The truss in Figure 4 is loaded as shown. Both the nodes 1 and 5 are hinged supports. Take P = 27.8, L = 2.7, A = 0.0015 m2 and E=200 GPa. AE is constant for all the members. Use the stiffness method approach to solve parts (a) to (d) below. Write down your P and L values and answer parts a) to d) below. (a) Determine the stiffness matrices of the truss members 1, 4 and 5 in the global co-ordinate system with the origin at node 1. Use the member directions shown and clearly indicate the corresponding degrees of freedom numbers in the stiffness matrices. (b) Determine the stiffness matrices of elements 1 and 4 in the local co-ordinate system and then convert the respective local stiffness matrices to the global stiffness matrices. Show all calculations. Check the results with those obtained in part (a) above and comment. (c) Determine the load vector (Q) and displacement vector (D) and write the load-displacement relationship for the entire truss in the global co-ordinate system. Assume that the global stiffness matrix is denoted by K. Assembly of the global stiffness matrix K is not required. (d) Assuming that all the D values are calculated or known from part (c), determine the force in member 5 in terms of the displacements D’s. Show all calculations.
The truss in Figure 4 is loaded as shown. Both the nodes 1 and 5 are hinged supports. Take P = 27.8, L = 2.7, A = 0.0015 m2 and E=200 GPa. AE is constant for all the members. Use the stiffness method approach to solve parts (a) to (d) below. Write down your P and L values and answer parts a) to d) below.
(a) Determine the stiffness matrices of the truss members 1, 4 and 5 in the global co-ordinate system with the origin at node 1. Use the member directions shown and clearly indicate the corresponding degrees of freedom numbers in the stiffness matrices.
(b) Determine the stiffness matrices of elements 1 and 4 in the local co-ordinate system and then convert the respective local stiffness matrices to the global stiffness matrices. Show all calculations. Check the results with those obtained in part (a) above and comment.
(c) Determine the load
(d) Assuming that all the D values are calculated or known from part (c), determine the force in member 5 in terms of the displacements D’s. Show all calculations.
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