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For the plane bar trusses shown in Figure 2. All bar elements have E= 210GPa and A-4.0 x 10-4 m2....
A plane structure consists of three truss elements connected to four nodes, as shown below. All t...
A plane structure consists of three truss elements connected to four nodes, as shown below. All trusses have cross sectional area A -7.104 m2 and elastic modulus E = 210 GPa. The length of each truss element is L = 1 m. A point force, P -5 kN, is acting on node 4 L/2 3.1 Calculate the displacements at the nodes 3.2 Calculate the reaction forces 3.3 Calculate the stress in each bar
A plane structure consists of three truss...
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...
i need help with c and d but explain why Question 1 (10 marks). Assembly A model consists of two 1D trusses with dimens...
i need help with c and d but explain why
Question 1 (10 marks). Assembly A model consists of two 1D trusses with dimensions as given in Figure 1. Element 1 runs angle, connecting parallel to the x-axis, connecting node 1 and 2. Element 2 is running at an node 1 and 3. Node 1 has an applied force in the negative y-direction. Node 1 can only in y-direction, while nodes 2 and 3 are fixed in both x and...
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...
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...
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...
Element 1 is a steel bar that has a circular cross-section with a radius of 30...
Element 1 is a steel bar that has a circular cross-section with a radius of 30 mm. Element 2 is an aluminum bar that has a circular cross-section with a radius of 50 mm. Element 3 is a steel bar that has a circular cross- section with a radius of 60 mm. Assume for steel, the moduļus, E, is 2.0E11 Pa, and the density, p, is 7800 kg/m3. Assume for aluminum, E-7.0E10 Pa, and p-2700 kg/m3. The rigid, massless rod...
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.
Consider the frame in Fig. 1, the node and element numbers as well as the material and geometrica...
Consider the frame in Fig. 1, the node and element numbers as well as the material and geometrical characteristics of the beam elements are also displayed on the same figure. The frame is subjected to two concentrated loads at nodes 2 and 3 and a uniform distributed load over beam 3. The frame is fixed at nodes 1 and 5. A global coordinate system is established with origin at node 1 and x-y axes positively directed to the right and...
A plane structure consists of three truss elements connected to four nodes, as shown below. All trusses have cross sectional area A -7.104 m2 and elastic modulus E = 210 GPa. The length of each truss element is L = 1 m. A point force, P -5 kN, is acting on node 4 L/2 3.1 Calculate the displacements at the nodes 3.2 Calculate the reaction forces 3.3 Calculate the stress in each bar
A plane structure consists of three truss...
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...
i need help with c and d but explain why
Question 1 (10 marks). Assembly A model consists of two 1D trusses with dimensions as given in Figure 1. Element 1 runs angle, connecting parallel to the x-axis, connecting node 1 and 2. Element 2 is running at an node 1 and 3. Node 1 has an applied force in the negative y-direction. Node 1 can only in y-direction, while nodes 2 and 3 are fixed in both x and...
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...
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...
Element 1 is a steel bar that has a circular cross-section with a radius of 30 mm. Element 2 is an aluminum bar that has a circular cross-section with a radius of 50 mm. Element 3 is a steel bar that has a circular cross- section with a radius of 60 mm. Assume for steel, the moduļus, E, is 2.0E11 Pa, and the density, p, is 7800 kg/m3. Assume for aluminum, E-7.0E10 Pa, and p-2700 kg/m3. The rigid, massless rod...
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.
Consider the frame in Fig. 1, the node and element numbers as well as the material and geometrical characteristics of the beam elements are also displayed on the same figure. The frame is subjected to two concentrated loads at nodes 2 and 3 and a uniform distributed load over beam 3. The frame is fixed at nodes 1 and 5. A global coordinate system is established with origin at node 1 and x-y axes positively directed to the right and...
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