23.4 : 平面应力的莫尔圆

Mohr's circle is a visual representation of stress transformation on an element. The stress components in this element are plotted on a graph to create Mohr's circle for a square element experiencing plane stress.

If the shearing stress is positive, point A is plotted below the horizontal axis, and point B is plotted above. If it is negative, their positions are reversed.

The midpoint, O, of the line connecting points A and B lies on the horizontal axis and serves as the circle's center. A circle, drawn with O as its center and the line AB as its diameter, is called Mohr's circle.

The abscissae of points X and Y, where the circle intersects the horizontal axis, represent the maximum and minimum principal stresses, respectively.

The angle AOX equals twice the angle θp. The orientation, θp, of the principal plane corresponding to point X, can be obtained by halving the angle AOX measured on Mohr's circle.

The radius of Mohr's circle in the vertical direction corresponds to the magnitude of the maximum shearing stress.