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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...
4. Three spring structure. Node and element are indicated in the Figure. A force, f3-10K, is...
4. Three spring structure. Node and element are indicated in the Figure. A force, f3-10K, is loaded at node #3A11 the spring has same spring constant k. Node #1 is constrained in all directions. (20 pt) k1) k-3) F3 k2) a. Assemble the global stiffness and force matrix. b. Partition the system and solve for the nodal displacements, u2 and U3. C. Calculate the reaction forces at Node #1. 5. A spring system is designed as follows. Node and element...
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...
Solve all problems using the finite element stiffness method. For the rigid frame shown in Figure P5-4, determine (1) the nodal displacements and rotation at node 4, (2) the reactions, and (3) the fo...
Solve all problems using the finite element stiffness method. For the rigid frame shown in Figure P5-4, determine (1) the nodal displacements and rotation at node 4, (2) the reactions, and (3) the forces in each element. Then check equilibrium at node 4 Finally, draw the shear force and bending moment diagrams for each element. Let E 30x 103 ksi, A 8 in2, and I 800 in.4 for all elements. 20 kip 25 ft 25 ft 40 ft Figure P5-4...
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...
Solve the following truss problem. All truss members are ANSI 2x2x0.25 hollow square tubes (with rounded...
Solve the following truss problem. All truss members are ANSI 2x2x0.25 hollow square tubes (with rounded corners) for which the cross-section area is A-1.5891 in2. The material has a modulus of E-29E6 psi. Length of element 1 and 5 is L-20 inches, and length of element 3 and 6 is 2L 40 inches. 7 5 6 P-1000 lb 2. 1. Solve in an Excel spreadsheet using the truss element. Note that there are only four different element stiffness matrices (look...
Mid-Term # 2 for MAE409A, Sec 3, 3/28/2019 Student Name& ID: Instructor: Dr. George Tzong Problem...
Mid-Term # 2 for MAE409A, Sec 3, 3/28/2019 Student Name& ID: Instructor: Dr. George Tzong Problem i (1196): Please use one dimensional finite elem by following Element and Node IDs as defined in the figure. Node 3 is fixed, and Nodes 3 and 4 are 2 units away from rigid walls. (1) Assemble and show the reduced global stiffhess matrix and load vector for the model; and (2) Find the nodal displacements, reaction forces at Node 1, and stress in...
Analyse the beam shown in Figure 4 using the stiffiness method. Node D is fixed and...
Analyse the beam shown in Figure 4 using the stiffiness method. Node D is fixed and node 2 and 3 are rollers. A uniform distributed load of 1 kN/m is acting on member 1 . And a load of 10 kN is acting at the middle of member2. EI is constant for all members a) Identify the force vector of the structure; [4 marks] b) Identify the displacement vector of the structure; [2 marks] c) Determine the stiffness matrices of...
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...
1. Find displacements at each node and forces in each element for the series of spring...
1. Find displacements at each node and forces in each element for the series of spring shown below. (20 points) 3 4 3 100 K k1 k4 u2 k3 из U4 k1 50 k/in k2- 20 k/in k3-40 k/in k4-50 k/in 2. For the following truss structure, all the members has the same elastic modulus E and cross section area A. (10 points) 2 4000 lb 10.000 lb 3 3 4 30 in. 30 in. 30 in Find the structural...
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...
4. Three spring structure. Node and element are indicated in the Figure. A force, f3-10K, is loaded at node #3A11 the spring has same spring constant k. Node #1 is constrained in all directions. (20 pt) k1) k-3) F3 k2) a. Assemble the global stiffness and force matrix. b. Partition the system and solve for the nodal displacements, u2 and U3. C. Calculate the reaction forces at Node #1. 5. A spring system is designed as follows. Node and element...
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...
Solve all problems using the finite element stiffness method. For the rigid frame shown in Figure P5-4, determine (1) the nodal displacements and rotation at node 4, (2) the reactions, and (3) the forces in each element. Then check equilibrium at node 4 Finally, draw the shear force and bending moment diagrams for each element. Let E 30x 103 ksi, A 8 in2, and I 800 in.4 for all elements. 20 kip 25 ft 25 ft 40 ft Figure P5-4...
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...
Solve the following truss problem. All truss members are ANSI 2x2x0.25 hollow square tubes (with rounded corners) for which the cross-section area is A-1.5891 in2. The material has a modulus of E-29E6 psi. Length of element 1 and 5 is L-20 inches, and length of element 3 and 6 is 2L 40 inches. 7 5 6 P-1000 lb 2. 1. Solve in an Excel spreadsheet using the truss element. Note that there are only four different element stiffness matrices (look...
Mid-Term # 2 for MAE409A, Sec 3, 3/28/2019 Student Name& ID: Instructor: Dr. George Tzong Problem i (1196): Please use one dimensional finite elem by following Element and Node IDs as defined in the figure. Node 3 is fixed, and Nodes 3 and 4 are 2 units away from rigid walls. (1) Assemble and show the reduced global stiffhess matrix and load vector for the model; and (2) Find the nodal displacements, reaction forces at Node 1, and stress in...
Analyse the beam shown in Figure 4 using the stiffiness method. Node D is fixed and node 2 and 3 are rollers. A uniform distributed load of 1 kN/m is acting on member 1 . And a load of 10 kN is acting at the middle of member2. EI is constant for all members a) Identify the force vector of the structure; [4 marks] b) Identify the displacement vector of the structure; [2 marks] c) Determine the stiffness matrices of...
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...
1. Find displacements at each node and forces in each element for the series of spring shown below. (20 points) 3 4 3 100 K k1 k4 u2 k3 из U4 k1 50 k/in k2- 20 k/in k3-40 k/in k4-50 k/in 2. For the following truss structure, all the members has the same elastic modulus E and cross section area A. (10 points) 2 4000 lb 10.000 lb 3 3 4 30 in. 30 in. 30 in Find the structural...
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