Final Notes on Chapter 2. Sections 2.10, 2.11, 2.12

This blog post will contain my notes from the final sections of chapter 2.

2.10: Stress Concentrations

Stress concentrations: High stresses in very small regions of a bar.

Stress Concentration Factors:
The intensity of a stress concentration is usually determined by the ratio between maximum stress and normal stress, this is depicted by the stress-concentration factor K: $$K = \frac{{{\sigma _{\max }}}}{{{\sigma _{nom}}}}$$  ${\sigma _{nom}} = \frac{P}{{ct}}$ = nominal stress (where ct is the net area at the cross section of the hole.)

2.11: Nonlinear Behavior
Perfect Plasticity: perfectly plastic regions on a stress-strain curve continue until the strains are 10 or 20 times larger than the yield strain.

A material having a stress-strain diagram with theses types of characteristics is called an elastoplastic material.

2.12: Elastoplastic Analysis

Yield displacement is the downright displacement of the bar at the yield load and is equal to the elongation of the inner bar when first releasing yield stress ${\sigma _y}$ : $${\delta _Y} = \frac{{{\sigma _y}{L_2}}}{E}$$ The plastic displacement ${\delta _Y}$ at the instant the load just reaches the plastic load ${P_p}$ and is equal to the elongation of the outer bars at the instant they reach yield stress.
$${\delta _P} = \frac{{{\sigma _y}{L_1}}}{E}$$ Now Compare ${\delta _P}$ with ${\delta _y}$ and get the ratio:  $$\frac{{{\delta _P}}}{{{\delta _y}}} = \frac{{{L_1}}}{{{L_2}}}$$ My next blog posts will be about my first few days at my internship and some of the interesting and new experiences I will have had working in a lab.

Thanks for reading,

-Nick Thompson