Consider three truss elements representing a steel rod (E =200 GPa) as shown Figure 1. The...

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Consider three truss elements representing a steel rod (E =200 GPa) as shown Figure 1. The length of each element is Le=10 cm, and the cross-sectional area is Ae=0.002 m. It is fixed at node 1 and the displacement is prescribed at node 4 (i.e., u = A). Here the unit of is mm and the magnitude is the fourth digit of your student ID. If it is zero, use 4 instead. An external force P is applied at node 2 (i.e., f = P). The unit of P is MN and the magnitude of P is the fifth digit of your student ID. If it is zero, use 4 instead. Do not leave the answers in fractions or parameters (i.e., A, P, E, etc.). Be careful with the units and magnitudes. (a) Setup the 4x4 global stiffness matrix K from three local stiffness matrices K. (25 Points) EA Hint: Here, the stiffness matrix for each element can be calculated as K = (b) Write out the components of known nodal displacement vector u, and unknown u', separately. Do the same for the nodal force vector f' (known) and f, (unknown). (10 Points) (c) Construct the equation Ku'=f' -Ku. Show all the components of matrices and vectors explicitly. (15 Points) (d) 1 Solve for the unknown nodal displacements, stresses, and forces. (15 Points) (1) 10 cm 2 (2) 10 cm 1 L 1 Figure 1. (3) 1). 3 10 10 cm A 4 Consider three truss elements representing a steel rod (E =200 GPa) as shown Figure 1. The length of each element is Le=10 cm, and the cross-sectional area is Ae=0.002 m. It is fixed at node 1 and the displacement is prescribed at node 4 (i.e., u = A). Here the unit of is mm and the magnitude is the fourth digit of your student ID. If it is zero, use 4 instead. An external force P is applied at node 2 (i.e., f = P). The unit of P is MN and the magnitude of P is the fifth digit of your student ID. If it is zero, use 4 instead. Do not leave the answers in fractions or parameters (i.e., A, P, E, etc.). Be careful with the units and magnitudes. (a) Setup the 4x4 global stiffness matrix K from three local stiffness matrices K. (25 Points) EA Hint: Here, the stiffness matrix for each element can be calculated as K = (b) Write out the components of known nodal displacement vector u, and unknown u', separately. Do the same for the nodal force vector f' (known) and f, (unknown). (10 Points) (c) Construct the equation Ku'=f' -Ku. Show all the components of matrices and vectors explicitly. (15 Points) (d) 1 Solve for the unknown nodal displacements, stresses, and forces. (15 Points) (1) 10 cm 2 (2) 10 cm 1 L 1 Figure 1. (3) 1). 3 10 10 cm A 4