Using the result of Problem 12.9, find the assembled stiffness matrix of the truss and formulate the

Question:

Using the result of Problem 12.9, find the assembled stiffness matrix of the truss and formulate the equilibrium equations if the vertical downward load applied at node 4 is \(5 \mathrm{kN}\).

Data From Problem 12.9:-

Find the global stiffness matrix of each of the four bar elements of the truss shown in Fig. 12.5 using the following data:

Nodal coordinates: \(\left(X_{1}, Y_{1}\right)=(0,0) \mathrm{m},\left(X_{2}, Y_{2}\right)=(1.25,2.5) \mathrm{m},\left(X_{3}, Y_{3}\right)=(2.5,0) \mathrm{m}\), \(\left(X_{4}, Y_{4}\right)=(5,3.75) \mathrm{m}\).

Cross-sectional areas: \(A_{1}=A_{2}=A_{3}=A_{4}=13 \mathrm{~cm}^{2}\).

Young's modulus of all members: \(200 \mathrm{GPa}\).

Figure 12.5:-

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