a. Compute the total stiffness matrix [K] of the assemblage shown in Figure 3-1 by superimposing...
For the spring assemblage shown in Figure 2-13, obtain (a) the global stiffness matrix, (b) the displacements of nodes 2-4, (c) the global nodal forces, and (d) the local element forces. Node l is fixed while node 5 is given a fixed, known displacement δ= 20.0 mm. The spring constants are all equal to k = 200 kN/m.
For the truss shown in the below figure, determine the stifness matrix for each truss element, the stiffness matrix for entire truss, the displacements at nodes 1 through 4, and the force in elements 1 through 5. Also, determine the force in each element. Let A = 3 in2, E = 30 x 106 psi for all elements. 8 kips 8 kips 10 ft. 3 4 2 トー-10ft.-*-10 ft.
N is 1 QUESTION 2 For the bar assemblage shown Data: in the figure, determine the nodal displacements, the E =nx10" Pa forces in each element, the A=nx10-?m? reactions and the stresses. L =nx 500mm Ly =n x500mm F=nx104N L2 =nx 250mm F, = 2.5x F, MITT L 1 L2
Finite element problems For the bar elements shown in Figure P3–16, the global displacement have been deter- mined to be up = 0.5 in., V = 0.0, uy = 0.25 in., and V2 = 0.75 in. Determine the local x' displacements at each end of the bars. Let E = 12 x 106 psi, A = 0.5 in?, and L = 60 in. for each element. 45° 30° (a) (b) - Figure P3–16
Solve all problems using the finite element stiffness method. For the rigid frame shown in Figure P5-4, determine (1) the nodal displacements and rotation at node 4, (2) the reactions, and (3) the forces in each element. Then check equilibrium at node 4 Finally, draw the shear force and bending moment diagrams for each element. Let E 30x 103 ksi, A 8 in2, and I 800 in.4 for all elements. 20 kip 25 ft 25 ft 40 ft Figure P5-4...
2 k3 2 3 4 a. (10 points) Obtain the global stiffness matrix K using direct stiffness method (k1- 100 1b/in, k2 200 lb/in, k3 3001b/in, P-500 Ib). (10 points) If nodes 1 and 4 are fixed and a force P acts on node 2 in the positive x direction, fin the values for the displacements of nodes 2 and 3. b. c. (10 points) Deter odes 1 and 4
For the system shown below, (a) the global stiffness matrix (b)displacements of nodes 2 and 3 (c)the reaction forces at nodes 1 and 4 (d)the force in the members EA TRATAMI 70-400 = 100 x 10 kN/m 0.28 ATT L ( EA k, 100 - 200 = 200 x 10 kN/m 0.1 L (4 EA k, 200.70 =140x10 kN/m 0.1 I (4.2 X tretiet 0.28 2 vyos Imool
Given the indeterminate beam shown below, use FEM to compute the final stiffness matrix and force vector of the Ku f problem using three elements with the lengths prescribed in the figure. Your work should include all boundary conditions. The beam has the properties E 3.0E6 psi and I 4.5 in 30 lb/in Fo-500 q2 20 lb/in 12 in The weak formulation gives the following expressions for the generic element force vector qe and stiffness matrix Ke. 12Eele 6Eel 20...
Problem 2 135 pts The grid shown in figure 2 is rigidly fixed at nodes 2 and 3. Node 1 is subjected to a downward force and two moments. 4m Let E = 210GPa, G = 84GPa, 4m 1-2 × 10-4m", J = 2 × 10-4m" for elements ① and ② Calculate the reduced stiffness matrix Write the system of equations that yield the global displacements and rotations of node 1 (no need to solve them!) a) b) 30kN Figure...
1. (60%) For the truss system shown below (a) (12%) Determine the element stiffness matrix w.r.t. the global coordinate system for all elements. (b) (10%) Determine the global stiffness matrix, [K]. (c) (5%) List all the boundary conditions. (d) (33%) Determine the internal force, elongation, stress, and strain for each element. Indicate whether it is under tension or compression. My LLLLLLLL 1 0 1-2=45° \ 30° 30° / 14116 141 16 12 2-3 = 30 3 1-4=300 Join But 45=225...