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User:Eml4500.f08.ateam.boggs.t/Lecture 29

The Principle of Virtual Work: A Continuation of the Dynamics of an Elastic Bar
For the initial conditions, at t = 0, prescribe,

 * $$ U(x,t=0) = \overline{U}(x) $$       The known functional displacement
 * $$ \dot{U}(x,t=0) = \overline{V}(x) $$       The known functional velocity

To create an equation for a multiple degree of freedom system, start with

 * $$ \frac{d}{dz}[EA \frac{du}{dx}] + f = m \ddot{u} $$    Equation (1)

This becomes,

 * $$ -kd + f = m \ddot{d} $$

or

 * $$ m \ddot{d} + kd = f $$    Equation (2)

To derive Equation 2 from 1 move all the terms to one side and take the integral with respect to x, producing,

 * $$ \int_{x=0}^{x=L} w(x)(\frac{d}{dx}[EA \frac{du}{dx}] + f - m \ddot{u}) \,dx = 0 $$    Equation (3)

This is true for all w(x), the weighting function. It should be noted that producing Equation 3 from Equation 1 is a trivial solution, but producing Equation 1 from Equation 3 is not. Equation 3 can be re-written as,

 * $$ \int_0^L w(x)g(x) \,dx = 0 $$

Here g(x) is substituted into Equation 3 for

 * $$ \frac{d}{dx}[EA \frac{du}{dx}] + f - m \ddot{u} $$

Because 3 holds true for all w(x), select w(x) that equals g(x). Doing so allows Equation 3 to become:

 * $$ \int_0^L g^2(x) \,dx = 0 $$

for $$ g(x) \ge 0 $$


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User talk:JWSchmidt/Blog/14 November 2008

"Since I am apparently not going to be permitted to ask certain questions in a community forum, I'm going to move my questions to this page and incorporate them into a broader discussion of related issues."

John, Communication involves the reader as much as the author. Mortal human beings often find that many question being lumped together is so difficult and painful that communication is nigh impossible. I would propose that "one question a time, at most three" as a reasonable compromise. You want to ask Mike about his deletions and his use of an unauthorised bot? Maybe we can focus on these matters. Hillgentleman | //\\ |Talk 17:48, 14 November 2008 (UTC)

It can also be discussed whether (Johnny's statement) "Mike can be a bit terse and stubborn at times, but he also strongly believes in consensus." makes Mike a good candidate. But please keep focused! Hillgentleman | //\\ |Talk 17:51, 14 November 2008 (UTC)

 * "Mortal human beings often find that many question being lumped together is so difficult and painful that communication is nigh impossible" <-- I had similar thoughts about this page. "his deletions and his use of an unauthorised bot" <-- I agree that policy violations are important, but interestingly enough, I am more concerned about other aspects of his editing that, in my view, make him a poor choice for custodian.....I'm thinking about his own stated concern that Wikiversity be welcoming. --JWSchmidt 19:20, 14 November 2008 (UTC)

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/


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User:La comadreja/People/AFriedman

This page has moved here.

title: User:La comadreja/People/AFriedman


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User:Eas4200c.f08.vqcrew.c/Homework 6

 See my comments below. Please don't remove these comment boxes; just add your comment to these comment boxes in case you fix the problems. Eml4500.f08 13:27, 23 November 2008 (UTC)

In addition to fixing the errors placed in the comment boxes in the report below, I have also made a change to the overall MATLAB code as a result of a discussion with a group member of Team Carbon. The end result of this change is the new average compressive stress calculated is roughly 3 MPa, which is much lower than the previously calculated value of 59 MPa. This error was also present in the code from HW5, where the maximum buckling stress was found to be 81 MPa. I changed the code for HW5, and found the max buckling stress to be on the order of 4 MPa. Thus, the ratio between the values remains constant, but the overall magnitude is now lower- I am not sure of the correctness of this solution, but I am certain the moment of inertia components are now being calculated correctly. I cannot find any error in my stress calculations, so I am presenting these results as our final solution. Eas4200c.f08.vqcrew.c 03:47, 28 November 2008 (UTC)

Please add a table similar to that at the end of your HW5 report to list the newly corrected values of the moment of inertia components together other corrected results so to document the differences (e.g., angle for neutral axis, etc.) between what you obtained now and what you obtained before the correction of the bug. Eml4500.f08 21:54, 29 November 2008 (UTC)

Equation of Equilibrium
Recall the 1-dimensional case and apply dimensional analysis:

 * $$[f]=\frac{F}{L}$$

where F is force units and L is length units. Additionally, square brackets "[]" represent the "dimension of" the variable. Furthermore, dimensions of other parameters can be assessed, as shown:

 * $$[A]=L^2\;$$
 * $$[\frac{f}{A}]=\frac{F}{L^3}$$
 * $$[\sigma]=\frac{F}{L^2}$$
 * $$[\frac{d\sigma}{dx}]=\frac{[d\sigma]}{[dx]}=\frac{\frac{F}{L^2}}{L}=\frac{F}{L^3}=\frac{force}{volume}=body\;force$$
 * $$\epsilon=\frac{du}{dx}=\frac{\Delta L}{L}\therefore[\epsilon]=\frac{[du]}{[dx]}=\frac{L}{L}=1\;nondimensional$$
 * $$\nu=-\frac{\epsilon_{yy}}{\epsilon_{xx}}\therefore[\nu]=\frac{[\epsilon_{yy}]}{[\epsilon_{xx}]}=\frac{1}{1}=1\;nondimensional$$

Step D: Prandtl Stress Function
For a little clarification from the previous lectures, we know that the change in stresses with respect to the change in location is analogous to the total force applied with respect to the volume...

 * $$ \begin{bmatrix} \frac {d \sigma_{ij}}{dx_i} \end{bmatrix} = \frac {F}{L^3} = \frac {Force}{Volume} \, $$

But now, on to the next step of our Road Map! Next up: Step D, the Prandtl Stress Function! The equations that governs this relationship are (3.15), shown as:

 * $$ \sigma_{yx} = \frac {d\phi}{dz} \, $$

 * $$ \sigma_{zx} = \frac {-d\phi}{dy} \, $$

In this case $$\phi_\,$$ plays the role of a potential function, where as $$ \sigma_{yx} \, $$ and $$ \sigma_{zx} \, $$ serve as components of the "gradient" of $$\phi_ \,$$ with respect to (y,z). Now recalling the scalar function for the f(x,y,z) gradient...

 * $$ \frac{df}{dx}\vec{i} + \frac{df}{dy}\vec{j} + \frac{df}{dz}\vec{k} \, $$

which is of course a vector, thus implying that F is a potential. Now, if we analyze equation (3.15) stated above utilizing equation (1), from lecture notes 27-1, we derive the following relation:

 * $$ \frac {d}{dy}(\frac{d\phi}{dz}) + \frac {d}{dz}(\frac{-d\phi}{dy}) = \frac {d^2\phi}{dydz} - \frac {d^2\phi}{dzdy} = 0 \, $$

The reason this relation works is that $$ \phi_ \, $$ is continuous and smooth, such that its second mixed derivative is interchangeable, ie:

 * $$ \frac {d^2\phi}{dydz} = \frac {d^2\phi}{dzdy} \, $$

The next step is to take the above relation and put it in Laplacian terms. These manipulations give us the following result for the Laplacian of $$ \phi_ \, $$.

 * $$ \frac {d^2\phi}{dydz} + \frac {d^2\phi}{dzdy} = -2G\theta \, $$

 * $$ \nabla^2\phi = -2G\theta \, $$

Traction Force
The traction force is defined as the product of the components of the stress tensor matrix, $$ \begin{bmatrix}\sigma\end{bmatrix} \;$$, and the components of the normal vector, $$  \begin{Bmatrix}n\end{Bmatrix} \;$$.

This relation can be derived using Figures 1-3. The normal vector, $$ \begin{Bmatrix}n\end{Bmatrix} \;$$, is a unit vector with magnitude equal to one.

 * $$ \begin{Bmatrix}t\end{Bmatrix}_{3x1} = \begin{bmatrix}\sigma\end{bmatrix}_{3x3} \begin{Bmatrix}n\end{Bmatrix}_{3x1} \;$$, where $$\begin{Vmatrix}n\end{Vmatrix} = 1\;$$

The traction force can then broken into its components in the y and z directions.

 * $$\vec{t} = t_y\vec{j} + t_z\vec{k}\;$$

 * $$\vec{n} = n_y\vec{j} + n_z\vec{k}\;$$

The differential lengths of the section and the components of the normal vector can be found using the surface length, ds, and the angle between the normal vector and the y-axis, $$\theta\;$$.

 * $$dz = ds(cos\theta)\;$$

 * $$dy = ds(sin\theta)\;$$

 * $$n_y = cos\theta\;$$

 * $$n_z = sin\theta\;$$

The sum of the forces in the y and z directions must be zero, so an expression relating the traction force, normal force and stresses can be derived. The depth of the section is set to be equal to one. Below is the development for the component of the traction force in the y-direction. The development of the component in the z-direction is reserved for the homework section.

 * $$\sum F_y = 0 = -\sigma_{yy}(dz)(1) - \sigma_{yz}(dy)(1) + t_y(ds)(1)\;$$

 * $$ 0 = -\sigma_{yy}(ds)(n_y) - \sigma_{yz}(ds)(n_z) + t_y(ds)\;$$

 * $$t_y = \sigma_{yy}(n_y) + \sigma_{yz}(n_z)\;$$

The components of the traction force can be written in matrix form.

 * $$\begin{Bmatrix}t_y\\t_z\end{Bmatrix} = \begin{bmatrix}\sigma_{yy} & \sigma_{yz}\\ \sigma_{zy} & \sigma_{zz}\end{bmatrix}\begin{Bmatrix}n_y\\ n_z \end{Bmatrix}\;$$

The three dimensional case can be expanded from the two dimesional case.

 * $$\begin{Bmatrix}t_1\\t_1\\t_3\end{Bmatrix} = \begin{bmatrix}\sigma_{11} & \sigma_{12} & \sigma_{13}\\ \sigma_{11} & \sigma_{12} & \sigma_{13}\\ \sigma_{11} & \sigma_{12} & \sigma_{13}\end{bmatrix}\begin{Bmatrix}n_1\\ n_2\\n_3 \end{Bmatrix}\;$$

This result then can be compressed into a compacet notation. This brings the derivation back to the origin point with the original definition of the traction force in a general notation.

 * $$t_i = \sum_{j=1}^3\sigma_{ij}n_j$$ where i = 1, 2, 3

 * $$\begin{Bmatrix}t_i\end{Bmatrix}_{3x1} = \begin{bmatrix}\sigma_{ij}\end{bmatrix}_{3x3} \begin{Bmatrix}n_{j}\end{Bmatrix}_{3x1}\;$$

Boundary Conditions for Phi
For solid cross sections, the constant value of $$\phi \;$$ is arbitrary, therefore it can be set to zero. Thus, we have the boundary condition $$\phi =0 \;$$ on the lateral surface of a solid bar. This boundary condition is depicted in Figure 4, where $$\phi \;$$ is equal to zero on $$S_0$$.

In the case of a thin-walled cross section, $$\phi \;$$ has a different constant value on each surface. This is depicted in Figure 5, where $$\phi =C_0\;$$ on $$S_0$$ and $$\phi =C_1\;$$ on $$S_1$$.

For a solid bar with circular cross section, as shown in Figure 6, the Prandtl stress function is assumed to be
 * $$\phi = C\left(\frac{y^2}{a^2} + \frac{z^2}{a^2}-1 \right)$$
 * {| class="collapsible collapsed"

!HW Problem - Proof that this equation satisfies the boundary condition We can prove that this satisfies the surface boundary condition of $$\phi =0\;$$ as follows:
 * $$\phi = C\left(\frac{y^2}{a^2} + \frac{z^2}{a^2}-1 \right) = C\left(\frac{y^2+z^2}{a^2}-1 \right)$$

Substituting in the Pythagorean theorem, $$a^2=y^2+z^2$$, we get:
 * $$\phi = C\left(\frac{a^2}{a^2}-1 \right)=C(1-1)=0$$

To find C, we can plug this function into the compatibility equation:
 * }
 * $$\frac{\partial^2 \phi }{\partial y^2} + \frac{\partial^2 \phi }{\partial z^2}=-2G \theta$$

which results in:
 * $$\frac{2C}{a^2} + \frac{2C}{a^2} = -2G \theta \Rightarrow C=-\frac{1}{2}a^2G\theta$$

This can also be expressed in terms of torque $$T$$ and polar moment of inertia $$J$$:
 * $$C=-\frac{1}{2}a^2TJ$$

Relating $$\theta$$ to $$\phi$$
It can be shown that torque and $$\phi$$ can be related by the relation

 * $$T = 2\ \int_A \phi\ dA$$

where $$\phi$$ is the Prandtl stress function. It can be defined that

 * $$T = G\ J\ \theta$$

Relating these together it can be deduced that

 * $$2\ \int_A \phi dA = G\ J\ \theta$$

It can also be defined that the Prandtl stress function

 * $$\tau_{yx} = \frac{\partial \phi}{\partial z}$$
 * $$\tau_{zx} = - \frac {\partial \phi}{\partial y}$$

It can be further shown that the shear strain can be related as

 * $$\tau_{yx} = -G\ \theta\ z$$
 * $$\tau_{zx} = G\ \theta\ y$$

Therefore it is shown that

 * $$\frac{\partial \phi}{\partial z} = -G\ \theta\ z$$
 * $$\frac{\partial \phi}{\partial y} = G\ \theta\ y$$

 * {| class="collapsible collapsed"

!HW Problem - Proof of Zero Warping for Solid Circular Bar Consider the following two relations for the shear strains $$\gamma_{yx}\;$$ and $$\gamma_{zx}\;$$:

 * $$\gamma_{yx} = \frac{\sigma_{yx}}{G} = \frac{\partial u_x(x,y)}{\partial y} - \theta_z$$

 * $$\gamma_{zx} = \frac{\sigma_{zx}}{G} = \frac{\partial u_x(x,y)}{\partial z} + \theta_y$$

Note also the following two relations for the shear stresses $$\sigma_{yx}\;$$ and $$\sigma_{zx}\;$$:

 * $$\sigma_{yx} = -G \theta_z\;$$

 * $$\sigma_{zx} = G \theta_y\;$$

Substituting the shear stress equations into the shear strain equations yields the following relationships:

 * $$\frac{-G \theta_z}{G} = -\theta_z = \frac{\partial u_x(x,y)}{\partial y} - \theta_z$$

 * $$\frac{G \theta_y}{G} = \theta_y = \frac{\partial u_x(x,y)}{\partial z} + \theta_y$$

By moving the $$\theta\;$$ from the left hand side to the right hand side of the above relations, the following conditions are immediately apparent:

 * $$\frac{\partial u_x(x,y)}{\partial y} = 0$$

 * $$\frac{\partial u_x(x,y)}{\partial z} = 0$$

The combination of these two conditions results in the overall condition $$u_x(y,z) = c\;$$, where $$c\;$$ is a constant that is not necessarily 0. Given that the bar is under "clamped" conditions at $$x\;=\;0$$, and that this in turn means that $$u_x(y,z) = 0\;$$ at $$x\;=\;0$$, noting that the displacement in the x plane is not dependent on $$\;y$$ or $$\;z$$ leads directly to the condition $$c\;=\;0$$; thus, there is no warping for a uniform bar with a solid circular cross-section.
 * }

 Error: You need to use the fact that the bar is "clamped" at $$\displaystyle x=0$$, i.e., $$\displaystyle u_x (y,z) = 0$$ at $$\displaystyle x=0$$, and since $$\displaystyle u_x (y,z)$$ is independent of $$\displaystyle x$$, and hence $$\displaystyle c = 0$$. Eml4500.f08 13:21, 23 November 2008 (UTC)

This error has been fixed. Eas4200c.f08.vqcrew.c 22:46, 27 November 2008 (UTC)

Flexural Shear Flow in Thin Walled Sections

In dealing with Aerospace Structures it is sometimes easier to examine idealized cases to have an easier look at the forces acting on the structure. For this case we would like to examine an aircraft wing and idealize the wing as a cantilever beam. In Figure 7 a nonuniform stress field can be seen acting on the beam.

The cantilever beam can then be broken up even more into two parts to examine the internal shear force and bending moments acting on a specific spot on the beam a distance x from the end. This image can be seen in Figure 8 The beam has been cut at a distance x, and separated for a view of the internal forces.

Asymmetrical Thin-walled Cross-Section
Now that we have examined a simple cantilever beam, we can now broaden our scopes to an unsymmetrical case. Figure 9 shows a sample unsymmetrical case over a small area, A_s, of the cross-section. The cross-section shown displays that a variable thickness and area along the path s. Examining the small section, s, of the cross section gives us the following relationship for the general case for unsymmetrical cross-sections:

$$\int_{A_s} \frac {d\sigma_{xx}}{dx} \,dA = -q(s)$$

Now that we have a brief introduction to unsymmetrical cross sections, it will help to examine the similarities and differences between symmetrical cross-sections about the z-axis and unsymmetrical cross-sections.

For Symmetrical cross-sections about the z-axis the relations come straight forward. The stress field can be written as the following:

 * $$\displaystyle \sigma_{xx} = \frac{M_y z}{I_y}$$

The shear flow can be represented as the following:

 * $$q(s) = - \frac{V_z Q_y}{I_y}$$

$$Q\;$$ is known as the first moment of the, which can be represented as the following:

 * $$Q_y = \int_{A_s} z \,dA = Z_c A_s$$

Now that we have the equations for a symmetrical case, lets examine the unsymmetrical case and see the differences:

 * $$\displaystyle \sigma_{xx} = (k_y M_z - k_{yz} M_y)y + (k_z M_y - k_{yz} M_z)z$$

Where the coefficients for k determined by the following equations:

 * $$k_y = \frac{I_y}{I_y I_z - (I_{yz})^2}\;$$

 * $$k_z = \frac{I_z}{I_y I_z - (I_{yz})^2}\;$$

 * $$k_{yz} = \frac{I_{yz}}{I_y I_z - (I_{yz})^2}\;$$

The equation for the stress can also be looked at in matrix form.

 * $$\left[\displaystyle \sigma_{xx} \right]_{1x1} = \left[ z y \right] \begin{bmatrix} k_y & -k_{yz} \\ -k_{yz} & k_z \end{bmatrix} \begin{Bmatrix} M_y \\ M_z \end{Bmatrix}$$

This can then be simplified to a 1x2 matrix and a 2x1 matrix forming the correct 1x1 matrix from $$\sigma_{xx}$$.

 * $$\left[\displaystyle \sigma_{xx} \right]_{1x1} = \left[ z y \right]_{1x2} \begin{bmatrix} k_z M_y - k_{yz} M_z \\ -kyz M_y + k_y M_z \end{bmatrix}_{2x1}$$

Now look at the shear flow:

 * $$q(s) = -(k_y V_y - k_{yz} V_z)Q_z - (k_z V_z - k_{yz} V_y) Q_y\;$$

Where:

 * $$ Q_z = \int_{A_s} y \,dA$$

 * $$ Q_y = \int_{A_s} z \,dA$$

Read and Report - Plate Buckling Page
The plate buckling analysis page is split into two main sections: one for simply-supported boundary conditions and one for clamped boundary conditions.

The first portion of the simply-supported section considers the buckling mode shape relation $$\psi(x,y)\;$$, followed by a a relation for the out-of-plane displacement due to buckling. These relations describe the physical response of a "flat plate" to buckling stresses. The section further describes the critical buckling load $$(P_x)_{cr}\;$$, followed by a discussion of the dimensions of the quantities involved. This information can be used to determine the critical buckling stress $$(\sigma_{xx})_{cr}\;$$, which can be used to characterize the plate's resistance to buckling loads.

The second portion consists of essentially the salient equations from the simply-supported section, but adjusted for the different boundary conditions.

MATLAB Coding Portion

 * {| class="collapsible collapsed"

!Full MATLAB Code - Buckling Analysis

 * }

 * {| class="collapsible collapsed"

!Command Window Output for MATLAB code

 * }

The above tables contain the full MATLAB code for buckling analysis as well as the command window output for a run of the code using the parameters listed in | Homework 5. The first part of the question requested a graph of of normal bending stress in the panels BF and EH (as described in Figure 10), with another curve showing the average compressive stress in the appropriate panel. This graph is shown in Figure 11. The red curve represents the stress in panel BF, the blue curve panel EH, and the average stress by the green curve. It is readily apparent from this plot that the compressive stress is experienced by panel BF.

Next, the problem requests a replotting of a figure from the MIT OpenCourseWare notes relating to the loading and support conditions on a flat plat; this is provided in Figure 12. The buckling mode shapes for the cases of $$m\;=\;1\;,\;n\;=\;1$$ and $$m\;=\;2\;,\;n\;=\;1$$ are plotted in Figures 13 and 14 respectively. The next portion of the question refers to determining the period of a portion the buckling mode shape function; that analysis is provided below.

 The figures you plotted were not the perspective view of the buckling mode shapes; see Team Aero. Eml4500.f08 15:42, 23 November 2008 (UTC)

This error has been fixed. Eas4200c.f08.vqcrew.c 03:42, 28 November 2008 (UTC)

Determining Period of Buckling Mode Shape Function
Consider the term of the $$\psi (x,y)\;$$ function represented as $$\;\sin ( \frac{m \pi x}{a} )$$. In order to find the period of this function, the following relationship is useful:

 * $$\sin ( \frac{m \pi (x + T)}{a} ) = \sin ( \frac{m \pi x}{a} )\;$$

Rudimentary algebra makes it immediately obvious that the following is also true:

 * $$\sin ( \frac{m \pi x }{a} + \frac{m \pi T}{a} ) = \sin ( \frac{m \pi x}{a} )\;$$

Noting the trigonometric relationship that $$\sin(\theta + 2\pi) = \sin(\theta) \;$$, the following can be written:

 * $$\frac{m\pi T}{a} = 2\pi\;$$

Thus, an equation for the period of this function is immediately apparent:

 * $$T = \frac{2a}{m}\;$$

For $$m\;=\;1\;$$, the period of this function is $$2\;a$$, indicating one half-wavelength present in the plate. For $$m\;=\;2\;$$, the period is $$a\;$$, indicating the presence of two half-wavelengths, or one full wavelength. Finally, for $$m\;=\;3\;$$, the period is $$\frac{2a}{3}$$, indicating the presence of 3 half-wavelengths, or 1.5 full wavelengths. Thus, it is apparent that $$\;m$$ is the number of half-wavelengths.

MATLAB Coding Portion Continued
The problem further requests the replotting of another figure from the MIT notes; this time, the $$k_c\;$$ vs. $$a/b\;$$ curves for various values of m. This plot is provided in Figure 15. Each curve refers to a different value of m; $$m\;=\;1$$ is plotted as a solid blue line, $$m\;=\;2$$ as a red dotted line, $$m\;=\;3$$ as a green dash-dotted line, and $$m\;=\;4$$ as a magenta dashed line.

The final portion of the question referred to an analysis of the airfoil skin panel as a flat plate, such as the type shown in Figure 12. The height of this idealized plate will be equivalent to the airfoil's skin thickness, and the length $$b\;$$ equivalent to the length of the airfoil skin panel. The skin material was considered to be Aluminum 2024-T3, as enumerated in a separate email about the problem. Using this idealized plate, the critical buckling stress $$(\sigma_{xx})_{cr}\;$$ for both simply supported and clamped boundary conditions was calculated for a range of aspect ratio such that $$(a/b) \in [.5,2]\;$$, and plotted in Figure 16. The red curve is for the clamped conditions, and the blue curve for the simply supported. Also, the buckling mode shape for the clamped case was also determined, and is provided in Figure 17.  Error: In Fig.16, the critical buckling stress for the clamped plate is lower than that for the simply-supported plate; there must be something wrong. Eml4500.f08 22:01, 29 November 2008 (UTC)

One important note about the determination of critical buckling stress for the simply-supported conditions relates to the determination of $$m\;$$ for the calculations. There was no condition enumerated in any communication on the problem about this issue; thus, the assumption of using the $$m\;$$ corresponding to the minimum $$k_c\;$$ at a given aspect ratio would be used. Thus, for aspect ratios less than $$1.414\;$$, $$m\;=\;1$$ was used; otherwise, $$m\;=\;2$$ was used.

When comparing the previously calculated average compressive stress to these two critical buckling stress curves, when noting that the actual support condition is somewhere "inbetween" the two conditions considered, it is apparent that the airfoil skin is not particularly suited for bending resistance. The average compressive stress was approximately $$3x10^6\;$$ Pascals. From the critical stress graph, for any aspect ratio greater than approximately .75, this would be a higher stress than could be handled by the simply supported condition, which indicates the airfoil skin would experience buckling failure under those conditions. Only very small aspect ratio panels would be able to handle that kind of loading. Thus, it is apparent that the airfoil skin is not useful from the standpoint of bending resistance.

Read and Report: Section 3.2 Torsion of Uniform Bars
When carrying out structural analyses on aircraft, torque is a major factor that must be considered. Torque is a moment, with units of N*M applied about the longitudinal axis of a beam. Due to Saint-Venant's principle, a torque symbol can represent infinitely many different statically equivalent load distributions. It must be noted, however, that for shafts made up of thin-walled cross-sections, Saint-Venant's principle may not apply.

In an elementary analysis of torsion, two significant assumptions are made:
 * 1. Upon torque application, deformations do not cause plane sections of the shaft to become non-circular or non-planar.
 * 2. All diameters within the plane section continue to be straight upon torque application and subsequent deformation.

These assumptions, however, are not valid in the current analysis due to the fact that the particular shafts being considered are of non-circular cross-section. In order to solve these types of structural analysis problems, two approaches can be utilized:
 * 1. The Prandtl stress function method
 * 2. The Saint-Venant warping function method

The latter will first be derived. Consider a constant cross-section straight shaft upon which equal and opposite torques T are applied to each side. The center of twist (COT) of the cross-section is chosen as the origin of the coordinate system. $$\alpha$$ signifies the twist angle (or angle of rotation) at z relative to the end at z = 0. The twist angle per unit length at z can be expressed as:

 * $$\theta=\frac{\alpha}{z}$$

Here it is assumed that plane sections warp during the application of torsional deformation, but projections of those plane sections rotate on the x-y plane as a rigid body. Consider P, an arbitrary point at z on the cross-section that, upon application of torque, moves to P' through a small angle $$\alpha$$. Note that the cross-section at z = 0 does not move. The displacement components at this arbitrary point P can be expressed as follows:

 * $$u=-r\alpha sin(\beta)=-\alpha y=-\theta zy\;$$
 * $$v=r\alpha cos(\beta)=\alpha x=\theta zx\;$$

where r is defined as the distance between the origin and point P. w, the displacement in the z-direction, is given by:

 * $$w(x,y)=\theta \psi (x,y)\;$$

where w and $$\theta$$, the rate of twist, are independent of z. In the previous equation, $$\psi(x,y)$$ is the warping function. The displacement given by the previous three equations yields:

 * $$\epsilon_{xx}=\epsilon_{yy}=\epsilon_{zz}=\gamma_{xy}=0\;\therefore\;\sigma_{xx}=\sigma_{yy}=\sigma_{zz}=\tau_{xy}=0$$

Therefore, $$\tau_{yz}$$ and $$\tau_{xz}$$ are the only two remaining components of stress. Next, the equations of equilibrium become:

 * $$\frac{\delta \tau_{xz}}{\delta x}+\frac{\delta \tau_{yz}}{\delta y}=0$$

A stress function $$\phi(x,y)$$ is subsequently introduced:

 * $$\tau_{xz}=\frac{\delta \phi}{\delta y}\;\;\;\;\;\tau_{xz}=-\frac{\delta \phi}{\delta x}$$

These stress components clearly conform to the equations of equilibrium. From the strain-displacement relations, the following is derived:

 * $$\gamma_{xz}=\frac{\delta w}{\delta x}-\theta y$$
 * $$\gamma_{yz}=\frac{\delta w}{\delta y}+\theta x$$
 * $$\therefore\;\frac{\delta \gamma_{yz}}{\delta x}-\frac{\delta \gamma_{xz}}{\delta y}=2\theta$$

Utilizing the stress-strain relations and the newly defined Prandtl stress function:

 * $$\frac{\delta^2 \phi}{\delta x^2}+\frac{\delta^2 \phi}{\delta y^2}=-2G\theta$$

Taking into account that no loads are applied on the lateral surface of the bar, the stress function can be found using traction t:

 * $$t_x=0\;\;\;\;\;t_y=0$$
 * $$t_z=\tau_{xz}n_x+\tau_{yz}n_y=\frac{\delta \phi}{\delta y} n_x-\frac{\delta \phi}{\delta x} n_y$$

where $$n_x=\frac{dy}{ds}\;and\;n_y=-\frac{dx}{ds}$$

Plugging these derivations into the previous equations yields:

 * $$t_z=\frac{\delta \phi}{\delta y}\frac{dy}{ds}+\frac{\delta \phi}{\delta x}\frac{dx}{ds}=\frac{d\phi}{ds}$$

The boundary condition for traction $$t_z=0$$ now corresponds to a boundary condition of:

 * $$\frac{d \phi}{ds}=0\;\therefore\;\phi=constant$$ on the lateral surface. This constant can be set to zero when analyzing solid sections with a single contour boundary.  The total resultant torque is subsequently obtained with the integration of dT over all of the cross-section:

 * $$T=-\int\int(x\frac{\delta \phi}{\delta x}+y\frac{\delta \phi}{\delta y})dxdy=2\int\int\phi dxdy-\int[x\phi]_{x_1}^{x_2}dy-\int[y\phi]_{y_1}^{y_2}dx$$
 * $$\therefore T=2\int\int\phi dxdy$$

Applying these results to the equation of the torsion constant J yields:

 * $$J=-\frac{4}{\nabla^2 \phi}\int\int\phi dxdy$$

Read and Report: Section 3.3 Bars with Circular Cross-Sections
Now, a uniform bar of circular cross-section is considered. For this case, the origin of the coordinate system lies on the center of the cross-section. Let a be the radius of the circular boundary. Then the stress function is:

 * $$\phi=C(\frac{x^2}{a^2}+\frac{y^2}{a^2}-1)$$

Analyzing the compatibility equation with this new phi considered yields:

 * $$C=-\frac{1}{2}a^2G\theta$$

The torque is then:

 * $$T=2C(\frac{I_p}{a^2}-A)\;where\;I_p=\int\int r^2 dA=\frac{1}{2}\pi a^4$$ denotes the polar moment of inertia of the cross-section.

Substituting $$a^2 A=2I_p\;$$ into the torque equation yields:

 * $$T=-\frac{2CI_p}{a^2}=\theta G I_p$$

The shear stresses then become:

 * $$\tau_{xz}=\frac{\delta \phi}{\delta y} = 2C\frac{y}{a^2}=-G\theta y$$
 * $$\tau_{yz}=-\frac{\delta \phi}{\delta x}=-2C\frac{x}{a^2}=G\theta x$$

Using relations for traction it can be shown that:

 * $$t_z=-G\theta\frac{xy}{r}+G\theta\frac{xy}{r}=0$$

Subsequently,

 * $$\tau=-t_z=G\theta r=\frac{Tr}{J}$$

From all of the previous equation and the stress-strain relations it can be shown that:

 * $$w=0\;$$

Which indicates that there is no warping in a circular cross-section under torsion.

Contributing Team Members
Adam Edstrand - Eas4200c.f08.vqcrew.a 20:56, 21 November 2008 (UTC)

Javier Stober - Eas4200c.f08.vqcrew.b 21:09, 21 November 2008 (UTC)

John Saxon - Eas4200c.f08.vqcrew.c 21:27, 21 November 2008 (UTC)

Darin Toscano - Eas4200c.f08.vqcrew.d 20:46, 21 November 2008 (UTC)

Kevin Klauk - Eas4200c.f08.vqcrew.E 02:17, 21 November 2008 (UTC)

Steven Hepsworth - Eas4200c.f08.vqcrew.f 18:23, 19 November 2008 (UTC)

Casey Barnard - Eas4200c.f08.vqcrew.g 20:03, 19 November 2008 (UTC)

title: User:Eas4200c.f08.vqcrew.c/Homework 6


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User:Eml4500.f08.ateam.shah/Week 6

Continuation from the Lecture: Friday 7, Nov 2008

Stiffness Terms:

Assume displacement u(x) for xi <= x <= xi+1
 * (i.e. x belongs to [xi, xi+1])

Motivation for linear interpolation of u(x): 2 Bar Truss

Deformed shape is a straight line, i.e. there was an implicit assumption of linear interpolation of displacement between 2 nodes.

Consider the case where there are only axial displacements (i.e. 0 translational displacement).

Question: Express u(x) in terms of di=u(xi) and di+1=u(xi+1) as a linear function in x (i.e. linear interpolation)

u(x) = Ni(x)di + Ni+1(x)di+1

where Ni(x) and Ni+1(x) are linear function of x.

N i+1 (x)= (x - xi) * (xi+1 - xi)-1

title: User:Eml4500.f08.ateam.shah/Week 6


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Activity:Cassiopeia and Ursa Major

Since Cassiopeia (constellation) and Ursa Major are circumpolar_star constellations they are an ideal first target to finding constellations and learning how the sky rotates.

Begin by finding a place with a good low Northern horizon and with minimal light pollution. Get a chart and a red light.

 * find out whether Cassiopeia or Ursa Major is prominent. Generally:
 * Cassiopeia is prominent in the fall
 * Ursa Major is prominent in the spring

Both constellations have a compact distinctive shape. Cassiopeia looks like a W or a M. Ursa Major (aka the Big Dipper looks like a spoon, or a pot.

 * Between the two constellations is the north star. People generally like to use the last two stars of the bowl, since it points right to it.

People also like to know where the Little Dipper is. In dark skies this is straightforward to do; you need to look for a dipper shape with the north star, defining the end of its handle.

 * In the big dipper, most of the stars are very similar in brightness and that is explained at [Ursa_Major_Moving_Group]; however the Little Dipper some of its stars are much dimmer. Polaris and the two stars in the bowl of the Little Dipper are the brightest stars of the constellation.

title: Activity:Cassiopeia and Ursa Major


text:
Talk:Creating imagemaps for use on wikis

helloooo
in nosying around, I came across this project, and having spotted this in action on the english wiki, I too would like to figure out a bit more about how to do it....

folk might be interested to take a look at this example, and I'm now going to do my homework a bit and figure out how it works! :-) Privatemusings 21:36, 14 November 2008 (UTC)


text:
User:Eml4500.f08.a-team.melvin/Lecture 34

p.31-4: N1(1) $$ (\tilde{x}) $$ = HW6

N2(1) $$ (\tilde{x}) = \frac{\tilde{x}}{L^{(i)}} = \begin{cases} 0, & \mbox{at }\tilde{x}\mbox{ = 0} \\ 1, & \mbox{at }\tilde{x}\mbox{ = L} \end{cases} $$

shape function N1(i), N2(i)

(basis)

HW6 : book p.159

set E1 = E2 = E

Let A($$ \tilde{x} $$) be linear as on p.33-5

Obtain k (i) from previous problem (p.33-5) and compare to expression given in book.

$$ \frac{E}{L^{(i)}} \underbrace{\frac{(A_1 + A_2}{2}}_{Ave. \ Area} \begin{bmatrix} 1 & -1 \\ -1 & 1 \end{bmatrix} $$ = k (i)

Next, compare the general k (i) on p.33-5 to the stiffness matrix obtained by using $$ \frac{1}{2} (A_1 + A_2) $$. Note: $$ E_1 \ne E_2 $$

$$ \frac{(E_1 + E_2)(A_1 + A_2)}{4L^{(i)}} \begin{bmatrix} 1 & -1 \\ -1 & 1 \end{bmatrix} $$ = k (i)ave.

Find k (i) - k (i)ave.

Rem : Recall the Mean Value Theorem (MVT) and its relation to centroid:

MVT: $$ \int_{x=a}^{x=b} f(x)\, dx = f(\overline{x})[b-a] $$

for $$ \overline{x} \ \epsilon \ [b-a] $$

$$ \epsilon \ $$= "belongs to"

$$ a \le \overline{x} \le b $$

$$ \int_{A}^{} x\, dx = \overline{x} \int_{A}^{} \,dA = \overline{x} A $$

$$ \int_{x=a}^{x=b} f(x)g(x)\,dx = f(\overline{x})g(\overline{x}) [b-a] $$

$$ a \le \overline{x} \le b $$

But $$ \ f(\overline{x}) \ \ne \ \underbrace{\frac{1}{b-a} \ \int_{a}^{b} f(x) \, dx}_{Ave. \ value \ of \ f} $$

In general

$$ \ g(\overline{x}) \ \ne \ \underbrace{\frac{1}{b-a} \ \int_{a}^{b} g(x) \, dx}_{Ave. \ value \ of \ g} $$

Modify 2-bar truss code to accommodate general k (i) on p.33-5


text:
Wikipedia/syllabi

This page shows suggestions for syllabi for university level courses on Wikipedia.

Syllabus suggestion 1: Wikis and Wikipedia - publishing, reliability and technology
This syllabus suggestion is based on a translation of the syllabus for the Swedish university level course Wikipedia - publishing, reliability and technology, adjusted for Wikiversity.

Extent: 7.5 ECTS credits (corresponding to 5 weeks of full-time studies)

Subject: Informatics

Educational level: Introductory Tertiary (university or college)

Course aim
The course aims at answering questions such as: The course aims at providing knowledge that all Wikipedia or Mediawiki users, editors and administrators should have.
 * What is a wiki?
 * How is Wikipedia edited and administrated?
 * How can students, teachers, librarians and journalists use and relate to Wikipedia?
 * What are the main criticisms of Wikipedia?
 * What research exists related to Wikipedia as phenomenon?

Learning outcomes
After the course, the course participant should be able to:
 * Create and edit wiki-type (particularly MediaWiki, including Wikipedia) articles of good quality, with references, tables, illustrations and templates.
 * Discuss what is a reasonable source critical approach to using Wikipedia as a reference
 * Outline the common criticism of Wikipedia's reliability and discuss how the reliability problems can be tackled
 * Be an administrator of Wikipedia as well as other MediaWiki servers

Contents
The student can choose between a technical project or writing a social science essay.
 * 1) INTRODUCTION: WHAT IS WIKIPEDIA?
 * 2) The history of online encyclopedias, wikis, and Wikipedia
 * 3) Wiki as part of Web 2.0 - the social and interactive web
 * 4) Relation between wikis, web content management systems (CMS), blogs, social networks, and other online encyclopedias
 * 5) Basic wiki terminology
 * 6) HOW TO EDIT AND PUBLISH ARTICLES
 * 7) How to edit an article
 * 8) Wikification: Intra-wiki links, headings, categorization and disposition
 * 9) Policies and guidelines
 * 10) Legal Aspects
 * 11) Tackling vandalism
 * 12) Common templates
 * 13) To add tables, references, photos and illustrations
 * 14) Tools for producing illustrations
 * 15) RELIABILITY AND SOCIAL SIGNIFICANCE
 * 16) Wikipedia statistics
 * 17) Understanding Wikipedia as phenomenon
 * 18) Criticism
 * 19) When and how can we use Wikipedia as a source, and quote Wikipedia?
 * 20) How can students, teachers, librarians and journalists use and relate to Wikipedia?
 * 21) How to measure and improve Wikipedia quality
 * 22) Wikipedia as a social community
 * 23) Censorship, decision-making and voting procedures
 * 24) Is knowledge produced at Wikipedia?
 * 25) Is Wikipedia a democratic  project?
 * 26) Wikipedia ethics
 * 27) History critical analysis of the Wikipedia policies
 * 28) Examples of social science and behavioural science research related to Wikipedia
 * 29) Other uses for a Wiki engine - by teachers, project leaders, communities, etc
 * 30) TECHNOLOGY AND ADMINISTRATION
 * 31) Orientation on the underlying web technology
 * 32) Comparison of wiki software
 * 33) To what extent can the Google ranking formula explain the success of Wikipedia - and the failure of other wikis and online encyclopedias?
 * 34) Development of parameter controlled wiki templates
 * 35) To install, configure and administrate an own Mediawiki server
 * 36) Wikipedia administrator roles and tools
 * 37) Applications, extensions and robots for wiki engines
 * 38) Current web technology trends
 * 39) Examples of ongoing development projects and IT research related to Wikipedia (semantic wikis, etc)
 * 40) PROJECT PART

Assignments and assessments
(In the Wikiversity version of the course, these are exercises)
 * Quiz 1: What is Wikipedia?
 * Quiz 2: Editing
 * Publication of articles on the course wiki as well as Wikipedia
 * Quiz 3: Reliability and social significance
 * Discussion assignments
 * Quiz 4: Technology and administration
 * Lab: Administration of a wiki engine
 * Exam (Not in the Wikiversity version of the course)
 * Project or essay assignment

Literature
Required literature:
 * Wikipedia and MediaWiki documentation (available online)

Recommended reference literature:
 * John Broughton, Wikipedia – the missing manual, 2008
 * Phoebe Ayers, Charles Matthews, and Ben Yates, How Wikipedia Works: And How You Can Be a Part of It, 2008

Required literature for the Swedish university version of the course, but not the Wikiversity version:
 * Research article collection
 * Lennart Guldbrandsson, Så fungerar Wikipedia, September 2008.

title: Wikipedia/syllabi


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User:Ohara~enwikiversity

$$s=ut+1/2at^2$$

title: User:Ohara~enwikiversity


text:
User:Eml4500.f08.ramrod.c/11/14/08

Meeting 34 November 14, 2008
$$N_1^{(i)}(\tilde{x}) = N_2^{(i)}(\tilde{x}) = \frac{\tilde{x}}{L^{(i)}} = \begin{cases} 0 \; at \; \tilde{x}=0\\ 1 \;at \; \tilde{x}=L^{(i)}\end{cases}$$

Shape Functions N1(i), N2(i)

Comparing Value in Notes with Value in Textbook
Set E1 = E2 = E

Let $$A(\tilde{x})$$ be linear. k(1) will be obtained from the problem above and will be compared to expression given in the textbook, which uses the average area.

From Above: $$\mathbf{K}^{(i)}(\tilde{x})=\frac{\left[N^{(i)}_1(\tilde{x})E_1+N^{(i)}_2(\tilde{x})E_2 \right]\left[N^{(i)}_1(\tilde{x})A_1+N^{(i)}_2(\tilde{x})A_2 \right]}{L^{(i)}}\begin{bmatrix} 1 &-1 \\ -1& 1 \end{bmatrix}$$ From Book: $$\frac{E}{L^{(i)}}\frac{(A_1+A_2)}{2}\begin{bmatrix} 1 &-1 \\ -1 & 1 \end{bmatrix} = \mathbf{k}^{(i)}$$

$$\frac{(A_1+A_2)}{2}$$ = Average Area

Comparing General Value with Average Value
Next, compare the general k(i) from above to the stiffness matrix obtained by using 1/2(A1+A2) and 1/2(E1+E2)
 * Note: $$ E_1 \neq E_2$$

General Value: $$\mathbf{k}^{(i)}=\frac{EA}{L^{(i)}}\begin{bmatrix} 1 &-1 \\ -1 & 1 \end{bmatrix}$$

Average Value: $$\mathbf{k}_{ave}^{(i)}=\frac{(E_1+E_2)(A_1+A_2)}{4L^{(i)}}\begin{bmatrix} 1 &-1 \\ -1 & 1 \end{bmatrix}$$ Find k(i) - k(i)ave $$\mathbf{k}^{(i)}-\mathbf{k}_{ave}^{(i)} = \frac{EA}{L^{(i)}}\begin{bmatrix} 1 &-1 \\ -1 & 1 \end{bmatrix} \; - \; \frac{(E_1+E_2)(A_1+A_2)}{4L^{(i)}}\begin{bmatrix} 1 &-1 \\ -1 & 1 \end{bmatrix} = \frac{4EA-(E_1+E_2)(A_1+A_2)}{4L^{(i)}}\begin{bmatrix} 1 &-1 \\ -1 & 1 \end{bmatrix}$$

Remark: Mean Value Theorem
Recall the Mean Value Theorem (MVT) and its relation to the centroid.

MVT: $$\int_{x=a}^{x=b}{f(x)dx} = f(\bar{x})[b-a]$$
 * for $$\bar{x} \;in \;interval \;[a,b]$$ (that is $$a \leq \bar{x}\leq b$$)

$$\int_{x=a}^{x=b}{f(x)g(x)dx} = f(\bar{x})g(\bar{x})[b-a]$$

 * $$a\leq\bar{x}\leq b$$

But in general:

 * $$f(\bar{x})\neq \frac{1}{b-a}\int_{a}^{b}{f(x)dx}$$

 * $$\frac{1}{b-a}\int_{a}^{b}{f(x)dx}$$  is the average value of f

 * $$g(\bar{x})\neq \frac{1}{b-a}\int_{a}^{b}{g(x)dx}$$

 * $$\frac{1}{b-a}\int_{a}^{b}{g(x)dx} $$ is the average value of g

Modifying 2-Bar Truss Code
The 2-bar truss code is modified to accommodate for the general stiffness, k(i)

title: User:Eml4500.f08.ramrod.c/11/14/08


text: Template:Administering Wikiversity horizontal


text:
User talk:Tehdrago

 Hello Tehdrago, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. To get started, you may

 * Take a guided tour and learn to edit.
 * Visit a (kind of) random random project.
 * Browse everything on Wikiversity, or visit a portal corresponding to your educational level: pre-school, primary, secondary, tertiary, non-formal education.
 * Find out about research activities on Wikiversity.

 * Read an introduction for teachers and find out how to write an educational resource for Wikiversity.
 * Give feedback about your initial observations
 * Discuss Wikiversity issues or ask questions at the colloquium.
 * Chat with other Wikiversitans on #wikiversity-en.

And don't forget to explore Wikiversity with the links to your left. Be bold to contribute and to experiment with the sandbox or your userpage, and see you around Wikiversity! Jtneill - Talk - c 11:16, 15 November 2008 (UTC)

 Hi! My name is WikiversityJack. I am a pumpkin and a Wikiversity mascot. My aunt told me that fun + learning = Wikiversity. Let me know if I can help you out.

title: User talk:Tehdrago


text: User:Tehdrago

title: User:Tehdrago


text: User talk:Georgez

title: User talk:Georgez


text:
Talk:Student Safety on the Internet

Uh..

I was pretty sure that using the internet is a right, unless you're only referring to inside of schools. Outside of school it should be easily accessible by everyone, and others have no right to restrict your use of it. We are not China.

title: Talk:Student Safety on the Internet


text:
Portal talk:Tertiary Education

The "Guide to Tertiary Education" contains a listing of subjects. Two of the subjects "ERP *" and "The Web Economy *" list subsections of the subjects. I would like to compress them into one subject each. Any objections to this course of action? I would also like to retitle the subsections so that they sort properly: (01, 02, 03) instead of (1, 10, 11, 2, 20).

I think that compressing them would be fine, provided that you made a link to an expandable list so that people searching for the particular page could access it easily. And can anyone tell me how to edit the "Help box" on the right hand side so that it no longer references "teacher orientated" and "student orientated" tutorials, but instead references teacher and student oriented materials instead?

I plan to edit this page
I want to do three things:
 * 1) Remove or greatly demote the long list of pages that contain the tertiary education template.✅
 * 2) Lead to an introduction that a college or department can use.  It will include instructions for faculty/staff members to acquire the new "Teacher" position (just below Custodian), as well as how to register large numbers of students, and also the use of permalinks to facilitate students submitting written projects to whatever course management system is in use at the college or university.
 * 3) Find a way to recruit colleges and universities not yet aware of Wikiversity--Guy vandegrift (discuss • contribs) 15:24, 16 November 2015 (UTC)

Please excuse the self-promotion of Bell's theorem. But the astronomy feature was there for 5 years, and I think this is my best work.--Guy vandegrift (discuss • contribs) 16:43, 16 November 2015 (UTC)

title: Portal talk:Tertiary Education


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User:La comadreja/Software

 * HMMER, a downloadable program to construct profile Hidden Markov Models
 * MUSCLE, a multiple sequence alignment program that outputs files in .msf form

title: User:La comadreja/Software


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User:Eas4200c.f08.vqcrew.f/hw5

Equation of Equilibrium Stresses

We now want to look at a non uniform stress field. To accomplish this we must first start with the basics and consider a 1-D case as a model. We will have to consider both a Uniform and Nonuniform case. The uniform case can be seen in Figure ##, while the nonuniform case can be seen in Fig #. The uniform stress includes a single force acting on the end of a cantilever beam, while the nonuniform case has a varying shear stress acting horizontally across the top face of the beam along with the force on the end of the beam.

In the nonuniform case, the shear stress f(x) changes along the beam, thus f(x) is not a constant.

Bidirectional Bending

The recipe for Bidirectional Bending can be seen in Figure ##. The figure shows nonuniform stresses acting on a nonuniform cylinder. The equations below show the Moments about the y and z axis from $$ \displaystyle \sigma_{xx}$$. The Area over which the following integrals will be integrated are $$ dA = dy dz\;$$.

 * $$ M_y = \int_A z \displaystyle \sigma_{xx} \,dA $$

 * $$ M_z = \int_A y \displaystyle \sigma_{xx} \,dA $$

The next step is to look at the Moment of Inertia Tensors. First it is helpful to look at how the tensors can be transformed into both uniform and indicial notations.

 * $$ I_y = I_{yy} = I_{22}\;$$

 * $$ I_z = I_{zz} = I_{33}\;$$

 * $$ I_{yz} = I_{23}\;$$

Now from Figure ##, the Moment of Inertia Tensors can be determined.

 * $$ I_y = \int_A z^2 \,dA$$

 * $$ I_z = \int_A y^2 \,dA$$

 * $$ I_{yz} = \int_A yz \,dA$$

Now we will examine Hooke's Law:

 * $$\displaystyle \sigma_{xx} = E \epsilon_{xx}$$

Another way of looking of looking at Hooke's Law:

 * $$\displaystyle \sigma_{xx} = M_yy + M_zz$$

 * $$\displaystyle \sigma_{xx} = \frac{I_y M_z - I_{yz} M_z}{I_y I_z - I_{yz}^2}y + \frac{I_z M_z - I_{yz} M_{z}}{I_y I_z - I_{yz}^2}z$$

Note that the denominator is the determinant of the moment of inertia matrix.

Note that the nuetral axis where $$\displaystyle \sigma_{xx} = 0$$. Thus Hooke's Law can be transformend into the following:

 * \displaystyle \sigma_{xx} = M_yy + M_zz = 0

 * $$ z = \frac{-M_y}{M_z}y$$

By looking at the simple geometry of Fig ##.

 * $$tan \displaystyle \beta = \frac{M_y}{M_z}$$

Thus the equation can be simplified:

 * $$ z = (tan\displaystyle \beta)y$$

title: User:Eas4200c.f08.vqcrew.f/hw5


text:
User:La comadreja/Software/SpaceRemover

Overview
This program is used to format .aln files before constructing hidden Markov models (HMMs).

Description
A ClustalW2 output file in .aln form (align with numbers) is written like this:

Sequence1Name     SpecificSequence Number_of_Nucleotides_or_AAs Sequence2Name     SpecificSequence Number_of_Nucleotides_or_AAs

Sequence1Name     SpecificSequence Number_of_Nucleotides_or_AAs Sequence2Name     SpecificSequence Number_of_Nucleotides_or_AAs

etc.

This program takes such an .aln file, removes the spaces between the sequence name and the sequence, changes the count of nucleotides or aas at the end of the line to "83," and outputs another .aln file for use in HMMER.

Instructions
Supply the names of the files on the command line, e.g.: $java SpaceRemover < inputTest.aln > outputTest.aln

Completion Stage

 * November 22, 2008: Files parsed by this program could be used to build hidden Markov models. When the HMM files were calibrated, however, the error message of "FATAL: fit failed; --num may be set too small?" was returned.  The programmer (R.S.) will next convert files that are supplied in the HMMER tutorial to ClustalW2 form, construct hidden Markov models, and attempt to calibrate these files.

 * November 30, 2008: A new version of SpaceRemover, SpaceRemoverV2.java, is in the works and shows several improvements over its predecessor (e.g., that command line arguments are no longer required and the .aln file no longer needs to be further reformatted). R.S. was able to use ClustalW2 to convert the .msf file supplied in the HMMER tutorial (globins50.msf) to .aln form.  SpaceRemover.java (the original) cannot parse globins50.aln.  When SpaceRemoverV2.java was used to reformat globins50.aln, the program ran excessively slowly.  The next step for R.S. is to understand why it is so slow, fix it and make the program available online.

 * December 2, 2008: SpaceRemoverV2.java can parse globins50.aln supposedly successfully. However, when an HMM model of globins50.aln is built, the error message "FATAL: Parse error: sequence myg_escgi-VLSDAEWQLVL: length 2, expected 6 in alignment" is returned.  R.S. does not know what this means and the next step is to figure out its meaning and fix it.

 * January 18, 2009: "length 2, expected 6 in alignment"--when the length was increased to 6, the program printed "length 6, expected 18 in alignment." R.S. still does not understand the meaning.
 * HMMs of ADRA1A1.txt, based on SpaceRemoverV2.java, appear to be able to find sequences, e.g. in the FASTA file Artemia.fa, but R.S. does not know if they are correct sequences.
 * globins50.phylip contains an excessive number of gaps and cannot be recognized by hmmbuild.
 * The next step is to search for a better HMMER tutorial than the one in the Userguide.

Code
Code for the driver class is here.

Code for StdIn.java, a blueprint class that is used with the program, is here. StdIn.java is supplied for programming assignments by the instructors of Princeton University's introductory computer science class.

title: User:La comadreja/Software/SpaceRemover


text: User:La comadreja/Software/SpaceRemover/SpaceRemover.java


text: User:La comadreja/Software/SpaceRemover/StdIn.java


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text: User talk:Uf.team.aero/HW7

title: User talk:Uf.team.aero/HW7


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User:Eml4500.f08.team.guan/hw61114

Evaluating and Comparing Stiffness Matrices with Constant and Varying Areas and Modulus of Elasticities
 Referring to the figure above which is the graphical representations of the shaping functions, x tilda is the coordinate transformed from the global coordinate x to be the local coordinate of the element i. This coordinate is used to describe the linearly varying area or modulus of elasticity or both. Using the figure above, the shape functions for the element i $$N_1^{(i)}(\tilde{x})$$ and $$N_2^{(i)}(\tilde{x})$$ can be derived in terms of the local coordinate and the length of the element. $$N_2^{(i)}(\tilde{x})=\frac{\tilde{x}}{L^{(i)}} \begin{cases} 0, \tilde{x}=0\\ 1, \tilde{x}=L^{(i)}\\ \end{cases} $$ $$N_1^{(i)}(\tilde{x})=\frac{-\tilde{x}+L^{(i)}}{L^{(i)}} \begin{cases} 1, \tilde{x}=0\\ 0, \tilde{x}=L^{(i)}\\ \end{cases} $$ For the case in which there is linearly varying area and linearly varying modulus of elasticity on the axial element i, the bar will have a stiffness varying a parabolic manner because multiplying the two linear functions together will yield a parabolic function. In the collapsible box below, the stiffness matrix for the this case is derived below. Now, we will set the modulus of elasticity to be constant and letting the area vary linearly with respect to the local coordinate. The stiffness matrix will be calculated and then compared with the one in the book.

Now, we will use the average modulus of elasticities and the areas to calculate the stiffness matrix then subtract this expression from the stiffness matrix of the variable area and modulus of elasticity case. This stiffness matrix will be denoted as the average stiffness matrix. Note: Recall that the mean value theorem (MVT) and its relation to the centroid of an area. MVT: $$\int_a^bf(x)dx=f(\bar{x})[b-a]$$ for $$\bar{x}\in[a,b]$$ or $$a \le \bar{x} \le b$$ The application to the centroid calculation is as follows: $$\int_AxdA=\bar{x}\int_AdA=\bar{x}A$$ Now, how is connected to the homework problem? Consider the following expressions. $$\int_{x=a}^{x=b}f(x)g(x)dx=f(\bar{x})g(\bar{x})[b-a]$$ for $$a \le \bar{x} \le b$$ but $$f(\bar{x}) \ne \frac{1}{b-a}\int_a^bf(x)dx$$ where then above expression is the average value of f. This is true for the function g(x) as well. $$g(\bar{x}) \ne \frac{1}{b-a}\int_a^bg(x)dx$$ What this essentially means is that the value resulting from the products of the mean value of the modulus of elasticity and the mean value of the area does not equal the value obtained by the integration of the parabolic stiffness function $$EA(\tilde{x})$$ along the length of the element.

title: User:Eml4500.f08.team.guan/hw61114


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text:
Google/Matrix

Page-ranking Problem
There are billions of web pages accessible over the internet, but how can someone find the ones with the most relevant information to the topic they are interested in? We need a way to compare the importance and/or relevance of all of these pages. A primary concern for the search engine (beyond being able to index every page) is to be able to rank pages with an algorithm that incorporates common usage patterns (i.e. a user who visits web page X is more likely to click the link to page Y than the link to page Z).

Similar Problems
A similar problem is the BCS (Bowl Championship Series)Bowl_Championship_Series rankings for college football. Since many football teams do not play each other during the regular season, how can they be ranked against one another? In this case, the BCS standings are calculated by summing three results: the Harris Interactive Poll, the USA Today Coaches PollCoaches_Poll, and the average from six computer ranking systems.

Eigenvalue Solution Techniques
Google uses the PageRank algorithm which primarily ranks pages by the number of links to a web page, and the weights of the links. Initially every indexed page is given an equal rank, and a n x n connectivity matrix A is created (where n is the number of indexed pages). Position Ai,j is 1 if page i links to page j, otherwise it is 0. (Note: Since n is a very large integer, storing and working with A as a full matrix would be very inefficient, so it is usually stored as a sparse matrix.)

Once the initial rankings of every indexed page is calculated (simply 1/n), the PageRank of a new page is determined by how many links there are to the page, and the PageRanks of those 'linking' websites. The rank of a page is the probability that a web-surfer with an infinite amount of time will visit it.

In order to compute the PageRank of each website, we can use the Power Method to get the dominating eigenvector. This eigenvector will be n x 1, and will be made up of the PageRanks of all n websites. The connectivity matrix A is not initially in the correct format for use in the Power Method algorithm, so we will adjust A by dividing each row by the number of ones in that row and then (in order to keep track of everything) call the resultant matrix B.

Algorithm Outline
The Power Method x ← Bx will converge if B is:
 * Stochastic: each row contains strictly nonnegative values and the sum of the values in a row equals one
 * Irreducible: in the connectivity matrix it must be possible to get from any web page to any other web page
 * Aperiodic: every web page has a link to itself (or the user can simply refresh the page)

In order to calculate our dominant eigenvector, we need to satisfy the rules listed above. Let C be a n x n matrix whose elements are Ci,j = p*Bi,j + δ.

(where p is the probability of the user clicking a link on the page, usually taken to be 0.85, and δ = (1 - p)/n, where n is the total number of pages).

C now satisfies the above conditions (and is the transition matrix of the Markov chain of a random progression through web pages). Next, we iterate through the Power Method until we find a dominating eigenvector, x, such that x = Ax. Once we have x, we can "assign" its components (the PageRanks) to the corresponding web pages in A.

Example of Use
As an example, let's say we have websites X, Y, and Z. X links to both Y and Z. Y links to X. Z links to Y. This then gives us matrix A,

\mathbf A = \begin{bmatrix} 0 & 1 & 1 \\ 1 & 0 & 0 \\ 0 & 1 & 0 \end{bmatrix} $$

but then we must divide each element of a row by the sum of the elements in that row, giving us matrix B,

\mathbf B = \begin{bmatrix} 0 & .5 & .5 \\ 1 & 0 & 0 \\ 0 & 1 & 0 \end{bmatrix} $$

and then we compute matrix C by taking into account p,

\mathbf C = .85\begin{bmatrix} 0 & .5 & .5 \\ 1 & 0 & 0 \\ 0 & 1 & 0 \end{bmatrix} + \frac{(1-.85)}{3}\begin{bmatrix} 1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1 \end{bmatrix} $$

\mathbf C = \begin{bmatrix} 0 & .425 & .425 \\ .85 & 0 & 0 \\ 0 & .85 & 0 \end{bmatrix} + \begin{bmatrix} .05 & .05 & .05 \\ .05 & .05 & .05 \\ .05 & .05 & .05 \end{bmatrix} $$

\mathbf C = \begin{bmatrix} .05 & .475 & .475 \\ .9 & .05 & .05 \\ .05 & .9 & .05 \end{bmatrix} $$

and then we use some initial guess, x(0), for our Power Method, and calculate x(1), x(2), and so on,

\mathbf x^{(0)} = \begin{bmatrix} 3 \\ 1 \\ 2 \end{bmatrix} $$

\mathbf x^{(1)} = Ax^{(0)} = \begin{bmatrix} .05 & .475 & .475 \\ .9 & .05 & .05 \\ .05 & .9 & .05 \end{bmatrix} \begin{bmatrix} 3 \\ 1 \\ 2 \end{bmatrix} \mathbf = \begin{bmatrix} 1.575 \\ 2.85 \\ 1.15 \end{bmatrix} $$

\mathbf x^{(2)} = Ax^{(1)} = \begin{bmatrix} .05 & .475 & .475 \\ .9 & .05 & .05 \\ .05 & .9 & .05 \end{bmatrix} \begin{bmatrix} 1.575 \\ 2.85 \\ 1.15 \end{bmatrix} \mathbf = \begin{bmatrix} 1.97875 \\ 1.6175 \\ 2.70125 \end{bmatrix} $$

\mathbf x^{(3)} = Ax^{(2)} = \begin{bmatrix} .05 & .475 & .475 \\ .9 & .05 & .05 \\ .05 & .9 & .05 \end{bmatrix} \begin{bmatrix} 1.97875 \\ 1.6175 \\ 2.70125 \end{bmatrix} \mathbf \approx \begin{bmatrix} 2.15 \\ 2.0 \\ 1.69 \end{bmatrix} $$

\mathbf x^{(4)} = Ax^{(3)} \approx \begin{bmatrix} .05 & .475 & .475 \\ .9 & .05 & .05 \\ .05 & .9 & .05 \end{bmatrix} \begin{bmatrix} 2.15 \\ 2.0 \\ 1.69 \end{bmatrix} \mathbf \approx \begin{bmatrix} 1.86 \\ 2.12 \\ 1.99 \end{bmatrix} $$

Convergence
To more easily see which component is increasing the most, we can break down the vectors, x(i), into unit vectors and their coefficients,

\mathbf x^{(0)} = 3\begin{bmatrix} 1 \\ 0 \\ 0 \end{bmatrix} \mathbf + 1\begin{bmatrix} 0 \\ 1 \\ 0 \end{bmatrix} \mathbf + 2\begin{bmatrix} 0 \\ 0 \\ 1 \end{bmatrix} $$

\mathbf x^{(1)} = 3\begin{bmatrix} .525 \\ 0 \\ 0 \end{bmatrix} \mathbf + 1\begin{bmatrix} 0 \\ 2.85 \\ 0 \end{bmatrix} \mathbf + 2\begin{bmatrix} 0 \\ 0 \\ .575 \end{bmatrix} $$

\mathbf x^{(2)} \approx 3\begin{bmatrix} .66 \\ 0 \\ 0 \end{bmatrix} \mathbf + 1\begin{bmatrix} 0 \\ 1.62 \\ 0 \end{bmatrix} \mathbf + 2\begin{bmatrix} 0 \\ 0 \\ 1.35 \end{bmatrix} $$

\mathbf x^{(3)} \approx 3\begin{bmatrix} .72 \\ 0 \\ 0 \end{bmatrix} \mathbf + 1\begin{bmatrix} 0 \\ 2.0 \\ 0 \end{bmatrix} \mathbf + 2\begin{bmatrix} 0 \\ 0 \\ .845 \end{bmatrix} $$

\mathbf x^{(4)} \approx 3\begin{bmatrix} .62 \\ 0 \\ 0 \end{bmatrix} \mathbf + 1\begin{bmatrix} 0 \\ 2.12 \\ 0 \end{bmatrix} \mathbf + 2\begin{bmatrix} 0 \\ 0 \\ 1.0 \end{bmatrix} $$

and so, from the looks of it, Y seems to have the highest PageRank, followed by Z, and then X.

title: Google/Matrix


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User:Vchorozopoulos

 * I mainly write/edit articles for the greek language Wiki. I understabd fully what you write to me in English, but I admit some difficulties in writting. Except that I do it because I feel that we have left behind I wish to help to cover some ground. You must expect from me mainly corrections when I see errors, or addings for signifficat miaaings.

I'm interesting in amny subjects, but I'm better in the following ones: Mathematics, Chemistry, Information, Physics, Astronmy, Biology, Geology, History. I'm good in finding sources and I own a signifficant amount of them in books at home. I take ideas and data from them, but never exact texts, to avoid (c) ptoblems. I also feel free to use their formulas direct or after mathematical operations. --Vchorozopoulos 01:43, 16 November 2008 (UTC)

title: User:Vchorozopoulos


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Telecommuting

Telecommuting, a workplace phenomenon that stems from organisational embrace of new technology, enables employees to maintain a work-life balance by working from home (Gajendran & Harrison, 2007). However, the impact that these ‘mobile’ work arrangements have for interpersonal communication with colleagues in the workplace have been questioned. Studies have found that telecommuting places a strain on the quality of interpersonal relationships amongst co-workers due to the nature of their non face-to-face interactions (Gajendran & Harrison, 2007). Thomson and Covert (2007) advise employers to act cautiously when choosing employees that should have access to remote network access, as the negative impacts that telecommuting can have for teamwork are significant. Their research findings suggest that organisations that use telecommuting for complex tasks and projects, should consider using alternative means of communication such as face-to-face methods to increase clarity and overall employee job satisfaction (Thomson & Covert, 2007). If face-to-face communication is not physically possible, they encourage the use of face-to-face video conferencing as another more viable option (Thomson & Covert, 2007). This demonstrates that by utilising different forms of new technology, that are not purely text based like email, organisations can have the capacity to increase productiveness at work and maintain interpersonal connections amongst their colleagues.

title: Telecommuting


text:
User:Jestermeister/Categorical Syllogism/Preface

This is a small and short article on Aristotle's Logic. Feel free to comment about this article. I am after all, nothing more than just a student of philosophy. Do make changes to this article, but make sure that they are correct. Let me know though, so that I know where I have gone wrong.

Warm Regards,

Jestermeister 05:24, 31 January 2009 (UTC)


text:
User talk:Dwalter

Welcome
Hello Dwalter, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. To get started, you may
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And don't forget to explore Wikiversity with the links to your left. Be bold, and see you around Wikiversity! --Emesee 09:47, 16 November 2008 (UTC)

PCP HIV AIDS Toolkit/Anatomy and Physiology
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title: User talk:Dwalter


text: PCP HIV AIDS Toolkit/HIV AIDS Fact Sheet


text:
PCP HIV AIDS Toolkit/Elementary & High Schools

Implementing HIV/AIDS Activities in a High School Setting
Grant Tse

Establishing the Project
When getting a HIV/AIDS seminar off of its feet, as with most projects in the Philippines, the first thing the project needs is legitimacy and approval. In a high school setting, that usually means approaching your school's principal first. If the event is situated outside of your high school, contact your mayor, and perhaps your barangay captain. Contact with your DepEd division office is not necessary, but doesn't hurt.

If there is a reliable and appropriate person that could serve as your counterpart, feel free to approach him or her before the principal and then present the proposal together.

Before meeting with the principal, establish a rough outline of what you want to accomplish and what resources it will take. How many days will it be? Where will it be held? Will the school need to donate time, staff, or equipment to the project? Will students need to be excused from class? What exactly will the activities entail; some topics--such as certain aspects of family planning--should be mentioned ahead of time. After a rough outline has been drafted bring the proposal to your principal for approval.

It may be a good idea to have him sign a preliminary agreement supporting the idea; something along the lines of "PCV X has my full support in developing Y, a HIV/AIDS activity." This will go a long way to smoothing out the rest of your work, since many staff members, when confronted with a request, will tell you to see the principal first. This way you can simply flash the paper and move on.

Gathering Your Resources, Developing Activities, and Getting the Word Out
After you have your principal's blessing, find a counterpart, if you haven't already. If you don't plan on working with an outside organization, it's best to approach the head of your MAPEH Department first. MAPEH stands for Music, Arts, Physical Education, and Health. This is the Department that teaches Reproductive Health. The head can suggest someone or serve as your counterpart. Another alternative is the school nurse, or an interested teacher.

Also, ask the MAPEH what reproductive health is currently taught. While it is a part of the curriculum, some schools never "get" to that part of the curriculum. Review the school's textbook--while the teachers may say they cover family planning, their textbooks are often outdated and leave out what many PCVs may consider vital information. This can help in shaping what your seminars or activities need to cover.

The school's faculty also serves as an excellent gateway to the groups you want to invite. There is almost always an advisor for the Boy Scouts, Girl Scouts or the Supreme Student Government Organization (SUSGO) on the staff. Ask around and they will be able to get their respective demographics to attend your seminar. The SUSGO advisor will also be in touch with the SUSGO members of other schools, as they often attend events together.

Also, students in any of your classes will be able to tell you the names of the students that are SK members. Get in touch with these students and ask for the time and location of the next municipal SK meeting. They are usually held once a month. Mine is held every second Sunday, at 1 p.m. at the municipal hall. Attend the meeting, outline (sell) the seminar, ask how many SK members you can expect and for their names and contact information. Hammer the date into their minds, and make sure you send out reminder the day before.

The best way to invite guest speakers or specific groups is through a formal letter signed by yourself, your counterpart and noted by your principal. When asking for guest speakers, tell them how much time they have and what, specifically, you want them to discuss. Be sure to note whether the activity requires a registration free, or if lunch or merienda will need to be brought by attendees, or you will face an endless stream of texts asking about those things. Find the appropriate office or ask the advisor to deliver the letter. Make sure you allow plenty of time for a reply, a week at least.

In terms of resources, approach your school's supply officer and formally request (preferably weeks in advance) the use of any sound systems, microphones or other materials (copies?) your seminar or workshop may require. Schools usually do not mind covering overhead costs like electricity, venue, equipment, certificates and snacks/lunch for guest speakers, but funding for anything more will be harder to obtain. You may consider approaching the PTCA or your mayor for additional funds‚ but at least a month ahead of time.

Implementation
Follow-up is key. In the days before the implementation date, approach everyone involved and remind them of what they promised. Provide advance schedules to attendees and faculty. If the event is open to the public, have students put up posters beforehand or make an announcement during a flag ceremony--this is an excellent way to get information to students, since this is the one time they congregate as a group.

Make sure the venue is ready the day before (appropriate amount of chairs, sound system in place, and a board if necessary), along with your counterpart. If your students are excused from class if they want to attend, make sure their advisors make that announcement the day before.

Some things to consider: back-up generators, tarps for rain, and back-up seminars for guest speakers that don't show up. Don't forget certificates for invited attendees (SK, SUSGO etc.) and certificates/mementos for guest speakers. And for God's sake, don't forget the icebreakers. Anything longer than an hour requires lots and lots of icebreakers, and for a whole day event, they expect at least two intermissions.


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User talk:Xu rui

 Hello Xu rui, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. To get started, you may

 * Take a guided tour and learn to edit.
 * Visit a (kind of) random random project.
 * Browse Wikiversity, or visit a portal corresponding to your educational level: pre-school, primary, secondary, tertiary, non-formal education.
 * Find out about research activities on Wikiversity.

 * Read an introduction for teachers and find out how to write an educational resource for Wikiversity.
 * Give feedback about your initial observations
 * Discuss Wikiversity issues or ask questions at the colloquium.
 * Chat with other Wikiversitans on #wikiversity-en.

And don't forget to explore Wikiversity with the links to your left. Be bold to contribute and to experiment with the sandbox or your userpage, and see you around Wikiversity! --Cormaggio talk 12:07, 16 November 2008 (UTC)

 * Hi Xu Rui, I noticed you experimenting with math formatting on CT Fourier series - can I help you with anything? What are you thinking of doing on that page, or in general? Cormaggio talk 12:07, 16 November 2008 (UTC)

title: User talk:Xu rui


text:
Talk:Wikiversity courses

Interesting thoughts - but what exactly is this page attempting to do that isn't provided for on Courses? Should these two pages not be merged, and worked into a coherent yet diverse view of "courses" on Wikiversity? I totally agree with the statement that we shouldn't prescribe one single view of what a course is - but I'm also wary of creating too many similar pages (on top of all the similar pages we already have), when we still need to work on some sort of unifying vision for Wikiversity. Cormaggio talk 12:18, 16 November 2008 (UTC)

title: Talk:Wikiversity courses


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PCP HIV AIDS Toolkit

Introduction
Peace Corps Philippines has developed this manual and toolkit as an evolving collection of presentations, activities, resources and guides for HIV/AIDS advocacy.

The toolkit includes guides for HIV/AIDS awareness campaigns and events in schools, among at-risk groups and among faith leaders in the Philippines, as well as general information about HIV/AIDS, sex education, and HIV/AIDS in the Philippines. Users are encouraged to submit improvements, supplementary materials and new modules.

Situation in the Philippines

 * [[media:HIVAIDSInThePhilippinesSeptember08.pdf|HIV/AIDS in the Philippines Presentation (pdf)]]
 * [[media:HIVAIDSAwarenessInPhilippines.pdf|HIV/AIDS Awareness in Philippines Presentation (pdf)]]
 * HIV/AIDS Fact Sheet

General Information

 * [[media:AIDS101.pdf|AIDS 101 Presentation (pdf)]]
 * Anatomy and Physiology
 * Sex Education Questions
 * [[media:LetsTalkAboutSex.pdf|Let’s Talk About Sex Presentation (pdf)]]
 * Sex Education Thru Text (SET)

How to Get Started

 * Elementary & High Schools
 * Universities
 * NGOs & Centers
 * LGUs
 * Faith Leaders
 * OFW
 * CRM

Anti-Trafficking Advocacy

 * [[media:TraffickingInPersons.pdf|Trafficking in Persons Presentation (pdf)]]
 * [[media:ANTI-TRAFFICKING_IN_PERSONS_PROGRAM_FOR_THE_LGU_(Manual).pdf|Anti-Trafficking in Persons Program for the LGU Manual (pdf)]]
 * Republic Act 9208
 * True Stories Video - I do not have this video.

PCV Generated Materials

 * Biology of HIV/AIDS
 * AIDS Handshake Game
 * Session for College/Young Adult
 * HIV/AIDS Pre & Post Tests
 * HIV/AIDS Education & Prevention Seminar
 * HIV Myths and Facts
 * Sexuality and Masturbation Quiz and Answers

Appendices

 * Summary of RA 8054
 * Updated Philippines Partners Directory (pdf) - Is there an online version of this that we can link to?
 * STI brochure - I don't have this brochure
 * HIV/AIDS brochure - I don't have this brochure
 * Games for Reproductive Health (pdf)
 * HIV Transmission Fact Sheet (pdf)
 * The Female Condom (pdf)
 * What are STDs (tagalog) word - This document appears to be copyright by The StayWell Company. I cannot find an online version to link to.

Friends Tell Friends on the Street
This is a life skills manual that has a variety of lesson plans addressing many areas of interest for adolescents. It is available from the Peace Corps Philippines IRC.

title: PCP HIV AIDS Toolkit


text: Template:PCP HIV AIDS Toolkit/header

title: Template:PCP HIV AIDS Toolkit/header


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Summary of Philippine AIDS law

RA 8504 - The Philippine AIDS Law
(This is a condensed version of the RA 8504)

Article 1
The Government must promote education and information campaigns.
 * Schools and non-formal education programs must include HIV education.
 * The DOH must conduct public health education campaigns.
 * The government must provide education for Filipinos going abroad.
 * Employers, working with DOLE must develop workplace education and safety.
 * The Department of Tourism must provide education for tourists and transients.
 * LGUs must develop local HIV prevention and education efforts.
 * Accurate information about prophylactics will be provided.
 * It is against the law to give false or intentionally misleading information on HIV/AIDS.

Article 2
The Government will develop and promote safe medical practices
 * All blood, organs, and tissue for donation will be tested. If it tests positive, it will be disposed of safely, and not used.
 * The DOH will provide guidelines on safe surgery and medical procedures.
 * Willfully or negligently dangerous practices will be against the law.

Article 3
The Government will provide appropriate confidential HIV testing.
 * HIV testing can only be done with the consent of the person tested.
 * The DOH will provide anonymous HIV testing.
 * Counseling will be conducted before and after testing.
 * The DOH will make adequate and affordable HIV testing available in all of the Philippines.

Article 4
The Government will ensure adequate health and support services for people with HIV.
 * Hospitals will provide adequate care for persons with HIV.
 * LGUs must provide community-based prevention and care efforts.
 * Livelihood efforts will be made available for people with HIV.
 * The DOH is to do STD prevention and control efforts.
 * The DOH is to make sure that health insurance is available to people with HIV.

Article 5
The Government will monitor HIV/AIDS
 * The Government will establish an AIDSWATCH council.
 * Reporting procedures will be developed to track HIV rates, while respecting client confidentiality.
 * Contact tracing is permitted provided confidentiality is not breached.

Article 6
Confidentiality will be protected on HIV status.
 * All healthcare workers, and anyone handling health records will strictly preserve patient confidentiality on HIV status, and the identity of people with HIV.
 * HIV status can be shared by health officials in three circumstances; officials of the AIDSWATCH council, Health workers who are involved in treatment and need to know for their own safety, and a judge if under subpoena for an official court case.
 * HIV results may be given to the person tested, an official of the AIDSWATCH council, and a parent or guardian.  It cannot be given to anyone else.
 * Legal penalties can be provided for breaching confidentiality.
 * People with HIV must inform spouses and sex partners as soon as reasonably possible.

Article 7
Discrimination against people with HIV is illegal.
 * Employers cannot discriminate in hiring, firing, promotion, or assignment based on actual or suspected HIV status.
 * Schools are not allowed to refuse admission, punish students, or deny participation in activities based on real or perceived HIV status.
 * A person with HIV has the legal right to travel, live, and lodge with the same freedom as any other citizen.  Quarantines and other restrictions are illegal.
 * A person with HIV has every legal right to seek pubic office.
 * Credit services cannot be denied based on HIV status.  Insurance cannot be refused based on HIV status, provided the person does not lie about their HIV status.
 * Hospitals can heath services cannot refuse treatment or discriminate based on HIV status.
 * Decent burials cannot be denied based on HIV status.
 * Legal penalties for discrimination will be enforced.

Article 8
The government will establish a Philippine National AIDS Council
 * This council will be responsible for implementing the act and conducting all national AIDS performances.

title: Summary of Philippine AIDS law


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Wikiversity talk:Sandbox/to do

 * 1) First
 * 2) Then
 * 3) Finally

--67.65.39.44 16:00, 20 March 2009 (UTC)I NEED HELP PLEASE!!!!!!!!!!!!!!!!!!!

I have constructed a Martin birhouse 2'x2'x2' and it weighs 30 pounds. It is mounted on top of a 16' pressure treated 4"x4" post. I now need to have the bottom of the post 2' off the ground and erect it vertical ( so the birds will come live in it). I figure I need to use concrete and some more lumber. But how??? so mother nature won't destroy it????

HELP!!!!HELP!!! PLEASE!!! My name is Paul email is deanp@stmary.edu

title: Wikiversity talk:Sandbox/to do


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Talk:Wikipedia/to do

Suggestions for tasks:
 * 1) Add your name to the list of interested course developers
 * 2) Invite more people to this project
 * 3) Fact-check and improve the quizzes
 * 4) Suggest more quiz topics at Talk:Wikipedia/Quizzes.
 * 5) Suggest some common misconceptions about Wikipedia that can be used as quiz distraction alternatives, at Talk:Wikipedia/Quizzes.
 * 6) Suggest more assignments, for example discussion questions related to the videos, the wikipedia essays or the scientific articles.
 * 7) Improve the syllabus. Can this course serve as a recommended Wikimedia administrator certification course?
 * 8) Collect links to already existing learning resources (Almost done)
 * 9) Develop more slides that sumarize the theory and demonstrate how to use various tools. (Where can we upload OpenDocument Presentation files .odp or similar?)
 * 10) Organize the material into course modules, course sections, sub-topics, etc.
 * 11) Coordinate other related wikiversity projects, by transferring material to them, agreeing on merging or splitting of them, and harmonizing their web structure

title: Talk:Wikipedia/to do


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User:Eml4500.f08.delta 6.krueger/Notes Monday November 10th

Continuous Principle of Virtual Work to Discrete Principle of Virtual Work (continued) Now three motivations will be given for the equation being used in the form $$N_{i}(x)+N_{i+1}(x)$$. 1st Motivation: It can be observed from earlier discussion that $$N_{i}(x)+N_{i+1}(x)$$ are linear or represented by straight lines. Therefore the expression for U(x) is linear. This is true because the combination of $$N_{i}(x)$$ and $$N_{i+1}(x)$$ is linear. $$N_{i}(x)$$ and $$N_{i+1}(x)$$ can be written in the typical linear format:

$$N_{i}(x)=\alpha_{i}+\beta_{i}x$$

$$N_{i+1}(x)=\alpha_{i+1}+\beta_{i+1}x$$

where $$\alpha_{i}$$ is the y-intercept of the line and $$\beta_{i}$$ is the slope of the line and they both represent real numbers.

So the linear combination of $$N_{i}(x)$$ and $$N_{i+1}(x)$$ is:

$$N_{i}d_{i}+N_{i+1}d_{i+1}=(\alpha_{i}+\beta_{i}x)d_{i}+(\alpha_{i+1}+\beta_{i+1}x)d_{i+1}$$

Now the like terms are combined to give:

$$U_{x}=(\alpha_{i}d_{i}+\alpha_{i+1}d_{i+1})+(\beta_{i}d_{i}+\beta_{i+1}d_{i+1})x$$

Where $$d_{i}$$ is the weighting coefficient. It can clearly be seen that this is a linear function of x.

2nd Motivation:

Recall the equation for the interpolation of U(x):$$U(x)=N_{i}(x)d_{i}+N_{i+1}(x)d_{i+1}$$

Now replace x with $$x_{i}$$ and the equation becomes:$$U(x)=N_{i}(x_{i})d_{i}+N_{i+1}(x_{i})d_{i+1}$$

In the drawing above it was shown that $$N_{i}(x_{i})d_{i}=1$$ and that $$N_{i+1}(x_{i})d_{i+1}=0$$. The eqaution for $$U(x_{i})$$ becomes:

$$U(x)=d_{i}$$

The equation shows that $$U(x_{i})$$ is equal to the weighting coefficient $$d_{i}$$.


text:
User:Sri-ganesh

New to Wikiversity. Interested in adding content. Degrees include a Bachelor's in Engineering, and a Master's in Education. ttfn

title: User:Sri-ganesh


text:
Talk:Wikipedia/syllabi

I suggest a bit broader course name and title, incorporating wikis in general. Ex: full course name: "Wikis - publishing, reliability and technology. Case study of Wikipedia."--Piotrus 18:19, 16 November 2008 (UTC)

 * Me and my colleages have discussed whether is should be named Wikis or Wikipedia back and forth. To have both in the name as you suggested is perhaps the solution to the problem. What about "Wikis and Wikipedia - publishing, reliability and technology." (The Swedish course name is already decided and announced, but I think an alternative course name can be presented at this Wikiversity page.) Mange01 14:00, 17 November 2008 (UTC)

 * Sounds good! --Piotrus 21:22, 20 November 2008 (UTC)

Prerequisite
brief little detail. you state "Prerequisites: Basic university eligibility. "

This goes against the grain of wiki philosophy. Since there is NO required university elgibility to contribute to Wikipedia- how can be for Studying wikipedia?--JoliePA 14:30, 17 November 2008 (UTC)

 * It should be noted its optional. In many real universities, this course may have some prerequisites, and if we can agree that something is logical, we may want to suggest it. That said, I don't consider prerequisites to be a major issue, and most people using this course will ignore them.--Piotrus 21:22, 20 November 2008 (UTC)

Required Reading
Lennart Guldbrandsson, Så fungerar Wikipedia, September 2008. Is this a swedish book? That might be very difficult for me to get. I am not an acedemic and scholarly articles can be very hard for me to find.--JoliePA 14:30, 17 November 2008 (UTC)
 * Thanks for valuable comments! I have addressed them. I suppose this syllabus should describe the intention of the wikiversity course, and not a real university course. Mange01 00:11, 18 November 2008 (UTC)

I'd like to learn more about that book, but if it is in Swedish, unfortunately it's more of a curio than a useful piece for us. We can certainly add a section: "non-English resources", and I am sure that for Swedish speakers it will be a valuable resource, but unless parts of those books are translated into English, it's not something of major importance to us.--Piotrus 21:22, 20 November 2008 (UTC)

Integration with Wikipedia service learning course?
Is there a big difference between this page and the Wikipedia service-learning courses? Maybe the efforts could be integrated. --tomaschwutz 21:53, 28 November 2008 (UTC)

 * An integration between Wikipedia and Wikipedia service-learning courses is definitely of interest! One option is a merge. Another option is to keep the courses separate, and have different syllabus for them (one university level/research oriented course, one one more practical course), but reuse some of the course materials in both courses by linking between them.

 * We may continue the discussion atTalk:Wikipedia.

 * You are welcome to add your name to the list of course developers, and contribute to the Wikipedia. Mange01 20:15, 29 November 2008 (UTC)

title: Talk:Wikipedia/syllabi


text:
User:Mike.lifeguard/Editintro/User talk:Mike.lifeguard

 * Blacklist-related enquiries
 * Please do not ask me about removing blacklisted domains etc here. That needs to be considered by more than just myself, so please make such requests at Talk:Spam blacklist. As well, you will probably get a faster answer by doing so.


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User:Eas4200c.f08.carbon.orear/HW6

=Homework 6=

 * Lecture Notes (current version) Lecture Notes (archived version)
 * MATLAB Code (current version) MATLAB Code (archived version)
 * Composite Laminate Analysis: A Study in MATLAB (current version) Composite Laminate Analysis: A Study in MATLAB (archived version)
 * HW6 Contributing Team Members (current version) Contributing Team Members (archived version)

title: User:Eas4200c.f08.carbon.orear/HW6


text: File:HW6 DOF's.jpg

title: File:HW6 DOF's.jpg