Base Plate Modeling in STAAD.Pro 2007

Transcription

1 Base Plate Modeling in STAAD.Pro 2007 By RAM/STAAD Solution Center 24 March 2007

2 Introduction: Base plates are normally designed using codebase procedures (e.g. AISC-ASD). Engineers often run into situations where there are no codes available to design a particular type of a base plate or there are instances where base plate were simply over designed in the past and the engineer has to check the design of this old base plate based upon new loadings and make modifications as required. In these situations, an engineer may opt to do a finite element analysis on the base plate. STAAD.Pro 2007 is equipped with a lot of mesh generation and loading tools. The purpose of this document is to demonstrate how engineers can analyze base plates using STAAD.Pro Figure 2: Plan view of tank base plate We would like to thank Mr. Indranil Roy Chowdhury, P.Eng. from Hartford Installations, Missisauga, Ontario for allowing us to publish this document. Please note that this document assumes that the user has basic knowledge of STAAD.Pro and Finite Element Analysis. Exercise Problem: We would like to create the following base plate geometry in STAAD.Pro. This base plate was used to support a tank leg. The tank leg pipe diameter is 0.9ft and the thickness of the pipe is 0.5 in thick. Figure 3: Elevation view of base plate stiffener 1. Open a new STAAD.Pro file using the space option and the units of ft and kip. Figure 4: File creation dialog box Figure 1: Isometric sketch of tank base plate 2. Give an appropriate file name. 3. Click on the Next button and then click on the Finish button on the following screen. 2

3 The STAAD.Pro interface will appear as shown in Figure 5. Figure 7: The Base_Plate grid is shown in the Graphics Window. 7. Draw the outline of the base plate using beam elements. Press the Snap Node/Beam button in the Data Area. Figure 5: STAAD.Pro user interface 4. Create a new grid. Click on the Create button in the data area. The Linear input box will appear as shown in Figure 6. Figure 8: Outline beams created using the grid system. 8. Now we have to create the pipe section/base plate and the stiffener/base plate interface. 9. Click on the Create button in the Data Area. 10. Select the Radial grid option and enter the input parameters as shown in Figure 9. Figure 6: Linear grid box 5. Input the parameters as shown in Figure Click on the Ok button. You will notice the Base_Plate Entry in the Data Area. Figure 9: Circular grid layout for base plate/stiffener and column/stiffener interface. 11. Click the Ok button. 12. Turn on the stiffeners grid and the radial grid will appear in the STAAD.Pro graphics window as illustrated in Figure 10. 3

4 purpose of finite element analysis we should always try to maintain the aspect ratio of the elements. In this case, we performed the translational repeat on the beam elements because we wanted to do a plate infill and create the plate elements. We simply broke the 2.5 long pipe into 5 sections because we knew that the pipe circumference is broken down into eight 0.5 lengths. Figure 10:Stiffners grid in the STAAD.Pro Graphics window. 13. Draw the base plate/stiffener and column/stiffener interface using the stiffeners grid. Figure 13:Translational Repeat Command. 19. Now we need to create the top portion of the stiffener. You can do this by creating a new stiffener grid at 2.5 elevation. Figure 11 Base plate/stiffener and column/stiffener interface drawn using the Stiffeners grid. 14. Select the beam elements that represent the column/base plate interface. 15. Select the Geometry->Translational Repeat menu command. 16. The 3D Repeat dialog box will appear as shown in Figure Click on the Geometry->Snap/Grid Node- >Beam menu command. 21. Click on the Create button in the Data Area. 22. Turn on the stiffeners grid and the radial grid will appear in the graphics window as illustrated in Figure 14. Figure 12:Translational Repeat Command. 17. Enter the values in the 3D Repeat dialog box as shown in Figure Click the Ok button. The pipe connected to the base plate will be displayed. For the Figure 14:Stiffners grid in the STAAD.Pro Graphics window. 23. Click on the Copy button in the Data Area. Type Stiffener_top as the name for the new stiffener grid. 4

5 29. Select the four base nodes of the stiffeners as illustrated in Figure 18. Figure 15: Copy grid option. 24. You will notice a Stiffener_top entry in the Data Area. Turn on the Stiffener_top grid. 25. Click on the edit button in the Data Area. 26. The Radial grid options dialog box will appear. Enter the parameters as shown in Figure 16. Figure 18: Four bottom nodes of the stiffener plates selected. 30. Click on Geometry->Translational Repeat menu command. Figure 19: Translational repeat on the bottom four nodes. 31. Enter the values in the 3D Repeat dialog box as shown in Figure 19. Figure 16:Stiffners grid in the STAAD.Pro Graphics window. 32. Click the Ok button. 27. Click on the Ok button. 28. Draw the top edges of the stiffeners as highlighted in Figure 17. Figure 20: Vertical edges of plate stiffeners created. Figure 17:Top edges of stiffeners created using the Stiffener_top grid. 33. Click on Geometry->Add Beam->Add Beam from Point to Point menu command and draw the sloping edges of the stiffeners as shown in Figure 21. 5

6 Figure 23: Unwanted elements selected in the graphics window. Figure 21: Sloping edges of plate stiffeners created. 34. We would like to use the Plate Infill command to create the plate elements for the pipe. We will use the Generate Surface Meshing Tool to generate the mesh for the stiffeners. The Parametric Meshing Tool will be used to generate the mesh for the base plate. Select the plan view of the geometry that we have created. 35. Rubberband the beam elements that represent the pipe section. You will end up picking up some unwanted elements also. 38. Select the Select->By Inverse->Inverse Beam Selection menu command. 39. The elements that represent the pipe section will be highlighted. 40. Right click in the graphics window and select the New View option. 41. Select the Display View in Active Window option. 42. Select the isometric view option. 43. Select all the beam elements as shown in Figure 24. You could use the Ctrl+A shortcut keys on your keyboard to select all the beam elements. Figure 22: Rubberband the elements that represent the pipe section. 36. Click on the View->View Selected Objects Only menu command. 37. Now in the plan view, you will only see the elements that represent the pipe and some stiffener elements. Select all the unwanted elements in the graphics window as shown in Figure 23. Figure 24: Unwanted elements selected in the graphics window. 44. Select the Geometry->Create Infill Plates menu command. The dialog box shown in Figure 25 will appear. 6

7 51. Enter that inputs in the Insert Node/Nodes dialog box as shown in Figure Get a good isometric view of one of the stiffener plates. Figure 25: Message Box - 40 plates are created. 53. Rubberband the stiffener plate elements as shown in Figure Click on the Ok button and you will notice that new plate elements are created between the areas bounded by the beam elements. 47. Click on the View->Whole Structure menu command. 48. We will break the sloping part of the stiffeners into five parts. Select the sloping part of the stiffeners in the graphics window as shown in Figure 26. Figure 26: Stiffener plate selected 54. Click on View->View Selected Objects Only menu command. 55. Select the Geometry->Generate Surface Meshing menu command. Figure 26: Sloping edges of stiffeners are selected. 49. Click on the Geometry->Insert Node menu command. 50. The Insert Node/Nodes dialog box will appear as shown in Figure 27. Figure 27: Node Points for Generate Surface Meshing command 56. You will notice that your mouse cursor has changed. Select the nodes on the edge of the stiffener plate in clockwise or counterclockwise fashion as indicated in Figure 27. Select the node that you started off from when you are done. Figure 25: Insert Node dialog box 7

8 59. Select the Plates cursor and select all the newly created plate elements in the graphic window. 60. Click on Geometry->Circular Repeat menu Command. 61. The 3D Circular dialog box will appear as shown in Figure 31. Figure 28: Sloping edges of stiffeners are selected. 57. The Define Mesh Region dialog box will appear as shown in Figure 28. Enter 1 for all rows in the Div. column as illustrated in Figure 29. We are telling STAAD.Pro to avoid dividing each of the divided edges into smaller pieces. Figure 31: Meshing for stiffeners. 62. Enter the inputs in the 3D Circular dialog box as shown in Figure Click the Ok button. You will notice that all the stiffener plates have been created as shown in Figure 32. Figure 29: Number of edge divisions set to Click on the Ok button. You will note that the meshing for the stiffener has been created as shown in Figure 30. Figure 32: Meshing for stiffeners. 64. Select the View->Whole Structure menu command. 65. We will need to divide the base plate edges into 12 parts. Select the four base plate edges and select the Geometry->Insert Node menu command. Figure 30: Meshing for stiffeners. 8

9 74. The Mesh Parameters dialog box will appear as illustrated in Figure 35. Figure 33: Meshing for stiffeners. 66. The Insert Node/Nodes dialog box will appear as shown in Figure Enter that inputs in the Insert Node/Nodes dialog box as shown in Figure We will draw the base plate using the Parametric Meshing Tool. Click on the Geometry->Parametric Meshing control tab on your left. 69. Click on the Add button in the Data Area. The New Mesh Model dialog box will appear as shown in Figure 34. Figure 33: Meshing for stiffeners. 75. Set the inputs as shown in Figure 33 and click the Ok button. 76. Click on the No button for the following dialog box. 77. You will see a mesh preview. This preview mode lets the user identify any problems in the FEM model. In Figure 34, we can see that there is a plate connectivity problem at the pipe/base plate interface. Figure 34: Meshing for stiffeners. 70. Type a mesh name as shown in Figure 34 (i.e. BasePlate). 71. Click on the Ok button. 72. You will notice that the mouse cursor will change. Figure 34: Meshing for stiffeners. 78. You can resolve this issue by only generating the mesh for regions marked as R1 and R2 and then doing a circular repeat on the mesh. 73. Select the four corner nodes in the clockwise or counter-clockwise fashion and select the starting node once you have selecting four nodes. 9

10 Note that we do not have any connectivity problems in this case. 82. Click on the Setup control tab on the left. 83. Select the Select->Plates Parallel to->xz menu command. 84. Click on Geometry->Circular Repeat menu command. Enter the inputs as shown in Figure 38. Figure 35: Mesh generation by regions. 79. We have not documented all these steps in detail in this document. 80. Parametric meshing Type A for B1 (see Figure 36). Figure 38: Circular repeat for Base Plate 85. Click on the Ok button. 86. Select the Select->Plates Parallel to->xz menu command. 87. Click on View->View Selected Objects Only menu command. Figure 36: Mesh generation by regions Region R1 88. Select the Geometry->Generate Surface Meshing menu command. Click on the nodes shown in Red in Figure Click on the Merge Mesh button. Figure 39: Node outline for the Geometry->Generate Surface Meshing menu command Figure 37: Mesh generation by regions Region R2 89. The Define Mesh Region dialog box will appear as shown in Figure 40. Enter 1 for all rows in the Div. column as illustrated in Figure 29. We are telling STAAD.Pro to 10

11 avoid dividing each of the divided edges into smaller pieces. 97. Check if the model is ok from the plate to plate connectivity point of view by clicking on Tools->Check for improperly connected plates menu command. Property Assignment: 98. We will assign 0.5, 0.4 and 0.6 thickness to the pipe, stiffeners, and base plates respectively. Figure 40: Number of edge divisions set to Click on the Ok button. 91. Select the View->Whole Structure menu command. 92. Press the Esc key on your keyboard to cancel the Generate Surface Meshing command. 93. Select the beams cursor and press the Ctrl+A key to select all the beams. 99. In a 3D model, it is sometimes difficult to extract a particular section and assign a property to it. For example, it is difficult to select the pipe section out of the 3D model we have and assign the appropriate thickness to it. One could assign plate elements to groups when the geometry is being created. In the case of this example, we know that the number of plates along the circumference = 8 and number of divisions along the height of the pipe= 5. Hence, the number of plates used to create the pipe = 8x5=40 plate elements. Click on Select -> By List -> Plates menu command The Select Plates dialog box will appear as shown in Figure Press the delete key on your keyboard and press Ok on the following dialog box. 95. Right click in the graphics window and select the 3D Rendering option. Figure 42: Rendered view of the base plate geometry. Figure 41: Rendered view of the base plate geometry. 96. Close the rendered mode by simply clicking on the Setup control tab on the left The first plate numbering starts from 117. Hence, to select the first fifty plates in the model, we will need to provide the range of 117 to 167 in the Enter List input box Click on the Select Listed Entities button in the Select Plates dialog box. 11

12 103. You will notice that the pipe elements will be selected in the Graphics window as illustrated in Figure Press the F2 key on your keyboard. A yellow dialog box will appear as shown in Figure 45. Figure 45: Unit converter tool 112. Type 0.5 in in the input box and press the Enter key on your keyboard. Figure 43: Pipe plate elements selected in the graphics window Click on the Close button Click on General control tab on the left The Properties dialog box will appear in the Data Area Click on the Thickness button in the Properties dialog box The Plate Thickness dialog box will appear as illustrated in Figure You will notice that STAAD.Pro will automatically convert 0.5 in to ft Click on the Assign button Click on the Close button Click on the whitespace in the graphics window to get rid of the plate selection We will now assign the properties to the base plate Select the Select->Plates Parallel to->xz menu command Click on the Thickness button in the Properties dialog box The Plate Thickness dialog box will appear as illustrated in Figure 46. Figure 44: Plate Thickness Dialog Box 109. Select Steel in the Material selection box We know that the pipe thickness is 0.4 but the input system in the Plate Thickness dialog box is in ft. We can use the unit converter to convert 0.5 to ft. Click in the Node 1 input box. Figure 46: Plate Thickness Dialog Box 121. Select Steel in the Material selection box. 12

13 122. We know that the base plate thickness is 0.6 but the input system in the Plate Thickness dialog box is in ft. We can use the unit converter to convert 0.6 to ft. Click in the Node 1 input box Press the F2 key on your keyboard. A yellow dialog box will appear as shown in Figure 47. Figure 48: Plate Thickness Dialog Box 133. Select STEEL in the Material selection box. Figure 47: Unit converter tool 124. Type 0.6 in in the input box and press the Enter key on your keyboard You will notice that STAAD.Pro will automatically convert 0.6 in to 0.05 ft We know that the stiffener thickness is 0.4 but the input system in the Plate Thickness dialog box is in ft. We can use the unit converter to convert 0.4 to ft. Click in the Node 1 input box Press the F2 key on your keyboard. A yellow dialog box will appear as shown in Figure Click on the Assign button Click on the Close button Click on the whitespace in the graphics window to get rid of the plate selection We will now assign the properties to the stiffener plates Select the Select->By Missing Attributes- >Missing Properties menu command Click on the Thickness button in the Properties dialog box The Plate Thickness dialog box will appear as illustrated in Figure 48. Figure 49: Unit converter tool 136. Type 0.4 in in the input box and press the Enter key on your keyboard You will notice that STAAD.Pro will automatically convert 0.4 in to ft Click on the Assign button Click on the Close button Click on the whitespace in the graphics window to get rid of the plate selection Right click in the graphics window and select the 3D Rendering option. You will be able to see the plate thickness in the 3D Rendered mode as illustrated in Figure

14 Figure 52: Adding new node Figure 50: 3D Rendering with plate thickness 142. Close the rendered mode by simply clicking on the Setup control tab on the left We will need to create a node at the top at (3,2.5,3) to which we will apply a point load. This node will distribute the loading to the column node points Click on the General->Spec control tab on the left Click on the Node button The Node Specification dialog box will appear. Enter the master node number in the Master Node selection box (e.g. 658 in this example as noted in Step# 148 above) Click on the Geometry control tab on the left You will notice the Nodes Table in the data area as illustrated in Figure 51. Close the Snap Node/Beam dialog box if it is open. Figure 52: Adding new node 152. Click on the Add button Select the plan view of the structure Using the Nodes cursor, select all the nodes at the top of the FEM model as illustrated in Figure 53. Figure 51: Nodes Table 146. Scroll down to the end of the Nodes Table You will notice a blank cell at the end Type in coordinates of the new node as shown in Figure 52. This node is the Master Node. Remember this node number. The node number used in this example is 658. Figure 53: Top nodes of the FEM model selected 14

15 155. Select the View->View Selected Objects only menu command Unselect the four extra stiffener nodes. Your node selection should look as illustrated in Figure Open the General->Support control tab on the left Click on the Create button. The Create Support dialog box will appear Select the Foundation tab in the Create Support dialog box Enter the inputs as illustrated in Figure 56 Figure 54: Top nodes of the FEM model selected 157. Select the Assign button in the Data Area Check the Highlight Assigned Geometry box in the Specifications dialog box and select the SLAVE RIGID MASTER entry You will note that the Master node is indicated double circles and the attached slave nodes are highlighted in red as shown in Figure 55. Figure 56 Support Input Parameters 167. Click the Add button Select the Support 2 entry in the supports dialog box in the Data Area. Figure 55: Master node highlighted with double blue circles in the STAAD.Pro interface 160. The Master/Slave node specification was assigned so that we can apply a moment and axial force value at the master node and that moment will be distributed to the pipe section as forces using the rigid diaphragm action Select the Select->Plates Parallel to->xz menu command Select the Assign To Selected Plates option in the Supports dialog box Click on the Assign button Click on the whitespace in the graphics window to get rid of the plate selection Select the View->Whole Structure menu command. Support Conditions: 162. Let us assume that the base plate is resting on compacted soil with a sub-grade modulus of 144 kip/ft 2 /ft. 15

16 Loading: 173. Select the General->Load control tab on the left Click on Load Case Details tree item in the Data Area Select the Nodal Load->Node tree item on the left Enter the nodal loads (i.e. -25 kips Fy, -0.2 kip-ft Mx) as shown Figure Click the Add button The Add New: Load Cases dialog box will appear. Enter Dead Load + Wind Load in the Title text box as shown in Figure 57. Figure 58: Nodal Load Definition 183. Click the Add button. Click the Close Button. Figure 57: Load Definition 177. Click the Add button. Click the Close button Select the Dead Load + Wind Load tree item in the Data Area Click the Add button The Add New: Load Items dialog box will appear. Select the Selfweight tree item on the left and click on the Add button Select the entry for the nodal load in the Dead Load + Wind Load tree item Select the nodes cursor Select the master node in the graphics Select the Assign to Selected Nodes option in the Data Area Click on the Assign button The nodal load will be displayed in the graphics window as shown in Figure 59. Figure 58: Load Definition Figure 59: Nodal Load 16

17 Specifying Analysis Type: 190. Select the Analysis/Print control tab on the left. The Analysis/Print Commands dialog box will appear. Analysis Results: 194. Click on the Postprocessing tab at the top Click on the Ok button on the Results Setup box Click in the white space of the graphics window. Press Shift+S to turn off the supports Exaggerate the displacement scale. You will be able to see the displacement of the base plate as shown in Figure 62. Figure 60: Analysis/.Print Commands 191. Select the All option on the left and click on the Add button Click the Close button Select the Analyze->Run Analysis menu command. The STAAD Analysis and Design dialog box will appear and show you the progress of the Finite Element Analysis calculations. Figure 62: Displacement Diagram 198. You will be able to see the deflection values in the Displacement Table on the right. Click on the Nodes tab if the displacement tables are not visible Let us say that you were only interested in the displacement results for the base plate. Figure 61: Analysis/.Print Commands 200. Right click on the Displacement Table on the right and select the Results Setup option. 17

18 201. Select the Range tab. Select the Property option Select P2:Plate Thickness in the Property selection box Select Base Pressure in the Stress Type selection box You will be able to see the Base Pressure diagram as shown in Figure Click the Ok button Select the Summary tab in the displacement table You will notice that STAAD.Pro had reported the maximum and minimum deflections for all the node points connected to the base plate. The maximum displacement is in for node#10. Figure 65: Base Pressure Diagram Figure 63: Displacement Table 206. Select the Plate tab on the left. The Diagrams dialog box will appear as shown in Figure This base pressure can be compared with the soil bearing capacity. If the soil bearing capacity is exceeded, you may have to increase the base plate dimensions or increase the size of the plates, provide more stiffeners etc. In this case, the maximum base pressure is ksi. If the allowable base pressure is ksi, this base plate design in ok from the serviceability check point of view Select the Plate tab on the left. The Diagrams dialog box will appear as shown in Figure Select Max Absolute in the Stress Type selection box Click on the Ok button You will be able to see the stress distribution diagram as illustrated in Figure 66. Figure 64: Displacement Table 18

19 Existing Model was modified to add more stiffeners (Approx. 20 min to modify the existing model): Figure 66: Stress Distribution Diagram 214. You can compare these values with the allowable steel stress. In this case, the stress in the steel is about 12 ksi. Recommended Exercises: - Try to increase the moment until you see some uplift. What is the best way to see if your base plate is experiencing uplift? - Try increasing the thickness of the stiffeners. How does this affect the base pressure distribution? Try a thinner base plate. - What if you want to put in more stiffeners? Figure 66: Uplift Conditions 19

20 STAAD.Pro Input File STAAD SPACE START JOB INFORMATION ENGINEER DATE 24-Mar-08 END JOB INFORMATION INPUT WIDTH 79 UNIT FEET KIP JOINT COORDINATES ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; 20

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23 ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ELEMENT INCIDENCES SHELL ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; 23

24 ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; 24

25 ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; 25