A2 FEM Assignment PDF

Assignment-1 1. The spring system as shown below is subjected to a force P. Determine the displacement of node 2 and reaction forces at node 1, 3 and 4 using matrix method. Assume P = 100 kN and k1 = k2 = k3 = 200 N/m. 2. Obtain the system stiffness matrix for the linear spring system below....

Assignment-1 1. The spring system as shown below is subjected to a force P. Determine the displacement of node 2 and reaction forces at node 1, 3 and 4 using matrix method. Assume P = 100 kN and k1 = k2 = k3 = 200 N/m. 2. Obtain the system stiffness matrix for the linear spring system below. Also find the force in spring ‘3. K1 = 100 N/m k2 = 200 N/m 3 k3 = 100 N/m k4 = 200 N/m F1 = 5kN and F4 = 8 kN. 3. Calculate element forces when F3 = 1000N is applied. Use spring constants (N/mm): k(1) = 500, k(2) = 400, k(3) = 600, k(4) = 200, k(5) = 400, and k(6) = 300. 4. For the Statically indeterminate bars E = 100 GPa F = 10,000 N A1 = 10−4 m2, A2 = 2×10−4 m2. Calculate the forces in each member, reaction force RL and RR and displacement of joint B using matrix method.  5. A straight uniform bar AD is clamped at both ends and loaded as shown in Figure below. Initially the bar is stress free. Determine the stresses in all the three parts (AB, BC, CD) of the bar if the cross-sectional area of the bar is 1000 mm2. E = 200 GPa. 6. A member LMNP is subjected to point loads as shown in Figure below. elongation and stresses in each bar. Take E = 210 GN/m2. 7. For the two bar truss shown in fig below. Determine the displacement of node 1 & stress in each element. 8. Determine i) forces in each member ii) deformation of point a and b, for the pin jointed truss as shown below 9. For the plane truss with inclined support as shown below, solve for the nodal displacement and element stresses in the bars. Let A = 1000 mm2. E = 2 x 105 N/mm2is same for all the members and L = 500 mm. Calculate the stress n each members and nodal displacements. 10. For the plane truss with inclined support shown below, solve for the nodal displacements and element stresses in the bars. Let A = 12 x 10-4 m2, L = 0.75 m and E = 2x1011 N/m2.