Compute the stiffness matrices of elements 1 and 2 of the two-triangle element model of the rectangular plate in plane stress shown below.
: Compute the stiffness matrices of elements 1 and 2 of the two-triangle element model of the rectangular plate in plane stress shown below. Then use them to compute the global stiffness matrix of the rectangular plate. Where b = 40 in., h = 20 in., thickness = 1 in., Poisson's ration=0.3, and E = 30 x 10 psi. 4 3 0 h 2 b
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Compute the stiffness matrices of elements 1 and 2 of the two-triangle element model of the rectangular plate in plane stress shown below.
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. (60%) For the truss system shown below (a) (12%) Determine the element stiffness matrix w.r.t....
1. (60%) For the truss system shown below (a) (12%) Determine the element stiffness matrix w.r.t. the global coordinate system for all elements. (b) (10%) Determine the global stiffness matrix, [K]. (c) (5%) List all the boundary conditions. (d) (33%) Determine the internal force, elongation, stress, and strain for each element. Indicate whether it is under tension or compression. My LLLLLLLL 1 0 1-2=45° \ 30° 30° / 14116 141 16 12 2-3 = 30 3 1-4=300 Join But 45=225...
For the truss shown in the figure below, develop element stiffness matrices in the global co-ordinate system. AE 200 [M...
For the truss shown in the figure below, develop element stiffness matrices in the global co-ordinate system. AE 200 [MN] is the same for all members. Use the direct stiffness matrix method to: i. Establish all element stiffness matrices in global coordinates ii.Find the displacements in node 3 ii. Calculate the member stresses 4m 3m 20kN 2 2 Use HELM resources on Moodle to find required determinant and inverse matrix. Answer 9.6x103 [MPa] 0.24mmm u3-0.20mm 0.45mm 16x10-3 MPa σ2-3- 1...
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...
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...
Problem No-3: The coordinates are shown in units of inches. Assume plane stress conditions. Let E...
Problem No-3: The coordinates are shown in units of inches. Assume plane stress conditions. Let E 45x1 displacements have been determined to be u 1-0, v1 0.0025 in., u2 = 0.0012 in, v2 0.0001 in, u3 0, and v3 0.0025 in. Determine: (a) the stiffness matrix for the element shown [k] (b) the element stresses: ??, dy, and ? y and the principal stresses 06 psi, v = 0.25, and thickness t 1 in. The element nodal (15p) (20p) (0....
Using the Stiffness Method procedure identify nodes, elements and degrees of freedom (neglect axial stiffness) for the beam shown below. Form member and structure stiffness matrices and compute displ...
Using the Stiffness Method procedure identify nodes, elements and degrees of freedom (neglect axial stiffness) for the beam shown below. Form member and structure stiffness matrices and compute displacements, reactions and internal forces developed in the beam Note that there is a hinge at B. Take E = 250 GPa, 1-2000 cm 10 kN 2 kN/m 5 kN-m 10 m
Using the Stiffness Method procedure identify nodes, elements and degrees of freedom (neglect axial stiffness) for the beam shown below....
Using the Stiffness Method procedure identify nodes, elements and degrees of freedom (neglect axial stiffness) for the beam shown below. Form member and structure stiffness matrices and compute di...
Using the Stiffness Method procedure identify nodes, elements and degrees of freedom (neglect axial stiffness) for the beam shown below. Form member and structure stiffness matrices and compute displacements, reactions and internal forces developed in the beam. Note that there is a hinge at B. Take E= 250 G Pa, 1 = 2000 cm- 10 kN 5 kN-m 2 kN/m 10 m
Using the Stiffness Method procedure identify nodes, elements and degrees of freedom (neglect axial stiffness) for the beam...
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...
The rectangular steel plate below measures 1 m x 0.5 m x 10 mm. Assume that...
The rectangular steel plate below measures 1 m x 0.5 m x 10 mm. Assume that the 1 m dimension is in the x-direction and the 0.5 m dimension is in the y-direction. The plate is made of a material with an elastic modulus of 200 GPa and Poisson's Ratio of 0.3. Suppose a uniform normal stress, Ox, of 125 MPa is applied in the x-direction a) Calculate the stress, ay, required to produce a transverse strain Ey 0 (in...
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. (60%) For the truss system shown below (a) (12%) Determine the element stiffness matrix w.r.t. the global coordinate system for all elements. (b) (10%) Determine the global stiffness matrix, [K]. (c) (5%) List all the boundary conditions. (d) (33%) Determine the internal force, elongation, stress, and strain for each element. Indicate whether it is under tension or compression. My LLLLLLLL 1 0 1-2=45° \ 30° 30° / 14116 141 16 12 2-3 = 30 3 1-4=300 Join But 45=225...
For the truss shown in the figure below, develop element stiffness matrices in the global co-ordinate system. AE 200 [MN] is the same for all members. Use the direct stiffness matrix method to: i. Establish all element stiffness matrices in global coordinates ii.Find the displacements in node 3 ii. Calculate the member stresses 4m 3m 20kN 2 2 Use HELM resources on Moodle to find required determinant and inverse matrix. Answer 9.6x103 [MPa] 0.24mmm u3-0.20mm 0.45mm 16x10-3 MPa σ2-3- 1...
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...
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...
Problem No-3: The coordinates are shown in units of inches. Assume plane stress conditions. Let E 45x1 displacements have been determined to be u 1-0, v1 0.0025 in., u2 = 0.0012 in, v2 0.0001 in, u3 0, and v3 0.0025 in. Determine: (a) the stiffness matrix for the element shown [k] (b) the element stresses: ??, dy, and ? y and the principal stresses 06 psi, v = 0.25, and thickness t 1 in. The element nodal (15p) (20p) (0....
Using the Stiffness Method procedure identify nodes, elements and degrees of freedom (neglect axial stiffness) for the beam shown below. Form member and structure stiffness matrices and compute displacements, reactions and internal forces developed in the beam Note that there is a hinge at B. Take E = 250 GPa, 1-2000 cm 10 kN 2 kN/m 5 kN-m 10 m
Using the Stiffness Method procedure identify nodes, elements and degrees of freedom (neglect axial stiffness) for the beam shown below....
Using the Stiffness Method procedure identify nodes, elements and degrees of freedom (neglect axial stiffness) for the beam shown below. Form member and structure stiffness matrices and compute displacements, reactions and internal forces developed in the beam. Note that there is a hinge at B. Take E= 250 G Pa, 1 = 2000 cm- 10 kN 5 kN-m 2 kN/m 10 m
Using the Stiffness Method procedure identify nodes, elements and degrees of freedom (neglect axial stiffness) for the beam...
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...
The rectangular steel plate below measures 1 m x 0.5 m x 10 mm. Assume that the 1 m dimension is in the x-direction and the 0.5 m dimension is in the y-direction. The plate is made of a material with an elastic modulus of 200 GPa and Poisson's Ratio of 0.3. Suppose a uniform normal stress, Ox, of 125 MPa is applied in the x-direction a) Calculate the stress, ay, required to produce a transverse strain Ey 0 (in...
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