A graphical method to transform stresses and find principal stresses.
Mohr's circle plots normal against shear stress for all planes at a point. Centre (σx+σy)/2, radius √(((σx-σy)/2)²+τxy²). It gives principal stresses, maximum shear and stress on rotated planes, with angles doubled.
σx=80, σy=20, τ=40 MPa gives principal stresses of 110 and -10 MPa.
Mohr's circle gives a graphical way to transform stresses and locate principal values, which helps interpret results from strain gauges and FEA.
A graphical method to transform stresses and find principal stresses.
Mohr's circle gives a graphical way to transform stresses and locate principal values, which helps interpret results from strain gauges and FEA.
Plot normal stress on the horizontal axis and shear on the vertical. Use the two stresses on perpendicular planes as points and find the centre and radius.
Yes. Angles on the circle are twice the physical angles between planes, which is a common source of mistakes.
Typical applications include finding the maximum shear stress at a point in a pressurised pipe, interpreting a three-gauge rosette on a machine frame and checking the orientation of the principal stresses in a shaft under torsion.
Study "Combined loading" first (topic 60 of 106 in Engineering Mechanics). It covers the groundwork this topic builds on.
Principal planes have no shear. τmax = radius. Also works for strain and inertia tensors.
σx=80, σy=20, τ=40 MPa gives principal stresses of 110 and -10 MPa.
The next topic is "Principal stresses", which builds directly on this one.
It is classed as Intermediate in Engineering Mechanics (topic 61 of 106). It is an intermediate topic. Work through the beginner topics in Engineering Mechanics first.
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