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Problem 2 135 pts The grid shown in figure 2 is rigidly fixed at nodes 2...
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,...
For the plane bar trusses shown in Figure 2. All bar elements have E= 210GPa and A-4.0 x 10-4 m2....
For the plane bar trusses shown in Figure 2. All bar elements have E= 210GPa and A-4.0 x 10-4 m2. Note: 1GPa=UPKN/m? 3 m 45° IO KN 3 m 20 kN FIG. 3: Plane trusses Determine: element 1 stiffness matrix element 2 stiffness matrix, element 3 stiffness matrix global stiffness matrix [K], global balance equation, boundary conditions, the horizontal displacement of node1 the vertical displacement of node 1 the horizontal reaction force at node 3, the vertical reaction force at...
A system shown in Figure Q2 has a cross-sectional area, A- 15cm and is made of...
A system shown in Figure Q2 has a cross-sectional area, A- 15cm and is made of aluminum alloy (E= 70.0x 10 N/mm). Assume each node of the system can only move in a horizontal direction and assume the right direction as positive. The general equation of an element is: . Use the direct method to complete the following: -kk 5 kN 15 kN 3 m 3 m Figure Q2 Draw the schematic diagram of the system. Mark the indices of...
Grid 4 Grid 3 Po 15 in Grid 1 Grid 2 10 in Figure 1: Problem...
Grid 4 Grid 3 Po 15 in Grid 1 Grid 2 10 in Figure 1: Problem 1 Schematic Problem 1 The truss (all joints are pinned) structure in figure 1 is made of members with cross sectional area A- 1 in2, with a linear elastic, homogeneous, isotropic material with an elastic modulus, E, 10E6 psi and a coefficient of thermal expansion. α-6E-6 op-1. The structure starts out at a uniform temperature of 65°F and is raised to a final temperature...
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.
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 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...
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...
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...
Using the stiffness method, Calculate the stiffness matrix of the frame and show all displacements and reactions at node #2. Assume that all joints are fixed. Calculate the all bending moments and sho...
Using the stiffness method, Calculate the stiffness matrix of
the frame and show all displacements and reactions at node #2.
Assume that all joints are fixed.
Calculate the all bending moments and show in a diagram.
E=200GPa, I=300(106) & A=10(103)
24 kN/m 4m 8m 20 kN 4m
24 kN/m 4m 8m 20 kN 4m
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...
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,...
For the plane bar trusses shown in Figure 2. All bar elements have E= 210GPa and A-4.0 x 10-4 m2. Note: 1GPa=UPKN/m? 3 m 45° IO KN 3 m 20 kN FIG. 3: Plane trusses Determine: element 1 stiffness matrix element 2 stiffness matrix, element 3 stiffness matrix global stiffness matrix [K], global balance equation, boundary conditions, the horizontal displacement of node1 the vertical displacement of node 1 the horizontal reaction force at node 3, the vertical reaction force at...
A system shown in Figure Q2 has a cross-sectional area, A- 15cm and is made of aluminum alloy (E= 70.0x 10 N/mm). Assume each node of the system can only move in a horizontal direction and assume the right direction as positive. The general equation of an element is: . Use the direct method to complete the following: -kk 5 kN 15 kN 3 m 3 m Figure Q2 Draw the schematic diagram of the system. Mark the indices of...
Grid 4 Grid 3 Po 15 in Grid 1 Grid 2 10 in Figure 1: Problem 1 Schematic Problem 1 The truss (all joints are pinned) structure in figure 1 is made of members with cross sectional area A- 1 in2, with a linear elastic, homogeneous, isotropic material with an elastic modulus, E, 10E6 psi and a coefficient of thermal expansion. α-6E-6 op-1. The structure starts out at a uniform temperature of 65°F and is raised to a final temperature...
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...
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...
Using the stiffness method, Calculate the stiffness matrix of
the frame and show all displacements and reactions at node #2.
Assume that all joints are fixed.
Calculate the all bending moments and show in a diagram.
E=200GPa, I=300(106) & A=10(103)
24 kN/m 4m 8m 20 kN 4m
24 kN/m 4m 8m 20 kN 4m
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...
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