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Fundamentals: Plane Stress and Strain

Fundamentals: Plane Stress and Strain

What do Daniel Shenton and Civil Engineers have in common? They both believe that the world is flat. In the case of Mr Shenton, it’s because he’s belligerently antiquated; but for engineers it’s because working in two dimensions is easy, and three dimensions is hard (let’s leave alone time and probability for now.)

It’s a lazy way to introduce a subject, but: The New Dictionary of Civil Engineering defines Plane Strain as “strain in two dimensions with zero strain in the third dimension”, and Plane Stress as “stress in two dimensions with zero stress in the third dimension”. As such it’s been nominated for the least helpful explanation in the world [citation needed].

In this second post of Engineering Fundamentals I’m aiming to do a little better.

Plane Stress

Totally accurate representation of plane stress.

Certainly Plane Stressful…

To get plane stress we take a plate and promise not to load the faces. This means that we can stretch and crush the plate to our heart’s content, but we can’t bend it. Considering that we’re now living in a cardboard cut-out of a world, where we can’t get in-front of the plate to push it; this shouldn’t be too much of an issue.

As we gradually increase the thickness of the plate, however, there comes a point where the inside of the plate is constrained by the outside of the plate, and a bevel will start to appear at the edges of the plate- shattering our belief in a world without thickness.

It’s at this point that us flat-earthers have to start acknowledging the third dimension…

Plane Strain

Totally accurate representation of plane strain.

Taking the Plane Strain…

Plane Strain is the chronically obese brother of plane stress. As we keep fattening out once plane-stress plate into a prism, there comes a point where the magnitude of these thru-thickness effects are nothing compared to our push and pull.

It’s at this stage where we can once again start to believe the world is flat.

While plane Stress is sometimes used for plate girders, etc., Civil Engineers tend to use the Plane Strain assumption more- where long structures (like dams or retaining walls) can be simplified down to a single cross-section.

So who to say it’s not turtles all the way down?

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  1. Ed Dablin

    Useful refresher!