# Plane Stress and Mohr's Circle

## ES 302 Assignment 4

Using Matlab, set up a computer program as described in
Problem 6.C2, on page 407 in Beer and Johnston
*Mechanics of Materials*, second edition. However,
only work Problems 6.8 and 6.66 which you did for homework.
Begin by copying the previous program to a new file name.
As before use an **input** statement to get the above three values:
**sigx, sigy, and tauxy**

Make a table to show the three original stresses and the principal
stresses and maximum shear for the three problems.

As usual, put your name, date, and subject in the program with lines such as:

% print the results
fprintf('\n Plane Stress, Problem 6.')
fprintf('\n Your name, ES 302, ')
disp(date)

Copy the output from Matlab and paste it into the bottom of your
Matlab program. Include the while loop so you can several several
problems easily.
Attach the regular solutions to the problems.

Be sure that you use the Matlab **atan2** function,
not the **atan** function because the latter
will fail when sigx equals sigy.

When the program is running satisfactorily,
add an **if** statement to find the maximum shear stress.
This step is more complicated since you have to find if both
principal stresses have the same sign. Hint: see if the product
of the principal stresses is negative. If so, the maximum shear
stress is just the radius. Then check to see if the maximum
normal stress is positive. If so, the maximum shear is just
half of the normal stress. Otherwise, it is half the negative
of the other.

if sigxr*sigyr < 0
taumax = % tau max is in plane
elseif sigxr > 0 % tau max is out of plane
taumax =
else
taumax =
end

Your results should look like this:

Principal Stresses, Problem 6.
Your name, ES 302, 19-Oct-1998
Rotation angle -63.435 degrees
Sigma X Sigma Y Tau XY Angle
Ksi Ksi Ksi Degrees
Original -9.00 -6.00 -2.00
Rotated -5.00 -10.00 2.50 -63.43 (in plane)
Maximum shear= 5.00

Make sure each problem printout is identified. Better yet,
add another string input line to read and print the problem number.
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Last revised: March 17, 2000