For the seven-member planar truss considered in Problem 12.6 (Fig. 12.18), determine the following:

a. The system stiffness matrix after applying the boundary conditions.

b. The nodal displacements of the truss under the loads indicated in Fig. 12.18.

Data From Problem 12.6:-

A seven-member planar truss (with pin joints) is shown in Fig. 12.18. Each of the seven members has an area of cross section of \(4 \mathrm{~cm}^{2}\) and a Young's modulus of \(207 \mathrm{GPa}\).

a. Label the complete set of local and global nodal displacement degrees of freedom of the truss. Assume the \(X\) and \(Y\) coordinates shown in Fig. 12.18 as global coordinates.

b. Find the coordinate transformation matrix of each member.

c. Find the local and global stiffness matrices of each member.

Figure 12.18:-

Transcribed Image Text:

1000 N 3 Y 60 4' 60 7 5 X 1 1500 N 1 m + 1 m- FIGURE 12.18 Seven-member planar truss. 500 N 6 60 2