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Subsections



Analysis and results

Displacement, moment and shear distribution

Double-click within one of the windows of the Results Window, and the results are shown in these areas, only when a proper combination of geometrical boundary conditions are specified and also some applied forces are given. If such conditions are not satisfied, an error message appears in the message window at the bottom of the main window. In such a case, please re-consider the boundary conditions.

Traditionally in the civil engineering field, the bending diagram is positive in the downward direction. However recently at some schools this direction is reversed. This program originally set the positive direction downward. But you can change it by clicking either \fbox{$+$} or \fbox{$-$} to the left of the moment-diagram window. This setting is saved in the `ini file, and you can always use the same setting until you change again.

If you want to check boundary and loading conditions without solving the equilibrium equation, simply right-click in the window of the deflection diagram.

Fig.: Stress distribution
\includegraphics*{stress-e.ps}

Stress distribution

Click below the blue line in the Setup Window after obtaining proper results, and a small window as in Fig. [*] will appear. In this window, stress distributions at the node indicated by a red circle are plotted. Both the normal and shear stresses are divided by the corresponding yield stresses. You can choose a node by the scroll button. If you double-click within the stress distribution window, all the cross-sections at the nodes are scanned consecutively to show the stress distribution. It can be stopped by double-clicking within that window.

As will be explained later, as calculations are carried out for steel members as an example, the plot may not be within the range below the yield stresses; i.e. the plot may exceeds over 1. In that case, you can broaden the range of plot by the horizontal scroll button up to 100 which may not be meaningfull from an engineering point of view.

The cross section is assumed to be rectangular. And formulas in the structural mechanics lead to

$\displaystyle \frac{\sigma}{\sigma_{\mathrm Y}}$ $\textstyle =$ $\displaystyle \frac{ML}{EI}\frac{1}{\sigma_\mathrm{Y}/E}
\frac{64\sqrt{3}}{\lambda}\left(\frac{y}{h}\right),$ (5)
$\displaystyle \frac{\tau}{\tau_{\mathrm Y}}$ $\textstyle =$ $\displaystyle -\frac{SL^2}{EI}
\frac{\sqrt{3}}{2\sigma_\mathrm{Y}/E}
\left(\fra...
...mbda}\right)^2
\left\{\left(\frac{y}{h}\right)^2-\left(\frac12\right)^2\right\}$ (6)

where $\sigma_\mathrm{Y}$ is a tensile yield stress; $\tau_\mathrm{Y}$ a shearing yield stress; $\lambda$ is the slenderness ratio with respect to the entire beam length, $32L$; $h$ is the height of the cross section; and $y$ is a downward coordinate from the neutral axis. And thus we have relations as
\begin{displaymath}
\lambda\equiv\frac{32L}{r}, \quad r\equiv\sqrt{\frac{I}{A}}=...
...3}}, \quad \tau_\mathrm{Y}=\frac{\sigma_\mathrm{Y}}{\sqrt{3}}.
\end{displaymath} (7)

Furthermore we set
\begin{displaymath}
\lambda=20, \quad \frac{\sigma_\mathrm{Y}}{E}=0.001
\end{displaymath} (8)

as a simple example.

Fig.: Displaying numerical results
\includegraphics*{results.ps}

Numerical results

Double-Click at the string `Dsplmnt' opens a small window as is shown in Fig.[*]. Re-analysis of the system outputs the numerical results of deflection, shear force, bending moment and maximum of shear and normal stresses in this window.


next up previous contents
Next: File outputs Up: cbeam Previous: Setup of a problem
Iwakuma Tetsuo
Wed Mar 31 21:43:28 2004 : Stardate [-29]1892.65