OREGON STATE UNIVERSITY
ME 453 – STRUCTURE AND MECHANICS LABORATORY
Lab Experiment Guidelines – Project #1– Winter 2010
The following illustration (Figure 1) shows the fixed end of the beam for the rosette strain gauge
experiment we are conducting. Please use the labeling scheme for the gauges and the coordinate
system as shown.
y
a
b
c
x
z
Figure 1. Coordinate system and rosette strain gauge orientation and labeling.
LABVIEW PROGRAM
Write a State Machine style LabVIEW program that does the following:
1. Collect “continuous” readings from each strain gauge.
2. Filter signals to eliminate high-frequency noise and produce steady output.
3. Allow zeroing (nulling) of all the channels.
4. Provide both graphical and numerical indicators of the strain levels. Clearly label the signals
from each of the individual gauges (ma =, mb =, mc =).
5. From the individual strain gauge readings calculate and display the strain tensor components
with respect to the coordinate system shown above (xx = , yy = , xy = ).
6. Calculate the principal strain values, the maximum shear strain, and the angle from the xaxis to the maximum principal strain axis. Also display these, clearly labeled, on the front
panel (1 = , 2 = , /2max = ,  = ). Provide a graphical illustration of these values.
7. Create on the front panel a control where the beam end displacement value can be entered
manually (as read from the micrometer).
8. Allow the user to save at any point a set of values to a file: the strain gauge readings, the
beam end displacement, and the calculated strain tensor components, principal values,
maximum shear, and angle to the principal axes.
PROGRAM DOCUMENTATION
1. Layout the program, both front panel and block diagram, so that its function could be
understood by one of your classmates.
2. Include comments that describe what the program is doing and how to use it.
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STRAIN TENSOR MANIPULATION
1. The first calculation you need to perform is creating the strain tensor from the strain gauge
readings. The following matrix equation (Eq. 1) will do this for the coordinate system and
gauge orientation we are using. I will derive this in lecture; for now just implement in your
program to execute step 5 above.
xx   1
1 1 ma 
  
 
xy  0.5 0 0.5mb 
   0
 
1 0 
mc 
 yy  
Eq. 1
2. Next include a functional program block that allows you to set a coordinate rotation angle (
 in Eq. 2) and observe how the strain tensor components change (Eq. 3). I will ask you to
vary the angle in order to confirm your principal value and axis calculations.
cos x' x
l  cos

y' x
Eq. 2
  ll
'

cos x' y 

cos y' y 
T
Eq. 3
3. Next extract invariant information from the strain tensor. There are several ways to do this.
 LabVIEW has functions for eigen analysis; give these a try (Lvf. 1). You can also get started
by using the following equation (Eq. 2) to find the principal. The roots of this quadratic are
the principal values of strain. I will cover this in an upcoming lecture.
Lvf. 1
2  xx  yy  xxyy  xy2  0
Eq. 4
4. Finally, perform a calculation that allows you to determine if you have eliminated lateral
 loading or not. I am leaving the details up to you, but here are some suggestions. You need
to understand the strain state at the gauge location for both vertical and lateral loading. This
is best done by finding the stress state using basic beam formulae, then finding the
corresponding strain state using the biaxial Hooke’s Law. Mohr’s Circle is also a great tool
for evaluating these strain states, and I will ask you to append this to your report anyway, so
you might as well do it!
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LABVIEW PROGRAM STRUCTURE
The following example front panel should help you organize your program (Figure 2). The values
shown are illustrative; you should not expect the same numerical values. It shows the general
information processing flow from raw strain gauge readings to evaluation of the strain tensor
invariants. Your program does not have to look identical, but should include the same basic steps. It
should also extend beyond what is shown here, as indicated at the bottom of the figure.
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Figure 2. A sample LabVIEW front panel (partially complete) for the beam bending experiment.
LABVIEW PROGRAMMING DETAILS
Never forget about the context help system (actually an on-line documentation system) or the
function search button in LabVIEW; these are your main guides to making LabVIEW work.
However, there are a few things that are somewhat obscure. I have listed here a few helpful
functions and suggestions on implementation.
From the Array functions palette:
Build Array
Index Array
Array Constant
From the Linear Algebra functions palette:
AxB
Transpose
Eigenvalues and Eigenvectors
THE EXPERIMENT
It will seem like a bit of a let-down after all the programming, but here is what I want you to do. Take
the beam through a series of 5 fixed displacements, starting at zero and going to a reasonable
maximum displacement value. At each displacement attempt to adjust the beam alignment to
eliminate lateral loading. With this done, record the displacement value and the raw strain gauge
readings. Also record the strain tensor components, and the principal values and principal axis
orientation calculated from the strain tensor. All of these values will be compared with your analysis
of the beam shear strain. Make sure that you have your analysis results compiled before you do
final data collection so that you can spot potential problems. Also remember that your independent
variable is beam end deflection. All plots and tables of data will show how the dependent variables
(gauge readings, strain tensor components, etc.) vary with respect to the independent variable.
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