Mohrs

Mohrs

Applet link

What:
Mohr’s Circle (efunda link) is a simple graphical method that allows engineers to visualize and analyze internal stress (force per unit area) within engineering materials. The Mohrs applet is designed to interactively explore the relationship between a given stress state, the frame of reference and the graphical Mohr’s circle representation.

How:
Stress element: The left hand graphic displays a stress element - an infinitesimally small square segment of the material being represented, outlined in black. All four sides of the element are subject to two types of stress. Normal stresses are perpendicular to the element face (representing pressing or pulling on the face) and shear stresses are parallel to the element face (representing a ‘dragging’ force across the face). These stresses are each represented by arrows in the appropriate direction and sized according to their magnitude.
Clicking and dragging the cursor across this graphic will rotate the black stress element in space, leaving a red outlined version in the original orientation. The stress arrows in the rotated element will change in magnitude along with the new orientation, maintaining the same stress state, but through different combinations of the normal and shear stresses. This motion will result in updates to the numbers displayed in the ‘Rotated Frame’ data section and changes to the circle graphic plot.
Plot canvas: The right hand side displays two axes - the horizontal axis representing normal stress (sigma) and the vertical axis representing shear stress (tau). The graphic displays two segments - red and black (which may overlap) representing the interpretations of the stress state corresponding to the ‘original’ and ‘rotated’ elements displayed on the stress element graphic. Each endpoint of the plotted segment represents the normal and shear stress pair on two faces of the stress element.
In the default configuration, the vertical sides (left and right) of the element are being pulled with a magnitude of 40, but have no shear component. The horizontal sides (top and bottom) are also being pulled, but with a much smaller magnitude of 5, again with no shear component. The line on the plot canvas runs from (5,0) to (40,0).
As the stress element is rotated, the endpoints of the various configurations will be left on the plot canvas, tracing out the circle that is known as Mohr’s Circle.
Original Frame values: These text boxes, outlined in red, list the two normal (Sigma X and Sigma Y) and one shear component (Tau XY - vertical shear along the horizontal face must have the same magnitude as horizontal shear along the vertical face) of the stress state defined in the original frame and corresponding to the red stress element. The orientation of this element - as pictured on the graphic - is listed in radians of rotation (Theta). All of these values can be incremented using the spinner arrows or can be set directly by entering a new value. Changes to these values change the stress state, and therefore the past states traced in the circle graphic are erased. The corresponding stress state in the black, rotated frame is also updated.
Rotated Frame values: These text boxes, outlined in black, list the two normal and one shear component of the rotated stress state corresponding to the black stress element, with a rotation relative to the original vertical orientation. All of these values can be incremented using the spinner arrows or can be set directly by entering a new value. Changes to these values change the stress state, and therefore the past states traced in the circle graphic are erased. The corresponding stress state is the red, ‘original’ frame is also updated.
View Window values: These values define the range and domain of the plot canvas, and can be altered to change the size of the graph.
Show Circle checkbox: Toggling this box ‘on’ will draw the Mohr’s Circle corresponding to the given stress states.
Settings: Clicking this button will bring up a set of six values defining the appearance of the applet that can be adjusted either with spinner increments or text entry. These values are
Box size: adjusts the size (in pixels) of the square representing the stress element
Sigma buffer: adjusts the space (in pixels) between the normal stress arrow and the element box
Tau buffer: adjusts the space (in pixels) between the shear stress arrow and the element box
Scale: adjusts the length of the stress arrows as a multiplier
Arrow scale: adjusts the size of the arrowheads on the stress arrows, also a multiplier

Why:
This applet was originally created in collaboration with the department of Civil and Environmental Engineering at Duke University.
Analysis of principal stresses (the maximum magnitudes and corresponding orientations for normal and shear stresses) using Mohr’s Circle is generally part of sophomore level undergraduate engineering courses on the strength of materials.