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UBC MECH326 Ch 2 Materials.tex
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\documentclass[10pt]{article} \usepackage{amssymb,amsmath} \usepackage[hmargin=1cm,vmargin=1cm]{geometry} \begin{document} {\large MECH326 Chapter 2 -- Materials} \begin{align*} &\text{2-1 \underline {Material Strength and Stiffness}}\\ &\text{\bf {True} \rm stress-strain diagrams take into account of reduced area in $\sigma=\frac{P}{A}$, instead of using the original area $A_0$}\\ &\text{as in \it engineering \rm (or \it nominal\rm) stress-strain diagrams.}\quad \text{True strain }\epsilon=\int_{l_0}^l\frac{dl}{l}=\ln\frac{l}{l_0}\quad\ldots~\text{Eq 2-4 p.34}\\ &\text{Also, for constant volume part,}\quad\epsilon=\ln\frac{A_0}{A}\quad\ldots~\text{Eq 2-17 p.40.}\\ % &\text{Shear stress }\tau=\frac{G\rho}{l_0}\theta\quad\text{where $\rho (