Stress Concentration

Or Would that be Concentration Stress?

Parallel Reading

Chapter 12.2

A Look at the Big PictureStatics

Shows how stress on systemIs distributed onto the

components

Mechanics of Materials

Understanding howStress spreads

through a component

Mohr’s CircleChecking for Critical Stress Values on

Potential Failure Planes

I want a TV like thatFor my room.

General Stress Distributions

Shape Changes Can Become Points of Stress Concentration

Axial stress spreads evenlyAcross a Plate. But what happens if there is a hole in

The Plate?

Stress Diverts AroundAnd None too Evenly at That

σnew = σold * K

Where K is a stressConcentration 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 inA high priority application.

Smoother transitionsAllow the stress toSpread out moreEvenly.

Looking at the Stress Concentration Diagram

One factor is how drasticThe drop in size is!

The Other Factor is the Radius of the Fillet

As can be seen a largerRadius on the fillet givesThe stress a chance toReally smooth out.

Illustrating the Importance of Fillets

I’m convinced already!0.4

We Compute Our Key Measures to Read the Chart

60mm 40m

01.040

4.0

mm

mm

d

r

Holly Cow!

K is about 5

So How is that Significant?

60mm 40m

Because of stress concentration we areGoing to have to keep the average a lotLower to avoid triggering failure at theConcentration point.

Adjusting for Concentration

MPaMPa

335

165

Now calculate the allowable load

0.04*0.01

= 13.2KN

Stress Concentration not good.

Lets See if a Good Fillet Will Make Things Better

Calculate the Magnitude of Our Stress Concentration

It’s still stress but it couldHave been a lot worse.

Picking Off an Answer

Adjust our allowable average stress

This is a dramatic increase from 13.2 KNWith a sharp turn and small fillet.

Do Only Normal Stresses Concentrate?

Shear stress increasesLinearly to the outsideEdge of a torsionElement. What happens if we

Change the diameter ofA rod in torsion

We Jack Up the Forces

NormallyOur highestShear is atThe outerFibers of theshaft

With stress concentrationThis 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