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