For the truss shown in the figure, assemble the stiffness matrix of the structure
For the truss shown in the figure, assemble the stiffness matrix of the structure, and calculate the end displacements of joint 2.
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For the truss shown in the figure, assemble the stiffness matrix of the structure
The plane truss is subjected to a load as shown in Figure 4. Take E = 200 GPa and cross sectional areas of members 1, 2...
The plane truss is subjected to a load as shown in Figure 4. Take E = 200 GPa and cross sectional areas of members 1, 2 and 3 as 150, 250 and 200 mm2 respectively a) Assemble the upper triangular part of the global stiffness matrix for the truss b) Determine the horizontal and vertical displacements at node 4 c) Calculate the forces in each member of the truss. (25 marks) 20 kN 3 60° 4 1.5m 2 2 20m...
Analyze the given truss structure using the stiffness method. Clearly state the steps and (matrix) equations...
Analyze the given truss structure using the stiffness method.
Clearly state the steps and (matrix) equations used in the
problem-solving process.
a) Label the degrees of freedom (both free and restrained DOFs)
of the structure.
b) Determine the stiffness matrix of each element in the local
and global coordinates.
c) Assemble the structure stiffness matrix Kff
considering free DOFs, then write the complete equilibrium
equations Kff Uf = Pf and solve
for the unknown displacement vector Uf.
d) Calculate the...
13. Based on the stiffness method, determine the stiffness matrix K for the truss shown in...
13. Based on the stiffness method, determine the stiffness matrix K for the truss shown in figure. Use the stiffness matrix to calculate the unknown displacement (D1 and D2) at the node where the load 5 kN and 10 kN are applied, and then determine the reactions at the pinned supports (Q3, Q4, Q5 and 26). Note that the degrees of freedom (DOFs) of the truss are indicated in the figure. Take EA as constant. The supports are pinned. 4....
Question 4 The plane truss is subjected to a load as shown in Figure 4. Take E = 200 GPa and cross sectional areas of m...
Question 4 The plane truss is subjected to a load as shown in Figure 4. Take E = 200 GPa and cross sectional areas of members 1, 2 and 3 as 150, 250 and 200 mm2 respectively a) Assemble the upper triangular part of the global stiffness matrix for the truss. b) Determine the horizontal and vertical displacements at node 4. c) Calculate the forces in each member of the truss. (25 marks) 20 kN 3 600 4 3 1.5m...
For the truss shown in the below figure, determine the stifness matrix for each truss element,...
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.
Week 9. Question 1: Use the stiffness method to analyse the structure shown below. For the...
Week 9. Question 1: Use the stiffness method to analyse the structure shown below. For the beam ABC, E = 2 -10% kPa, A -00, = 1.2e - 4 m. For the truss member DB, E = 200000000 kPa, A = 0.002 m. Also, take L54 m and w37 kN/m с 7 Degrees of freedom 22 Calculate the the bending moment at Joint B following the steps below. Part 1: Assemble the global structure stiffness matrix. Note that ABC is...
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...
Week 9, Question 1: Use the stiffness method to analyse the structure shown below. For the...
Week 9, Question 1: Use the stiffness method to analyse the structure shown below. For the beam ABC, E = 2-108 kPa, A=00, I = 1.2e - 4 mº.. For the truss member DB, E = 200000000 kPa, A=0.002 m2. Also, take L=6.9 m and w=30 kN/m. Degrees of freedom l- _-2L Calculate the the bending moment at Joint B following the steps below: Part 1: Assemble the global structure stiffness matrix. Note that ABC is infinitely rigid in the...
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...
Week 9, Question 1: Use the stiffness method to analyse the structure shown below. For the...
Week 9, Question 1: Use the stiffness method to analyse the structure shown below. For the beam ABC, E = 2.108 kPa, A = 0,1 = 1.2e – 4 mº.. For the truss member DB, E = 200000000 kPa, A = 0.002 m². Also, take L = 4.8 m and a = 25 kN/m. 0 2 A B C III 7 L 3 4 Degrees of freedom D L -2L Calculate the the bending moment at Joint B following the...
The plane truss is subjected to a load as shown in Figure 4. Take E = 200 GPa and cross sectional areas of members 1, 2 and 3 as 150, 250 and 200 mm2 respectively a) Assemble the upper triangular part of the global stiffness matrix for the truss b) Determine the horizontal and vertical displacements at node 4 c) Calculate the forces in each member of the truss. (25 marks) 20 kN 3 60° 4 1.5m 2 2 20m...
Analyze the given truss structure using the stiffness method.
Clearly state the steps and (matrix) equations used in the
problem-solving process.
a) Label the degrees of freedom (both free and restrained DOFs)
of the structure.
b) Determine the stiffness matrix of each element in the local
and global coordinates.
c) Assemble the structure stiffness matrix Kff
considering free DOFs, then write the complete equilibrium
equations Kff Uf = Pf and solve
for the unknown displacement vector Uf.
d) Calculate the...
13. Based on the stiffness method, determine the stiffness matrix K for the truss shown in figure. Use the stiffness matrix to calculate the unknown displacement (D1 and D2) at the node where the load 5 kN and 10 kN are applied, and then determine the reactions at the pinned supports (Q3, Q4, Q5 and 26). Note that the degrees of freedom (DOFs) of the truss are indicated in the figure. Take EA as constant. The supports are pinned. 4....
Question 4 The plane truss is subjected to a load as shown in Figure 4. Take E = 200 GPa and cross sectional areas of members 1, 2 and 3 as 150, 250 and 200 mm2 respectively a) Assemble the upper triangular part of the global stiffness matrix for the truss. b) Determine the horizontal and vertical displacements at node 4. c) Calculate the forces in each member of the truss. (25 marks) 20 kN 3 600 4 3 1.5m...
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.
Week 9. Question 1: Use the stiffness method to analyse the structure shown below. For the beam ABC, E = 2 -10% kPa, A -00, = 1.2e - 4 m. For the truss member DB, E = 200000000 kPa, A = 0.002 m. Also, take L54 m and w37 kN/m с 7 Degrees of freedom 22 Calculate the the bending moment at Joint B following the steps below. Part 1: Assemble the global structure stiffness matrix. Note that ABC is...
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...
Week 9, Question 1: Use the stiffness method to analyse the structure shown below. For the beam ABC, E = 2-108 kPa, A=00, I = 1.2e - 4 mº.. For the truss member DB, E = 200000000 kPa, A=0.002 m2. Also, take L=6.9 m and w=30 kN/m. Degrees of freedom l- _-2L Calculate the the bending moment at Joint B following the steps below: Part 1: Assemble the global structure stiffness matrix. Note that ABC is infinitely rigid in the...
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...
Week 9, Question 1: Use the stiffness method to analyse the structure shown below. For the beam ABC, E = 2.108 kPa, A = 0,1 = 1.2e – 4 mº.. For the truss member DB, E = 200000000 kPa, A = 0.002 m². Also, take L = 4.8 m and a = 25 kN/m. 0 2 A B C III 7 L 3 4 Degrees of freedom D L -2L Calculate the the bending moment at Joint B following the...
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