User:Eml4500.f08.wiki1.aguilar/hw7

Wikiversity vs. E-Learning - Wiki1 Group Verdict
While both the Wikiversity and the E-Learning systems are very useful, each was designed for a specific purpose in mind. While E-Learning was designed to facilitate the communication between instructors and students, wikis are more designed to allow groups and organizations to easily post, edit, and share information. Because they are used with different purposes in mind, they are difficult to compare.

While E-Learning is in no way perfect, it does facilitate communication between professors and students when used correctly. By using E-learning as the standard and trying to familiarize all the professors with it, it bypasses the need for teachers to create a website to post information that needs to be accessible to all the students. We are not familiar with the back end of E-Learning, but we are sure that using E-learning to post files and information is easier than teaching professors how to build their own websites with attached files and documents. E-Learning does allows easy methods for professors to do a variety of different things. For example, E-Learning allows professors and TA's to upload grades and then for the various assignments and exams, students can view their grades at any time throughout the semester. Professors can also allow it to provide statistics on the assignment or exam like the average, the high and low scores, as well as histograms showing the grade distributions. E-Learning allows the professors to easily post announcements and documents as well, like homework solution PDFs and course syllabi. There is a feature for a discussion board which could easily be used to allow students to ask other students and TAs various questions, and there is also a calendar to allow various important dates to be posted. This are just some of the features provided for by the E-Learning system, many of which cannot be adequately provided for through Wikiversity.

It becomes more of a question what is it that we are trying to do? If, for example, the end goal is to provide a large, multimedia report that is to be worked on by an entire group, then Wikiversity does indeed provide a very good solution for this. But E-Learning is currently not meant to serve this function. For the purposes of this class, "E-Learning" is more of an indirect method for group collaboration. If you had to use E-Learning to do this, the process would vary group by group. Groups could come up with various ways to create these reports. Some groups might use sharing features of Google documents to write up the report and allow all members of the group to contribute text, images and various other elements to the report. This could then be saved as either a PDF or a Word document which could then be submitted on E-Learning. The advantage to this method would be that there isn't any "coding" to learn so that would minimize some of the learning curve, and it would also protect reports from being viewed by others outside the group. The downside to this would be that reports from group to group would be much less streamlined, and having to save equations as images could become quite a hassle. Another alternative would be to use Word to allow groups to create the report. Word 2007 does contain a much improved equation editor and almost everyone uses Microsoft Word already. E-Learning could be set up to allow groups members to upload their parts, and then someone at the end would combine into a final report. This method would have similar pros and cons to the Google Shared documents method.

Clearly, for a group to put together an entire report like what was required of us, Wikiversity does seem to provide a very good solution, keeping in mind that no solution will be perfect. Wikiversity allows for students to be introduced to wikis, something that is becoming much more widespread throughout the "real world." These skills are much more likely to becomes valuable later on down the road. Wikiversity is major project and it's performance will not be affected by the activity of our groups even under peak conditions. The downside is that the Wikiversity approach does, however, lend itself to the possibility of being vandalized or copied by members from other groups.

As a group, we think that for our class purposes, the Wikiversity method could be improved. This could be done by cutting out much of the tedious busy work that tends to be more "filler" within our reports. While each homework report usually looked impressive when it was turned in, by essentially having each of the groups rewrite all the notes from the course lectures was of little added benefit to each student. Much time was spent tediously formatting the lengthy equations that time was taken away from more beneficial areas of the homework. Each student should be responsible for taking his or her own notes thus emphasizing the importance of class attendance. The reports should focus on actual homework with each group's solutions to various problems and MATLAB assignments with included images, videos, and coding from all the members of the group. In our opinion, this approach to the Wikiversity homework reports would be more beneficial to the students, and should be used in conjunction with many of the features of E-Learning, such as grade statistics and feedback, as well as others.

Frame Analysis
A frame element is a combination of a truss (bar element) with a beam element.

The differences between a truss and a beam is that because of it's pin connections, a truss only incurs only axial deformation while the fixed nature of the nodes of a beam experience transverse deformation.

2-D Frame Local DOFs


In general, $$d_{(i)}^{(e)}\Rightarrow f_{(i)}^{(e)}$$, where $$f_{(i)}^{(e)}$$ are the generalized forces. Here, e=1,2 and i=1,...,6

$$\left.\begin{matrix} d_{(3)}^{(e)}\\d_{(6)}^{(e)} \end{matrix}\right\}$$ rotational degrees of freedom

$$\left.\begin{matrix} f_{(3)}^{(e)}\\f_{(6)}^{(e)} \end{matrix}\right\}$$ bending moments

2-D Frame Global DOFs


Therefore, there are two element stiffness matrices, $$k_{6\times6}^{(e)}$$ where e=1,2.

This means the global stiffness matrix is $$K_{9\times9}^{(e)}=Ak_{6\times6}^{(e)}$$.

This is assembled by combining the two element stiffness matrices as shown below.



Transformed Coordinate System


$$\mathbf{\tilde{k}}_{(6\times 6)}^{(e)} \mathbf{\tilde{d}}_{(6\times 1)}^{(e)}=\mathbf{\tilde{f}}_{(6\times 1)}^{(e)}$$, where each is defined below.

$$\mathbf{\tilde{d}}_{(6\times 1)}^{(e)}=\begin{Bmatrix} {\tilde{d}}_{1}^{(e)}\\ {\tilde{d}}_{2}^{(e)}\\ {\tilde{d}}_{3}^{(e)}\\ {\tilde{d}}_{4}^{(e)}\\ {\tilde{d}}_{5}^{(e)}\\ {\tilde{d}}_{6}^{(e)} \end{Bmatrix}$$     and $$\mathbf{\tilde{f}}_{(6\times 1)}^{(e)}=\begin{Bmatrix} {\tilde{f}}_{1}^{(e)}\\ {\tilde{f}}_{2}^{(e)}\\ {\tilde{f}}_{3}^{(e)}\\ {\tilde{f}}_{4}^{(e)}\\ {\tilde{f}}_{5}^{(e)}\\ {\tilde{f}}_{6}^{(e)} \end{Bmatrix}$$

Note: The rotational displacements and moments remain unchanged. $$\tilde{d}_{3}^{(e)}={d}_{3}^{(e)}$$ $$\tilde{d}_{6}^{(e)}={d}_{6}^{(e)}$$ $$\tilde{f}_{3}^{(e)}={f}_{3}^{(e)}$$ $$\tilde{f}_{6}^{(e)}={f}_{6}^{(e)}$$

and

$$ \mathbf{\tilde{k}}_{(6\times 6)}^{(e)}= \overbrace{

\begin{bmatrix} \frac{EI}{L} & 0 & 0 & -\frac{EI}{L} & 0 & 0\\ 0 & \frac{12EI}{L^3} & \frac{6EI}{L^2} & 0 & -\frac{12EI}{L^3} & \frac{6EI}{L^2}\\ 0 & \frac{6EI}{L^2} & \frac{4EI}{L} & 0 & -\frac{6EI}{L^2} & \frac{2EI}{L}\\ -\frac{EI}{L} & 0 & 0 & \frac{EI}{L} & 0 & 0\\ 0 & -\frac{12EI}{L^3} & -\frac{6EI}{L^2} & 0 & \frac{12EI}{L^3} & -\frac{6EI}{L^2}\\ 0 & \frac{6EI}{L^2} & \frac{4EI}{L} & 0 & -\frac{6EI}{L^2} & \frac{4EI}{L} \end{bmatrix}}

^{\begin{matrix} \;\tilde{d}_{1}^{(e)} \;\;\;& \tilde{d}_{2}^{(e)} \;\;\;& \tilde{d}_{3}^{(e)} \;\;\;& \tilde{d}_{4}^{(e)} \;\;\;\;& \tilde{d}_{5}^{(e)} \;\;\;\;& \tilde{d}_{6}^{(e)} \end{matrix}}

\left.\begin{matrix} \\ \\ \\ \\ \\ \end{matrix}\right\}

\begin{matrix} \tilde{d}_{1}^{(e)}\\ \tilde{d}_{2}^{(e)}\\ \tilde{d}_{3}^{(e)}\\ \tilde{d}_{4}^{(e)}\\ \tilde{d}_{5}^{(e)}\\ \tilde{d}_{6}^{(e)} \end{matrix} $$

Dimensional Analysis
The square bracket notation around a variable means "dimension of".

$$ \begin{bmatrix} \tilde{d}_1 \end{bmatrix}=L = \begin{bmatrix} \tilde{d}_i \end{bmatrix} $$, where i=1,2,4,5 and L signifies that it has a dimension of length.

Note: There is a difference between 'units' and 'dimensions'. Displacement has a dimension of length Mass, length, time, charge and temperature are all fundamental dimensions. They cannot be broken down any further, while a dimension such as force can be broken down even further as shown below.

$$Force=mass \times acceleration = \frac {mass \times distance}{{time}^2}=\frac{m\times L}{t^2}$$

$$\begin{bmatrix} \tilde{d}_3 \end{bmatrix}=1$$, meaning it has no dimension.

$$\sigma = E\varepsilon \Rightarrow \begin{bmatrix}\sigma \end{bmatrix}= \begin{bmatrix}E\end{bmatrix} \begin{bmatrix}\varepsilon   \end{bmatrix} =1$$

$$\left[\varepsilon \right]={[du] \over [dx]}={L \over L}=1$$