ML20090H180
| ML20090H180 | |
| Person / Time | |
|---|---|
| Site: | Waterford  |
| Issue date: | 10/12/1983 |
| From: | Bouchet A, Du Bouchet, Harstead G, Unsal A HARSTEAD ENGINEERING ASSOCIATES, INC. |
| To: | |
| Shared Package | |
| ML20090H172 | List: |
| References | |
| 8304-2, NUDOCS 8310280006 | |
| Download: ML20090H180 (104) | |
Text
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H f HARSTEAD ENGINEERING ASSOCIATES
- INC.
169 KINDERKAMACK ROAD, PARK RIDGE, N.J. 07656
- Phone:(201)391-2115 WATERFORD III SES ANALYSIS OF CRACKS AND WATER SEEPAGE IN FOUNDATION MAT -
LOUISIANA POWER & LIGHT COMPANY REPORT No. 8304-2 OCICBER 12, 1983 .
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O Prepared by: 04 L ?&-
A. V. du Bouchet Reviewed by: 5A A. I. Unsal Approved by:
. A. Harstead 8310280006 831020 PDR ADOCK 05000382 A PDR
TABLE OF CONTENTS
! 1.0 Introduction 1 2.0 Ebasco Basemat Computer Model 2 3.0 Finite Element Model Geometry 3 3.1 Drawings and Plots 3 1
3.2 Basemat Finite Element 3 .
3.3 HEA Benchmark Run 4
~3. 4 Benchmark Shear and Moment P_ lots 5 3.5 Simulation of Shield Building Wall 6 4.0 -Loads and Load Combinations 7 4.1 Dead and Seismic Loads 7 4.2 Load Combinations 8 (Chs 5.0 HEA Computer Analysis 9 D
5.1 Basemat Shear'and Moment Capacity 9 5.2 Analysis Review Criterion 9 5.3 Analysis Shears and Moments' 11 5.4 Plots of Analysis Displacements 14 5.5 SRSS of Basemat Shears 15 t"
6.0 Discussion of Results 17 6.1 Comparison of Results with Previous l Analyses and Design 20 6.2 Effect of Cracking on Structural l Response 20 l
[ 6:3 Conclusions and Recommendations 21 REFERENCES 24 l
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4 TABLE OF CONTENTS (Cont ' d . )
Appendix A Fig. A-1 Waterford 3 Basemat Plan at E1 -41.0 (nodes numbered)
Fig. A-2 Waterford 3 Basemat Plan at El -41.0 (elements numbered)
Fig. A-3 Waterford 3 Elevation A-A Fig. A-4 Waterford 3 Elevation B-B Fig. A-5 Waterford 3 Elevation C-C Fig. A-6 Waterford 3 Elevation D-D Fig. A-7 Waterford 3 Elevation at Col Line T2 Fig. A-8 Waterford 3 Elevation at Col Line 1FH Fig. A-9 Waterford 3 Elevation at Col Line 7FH Appendix B
, HEA Calculations Appendix C Fig. C-1 Directions for' Direct Stresses (w/ 2 pp. enclosure)
Appendix'D l
Fig. D-1 Common Foundation Mat - Plan at El 35.00 ft Fig. D-2 Shear Curves - Section B-B Fig. D-3 Moment Curves - Section C-C (w/ 6 pp. HEA Calculation)
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TABLE OF CONTENTS (Cont'd.)
Appendix E Fig. E-1 Plot of Normal Displacement
- Normal Operation Fig. E-2 Plot of Normal Displacement
- D.B.E. West East Fig. E-3 Plot of Normal Displacement
- D.B.E. North South Fig. E-4 Plot of Normal Displacement
- D.B.E. South North O
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r l.0 Introduction This report summarizes a study undertaken by Harstead Engineering Associates (EEA) on behalf of Louisiana Power and Light Company to evaluate the structural adequacy of the Waterford 3 Nuclear Power Is26nd Structure (NPIS) basemat.
The following major evaluation items are addressed in this report:
a) The geometric criteria employed'by Ebasco to fornu-late the finite element model used to evaluate the structural adequacy of the basemat; b) The magnitudes and distribution of the loads em-ployed by Ebasco to evaluate the structural adequacy of the basemat; c) A benchmark comparison between an initial HEA test
, run (in which only the finite element used to model (h the basemat is revised) against the comparable Ebasco basemat computer analyses; d) A detailed comparison between a final HEA computer analysis and the corresponding ba'semat shear and moment capacity.
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r 2.0 Ebasco Basemat Computer Model The finite element model and the corresponding loads and load combinations generated by Ebasco to perform a
- . structural analysis of the basemat were transmitted by Ebasco to a permanent HEA file (on'a computer system operated by-United Information Seriices) on September 1, 1983.
Additional supporting documentation which describes -
the formulation of the geometry and the loads used to analyze the basemat is found in References 1 - 3.
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i 3.0 Finite Element Model Geometry i 3.1 Drawings and Plots The extent of the finite element model of the base-mat and additional structures modeled by Ebasco is detailed on a series of five Ebasco drawings (References 4-8) , which show the plan cf the basemat, as well as additional plans and elevations of floors and walls lo-cated above top of mat.
In order to confirm the modeling s'hown.on these drawings a number of computer plots were executed and are contained in Appendix A: the plan of the basemat at .
elevation -41.0 ft (one plan with node points numbered, one plan with elements numbered), elevations A through i D, and elevations at column lines T2, 1FH and 7FH.
I 3.2 Basemat. Finite Element
- i The STARDYNE computer code used by Ebasco to per-form the structural analysis of the basemat enables the use of two types of triangular plates.
( As noted on page M-60 of Reference 9, "Two types of triangular plates are available:
f (1) A linear curvature compatible triangle l which simulates thin plate behavior (without consideration of transverse shear effects) j for non-sandwich structures (see Reference A (1)) and (2) the " Martin" element which simu-lates thin or thick plate behavior in a sandwich or homogeneous (solid)" structure. The
" Martin" plate must be used when transverse shear effects and/or transverse shear stresses are desired. A denser nodal grid mesh is desirable with this element. See Reference
- A (2) , page M-200".
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, 3.3 HEA Benchmark Run In order to confirm the validity of the basemat internal shears and moments obtained by Ebasco using the
- thin plate (type 1) element, a benchmark run for the load combination designated as " South to North Design Basis Earthquake" was executed. See Section 4 for a de-tailed discussion of the loads and load combinations used in the analysis.
This HEA benchmark run contained the following two revisions to the input geometry:
. a) the " Martin" plate element was used to model the basemat; b) the local coordinates of a number'of finite ele-ments contained in the basemat were. rotated to become parallel to the global coordinate system of the basemat, in order-to facilitate interpre-tation of the output shears and moments.
) Page 1-4 of the HEA calculation contained in Appendix B shows a typical basemat element, describes the formula-tion of the local coordinate system for that element as a function of node point order (connectivity) and de-( fines the global coordinate system used to reference the locations of the node points.
, Pages 1-6 through 1-8 of the Appendix B HEA calcula-tion tabulate the identification numbers of the basemat .
elements having their element coordinate axes rotated
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i parallel to the global coordinate axes, and the respec-l l tive angles of rotation.
Page 1-5 of the Appendix B HEA calculation defines the positive sense of the membrane forces Fx and Fy, the transverse shears Fxz and Fyz, and the bending moments Mx and My with respect to the element local coordinate a' axes. -Note that the positive sense of the transverse 4
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shears Fxz and Fyz, as shown on page 1-5, is opposite to the definition given on page M-70 of Peference 9.
The letter and two-page attachment contained in Appendix C document the sign convention for the trans-verse shears used in this report.
3.4 Benchmark Shear and Moment Plots Appendix D contains three calculation pages excerpted from the Reference 3 Ebasco calculation book.
Page El indicates the plan of the basemat at eleva-tion -35.0 ft, and shows section marks A-A and B-B. Pages E4 and E7 show plots of the shear and moment in the base-mat along section B-B for the load combination containing the North to South Design Basis Earthquake, for three different soil spring moduli, as well as a plot of the design envelope. -
The shears and moments derived from the HEA bench-() mark run are superimposed on these plots, and are labeled "HEA (Variable Modulus)" .
The extraction and interpretation of the shears and
, moments..from the HEA computer run is also detailed in l Appendix D. The shear and moment output for tha basemat finite elements cut by section B-B are tabulated, the local coordinate system for each of these elements is defined, and either Fxz or Fyz and Mx or My (along with the appropriate sign) is plotted based on the orienta-tion of the local coordinate system and the sign conven-tion defined for the shears and moments.
Note that the rational procedure defined above for the selection of the shears and moments to be plotted
. does not accord with the procedure used by Ebasco. See I
pages E36 and E49 of the Reference 3 Ebasco calculation.
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There is an excellent correspondence between the plot of the REA benchmark moments and the plot of the moments (for variable spring modulus) generated by Ebasco, and this was expected.
The correspondence between the equivalent shear plots is not as good, even if the differences in the procedures used by EEA and Ebasco to select the magnitude and sign of the shear to be plotted are taken into account. -
The decision was therefore made to retain the " Martin" finite element for the fonnal structural analysis, which incorporates additional revisions to the model geometry (see Section 3.5) and to the magnitudes and distribution of the input loads (see Section 4.1) . ,
3.5 Simulation of Shield Building Wall Ebasco sfmulated the stiffness of the Shield Build-ing wall by a series of 3 ft wide by 40 ft deep beams
() spanning between (adjacent) ' node points 21-40.
The moment of inertia of the beam about a horizontal 3 4 axis (3 x 40 /12) is 16000 ft . The magnitude of the
! moment of inertia employed in the Ebasco computer anal-yses was 1600 ft 4 .
In order to simulate the Shield Building wall more realistically, a moment of inertia of 250,000 ft4 was selected, equivalent to a beam 100 ft desp. Review f
( Section A-A of the Reference 10 Ebasco drawing, which
( shows the cylindrical portion of the Shield Building wall to be 10 ft thick from top of mat (elevation -35.0 l ft) to elevation -18.17 ft, and 3 ft thick thereafter to elevation 184.07 it.
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- 4.0 Loads and Load Combilnations 4.1 Dead and Seismic Loads The dead and seismic loads employed by Ebasco in their computer analyses were reviewed by HEA against the applicable Ebasco calculations (References 1-3, 11).
The total Reactor Building dead loads tabulated by Ebasco on page 39 of Reference 1 were reviewed, as shown on pages 2-1 through 2-3 of the HEA calculation contained in Appendix B. ,
As shown therein, the total dead weight of the Reactor Building less the weight of ,the concrete shield- .
ing is 108,270 k, which yields a uniformly distributed load of 6.1 ksf over the circular area having a radius of 75.5 ft to centerline of Reactor Building wall, and con-tained within the ring of basemat node points 21-40.
The magnitude of the distributed dead load acting
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over the above defined area was therefore revised from 5.3 ksf to 6.1 ksf for the formal computer analysis.
An additional 39,680 k was distributed equally to node points 21-40 to account for the dead load of the Reactor
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Shield Building, which had not been input by Ebasco.
l The Design Basis Earthquake (DBE) seismic loads used by Ebasco for the Fuel Handling Building and Auxiliary Building in their computer analyses were reviewed against the maximum accelerations tabulated on page 5 of the Reference 11 Ebasco calculation (FHB mass Nos.
l 1 29-32, AB mass Nos. 33-38, from page 2 of that calcula-tion), and were found to be consistent.
The DBE seismic loads used by Ebasco for the Reactot
' Building Internal Structure in their computer a.talyses were compared against the base shear and moment tabulated on page 5 of the Reference 11 Ebasco calculation.
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As reviewed on page 2-4 of the HEA calculation con-tained in Appendix B, the base shear used in the Ebasco computer analysis is approximately 70 percent of the base shear tabulated in the referenced Ebasco calcula-tion (not considered critical) , while the total moment
, is substantially higher. The magnitudes and distribution of the total base shear and moment as generated by Ebasco were therefore left unchanged.
Finally, the total base shear and moment used by Ebasco for the Reactor Shield Building in their computer analyses were reviewed against the base shear and moment tabulated on page 5 of the Reference 11 Ebasco calculation, and were found to be consistent, as shown on page 2-6 of the Appendix B HEA calculation.
The decision was made, however, to re-distribute the base shear and moment in accordance with simple beam
.fh theory, as shown on pages 2-7 through 2-11 of the Appen-dix B HEA calculation.
4.2 Load Combinations 4
Four load combinations were analyzed in the formal HEA computer run:
j a) Normal Operating l b) DBE East West Seismic c) DBE North to South Seismic d) DBE South to North Seismic These load combinations -contain the component loads and corresponding load factors originally formulated by l Ebasco. There were, however, revisions made to the dead and seismic component load files, as noted in Section 4.1.
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5.0 HEA Computer Analysis The formal HEA computer run executed to assess the structural adequacy of the basemat was run with the changes to the input geometry and loads previously noted in Sections 3 and 4.
The primary objective in performing this computer run was to make a direct comparison between the analysis shears and moments derived from this analysis, and the point-to-point shear and moment capacity of the basemat, which is a function of the number, size and placement of the rebar.
5.1 Basemat Shear and Moment Capacity The reinforcing steel contained in the basemat is detailed on three Ebasco drawings (References 12-14).
As shown on the referenced Ebasco drawings, the top rebar is #11,0 6 in each way, over the entire mat. The ifh bottom reinforcement varies fran zone to zone, both in the E-W and N-S directions. The shear reinforcement is dis-tributed over two broad bands located on either side of the Reactor Building. The distribution of the bottom steel and shear reinforcement is detailed on pages 1-10 through 1-12 of the HEA calculation contained in Ap -
pendix B. The point-to-point shear and moment capacities of the basemat are given on pages 1-13 through 1-15 of that calculation.
5.2 Analysis Review Criterion As detailed on pages 2-12 through 2-14 of the HEA analysis contained in Appendix B, the analysis shears for j elements adjacent to basemat node points 21-40, the peri-meter of the Reactor Building, are not evaluated in this Report, because the Reactor Building was modeled only in a global, rather than in a detailed, sense. That is, the l 9 I - . . _ , _ _ - - _ . . _ , _ _ _ _ . . . - . _ _ , _ _ _ , _ . _ , _ _ . . _ _ . . _ . _ _ . _ . , _ _ _ _ .
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4 dead and seismic loads imposed on the basemat by the Reactor Building and Internal Structure,were modeled, and a series of deep beams were modeled (see Section
- 3. 5) to simulate the stiffness of the Reactor Building, but no detailed finite element model of the lower portion of the Reactor Building is contained in the structural model originally formulated by Ebasco.
This assumption is consistent with the assumption .
made by Ebasco. See Section II, pages 3-4 of the Refer-ence 2 Ebasco calculation book.
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i 5.3 Analysis Shears and Moments
, There are approximately 600 basemat elements. For each element there is a corresponding line of output which tabulates the membrane forces, transverse shears and moments. In order to review this output in a systematic manner the following approach is adopted:
a) any shear ' force greater than 172 k/ft is tabulated, where 172 k is the lesser shear capacity of the basemat; b) any positive moment greater than 1915 k ft/ft is tabulated, where 1915 k~ ft/ft is the lesser .
1 moment capacity of the top rebar; c) any negative moment greater.than 3643 k ft/ft is tabulated, where 3643 k ft/ft is the least moment capacity of the bottom steel..
This summary is performed for each of the load com-kk binations tabulated in Section 4.2, as shown on pages 3-l' through 3-6 of the Appendix B KEA calculation. Each anal-ysis shear and moment summarized is then evaluated with respect to the shear and moment capacity of the basemat at that location.
As shown on pages 3-1 through 3-6 of the HEA calcu-lation, there were only four entries tabulated for moment
! greater than the least moment capacity of the bottom steel (elements 192-195, S to N DBE), which were less than the corresponding basemat moment capacities at those locations.
The analysis, therefore, clearly confirms the design adequacy of the basemat with respect to the internal moments generated by the imposed loads.
i A total of thirty-five shears cre tabulated with magnitudes in excess of the lesser shear capacity of the l
basemat.
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Twelve of these shears act on elements located in areas having shear reinforcement and have magnitudes less than th? higher shear capacity of 270 k in these areas (see page 1-13,of the Appendix B HEA calculation) .
The remaining twenty-three tabulated shears are evaluated with respect to Equations 11-4 through 11-7 of ACI Standard 318-71, which permit a detailed calcula-tion for the allowable shear stress (instead of the de-fault magnitude specified in Section 11.4.1) for members subjected to axial compression. See pages 3-7 through 3-15 of the REA calculation.
i Of these twenty-three shears all'but three satisfy the detailed code requirements: the shears acting on ele-ments 172, 188 and 199 for the load combination which con-
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tains the S to N DBE.
The following table summarizes the analysis shears hk and shear capacities for these three elements.
Element Analysis Shear l Number Shear Capa' city (k) (k) 172 429 420 188 232 204 199 433 422 These magnitudes o.f analysis shears in excess of l shear capacity can be re-evaluated with respect to a more realistic concrete compressive strength. For example, a test report appended to the Reference 16 Ebasco Concrete ,
Masonry Specification entitled " Compressive Strengths of l
Cores Taken from Placement 499-19 (4-28-76) Lab. Nos.
A0826-A0838" by Peabody Testing, sunmarizes the results k "
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k of compressive tests performed on thirteen cores taken sixty-nine days after concrete placement. The compres-sive strengths varied from a minimum of 4360 psi to a maximum of 5930 psi, with an average compressive . strength of 4979 psi.
As the cores were tested on July 6, 1976 (sixty-nine days after date of concrete placement, as previously noted),
the average compressive strength can be conservatively employed to re-evaluate the shear capacities of elements 172, 188 and 199.
The following table summarizes the results of the re-analysis.
Element Analysis Shear Number Shear Capacity (k) (h) .
.s 172 429 456
- q'a- 188 232 223 199 433 459 O'ly n the analysis shear for element 188 exceeds the re-computed shear capacity, by about 4 percent. We judge this to be acceptable, because of the proximity of element 188 both to the Reactor Building and to an adjacent zone of shear reinforcement, and because this slight overstress is localized.
HEA, therefore, additionally confirms the design adequacy of the basemat with respect to the internal shears generated by the imposed loads.
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5.4 Plots of Analysis Displacements Plots of the vertical displacements of the basemat for the four load cases generated are presented in Ap-pendix E.
A number of qualitative observations can be made which confirm the validity of the structural analysis, and provide additional insight into the response of the finite element model to the applied loads.
Note, for example, that the contours of constant vertical displacement are symmetric with respect to the vertical centerline of the Reactor Building for the Normal operation load combination, while they are skewed for
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the load combinations which contain the E-W, N to S and
' S to N Design Basis Earthquakes.
Note also that the inter.nal bending moments and shears are functions of the second and third derivatives of the displacements. Therefore, the moment and shear acting on ff($
I any_ element whose normal is tangent to a constant dis-placement contour will be nominal (zero for a beam), while the moments and shears acting on any element whose normal i
is perpendicular to a constant displacement contour will be local maxima.
.Furthermore, the more closely spaced the contours of constant displacement, the greater the magnitudes of the moments and shears.
It is clear, for example, that the most highly stressed regions within the base mat for the E-W DBE and the N to S DBE (or for the S to N DBE) occur at different locations, as would be expected.
It is finally observed that the southerly region of
, the basemat underlying the Reactor Auxiliary Building is i loaded relatively lightly with respect to the northerly i
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region of the.basemat, which supports the Reactor and Fuel Handling Buildings.
5.5 SRSS of Basemat Shears To quantify the observation made in Section 5.4 that the most highly stressed regions within the basemat occur at different locations, the square root of the sum of the squares (SRSS) of the shears generated by the E-W and N to S Design Basis Earthquakes were generated, as tabu-lated on page 3-17 of the Appendix B HEA calculation.
The sample of elements for which this calculation was performed included all elements initially tabulated -
on pages 3-1 through 3-6 of the HEA calculation, for which the analysis shear exceeded the lesser shear ca-pacity of the basemat.
Excerpted from that tabulation are the six largest SRSS values of the shears Fxz and Fyz, along with a per- ,
ws ;r cent increase in the magnitude of the shear, computed with respect to the larger component.
Element -
Numbers (Fxz) EW (Fxz)NS SRSS % INC 353 16.7 66.1 68.2 3.1 261 -16.1 45.7 48.5 6.0 150 - 8.4 36.6 37.6 2.6 l 172 -34.1 13.4 36.6 7.4 188 16.3 31.9 35.8 12.3 l 404 32.9 9.2 34.2 3.8 l
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J Element
' Numbers (Fyz)EW (Fyz)NS SRSS % INC 261 -46~.1 -24.9 52.4 13.7 230 38.1 21.9 43.9 15.3 391 -39.8 -16.1 42.9 7.9 188 13.5 26.6 29.8 -
12.1 235 -15.9 -21.1 26.4 25.2 211 9.8 -16.8 19.4 15.8 Recalling thab'the lesser shear capacity was exceeded for all of the elements tabulated (for at least one load combination) , we first note that relatively little shear capacity is employed to resist the internal shears gener-ated by the SRSS response of _the Design Basis Earthquakes.
It is finally noted that the percent increases in the SRSS shears calculated with respect to the larger compon-O* ents are naminal.
EEA therefore concludes that a load combination con-taining the SRSS of the Design Basis Earthquakes will not significantly alter any of the analysis shears and moments, and therefore need not be evaluated.
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6.0 Discussion of Results The basis of our evaluation of the basemat was the finite element analysis of the model and loads as modi-fled by HEA. All the elements are assumed to be homo- ,
geneous uncracked concrete as far as stiffness relation-ships are concerned. For each plate element of the computer model, moments, shears and axial forces are calculated for each plate element. In addition, displace-ments at each node are calculated for each load combina-tion of interest. Vertical displacements have been plotted and are presented in Appendix E.
The controlling load combinat' ions are:
a) Normal Operating b) DBE East West Seismic c) DBE North to South ~ Seismic d) DBE South to North Seismic l The East-West component of the earthquake was taken in only one direction due to the symmetry of the struc-ture about a north-south axis. On the other hand, the North-South component of the earthquake was taken from North to South and from South to North. This was required due to the lack of symmetry about an east-west axis.'
The moments and shears due to the EW and N to S (or S to N) Design Basis Earthquakes are greatest at dif-farent locations and, therefore, an SRSS combination would not significantly increase any of the design values.
Therefore, this combination was not required for the eval-untion of the basemat.
While the perimater walls and a few major walls were represented in the finite element model, many walls were ignored. This is conservative because such walls would assist the basemat in carrying loads and in redistributing 17
any moments and shears which might be substantially greater than in surrounding areas.
A review of the results indicates the response of the structural system to the load combinations. Under normal load conditions the maximum displacements occur under the Reactor Building. This is because this region has the softest soil springs and the greatest dead loads. It is very evident for the normal load conditions that the establishment of variable soil springs will result in greater calculated ~ shear and moments as discussed in the Reference 17 EEA Report.
We are in complete agreement with the conservative selection of the variable soil springs based upon the expected soil subgrade modulii.
The seismic loading combinations in general ~did not control as much as the normal loading conditions due to (f) the fact that the dead load is increased by a factor of 1.5 and 1.1 in normal and seismic load combinations, respectively. Inasmuch as the Waterford 3 plant is in a low seismic site, the dead load is the major load.
Since the basemat is located well below grade, active soil pressures are acting on the perimeter walls during
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normal conditions. During seismic events passive soil pressures will develop on the face of the perimeter wall l which is being pushed into the soil by the earthquake forces.
! With'the resultant moments, shears and axial forces, the adequacy of the various sections of the mat was in-vestigated to the requirements of ACI 318-71. In general, the stresses due to bending moments are well belo,i the l , allowables for all of the controlling load combinations.
l In no case was it found that the reinforcing steel stresses 1
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were close to allowables; in fact, the imposed bending moments were usually only a fraction of the section capacity.
While a similar situation exists for shear, there are a few cases where the applied shear is very close to
, structural shear capacity as developed by ACI 318-71.
However, the ACI capacity reduction factor, d, for calculation of shear capacities is 0.85. This factor is applied during design due to uncertainties in random phenomena which could cause loss in strength. These phen-omena cover items such as isolated drops in concrete ,- +
strength, reinforcing steel, and errors in the placement of reinforcing bars. The basemat was constructed under -
controlled conditions, and avidence of strengths indicates
' that values are well above the minimum. For example, the i age of the basemat concrete is now almost seven years, ,
fh so that the concrete strength is considerably above the 28-day strength which was conservatively used in the cal-culations. Since the mat is twelve feet thick, errors in the placement of steel would have .little effect on the section geometry. In fact, the job records indicate no problems in placement of reinforcing bars.
f A very strong case, indeed, could be made for justi-fying substantially increased section shear strengths.
However, without taking advantage of this, the results indicate that the basemat has adequate shear strength for the i,mposed load combinations.
l The basemat is very structurally redundant and is very capable of carrying loads well in excess of the ap-plied loading combinations. This is due to the fact that if local capacities were exceeded, there would be a re-i distribution, rather than a progressive failure.
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. In fact, there is no structural reason why the basemat could not consist of individual building mats or even spread footings and still function very well.
The use of a continuous monolithic mat combined with the very low soil bearing pressures provides the structurally most conservative foundation solution.
.Although the top and bottom reinforcing appears quite substantial it is quite low when compared to the concrete area. From a structural point of view, this is very beneficial since the basemat will possess greater ductility. Furthermore, the concrete compressive stresses due to bending will be quite low, probably up to.only about 10% of the 28-day compressive strength of the con-crete.
6.1 Comparison of Results with Previous Analyses and Design Due to certain refinements, more complete and con-Qyp sistent results were obtained which were used in this evaluation, as discussed in Section 5.
It must be kept in mind that the top and bottom rein-forcing bars were conservatively selected on the basis of primarily manual computations and, therefore, the quantities of top and bottom reinforcing are well in ex-cess of ACI 318-71 requirements. This also applies to shear except for a few isolated elements in which the ,
applied shear did approximate the capacity as r'equired by ACI 318-71.
6.2 Effect of Cracking on Structural Response Cracking of the type evidenced at the top of the Waterford 3 basemat is expected in reinforewd concrete construction, and is assumed in establishing the struc-tural capacity requirements in the ACI 318 Code. The fundamental reason that cracking has little influence on the structural capacity is, of course, that concrete is
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8 not assumed to have tensile strength, the tensile forces being carried by the embedded reinforcing bars. The reinforcing bars are bonded to concrete'by adhesion as well as the mechanical interlock' of the deformed reinfore-ing bars themselves. The loss of bond across a very narrow crack is insignificant. If a crack exists where compres-sive forces will develop, the crack will tend to close up so that the compressive forces are_ transmitted in bearing in local regions across the crack. Therefore, while the crack may still be in evidence it will have closed suf-ficiently to transfer the compressive forces.
The effect of the closing of a narrow crack on the total compressive strain of the concrete is negligible for widely spaced cracks.
The completed analyses were performed using currently accepted methods for the design of reinforced concrete h structures in nuclear power pl. ants. For a complicated model such as was developed for the Waterford 3 basemat and superstructure, this was a formidable task in itself.
Nevertheless, consideration was given to refinements such as incorporation of cracking. While this would have in-troduced complex nonlinearities into the analysis, 'its effect upon the structure would have been negligible.
Therefore, such exotic approaches were discarded. The general low state of stresses calculated offers further justification for this assessment.
6.3 Conclusions and Recommendations The results of the finite element analyses indicate
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that the basemat will be functional for all the required load combinations for the design life of plant. The minor amount of cracking is insignificant in affecting structural response and has no effect whatsoever on the structural integrity of the mat.
21
The fundamental purpose of a foundation is simply to transmit-the dead weight and any other applied loads to competent soil. ' Of all the foundation systems that are possible from a structural point of view, the continuous monolithic 'basemat provides the most conservative system.
Furthermore, this type of foundation tends to smooth out locally high soil bearing pressures. Such large con-struction tends to be most susceptible to cracking from benign causes such as_ shrinkage, differential soil settle-ment, and temperature changes., However, the evidence of such cracks should not be a cause for concern any more than deliberately constructed expansion joints would have
~
been a cause for concern. The cracks are expected and should not deflect consideration of the inherent superior
~
structural capability of multiple redundant structures i
such as the Waterford 3 basemat.
( ,The present soil bearing pressures are a small frac-tion of the soil capability and are in fact less than the pressures existing in the soil prior to the start of excavation and construction. .Thereforc, the functional i requirements of the design have been met.
The major loading on the basemat is, of course, al-ready present, namely, the structural dead load and equipment load. The observations of the basemat covered in the Reference 17 HEA Report provide additional corrob-oration not usually encountered when a structure is under design.
In closing, the information presented herein as well as in the~ Reference 17 HEA Rwport are the result of an ex-amination of all aspects of the design of the basemat.
. While the seepage of water from the cracks precipitated 22
the investigation, all aspects of the design were con-sidered, not just that which could be associated with the cracks and seepage. It is our conclusion that the design of the mat is extremely conservative, which, under the circumstances in which the design was carried out, we consider prudent and justifiable. Therefore, we see no need for any remedial measures or the necessity of additional analysos.
O d
23 .
o REFERENCES 1.. Ebasco calculation book entitled "Waterford 3 Base Mat dated 06/02/72.
~
4 Design - Book 1",
, 2. Ebasco calculation book entitled "Waterford 3 Base Mat Design - Book 2", dated 07/29/74.
- 3. Ebasco calculation book entitled " Common Mat Finite Element Analysis, June '81 - In Response to NRC Audit", dated 06/15/81.
4.- Ebasco drawing (untitled, undated) showing keyplan of basemat and elevations A-D.
- 5. Ebasco drawing (untitled, undated). showing partial plans at elevations -4.0ft, +21.0 ft, +46.0 ft, +91.08 ft, and elevations at column lines 1FH, 3FH, 4FH, SFH, 7FH, T2 and V..
- 6. Ebasco drawing - (untitled, undated) showing a plan at j elevation +21.0 ft and twenty-six (26) partial elevations (untitled).
- 7. Ebasco drawing (untitled, undated) showing plans at ele-vations -4.0 ft, +35.0 ft, +46.0 ft, +69.0 ft.
- 8. 'Ebasco drawing entitled " Common Mat (Finite Element Model)"
undated, showing.the plan of the basemat at (centerline) elevation -41.0 ft.
- 9. STARDYNE User Information Manual, dated September, 1980.
- 10. Ebasco drawing entitled Reactor Building Structural Layout, LOU-1564-G-509, Revision 2, dated 10/28/77.
24
. . , - - ~ _ _ . - - . - . . .- . _- -
Y
- 11. Ebasco calculation entitled Steel Containment Stability, OFS NO 1352.063, DEPT NO 650, Rev. 1, dated 07/28/83,
- 12. Ebasco drawing entit~ed Common Foundation Struct.ure Rein-forcing Sh. 1, LOU-156 4-G-500S01, Rev. 9, dated 12/12/78.
- 13. Ebasco drawing entitled Common Foundation Structure Rein-forcing Sh. 2, LOU-1564-G-500S02, Rev. 2, dat;ed 01/20/75.
- 14. Ebasco drawing entitled Common Foundation Structure Rein-forcing Sh. 3, LOU-1564-G-500S03, Rev. 3, dated 05/09/75,
- 15. Ebasco calculation entitled Comm Fdn Mat - Moment Capacity, OFS No. 5234.014, Dept. No. 650, Sheet E55, dated 05/11/81.
- 16. Ebasco Concrete Masonry Specification, PID No. LOU-1564.472, Revision 5, dated 03/11/75.
- 17. HEA Report entitled Waterford III SES Analysis, of Cracks -
and Water Seepage in Foundation Report No. 8304-1, dated 09/19/83.
t 25
e h "-
.,m%e wa',-4*w ae 8 e
- 4 ,
4 4
e 4
APPENDIX A Plots of Plans and Elevations
WATERFORD 3 BRSEN NLAN RT EL -41.0 101 130 159 188 207 222 236 249 261 271 287 310 322 334 346 358 ' .
):. 6 :
xxxx xx :2 x sxe - - - - .
j 356 35.
354 353 $
keexV X A / 'NK/// / 7 ast 3s0 p 2 m
2 x xxx 4.
2
-x u /
348 XXX X XX X XX XX N '"
XXXXXX X XXX X 7/// 34>
STARDYNE FINITE ELEMENT N0 DEL PROJECTION ON X1-X2 PLANE CASE NO. 1
N ,
WRTERFORD 3 BRSENRT4iFLRN RT EL -41.0 l : .
, x 42 ,Ts 56 ,Ts i5i'rs i i 4Ts 4 4 ^ 5s 4 25,v 4 A G.,'r qD7 4 *s 355, s 37D,'l ,1 I /t '
b
, 8 , ' , 11 , g 7 Y / / / /
1 t, gt , g7 , T5 M 'H ' 4'28,'
'g s I /4 Obs, I e f'10't!s I /37h I ,/ 553 I / / /
--j l
'[8s"",Y32 "*[Yst
~
['a~s*3' p'o~ s
'M '"h's.'T/sY4A*hS"
', C 5Q
!" t1 4i "f
4,39i" f5"f,','k2 g ,a
'f' [ 46T'57r -d[
36I6r'~d,7 l 863,/ i 58s,/ j 607,/
575 d 1[- 597 1[- 6 I9-, l 1 ,'26's ,112s s1 i /2 0'4, I, 4 i f 4 / 28 O , 13 g _'3 I ,/I90h8M7 7 ><'36} 5/ 552 I
/ 596 1 / 618
- -~-
go , s es-A,ismA'penqd33[6v~*28d37'*Mallbl"?Masj' i '26's i x$3i ill7'x'iOli2%'%
s I '13 ijpin , i,,2661/A$%5d ,,,
,,+! 72ys, d'-)"k,3,4 my'N',----d',/
,,I S',3e 5 ,g,s,, i i my i 606 7 57 4 Sis i ,,604 S
- f f f / / 7 617 SI N 52 8 'e'36)E'y 551 l ',/ 573 l',/ 595 l G---
- ,[8gsi'4 a', e ff--
y/45p/(I----t--- \ Y's 501 : -t510 /
' t 4 4 >
I 4s , , g 4691478/ l s ,
35[354 /550 I 538 / 561 / i 583 / i 605 /
! t' 3"7 9'3 s n s f /457 l 465 /diBl 527,s N 3
,/572 e, /594 8 f /616 8
l /485l 49'4s '
i j
3 'x6L EI'x10 2h46
, '23'_s i /79N i ,'13E, i N
_ _ _ .g.__
s 456 1 463 gl \ 4881 f 'l
__g._ 496 f l 's 516l _9_526
'gl _)
_ _/
' @ 537 / l 560 / i 582 / l 604 /
/ -
?.
x6'0) 10)2 4 45h l f'471l 48'bs I 1 / 525 ,/549 l f/571 l ,593 8 f'615
-- --- $,--- t - -)$ f'$03l 51 -) \
5
\ ,
^
/22\ t /18's s ,'13'4s I --
$ > m j
's35,tC91,$sn7,h,2 454 / l \ 4681 477f / l \ 500}l 6f 09 /s l% 524 536 / I 559 / l-Y 581--- / I- Y603 ---
/ p I X'49h3 X 10) l'9,,c4 6 /453 1 46\ l '/'4841 49h I
- g f
$17l52h s ' ' ,/548 l ',/570 l',/592l'/614 4
-_ k'
gI3f.
i
s f4'g s ')j90 \s 452
}i 452/ I \
_g.
487i 495 / \ 515: 4 522 , 3
( ' I
( 80 /( ---- 7 602 '
4'O 6 # , 8 ,
,'2 0 \ I ,'7 6' ,s I ,'1 3 h 'l 18b 4ha, g l,/I70l47bs j f'502151k l,A y 336l ,/547 l p/56", l ,/591 l ,/ 613 Y475~ b 499508N N 325,Y 45 115 h--hi~457 s 4S X'47h'Is8 X10 1%~'I'N) M3y' l i 3 AIO7 lS 0 th)<'33 534
/8'8I 557
/ I 579 'I 601
' ' Ss0 l ,/590 l ,e/
19N M/ 4ggk483l 4D2!,M i 13'Is,1 A i
' ' 612 j 'C32 ,4,'? C8B ,5's4 1W, s ] --75 ---49Qgg, _3, 01_ .32h325-l Y - - - 'l - - -Y - - - I' 600 Y - - -
j i'y'46h0y40hl%45 R ikI3 '
hy%'20 9h'30 thy'33h / /645Il /567 ' 7
'/18's
-'71 I,+/14s 3 d
I
,'13h lei ?\ 1,t 2'1f I' 24' s
' 611 C87 - I-1-4 1/' 689 l /
s
'9 1 32h I ' I/
h8f 285
'P , s I / 9 eb i , i' f s,\ ' fd4 I 555 / 577 / 599 j *-30 s , c86 ,4cl-4 cl it ,-253 #c 283- Mc, ?8't-Yc'30 ' 123- 4 % 5 1
/566 8 /588 3 /610 i ? 'x1458' 2,, 108 6 13 2833 4E4%YSEEM7277 '[83 031'3 d20 l/ I/ I/
1 16's - f'1 , 71i. ,z2tl 83% 1 873,, 9L , 'NB s I 53T~f~t -
Y --- >
'c29 5 ?4 ,45h.
25 ,4 65,, 288-it,e t c21 .:- -522- T '5 3 0,,' i 554 / i 576 / Y 598 /
I 'x'4 5'P l'S Ti% 484 16% '[? E7Bx 82 GBINd27 918,-317s, I // 543 [I / /665 1I/ /587[8/ /609 I1%1 1 I,'21'5Ll /23K 1,%
j /15\ 8 , ls,1,12'Q A 2Sk,1,465Q,47Bd, ,
)
j PLOT OF GEONETRY PLOT i .
a a - --. n s i, , !
~
HATERFORD 3 ELEVATION A-A [X=0.01 l - !l l ... .i .2 .3 .4 se5 ses ;2 l 1a i
53 54 55 56 57 5. .59
.52 737 73. 739 74.
! 72e m us ne so 3i 32 33 3.
//
! /// /////// D ' ""
// / / / /// // N/// 4,.
1
////////////// 3..
!///// / / ///////
j STARDYNE F]N1TE ELEMENT MODEL PROJECTION ON'X2-X3 PLANE CASE NO. 1 l
! l
1 .
HATERFORD 3 ELEVRTION 8-8 [ X:371.51 ,
106. 1066 1067 1068 1069 1070 1011 1012 1013 1014 1015 1016 17 18 19 20 21 1022 y J1 y 92 923
/ / / / / / / / / // ..!
//// // / / / / / ,11
/ / //// / / /// ...
/// / / / / / /// ...
//////// /// .
STARDYNE F]N1TE ELEMENT MODEL PROJECTION DN X2-X3 PLANE CASE NO. 2 ;?.
A i
g 1
358 532 596 711 851 923 1022 1070 Cn
] 46 36 84 15 39 941, 010 1064 8
4 m
y 34 35 72 14 27 94] 98 1058 Z
5 22 34 60 13 15 93!. 86 -
1046 1
m.
a 10 33 48 12 03 211 74 1034 g 8 E R 9 r 87 32 16 695 791 h 790 s - @
a R g 61 0 14 93 789 $
788 X U Y
U 36 28 12 91 787 -
786 785 784 783 782 740 - .,
s-y e.TnSu - -
r rgNk$ i oZ ab h 7 5 3
. 4 3 2 0 0 0 1 1 1 1
1 9 7 5 3 0 9 8 7 6 1 9 9 2 1
(
l l' 1 1 1 1 O 0 9 9 9 9 0 9 . 7 6 5 4 3 2 5 4 . 4 4 4 4 4 4 0 8 6 4 7 7 7 7 7 7 7 7 7 4
2 2 1 6
- 8 1 0 9 2
d 5 2 1 7 0 9 8 7 6 5 5 5 0 9 9 9 9 6
. 7 6 6
5 3 1 9 7 0 8 7 6 4 7 6 3 8 7 7 5 4
. 1 0 9 8 7 u
1 8
_ 2 2 1 1 7 5
1 9 8
/
7 5 3 1 7 9 4 3 2 3 0 3
1 9 7 4 3
/
8$m 2Z[m Pmk* 2$ i a b S 3
7
- 5 -
. n 2
- e V
9
Figure A-7 D
WATERFORD 3 ELEVATION RT COL LINE T2 set see ses so4 ses ses so?
4 s7s m
I 1 455
/
l l 7e 7s se et se es ts4 STAROYNE FINITE ELEMENT N00EL PROJECTION ON X2-X3 PLANE CASE NO. 2 l
.. - ,, Figuro A-8 4
6 WRTERFORD 3 elf.VRTION RT COL LINE 1FH 179 440 023 873 901 S 894 x
l I -
91 1 408 See i
STAROYNE FINITE ELEMENT MODEL PROJECTION ON X3-X1 PLANE CASE NO. 1
Figuro A-9 O
e f
NATERFORD 3 ELEVRTION RT CDL LINE 7FH tes 4es , ses eTo so?
m 8
- 4. 303 G
~
4 STAROYNE FINITE ELEMENT MODEL PROJECTION ON X3-X1 PLANE CASE NO. 3
. - , . , . - . - _ . *. - - - - . - . - . - . - . - - - _ _ . . _ , , , , - , . _ . - , - .-n_-..n, . , , - - -- - ~ , - . . , , - , , - - - - , - - , - , .
APPENDIX B HEA Calculation I
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'HARSTEAD ENGINEERING ASSOCIATES
- INC. PR J. NO. b30$
A 169 KINDERKAMACK ROAD. PARK RIDGE. N. J. 07656 C~ L =
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PROJECT W3 SUBJ. SU B0lV. SHEET CLIENT LPYl PREP. BY Ad b QATE.0*d7/ 3 $.
SUBJECT 5 A !! W A
- 14rrI4A: Fo Icr 3 CHCKD.BYd h DATE io[3/33 i
I Q T t. 0 p u C T t O d T It h P o lt P O S E OF T&tS ChlCU L A TIO U lt 70 P G 1. F O L M h4 EUkluAtl04 0F 7tG 14 TE L 4 h l F 0 F CE E h 11 0 M0M54T3 GEMEIATFD 14 T ir G MPr5 E A : s tA A r DOE l TO T&E F O L L O W 1 11 G 10AD CO M El4 A 7 5 0 4 5 :
1 M 0 L IA h l OfFLhTfyG L- 5- 4 DEE En(VkAIAELS : P I : 4 G) 3 4-3 DEE 24 (VAEfALLF SPAl4G)
- 4. E-W D5E _
E G, C.V A L ( h 5 L i S { E l 4 G)
Tt5 FiulTE ELFMEMi M.0 D E L OF TtG L AS E M A ~
A40 A S S O C I A T E D. 3 T E U C T tI A E , AS WE'L AI T .1 ; .
toad $ Co 4 T A l u F D IN T .t f A30VE-Off24Ep LO A C C O M 514 A T10 4 5, WERF PKOViDID 5T E b h 5 C O.
TWO CHAMGFI WEK! MADE 70 fti CO D 4G OP 71; G F o M i F r. T :
- 1. TRS 'MALTIN T L i k u C V t. A A ELE V: f; 7 WAS E M P L 01 10 14 TEE SIAUCTULAL A M A Li: 2 5 PEEFOLMrD ET R F A.
- 2. . TR Lockl 10 0 T. D : U k T E ! 0F A M U V t ! i. OF Fluiti I Lf u f 4 TS co u F A I N E D 8J T .Y G Eh;fMAT WELE LOTAPED 70 K E CO M E PAAALLf. ^o T&G G L o s hl CO O L D ! M A T 07 T U M OF 74 2 L A l t u A T, To F A C I L I T A T E f u T F ;t ? A. E T k f l > ti
- 0F fFE 10rPuT O 't F A A : A43 M'W!81?!.
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HARSTEAD ENGINEERING ASSOCIATES
- INC. PR O J. NO. @ sod -
A 169 KINDERKAMACK ROAD PARK RIDGE, N. J. 07656 C- T -
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7, PROJECT W3 susJ. susoiv. SHEET CLIENT LP4L P_B_EP_sy Ad 5 DATE39/a7/83 SUBJECT 5 A S E IA A r l u f t T 4 A L F06cE CHCKD.sY 4N DATE l3/}/ft 75% ' tr. k T : : ll ' T Flk M G UL h l E L E L4 2 U T C. h 4 6G USED To ADVh41kGE WWrM h T & IC K ? l h 75 I5 LEtMG h4hLTEEV OK W ftf M TAA4 V fc L S E t it E A A O T A F S f. E S A LE R E d. U ; A T C 14 f If 5 0 U rr U T. LEFCE54C3
- s T A E p i u 5 + 5 F): 14 Fo t i/ /-T! 911 M AMUAL , 5 5 P[ 7 i, P7 M - G 0, 7 0 foe A D F F ! fi . ' : J N' 0F TH& ' M A A r i u ' E l F M 7 4 7.
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- INC.
PR OJ. NO. 55ON A 169 KINDERKAMACK ROAD, PARK RIDGE. N. J. 07656 C- %. - \
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3 W3 susa. SUSDIV. SHEET PROJECT CLIENT LP&L PREP. BY Ad d DATEW/27/23 SUBJECT L A I F AA A T furrkukL FOLcis CHCKD.BY.6 h DATE lc[3fg3 E Vkl0 A T io M OF f u P S LU hl TNJhES AuD u o M F U TS in O L O E t TO 7ETF0&M A T h o l s .C k Vk l U k rio U OF T#E B A IE W A T CH T A E! A40 MoMfutJ GINFAATFD Er s
T if f C0 M P V T E I A 4 A LT !!3, IT 13 UrcEI ALT to GTtPOLATE:
- l. TtS D E F tti ! 7 80 4 5 0F rkE LOCkL C00F.D;Uh7E AXFS A4D TEF O L !r u T A rlo 4 AMD !!,4 C04VE478045 of TW& Lo h D3 F0K tgE T L i h n G t1 L A i E L E Lt. E N T S USED To V007L TWE 5 A 51 M A T.
3.. TRE PATTETM OF T. E E A T (4VM5Ef kMO o A lf M T A tl0 M) CO N T A luf D 4EAI T&F 70P
>j kMD toTTOM OF TRE MAT, A3 WELL A; TEE TREhR L E ! M F 0 E C E M f 4 7, 3, t ,15- GO lt it. T ! T Q 4 0 i d G M O M 5 117 A40 t if f A R CAPACI77 GF t55 E A !E M A 7 R S I U F 0 R C E M E lI 7 .
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'HARSTEAD ENGINEERING ASSOCIATES
- INC. PROJ. NO. 8 ~5 04
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fA 169 KINDERKAMACK ROAD. PARK RIDGE. N. J. 07656 C~ *1= ~ *? ~
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, PROJECT CUENT L.P 4 L PREP. BY 4It h DATE i f jj /f3 SUBJECT 12. E\1\ E %/ C1 MODEL. 3 L,0 AOf MG CHCKD.BY Av DATE % lq 3 4 o uPA R.t So N G.\4EECKS ON LOAOINC, F:oveL doVM Pu TE F Ah)/4Ls/. sI.s TOTAL 9.5Ac T oR. B LO 4, itsF: p ~3 9 Ebac o w7 G a 41 "LM TE4.N AL 6T A 6 5,550' M h To R, ga u tP t STL couT \ 6,700 '
4 e 44. 6IflELDIkJCa Si,3el.o"-
rd.s FusL N A 9ooL 4c5c' "T o *T A-1 Lb'2.,(oI0 LE51 (.,cM C, iht O.0 54, ~54 o 1 e 82') O s
@ Aia.sA Nsi os. wooss 2i_ 4o 77 (7 s. 5)* .=. g 7 9 o 7, g l p = 5. o s z c.t w w
dMANGE E S A S 4. o VA. t v 6 O r 5 'S *-To 61 ESAsco twPuT ot D N OT AGCOUMT ;:o 2_
- WT OF d o M c g2.E T E SRlELD l Nots: VALUE o 1: 6 fttELP U S E o S Y . I+64 I N .g.
do M PU T 64 rd. u M 38527+ 9697
- 4 82l9 dO M PME S W E LL W i T14 54,3-10 *
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'HARSTEAD ENGINEERING ASSOCIATES
- INC.
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A 169 KINDERKAMACK ROAD, PARK RIDGE. N. J. 07656 C- L. 2 -
1
,- kJ~h SUBJ. SU BDIV. SHEET PROJECT CLIENT \. P E l PREP.BY 45 }h DATE414ff%
SUBJECT W EN/IE W O F- M ODE'L 4 LO ADialC3 CHCKD.BY ArV DATE9 9/83 TOTAL STR.0 (_T t) 9 A L ~~2EAD 'L_oAD ICF-o M E 6 AS C C 4 o M PUTE 4 FLUN D L. k
-roTA L - 513,ooo E8h$co -
W o 64 Seo v 4 1 ToThL 0L 686, C6 I
(). A l f P A 5 (,,, D L Moi \McL SG ulP)
AOc t Tion AL ~ tcAo ADDED SY itEA "
u e4if cre.M Lo 40 wit 4.s oj 2 sac.To fl 8 LO 4 '
- l. 7 4 o 7 6 C ca . I - 5 2) s 14 3 2, c,,
EsAcTort. GMto _
19 84 (zo) 3 9, & % o
- TOTAL l oAo Apogo sy, RFA 64ooG h$ .-
WEW TcTAL l hJ com pu7 E e.
5% gru + 5 4 o c-6' 567,rD6" c o R- Vt EC.TE D VALUE oF . tot 4L O EAO lcAO oF + T rt. v c "T U (2. s 5 c'o M FA rag 5:
N/ 614.Y W E,L L M/ i T4 PrEEvtcusty
(,,,ALc u LATEP VALUES 6 (o7,, 00 la X 586,OSl
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'HARSTEAD ENGINEERING ASSOCIATES
- INC.
PROJ. NO. 830A
. A 169 KINDERKAMACK ROAD. PARK RIDGE, N. J. 07656 C- '2. ~ 'L *:
W3 SUBJ. suBDiv. 5HEET PROJECT CLIENT L P S L. PREP. BY 4 14 DATE i/14/f3 SUB-!ECT A ?"'VI EV/ CG M00FL $ LDADINd2 CHCKD.BY M DATE9/14[2s l C o wC., c.y Li n o s ta, g wg a, o te \ ,pq 15 r. 2 7 7 c. i=
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Vol = 6 4/. 11 W' 4492 *
@ Y ooog = 465*
TOTAu pro ogo na ce gp . iaa o g ( g,,1 4o W[g ,e : 74)l 6 0 6T EArcT BEAM s'x + o' W/g : 3 C4 oX 23.7)(,is ) - 4 27 NET AODlTIOM ht L, o m g N o g g,$ 7,,,I . 4 o S
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C~ L ~
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1MB t AvY BLD6 Epub g u g g t7c,, g ,, R y nA 0 r , u ,4r y 3 Lg , ,
t=e sz. oaE
^
H ovi z. . A u. = o.o75e F
To B c. APPL)EO TO 5 T F-u c T u r2 4 L ISkSMENTS M O OfL.GO.
To d.c M P EM SAT E l= o ;a, } N c g. GAS /N di
/\C.CEL. ER-ATI o r4 W i rit itFL4 (tTj Tif E.
WEMST D Et4 SI W WA5 V GA\ED ITF-o M Sea A1H$ To O.7746 e to M P u Te r2 C o uT PuT E F F:df 71V E dt DIST9 )B OTIo N tjp) - o 7 5 (,'l [ ,
= o ,) o S T
I
.o 75 (.27+e}
o,1374
.is l 1 o G- DBE SSA6C.c DOUBLED TlYESl? VA1 l/E l
d.c N PO~TE 4 D'/14 h M t <-
VALUES PO G~
AN A LYSij
/pe.oM ESM:o GT/t T LC (LU N L4 a M Tat u M E N-[ V Sif ft.
4T Adil.17Y (. Ab d, i o 1: \4 e A u y s t. o A M t M. s , 2 z. 0,22 c .1 l
u g. o.27 0,28 0 ,'2 7 5 G S h 's t o PR.odGOU25 '= 0 %
4 Ets M tc r2.s p res s, eWA T i o N
- For2 Ir FL o H 4N o L t N c3 G l.oc, 4 A u v., e to a u .
is co u s.i s rswr wra c, t o w s ,
a m SARSTEAD ENGINEERING ASSOCIATES o INC. PR * N*' 0 ~ib O S A 169 KINDERKAMACK ROAD, PARK RIDGE, N. J. 07656 C- ~L - % -5 W "S SUBJ. SUBDIV. SHEET
, PROJECT CLIENT L P 4 L-. PREP. BY dlk DATE 4/14[h SUBJECT EE VI E W OF McD EL e L oADI AICA _CHCK D. BY Ad 5 DATE:0!07.'2 ' _
6 ElS Mic LoAp5 -
g.shcTc2 6L D A, INT!ic.N4!_
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EG U ALLY l TOTAL MOMENT e 6IWAR.,'D16TF-180TSD C V E Gik. }4 McO gjs ,
(,' o M F Ar4ts.o N OF E6ASco VALVCI M %f,UT Ttc M A T
- 6 E-WRf 3 /,4 9 '- 243,/,2o '
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PROJ. NO. 8504 A 169 KINDERKAMACK ROAD, PARK RIDGE. N. J. 07656 C- 7.,,, -
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- 3 's HARSTEAD ENGINEERING ASSOCIATES
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A 169 KINDERKAMACK ROAD. PARK RIDGE. N. J. 07656 C- 1., -
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- PROJECT w3 CLIENT I4l PREP. BY Ab DATElo-/e-T3 SUBJECT 5A5&uAT :UTsL4AL F O F. C I S CH CK D. BY Adh DATE 10[9./2.@
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A 169 KINDERKAMACK ROAD. PARK RIDGE. N. J. 07656 C- 2. - 3- t c>
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APPENDIX C STARDYNE Shear Convention for MARTIN Element
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. . . xi A se s XI rigure 1 Triangle Local coordinate system rigure 3 Differential Element for Identifying stress components Eh L..1 A3 ase a is d.rected ' ate *he pare *.
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,xs h#T,...e i A me a XI rigure 2 Alternate Local coordinate system rigure 4 Directions for Transverse Shear Stress l
l SY en + t 4*** \ $x ea +2 N p fase l
gy = -t = ,N,
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- .=.: = e a l Directions for Direct Stresses i
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t- .
r SDC-stem Deveioprnent Corporation
. . A N. Sepulveda Boulevard. O Segundo, CA 90245. Telennone (213) 6151188 f
September 29, 1983 Mr. Andy DuBouchet Harstead Engineering Associates 169 Kinderkamack Road Park Ridge, New Jersey 07656
Dear Andy,
As a result of our -telephone conversation, last Monday morning, I am sending a description of the stress sign convention for our " thick plate" triangle element.
Please call if you have any additional questions.
~
l Sincerely, efe A AdP p$h Charles A. Bell b STARDYNE Division Enclosure CAB /mgf 4
6
f Directions of Stress Components ... Triangle Elements Ascertaining the directions of the stress components, for the triangle plate element, begins with the orientation of the local coordinate system for each plate element. From the input on the TRIAB cards, node numbers are associated with the designations JA , JB , and JC . The origin of the local system is at node JA, with the local X1 axis directed toward node JB . The local X2 axis-is in the direction of node JC , and the local X3. axis completes the right-handed triad. Figure 1 illustrates a possible local coordinate system for a triangle element; Figure 2 shows a second possible local system for the same triangle. The choice of which node is designated JA is left to the user's discretion. An addi-tional option is the-AXIS' ANGLE input on the TRIAB card; this
. allows an angle between the JA - JB line and the local X1 axis.
j once a local coordinate system has been selected and identified, a differential element can be located near the triangle center, Figure 3.- This element has sides parallel to the local X1 and X2 axes. The output stress values are located on the two faces, of the differential element, that are furthest from the local coordinate origin. Figure 4 shows the directions when the listed transverse shear stresses are positive; a positive stress value means that the stress arrow is in the local X3 axis direction on the indicated face. Figure 5 shows the direction for positive direct stresses. Negative algebraic signs, in the printed output, reverses the sense of the stress arrows in the two figures.
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APPENDIX D Ebasco/HEA _
Shear and Moment Plots 5f 4 l
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