Another Type of Stress and Strain (Credit for many illustrations is given to McGraw Hill publishers...

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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

Transcript of Another Type of Stress and Strain (Credit for many illustrations is given to McGraw Hill publishers...

Page 1: 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.

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

Page 2: 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)

Page 3: 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.

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

Page 4: 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.

One Common Location Is at Pin Connections

Page 5: 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.

Applying a Shear Load Causes Our Material to Twist

Page 6: 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.

That Twist Angle is Called Shear Strain

Note the units of shear strain are radians.

Page 7: 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.

We’re In Heaven Because We Find Another Linear Relationship

τ

ϒ

We call the SlopeG Modulus of RigidityOr Shear Modulus

Page 8: 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.

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).

Page 9: 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.

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

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

Page 10: 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.

But Shear Can Show Up in Some Unexpected Places

We met ourTensile test

Page 11: 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.

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.

Page 12: 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.

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!

Page 13: 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.

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.

Page 14: 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.

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)

Page 15: 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.

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.

Page 16: 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.

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

Page 17: 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.

Draw a Graph of Shear and Normal Stress

σ

τ

Page 18: 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.

Consider Our Bar Subject to Tension of Magnitude P

τ

σPlot our normal stress in theX direction

τ

Tension thisside

CompressionThis side

Page 19: 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.

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

Page 20: 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.

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.

Page 21: 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.

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.

Page 22: 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.

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.