Transformation of Stresses/Mohrís Circle



Key Concept:Mohr's Circle provides a graphical method to find the normal and shear

stresses on the faces of an element.Of interest are the maximum value of normal stress, the minimum value of normal stress, and the maximum value of shear stress at any given point.



In a Nut Shell:In-plane (xy-plane) stresses at an arbitrary point in a structure consist

of normal stresses, σx and σy, in both the x and y-directions, as well as shearing stresses

τxy and τyx.The values of these stresses at an arbitrary point change depending on direction.i.e. The values from a single element strain gage placed at a point on a structure will give different values depending on the orientation of the gage.


Sign Convention:Consider a rectangular element taken from a structure as shown in

the figure below.The element depicts the positive normal and shearing stresses on the


††† †††††††††††††††††††††




†††††††††††††††††††††††† σ x =normal component of stress in x-direction

†††††††††††††††††††††††† σ y ††= normal component of stress in y-direction

†††††††††††††††††††††††† τ xy = shearing stress on the x-face in the y-direction

†††††††††††††††††††††††† τ yx = shearing stress on the y-face in the x-direction


From equilibrium it can be shown that†††† τxy=τyx.


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