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h1. Bending of a Curved Beam: Pre-Analysis & Start-Up

h3. Pre-Analysis

There are three difference theories for finding the solution for the bending of a curved beam. There is elasticity theory, where
{latex}
$$
\sigma_r = (\frac{4M}{tb^2N}) [( 1 - \frac{a^2}{b^2}\ln(\frac{r}{a}) - (1 - \frac{a^2}{b^2})\ln(\frac{b}{a})]
$$
and
$$
\sigma_\theta = (\frac{4M}{tb^2N}) [(1 - \frac{a^2}{b^2})(1+\ln(\frac{r}{a})) - (1 + \frac{a^2}{r^2})\ln(\frac{b}{a})]
$$
where
$$
N = (1 - \frac{a^2}{b^2})^2 - 4(\frac{a^2}{b^2})\ln^2(\frac{b}{a})
$$
{latex}

There is Winkler Bach Theory, where

{latex}
$$
\sigma_x = \frac{M}{AR} [ 1 + \frac{y}{Z(R + y)}]
$$
where
$$
Z = -1 + \frac{R}{h}\ln[(R+\frac{h}{2})/(R - \frac{h}{2})]
$$
{latex}

And there is the straight beam theory, where
{latex}
$$
\sigma_x = \frac{My}{I}
$$
{latex}


h3. ANSYS Simulation

Now, let's load the problem into ANSYS and see how a computer simulation will compare. First, start by [downloading the files here|Bending of a Curved Beam - Pre-Analysis & Start-Up^Curved Beam Simulation Files.zip]
The zip file should contain the following contents:
- Curved Beam Solution_files folder
- Curved Beam Solution.wbpj

Please make sure to extract both of these files from the zip folder, the program will not work otherwise. (Note: The solution was created using ANSYS workbench 12.1 release, there may be compatibility issues when attempting to open with other versions).

2. Double click "Curved Beam Solution.wbpj" - This should automatically open ANSYS workbench (you have to twiddle your thumbs a bit before it opens up). You will be presented with the ANSYS solution.

!Bending of a Curved Beam Menu.png!

A tick mark against each step indicates that that step has been completed.

3. To look at the results, double click on "Results"  - This should bring up a new window (again you have to twiddle your thumbs a bit before it opens up).

4. On the left-hand side there should be an "Outline" toolbar. Look for "Solution (A6)".

!Curved Beam Outline.png!

We'll investigate the items listed under Solution in the next step in this tutorial.

Continue to [Step 2 - Results|Bending of a Curved Beam - Numerical Results]
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