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Response Details:
This propped beam can be simply analyzed using different deflection methods, but for a much simpler and easy-to-understand solution, we will be using the Moment-Area Method.
By the second theorem of M-A method, it states that (with respect figure below which i mark the roller support as point A and the fixed as point B, anyway its just a designation, the results will be the same) the deviation of A with respect to B (t B/A) is equal to the area of the moment diagram between A and B, multiplied by the distance from A to the centroid of the area of moment diagram.
By formula:
But if you notice, since there is roller support at point A, we can say that:
For the moment diagram by parts:
Hence,
= 0
Solving for Ra:
But if you notice, a + b = L and therefore, b = L - a, substitute this in the working equatiion:
Finally,
 (Note: this Ra is the value of the reaction at the roller support)
I will not spoil the fun here, the reaction on the fixed end as well as its moment can be computed by summing forces at point A and point B respectively (with respect to my figure). But I will give you the answers for Rb and Mb.
Here it is:
Also, here's the shear and moment diagram:
Note: Please bear with me for I have reversed the figure as well as its letter designation, but anyway, the results are the same.
If you still have questions regarding this problem, feel free to message me. And please don't forget to rate me. Thanks and GOD bless
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