Another Type of Stress and Strain

(Credit for many illustrations is given to McGraw Hill publishers and an array of

internet search results)

Or Shear Bliss

Parallel Reading

Chapter 2 Section 2.7 (Do Reading Assignment Chapter 2B) Section 2.11 Section 2.9 (Do Reading Assignment Chapter 2C)

Shear Forces Try to Cut the Material in Two Across its Width

One Common Location Is at Pin Connections

Applying a Shear Load Causes Our Material to Twist

That Twist Angle is Called Shear Strain

Note the units of shear strain are radians.

We’re In Heaven Because We Find Another Linear Relationship

τ

ϒ

We call the SlopeG Modulus of RigidityOr Shear Modulus

Assignment 6

Do Problems 2.8-4 and 2.7-14

As you do the problems explain step by step what you are doing in eachcalculation until you reach the answer. (Just putting down an answerwith scribbles above and expecting the grader to figure out your steps will get you marked Wrong even if your result is correct).

Even More Delightful Young’s Modulus, Shear Modulus and Poisson’s Ratio are Related

If you know 2,You can alwaysGet the 3rd.

But Shear Can Show Up in Some Unexpected Places

We met ourTensile test

What If I Reversed That And Tried to Mash my Specimen in

Compression?

Comment on Engineer’s tricks. Do you notice that I am doing very simpleTests on small specimens and then using mathematical models to extendThose results to very large structures.

Its Crush Time!

Wait a Cotton PickinMinute Here!

Its as if the material is failing by pushing out wedges on a 45 degreeAngle rather than mashing flat like a pancake.

What is going on here!

Back to the Drawing Board

Something very interesting is happening when we put an axial load on things.Ya it stretches, just like Hooke’s Law said. Yes it thins down as we wouldExpect from Poisson’s Ratio. But we are also producing shear strains in the bar.The presence of a shear strain means we are also producing shear stresses.

It Turns Out

If you put an axial load on a specimenYou will get a shear stress maximum thatIs ½ the axial stress on a 45 degree plane(see Bear’s and Johnson 1.3 for the bigUgly proof)

What Happens If You Hit a Shear Stress Limit Sooner than a Crush

Limit?

The specimen will fail on the shear plane!

The mystery of the wedgee failed compressionTest is solved.

A Handy Device for Seeing Where Normal and Shear Stresses Are At

It’s called Moore’s Circle and it shows usWhat kinds of stress are on a plane of anyorientation

Draw a Graph of Shear and Normal Stress

σ

τ

Consider Our Bar Subject to Tension of Magnitude P

τ

σPlot our normal stress in theX direction

τ

Tension thisside

CompressionThis side

Now Plot Any Y Axis Compression(of course there is none)

τ

σ

Similarly there is no needTo move the points off theτ = 0 line since there isNo shear being applieddirectly

Now Draw a Circle That Hits the Points on the Outer Edges

τ

σThis is Moore’s Circle. WeCan use it to find the stressOn planes of differentOrientation.

Where Is the Shear Stress Maximum?

Moore’s circle doubles the angleSo 90 degrees on the circle means45 degrees from our pull direction.

The shear stress is ½ the magnitude of our tensile stress.

Assignment 7

Do problems 2.9-2, 2.9-3, 2.9-4 using Mohr’s Circle

Explain how you drew the circle and how you read the answers off of Mohr’sCircle. Obviously show the answer too. Do not just put down a circle withA few points labeled and write down an answer – you’ll get marked wrong ifYou do.