Water Tank Support Structure Design_RISA Tutorial Example

RISA Design ExampleProblem StatementLets assume we are to design a scale model of a water tower and ensure it can survive a known historical earthquake. Possible designs are shown in Figure 1. Figure 1. Possible water tower configurations.We will used a fixed weight of 6lb to represent the container and water and will be concerned with designing the supporting frame. The structural frame will be 18 between the base plate and the roof plate (the 6lb weight will be affixed 1 above the roof plate). The footprint of the structure is not to exceed 4x4. As mentioned, the structure will be subjected to a known earthquake, with response spectrum given in Figure 2.

Figure 2. 1940 El Centro ARS.The scale model will be built out of Balsa wood. The assumed material properties of Balsa wood are given in Table 1. The stress properties are used in the demand-capacity check while the modulus properties are used in the actual computer modeling.

Table 1. Assumed Balsa wood properties.Note that the RISA 2D license that you have available can solve models of any size, however, in order to save models, the model must contain less than 20 joints and 20 beam members. We will be simplifying our 3D model to 2D in order to use the software.Design Process1. We start by opening RISA 2D. The software is free to download for students and comes with a number of tutorials that you may investigate if you have time. The example we are currently going through should address most (hopefully all) of the functions youll need.2. Define units. It is always important to keep your units consistent. For this project, we will be working with pounds and inches.a. Main Menu -> Units -> put everything except the Rotational Springs and Temperature into units of inches and pounds. Use default values for Rotational Springs and Temperature. See Figure 3.

Figure 3. Updated units.3. Update the grid dimensions. The default grid is 360x360. For our purpose, we know that the grid doesnt need to be larger than 4x18 plus an allowance for the roof.a. Main Menu Bar -> Modify -> Grid -> set to Xaxis: [email protected], Yaxis: [email protected]. Note that if we move the mouse over the grid, the location of each grid point is displayed in the lower right hand corner. See Figure 4.

Figure 4. Updated grid.4. Define balsa wood. At this point we will define the stiffness due to the material (i.e. the modulus of the balsa wood); see Figure 5. The strength checks (i.e. when we ensure that the balsa wood is strong enough to support the loads we are going to apply) will be done later with Excel spreadsheets.a. Main Menu -> Spreadsheet -> Materials. Change the first row in the General tab to: i. Label: Balsaii. E: 500e3psi (Youngs Modulus)iii. G: 25e3psi (Shear Modulus) ignore the error that may pop up.iv. Nu:0.3 (Poissons Ratio)v. Therm:0.3 (Thermal Coefficient)vi. Dens:0.006lb/in^3 (Density)

Figure 5. Material properties.5. Define the cross section. The balsa members that you will use for construction are 0.25x0.25 square. Although it is possible for you to glue members together to make larger members, the owner thinks it is unaesthetic and discourages such construction. See Figure 6. Be sure not to change the RIGID section as we will also be using that section later.a. Main Menu -> Spreadsheet -> Section Sets. Change the first row in the General tab to:i. Label: Squareii. Shape: 0.25x0.25 (Rectangle)iii. Type: Beamiv. Material: Balsa

Figure 6. Cross section.6. Define a rigid roof. The top of our structure will be connected to a water tower. For design purposes, we will consider the roof to be very rigid (i.e. stiff) relative to the structural frame. Also, the center of the water tower is slightly above the top of our frame, thus we will include a 1 offset above our roof to which we will apply our loads. For my particular design, the frame will taper along the height and so I have drawn my roof only 2.5 wide. See Figure 7.a. Main Menu -> Insert -> Members. Since the roof will be solid, it is treated as fixed:

Figure 7. Rigid roof.7. Draw a structural frame. The frame can be any design you think is optimal. For inspiration, you can look up water tower frames that have actually been constructed. There is no wrong design when developing your first frame: whatever you design, you can always go back and update/improve upon.a. Main Menu -> Insert -> Members. Note that we have changed the Assign a Section Set from RIGID to Square. Also, depending on how you connect the balsa beams, you may change the Release Codes from Fixed to Pinned. (In reality, it is very unlikely that you will have a pinned connection.) Note that the center of the beams at the ground level are spaced 3.5 apart so that when I add the thickness of my beams and a little space for glue, Im still within the 4 footprint requirement. See Figure 8. Figure 8. Structural frame.8. Fix the base of the frame. The frame will most likely be rigidly glued to the base plate.a. Main Menu -> Insert -> Boundaries -> Click the Fixed Button -> Apply. Select the nodes at the base of the structure. Figure 9. Base fixity.9. Determine the stiffness of the frame. This is a multi-part step whereby we apply a 1lb horizontal test force, measure the deflection of the frame and determine the frame stiffness.a. Apply a 1lb horizontal force to the roof. See Figure 10.i. Main Menu -> Spreadsheets -> Loads -> Joint Loads/Disp. We apply 1lb to the center node (just above the roof) in the horizontal (X) direction under BLC1.

Figure 10. Applying a 1lb test force.b. Define a basic load case. We are essentially assigning a name to the 1lb horizontal load weve just defined. i. Main Menu -> Spreadsheets -> Basic Load Cases. Change the name to of the first line (i.e. BLC1) to 1lb Horiz Test Load. See Figure 11.

Figure 11. Define basic load case 1.c. Define a load combination. If we were designing a complex structure, we would have multiple loads to deal with: live loads, dead loads, wind loads, etc. Defining a load combination allows you to combine the effects of all of the various loads in an easy manner. Currently, we are only going to have a single load (the 1lb test load) in the load combination.i. Main Menu -> Spreadsheets -> Load Combinations. Change the name to 1lb Horiz Push. We want to include the BLC1 (see above) with a factor of 1 (if we set factor =2, we would be applying 2x1lb=2lbs). See Figure 12.

Figure 12. Define load combination.d. Solve for the deflection. After defining our load case, we have RISA run the computer model to determine the effects the 1lb force will have on the frame. See Figure 13.i. Main Menu -> Solve. Select Single Load Combination: 1lb Horiz Push.

Figure 13. Solve.As a check, ensure that the base horizontal reaction matches the applied load (in this case, 1lb).e. Determine joint deflections. Knowing the applied force, we use the horizontal displacement to determine the frame stiffness.i. Main Menu -> Results -> Joint Deflections. Im interested in the roof deflection which corresponds to joints N1-N4for my model. I see that my horizontal displacement (X) is 0.014in. See Figure 14.

Figure 14. Joint deflections under 1lb horizontal test force.f. Determine the stiffness of the frame. Keep in mind that this is just one frame and that the actual structure will have two frames (your structure could have more).

10. Determine the period of the structure. Since my actual (built) structure will have two frames, it will have two times the stiffness of the single frame I just calculated. Thus:

11. Determine the equivalent lateral load from the earthquake. Looking at the provided response spectrum, we see that my period is so short that Im at the very far left of the plot. My acceleration is 0.6g. To determine the applied horizontal force for the total structure, I calculate:

12. Apply seismic force. Since we have two frames in our actual structure, each frame will see half of the total seismic load. Thus, we apply 3.6lb/2=1.8lb to our modeled frame. We will apply this load under a new BLC: BLC2. See Figure 15, Figure 16, and Figure 17.a. Define load. Main Menu -> Spreadsheets -> Loads -> Joint Loads/Disp.

Figure 15. Apply seismic force.b. Define basic load case. Main Menu -> Spreadsheets -> Basic Load Cases.

Figure 16. Basic load case.c. Define load combination. Main Menu -> Spreadsheets -> Load Combinations.

Figure 17. Load combination.13. Apply vertical force. The structural members will experience internal forces generated from both the earthquake and the 6lb sitting on top of the roof (i.e. the frame has to support the 6lb regardless if an earthquake is occurring). For our single frame, we will apply half the total roof vertical load (3lb) under BLC3. See Figure 18, Figure 19, and Figure 20.a. Define load. Main Menu -> Spreadsheets -> Loads -> Joint Loads/Disp.

Figure 18. Define load.b. Define basic load case. Main Menu -> Spreadsheets -> Basic Load Cases.

Figure 19. Basic load case.c. Define load combination. Main Menu -> Spreadsheets -> Load Combinations.

Figure 20. Load combination.14. Solve for seismic and vertical load cases. We will need to solve the two load cases separately and then combine them in excel. We will combine the demands (what RISA calculates) and check them against the actual capacities of the 0.25x0.25 balsa members.a. Solve vertical load combination. Main Menu -> Solve -> Select Single Load Combination: 3lb Vertical. b. Obtain force output and copy to excel. Main Menu -> Results -> Members -> Forces. Take the output and copy it over to the correct cells in excel. Note, to check which member is which, we can turn on member titles by going to: Main Menu -> View -> Member Labels. See Figure 21. Figure 21. Force output.15. Determine the length of each member. For members in compression, buckling becomes a concern. The longer a member is, the less compression force it can carry. Thus, we need the length of each member to determine the capacity (in the excel spreadsheet). This information will also be useful during construction.a. From the icons, select Show Beam Labels and toggle between Label and Length. See Figure 22. Copy the lengths to the excel spreadsheet.

Figure 22. Member length.16. Check the Demand-Capacity ratios in Excel. We are taking the RISA output (demand forces) and copying them into the provided Excel spreadsheet. The spreadsheet calculates the capacities of the 0.25x0.25 balsa wood sections for shear, tension, compression, and bending. When inputting your data, only update the cells highlighted in red. The other cells are computations that you shouldnt change. To check if your frame is structurally sound, look at the colored cells under Capacity Check. If the D/C ratios are less than 1.0, youre structure should survive the seismic event. Looking at the example structure (see Figure 23), it is apparent that the designed structure should survive the seismic event. Note that the first 3 sections correspond to the RIGID elements representing the roof. Since these elements arent actual elements (the roof will be a solid plate), if the D/C ratios exceeded 1.0, I would still be okay.

Figure 23. Example structure D/C ratios.A note on compression: the compression limit is taken as the more severe case of crushing or buckling.What would an under-designed output look like? See Figure 24. Those members who are not structurally sound (i.e. dont have enough strength) are automatically highlighted in red.

Figure 24. Example structure with D/C ratios exceeding 1.0.

17. Optimize the structural design. Again looking at the sample structure, we see that for all of the 0.25x0.25 balsa elements, the D/C ratio is less than 0.5. Thus, I can go back through and change my design, perhaps using less material. If my D/C ratio exceeded 1.0 anywhere, my structure would collapse during the El Centro earthquake. If my D/C ratio is just under 1.0, than I know that that particular element cannot handle any more demand forces without breaking.