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Problem 2: Consider the three-spring structure given below. It is...
Three rigid bodies (Nodes 2, 3, and 4) are connected by five springs as shown below....
Three rigid bodies (Nodes 2, 3, and 4) are connected by five
springs as shown below. Assume that the
bodies can only undergo translation in the horizontal direction.
Horizontal force P2=1000 N and
P4=1500 N is applied to Elements 2 and 4, respectively. The spring
constants in (N/mm) are given as:
k1=400, k2=500, k3=600, k4=100, and k5=300. Nodes 1 and 5 are
fixed. Determine the nodal
displacements and reaction forces at the walls.
Problem 1. (3 points) Three rigid bodies...
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.
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...
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...
I need some help with this spring assemblage question. In the image below the nodes are...
I need some help with this spring assemblage question. In the
image below the nodes are actually reorganized in the question in
the order of 1-5-4-3-2. Now Knowing that I have to a) write the
global stiffness matrix for it b) if nodes 1 and 2 are fixed and a
force P is at node 4 what is the nodal displacement, c) I need to
find the reactions at 1 and 5 and finally d) I need to find the...
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...
Three springs are connected according to the figure below, also showing the applied external forc...
Three springs are connected according to the figure below, also showing the applied external force P. The spring constants are: k5k, k2 k and k3 2k. 4a 2 2 3a rigid beam Determine 1.1 the system stiffness equation with boundary conditions 1.2 the nodes displacement field 1.3 the nodal forces field (12)
Three springs are connected according to the figure below, also showing the applied external force P. The spring constants are: k5k, k2 k and k3 2k. 4a 2...
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...
3. Consider the spring - mass system shown below, consisting of two masses mi and ma sus- pended ...
3. Consider the spring - mass system shown below, consisting of two masses mi and ma sus- pended from springs with spring constants ki and k, respectively. Assume that there is no damping in the system. a) Show that the displacements z1 and 2 of the masses from their respective equilibrium positions satisfy the differential equations b) Use the above resuit to show that the spring-mass system satisfies the following fourth order differential equation. and ) Find the general solution...
Please show work Answer shown below Problem 8: Consider the statically indeterminate beam shown below with...
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Answer shown below
Problem 8: Consider the statically indeterminate beam shown below with the given loading. E and I are constant. a) Find the rotation at node 2 using the stiffness method. b) Find the unknown reactions using equilibrium and the force-displacement relationships. Draw final free body diagrams of the two beam elements and node 2, showing all forces with the correct values and directions. c) 2.5 k/ft 30 ft 20 ft Problem : θ2=562.5k-ft2 rad a)...
Three rigid bodies (Nodes 2, 3, and 4) are connected by five
springs as shown below. Assume that the
bodies can only undergo translation in the horizontal direction.
Horizontal force P2=1000 N and
P4=1500 N is applied to Elements 2 and 4, respectively. The spring
constants in (N/mm) are given as:
k1=400, k2=500, k3=600, k4=100, and k5=300. Nodes 1 and 5 are
fixed. Determine the nodal
displacements and reaction forces at the walls.
Problem 1. (3 points) Three rigid bodies...
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...
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...
I need some help with this spring assemblage question. In the
image below the nodes are actually reorganized in the question in
the order of 1-5-4-3-2. Now Knowing that I have to a) write the
global stiffness matrix for it b) if nodes 1 and 2 are fixed and a
force P is at node 4 what is the nodal displacement, c) I need to
find the reactions at 1 and 5 and finally d) I need to find the...
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...
Three springs are connected according to the figure below, also showing the applied external force P. The spring constants are: k5k, k2 k and k3 2k. 4a 2 2 3a rigid beam Determine 1.1 the system stiffness equation with boundary conditions 1.2 the nodes displacement field 1.3 the nodal forces field (12)
Three springs are connected according to the figure below, also showing the applied external force P. The spring constants are: k5k, k2 k and k3 2k. 4a 2...
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...
3. Consider the spring - mass system shown below, consisting of two masses mi and ma sus- pended from springs with spring constants ki and k, respectively. Assume that there is no damping in the system. a) Show that the displacements z1 and 2 of the masses from their respective equilibrium positions satisfy the differential equations b) Use the above resuit to show that the spring-mass system satisfies the following fourth order differential equation. and ) Find the general solution...
Please show work
Answer shown below
Problem 8: Consider the statically indeterminate beam shown below with the given loading. E and I are constant. a) Find the rotation at node 2 using the stiffness method. b) Find the unknown reactions using equilibrium and the force-displacement relationships. Draw final free body diagrams of the two beam elements and node 2, showing all forces with the correct values and directions. c) 2.5 k/ft 30 ft 20 ft Problem : θ2=562.5k-ft2 rad a)...
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