ML20010G998

Comparison Between Finite Element Plate Analysis & One Way Beam Action.

ML20010G998
Person / Time
Site:	Point Beach
Issue date:	09/30/1981
From:	COMPUTECH ENGINEERING SERVICES, INC.
To:
Shared Package
ML20010G963	List: ML20010G962 ML20010G974 ML20010G981 ML20010G988 ML20010G992 ML20010G998
References
IEB-80-11, R553.12, TAC-42896, TAC-42897, NUDOCS 8109220765
Download: ML20010G998 (6)

Text

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ACTION ITEM 16 COMPARISON BETWEEN FINITE ELEMENT PLATE ANALYSIS AND ONE WAY BEAM ACTION Prepared for Point Beach Nuclear Power Plant, Units 1 and 2 WISCONSIN ELECTRIC POWER COMPANY willwaukee, Wisconsin Prepared by COMPUTECH ENGINEERING SERVICES, INC.

Berkeley, California September,1981 REPORT NO. R553.12 hh OO G

TABLE OF CONTENTS

.. 1 1 INTRODUCTION . . . .. .... ... .

1 2 ANALYSIS METHODOLOGY . . . . . . . .. .. .. .....

1 3 RESULTS .. ....... .. . .. .. .

2 4 DISCUSSION OF RESULTS .... . ..... .. .

2 5 CONCLUSIONS .... .... ... ..... ... .. .

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1 INTRODUCTION The Nuclear Regulatory Commission (NRC) staff on June 9-11,1981 reviewed the criteria and calculations performed on IE Bulletin 80-11

• Masonry Wall Design

• for the Point Beach Nuclear Power Plant. Action item 16 resulting from the review meeting stated that the licensee will provide comparative analyses on three types of Point Beach masonry walls (four s! des simply supported, three sides simply supported, and two sides - vertical and horizontal - simply supported) using both the plate assumption and one-way beam action in two orthogonal directions.

This short report is in response to that action item and presents the analysis methodology, the analysis results, a discussion of the results, and the conclusions.

2 ANALYSIS METHODOLOGY All walls were analyzed in accordance with the procedures given in " Criteria for the Re-evaluation of Concrete Masonry Walls for the Point Beach Nuclear Power Plant." Specifically, a finda element plate analysis was used to assess the out-of-plane response of the wall. The computer program SAPSA was used to perform the finite element dynamic analysis, utill::ing the response spectrum method.

This method of anclysis was selected because it was capable of explicitly incorporating the effects of equipment and pipe loads. openings due to doors, pipes and cable trays, and different boundary conditions.

In order to provide a comparative analysis based on a beam solution, the formulation of the beam sclution is derived as follows. The beam was assumed to be uniform and prismatic. The fundamental frequency and mode shape was calculated with either simply supported or cantilever coundary conditions and these were then used to calculate the maximum moment in the beam. The relevant formulas for the simply supported beam and cantilever beam are given in Table 1.

3 RESULTS A summary of the maximum mornents obtained on both horizontal and vertical strips for two walls (19/9 and 20/9) with four sides simply supported, for one wall (65-1/15) with two sides simply supported, and for two walls (111-1/23 and 113/23) with three sides simply supported are given in Table 2.

In the case of the two walls with four simply supported sides the beams were simply supported in both the horizontal and vertical directions. In the case of the two walls with three simply supported sides the beams were simply supported in the horizontal direction and a cantilever in the vertical direction :!nce the wall was not supported at the top. In the case of the wall with two simply supported sides the beams were Cantlievers in both the horizental and vertical directions.

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4 DISCUSSION OF RESULTS The maximum moments caiculated on a vertical strip from the beam formulae were all greater than ti e maximum moments calculated from the plate analysis. The maximum moments calculated on a horizontal strip from the beam formulae were greater than the maximu.n moments calculated from the plate analysis for the walls with four and two sides simply supported. For the walls with three sides simply supported the maximum moments obtained from the beam formulae were less than those calculated from the plate analysis.

For the examples given a beam analysis of walls in both orthogonal directions and simply supported on four and two sides would be conservative. For the examples given of a wall supported on three sides and not on the top a beam analysis would have produced non-conservative results if the wall had been assumed to span or1y in the horizontal direction. If, however, it had been checked as a cantilever beam in the vertical dir,ection, the vertical moments would have exceeded those obtained from a chie analysis.

5 CONCLUSIONS The walls at Point Ocach Nuclear Power Plant were dynamically analyzed as finite element plates so that the effects of equipment and pipe loads, door and other openings and different boundary conditions could be explicitly included in the analytical results. If beam analyses had been used on walls with two and four sides simply supported this method of analysis would have been conservative for the three examp!es given. If beam analyses had been used for walls with three simply supported sides and they had been assumed to span in only the horizontal direction then a beam analysis would have been non-conservative.

It is clear that a beam analysis may not always produce con'lervative results and furthermore it is very difficult to account for the effects of openings and equipment and pipe loads in a beam analysis. Therefore the finite element plates used to analyze the walls is considered to produce a realistic evaluation of the stresses in the walls and to accurately account for the effects of openings and equipment loads.

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d TABLE 1 FORMULAE FOR BEAMS Simply Supported Beam Cantilever Beam Fundamental tr I (1.875)2 EI

- -r Frequency 2 m L" 2u liiL Fundamental Mode Shape sin 1*

L sin ax - sinh ax + 0.742 (cosh ax -

cos ax) a = 1.875/L Maximum g ( L_ ) a ~y L m

Moment u 2.3700 E = modulus of elasticity I = modulus of inertia iii = mass per unit length L = span length 0 = seismic acceleration 3.

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TABLE 2 COMPARISON OF MAXIMUM MOMENTS OBTAINED E ROM PLATE AND BEAM ANALYSES Wall No. Status Mx Mxb Mx Mb y

19/9 P 398.9 565.7 184.7 988.1 Four Sides U 319.8 469.9 148.1 823.4 20/9 P- 173.9 313.2 122.7 989.2 Four Sides U 142.2 259.9 100.3 824.3 64-E/15 G~ 85.96 223.64 103.2 1351.70 Two Sides U 44.58 121.37 53.51 653.07 111-1/23 P 205.8 103.6 202.7 999.2 i Three Sides U 179.9 90.4 176.9 813.5 113/23 P 265.3 107.6 631.8 999.2 Threc Sid;;s U 236.6 90.5 563.8 813.50 Note: (1) P = Fartially Grouted; G = Grouted; U = Ungrouted (2) Mx and My are the maximum moments on the horizontal and vertical strips respectively obtained from the plate analyses (3) Mx3 and Myb are the maximum moments on the horitental and vertical strips respectively obtained from the beam analyses 4

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