![Problem (1) Use the principle of minimum potential energy to develop the stiffness matrix [K] of the spring assemblage shown in the figure below. Also, construct the structure stiffhess relationship. showing all boundary condition values. Show all steps of your solution in details k 200 kN/m k 200 kN/m k 200 kN/m 5 kN 20 kN 2 ONLY USE PRINCIPLE OF MINIMUM POTENTIAL ENERGY TO SOLVE! il p 111 ?](http://img.homeworklib.com/questions/40157790-d24d-11ea-a71f-cf03ee9c6d80.png?x-oss-process=image/resize,w_560)
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Problem (1) Use the principle of minimum potential energy to develop the stiffness matrix [K] of...
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.
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...
A spring has a spring stiffness constant k of 80.0 N/m . How much must this spring be compressed to store 50.0 J of potential energy?
A spring has a spring stiffness constant k of 80.0 N/m . How much must this spring be compressed to store 50.0 J of potential energy?x= (?)m
Week 7. Question 1: Use the stiffness method to determine the horizontal and vertical displacements at...
Week 7. Question 1: Use the stiffness method to determine the horizontal and vertical displacements at joint A. For all members, E-206.8 GPa and A - 1290 mm? Take a - 8 mandb-6.1 m B 2 انها 160 kN Solve the problem by following these steps Part 1) Calculate the stiffness matrix of each member in the global coordinate system. Check kna (the value at the second column and second row) in each member stiffness matrix a) Member 1: ky...
16-5. Determine the structure stiffness matrix K for the 200 GPa, are fixed. Take E and frame. Assume 1-300 105) mm,A 1...
16-5. Determine the structure stiffness matrix K for the 200 GPa, are fixed. Take E and frame. Assume 1-300 105) mm,A 10(10) mm2 for each member. 16-6. Determine the support reactions at the fixed supports D and . Take E-200 GPa,1 300 (10) mm, A 10(10) mm2 for each member. 12 kN/m 2 m 4 m 12 2 m Probs. 16-5/6
16-5. Determine the structure stiffness matrix K for the 200 GPa, are fixed. Take E and frame. Assume 1-300...
Week 9. Question 1: Use the stiffness method to analyse the structure shown below. For the...
Week 9. Question 1: Use the stiffness method to analyse the structure shown below. For the beam ABC, E = 2 -10% kPa, A -00, = 1.2e - 4 m. For the truss member DB, E = 200000000 kPa, A = 0.002 m. Also, take L54 m and w37 kN/m с 7 Degrees of freedom 22 Calculate the the bending moment at Joint B following the steps below. Part 1: Assemble the global structure stiffness matrix. Note that ABC is...
Advanced structures questions: Please provide short answers to the following questions: 1) Why do we use...
Advanced structures questions: Please provide short answers to the following questions: 1) Why do we use the PMPE (principle of minimum potential energy) versus the exact differential equation to derive the element stiffness equations? 2) What response modes are represented by a plate element? What are the response modes represented by a shell element? 3) What is the connectivity matrix? Why is it used in finite element software? Construct the connectivity matrix for a given structure. 3) What is the...
k Problem 2 (30 pts) Blocks A and B are released from rest when the spring...
k Problem 2 (30 pts) Blocks A and B are released from rest when the spring is unstretched. Block A has a mass my=3kg, and the linear spring has stiffness k=8N/m. If all sources of friction are negligible, determine the mass of block B such that it has a speed vp=1.5m/s after moving 1.2m downward, assuming that A never leaves the horizontal surface shown and the cord connecting A and B is inextensible. Use the work-energy principle. A B
Now let’s use the concept of elastic potential energy to solve a problem involving a spring....
Now let’s use the concept of elastic potential energy to solve a problem involving a spring. A glider with mass m=0.200kg sits on a frictionless horizontal air track, connected to a spring of negligible mass with force constant k=5.00N/m. You pull on the glider, stretching the spring 0.100 m, and then release it with no initial velocity. The glider begins to move back toward its equilibrium position (x=0). What is its speed when x=0.0800m? Part a: What is the value...
a) Develop a finite difference equation, based on an energy balance for a node on the upper-left corner of a domain, as in the figure below: Too, h Ti Ay k,q Ax Note that both the top and left surfac...
a) Develop a finite difference equation, based on an energy balance for a node on the upper-left corner of a domain, as in the figure below: Too, h Ti Ay k,q Ax Note that both the top and left surfaces are exposed to an ambient temperature of Too and require a convection boundary condition, and that there is constant heat generation per volume (q) throughout the domain. The control volume surrounding the node, on which the energy balance should be...
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...
Week 7. Question 1: Use the stiffness method to determine the horizontal and vertical displacements at joint A. For all members, E-206.8 GPa and A - 1290 mm? Take a - 8 mandb-6.1 m B 2 انها 160 kN Solve the problem by following these steps Part 1) Calculate the stiffness matrix of each member in the global coordinate system. Check kna (the value at the second column and second row) in each member stiffness matrix a) Member 1: ky...
16-5. Determine the structure stiffness matrix K for the 200 GPa, are fixed. Take E and frame. Assume 1-300 105) mm,A 10(10) mm2 for each member. 16-6. Determine the support reactions at the fixed supports D and . Take E-200 GPa,1 300 (10) mm, A 10(10) mm2 for each member. 12 kN/m 2 m 4 m 12 2 m Probs. 16-5/6
16-5. Determine the structure stiffness matrix K for the 200 GPa, are fixed. Take E and frame. Assume 1-300...
Week 9. Question 1: Use the stiffness method to analyse the structure shown below. For the beam ABC, E = 2 -10% kPa, A -00, = 1.2e - 4 m. For the truss member DB, E = 200000000 kPa, A = 0.002 m. Also, take L54 m and w37 kN/m с 7 Degrees of freedom 22 Calculate the the bending moment at Joint B following the steps below. Part 1: Assemble the global structure stiffness matrix. Note that ABC is...
k Problem 2 (30 pts) Blocks A and B are released from rest when the spring is unstretched. Block A has a mass my=3kg, and the linear spring has stiffness k=8N/m. If all sources of friction are negligible, determine the mass of block B such that it has a speed vp=1.5m/s after moving 1.2m downward, assuming that A never leaves the horizontal surface shown and the cord connecting A and B is inextensible. Use the work-energy principle. A B
a) Develop a finite difference equation, based on an energy balance for a node on the upper-left corner of a domain, as in the figure below: Too, h Ti Ay k,q Ax Note that both the top and left surfaces are exposed to an ambient temperature of Too and require a convection boundary condition, and that there is constant heat generation per volume (q) throughout the domain. The control volume surrounding the node, on which the energy balance should be...
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