Homework Answers
![glotal Now finding the apzing shikness for Link 3. =50x/03A1/m.. cos 0,-0 [32] Ginen kg sind,:l [32] -0:05 (3) Ky104 0.05 0.0](http://img.homeworklib.com/questions/994a8890-55e2-11eb-8468-ddc1038e71d3.png?x-oss-process=image/resize,w_560)
Summary: The global displacement in
x-direction is 3.8543m and in y-direction it is 11.1804m. The
reaction forces of link1 in x-direction =14.575kN and in
y-direction =-10.931kN.Reaction forces of link2 in
x-direction=-24.217kN and in y-direction=0.Reaction forces of link3
in x-direction=0 and in y-direction=-0.559kN.
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Problem 2: The figure below shows a two-member plane truss supported by a linearly elastic spring....
Figure Q5(a) shows a plane truss supported by a horizontal spring at the top node. The...
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...
Plane truss
The lower-right joint of the three-member plane truss shown in Figure 2 is supportedby a skew roller. The truss members are of a solid circular cross section having diameterd D 25 mm and elastic modulus E D 50 GPa. The force P D 70 kN is applied to theunconstrained joint. Number the nodes and elements, and solve for unknown nodaldisplacements and reaction forces using:a) Master-slave method,b) Penalty element method,c) Lagrange multiplier method.
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...
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 truss shown below a vertical load of 25 KN and Horizontal Load of 30 KN...
For truss shown below a vertical load of 25 KN and Horizontal
Load of 30 KN applied at Node 3 ( Use FEM Nodal displacement,
Direct stiffness method)
1). Calculate clearly the member length and distance between
members A = 5 x 10^-4 m^2 and E = 200 GPa
2). Determine the member and global stiffness matrix and show
the calculation fot Sinθ and Cosθ clearly
3). determine the displacement and
member forces
All Load and dimensions are in meter...
2. For the pin-jointed truss shown in Figure Q2.1 applied at node 4. The Young's modulus E(GPa) is the same for...
2. For the pin-jointed truss shown in Figure Q2.1 applied at node 4. The Young's modulus E(GPa) is the same for the three truss vertical downward force P(kN) is a members. The cross sectional area of each of the truss members is indicated below and expressed in terms of a constant A. By using the stiffness method: (a) Compute the reduced stiffness matrix Kg [5 marks [10 marks (b) Calculate the global displacements of node 4 in terms of P,...
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...
The plane truss shown in Figure is composed of members having a square 15 mm ×...
The plane truss shown in Figure is composed of members having a
square 15 mm × 15 mm cross section and modulus of elasticity
E = 69 GPa.
a. Assemble the global stiffness matrix.
b. Compute the nodal displacements in the global coordinate
system for theloads shown.
c. Compute the axial stress in each element
3 kN 3 5 kN 2 1.5 m 4. 1.5 m
Week 8, Question 2: Member AC of the following truss is subjected to a temperature change...
Week 8, Question 2: Member AC of the following truss is subjected to a temperature change of +50 °C. Calculate the displacements of node A and the forces in each member using the stiffness method. Take: a= 2x 10-5; EA= 2x 104 kN; the cross section area of AC as A; the cross section area of AD as AV2; the cross section area of AB as 2.0A. B 1.732 m 1 m D Part 1. The displacements at joint A:...
Week 8, Question 2: Member AC of the following truss is subjected to a temperature change...
Week 8, Question 2: Member AC of the following truss is subjected to a temperature change of +50 °C. Calculate the displacements of node A and the forces in each member using the stiffness method. Take: a= 2x 10-5; EA= 2x 104 kN; the cross section area of AC as A; the cross section area of AD as AV2; the cross section area of AB as 1A. B 1.732 m A 1 m D 1 m Part 1. The displacements...
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...
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...
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 truss shown below a vertical load of 25 KN and Horizontal
Load of 30 KN applied at Node 3 ( Use FEM Nodal displacement,
Direct stiffness method)
1). Calculate clearly the member length and distance between
members A = 5 x 10^-4 m^2 and E = 200 GPa
2). Determine the member and global stiffness matrix and show
the calculation fot Sinθ and Cosθ clearly
3). determine the displacement and
member forces
All Load and dimensions are in meter...
2. For the pin-jointed truss shown in Figure Q2.1 applied at node 4. The Young's modulus E(GPa) is the same for the three truss vertical downward force P(kN) is a members. The cross sectional area of each of the truss members is indicated below and expressed in terms of a constant A. By using the stiffness method: (a) Compute the reduced stiffness matrix Kg [5 marks [10 marks (b) Calculate the global displacements of node 4 in terms of P,...
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...
The plane truss shown in Figure is composed of members having a
square 15 mm × 15 mm cross section and modulus of elasticity
E = 69 GPa.
a. Assemble the global stiffness matrix.
b. Compute the nodal displacements in the global coordinate
system for theloads shown.
c. Compute the axial stress in each element
3 kN 3 5 kN 2 1.5 m 4. 1.5 m
Week 8, Question 2: Member AC of the following truss is subjected to a temperature change of +50 °C. Calculate the displacements of node A and the forces in each member using the stiffness method. Take: a= 2x 10-5; EA= 2x 104 kN; the cross section area of AC as A; the cross section area of AD as AV2; the cross section area of AB as 2.0A. B 1.732 m 1 m D Part 1. The displacements at joint A:...
Week 8, Question 2: Member AC of the following truss is subjected to a temperature change of +50 °C. Calculate the displacements of node A and the forces in each member using the stiffness method. Take: a= 2x 10-5; EA= 2x 104 kN; the cross section area of AC as A; the cross section area of AD as AV2; the cross section area of AB as 1A. B 1.732 m A 1 m D 1 m Part 1. The displacements...
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