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Plane stress, BEAM4S1

: Problem description: The cantilever beam shown is subjected to uniformly distributed loading l_y per unit length and the end force F_x, F_y. Calculate deflection and stresses for plane stress conditions.

$\begin{figure} \centering\hspace{0pt} \epsfclipon\epsfxsize=6cm\epsffile{beam6s1.ps} \end{figure}$

Mesh: Eight triangles--see appendix A.2.

Material properties: $E=2\times 10^5$ MPa, $\nu=0.3$ .

Support: Clamped at x=0. Statically determinate.


u=v=0 node:	 1 
u=0 nodes: 	 2 11

Loading: Given as


l_y=-100 unit: N/m 
F_x=20000 F_y=-20 unit: N

Solution: First, the end force is replaced with the equivalent surface traction as

$\begin{displaymath}q_x=\frac{20000}{0.01\times 0.02}=100\times 10^6 \,\mbox{[Pa]}~,~~~ q_y=-0.1\times 10^6\,\mbox{[Pa]} ~,~~~ \end{displaymath}$

Similarly, the distributed loading is replaced with

$\begin{displaymath}q_n(\verb*\vert S2\vert)=\frac{l_y}{0.01}=-0.01\times 10^6\,\mbox{[Pa]}~, \end{displaymath}$

where the normal surface traction q_n acts on the top areas $0.25\times0.01$ m² denoted as S2 of elements 2, 4, 6 and 8.

Execute from prompt:
>rmd2 beam4s1.I1
>rpd2 beam4s1.I2
>srh2 beam4s1.I3
>fefs beam4s1.I4
>str2 beam4s1.I5