprted here as perfrmed in the Engineering Mechanics Prgram f the Reactr Analysis and Safety Divisin at ANI.. under the spnsrship f the u.s. Department f Energy. REFERENCES I. A. H. MARCHERTAS and T. B. BELYTSCHKO, "Transient Analysis f a PCRV fr LMFBR Primary Cntainment," Nucl. Technl., 51, 433 (1980). 2. C. Y. WANG, "ICECO-An Implicit Eulerian Methd fr Calculating Auid Transients in Fast-Reactr Cntainment," ANL-75-81, Argnne Natinal Labratry (Dec. 1975). 3. A. H. MARCHERTAS et ai., "Analysis and Applicatin f Prestressed Cncrete Reactr Vessels fr LMFBR Cntainment," Nucl. Eng. Des., 49, ]-2 (1978). 4. A. AMOROSI et al., "An Overvie f Pl-Type LMFBRs: General Characteristics," ANL-76-61, Argnne Natinal Labratry (May 1976). 5. C. M. ROMANDER and D. 1. CAGLIOSTRO, "Structural Respnse f 1/20-Scale Mdels f the Clinch River Breeder Reactr t a Simulated Hypthetical Cre Disruptive Accident," SRI Internatinal Technical Reprt 4 t the U.S. Department f Energy (Oct. 1978). 6. H. NOEL, et al., "The Cntainment f the Creys-Malville Plant," 4th Int. Cn!. Structural Mechanics in Reactr Technlgy, San Francisc, Califrnia, August 15-19,1977, Paper 1-1/4 (1977). NUCLEAR TECHNOLOGY VOL. SI MII).DEC

10 NCR EASING PRIMARY CONTAINMENT CAPABILITIES F LIQUID METAL FAST BREEDER REACTOR PLANTS BY THE USE OF PRESTRESSED CONCRETE Ralph W. Seidensticker Aigirdas H. Marchertas Zdenik P. Baant Ralph W. Seidensti.-.. (tp) (BS, civil neering, Iis Institute f TechnlOlY. 1955; MBA, Uruverslty f Chicag, 1973) is a research cucineer in the Reactr Analysis and Safety I)iVisin at Argnne Natinal LabratlY (ANL). His current interest invlves the \lie f prestressed cncrete structures fr bth 'primbly and secndbly cntainment fr liquid-metal fast breeder reactr plants. He is active in the American Sciety f Civil Engineers (ASCE> cmmittees n nuclear structures and has rked n the arilinal ACI cmmittee that develped cde uirements fr DUdear cncrete cntainment structures. Algirdas H. March.. (center) (BS, mechanical engineering, University f Illinis, 1956; MS, theretical and applied mechanics, University f Illinis, 1957; PhD, applied mechanics, University f Nebraska, 1963) has been invlved in design, suess analysis, and muhematical mdeling f structural.prblems at ANL since Recently. he has been develping the DYNAPCON cde, hich is intended fr analytical mdeling f prestressed and n:idfrced cncrete structures under!ransient lading. P. Baiant (bttm) (civil engineer degree, Technical University, Prague, 1960; PhD, Cechslvak Academy f Sciences, 1963) has been n the faculty f Nrthestern University since ld became a prfessr in He has als served as crdiatr fr the Structural Engineering Prgram. He served as cluinnan f the ASCE Engineering Mechanics Divisin Cmmittee n Prperties f Materials and is a member f several editrial bards. Fr his research n inelastic behavir f cncrete as ell as stability and fracture, he received frm ASCE tile Huber Research Prie (1976) and the T. Y. Lin Aard (1977). During 1978 and 1979, he held a Guggenheim Fellship and he as recipient f the 1975 Medal frm RILEM, Paris.