ML19319D710
| ML19319D710 | |
| Person / Time | |
|---|---|
| Site: | Crystal River, 05000303  |
| Issue date: | 08/10/1967 |
| From: | FLORIDA POWER CORP. |
| To: | |
| References | |
| NUDOCS 8003240707 | |
| Download: ML19319D710 (10) | |
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APPENDIX SC
() DESIGN CRITERIA FOR REACTOR BUILDING 1 GENERAL The prestressed concrete Reactor Building vill be designed to have a low strain, elastic response to all conceivable loads, thereby ensuring that the integrity of the vapor barrier is never breeched. The intent of the design is also to provide a mode of failure in a ductile rather than a brittle manner. The design vill be further based upon various combina-tions of factored loads that are based upon factors by which loads are increased to approach the limit of an elastic response. These factors are developed in a similar manner to the Ultimate Strength Design provisions of ACI 318-63, where factors are applied for those factors outlined in the
" Commentary on Building Code Require-ants for Reinforced Concrete," ACI 318.
In the case of this design wherein a more exact analysis is performed than contemplated by ACI 318, the load factors primarily provide for a safety margin on the applied loads. The Reactor Building vill be analyzed to ensure proper performance of all components including the liner, concrete shell, and reinforcement under the following loading conditions:
- a. During construction but prior to prestressing
- b. During prestressing
( c. At normal operating conditions
- d. At test conditions
- e. At factored loads 2 METHOD OF ANALYSIS The shell of the Reactor Building vill be analyzed to determine all stresses, moments, shears, and deflections due to static loads, including temperature effects, by technique 3 developed by Dr. Arturs Kalnins of Lehigh University, Bethlehem, Pennsylvania. These techniques are developed for the general problem of deformation of thin elastic shells of revolution, symmetrically or non-symmetrically loaded, and with the development of a nunerical method of its solution employing a modified form of the direct integration techni-que for the exact numerical solutions of the general bending equating.
2.1 STATIC SOLUTION 1
The static load stresses and deflections that are in a thin, elastic shell of revolution are calculated by an exact numerical solution of the general bending theory of shells. This analysis employs the differential equations derived by E. Reissner and published in tha "American Journal of Mathematics,"
O 0239 5C-1 (Revised 1-15-68)
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1 Vol 63,19hl, pp.177-18h. These equations are generally accepted as the standard ones for the analysis of thin shells of revolution. The equations given by E. Reissner are based on the linear theory of elasticity, g and they take into account the bending as well as the membrane action W of the shell.
The method of solution is the multisegment method of direct integration, which is capable of calculating the exact solution of an arbitrary thin, elastic shell of revolution when subjected to any given edge, surface, and temperature loads. This method of analysis was published in the " Journal of Applied Mechanics," Vol 31,196h, pp. h67 h76 and has found vide ap-plication by many engineers concerned with the analysis of this shells of revolution.
The actual calculation of the stresses produced in the shell and foundation was carried out by means of a computer program written by Professor A. Kalnins of Lehigh University, Bethlehem, Pennsylvania. This computer program makes use of the exact equations given by E. Reissner, and solves them by means of the multisegment method mentioned above. The program can solve up to four layers in a shell and these layers can have different elastic and thermal properties and can vary in thickness in the meridional direction.
Applied loads can vary in meridional and circumferential directions.
2.2 DYNAMIC SOLUTION The stresses and displacements of the response of a shell of revolution to the excitation of an earthquake can be calculated by superimposing the normal modes of free-vibration of the shell. The modes of vibration are calcualted by means of the general bending theory of shells derived by g E. Reissner. The translatory inertia terms in the normal, meridional, W and circumferential direction of the shell are taken into account. The mass distribution is the actual mass distribution of the shell and no approximations are made. E. Reissner's shell theory is such that it predicts exactly the complete spectrum of natural frequencies of the shell without any approximations.
The differential equations given by E. Reissner are solved by means of the multisegment direct integration method of solving eigenvalue problems, which van published by A. Kalnins in the " Journal of the Acoustical Society of America," Vol 36, 1964, pp. 1355-1365 According to this method, the eigenvalue problem of a shell of reyclution is reduced to the solution of a frequency eauntion which vanishes at a natural frequency. The frequency equation consists of exact solations of E. Peissner's eauations, and no approximations'a're nade.
The calculation of the natural frequencies and the corresponding mode shapes of each mode of free-vibration is performed by means of a computer program vritten by A. Kalnins. Tne computer program has been used for the calcula-tion cf the dynam;; characteristics of many types of shells of revolution and its results have been verified with experiments en many occasions (a listing of previous applications is attached). The program calculates the natural frequencies of any rotationally symmetric thin shell within a given frequency interval and gives all the stresses, stress-corresponding to a natural frecucacy. consultants and distlacements at any prescribed point on the meridian of the shell.
SC-2 (Eevised 1-15-68) 0240
1 The normal modes of free-vibrfttion need only be added in order to construct
, the response of the shell to an earthquake. The relationship between free-(Q, ' vibration and a given excitation is given by the following equation:
n Ci Svi Y(x,t) =
[i=1 Yi(x) Wi Ni where Y(x,t) = fundamental variables of the response Yi (x) = fundamental variables of the ith mode Ci = constant for the i mode Wi = natural frequency of the i mode Ni = constant for the ith = ode Svi = maximum velocity from the response spectrum for a single degree of freedom system for a given value of Wi for the ith mode For analysis purposes the Reactor Building shell is divided into structural parts, and each part is divided into a specified number of segments as shown in Figure 5C-1.
p The Static Analysis and Dynamic Analysis have been used by the following L/ companies for the analysis of thin shells:
- 1. Martin Company - Orlando, Florida
- 2. Pratt and Whitney - Aircraft, East Hartford, Conn.
- 3. Central Electricity Generating Board, - London, England The Static Analysis has beeri evaluated by H. Kraus, in Welding Research Council Bulletin, No. 108, September 1965.
The Dynamic Analysie was described and its results compared to experiment by:
J. J. Williams, " Natural Drought Cooling Towers - Ferry bridge and after," in the Institution of Civil Engineers publication, 12 June 1967.
The large openings, including the opening for the equipment access hatch and the isolated personnel lock, will be analyzed on a preliminary basis using normal elasticity methods for a reinforced hole in a plate subjected to plainer stresses. The final analysis vill be on the basis of the finite element technique taking into consideration surface and concentrated loadings and the temperature distribution through the element thickness. The method to be used will be that developed by the Franklin Institute Research Labora-n) m 0241 SC-2a (Revised 1-15-68)
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1 tories wherein the element consists of a four-cornered cylindrical panel with the stiffness of each element lumped at its four corners. Equili'orium equations of the corners are written considering five degrees of freedom (three of displacement and two of rotation) to detemine corner displace- h ments, which are in turn used to evaluate stresses within the element.
The none.xisymmetric loads imposed upon the Reactor Building base slab will not have a contributing influence upon the design of the shell; therefore, the foundation slab vill be designed for nonaxisymetric loads by considering a circular slab on an elastic foundation.
O 024?
O SC-2b (Revised 1-15-68)
.f 3 LOADING STAGES
!,y 3.1 DURING CONSTRUCTION BUT PRIOR TO PRESTRESSING The Reactor Building vill be designed as a conventional reinforced concrete structure subjected to dead, live, vind, and construction loads with allowable stresses in accordance with the limits established by ACI 318.
3.2 DURING PRESTRESSING The Reactor Building vill be designed for prestress loads and will be checked to insure that the concrete stress vill not exceed .6f's at initial transfer.
Stresses due to shrinkage, creep, and elastic shortening of concrete vill be taken into account, and flexural creep t ending to relieve bending stresses vill also be considered. All remaining stresses will be in accordance with ACI 318-63, Chapter 26.
33 AT NORMAL OPERATING CONDITIONS The loads due to normal operating conditions are:
- a. Internal pressure of 2 5 psi less than. atmospheric
- b. Operating temperature transients
) c. Dead load
- d. Live load
- e. Prestress load
- f. Seismic load
- g. Wind including tornado load The stresses in the concrete and reinforcing steel resulting from these loads vill be in accordance with ACI 318-63, Chapter 26. The stresses and strains will be such that the integrity of the liner vill be maintained.
3.h TEST LOADS The Reactor Building vill be designed to function under the following loads at test conditions:
- a. Internal pressure of 1.15 times accident pressure t
- b. Dead load
- c. Live load
~h (o 0243 5C-3
- d. Prestress load
- e. Te=perature transients at test conditions The allowable stresses will be in accordance with ACI 318-63, Chapter 12 and 26.
The vessel vill be adequately instrumented to verify, during the pressure test, that the structural response of the principal strength elements is consistent with the design.
3.5 AT FACTORED LOADS The building vill be checked for the factored loads and load combination given in Appendix 5A, and compared with the yield strength of the structure.
The load capacity of the structure is defined, for our design, as the upper limit of clastic behavior of the effective load carrying struct' tral materials.
Forsteels(bothprestressedandnon-prestressedhthislimitisconsidered to be the guaranteed minimum yield strength. For concrete, the yield strength is limited by the ultimate values of shear (as a measure of diagonal tension: and bond per ACI 318, and the 28 day ultimate compressive strength for flexure (f'c). A further definition of " load capacity" is that deformation of the structure which will not cause compressive strain in the steel liner plate to exceed 0.005 in./in., nor cause average tensile otrains to exceed that corresponding to the minimum yield stress.
The load capacity of all load carrying structural elements will be reduced by a capacity reduction factor ($) as stated in the basic structural design criteria. This factor vill provide for "the possibility that small adverse variations in material strengths, workmanship, dimensions, control, and degree of supervision while individually within required tolerances and the limits of good practice, occasionally may combine to res' ult in under-capacity" (refer ACI 318-63, p.66, footnote).
tienbrane tension of 3 Yr5 vill be allowed in checkins; the load capacity strength of the structure. When principal flexural tension when combined h with the nenbrane stresses due to all loads exceeds 6 Vf'c due to thernal gradients through the vall, non-prestressed reinforcing shall be added to reslSt the ther: al stresses based on cracked section theory similar to that centainei in ACI 505. W s- velues are chosen vith a conservative narrin acainst cracking (rodulus of rupture) beenuse of the rossible reduction in tensile ntrencth at construction . Mints, iiovever, the construction joints vill be treated so that either curricient natural bond is obtained er a suitable 1 ondine acent will' tie used to gain the required continuity.
The crackine limit of the concrete in principal tension vill be governed by the allevable values of the shear as a measure of diagonal (principal) tension. The allowable shear values will be as follows:
02 0 g SC L (Revised 3-lh-68) c h (fjy
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- a. When membrane tension exists.or when membrane compression is less than 100 psi, the section vill be designed to the ul-timate shear ' provisions of Chapter 17 of the ACI Code 318-63.
Where shear reinforcement is required sufficient prestressed "
force remains in compression or zero tension so as to result in a condition analogous to that covered in Chapter 17
- b. When membrane compression of greater than 100 psi exists, the principal membrane tension vill be limited by the ulti-mate shear provision of Chapter 26 of the ACI Code 318-63.
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.._1 45' 0" 4 ' 0' PART NO.1 85EGMENTS
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OPEK TfP. SECTION THAU WALL 100uE
,y REACTOR BUILDlHG SHELL SEGMENTS
- \s) PART NO.3 PART NO. 2 _
CRYSTAL RIVER UNITS 3 & 4 2SEG. 4 SEG.
lll"L FIGURE SC- 1 AMEND. 7 (715 49)