(Solved): Q2. A circular cross section bar AB with diameter d and length L has a cylindrical hole of diamete ...

Q2. A circular cross section bar $$\mathrm{AB}$$ with diameter $$\mathrm{d}$$ and length $$\mathrm{L}$$ has a cylindrical hole of diameter $$d/2$$ over the length $$\mathrm{x}$$ as shown in Figure Q2. The bar has rigid supports at $$A$$ and $$B$$ and is acted upon, at central point $$C$$ by an axial force P. Take Young's modulus to be $$E$$ and assume that $$x<L/2$$. Flgure Q2 a) Draw a free body diagram and write the conditions of compatibility of displacements for the bar. [4 marks] b) Find the reactions at the rigid supports $$A$$ and $$B$$ as functions of the load and the dimensions of the bar. [6 marks] c) Determine the displacement of point of application of the load P, as a function of the load and the dimensions of the bar. [5 marks] d) Find the value of distance $$x$$ at which $$R_B=(6/5)R_A$$. [5 marks]