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Consider a prismatic bar loaded in tension as shown. I consider a point Q in the bar away from the ends. This point Q can be considered as an infinitesimally small element taken within the body.

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We can consider many different elements, representing point Q, which correspond to different rotations about the axis perpendicular to the plane of the screen. On each of these elements the stresses will be different and since we can obtain infinite number of elements by rotating at different angles we can have infinite number of stresses. Since all the elements correspond to point Q does that mean there are infinite number of stresses acting at point Q?

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    $\begingroup$ There is only one physical "stress" tensor. The components can be different depending on the coordinate system. The analogy is a physical vector (which has a unique magnitude and direction). However, the components of the vector will change depending on the coordinate system you use. $\endgroup$ Nov 1, 2021 at 23:23

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That is true. A point within a body which is acted upon by force(s), and if you make an element at different rotations/orientations at the same point, then you will get different values of stresses. A Mohr's circle is used to observe the limits of the stresses for a 2D as well as 3D element case. To draw a Mohr circle, you alteast need to be have a single stressed element, whose stress values at this orientation of the element should be known and will be used to draw the complete Mohr's Circle.

Most of the times, we are only interested in finding the maximum principle, minimum princple and maximum shear stress that can be experienced at a specific rotation/orientation of the element at that point.

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Yes there is an infinite number of normal and shear stress combinations, one for each different rotation angle.

However, there is a relationship between the magnitudes of the normal and shear stress at all different orientations.

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