1. Or Would that be Concentration Stress?
Stress Concentration
Or Would that be Concentration Stress?

2. Parallel Reading
Chapter 12.2

3. 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

4. General Stress Distributions

5. 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?

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

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

8. 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.

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

10. 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.

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

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

13. Holly Cow!
K is about 5

14. 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.

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

16. Lets See if a Good Fillet Will Make Things Better

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

18. 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.

19. 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

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

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

22. What About Bending Forces

23. Now What if We Change the Beam Size