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A plane structure consists of three truss elements connected to four nodes, as shown below. All t...
Determine the nodal displacements and reaction forces using the finite element direct method for the 1-D bar elements connected as shown below.
Determine the nodal displacements and reaction forces using the finite element direct method for the 1-D bar elements connected as shown below. Do not rename the nodes or elements when solving. Assume that the bars can only undergo translation in x (1 DOF at each node). Nodes 1 and 3 are fixed Element 1 has Young's Modulus of 300 Pa, length of 1 m and cross-sectional area of 1 m2. Element 2 has Young's Modulus of 200 Pa, length of 2...
Problem 1 Analyze the truss structure (statically determinate) shown below. The diameter of the c...
Problem 1 Analyze the truss structure (statically determinate) shown below. The diameter of the circular truss members is 4 cm. The material used has an elastic modulus E-160GPa 1. Calculate the forces in each truss member. 2. Calculate the horizontal and vertical displacements 1 KN of the truss nodes B and C Calculate the margin of safety. Note: Tension members can fail by stress failure and compression members can fail by stress failure or buckling. 3. 1.732 m 2 KN...
Problem 1 Analyze the truss structure (statically determinate) shown below. The diameter of the c...
Problem 1 Analyze the truss structure (statically determinate) shown below. The diameter of the circular truss members is 4 cm. The material used has an elastic modulus E-160GPa 1. Calculate the forces in each truss member. 2. Calculate the horizontal and vertical displacements 1 KN of the truss nodes B and C Calculate the margin of safety. Note: Tension members can fail by stress failure and compression members can fail by stress failure or buckling. 3. 1.732 m 2 KN...
Plane truss
The lower-right joint of the three-member plane truss shown in Figure 2 is supportedby a skew roller. The truss members are of a solid circular cross section having diameterd D 25 mm and elastic modulus E D 50 GPa. The force P D 70 kN is applied to theunconstrained joint. Number the nodes and elements, and solve for unknown nodaldisplacements and reaction forces using:a) Master-slave method,b) Penalty element method,c) Lagrange multiplier method.
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...
Problem 2 (3 points) 1m 1m For the planar truss below, determine the nodal oay displacements in t...
Problem 2 (3 points) 1m 1m For the planar truss below, determine the nodal oay displacements in the Global Coordinate system using the finite element direct method Global y Node 2 Node 1 Global x Element 1Element 2 2m Assume all the truss members are of the same Young's modulus E-65x 109 Nm. Element 1 and element 2 have the same cross-sectional area of 0.01 m and the cross-sectional area of element 3 is 0.02 m2. Do not rename the...
A plane truss element is shown in Figure 4, All elements have cross-sectional area of A = 8 in, a...
A plane truss element is shown in Figure 4, All elements have cross-sectional area of A = 8 in, and elastic modulus of E-2 x 10° psi. Use long-hand solution 6. 6.(a). Solve for the unknown displacements. 6.(b). Solve for strains and stresses in al 3 elements. Show your work and follow the finite element method matrix formulation we have covered in lectures. 4 5 kip 10 240 ft 30 ft30 ft Figure 4.
A plane truss element is shown...
Problem 2: a. For the plane truss shown in Figure 2, determine the nodal displacements, the element forces and stresses, and the support reactions. All elements have E-70 GPa and A-25 cm 100 k...
Problem 2: a. For the plane truss shown in Figure 2, determine the nodal displacements, the element forces and stresses, and the support reactions. All elements have E-70 GPa and A-25 cm 100 kN 50 kN 50 kN 4 4 6 Figure 2. Plane Truss
Problem 2: a. For the plane truss shown in Figure 2, determine the nodal displacements, the element forces and stresses, and the support reactions. All elements have E-70 GPa and A-25 cm 100 kN 50...
A plane truss element is shown in Figure 4. All elements have cross-sectional area of A = 8 in, a...
A plane truss element is shown in Figure 4. All elements have cross-sectional area of A = 8 in, and elastic modulus of E 2 x 10 psi. Use long-hand solution. 6. 6.(a). Solve for the unknown displacements 6.(b). Solve for strains and stresses in all 3 elements. Show your work and follow the finite element method matrix formulation we have covered in lectures 4 3 20 ft 5 kip 10 kip 240 ft ft 30 ft- Figure 4
A...
Problem 3. (3 points). Determine the nodal displacements and reaction forces using the finite element direct...
Problem 3. (3 points). Determine the nodal displacements and reaction forces using the finite element direct method for the 1-D bar elements connected as shown below. Do not rename the nodes or elements when solving. Assume that the bars can only undergo translation in x (1 DOF at each node). Nodes 1 and 3 are fixed. Element 1 has Young's Modulus of 300 Pa, length of 1 m and cross-sectional area of m. Element 2 has Young's Modulus of 200...
Determine the nodal displacements and reaction forces using the finite element direct method for the 1-D bar elements connected as shown below. Do not rename the nodes or elements when solving. Assume that the bars can only undergo translation in x (1 DOF at each node). Nodes 1 and 3 are fixed Element 1 has Young's Modulus of 300 Pa, length of 1 m and cross-sectional area of 1 m2. Element 2 has Young's Modulus of 200 Pa, length of 2...
Problem 1 Analyze the truss structure (statically determinate) shown below. The diameter of the circular truss members is 4 cm. The material used has an elastic modulus E-160GPa 1. Calculate the forces in each truss member. 2. Calculate the horizontal and vertical displacements 1 KN of the truss nodes B and C Calculate the margin of safety. Note: Tension members can fail by stress failure and compression members can fail by stress failure or buckling. 3. 1.732 m 2 KN...
Problem 1 Analyze the truss structure (statically determinate) shown below. The diameter of the circular truss members is 4 cm. The material used has an elastic modulus E-160GPa 1. Calculate the forces in each truss member. 2. Calculate the horizontal and vertical displacements 1 KN of the truss nodes B and C Calculate the margin of safety. Note: Tension members can fail by stress failure and compression members can fail by stress failure or buckling. 3. 1.732 m 2 KN...
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...
Problem 2 (3 points) 1m 1m For the planar truss below, determine the nodal oay displacements in the Global Coordinate system using the finite element direct method Global y Node 2 Node 1 Global x Element 1Element 2 2m Assume all the truss members are of the same Young's modulus E-65x 109 Nm. Element 1 and element 2 have the same cross-sectional area of 0.01 m and the cross-sectional area of element 3 is 0.02 m2. Do not rename the...
A plane truss element is shown in Figure 4, All elements have cross-sectional area of A = 8 in, and elastic modulus of E-2 x 10° psi. Use long-hand solution 6. 6.(a). Solve for the unknown displacements. 6.(b). Solve for strains and stresses in al 3 elements. Show your work and follow the finite element method matrix formulation we have covered in lectures. 4 5 kip 10 240 ft 30 ft30 ft Figure 4.
A plane truss element is shown...
Problem 2: a. For the plane truss shown in Figure 2, determine the nodal displacements, the element forces and stresses, and the support reactions. All elements have E-70 GPa and A-25 cm 100 kN 50 kN 50 kN 4 4 6 Figure 2. Plane Truss
Problem 2: a. For the plane truss shown in Figure 2, determine the nodal displacements, the element forces and stresses, and the support reactions. All elements have E-70 GPa and A-25 cm 100 kN 50...
A plane truss element is shown in Figure 4. All elements have cross-sectional area of A = 8 in, and elastic modulus of E 2 x 10 psi. Use long-hand solution. 6. 6.(a). Solve for the unknown displacements 6.(b). Solve for strains and stresses in all 3 elements. Show your work and follow the finite element method matrix formulation we have covered in lectures 4 3 20 ft 5 kip 10 kip 240 ft ft 30 ft- Figure 4
A...
Problem 3. (3 points). Determine the nodal displacements and reaction forces using the finite element direct method for the 1-D bar elements connected as shown below. Do not rename the nodes or elements when solving. Assume that the bars can only undergo translation in x (1 DOF at each node). Nodes 1 and 3 are fixed. Element 1 has Young's Modulus of 300 Pa, length of 1 m and cross-sectional area of m. Element 2 has Young's Modulus of 200...
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