MODELLING MULTISTOREY TIMBER WALLS – PART 2
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DEFINING THE BEHAVIOUR OF THE LINKS
The multilinear plastic links that you have put into the wall model will represent the force displacement behavior of
the model.
In the model we have been developing, the height of all walls, H is 3.5 m.
Assume the strengths (Fstrength) of the walls in the model as follows (yours will be different depending on the location
and earthquake characteristics etc). Note that these assumed strengths are for the example only, and are not based
on any detailed design:
Wall strengths
Storey
Strength
(Fstrength), kN
70
60
40
30
20
15
1
2
3
4
5
6
Firstly for each of the walls you need to define the force-displacement behavior and hysteretic characteristics of the
wall.
You do this separately for each of the walls. This is carried out in accordance with the separate handout called
DETERMINING LOAD SLIP CURVES FOR SHEAR WALLS and the accompanying spreadsheet. With the spreadsheet you
can carry out this process extremely rapidly. All you need are the respective wall heights (H) and wall strengths
(Fstrength).
From the spreadsheet (based on the wall strengths above), and H) load slip curves and hysteretic parameters for the
first storey wall is as follows:
Wall 1
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Displ (m)
Force (N)
-0.13409
-90234.4
-0.06475
-140000.0
-0.03259
-115937.5
-0.02154
-105273.4
-0.01579
-90234.4
-0.01048
-73828.1
-0.00775
-64257.8
-0.00517
-54687.5
-0.00258
-41015.6
-0.00072
-20507.8
0.00000
0.0
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0.00072
20507.8
0.00258
41015.6
0.00517
54687.5
0.00775
64257.8
0.01048
73828.1
0.01579
90234.4
0.02154
105273.4
0.03259
115937.5
0.06475
140000.0
0.13409
90234.4
α
β
12.62964448
0.455111111
Ke
28568412.16
N/m
We will enter these characteristics for wall 1 as an example and then you can do similar for the other links:
First select the following menu item:
Select the floor 1 link (you have previously created):
Then:
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The following dialogue box appears. Enter the force-displacement coordinates and other hysteresis characteristics as
below. Then click OK when you have finished, and exit all open dialogue boxes by clicking OK:
Save your work, and then start the previous 4 steps again, doing the same for each of the floor levels.
Once you have defined the behavior of all the floor levels your model is complete.
The next step is to enter in the earthquake records.
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THE ACCELERATION RECORDS
You will be provided with 8 acceleration records from historical earthquake events.
These are for El Centro, Kobe, Landers, Loma Prieta and Northridge. Note that the accelerations provided are in
terms of gravitational acceleration, g, which is something we will need to bear in mind for later on.
Place these text files into a folder called “EQ records” and then place the folder into the root directory (the C drive):
Now do the following steps for the El Centro earthquake:
Select the “From File” option and click “Add New Function….”
On the dialogue box that comes up, enter the settings indicated below. Once you have done this you can view the
resulting record if you like by clicking “display graph”. Then click the OK button to close the dialogue box.
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Now do the same for the remaining earthquake records.
Note that the “Header Lines to Skip” are all the same (ie 4), the Number of points per line remain the same for all
records, ie 5, but the “Values of Equal Intervals of” should be set as follows:
El Centro: 0.01
Kobe: 0.02
Landers: 0.02
Loma Prieta: 0.005
Northridge: 0.02
Once you have defined all the time history functions, naming them with the same name as the earthquake event
they represent, close all dialogue boxes, and save your project.
DEFINING THE LOAD CASES
We will now set up load cases which utilize the acceleration records which we referred to in the previous section.
First we need to define the gravity case, because we have dead loads:
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Select the DEAD load case and then click Modify/Show Load Case
Rename the load case gravity, make sure the load applied is same as indicated, and then click non-linear. Then select
Time History from the load case type. Rename the load case Gravity. Make sure your settings are exactly the same as
in the dialogue box below. Then click modify/show for modal damping as indicated:
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The following dialogue box will appear. Change Constant Damping for all Modes to 0.99. Then click OK, and then OK
again.
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We return to this dialogue box. This time select MODAL, then click the modify/show load case button:
Set the modal dialogue box as follows, then click OK:
The following dialogue box appears. Apply the settings as shown and then click OK:
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Now click add new load case:
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This time we first add the El Centro load case. Ensure your settings are EXACTLY the same as shown below. Note we
select the El Centro load function for the load case named El Centro. Click OK when you have done this.
Then in the same manner as the last two steps, add load cases for Kobe, Landers, Loma Prieta, and Northridge as
well (remember to change the function to match the load case). When you have done this your load cases box will
look like the following, with all these load cases displayed. Click OK to close the dialogue box, and then save your
work:
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EQ SCALE FACTORS
We need to scale the earthquakes to match the Ultimate limit state, and Maximum Considered earthquake spectra
of the location of interest.
The first thing we need to know is the fundamental period of our structure. To find this do the following:
On the Menu bar, click RUN:
On the dialogue box that appears, set everything to “DO NOT RUN” except for the Modal case, for which you set
RUN. Then click RUN NOW:
The programme will take a few seconds to run, and then you get something like this appear. The fundamental period
appears at the location indicated. Make a note of it. In the case of this example, it is 1.808 seconds:
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Now save the programme, and then close it. We now need to calculate scale factors using a spreadsheet.
Scaling earthquake records involve matching the spectrum of the event for which you are using acceleration records,
to the target design spectra obtained from the loadings code.
For example in the figure below, the Landers spectrum is compared to the target design level (ULS) spectrum for
Wellington.
BEFORE SCALING
AFTER SCALING (for T = 2 s) by multiplying by K = 1.4
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From the figure above, you will see that the spectra have been matched as closely as possible, for a range of periods
around T = 2 s. The scale factor used was K = 1.4
For our purposes the scale factors for Christchurch, Auckland, and Wellington have been plotted for building periods
up to 2.8, for El Centro, Kobe, Landers, Loma Prieta and Northridge. These are shown in the following three figures.
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For the structure we are modelling, the fundamental period is T = 1.8 seconds.
The ultimate limit state scale factors can be read off the charts and are summarized in the table below:
Table: Scale factors, K, for T = 1.8 s (read off charts –approximate)
Loma Prieta
Northridge
El Centro
Auckland
0.33
0.7
0.5
Christchurch
0.6
1.2
0.8
Wellington
1.4
2.7
1.8
Kobe
0.2
0.3
0.6
Landers
0.3
0.6
1.3
We now apply these scale factors to the programme we have been working on. For this example we will simply just
use the Wellington results. So open up the project again and follow the procedure outlined in the following
screenshots:
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Select the El Centro load case and click Modify/Show Load Case:
For the scale factor, K, we use 1.8 (El Centro scale factor for Wellington ULS event – refer table above).
However because the acceleration records are in terms of gravitational acceleration, g, we type for scale factor:
1.8 * 9.81 (this applies the scale factor and converts to m/s/s at the same time)
Type this in the scale factor box as indicated and then click modify, and then OK to close the dialogue box:
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Now do the same as above for the remaining 4 earthquake events, using the scale factors from the table as follows,
and multiplying by 9.81, that is:
Kobe: 0.6 * 9.81
Landers: 1.3 * 9.81
Loma Prieta: 1.4 * 9.81
Northridge: 2.7 * 9.81
RUN THE ANALYSIS (and view video)
Just to ensure that all the connections are pins, do the following, select the whole structure by ‘framing it’ with the
mouse:
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Then select the following menu:
A dialogue box appears. Ensure the settings are exactly the same as below, in order to have fully pinned joints at the
intersections of all members. After you have done this click OK to close the dialogue box:
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We will analyse the structure in 2D, so apply the Plane frame settings:
Save your project as a new project called: “Wellington ULS”
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Click the RUN button:
Select all cases to RUN , and then click RUN NOW to run the load cases:
The analysis will take several minutes to run, depending on the specs of your PC.
Once the analysis is complete, save the project.
We can view a video of the behavior of the structure under one of the load cases as follows:
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Try the settings below (you can experiment around with these yourself). Then click OK:
While the AVI file is being created you are provided with the following view:
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When the video completes, you have the option of saving it if you wish. If you do not wish to save it, simply click the
cancel button:
You have now completed the model, for “Wellington ULS”
Other projects you should consider are:
“Wellington MCE”
“Christchurch ULS”
“Christchurch MCE”
“Auckland ULS”
“Auckland MCE”
Note that MCE stands for maximum credible earthquake (1 in 2500 years). This compares with the ULS case which is
for a 500 year return period earthquake. The scale factors to use for the MCE are simply the ULS factors multiplied
by 1.8. This is not exact, but good enough for our purposes.
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So, for example, to do the analysis for the “Wellington MCE”, all you would need to do is save the “Wellington ULS”
project file as a “Wellington MCE” project, and then multiply by 1.8 all the currently used scale factors for the 5
earthquake events.
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