Wednesday, April 30, 2008

Microsoft Excel VBA - Mohr's Circle for Plane Stress

The German engineer Otto Mohr (1835-1918) developed a useful pictorial or graphical interpretation of the equations for finding the principal stresses and the maximum shearing stress at a point in a stressed member. This method, commonly called Mohr's circle, involves the construction of a circle in such a manner that the coordinates of each point on the circle represent the normal and shearing stresses on one plane through the stressed point, and the angular position of the radius to the point gives the orientation of the plane.

Normal stresses are plotted as horizontal coordinates, with tensile stresses (positive) plotted to the right of the origin and compressive stresses (negative) plotted to the left. Shearing stresses are plotted as vertical coordinates, with those tending to produce a clockwise rotation of the stress element plotted above the s axis, and those tending to produce a counterclockwise rotation of the stress element plotted below the s axis.

The results obtained from Mohr's circle are identical with the equation derived from the free-body diagram. Consequently, Mohr's circle provides an extremely useful aid in the solution for, and visualization of, the stresses on various planes through a point in a stressed body in terms of the stresses on two mutually perpendicular planes through the point. Although Mohr's circle can be drawn to scale and used to obtain values of stresses and angles by direct measurements on the figure, it is probably more useful as a pictorial aid to the analyst who is performing analytical determinations of stresses and their directions at the point.

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