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1. The plane truss shown in Figure P3.10 is subjected to a downward vertical load at...
Consider the truss subjected to a single point load P = 12 kN downward at point...
Consider the truss subjected to a single point load P = 12 kN
downward at point C (Figure 1). The members of the truss all have E
= 200 GPa and cross-sectional area 25 cm2.
<ME316 HW9 - Energy Methods Conservation of Energy View Available Hint(s) Learning Goal: To use conservation of energy to calculate the displacement of a point in a truss When a structure is subjected to a single point load and deforms in a linear- elastic fashion,...
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...
The plane truss is subjected to a load as shown in Figure 4. Take E = 200 GPa and cross sectional areas of members 1, 2...
The plane truss is subjected to a load as shown in Figure 4. Take E = 200 GPa and cross sectional areas of members 1, 2 and 3 as 150, 250 and 200 mm2 respectively a) Assemble the upper triangular part of the global stiffness matrix for the truss b) Determine the horizontal and vertical displacements at node 4 c) Calculate the forces in each member of the truss. (25 marks) 20 kN 3 60° 4 1.5m 2 2 20m...
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...
Question 4 The plane truss is subjected to a load as shown in Figure 4. Take E = 200 GPa and cross sectional areas of m...
Question 4 The plane truss is subjected to a load as shown in Figure 4. Take E = 200 GPa and cross sectional areas of members 1, 2 and 3 as 150, 250 and 200 mm2 respectively a) Assemble the upper triangular part of the global stiffness matrix for the truss. b) Determine the horizontal and vertical displacements at node 4. c) Calculate the forces in each member of the truss. (25 marks) 20 kN 3 600 4 3 1.5m...
The plane truss shown in Figure is composed of members having a square 15 mm ×...
The plane truss shown in Figure is composed of members having a
square 15 mm × 15 mm cross section and modulus of elasticity
E = 69 GPa.
a. Assemble the global stiffness matrix.
b. Compute the nodal displacements in the global coordinate
system for theloads shown.
c. Compute the axial stress in each element
3 kN 3 5 kN 2 1.5 m 4. 1.5 m
For the bar subjected to axial load shown in Figure 1 to 2, determine the nodal...
For the bar subjected to axial load shown in Figure 1 to 2, determine the nodal displacements and Reaction Force. Let Area = 2in^2, E= 30E6 psi = p(x) 300 lb/in 2 3 30 in 60 in x Figure 1 P(x) = 10x lb/in 2 3 30 in 60 in Figure 2.
Finite Element Method 5.17 Displacements of the three-member truss shown are confined to the plane of...
Finite Element Method
5.17 Displacements of the three-member truss shown are confined to the plane of the figure, and points 1, 2 and 3 are fixed to the stationary rim. All members have the same A, E, and L a) Obtain the 2x2 stiffness matrix that operates on the horizontal and vertical degrees of freedom of the central node. b) Obtain the corresponding global force vector c) Solve for the displacements and for axial stress in member (2-4), when the...
2.3-2 A truss ABC supports a load P= 3000 lb as shown in the figure. Members...
2.3-2 A truss ABC supports a load P= 3000 lb as shown in the figure. Members AB and BC have cross- sectional areas Aab-1.4 in.2 and Abc-4.1 n.2, respec- tively. The material is aluminum with E = 10,000,000 psi. Find the horizontal deflection and the vertical deflection 6, of joint B 30° 8 ft Prob. 2.3-2
(1)20points 0.12m 0.05m The simply supported beam shown in the figure is subjected to a uniform t...
(1)20points 0.12m 0.05m The simply supported beam shown in the figure is subjected to a uniform transverse load and a concentrated load. (1.) Using two equal-length elements (FEM) to determine the deflection and stress of bottom surface. (2.) Using elementary beam theory to determine the deflection and stress of bottom surface
(1)20points 0.12m 0.05m The simply supported beam shown in the figure is subjected to a uniform transverse load and a concentrated load. (1.) Using two equal-length elements (FEM) to...
Consider the truss subjected to a single point load P = 12 kN
downward at point C (Figure 1). The members of the truss all have E
= 200 GPa and cross-sectional area 25 cm2.
<ME316 HW9 - Energy Methods Conservation of Energy View Available Hint(s) Learning Goal: To use conservation of energy to calculate the displacement of a point in a truss When a structure is subjected to a single point load and deforms in a linear- elastic fashion,...
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...
The plane truss is subjected to a load as shown in Figure 4. Take E = 200 GPa and cross sectional areas of members 1, 2 and 3 as 150, 250 and 200 mm2 respectively a) Assemble the upper triangular part of the global stiffness matrix for the truss b) Determine the horizontal and vertical displacements at node 4 c) Calculate the forces in each member of the truss. (25 marks) 20 kN 3 60° 4 1.5m 2 2 20m...
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...
Question 4 The plane truss is subjected to a load as shown in Figure 4. Take E = 200 GPa and cross sectional areas of members 1, 2 and 3 as 150, 250 and 200 mm2 respectively a) Assemble the upper triangular part of the global stiffness matrix for the truss. b) Determine the horizontal and vertical displacements at node 4. c) Calculate the forces in each member of the truss. (25 marks) 20 kN 3 600 4 3 1.5m...
The plane truss shown in Figure is composed of members having a
square 15 mm × 15 mm cross section and modulus of elasticity
E = 69 GPa.
a. Assemble the global stiffness matrix.
b. Compute the nodal displacements in the global coordinate
system for theloads shown.
c. Compute the axial stress in each element
3 kN 3 5 kN 2 1.5 m 4. 1.5 m
For the bar subjected to axial load shown in Figure 1 to 2, determine the nodal displacements and Reaction Force. Let Area = 2in^2, E= 30E6 psi = p(x) 300 lb/in 2 3 30 in 60 in x Figure 1 P(x) = 10x lb/in 2 3 30 in 60 in Figure 2.
Finite Element Method
5.17 Displacements of the three-member truss shown are confined to the plane of the figure, and points 1, 2 and 3 are fixed to the stationary rim. All members have the same A, E, and L a) Obtain the 2x2 stiffness matrix that operates on the horizontal and vertical degrees of freedom of the central node. b) Obtain the corresponding global force vector c) Solve for the displacements and for axial stress in member (2-4), when the...
2.3-2 A truss ABC supports a load P= 3000 lb as shown in the figure. Members AB and BC have cross- sectional areas Aab-1.4 in.2 and Abc-4.1 n.2, respec- tively. The material is aluminum with E = 10,000,000 psi. Find the horizontal deflection and the vertical deflection 6, of joint B 30° 8 ft Prob. 2.3-2
(1)20points 0.12m 0.05m The simply supported beam shown in the figure is subjected to a uniform transverse load and a concentrated load. (1.) Using two equal-length elements (FEM) to determine the deflection and stress of bottom surface. (2.) Using elementary beam theory to determine the deflection and stress of bottom surface
(1)20points 0.12m 0.05m The simply supported beam shown in the figure is subjected to a uniform transverse load and a concentrated load. (1.) Using two equal-length elements (FEM) to...
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