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Author: Rajesh Bhaskaran, Cornell University

[Problem Specification|MATLAB Intro Problem Specification]
[Step 1: Find Reactions R{~}A~, R{~}B~|MATLAB Intro 1 Find Reactions]
[Step 2: Calculate _σ{_}{_}{~}x{~}_ for _r{_}{_}{~}i{~}_ = 1 cm|MATLAB Intro 2 Calculations]
[Step 3: Plot _σ{_}{_}{~}x{~}_ vs. _r{_}{_}{~}i{~}_|MATLAB Intro 3 First plot]
[Step 4: Plot _σ{_}{_}{~}x{~}_ vs. _r{_}{_}{~}i{~}_: Take 2| MATLAB Intro 4 Second plot]
[Step 5: Plot _σ{_}{_}{~}x{~}_ vs. _r{_}{_}{~}i{~}_, Take 3: File Input/Output|MATLAB Intro 5 Third plot]
{color:#ff0000}{*}Step 6: Plot{*}{color} {color:#ff0000}{*}{_}σ{_}{*}{color}{color:#ff0000}{*}{_}{~}x{~}{_}{*}{color} {color:#ff0000}{*}vs.*{color} {color:#ff0000}{*}{_}r{_}{*}{color}{color:#ff0000}{*}{_}{~}i{~}{_}{*}{color}{color:#ff0000}*, Take 4: Functions{*}{color}
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h1. Step 6: Plot _σ{_}{_}{~}x{~}_ vs. _r{_}{_}{~}i{~}_ , Take 4: Functions

Let's create a function to calculate the bending stress that outputs _σ{_}{_}{~}x{~}_ given (_M_, _r{_}{_}{~}i,~_ _r{_}{_}{~}o{~}_ ). Functions are really useful to break down your code into modules and also reuse parts of your code.

Let's first pick MATLAB's brain on how to create functions in MATLAB. Bring up the following page in the Help navigator:

*Help > Contents > MATLAB > Programming > M-File Programming > M-File Scripts and Functions > M-File Functions.*

This page has a simple example: a function called _average_ that calculates the average of the elements in a vector. Take a couple of minutes to peruse this example. MATLAB has extensive documentation on the use of functions; however, one has to poke around a bit before finding the most useful information. I personally go for the examples first.

The correct syntax for creating a function is:
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{{{color:#0000ff}function{color} return_value = function_name(parameter_1, parameter_2,...)}}

{{%function description - MUST  be in a comment}}

{{code...}}

{{return_value = value}}\\

A few noteworthy points to ponder:
# _return_value_ is the only data that gets passed back to the main code.
# You do not need to have a function description but it is good programming practice to add a comment on each function that describes what the function does. Also, if you add a description of the function, MATLAB will be able to index it and return a description of your function if you type {{help function_name}} in the Command Window.
# Once you have created a function you MUST name the .m file with the same name the function has. Otherwise MATLAB will not be able to access your function when you call it.
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We will start by creating the bending stress function that outputs _σ{_}{_}{~}x{~}_ given (_M_, _r{_}{_}{~}i,~_ _r{_}{_}{~}o{~}_ ). Create a new page in the editor. Type in the following statements into the new page:
\\  !matlab_2.png!

You can be lazy like me and copy-and-paste the last two statements from your previous code. Save this file as _bending_stress.m_, which is the name that MATLAB automatically assigns the file. Thus, the function name and the _.m_ have the same name.
Bring up _beam3.m_ in the MATLAB editor. Make a copy of _beam3.m_ using {color:#663399}{*}{_}Save As ..._{*}{color}  and call the new file _beam5.m_. In this file comment out the lines below since this calculation is now done within the function.

 !matlab_3.png! 

We'll replace these statements with a call to the _bending_stress_ function. The following statement does this:

 !matlab_4.png!\\
Add this to _beam5.m_. Run the file and check the output  You should get the same plot you got with _beam3.m_.
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h3. Subfunctions

Functions can be called within a function. As crazy as this sounds, this sometimes makes very complex code appear much more manageable by sectionalizing the code. To explain how to create a subfunction, let's look to the matlab help for an example:
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!subfunctions.png!

In the above example, there are three functions: the main function is called "newsstats". Within this function, there are two subfunctions; one called "mean" and the other, "median". The subfunction is defined the exact same way as the main function; but the difference is the subfunction can only used when the main function is used - you can not call your subfunctions in the command window. As you can see, the main function calls both of the subfunctions, making the code much shorter and simpler. For longer, more complex code, this can save you a lot of debugging time by breaking down your code into smaller pieces.
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Now, let's alter our code to include subfunctions. Open up your bendingstress.m file. Let's add a subfunction to calculate I in terms of {latex}$r_o${latex} and {latex}$r_i${latex}. At the bottom of the bendingstress.m file, add an "end". This will let Matlab know that we are done writing our main function. Now let's create a new subfunction called calc_I. 

function I = calc_I(ro,ri). 

Now, cut and paste the I assignment underneath the new subfunction call. Don't forget to add the end at the end of your subfunction!


That brings us to the end of this tour. Before we part, let's remind ourselves of some important programming guidelines that we have followed in this tour:
* Develop code incrementally, testing obsessively at each stage. Develop a plan for how you are going to build your code before you sit at the computer.
* Dig through the MATLAB help diligently to figure out how to use specific functions etc. Usually, the examples are the best place to start. This is a better strategy than desperately hunting for the TA every time you need help with your code.
* Comment your program liberally.
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