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Mohr's Circumvolve is a graphical method to decide the stresses developed inside any cloth when it is subjected to external forces. For this article, presume that the textile is subjected to external forces in two mutually perpendicular directions, and a shear stress along one of its planes.

Steps

  1. 1

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

  2. 2

    Label the intersection of the coordinates, i.eastward. the origin, as "O". Assuming that the external force in one of the directions ( say "ten" direction) is F1, convert it to a stress by dividing the force by the cantankerous department area normal to it. Usually the dimensions will be available for y'all to calculate the stress. Similarly summate the stress in the mutually perpendicular management also (i.due east. the "y" management). You tin can phone call these stresses sigma "10" and sigma "y".

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  3. three

    Mark off both sigma "x" and sigma "y" to some scale on the Normal Stress centrality on your cartoon sheet. Follow the convention that all tensile stresses are in the positive management i.e. to the correct of the origin and compressive stresses are in the negative management, i.e. to the left of the origin. Phone call these points "J" and "Chiliad". OJ so represents sigma "10" and OK represents sigma "y".

  4. 4

    Divide the tangential strength interim on the torso by the surface area to calculate the shear stress on the body. Remember that, for a torso subjected to a shear stress, there must be an accompanying shear stress in the opposite direction on the reverse face. These stresses will form a couple.

    • For the body to remain in equilibrium, an opposite couple volition 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. You lot will also follow a convention that clockwise shears are positive and anti-clockwise shears are negative. Correspondingly, the area above the horizontal Normal Stress axis, is positive and the area 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 indicate "D". Similarly,draw a vertical line (downwardly) from "K" and mark on it the same value of shear stress. This is downwards because the free shear stress volition exist contrary to the master shear stress couple. Call this point "Due east". Note that the value of shear stress and the complimentary shear stress will be the aforementioned because information technology is a free couple.

  6. six

    Bring together points "D" and "E". This will cutting the horizontal axis, OJ, at some signal. Call it "C". Draw a circle with "C" as the centre and CJ every bit the radius. This is called the Mohr'southward Circumvolve.

    • Mark the points where the Mohr's Circle cuts the horizontal centrality as 1000 and H respectively (Thousand being the farthest point on the centrality and H the nearer or negative cut point).

  7. 7

    To observe the values of the stress on a plane at any angle from the axis of the force, describe a radius CP at twice that angle, the bending existence measured from the radius CE. Drop a perpendicular from "P" to the horizontal axis at "Q". Join OP.OQ  represents sigma Northward i.due east. the normal stress at the plane, OG the maximum stress in the body, OH the minimum stress in the body, and PQ represents the shear stress on the plane.OP represents the resultant stress on the plane. Similarly the stresses on whatever aeroplane can exist measured past choosing betoken P appropriately.

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Things You'll Need

  • Drawing lath
  • Straight edge
  • Compass
  • Drawing sheets

References

  1. Standard text books on Strength of Materials.

About This Article

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