Tweet
Login
Mathematics Crystal
You may switch between
tex
and
pdf
by changing the end of the URL.
Home
About Us
Materials
Site Map
Questions and Answers
Skills
Topic Notes
HSC
Integration
Others
Tangent
UBC
UNSW
Calculus Advanced
Challenges
Complex Numbers
Conics
Differentiation
Integration
Linear Algebra
Mathematical Induction
Motion
Others
Polynomial Functions
Probability
Sequences and Series
Trigonometry
/
QnA /
UBC /
UBC MECH326 Ch 3 Load and Stress Analysis.tex
--Quick Links--
The Number Empire
Wolfram Mathematica online integrator
FooPlot
Calc Matthen
Walter Zorn
Quick Math
Lists of integrals
List of integrals of trigonometric functions
PDF
\documentclass[10pt]{article} \usepackage{amssymb,amsmath} \usepackage[hmargin=1cm,vmargin=1cm]{geometry} \begin{document} {\large MECH326 Chapter 3 -- Load and Stress Analysis} \begin{align*} &\text{3-1 \underline {Equilibrium and Free-Body Diagrams}}\\ &\sum F=0\text{ (N - force)},\quad \sum M=0\text{ (Nm - moment)},\quad V=\frac{dM}{dx}\text{ (N - shear force)},\quad q=\frac{dV}{dx}\text{ (Nm$^{-1}$ load intensity)}.\\ \\ &\text{3-10 \underline {Normal Stresses for Beams in Bending}}\\ &\sigma_x=-\frac{M_z y}{I_z}\quad\text{where the bending moment $M_z$ is on the $xy$-plane about the $z$-axis. (When $M_z>0$, it bends towards $+y$.)}\\ &\text{The \it neutral \rm axis is the $x$-axis, and the \it neutral \rm plane is the $xz$-plane.}\quad I_z=\int y^2~dA~~\text{\Big($\frac{\pi}{4}r^4$ for circular cross section $A$.\Big)}\\ &\sigma_{max}=\frac{Mc}{I}=\frac{M}{Z},\quad\text{where $Z=I/c$ is called the section modulus.}\\ \end{align*} \end{document}