Mohr's circle

Subject: MOHR
Size: 2646 by CRC: #B4E5h (G version) 2197.5 by CRC: #A314h (S version)
Autor: Mario de Lama, http://teleline.terra.es/personal/mdelama
Description: Numerical and graph solution of Mohr's circle (HP48S/G)
Date: 27-11-1999

NOTE: When you read Sx, Sy, S1 or S2 you must understand Sigma strees in direction x,y,1 or 2 and Txy will be shearing stress.

To begin with, it will be necessary to notice that when facing one of these problems, two cases can be presented:

  1. To find the stress state of a point in a specific direction, given the principle stresses and the angle that defines this direction.
  2. To find the principle stresses knowing the normal tensions in two perpendicular directions and their corresponding tangential stresses.
You can see that I have not included the state of triple tensions since the normal thing is the study of 2D systems.

For all the above-mentioned, when beginning the program we are asked to choose one of these two options, presenting a menu (48S) or a choose box (48G) with the "Principle stress" (S12) and "Stress in X dir" (Sxy) options and the message "Choose one". If we press Sxy flag 6 is activated and the program continues, in the event of pressing S12 the program simply continues.

Next will appear the screen for data input, after giving the corresponding values we press ENTER or OK. For the input of data, follow the approach of signs of the GROB.1; in it, the positive directions are all those that don't have expressly the negative sign. When we give the angle it will always be the one that forms the 1 axes with the X axes (the same one that forms 2 and Y)

For the numeric solution, we used the six equations that appear in the left figure (you can see that both first are in fact four, depending on the sign). If, by mistake, we have given some data such as S1<S2 the program aborts with a message, since it must be opposite or, as much, they can be same. An error can be made when trying to find the angle that gives us the direction of main stresses, it can be because numerator and denominator are zero or only the denominator. In the first case it is clear that the solution must be zero, since the circle is a point in which all the directions are principle. The second case would give us infinite and therefore the infinite arctangent is 90 degrees.

Once lapsed some seconds the solution appears in screen, we can move with the cursor for it and to request the value of the coordinates when we want it pressing the (x,y) menu. This value only will reflect real data while we don't leave the graphic environment, since when pressing ON the program finishes after to erase PPAR. If we return to the graphic environment we will meet with the same drawing, but now the coordinates are those of user, it is no longer to scale. When we leave the graphic screen we will be in the stack the labeled results.

If our data have been the angle and the principles stresses, it will always mark us the angle between the axes 1 and X (positive counter-clock wise).

If the program calculates the angle, it will always draw us the one that forms the address X with the nearest principle axis, it can be 1 or 2, it will be positive if to go from X to 1 or 2 we must follow a counter-clock wise way. We will know then that, in the point that we are analyzing, we must rotate the X axis in the marked way to arrive to the principle axis pointed out in the circle.

Thanks to Amir Degani amir@eddie.technion.ac.il for his help whit this document, if you don't understand Spanish (my native languaje) then you owe this program to Amir.

This is a sequence of the steps in the hp48G program:

Fig. 1Fig. 2
Fig. 3Fig. 4