Consider a cantilever beam in figure 3.28 of length \(L=1 \mathrm{~m}\) with flexural rigidity \(E I=\) \(1,000 \mathrm{Nm} \quad{ }^{2}\). The beam is subjected to an axial force \(P\) and a couple \(C=+1,000 \mathrm{Nm}\) at the tip. Find the deflection curve \(v(x)\) for the following three cases:

(a) \(P=0\);

(b) \(P=\) \(+2,000 \mathrm{~N}\); and

(c) \(P=-2,000 \mathrm{~N}\). Use one element for the entire beam.

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y X L Figure 3.28 A beam subjected to axial force and an end couple C P