Or Would that be Concentration Stress?

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Presentation transcript:

Or Would that be Concentration Stress? Stress Concentration Or Would that be Concentration Stress?

Parallel Reading Chapter 12.2

A Look at the Big Picture Statics Shows how stress on system Is distributed onto the components Mechanics of Materials Understanding how Stress spreads through a component I want a TV like that For my room. Mohr’s Circle Checking for Critical Stress Values on Potential Failure Planes

General Stress Distributions

Shape Changes Can Become Points of Stress Concentration Axial stress spreads evenly Across a Plate. But what happens if there is a hole in The Plate?

Stress Diverts Around And None too Evenly at That σnew = σold * K Where K is a stress Concentration factor

How Bad Is It? Diameter / w Small holes that make sharp turns can reach K = 3 That’s really bad.

Hypothesis – Sharp Corners are Bad We wouldn’t want to break something in A high priority application. Smoother transitions Allow the stress to Spread out more Evenly.

Looking at the Stress Concentration Diagram One factor is how drastic The drop in size is!

The Other Factor is the Radius of the Fillet As can be seen a larger Radius on the fillet gives The stress a chance to Really smooth out.

Illustrating the Importance of Fillets I’m convinced already! 0.4

We Compute Our Key Measures to Read the Chart 60mm 40m

Holly Cow! K is about 5

So How is that Significant? 60mm 40m Because of stress concentration we are Going to have to keep the average a lot Lower to avoid triggering failure at the Concentration point.

Adjusting for Concentration Now calculate the allowable load = 13.2KN Stress Concentration not good. 0.04*0.01

Lets See if a Good Fillet Will Make Things Better

Calculate the Magnitude of Our Stress Concentration It’s still stress but it could Have been a lot worse.

Picking Off an Answer Adjust our allowable average stress This is a dramatic increase from 13.2 KN With a sharp turn and small fillet.

Do Only Normal Stresses Concentrate? Shear stress increases Linearly to the outside Edge of a torsion Element. What happens if we Change the diameter of A rod in torsion

We Jack Up the Forces Normally Our highest Shear is at The outer Fibers of the shaft With stress concentration This becomes

Concentration is a Function of the Size Change and the Size of the Fillet Which Fillet is better?

What About Bending Forces

Now What if We Change the Beam Size