1. PH 201 Dr. Cecilia Vogel Lecture 21

2. WELCOME  PHYS 202  Dr. Cecilia J. Vogel  MWF lecture, Tue discussion, weekly lab OUTLINE  Course information  elasticity

3. Elasticity  When you push or pull on a spring, elastic, foam rubber, …  it clearly  when you push or pull on “rigid” objects  not clearly  but it does  A stress (exerted force per area or pressure)  produces a strain (fractional change in size or shape of object)  as a response

4. Elasticity & Springs  If you hang a weight from a spring  it stretches  x  If you hang the same weight from 2 identical springs side-by-side  they stretch  like increasing the  If you hang the same weight from 2 identical springs end-to-end  they stretch  like increasing the

5. Tension  Stress:  A force is exerted  to both ends  outward, perpendicular  Strain:  change in  increase  F = force on each end  A = area of each end  fractional change  Young’s modulus, E, Y

6. Compression  Stress: A force is exerted  to both  inward, perpendicular  strain  change in  decrease  ditto

7. Tension and Compression  A diving board is held up by two rods  So that  =0  one must exert a force  the other  one rod is in compression  the other is in tension

8. Bulk Compression  Stress: Pressure is exerted  to all  inward, perpendicular  strain  change in  decrease  P = pressure  P=F/A  fractional change  Bulk modulus, B, K

9. Shear  Stress: A force is exerted  to both  parallel (like friction)  strain  deformation  F/A similar (not pressure)   x = deflection  perpendicular to length  L = length  Shear modulus, G, S, 

10. Limits of Elasticity  The strain is proportional to the stress  only for small stress and strain  For large stresses  1 st, the relationship is no longer linear  “proportionality limit”  then the deformation becomes permanent  “elastic limit” or “yield strength”  it no longer “springs back” completely  “proof stress” is the stress that causes a 0.2% permanent deformation  Eventually material breaks, crushes, etc  “ultimate strength”

11. Example  Concrete strength testing:  Place a concrete cylinder in a breaking machine. Apply force until the concrete breaks, thus determining the concrete’s ultimate strength.

12. Summary  Elasticity  stress vs strain  tension  compression  bulk compression  Shear  Material strength