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I. Solve the following truss system (left) with global degrees of freedom given (right). Member 1-2:...
For the truss shown in the figure below, develop element stiffness matrices in the global co-ordinate system. AE 200 [M...
For the truss shown in the figure below, develop element stiffness matrices in the global co-ordinate system. AE 200 [MN] is the same for all members. Use the direct stiffness matrix method to: i. Establish all element stiffness matrices in global coordinates ii.Find the displacements in node 3 ii. Calculate the member stresses 4m 3m 20kN 2 2 Use HELM resources on Moodle to find required determinant and inverse matrix. Answer 9.6x103 [MPa] 0.24mmm u3-0.20mm 0.45mm 16x10-3 MPa σ2-3- 1...
Finite Element Method 5.17 Displacements of the three-member truss shown are confined to the plane of...
Finite Element Method
5.17 Displacements of the three-member truss shown are confined to the plane of the figure, and points 1, 2 and 3 are fixed to the stationary rim. All members have the same A, E, and L a) Obtain the 2x2 stiffness matrix that operates on the horizontal and vertical degrees of freedom of the central node. b) Obtain the corresponding global force vector c) Solve for the displacements and for axial stress in member (2-4), when the...
Part A AE | AA, A -AA, k= 41 -17 | Ng I - tedy A...
Part A AE | AA, A -AA, k= 41 -17 | Ng I - tedy A lady Ez L-ledy - lady X J A Notice the codes associated with the near end (N,N,) and far end (F., Fy) degrees of freedom. Once all the member stiffness matrices are formed the truss stiffness matrix can be constructed. Each element in each member stiffness matrix k is placed in the corresponding row and column designation in the truss stiffness matric K At...
For the 3-D indeterminate (4-member) TRUSS structure shown in Figure 2A. Given that Px 10K (in...
For the 3-D indeterminate (4-member) TRUSS structure shown in Figure 2A. Given that Px 10K (in X-direction); Py none (in Y-direction); E 30,000 ksi; A 0.2 square inches. The nodal coordinates, the earth-quake displacement/settlement, and members' connectivity information are given aS Applied Load! Earth-Quake MEMBER #1 NODE # X node-i node-j 120.00" 160.00"| 80.00"| Px=-10 Kips none Py- none 120.00" 160.00"0.00"none 120.00"0.00" 0.00" none 0.00" 0.00"0.00" none 0.00" 0.00" 80.00" none none 2 none 4 4 none 4 +2.00" (in...
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 ele...
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...
Q2. Statically determinate or indeterminate truss analysis by the stiffness method. (50 marks) a) Determine the stiffness matrix of the whole truss given in problems 14.9 and 14.10 (p. 583). Indicate...
Q2. Statically determinate or indeterminate truss analysis by
the stiffness method. (50 marks)
a) Determine the stiffness matrix of the whole truss given in
problems 14.9 and 14.10 (p. 583). Indicate the degrees-of freedom
in all the stiffness matrices. (18 marks)
b) Calculate all the nodal displacements and all the member forces
for the truss.
(16 marks)
14-9. Determine the stiffness matrix K for the trus Take A 0.0015 m2 and E 200 GPa for each member. 2 12 4...
2D truss elements (a) have rotational degrees of freedom. (b) can transmit axial forces. (c) cannot...
2D truss elements (a) have rotational degrees of freedom. (b) can transmit axial forces. (c) cannot resist bending. (d) always have nonlinear material properties. 3. Modal analysis is (a) an example of a Finite Element steady-state analysis. (b) an example of a Finite Element transient analysis. (c) an example of a Finite Element eigenvalue analysis. (d) None of the above. 4. In a static stress analysis using truss elements, the elements of the stiffness matrix will always depend on: (a)...
Problem 2 [Required]: For the truss below (and using the Stiffness Method): (a) Determine the global...
Problem 2 [Required]: For the truss below (and using the Stiffness Method): (a) Determine the global stiffness matrix; (b) Calculate the vertical and horizontal displacement at joint B; (c) Calculate the force in members 1 and 5; (d) Calculate the reaction forces. NOTE: Joint A is pinned and Joint D is a roller. AE is constant. Use the chart below for selecting near and far nodes and use the provided coordination numbers. u2 2m 5 2 kN 3 Element 2...
t is given that E 29.5 x 10 psi and 3- Consider the four-bar truss shown...
t is given that E 29.5 x 10 psi and 3- Consider the four-bar truss shown in the figure below Ae 1 in2 for all elements (a) Determine the element stiffness matrix for each element. (b) Assemble the global stiffhness matrix for the entire truss. (c) Using the elimination approach, solve for the nodal displacement. (d) Calculate the reaction forces (25 points) 25000 lb 4 4 30 in. 2 20000 lb _40 in.
Using the Stiffness Method procedure identify nodes, elements and degrees of freedom (neglect axial stiffness) for the beam shown below. Form member and structure stiffness matrices and compute displ...
Using the Stiffness Method procedure identify nodes, elements and degrees of freedom (neglect axial stiffness) for the beam shown below. Form member and structure stiffness matrices and compute displacements, reactions and internal forces developed in the beam Note that there is a hinge at B. Take E = 250 GPa, 1-2000 cm 10 kN 2 kN/m 5 kN-m 10 m
Using the Stiffness Method procedure identify nodes, elements and degrees of freedom (neglect axial stiffness) for the beam shown below....
For the truss shown in the figure below, develop element stiffness matrices in the global co-ordinate system. AE 200 [MN] is the same for all members. Use the direct stiffness matrix method to: i. Establish all element stiffness matrices in global coordinates ii.Find the displacements in node 3 ii. Calculate the member stresses 4m 3m 20kN 2 2 Use HELM resources on Moodle to find required determinant and inverse matrix. Answer 9.6x103 [MPa] 0.24mmm u3-0.20mm 0.45mm 16x10-3 MPa σ2-3- 1...
Finite Element Method
5.17 Displacements of the three-member truss shown are confined to the plane of the figure, and points 1, 2 and 3 are fixed to the stationary rim. All members have the same A, E, and L a) Obtain the 2x2 stiffness matrix that operates on the horizontal and vertical degrees of freedom of the central node. b) Obtain the corresponding global force vector c) Solve for the displacements and for axial stress in member (2-4), when the...
Part A AE | AA, A -AA, k= 41 -17 | Ng I - tedy A lady Ez L-ledy - lady X J A Notice the codes associated with the near end (N,N,) and far end (F., Fy) degrees of freedom. Once all the member stiffness matrices are formed the truss stiffness matrix can be constructed. Each element in each member stiffness matrix k is placed in the corresponding row and column designation in the truss stiffness matric K At...
For the 3-D indeterminate (4-member) TRUSS structure shown in Figure 2A. Given that Px 10K (in X-direction); Py none (in Y-direction); E 30,000 ksi; A 0.2 square inches. The nodal coordinates, the earth-quake displacement/settlement, and members' connectivity information are given aS Applied Load! Earth-Quake MEMBER #1 NODE # X node-i node-j 120.00" 160.00"| 80.00"| Px=-10 Kips none Py- none 120.00" 160.00"0.00"none 120.00"0.00" 0.00" none 0.00" 0.00"0.00" none 0.00" 0.00" 80.00" none none 2 none 4 4 none 4 +2.00" (in...
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...
Q2. Statically determinate or indeterminate truss analysis by
the stiffness method. (50 marks)
a) Determine the stiffness matrix of the whole truss given in
problems 14.9 and 14.10 (p. 583). Indicate the degrees-of freedom
in all the stiffness matrices. (18 marks)
b) Calculate all the nodal displacements and all the member forces
for the truss.
(16 marks)
14-9. Determine the stiffness matrix K for the trus Take A 0.0015 m2 and E 200 GPa for each member. 2 12 4...
Problem 2 [Required]: For the truss below (and using the Stiffness Method): (a) Determine the global stiffness matrix; (b) Calculate the vertical and horizontal displacement at joint B; (c) Calculate the force in members 1 and 5; (d) Calculate the reaction forces. NOTE: Joint A is pinned and Joint D is a roller. AE is constant. Use the chart below for selecting near and far nodes and use the provided coordination numbers. u2 2m 5 2 kN 3 Element 2...
t is given that E 29.5 x 10 psi and 3- Consider the four-bar truss shown in the figure below Ae 1 in2 for all elements (a) Determine the element stiffness matrix for each element. (b) Assemble the global stiffhness matrix for the entire truss. (c) Using the elimination approach, solve for the nodal displacement. (d) Calculate the reaction forces (25 points) 25000 lb 4 4 30 in. 2 20000 lb _40 in.
Using the Stiffness Method procedure identify nodes, elements and degrees of freedom (neglect axial stiffness) for the beam shown below. Form member and structure stiffness matrices and compute displacements, reactions and internal forces developed in the beam Note that there is a hinge at B. Take E = 250 GPa, 1-2000 cm 10 kN 2 kN/m 5 kN-m 10 m
Using the Stiffness Method procedure identify nodes, elements and degrees of freedom (neglect axial stiffness) for the beam shown below....
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