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Concentrated force, body force, BEAM53S1

Problem description: The cantilever beam shown is subjected to uniformly distributed loading ly, lz per unit length and the end force Fx, Fy, Fz. Calculate deflection and stresses for two load cases: i) the in-plane problem using lyFxFy only and ii) the complete three-dimensional loading ly, lz, Fx, Fy, Fz.

\begin{figure}
\centering\hspace{0pt}
\epsfclipon\epsfxsize=6cm\epsffile{beam56s1.ps}
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Mesh: Four beam elements--see appendix B.3.
Material properties: $E=2\times 10^5$ MPa, $\nu=0.3$.
Support: Clamped at x=0. Statically determinate.



$u=v=w=\varphi_x=\varphi_y=\varphi_z=0$ node: 1
Loading: Given as

ly=-100 lz=200 unit: N/m 
Fx=20000 Fy=-20 Fz=10 unit: N      
Solution: The end force Fx, Fy, Fz is directly assigned to node 5 as a concentrated (nodal) force. The distributed loading is replaced with the equivalent body force as

\begin{displaymath}Q_x=0~,~~~
Q_y=\frac{-100}{0.01\times 0.02}=-500\times 10^3 \,\mbox{[N/m$^3$ ]}~,~~~
Q_z=1000\times 10^3\,\mbox{[N/m$^3$ ]}
\end{displaymath}

which is assigned to all the elements 1 to 4.
 
Execute from prompt:
>rmd3 beam53s1.I1
>rpd3 beam53s1.I2
>srh3 beam53s1.I3
>fefs beam53s1.I4
>str3 beam53s1.I5