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harina [27]
3 years ago
7

Given that -5 ∆ x = 106, find x.

Mathematics
1 answer:
Digiron [165]3 years ago
6 0

Answer:

Draw the virtual load and show its magnitude on the figure in the answer sheet to calculate the maximum deflection, Amax, using Castigliano's Second Theorem. (b)

Step-by-step explanation:

Determine the moment equations of the segment AB, MAB(x), and BC, MBC (X), to calculate Amax using Castigliano's Second Theorem (including P terms, use the given x-coordinate, in m and kN unit). (C) Determine the maximum deflection, Amax, using Castigliano's Second Theorem (clearly show the integration equation in your calculation process).

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\bf \stackrel{\stackrel{\textit{volume of a}}{\textit{rectangular prism}}}{V=Lwh}~~ \begin{cases} L=length\\ w=width\\ h=height\\[-0.5em] \hrulefill\\ L=4\\ w=2\\ \end{cases}~\hspace{2em}\stackrel{\textit{volume of a cylinder}}{V=\pi r^2 h}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=1 \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}

\bf \stackrel{\textit{prism's volume}}{(4)(2)(h)}~~+~~\stackrel{\textit{cylinder's volume}}{(\pi )(1)^2(h)}~~=~~80 \\\\\\ 8h+\pi h=80\implies h(8+\pi )=80\implies h=\cfrac{80}{8+\pi }\implies h\approx 7.180301999

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