3 Fig. 3 shows a framework in a vertical plane constructed of light, rigid rods \(\mathrm { AB } , \mathrm { BC } , \mathrm { CD } , \mathrm { DA }\) and BD . The rods are freely pin-jointed to each other at \(\mathrm { A } , \mathrm { B } , \mathrm { C }\) and D and to a vertical wall at A . ABCD is a parallelogram with AD horizontal and BD vertical; the dimensions of the framework, in metres, are shown. There is a vertical load of 300 N acting at C and a vertical wire attached to D , with tension \(T \mathrm {~N}\), holds the framework in equilibrium. The horizontal and vertical forces, \(X \mathrm {~N}\) and \(Y \mathrm {~N}\), acting on the framework at A due to the wall are also shown.
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\caption{Fig. 3}
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- Show that \(T = 600\) and calculate the values of \(X\) and \(Y\).
- Draw a diagram showing all the forces acting on the framework, and also the internal forces in the rods.
- Calculate the internal forces in the five rods, indicating whether each rod is in tension or compression (thrust). (You may leave answers in surd form. Your working in this part should correspond to your diagram in part (ii).)
Suppose that the vertical wire is attached at B instead of D and that the framework is still in equilibrium.
- Without doing any further calculations, state which four of the rods have the same internal forces as in part (iii) and say briefly why this is the case. Determine the new force in the fifth rod.