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Model the bar with three finite elements and determine: a) The global stiffness matrix b)The global...
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...
1) A structural system is consisted of three 1D bar elements (A, B, C). Using the...
1) A structural system is consisted of three 1D bar elements (A, B, C). Using the given geometric and material properties, calculate the displacement at point"b" with finite element approach (40 points). (Note:The width of the bar element is negligible) L2 50 mm L350 mm 100 kN E 70 GPa A = 40 mm2 3 E 70 GPa A = 20 mm2 E 70 GPa A 20 mm
5. For the one-dimensional problem shown below, calculate: a. The global stiffness matrix before the application...
5. For the one-dimensional problem shown below, calculate: a. The global stiffness matrix before the application of boundary conditions. b. The reduced stiffness matrix after the application of boundary conditions. c. Solve for displacements d. Find strains e. Find stresses K1 = 4000 N/mm K2 = 8000 N/mm K3 = 6000 N/mm F = 1200 N L1 = L3 = 50 mm, L2 = 100 mm, A1 = A2 = A3 = 4 mm2 SWASTA 888888888888
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.
X=0 x = 1/2 x= L u U2 Uz (a) Trial solution for a 1-D quadratic...
X=0 x = 1/2 x= L u U2 Uz (a) Trial solution for a 1-D quadratic elastic bar element can be written as follows: ū(x) = [N]{u} where, [N] = [N1 N2 N3] and {u} u2 13 1 and Ni L2 L2 [N] and {u} are known as interpolation function matrix and nodal displacement, respectively. (272 – 3L + L´), N= = (22- La), Ns = 12 (2=– LE) Derive the expression for element stiffness matrix, (Kelem) and element force...
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...
.'ו Optus 11:56 AM Expert Q&A Finite element method QUESTION 4(20 Marks) - concept and calculatio...
finite element method
.'ו Optus 11:56 AM Expert Q&A Finite element method QUESTION 4(20 Marks) - concept and calculation question Consider axial vibration of the circular steel bar shown in Figure 4. The steel bar properties are: p- 7800 kg/m and E-200 GPa. (a)lf the first two natural frequencies are required, sketch the finite element model with clearly labelled element numbers and node numbers, State the element types and the degree of freedoms solved (5 Marks (b)Calculate the stiffiness and...
QUESTION 2 21 Finite elements can appear in many forms such as two-dimensional and three- dimensional domains Give two...
QUESTION 2 21 Finite elements can appear in many forms such as two-dimensional and three- dimensional domains Give two examples and a sketch for each domain. (4) 22 Explain the following terms as used in Finite element equations a Plain stress b Plain strain 23 Use the Finite element method to develop the stiffness matrix for element 2 of the steel cantilever beam structure shown in Figure 2 The elastic modulus IS 200 kN/mm2 with a thickness of 1 unit...
please show all work Arigid bar of negligible weight is supported as shown in the Figure....
please show all work
Arigid bar of negligible weight is supported as shown in the Figure. find the stress in each rod if the temperature rises 30°C after a load W = 120 kN is applied. (hint: for compatibility equation use the ratio and proportional relationship between material and 8t). Bronze L=2.5 m A=1300 mm E=83 GP Steel a=18.9 x10 m/m.°C L=1.25 m A=320 mm2 E=200 GPa a=11.7 x10-6m/m.°C -1.2 m !! -3 m 2 m w
A 3 m rigid bar AB is supported with a vertical translational spring at A and a pin at B The bar is subjected to a linearly varying distributed load with maximum intensity g Calculate the ver...
A 3 m rigid bar AB is supported with a vertical translational spring at A and a pin at B The bar is subjected to a linearly varying distributed load with maximum intensity g Calculate the vertical deformation of the spring if the spring constant is 700 kN/m. (ans: 21.43 mm) 2. A steel cable with a nominal diameter of 25 mm is used in a construction yard to lift a bridge section weighing 38 kN. The cable has an...
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...
1) A structural system is consisted of three 1D bar elements (A, B, C). Using the given geometric and material properties, calculate the displacement at point"b" with finite element approach (40 points). (Note:The width of the bar element is negligible) L2 50 mm L350 mm 100 kN E 70 GPa A = 40 mm2 3 E 70 GPa A = 20 mm2 E 70 GPa A 20 mm
5. For the one-dimensional problem shown below, calculate: a. The global stiffness matrix before the application of boundary conditions. b. The reduced stiffness matrix after the application of boundary conditions. c. Solve for displacements d. Find strains e. Find stresses K1 = 4000 N/mm K2 = 8000 N/mm K3 = 6000 N/mm F = 1200 N L1 = L3 = 50 mm, L2 = 100 mm, A1 = A2 = A3 = 4 mm2 SWASTA 888888888888
X=0 x = 1/2 x= L u U2 Uz (a) Trial solution for a 1-D quadratic elastic bar element can be written as follows: ū(x) = [N]{u} where, [N] = [N1 N2 N3] and {u} u2 13 1 and Ni L2 L2 [N] and {u} are known as interpolation function matrix and nodal displacement, respectively. (272 – 3L + L´), N= = (22- La), Ns = 12 (2=– LE) Derive the expression for element stiffness matrix, (Kelem) and element force...
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...
finite element method
.'ו Optus 11:56 AM Expert Q&A Finite element method QUESTION 4(20 Marks) - concept and calculation question Consider axial vibration of the circular steel bar shown in Figure 4. The steel bar properties are: p- 7800 kg/m and E-200 GPa. (a)lf the first two natural frequencies are required, sketch the finite element model with clearly labelled element numbers and node numbers, State the element types and the degree of freedoms solved (5 Marks (b)Calculate the stiffiness and...
QUESTION 2 21 Finite elements can appear in many forms such as two-dimensional and three- dimensional domains Give two examples and a sketch for each domain. (4) 22 Explain the following terms as used in Finite element equations a Plain stress b Plain strain 23 Use the Finite element method to develop the stiffness matrix for element 2 of the steel cantilever beam structure shown in Figure 2 The elastic modulus IS 200 kN/mm2 with a thickness of 1 unit...
please show all work
Arigid bar of negligible weight is supported as shown in the Figure. find the stress in each rod if the temperature rises 30°C after a load W = 120 kN is applied. (hint: for compatibility equation use the ratio and proportional relationship between material and 8t). Bronze L=2.5 m A=1300 mm E=83 GP Steel a=18.9 x10 m/m.°C L=1.25 m A=320 mm2 E=200 GPa a=11.7 x10-6m/m.°C -1.2 m !! -3 m 2 m w
A 3 m rigid bar AB is supported with a vertical translational spring at A and a pin at B The bar is subjected to a linearly varying distributed load with maximum intensity g Calculate the vertical deformation of the spring if the spring constant is 700 kN/m. (ans: 21.43 mm) 2. A steel cable with a nominal diameter of 25 mm is used in a construction yard to lift a bridge section weighing 38 kN. The cable has an...
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