Response Spectra Analysis of a Liquid Storage Tank

1. Response Spectra Analysis of a Liquid Storage Tank GT STRUDL Users Group 22nd Annual Meeting Double Tree Hotel New Orleans, LA June 23-26, 2010 Krishna Amirineni WorleyParsons Assoc. Structural Engineer

2. Contents • Introduction • Background • Tank Geometry • Problem Description • Problem Approach • Pre-processing • Tank Wizard vs. Excel • Joint Coordinates • Element Incidences • Applying Loads • Analysis • Sub dividing Input Files • Post-processing • P-M Interaction curves • Export GT Strudl Output to Excel • Secondary Loading (Thermal Load) Results

3. Background • Nuclear Power Plant • 3 Units • Pressurized Water Nuclear Reactor System • 3 x Turbine Generators (1311, 1314 and 1247 MWe) • Refueling Water Tank • Capacity – 750,000 Gallons • Stores borated water for refueling

4. Tank Geometry • Tank Properties: • Seismic Category I • Wall thickness 1’ - 9” • Mat depth 4’ - 0” • Wall height 68’ - 0” • Water volume 750,000 gal • Embedment 13’ – 10”

5. Problem Description • An additional 3’-0” of water required. • Overstress (Dead Load + EQ. Load) • Vertical Reinforcing Steel @ wall base mat junction (20%) • Hoop Reinforcing Steel @ El. 129’ – 0” (9.5%) El. 129’

6. Problem Description (cont’d) The seismic loading acting on the current tank three dimensional model is defined, by hand computations, from a lumped mass model

7. Problem Approach Perform Response Spectra Analysis of the three dimensional finite element model

8. Contents • Background • Tank Geometry • Problem Description • Possible Approach • Pre-processing • Tank Wizard vs. Excel • Joint Coordinates • Element Incidences • Applying Loads • Analysis • Sub dividing Input Files • Post-processing • P-M Interaction curves • Export GT Strudl Output to Excel • Secondary Loading (Thermal Load) Results

9. Pre processing Use of GT STRUDL Tank Wizard vs. Excel Triangular plate elements – NG for checking reinforcement. Basemat has the shape of the tank - rectangular basemat not possible. Basemat using Tank Wizard

10. Pre processing (cont’d) Use of GT STRUDL Tank Wizard vs. Excel • Rectangular basemat possible • Rectangular plate elements possible • Customized plate element size possible. Basemat using Excel

11. Pre processing (cont’d) Excel as Pre processor – Generating Joint Coordinates • X = R Sin θ • Z = R Cos θ • Y - varies

12. Pre processing (cont’d) Excel as Pre processor – Generating Element Incidences

13. Pre processing (cont’d) Excel as Pre processor – Applying Loads • Loads considered • Dead • Hydrostatic • Hydrodynamic • Earthquake • Thermal

14. Pre processing (cont’d) Excel as Pre processor – Applying Hydrodynamic Loads Dynamic Model Fluid Motion in Tank

15. Pre processing (cont’d) Excel as Pre processor – Applying Hydrodynamic Loads Per TID-7024, “Nuclear Reactors and Earthquakes” Chapter 6 where

16. Pre processing (cont’d) Excel as Pre processor – Applying Hydrodynamic Loads P1 and P0 are point loads. Hoop steel already overstressed at 9.5%. Therefore, tried alternative approach. El. 129’

17. Pre processing (cont’d) Excel as Pre processor – Applying Hydrodynamic Loads Distribute the Impulsive and Convective loads per TID 7024, Appendix F: Impulsive Pressure Convective Pressure

18. Pre processing (cont’d) Excel as Pre processor – Applying Impulsive Loads Calculation of Impulsive Masses The calculated Impulsive mass is applied as inertia mass to the tank structure. The GT Strudl Input file is generated using excel macros.

19. Pre processing (cont’d) Excel as Pre processor – Applying Convective Loads The calculated Convective loads are applied as Forces in X and Z directions separately on the tank structure. The GT Strudl Input file is generated using excel macros.

20. Pre processing (cont’d) Convective and Impulsive load on the tank basemat Convective load on the tank walls

21. Contents • Background • Tank Geometry • Problem Description • Possible Approach • Pre-processing • Tank Wizard vs. Excel • Joint Coordinates • Element Incidences • Applying Loads • Analysis • Sub dividing Input Files • Post-processing • P-M Interaction curves • Export GT Strudl Output to Excel • Secondary Loading (Thermal Load) Results

22. Analysis • Analysis Split in to 4 parts: • Static Analysis • Eigen Value Analysis • Response Spectrum Analysis • Post Processing Small input files help in managing the whole analysis and also in debugging the input files.

23. Contents • Background • Tank Geometry • Problem Description • Possible Approach • Pre-processing • Tank Wizard vs. Excel • Joint Coordinates • Element Incidences • Applying Loads • Analysis • Sub dividing Input Files • Post-processing • P-M Interaction curves • Export GT Strudl Output to Excel • Secondary Loading (Thermal Load) Results

24. Post processing • Tank Body • Vertical Reinforcing steel • Hoop Reinforcing steel • Radial shear and • Tangential shear • Basemat • Reinforcing Steel in orthogonal directions • Section shear.

25. Post processing (cont’d) • Check Vertical and Hoop Reinforcing Steel (P,M) sets are plotted on existing Interaction charts.

26. Post processing (cont’d) • Response Spectrum analysis gives the maximum peak values of displacements and forces. Stat : Static Load RS : Response Spectra Load Consider load cases: Therefore, possible (P, M) pairs (PStat+RS, MStat+RS) (PStat+RS, MStat-RS) (PStat-RS, MStat-RS) (PStat-RS, MStat+RS)

27. Post processing (cont’d) Export of GT Strudl Output to Excel

28. Post processing (cont’d)

29. Post processing (cont’d) (P, M) Interaction Curves

30. Post processing (cont’d) Primary Loading - Results • Tank Body • Vertical Reinforcing Steel OK • Hoop Reinforcing Steel OK • Radial Shear OK • Tangential Shear OK • Basemat • Reinforcing Steel (N-S) OK • Reinforcing Steel (E-W) OK • Shear OK

31. Post processing (cont’d) Evaluation of Tank for Secondary Loading (includes Thermal Loads) • Under thermal loading – concrete already cracked • Concrete sectional properties change • A second model used with changed sectional properties • Results from Primary loading and Thermal loading combined Externally.

32. Post processing (cont’d)

33. Post processing (cont’d) Secondary Loading - Results • Tank Body • Vertical Reinforcing Steel OK • Hoop Reinforcing Steel OK • Radial Shear OK • Tangential Shear OK • Basemat • Reinforcing Steel (N-S) OK • Reinforcing Steel (E-W) OK • Shear OK

34. Post processing (cont’d) Checking Soil Bearing Pressure – Node layout

35. Post processing (cont’d) Checking Soil Bearing Pressure – Dead Load – Stress Contour

36. Post processing (cont’d) Checking Soil Bearing Pressure – Seismic Load – Stress Contour

37. Post processing (cont’d) Checking Soil Bearing Pressure – Seismic Load – Actual Stress Contour

38. Post processing (cont’d) Checking Soil Bearing Pressure – Dead + Seismic Load – Stress Contour

39. Post processing (cont’d) Checking Soil Bearing Pressure – Negative Soil Springs = +

40. Post processing (cont’d) Checking Soil Bearing Pressure – No Tension Springs – Stress Contour

41. Results • No overstress in the tank (existing water level). • Tank can accommodate an additional 3 ft of water.

42. GT Strudl and Excel • GT STRUDL • Technically solid • Simple command structure • Helps creating input files easily • Command line gives more control over the analysis • Database driven system • Helps dividing the analysis in to smaller portions • Helps in input file debugging • Saves time in debugging • Excel • Ability to import large data and manipulate • Macros help in data formatting and manipulation.

43. Questions ?