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Mohr's Circle is a graphical method to determine the stresses developed inside whatever material when it is subjected to external forces. For this article, assume that the fabric is subjected to external forces in ii mutually perpendicular directions, and a shear stress along i of its planes.

Steps

  1. 1

    Draw two perpendicular lines. They're like axes in the 'x' and "y" coordinate systems but here, you call them stress coordinates. The horizontal line volition stand for  the Normal Stress coordinate and the vertical line will represent the Shear Stress coordinate.

  2. 2

    Label the intersection of the coordinates, i.e. the origin, as "O". Bold that the external force in 1 of the directions ( say "x" direction) is F1, convert information technology to a stress by dividing the force past the cross section area normal to it. Usually the dimensions will exist available for you lot to summate the stress. Similarly calculate the stress in the mutually perpendicular direction also (i.eastward. the "y" direction). You lot can call these stresses sigma "x" and sigma "y".

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  3. three

    Marker off both sigma "ten" and sigma "y" to some calibration on the Normal Stress axis on your cartoon sheet. Follow the convention that all tensile stresses are in the positive direction i.e. to the right of the origin and compressive stresses are in the negative management, i.e. to the left of the origin. Call these points "J" and "K". OJ then represents sigma "ten" and OK represents sigma "y".

  4. iv

    Divide the tangential forcefulness acting on the body by the surface area to calculate the shear stress on the torso. Recollect that, for a trunk subjected to a shear stress, there must exist an accompanying shear stress in the opposite direction on the opposite face. These stresses will course a couple.

    • For the body to remain in equilibrium, an opposite couple will automatically develop. This is called the complimentary shear i.e. every clockwise shear couple volition be accompanied by an anti-clockwise shear couple when a body is subjected to simple shear. Y'all will too follow a convention that clockwise shears are positive and anti-clockwise shears are negative. Correspondingly, the expanse in a higher place the horizontal Normal Stress axis, is positive and the expanse beneath it is negative.

  5. 5

    Draw a vertical line from "J" towards the positive (upwards) side and marker on it the value of the calculated shear stress. Call this point "D". Similarly,draw a vertical line (downwards) from "M" and mark on it the aforementioned value of shear stress. This is downwards because the gratis shear stress will exist opposite to the chief shear stress couple. Telephone call this bespeak "E". Note that the value of shear stress and the gratis shear stress will be the same because it is a complimentary couple.

  6. 6

    Join points "D" and "E". This volition cut the horizontal centrality, OJ, at some betoken. Phone call it "C". Draw a circle with "C" as the centre and CJ as the radius. This is called the Mohr'due south Circle.

    • Marking the points where the Mohr's Circle cuts the horizontal centrality as M and H respectively (Thou being the farthest indicate on the axis and H the nearer or negative cutting point).

  7. 7

    To notice the values of the stress on a aeroplane at any angle from the axis of the force, draw a radius CP at twice that angle, the angle being measured from the radius CE. Drop a perpendicular from "P" to the horizontal axis at "Q". Bring together OP.OQ  represents sigma N i.due east. the normal stress at the aeroplane, OG the maximum stress in the body, OH the minimum stress in the torso, and PQ represents the shear stress on the plane.OP represents the resultant stress on the plane. Similarly the stresses on any airplane can be measured past choosing point P accordingly.

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Things Yous'll Demand

  • Drawing board
  • Straight border
  • Compass
  • Cartoon sheets

References

  1. Standard text books on Force of Materials.

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