EARTHQUAKE RESISTANT DESIGN THE BALSA WOOD BUILDING PROJECT MODEL DIMENSIONS AND DETAILS •
Number of floors = 5
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Building Plan Dimensions = 12 in x 12 in (outside-to-outside)
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Floor height = 6 in (floor level to floor level)
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Building height = 30 in
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Diaphragms (floors) = 12 in x 12 in made of flat balsa wood sheets or of hardboard adjusted at edges to be properly attached to beams and columns
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Use two bays on each side (see attached sketch). No interior columns.
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Select the bracing type such that top floor horizontal movements is minimized. Adding more bracing will lower the displacement, but keep in mind, that the building with the minimum weight and the minimum displacement (least damage) is the best design. You can get the total weight of the building form the vertical reactions at the base joints.
SAP2000 PROGRAM 1. 2. 3. 4. 5.
run the program from the START button go to units in the lower right hand corner of the screen and input LB-IN under the FILE tab select NEW MODEL FROM TEMPLATE select the second template in the second row input the following: Number of stories = 5 Bays in the X direction = 2 Bays in the Y-direction = 2 Story height = 6 Bay width along X = 6 Bay width along Y = 6
6. two screens will pop up showing your model in 3-D and in the X-Y plane. 7. now we are going to remove the interior columns from the middle of the building 8. click with the mouse on all the middle columns. There should a total of 5 columns that need to be removed. Once you marked all the columns that need to be
removed, the selected columns will become dashes lines. Press DELETE to delete theses columns. Note make sure you select the right columns to remove because the 3-D model can be congested. To get better 3-D views, go to VIEW and select SET 3D VIEW, then you can change the view angle in plan, in elevation, and aperture 9. now we are going to add X-braces. 10. go to the left hand side tool bar and select the button that has a line (when you place the mouse on it, it shows DRAW FRAME ELEMENT. Click on that button and connect the two joints that form the brace members. Add only braces in the Xdirection. Add the X-braces in each floor as shown on the attached sketch. 11. since we are using balsa wood, we need to define the properties of this material for the program. The program has steel and concrete as default materials. To do that, go to the DEFINE tab and select MATERIAL. Click in OTHER, and then click on MODFIY/SHOW MATERIAL. Change OTHER to BALSA and input the properties given below in the appropriate cells: Use the following properties of Balsa wood: Weight per unit volume (or weight density), γ w = 0.0059 pci (~ 10 pcf) Mass per unit volume (or mass density), γ m = γ w /g = 1.526E-05 lb.s2/in4 (0.3105 lb.s2/ft4) Modulus of elasticity, E (parallel to grains) = 500,000 psi Poisson’s Ratio, υ ∼ 0.40 Coefficient of Thermal Expansion, α = 2 x 10-5 /oF 12. once you define the material, select all members in the building and assign frame sections. You can do that using the ASSIGN tab and then select SECTIONS or click on the I button from the top tool buttons. 13. Select all members of the building (beams, columns, and braces), then go to ASSIGN, then select FRAME, then select SECTIONS. Go to cell that says ADD I/WIDE FLANGE and scroll down to select ADD RECTANGULAR. A new window will show several cells. For DEPTH and WIDTH cells, input in each of these two cells 1/8 in or 0.125. 14. then change the cell showing the material to BALSA. 15. then change the SECTION NAME from FSEC1 to BALSA1, then click OK 16. we need to restrain the base of the building to make all the columns fixed at the base. To do that click on all the four joints at the base of the building and go to ASSIGN tab and select JOINTS and then select RESTRAINTS. Click on the first button from the left from the four buttons shown under FAST RESTRAINTS, this chow a check mark on all the translations and rotations of these joints which means that they can not translate or rotate in any direction, in other word they are fixed, which is what we want. Now all the elements (beams, columns, and braces) are frames section BALSA1 next we will define the loads. We will start with static loads. 17. go to the DEFINE tab and select STATIC LOAD CASES
18. you will see LOAD1 – leave that load as is – do not change – this static load case is typically reserved for the self weight loads. 19. in the cell where it shows LOAD1, type DL for dead load and change the SELF WEIGHT MULTIPLIER form 1 to 0, then click ADD NEW LOAD 20. do the same thing you did for DL and add W for wind loads, and click ADD NEW LOAD, then click OK 21. to add W on certain joints on the structure, click on the joint (s) that want to load, then go to ASSIGN tab and select JOINT STATIC LOADS, then select FORCES or you can use the button. 22. remember that direction 1 is the X, direction 2 is the Y and direction 3 is the Z. 23. let us say, you want to add wind load = 0.5 lbs on the top joint in the + Y direction. 24. to do that, follow the steps in 23, and then input +0.5 lb in GLOBAL Y cell. Then click ok. 25. to add earthquake loads, go to DEFINE, select, TIME HISTORY FUNCTIONS 26. click on the ADD FUNCTION FROM FILE, then click on OPEN FILE, then type file name, then check TIME AND FUNCTION VALUES, then click OK. 27. then under DEFINE, select TIME HISTORY CASES, and then click on ADD NEW HISTORY. The program will add time history case 1 or HIST1 28. in the new window, input in NUMBER OF OUTPUT STEPS = 600 and input in TIME STEP SIZE = 0.05, check ENVELOPES, then under LOAD ASSIGMENTS, change the cell that says RAMP to FUNC1, then click ADD, then click OK 29. Run the program either using the ANALYZE tab or from the button that has an arrow in it. 30. when the run is complete, the program will tell you ANALYSIS COMPLETE. 31. to view joint displacements, click on the ∆ button, then select which load you want to check (LOAD1, DL, W, or HIST1), let us say you want joint displacements due to earthquake loads, then select HIST1, then right click on the joint you want to check and you will see joint movements in direction 1, 2, and 3 give in inches.
Balsa wood compared to structural Steel Properties of Structural Steel: Weight per unit volume (or weight density), γ w = 0.283 pci (~ 490 pcf) Mass per unit volume (or mass density), γ m = γ w /g = 7.234E-04 lb.s2/in4 (15.21 lb.s2/ft4) Modulus of elasticity, E (parallel to grains) = 29,000,000 psi Poisson’s Ratio, υ ∼ 0.30 Coefficient of Thermal Expansion, α = .65 x 10-5 /oF
Base model
BracedMoment-Frame Frame (K-type)
Braced Frame Braced Frame (Diagonal type) (X-type))
