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A two-member beam structure is given in the figure. The load, P, is set to be...
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,...
two-member truss is subjected to a load P 8000 N. Me mber 1-2 is 400 mm...
two-member truss is subjected to a load P 8000 N. Me mber 1-2 is 400 mm long. 4.12. A ember 1-3 was manufactured to be 505 mm long instead of 500 mm. However, it was forced into place. Determine stresses in the members assuming that member 1-3 was manufactured to its correct (a) the length of 500 mm load P, of course). pression in the text.) Take cross-sectional areas 750 mm2, E 200 GPa (b) thestresses in the members as...
Problem 2: The figure below shows a two-member plane truss supported by a linearly elastic spring....
Problem 2: The figure below shows a two-member plane truss supported by a linearly elastic spring. The truss members are of a solid circular cross section having diameter, d = 20mm, and E = 80 GPa. The linear spring has a stiffness constant of 50 N/mm. A load of 15 kN is applied at 3 at an angle of 50 degrees with the horizontal. Find (a) The global displacements of the unconstrained node and (b) compute the reaction forces and...
Problem 2 (20 pts): Consider the following structure consisting of a set of bars. Assume the...
Problem 2 (20 pts): Consider the following structure consisting of a set of bars. Assume the Young's modulus and cross- sectional area of each bar are E = 200 kN/mm², A = 100 mm2. (a) Find the (complete) stiffness matrix of the structure (10 pts) (b) find the displacements of all the three nodes (5 pts) (c) find the reaction force at node B (5 pts) ܠܓܓܓܓܓܓܓ 2000 mm 45°A 10 kN + 20 kn
Figure 3b() shows a step beam with different moment of inertia in member 1 and 2. Assemble the structure stiffnes...
Figure 3b() shows a step beam with different moment of inertia in member 1 and 2. Assemble the structure stiffness matrix, Ke. Then, calculate the reactions at both supports by using matrik stifness method. Assuming the elastic modulus of beam, E 200 GPa. 150 kN 3 5m 2 10 m 1 = 500 x 106 mm4 I = 250 x 106 mm 4 Rajah 3b(@)/Figure 3b() Given: Stiffness relations for a beam element 12 6 12 6 z12 12 6...
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...
OUESTION 2 The solid cylindrical member in Figure 3 is under a point load of P...
OUESTION 2 The solid cylindrical member in Figure 3 is under a point load of P at point C. If the beam has a radius ofr 50 mm, length L = 4 m, and load P 5 kN and E= 200 GPa (a) Draw the free body, shear force, bending moment and torque diagrams for both sections of the member (4 Marks) (b) What is the maximum bending stress induced in the member? (3 Marks) (c) What is the maximum...
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...
Figure 2.11 Two-bar truss. -14 3 0 3-1 [A]=1 4 2.21 The potential energy of the...
Figure 2.11 Two-bar truss. -14 3 0 3-1 [A]=1 4 2.21 The potential energy of the two-bar truss shown in Fig. 2.11 is given by s (2s where E is Young's modulus, A the cross-sectional area of each member, I the span or the tru s the length of each member, h the height of the truss the applied load, θ the angle at which the load is applied, and x and x are, respectively, the horizontal and vertical displacements...
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...
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,...
two-member truss is subjected to a load P 8000 N. Me mber 1-2 is 400 mm long. 4.12. A ember 1-3 was manufactured to be 505 mm long instead of 500 mm. However, it was forced into place. Determine stresses in the members assuming that member 1-3 was manufactured to its correct (a) the length of 500 mm load P, of course). pression in the text.) Take cross-sectional areas 750 mm2, E 200 GPa (b) thestresses in the members as...
Problem 2: The figure below shows a two-member plane truss supported by a linearly elastic spring. The truss members are of a solid circular cross section having diameter, d = 20mm, and E = 80 GPa. The linear spring has a stiffness constant of 50 N/mm. A load of 15 kN is applied at 3 at an angle of 50 degrees with the horizontal. Find (a) The global displacements of the unconstrained node and (b) compute the reaction forces and...
Problem 2 (20 pts): Consider the following structure consisting of a set of bars. Assume the Young's modulus and cross- sectional area of each bar are E = 200 kN/mm², A = 100 mm2. (a) Find the (complete) stiffness matrix of the structure (10 pts) (b) find the displacements of all the three nodes (5 pts) (c) find the reaction force at node B (5 pts) ܠܓܓܓܓܓܓܓ 2000 mm 45°A 10 kN + 20 kn
Figure 3b() shows a step beam with different moment of inertia in member 1 and 2. Assemble the structure stiffness matrix, Ke. Then, calculate the reactions at both supports by using matrik stifness method. Assuming the elastic modulus of beam, E 200 GPa. 150 kN 3 5m 2 10 m 1 = 500 x 106 mm4 I = 250 x 106 mm 4 Rajah 3b(@)/Figure 3b() Given: Stiffness relations for a beam element 12 6 12 6 z12 12 6...
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...
OUESTION 2 The solid cylindrical member in Figure 3 is under a point load of P at point C. If the beam has a radius ofr 50 mm, length L = 4 m, and load P 5 kN and E= 200 GPa (a) Draw the free body, shear force, bending moment and torque diagrams for both sections of the member (4 Marks) (b) What is the maximum bending stress induced in the member? (3 Marks) (c) What is the maximum...
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...
Figure 2.11 Two-bar truss. -14 3 0 3-1 [A]=1 4 2.21 The potential energy of the two-bar truss shown in Fig. 2.11 is given by s (2s where E is Young's modulus, A the cross-sectional area of each member, I the span or the tru s the length of each member, h the height of the truss the applied load, θ the angle at which the load is applied, and x and x are, respectively, the horizontal and vertical displacements...
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...
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