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 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.
I need some help with this spring assemblage question. In the
image below the nodes are actually reorganized in the question in
the order of 1-5-4-3-2. Now Knowing that I have to a) write the
global stiffness matrix for it b) if nodes 1 and 2 are fixed and a
force P is at node 4 what is the nodal displacement, c) I need to
find the reactions at 1 and 5 and finally d) I need to find the...
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
4. Three spring structure. Node and element are indicated in the Figure. A force, f3-10K, is loaded at node #3A11 the spring has same spring constant k. Node #1 is constrained in all directions. (20 pt) k1) k-3) F3 k2) a. Assemble the global stiffness and force matrix. b. Partition the system and solve for the nodal displacements, u2 and U3. C. Calculate the reaction forces at Node #1. 5. A spring system is designed as follows. Node and element...
Figure Q5(a) shows a plane truss supported by a horizontal spring at the top node. The truss members are of a solid circular cross section having a diameter of 20 mm and an elastic modulus (E) of 80 GPa (10° N/m2). The spring has a stiffness constant of k-2000 kN/m. A point load of 15 kN is applied at the top node. The direction of the load is indicated in the figure. The code numbers for elements, nodes, DOFS, and...
structural analysis
Figure Q() Question 2 For the bar assemblages shown in Figure Q(2), determine the nodal displacements, the forces in each element and the reactions. Use the direct stiffness method (25 marks) 35 kN E-210 GPa 2 A4 x 10m2 1 m im
Figure Q() Question 2 For the bar assemblages shown in Figure Q(2), determine the nodal displacements, the forces in each element and the reactions. Use the direct stiffness method (25 marks) 35 kN E-210 GPa 2...
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
Question 1: For the plane (2D) truss shown below, evaluate the transformation matrix [T] and the stiffness matrix in the local axis system [KL] of all elements. Use these matrices to evaluate the element stiffness matrix in global axis system [KG] of the members and assembled them to generate the overall stiffness matrix [K of the truss. Modify the stiffness matrix [K] in order to incorporate boundary conditions following the elimination technique of rows and columns. Take E 200 GPa...
Using the stiffness method, determine the axial forces within
members and the displacements of joints of the truss shown in the
Figure 1. The truss was built using 50 mm x 50 mm x 3 mm SHS with
E= 200 GPa (approx). (Cross members BD and CE are not connected at
the middle)
(a) Show local stiffness matrices for each member and the
assembled global stiffness matrix. Show your step by step solution.
(30 Marks)
(b) Use an appropriate method...
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...
a. Compute the total stiffness matrix [K] of the assemblage shown in Figure 3-1 by superimposing the stiffness matrices of the individual bars. Note that should be in terms of A. As, A, E, E E, L. and L. Here A, E, and are generic symbols used for cross-sectional area modulus of elasticity, and length, respectively Figure P3-1 Now let As - Ag-A-A.E E, E E and L-L L -L nodes 1 and 4 are fixed and a force Pacts...