Since the transformation equations for plane strain are similar to those for plane stress, we can employ a similar form of pictorial representation. The state of plane stress at a point is represented by the stress element below. These stresses act on principal planes where the shear stresses are zero. Principal stresses and principal strains occur in the same directions. Mohr s circle is a geometric representation of the 2d transformation of stresses. As we learned in the previous two lectures, when a structural element is subjected to several types of loads acting simultaneously, say bending and torsion, principal stresses occur. The maximum shear strains are associated with axes at 45 to the directions of the principal strains.
Mohr s circle is the locus of points representing the magnitude of normal and shear stress at the various plane in a given stress element. The circle is centered at the average strain value e avg, and has a radius r equal to the maximum shear strain, as shown in the figure below, related topics the procedure of drawing mohr s circle from a given strain state is discussed in the mohr s circle usage and examples pages. Mohrs circle equation the circle with that equation is called a mohrs circle, named after the german civil engineer otto mohr. The idea and procedures are exactly the same as for mohrs circle for plane stress. The two principal strains are shown in red, and the maximum shear strain is shown in orange.
Mohrs circle strains at a point in the body can be illustrated by mohrs circle. Mohrs circle for plane stress university of arizona. The new strain state is the intersection of the new line green in the diagram and the circle. Remember, mohrs circle is just another way to visualize the strain state.
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