ML20084Q962
| ML20084Q962 | |
| Person / Time | |
|---|---|
| Site: | Comanche Peak  |
| Issue date: | 05/20/1984 |
| From: | Iotti R EBASCO SERVICES, INC. |
| To: | |
| Shared Package | |
| ML20084Q958 | List: |
| References | |
| NUDOCS 8405210610 | |
| Download: ML20084Q962 (61) | |
Text
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e May 20, 1984 UNITED STATES OF AMERICA NUCLEAR REGULATORY COMMISSION BEFORE THE ATOMIC SAFETY AND LICENSING BOARD In the Matter of )
) Docket Nos. 50-445 and TEXAS UTILITIES ELECTRIC ) 50-446 COMPANY, ET AL. )
) (Application for (Comanche Peak Steam Electric ) Operating Licenses)
Station, Units 1 and 2) )
AFFIDAVIT OF ROBERT C. IOTTI REGARDING UPPER LATERAL RESTRAINT BEAM I, Robert C. Iotti, having first been duly sworn hereby depose and state, as follows: I am Chief Engineer of Applied Physics for Ebasco Services, Inc. In this position I am responsible for directing analytical work in diverse technical areas, including analyses of the response of major structures, piping and support systems to dynamic events, including earthquakes and loss of coolant accidents. I have been retained by Texas Utilities Generating Company to coordinate and oversee the technical activities performed to respond to the Board's December 28, 1983, Merorandum and Order (Quality Assurance for Design). A statement of my educational and professional qualifications was transmitted with Applicants' letter of May 16, 1984, to the Licensing Board in this proceeding.
8405210610 840520 ppR ADOCK 0500044 p 9
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- 01. What is the purpose of this affidavit?
A1. The purpose of this affidavit is to respond to the Licensing Board's conclusion in its December 28, 1983, Memorandum and Order (at 56) that "in the face of the possibly conflicting engineering viewpoints of three different parties, we conclude that Applicant has not demonstrated the adequacy of its analysis of the upper lateral restraint beam."
Accordingly, Applicants have prepared detailed finite olement analyses to demonstrate the adequacy of the upper lateral restraint beam and of the associated reinforced concrete supporting walls. The results of these analyses confirm that the design of the restraint and the concrete walls which would be affected by the assumed accident conditions is adequate to withstand the postulated loads which are pertinent to this analysis.
Q2. Can you summarize the analyses which have been performed?
A2. This investigation was performed to determine the effects of a LOCA break on the upper lateral steam generator restraint and associated steam generator compartment walls from the thermal growth of the restraint, as well as from concurrent loads and other environmental effects which would occur during a postulated LOCA. In addition, although only the ef fects of a LOCA on the upper lateral restraint were discussed during the licensing hearings, it was recognized that the lower lateral restraint (approximately 24 feet
- below the upper and serving a similar function) would
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< likewise experience and cause similar and simultaneous effects elsewhere in the compartment. Therefore, the investigation was expanded to include the lower restraint to assure that the most significant effects were addressed, i.e., their overlapping effects.
- 03. Please describe the analytical methodology that was used.
A3. First we wish to define the extent of the geometry of the problem that was modelled.
The boundaries of the analysis were established as a section of the reactor building internal structures consisting of steam generator compartments 1 and 4 between elevation 819' (close to the top of the mat and 15' 10" below the lower lateral restraint) and elevation 883' (24' above the upper lateral restraint). Elevation boundaries were selected to assure that all stiffness contributions to the restraining walls from adjacent floors and walls were properly accounted for. Boundary limitations of the analysis (beyond compartments 1 and 4 defined in Appendix II Figures 1 & 2) were determined from the original finite element analysis of the internal structures, done as part of the original design effort on the internal structures.
. Figures 1, 2, 3, 4 and 5 of Appendix II (attached) show the portions of the internal structures included in the present analysis. l 1
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Next we describe the' finite element model employed.
The analysi_s of the upper and lower lateral restraints and compartment walls was performed using NASTRAN. The
'particular version of NASTRAN used has the capability to determine the cracking propagation in the concrete due to i
the interaction of thermal and mechanical loads. The crack developmentandhopagation-isdeterminedbymeansofa nonlidear itera tion'-technikue. The program provides, as an s
output, stressas in the} reinforcing steel, stresses in the concrete, displacements,' forces and moments in the finite elements, crach pa tternm for the structure used in the model.
Appendix III (attached) providee a summary description of
~ the theory employe\1 in the solution method of the version of NASTRAN.used for tbie analysis. This version has been N
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' verified and has been reviewed by the'NRC in other ,
applications. ~.-
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The' finite alepant model of; he structure is generated using . triangular ar,'t quadrilateral layered shell elements
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and beamielemeyt's. Tuoibounding analyses'h' ave been
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- d perfprmed. The first'ana{ysis prov'i$es the'upperbound on
'the effects on concEbte wa'lls. For this analysis no credit
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,ic given tS the tensile cappcity,of . .
the concrete. This is
"conpistent with ACI Code designb requirements which assume
\ e concrete has*no tensilo capacity. ,However, concrete tensile tg 4 -
strength can be approximately 10% of f e and will add to the compartment wall system stiffness'until cracking initiates.
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l Therefore, to assess the maximum loads on the beam, a value of 450 psi for concrete tensile capacity was used in the second analysis. This value is about 10% of the concrete strength actually produced at CPSES but it is 12.5 percent of the concrete strength used in the analysis. Applicants have used the higher figure for conservatism as explained later. Plots of the finite element models employed in the analyses are shown in Figures 1 through 19 of Appendix IV.
Q4. What type of loads were input into the finite element model?
A4. For purposes of these analyses, it was assumed that compartment pressure and temperature ef fects due to LOCA, would occur in combination with seismic loads. Mechanical loads, such as thrust load reacted by-the steam generator restraints and jet impingement were taken at their maximum peak values in combination with maximum dif ferential pressure although consideration of their time histories would have permitted significant reductions in mechanical loads. Further, although discussion at the hearings centered on effects of a LOCA, Applicants considered that a main steam line break would result in higher compartment temperatures than a LOCA break and might have a more significant impact on thermal stresses. Accordingly, the analyses were further expanded to calculate the temperatures, pressures and associated stresses in the compartment walls and restraints due to a main steam line break. For the main steam line break analysis, however,
O seismic loads were not assumed to occur simultaneously with mechanical and thermal loads caused by the break. This is consistent with the position taken by the NRC staff in NUREG-138,1.which states: -" consistent with the lesser importance of the secondary system boundary, the Staff does not require that an earthquake be assumed to occur coincident v L th- a postulated spontaneous break of the steam line piping."
The tempera ture and pressure effects and postulated loading conditions for both the LOCA and main steam breaks are as follows:
- 1. LOCA - The assumed critical break for purposes of this analysis is conservatively assumed to be a full double ended break at the reactor' coolant pump suction on the react r coolant loop. (Note that because of the primary system supports / restraints, this large a break cannot occur.) This break has been chosen because it provides the highest mass and energy flow rates into the compartment and results in the larges'. mechanical
~1nads, the largest differential pressure across the walls and the highest LOCA te mpe ra ture s . Figure 1 of Appendix I (attached) shows the time history of each of the noted effects. It can be seen that all mechanical l loads reduce'to czero in less: than 0.5' seconds.
1 NUREG-138,'"Treatme t of Non-Safety Grade EquipmentLin Evaluations of Postulated Steam:Line Break Accidents,"
November, 1976.
a
~7-Differential accident pressure across the walls rises rapidly to a maximum of 24 psi at 0.5 seconds and is reduced to essentially 0 after approximately 4 seconds.
For purposes of computing maximum differential pressure, the temperature in the compartment is assumed to be at 120 F. at the time of the LOCA. However, to compute the resulting effects, a temperature of 70 F is employed in the analysis. Both of these assumptions contribute to the conservatism of the results. The former maximizes the compartment pressure and temperature (hence the loads seen by the walls and beam). The latter maximizes the response of the beam and walls. Although the temperature of the atmosphere inside the compartment rises very rapidly, the tempera ture in the steel beams and concrete lag behind.
For the restraints of interest the average temperature rises to a peak of 282 UF. for the upper restraint (289 F. for the lower restraint) after 216 seconds and diminishes thereafter.
The temperature rise in the restraints has been computed by the finite difference computer program HEATING 5 Version 2. Input compartment atmosphere temperature histories to these heat transfer analyses have been developed via a multinodal compartment
b analysis which utilizes RELAP 4 Mod 5. Schematics of the models used for these analyses are shown in Appendix V.
Based on the above, two postulated loading conditions were considered for LOCA, as follows:
Stage 1 - At 0.5 seconds after the break / time of maximum pressure
- a. Maximum differential pressure across walls = 24 psi
- b. Coincident accident temperature of beam
= 128 F. (upper beam)
= 133 F. (lower beam)
- c. Peak mechanical loads were used in the analyses even though they occur at earlier times.
Mechanical loads refer to thrusts imposed by steam generator restraints, loads imposed by reactor coolant pump restraints and jet loads due to the postulated pump suction break. The thrust loads include both reaction loads to the break and seismic (full SSE) loadings from the primary system which are transmitted via the steam generator and reactor coolant pump restraints.2 (Actual peak mechanical loads occur at 0.2 seconds and are zero at 0.5 seconds and hence have been included conservatively.)
- d. Seismic loads generated in all the structures, restraint beams, major components from the SSE are included coincidentally.
2 Seismic reaction loads from the primary system seismic response are overestimated since the structural model also includes masses of steam generator and pump, already included in the Westinghouse seismic model which produced seismic reaction loads at structural interface.
0 a
i 9-Stage 2 - At 216 seconds after the break (time of maximum temperature) on upper lateral support
- a. Maximum accident temperature of the beam 3
= 282 F. - upper beam
= 289 F. - lower beam
- b. Coincident differential pressure across walls
= 1 psi even though thermo-hydraulic analyses indicate no differential pressure.
- c. In this instance the reaction load of the beam to the seismic excitation of the primary system had not been initially included in the NASTRAN analyses with the intent to maximize the reaction loads from beam thermal constraint and to maximize beam stresses. The stresses resulting from the reaction were computed separately and added in the most conservative fashion to the stresses generated by the NASTRAN analysis.- Structural. seismic loads, seismic loads or walls due to beams, steam generators and pump masses excitation are included. To verify the conservatism of this approach,.
Applicants have run the worst case problem (i.e.
LOCA Peak Temperature with concrete tensile strength equal to 450 psi) including the primary system seismic load.. The results of this analysis are also shown in Tables 1 & 2 and they confirm that conservatism of the analysis.
- 2. Main Steam Line Break - The assumed critical break for purposes of this analysis is a split break at 30%
power at the steam generator outlet nozzle. This break was selected as the critical break because it results-in the highest temperature in the compartment from the 8
3 Actually, the maximum actual temperature of 289 F. in'the lower. beam occurs at 144 seconds (approximately 285 F. at 216 seconds) but has been assumed to occur simultaneously withithe maximum in the upper beam at 216 seconds.
array of breaks considered, which included full double 1 ended and split breaks for full, 70% and 30% power ,
levels.
Figure 2 of Appendix I contains time history plots i of the effects of the main steam line break. It can be seen that a small but negligible pressure spike of 0.08 psi occurs in the compartment at 1.0 seconds and dissipates by 3.0 seconds. Also, all mechanical loads 4 are reduced to zero within 0.5 seconds. Temperature in I both upper and lower lateral supports rises to approximately 355 F. at about 300 seconds. A more preliminary and conservative figure of 370 F. was used in the actual analysis.
Based on the above, the postulated loading condition for the main steam line break is as follows:
- a. Maximum average temperature of the upper and lower lateral restraints = 370 0F.
- b. Coincident differential pressure across walls =
1 psi used even though analyses indicate that it is zero.
- c. Mechanical loads: none used since seismic loads are not combined in this analysis, and other mechanical' loads (i.e., steam line break reaction loads) are negligible at'the time of peak temperature.
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- 05. What are the results of the analyses?
A5. We would like to discuss the results of impact on the concrete structures and on the beams separately. First we address the impact on the concrete structure.
NASTRAN analysis for the concrete structures was conducted for zero concrete tensile strength and for 450 psi concrete tensile strength. The O psi value corresponds to the conventional approach in design which assumes that the concrete has no tensile capacity and hence tends to yiold conserva tive results with regard to concrete and steel stresses. Under laboratory conditions, concrete has been shown to have tensile strengths in the range of 8 to 12% of its compressive strength with 10% being an average. The 450 psi corresponds to 12.5% of the compressive strength of the concrete utilized in the analysis. It is used because it represents 10% of the actual minimum compressive strength of the concrete achieved at CPSES. Applicants recognize that for consistency, with the use of the 4000 psi design strength employed in the analyses, a more appropriate value would have been 400 psi. Further, it should be rdcognized that under actual field conditions, the chances of achieving perfect bond and continuity between various concrete pours and joints is considered to be remote, consequently it is not likely that the full potential tensile strength could be developed throughout the structure. Thus, 450 psi is considered to represent an absolute upper bound estimate of
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the tensile strength of concrete at CPSES. Applicants chose this value so that there could be no question on the conservatism of the reaction loads produced by constraint of thermal expansion of the beam restraints. Another beneficial effect that has been ignored so as to overestimate the reaction loads is the heating of the inner surface at the concrete walls surrounding the compartment during the accident. This surface heating would tend to introduce compressive stresses at the inner surface and tensile stresses at the outer surface. The latter could lead to cracking and additional relief.
The results of the analyses for the concrete structures are set forth in Table 1. As indicated therein, calculated stresses in the concrete and reinforcing steel for both O and 450 psi assumed values of concrete tensile strength are well below the conservatively established allowable for mechanical loads.4 The following interpretations should be placed on the values listed in the Table:
4 The allowable stresses indicated are conservatively based on
! loads which are mechanical type (non self-limiting) loads.
All the actual stresses shown are well within these elastic limits. However, when considering a load combination which includes a faulted, displacement limited effect such as the restraint of the free end displacement of the steel beam, a strain excursion beyond yield into the plastic steel, range is acceptable, provided there is no loss of function of any safety related system. When considering such self-limiting effects, the appropriate factor of safety is based on strain rather than stress; this is the basic philosophy behind the ASME Code NF-3231.1 not requiring any calculations to be made for such thermal ef fects on a steel support frame.
l 1
Max. Reinforcing stresses are tensile stresses.
Max. concrete. stresses are compressive stresses unless they are indicated as shear stresses.
Thrusts are positive if applied by the beam toward the i wall (compression in beam) and negative if away from the wall (tension in beam).
) Displacement of the wall at beam end is positive when i
beam displaces toward the wall and negative when beam displacos away from wall.
I
- 06. What about the impact on the beams?
A6. The primary purpose of the upper (and lower) lateral restraint beams is to provide restraint to the steam generator during a design basis accident due to the
] postulated breaks in the primary coolant loop and the amin j steam lines. The reaction loads from the breaks assumed in f the present analyses exist for less than 0.5 seconds, during which time the stress which is caused by constrained expansion of the beam following the increase of temperature within the compartment due to the pipe break, is negligible 4
(see Appendix I, Figures 1 and 2, Plots 1 and 2). During.
the time in which the constrained expansion stress builds up to its maximum (in the next few minutes), the beam has already served its primary function of resistin'g the broken
- pipe thrust.5 There are thus' two dif ferent stages to be 5 of course, even if.the thermal stress was coincident with the mechanical load, it could be neglected. See-FSAR (footnote continued)
- wr *-
T8BLE 1 Conc. Tensile Strength = 0 ps! Conc. Tensile Strength = 450 pst LOCA LOCA M.S. M.S. Notes' Peak Press. Peak Peak Peak Item at 0.5 Sec. Temp. Temp. LOCA Peak Temp. Tenn. See Footnote 5, p. 12 1 2
- 1. Max. Rober Stress (ksi) 22.0 13.7 17.1 11.4 14.06 20.7 Allowable Location (Element No.) (137) (1475) (1475) (1734) (1734) (1734) 54 ksi (.9fy)
- 2. Max. Concrete Compressive Stress (ksi) 0.83 0.91 1.23 1.21 I.41 1 88 Allowable Location (Element No.) (1023) (1389) (154) (2125) (2125) (2125) 3.4 ksi = .85 f'c
- 3. Max. Strain in Rober 0.00076 0.00047 0.00059 0.00039 0.00049 0 00071 Yield strain = .00207
- 4. Mex. Thrust Upper (kips) -2138 1591 2178 3892 3414 4918 Lower (kips) 156 2350 3210 2909 2868 3988
- 5. Total Expansion of .138/.099 !
.21/.14 .29/.19 .16/.06 .17/.06 .25/.08 Lateral Restraints Upper / Lower (In.)
Sa. Displacement At External .143/.046 .11/.06 .12/.08 l .07/.04 .07/.04 .07/.05 Wall End Upper / Lower (In.)
5b. Displacement At Reector .005/.053 .1/.08 .17/.11 .09/.02 .10/.02 .18/.03 Wall End Upper / Lower (In.)
1 - Analysis purposely excludes primary system seismic loads to maximize beam thrust.
2 - Analysis includes primary system seismic loads
i 6
considered. Initially the beam and walls will be exposed to the maximum mechanical loads. Later on the beam will impose the most severe thermal expansion constraint loads.
Applicants have analyzed the stresses in the beam at these two different stages: (1) when the mechanical loads peak at 0.5 sec.; (2) when the beam temperature peaks during LOCA.
The conditions assumed for the first stage analysis (simultaneous occurrence of maximum effects of mechanical (thrust), seismic, and differential pressure loads) are extremely conservative and bounding. The conditions shown for the second stage are also bounding as a result of imposing the most severe thrust expansion constraint.
Intermediate times would result in lower overall loads since differential pressure and mechanical (thrust) loads decay far more rapidly than the temperature rises within the compartment.
As previously stated two analyses have been in fact I conducted for the latter stage. One neglects the reactor systems seismic loads reacted by the restraint in order to J
(footnote continued from previous page)
Section 3.8.3.3.3, 2(b) which states, " thermal loads are neglected when they are secondary and self-limiting in nature and when the material is ductile." This steel beam satisfies these requirements and this is why the thermal loads were originally neglected. See also NRC Standard Review Plan, Section 3.0.3 (page 15T7 which also allows thermal stresses to be neglected. Even, if this support were classified as ASME-NF, the ASME's philosophy in this regard, is also to neglect such thermal stresses. See ASME Code Section NF-3231.l(c) (faulted condition) and also NF-3231.l(a) and (b) (no rma l , upset and emergency conditions).
i s
maximize the axial loads experienced by the beams. The other included those loads. Seismic excitation loads for all the structures (including the beams) are always included in the analyses for both stages.
For the steam line break analysis Applicants only analyzed the effects of peak temperature in compartment.
Since there is negligible differential pressure within the compartment from a main steam line break, the initial stage results would be bounded by the LOCA initial stage results.
The following Table 2 shows the stresses in the beam and clearly indicates that, even though the beam has already performed its function and is no longer required when the temperature reaches its peak, the stresses in the beam due to the peak temperatures are well within the allowables.
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I TABLE 2 Max. Stress In the
- Loading Condition Upper Lateral Beam Allowable Concrete Tensile Concrete Tensile Strength a 0 Strength = 450 pst
- 1) When mechanical load 18.4 ksi (not run) 45 ksi (90$ Fy) peaks at 0.2 sec.
+
- 2) When beam temperature 16.85' kst 22.75 ksI/16.3 ksi 45 ksi peaks during LOCA (7.1)** (13.0) "
- 3) When beam te,.perature 8.4 ksi 15.7 ksi 45 ksi peaks during M.S. line break
- 07. What do you conclude from these analyses?
A7. In summary, Applicants conclude that (1) the upper and lower lateral restraint beams are adequately designed; and (2) the stresses in steam generator compartment walls are well within the allowable stress and strain limits when the thrusts from the upper and lower lateral beam due to maximum accident thermal loads are applied to the walls.
Primary system seismic load contribution separately calculated and combined with other loads computed from computer analysis.
+ Computed by NASTRAN program when primary system seismic load is included directly in analysis.
Numbers in parentheses are results achieved when model is
-executed without primary system seismic load contribution.
e-y Robert C. Iotti Sworn to before me this 20th day of May, 1984.
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- J 4/6 NGtLDIEAR ANALYSIS & RC STRUCTURZ VITH Uff1RACTIGt >
& TMERMAL CRACXING AND MCRANICAL LOAD ,
E.5 CRANC, R ATKATSH
' Dasco Services. Ime. Two Rector Street, New York, NY 10006, USA
~
D N HERTINC
. Universal Analytic, Ios, 7740 West Manchester Blvd, Flays Del, CA 90291 USA '-
SUPMARY .
In resent years, finite element methods became a enjer tool ta the analyses of remeter concrete costaianeet and drywell structure of BWR type contaiammat. In these analyses, linese elastic mothed is acceptable for mechasiest loads beesuse the cracking of the concrete will met alter appreciably the strese distribution is the structure. Bewever, it breaks dews completely with the interacties of mechaai.
cat loads and high thermal leads, which is characteristic of containneet structure.
Usual practice is to adjust either the unterial property of the concrete before ....
the analysis or the solution after the sealysis. Complicated geometrical casfigura. ,
tion and thermal distributies make this kind of adjustaests act oely difficult, but its outcome unpredictable.
A series of flat shell elemoscs with coupled ta-plane stiffnees and off. plane ,
stiffness are formulated by using Kircheff's assumptions. These elements are divided tato layers along the thickaees, and each layer can have its own material characteristics. The crackings of the concrete are propagattag from layer to layer and free eteneet to elemmet. At each stage, the equivalent thermal lead vestar correspeeding to the currest material state are evaluated and seshined with external mechanical lead. The oeslinear soluties mothed used is a combiastice of se called variable stiffsees method and tattial strais mothed. This series of elements and nestinear* setuties methods are implemasted into the NASTRAM (NASA Structural Analysis) computer progree. Material assumptisee, formalattee of. the
. elemmets, criteria to estahtish creek opeatas and clostas, motheda to seestniset the thermal lead sed. eselinear lead, motheda to handle the Laternettee of thersest load and ancheetaal feed, see1 Laser iterettes ashese and soluties soeversease l'
- criteria, and composter progree configuration are discussed La the paper. Alse essaples to compare with experimental data and application to the sealysis are
! presented is the paper. A Loslinear finite element method is derived and taple.
seated to selve the prehles of interaction of thermal cracking and mechaatsal lead is reinforced coastete structure. The algoriths is designed to be effisiest for the solutiers of large. order and soeples structure, such as roaster seatstament.
and e11ainate the uncertainty is handling the thermal lead. Its results show that it cas predict. cracking propagation and stTess redistributies La resseeable agreement with available esperimental data.,
=g i
3
.\
9 I
- a. . .o . __ emme asy. .. we e se .
! p. . ,..e. . .
d 4 13-74.
>,- e
',, e o I Chang J 4/6 ,
- 1. Introducties In recent years, the finite element methol became a enjer teel in the analysis roaster soecrete sentainment and drywell structure of DWE type son-taianeet. In these aeslyses, the reinfersed seecrete is usually assumed to be linear elastis and homogeseaus. The stresses distributies characteristics,
~
such as off-plane shear, in-plaae forces, bending sement and twist, are obtained j from these analyses. Zhes, locally, the reinforced coesrete is designed as structurst members by following less established semi-empirical design method.
Under enternal mechanical lead, such as pressure and seisais lead, this proce=
dure is asseptable besseue the cracking of the seecrete will met alter appreciably the strees distributies is the seesrete. Bewever, it breaks deve sempletely ,
under the interesties of the therust and the amehasiaal leed, because the magnitude of the thermal etresses depend es the enterial of the seesrete (cracking), which is tura depeeds es the stress state is the seecrete. Zhus, they couple each other ess11aearly. Therefore, the stress characteristics ehtained from a linear elastic analysis does set represent the rest strees ,
distributies under the interesties of the thermal and the aoshanical lead. -
- To remedy this, the usual practise is te adjust either the ascertal property I of the seesrete before the analysis, er adjust the soluties after the analysis. ,
I 'However, for structures with semplicated geometrisat samfiguracies and templi-sated thermal distributies, this kind of adjustamat is met esly diffisult,
- but its outsame unpredictable. ,.
I yrom the above discussion, the analysis method for ttm reinfersed seecrete i
structures under the internaties of the thermal lead and the mechasiaal lead needs improvesess. In the past few years, the neolinear analysis of the see-
- l state structures gredcally gain asseptaase (1, 4, 3) . In these assitmane analysee, the meterial proporry of the senarece at each stage of leading see be assurately prediated and, thus, the therust lead saa be evaluated properly.
Furthermore, the advassement of high+ speed computer and astria manipulaties sof tware aske a, sealinear solut.ies of a large order structure model possible.
,i Is vies of the strigest safety requiremmate of sestaiammet structure and the-I uncertatacy of esisting analysis matheh ta dealing with the therent lead, s.
) eselinear saalysis for the interestime of thermal lead and the mechaatsal lead seems to be the answer, ,
In order to handle large. order and semples structure 1 models, met only a. ,
i.
valid sealinear easlysis prosedere but alae a large versatile finite element computer sede is. seeded. To assemplish thia, a series of flate layered shell elements and a. aselinear eenlysis prosedure are implemented into the semputer ,
i
/
- l i . . . . . . . . . . . . . . . . .
l
=>
l p. ,
l l
- l l .
l . ,
i 0
6
- _ _ _ . _ - _m - )
- ~ ~ ' -
, - ~ - . , . . . _ . -
. e 3
E Chang J f./6 code NASTRAN OtAsA stacture Analysis) Invet 16. The new elements are compatible with all other elemmets in the NASTRAN fasely. Input data reduction aed entrix easipulation are dose by standard NASTIAN. Special cessiderstica has been takaa to design the neolinear analysis algorithm se that it is efficient for i
- the solution of large-order and coepl'es structural models. .
.~
j 2. lavered Shell Element In geoeral, the stiffness entrix of a shell elemmet saa be expressed as m
(4 -4 M'H[>)= .
DI is the general-where L3 ). is the streia-displacement relation astrix and L4 3
, taad stress. strata relaties matrix. The 3,* astrix is a function of the
! geometrical shape of the elemoet and the assumed displacaneet shape function.
In this work, three new flat shelt elemoets have,been taplemented into NASTRAN.
The fotimalatieu of the (3 matrises of these three elements followed these In NASTRAN, the in plane of NASTRAN TRESC, TRIAL and QUADI elementa (7 and off plane stiffnesses are comysted independently. However, for the new elements, the is.plaae stiffness and off plaae stiffness are coupled. ,
Especially, for TRIA1 eleenst, which is a Clough triangle; the Clough's
! anthod of seestraint is antended to include the esupling of the in-plane and the off. plane terms.
The (D) escrix is a fuastion of the asterial property of the element only.
In evaluaties of the (D) entrix, the seesept of layer finite elements are adopted La this work. A typical layered element is shows in Ff gute 1. Each layer of the element is serresponding to a unique asterial property which any be defined indepeedestly or shaesed to a new asterial property as the ase-linear analysia progresses. Although the stress any be differest free one potat to asether in the place of each layer, it is assumed to be seestaac throughest the thiakness of the layer. For aselinear ,asterial, the asterial
! property of as layer is assumed to be a. fuesties of' the average stress is that tayer.
ror asterist eeslinearity, the (3} entris a inde,eedent of the asalinear behavier of the element. In order for offisteet asecuties of larger order ettustural model, the (3) anterial is sesyused outside of the maaliseer itera-ties leope aos stored en a readen file, whiek will be read best to generate the stiffness matria, equivelaat therust lead,. and unbalassed lead vester.
- 3. Meterial Preserty and '*mtitutive Relatione s Cesarece La seasidered to be a. linear elastia brittle anterial with s.
limited tensile strength fg. The reinferslagL steel is emesidered linear elastis. The fatture criterten for seeerste under ht astal stress state is.
shout ta Figure 2. The dested line is propeeed by Napper. 311sdorf and l
I l
, e -
l I
. e e e e *
, gg J 4/6 Rush (3 , and the solid 1134 is used la this analysis. The coocreta is too.
sidered cracked in Regione I, II and III. Since the matorist property of a layered element any be differest from ces layer to another, each layer has its o.e e tre.s .tr.a r.l. ties.. n ... c.lacios. = a he ,rses.d a.
~
1,1-[C]l.) m l
.here { I -1 ,z , ,y ,r}T i.a1.yer.tre..,ee= reed 1.l-l.,,ay,yjT is a layer streia voeter. Before erssking, the coen rete la considered to be homogeneens and isotropia, the (C) matrix is the sovel' isotropic elasticity ' )
matrix. For eenerete with one creek, the C estria La
.. 0 0 0 , .
C
==
= T(0) T 0 I. O T(# (3) 0 0 #Ge where Eg is the Young's modulus for soecreta sed *G g is the sheer endulus.
- is a shear retention esefficient assaveted for abgregate interlocking effect ;
of seecrete (1). (T(#)) is a transformation astrix from the coordtaate eyetem normal to the creek te the element coordinate system (Tigure 3). For concrete ,
with two cracks, in Region III of Figure 2, the C is assumed to,be identically sero. For reinforsenset, the C]astriais 4 0 0 C = T 0 0 0
'(T(3 (T(# (4) 0 0 0 where I g is the Youag's modulus for steel and (T(f) is the transformation matria from the coordinate system taegential to the reinfersing bar to the element coordinate.
As defined in Eq (1), the element internal force vector is related to the generalised strais vector by the (D astria, lTl =(D {Al (S) wher*lFl*lTaeTeFayeMmeMeMay}Ie y y Is, T , Tg y are membrase forces and Me, My, Mry are saments, l A l -l e , e,y, y, 23 , 27 , ray jT , . , . y, y, are strelas ac mid-surface of the element. In order to relate- the -layer strata veeter {* } and the element strata vester lAl, the Kircheff assumptions are used. The Kirehoff assumption can be empressed by 11
.'n'IAI m
L .0 0 -s 0 0 (t = 0 1 0 0 -s 0 j
0 0 L 0 0 -e I i .
O a . e. e e .. 8
- l
. l i
4 s
J 1
I Chang - J 4/6 where a is the location at which the strata vector {el is evaluated. Isow, the matrix can be evaluated by the equation, (D
~
m
[n] -[ [a]'[c][n] de ,
4 Chassina of Material State l
Staae the anterial state of a concrete layer is a function of the stresses
. and stratas in that layer, it v111 change from one stata to another as the moslinear analysis progresses. Dere are three major modes of changing states l 1) the formation of a new crack;
- 2) the sleeing,of an existing crack; l
I
- 3) the ,reepening of a closed creek.
Mode (1) is the only mode dealt by nest investigators (1, 4, $], and it is applicable to a monotonically increasing loading. Mode (2) is essential if it is to investigate the structural behavior imeluding the interaction of the thermal load and the mechanical Isad. In order to reduce the amount of book =
l keepias, it is assumed that mode (3) is identical to mode (1) is this work.
Bis assumption is true if the tensile strength of concrete is sero. Im visw -
that the tensile strength of concrete is small and that it is of teg neglected in most engineering saalyses because of its uncertatacy, this ass.ampties is a good approximaties.
De criteria, for the forestion of new crack is based os the layer stressess. a layer will crack if the computed principal teostle stress exceeds the teasile strength of the concrete specified La Figure 2 i.e. ,
- t D i t (8)
~~
where at is the everage principle stress of the layer and ff is defined by l, the solid lima La Figure 2. De normal of the crack is assumed to be is the .
principal tessile direction. De criteria for the closing of as existing crask is based os the layer strains: as amisting crask. will close if the everage
- layer streia aerust to the existing sreak becomme equal er less than sess, L.e.,
. sa +> sego if. o g < fg/ Eg ,
m e.S o it s e h ff / t.
where o gis the strata taaseettal to the existing. crack and
- is the Poisses ratio. De prosedisre to- evaluate the changing of asterial stats- for seek layee is preseeded as follever -
.) c.s., ate tae layee strata. br
. I'l - [n] [5] {=1 -l=1r .
(Io) 8 3
4 I
~
_ M 7 .~_-W' w
. . ,, , , . .. - . 1 E Chang J 4/6
, where fuf is the displacement solution vector of the current iteraties for .
the t.urrest element, of, the theras1 azpaesies coefficient vector and T.
ee la,er t p.r.t.re.
b) If the layer has existing cracks, the cesputed strains are tested
, , assinst Eq (9) to fers as latermediate new layer stress. strain relaties (C 1,
, L....
existina cracks cleetne? ;[C (11) where C, is the current layer stress-strain relations built into the global stiffness matrix, which is used to ehtain the displacement soluties vector uf.
=
c) If as existing treele la the layer, let (C g .
d) Based es the new.. layer stress. strain relaties (Ct ] . the layer stresses l are computed and tested against the criteria specified by Eq (8) to form the '
final new layer stress-strata relaties (C2] ~
(Cg] "" ; (C2 (12)
- 5. Eeutveleet Thermal taed vector The egetveteet thernst lead vester is dependent on the material pre.
party of the element.-
Withthenewmaterialpropertydefinedbythe(C] 2 ,
astriz et Eq (12), the equivalent thermal lead vector for the new material ,
is evaluated by KT e T(s) da da ff f =
t (3 (C2 (13)
- 6. Monitasar ,selueime Method Generally, two iteraties methods are available in the finite elemmat-method for the soluties of material ses11aear problems:. the so-called vertable stiffness mothed sed the fattial stress /streia method (9]. For variable stiffness mothed, a soluties is first obtained by the tattial lianer system. Based en thie soluties, the material state of each element is- updated, and a seis soluttes is obtained with the regisest lead voeter and the new material state. This prosess aestimaas until the- change of asterial state.
I of two consecutive states are suffisteetly sen11. For the initial stress /
1 streia method, the origiant elastic system stiffness is kept unaltered. At i a
esek itetettaa, the differsees between the element stresses > uttok are see. l sisteer with the surrest enterial state and the element stresses uhich are La equilibrius with the entennel leads are salted the unbalassed stresses.
Freer these sabelaesed stressee, the equivalese uebelaesed lead voeters are s
G 4- *
._- . -. -. _-_ __ . _ _ _ _ _ _ - . -_ . . - . - - -- 2
- **. .. . 6' 3 \- . . .
.e e -
., I Chang '
J 4/6 found. Then, a new solutium is obtained with these additional unbelsaced load vectors and the origiini 11amar system stiffness matria. n is process coe.
tirmane useil the change of unbalanced vector is negligible. The variable stiffness mothed has the deficiency of reassembling system stiffness at every itersties. This process is expensive. On the other hand, the initial stress /
struir meet.od has the deficiency of slow coevergense. In this work, a cam-binaties of both methods are used, and ca iteraties equation can be empressed l
(14)
(K.)uElf=f. .
+ fi,+f ;
share is the updated system stiffnads astru, r is the external load vector, f is the therust load vector based'ea.the current material state and f , the unbel.soced load vector given by m)
M-(I W L [=F NNM' Md PI .
where(C and (C,) are the stress / strain relation for the new material state (Eq (12)) and the state built into the currest system stiffness matria (K,], ,
respectively. De convergence criterion adopted are gives by ff3.f*,
3 fuh 43 %
rkub \
>- t.I 3
where ff f La total load vector on right-hand side of Eq (14) and 4 is a sufficiently ses11 samber. ,
- 7. 1 AsT11 Alt Imelementation -
The implementation of. the' cracking, analysis algorithm in NASTRAM requires only Laelated interisess, to the progra'a due to NASTIIAN's sedular design. Itat of the now solution iteration prosedure code are isolated to .
five new modules, which useo assy of the esistf.4 NASTRAK metria suhroutines.
- A brief description. of asch module appears belas:
a) Funscios Module CAgrg, (strais Mattiz Genersty-)
\ .r Generatestheelemmer. stress-straisrelatiene(3. This module is f
outside the iteration loops and store etw (3 estrix'on reados assess,filee called C&G" (Creaking Analysis Operaties Tile). These data will be used '
inside the iterstian loops to sempute thermal lead, element stresses and unbalanced lead vesters. .
. b) yunction Moduit CAUTIL (Crasking. Amatysia Utilities) .
Performa ett11ty fuastion susk a6. estrasting data freer car ist
\
previous material states and assemblind partise vectors for erlete CAITN1 (deoertbed below). '
s \ -
l l
, , ( !
s e
's \N , [
I % %
d
- * '\
.. 7 I i .
- g
. _ s *
. . }.
1 v
l
. A ,
-- - . - v + - . .. . . , ,. . ,, , , , ,l o* a 9e O
O E Chang . I 4/6 .
c) Tunction Module CAEW (Element Stiffness Generator)
Generates the seu element stiffness matricas.
d) Functional Module CAITER (Crock Analysis Iteration)
Generates the see11aear thenent twt vector and the unbalanced lead vector and perfores the unbalassed load iteration. '
e) Function Module C&OrF (Cracking Analysis Chitput Processor)
There are two itarecies toeps; the outer loop is called the stiffness iteration which updates-the system stiffeese se the left-hand side of Eg (14); ,
I the Laser loop is es11ed unbalanced load iteration which iterates the right.
hand side of Eq (11) with seestaat (Ke] . The stiffness iteresien is imple-mested by usian; the NASTIAN DMAP '(Direct Matrix Abstracties) control language
[4. Itsdale CA1 TEE perfores' the unbalanced toed iteration. , It recovers the
' stresses' evaluates aseliseer'estarial state, geserstes thermal load vector and unbalanced lead voeter, tests for convergence, and setting of parameters to control DMAP esecution. The CasMG module resides outside both iteration loops.
- 8. Essasle Problems .
a) McNeice's y1ste The McNeice's plate- (2j is a 36 inch square by 2 inch thick supported at four corners. It is a two-way slab with 0.85T. reinforcing bars. A consee=
trate force is acting. at the concet of the plate. Figure 4 shows the finite eteneet grid and the load deflection-curves free'emperisestal and computed l results for point 2 on the plate.
! b) Infinite long. Cylindrical Shell Under Thermal Lead l
71gure- 6 shows & cylindrical shell of 15 feet inside radius and 1 foot thickness with two-way reinforcing bar at outside face of the cylinder. It has .
I a as. built temperature of 508 T. This temperature grows. to 170* T outside of the cylinder and 808 T inside of the cy11ader. The results of classical theory and this analysis era shouet in Figure 4 The ses11 discrepaaey is creaking distance ,
- and the ameuet of Laeressing iar radius is due to the assumptiour that stresses are coastaat throughout the thiskaess.,of a layer.
s D
an l
O
! I l
4.-
. s.. , . .. .
1
. .o '., .~. . . .. ,. , ,
z .. ,
I Chang- J 4/6 References 1 BAND, F.1., FECENCID, D.A., SCENOBRICE, D.C., "Noelinear layered Analysis of RC Plates and Shells " JOURNAL & THE STRUCTURAL DIVISION, July, 1973.
. 1 JWRIII, J.C., McNEICE, C.M., " Finite Element Analysis of Reinforced Concrete Slabs," JOURNAL & THE STRUCTURAL DIVISIM, ASCE, Volume 97, No. ST3. Proc. Paper 7963 March, 1971, pp 785-406.-
- 3. EUFFER, R., II1JDMF, E.E., RUSCI, I., " Behavior of Coocrate Under 31sxial Strasses," JOURNAL & TEE AMERICAN CaecR.! !E IN*TTIUTE, Volume 64, No. 8. August,1969, pp 656-666.
4 VALLIAFFAN, S., D001AN, T.F., "Noolinear Stress Analysis of Reinforced Coocrate," J0llRNAL & THE STRUCTt2AL DIVISIGf, ASCE, Volume 98. ST4, Proc. Paper 8845, April,1972, pp 883-894. -l 3 FRILLIPS, D.V., ZIENKIEWICE, 0.C., " Finite Element Noelinear Analysis of concrete Structures " Proc. Imeta. Civil Engineers. Fort 2,1976, ,
21 March, 59-84. -
6 'RENTINT, D., HERENDEEN, D. , HMSLEY, R., CHANG, H., "Impleenstation on a Nonlinear concrete Cracking Algorithm in NAST3AN." Fif th NASTRAE User's Colloquium, Amers Research Center, October 5-6, 1976.
7 NASA SP-221(03), "The NASTRAN Theoretical Manual Level 16.0."
8 NASA 57-222(03), "The NASTRAN User's Manual Level 16.3."
9 ZIENKIEUICE, 0.C., "The Finite Elemoor Method in Engineering Science,"
NcCraw-Hill, 14 ados, 1971.
I i
e i
l M
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+
6
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~
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l l
4 Reference Coord{nate System Origin o
a y*
9 86 b, c
- grid points 6.A.A a offset vectoM s -
3 b c.
e' .
e
~
FIGURE 1. TRIAHoutAR 1AYERED 3tEMENT ,
0*
e 4
e e I o
e e, 4'
_____L____._____-- - - _ . . __
a- . .
'2 A
. II III ft g.. ~
i* ~~~~
m fe - fe et,'2: Principal Stress-t r
' f:
jj et t Tensile Strength
. .f
/ l f: Compressive Strength C
/ I l
/ I : Used in this work I
Suggested by Ref 2
/ II ----:
l i l i i !
I I I
\ /
\
\ ,
% /
% / i
%, ,e s .,,,.- -
~- 1 1
i EIGURE 2. CCMCRETE FAILURE CRITERIA UNDER BIAXIAL STRESSES 9
9 l
= - ' * *
- s ,
p'-
e "e* .,
- e
- O e *1, . * . . .
9 _,
9 g
w e
9 O
O e
. /
i 1
7 N x n es
~
~
e w
,h ,
0 L_
, - x _ _ _
4 FICURE 3. IAYER STRESSES IN CWCRETE WrIH' WE. CK l
1 1
~~ ~
.. . f, . ;.- ,
14 21 28'35 , 42. .g.
.- 4 -
A
. 49 7 .
E
! 6 48 I
e = 1.75"
~
d = 1.31" 5 47 E_ ff=550 psi 4 g 6
. E, = 29 x 10 p,i 45 3
6 Ee = 4.15 x 10 p,t
~
2 44
- = 0.15 P. . . = . . .0;0085 , . .:. .
8 15 22 29 36 43 ASSUMED ,
APPLIED CGIC.
fg = 770 psi p
't, .
=
-ASSUMED [LOUIR SUPPORT AT FOUR CORNERS
, 7 .
M V 18" 18" J
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'UOO i 1 1 I 1 I I I I I I I I l 1 1 I
- /
/
3200 f
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2400 - G f
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$ .1600 p' Experim atal
/ G Theoretical -
f
- - Theoretical, _
- 800- / Linear
/
I I i '! I l_ I I I I I I I I I I 0 4 8 12 16 20 24 28 32' 36 DEFLECTIGE (10*2 inch) AT POINT 2 t
FIGURE 4. McNEICE'S PLATE. ,
.e
.e .~ . . . ,. . '
- 4 .
~
' 0*
9 F
'p, 5
o \. E = 5.24 x 10 hf 17 0 F i \, Es = 4.32 x 106 ks f
'.. M=0 A A i fg . o
= 0.55 x 10-5
{' J- 15' '
~
l / ase a = 0.55 x 10-5 j To = 50 F s.
s'
\ / l
\ .
l
.125' 0.875'
- ' ~
CT.ASSICAL 3 , .
THIS ANALYSIS TsE0ay z ..-
Ae -
Growth of Radius 7.31 x 10-3 fe 7.49 x 10~3 fe 4o .
81 0 3... Stress in Reif. 1058 psf 1059 psf a u s*- Mr 9 O > .-
.. o ,.
T g .a-. . , Max Stress in 98.4 psf 98.4 psf -
8 . Concrete-a 8 O
- e. .
g '
MM Cracking Dis- 0.6 ft 0.621 ft
-k 8 , , . tance C
\ .
9 Io.,y O sfs -
.,s._ _ .. , _,
b CRACEED ZONE SECT. A-A FIGURE 5 INFINITE CYLINDRICAL SHELI. UNDE 3L THERMAL M r
- ~ . .: -
- - - - ^
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