PH 201 Dr. Cecilia Vogel Lecture 21
WELCOME PHYS 202 Dr. Cecilia J. Vogel MWF lecture, Tue discussion, weekly lab OUTLINE Course information elasticity
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
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
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
Compression Stress: A force is exerted to both inward, perpendicular strain change in decrease ditto
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
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
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,
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”
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.
Summary Elasticity stress vs strain tension compression bulk compression Shear Material strength