Stress Transformation- Analytical and Mohr's Circle Method.

Hi,

• Stress transformation is the process of transforming the stresses from one co-ordinate axis to another which is having some obliquity to the original axes. It is important because in practical civil Engineering problems, a structural element is subjected to combined stress, from more than one directions, so there resultant is going to be in some another axis. To find out the resultant we have to transform the given stresses along the required co-ordinate axis. We have two famous methods of transformation of stresses:

(a) Analytical method   (b) Graphical Method- Mohr's Circle method

• Analytical Method: In this method we analyse the given structural element for the given stress conditions and then we have to do the required mathematical calculations to find out the stresses along the required axis. Suppose n1, n2  are the normal stresses along principle axis and s1 is the applied shearing stress. You are asked to find normal stress(n) and shear stress(s) along a plane which is oblique to the normal with an angle o, then you can use the following formula, which is found after analyzing the given element for the above stresses

             n = [(n1+n2)/2] + [(n1-n2)/2]. (Cos2o) - (s1.Sin2o).
              s = (n1-n2)/2.Sin2o + s1. Cos20

• Graphical Method/Mohr's Circle Method:

Mohr'c Circle method is very simple method to find out the stresses along an plane which is oblique to the normal axis through some angle o. It is drawn on the two rectangular axis, n and s. n is drawn on the horizontal axis and s is generally drawn on the vertical axis, and rightmost value of n on the circumference of the circle and left most value of n gives the major and minor principle stress values. Radius of the circle gives us the maximum shearing stress.

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