shear flow

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Shear Flow

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Shear Flow. Beams Subjected to Bending Loads. So why did these Beams split down Their length?. Maybe they Just Dried Out – They are all Wood. Of course these aren’t wood. Maybe We Can Find Answers in Our Shear and Moment Diagrams. Hear is a shear and moment Diagram, but I don’t - PowerPoint PPT Presentation

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Page 1: Shear Flow

Shear Flow

Page 2: Shear Flow

Beams Subjected to Bending Loads

So why did theseBeams split downTheir length?

Page 3: Shear Flow

Maybe they Just Dried Out – They are all Wood

Of course these aren’t wood.

Page 4: Shear Flow

Maybe We Can Find Answers in Our Shear and Moment Diagrams

Hear is a shear and momentDiagram, but I don’tSee anything horizontal.

Page 5: Shear Flow

Consider a Beam in Bending

We all know the top of the beam compresses and the bottom goes into tensionAnd there is a neutral axis in the middle yada yada yada

.

Expected

NotExpected

Page 6: Shear Flow

Lets Grab a Little Piece of that Beam Where Shear is Constant

We have nice balancing verticalEquilibrium

But why doesn’t it spin?

Could it be that we have a mystery force?

Page 7: Shear Flow

What Else Could be Happening as a Beam Bends

Mystery Solved

Page 8: Shear Flow

So What Kinds of Numbers are We Talking?

We know we can’tHave shear at theAir interface

It can’t be even

Page 9: Shear Flow

Ok – So What is Q

Lets consider a horizontal planeOn a beam so distance y1 awayFrom the neutral axis

Page 10: Shear Flow

And What About I?

The moment of inertia of the beam

Page 11: Shear Flow

Lets Do Something With It

Obviously the neutral plane isRight through the middle

Lets go get theShear flow onThe edge of theBoards!

Page 12: Shear Flow

Round Up Q

Page 13: Shear Flow

Now for I

If this were a steel I beamWe could just look up I.Unfortunately we are goingTo have to calculate it.

Middle board part isEasy.

Of course we’re still missing the contributionOf the boards on the ends.

Page 14: Shear Flow

For Our End Boards we Will be rescued by the Parallel Axis Theorem

Page 15: Shear Flow

Getting the Shear Flow

Note that shear flow is shear force perUnit of beam length.

In our case we are interested in what is trying to shear our nails in two if they arePlaced every 25 mm

Page 16: Shear Flow

Nice Spot Check of Shear Stress, but What Does the Stress Profile Look Like?

Note this means the peak stress is

1.5 * Average Shear Stress

Page 17: Shear Flow

Then there are typical Steel Beams

So that’s why theWeb crumpled up.

Page 18: Shear Flow

Designing a Beam

This couldGo wrong!The beamCould splitIn axialTension.

Page 19: Shear Flow

Lets Make Sure That Doesn’t Happen

We will use our shear and moment diagramsTo find the maximum bending moment

Then we will zero in on the requiredSection modulus

Page 20: Shear Flow

Obviously the Next Thing I Need Is Section Modulus as a Function of Beam Depth

Remember – Section ModulusIs Moment of Inertia over cWhere c is the distance fromThe neutral axis to the edge ofThe beam.

Page 21: Shear Flow

Working Through Our Substitution

Page 22: Shear Flow

Plug it in Plug it in

Given in the problem

From Our Moment Diagram

Just worked out by ourSubstitution

Solving the equation for d

Page 23: Shear Flow

Looks Like We Need a 4 X 10 for Our Beam

After all – could anything else go wrong

Page 24: Shear Flow

Yes – We Better Check the Shear Flow

We know the maximum sheer will be at the centerOf the beam

T allowable is 120 psi

Page 25: Shear Flow

Plug and Chug

Yipes! We wereGoing to use a4 X 10

We didn’t watch the sheer flowAnd it nearly bit us in the _ _ _ _

We need a 4 X 12 for this.

Page 26: Shear Flow

Lets Use Mohr’s Circle to Take a Look at the Beam Center

An ElementAt theBeamCenter

This element is subject toStrong shear forces, butWhat about axial force?(assume its on the neutralAxis)

Page 27: Shear Flow

Pure Shear

Our worstCase is nearThe beamedges

29.11425.115.3

3000*5.1*5.1

XAV Max

MaxIf we assume we use a 4 X 12

Page 28: Shear Flow

Now to Mohr’s Circle

τ

σ

Plot the clockwise shear114.29

At 90 degrees toThat we find aCounter clockwiseshear

-114.29

Since we have pureShear there is noTension or compressionOn these faces.

Page 29: Shear Flow

Since We Have Pure Shear We Have No Tension or Compression? Right?

What is this?

What angleIs that on?

Is it possible that shear flow could buckleA ductile material in compression on a 45Degree diagonal plane?