The document provides instructions for modeling a 5-story balsa wood building in SAP2000 to analyze its earthquake resistance. Key steps include: 1) defining the building dimensions and braced frame layout; 2) assigning balsa wood material properties with lower density, elasticity and cost than steel; 3) applying gravity, wind and earthquake loads; and 4) analyzing deflections under different load cases and bracing configurations to find the design with minimum weight and displacement damage. Comparing balsa wood to steel shows balsa's lower density offers design advantages if structural integrity can be achieved.

1. EARTHQUAKE RESISTANT DESIGN
THE BALSA WOOD BUILDING PROJECT
MODEL DIMENSIONS AND DETAILS
• Number of floors = 5
• Building Plan Dimensions = 12 in x 12 in (outside-to-outside)
• Floor height = 6 in (floor level to floor level)
• Building height = 30 in
• 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
• Use two bays on each side (see attached sketch). No interior columns.
• 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. run the program from the START button
2. go to units in the lower right hand corner of the screen and input LB-IN
3. under the FILE tab select NEW MODEL FROM TEMPLATE
4. select the second template in the second row
5. 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

2. 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
X-direction. 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), γw = 0.0059 pci (~ 10 pcf)
Mass per unit volume (or mass density), γm = γw /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.

3. 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), γw = 0.283 pci (~ 490 pcf)
Mass per unit volume (or mass density), γm = γw /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

4. Base model

5. Moment-Frame Braced Frame (K-type)
Braced Frame Braced Frame
(Diagonal type) (X-type))