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# 2.4: Chapter 2 Exercises

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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.