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Mathematics LibreTexts

2.4: Chapter 2 Exercises

  • Page ID
    21808
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    Exercise \(\PageIndex{1}\)

    With regard to the unixial truss figure,

    1. Derive the \(A\) and \(K\) matrices resulting from the removal of the fourth spring,
    2. Compute the inverse, by hand via Gauss-Jordan, of the resulting \(A^{T} ⁢K⁢A\) with \(k_{1} = k_{2} = k_{3} = k\)
    3. Use the result of (ii) to find the displacement corresponding to the load \(\textbf{f} = (0, 0, F)^{T}\)

    Exercise \(\PageIndex{2}\)

    Generalize example 3, the general planar truss, to the case of 16 nodes connected by 42 fibers. Introduce one stiff (say \(k=100\)) fiber and show how to detect it by 'properly' choosing \(\textbf{f}\) the before-after plot in the general planar module, from which you conclude the presence of a stiff fiber.

    Screen Shot 2020-08-31 at 4.43.32 PM.png
    Figure 1. A copy of the before-after figure from the general planar module.