Question

P13.017 (Multistep) The principal strains are ep- 4 5 με, εμ2- 905 με, and - 20.50 for a point in a body subjected to plane strain. Construct Mohrs circle and use it to (a) determine the strains єх, ey, and ray. (Assume Ex > Ey) (b) determine the maximum in-plane shear strain and the absolute maximum shear strain (c) draw a sketch showing the angle 0p, the principal strain deformations, and the maximum in-plane shear strain distortions.

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Answer #1

Take principal strains on x axis and shear strain on y axis. Find center of circle right in between the principal axes at e = (-905+(-405))/2 = -655

Draw Mohr's circle. Draw clockwise angle of 20.5 deg from e1 = -405. where it intersect the circle, it will be one of the inplain strain. Now other in plain strain will be at a plain at 90 degrees fron this strain i.e. at 69.5 deg anticlockwise from e1, so find ex and ey = -465 & -840 respectively.

Draw horizontal lines from the intersection points at circle to cut at y axis. Intercept formed will be maximum inplain shear strain = 180

Overall maximum shear strain will be diameter of circle = 500

Co 25 180

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