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DKI=3 Problem 1: Determine the following vector and matrix expressions for the frame structure load system show...
Problem 3 Analyze the frame structure subjected to the following support movements: a beam-end settlement at...
Problem 3 Analyze the frame structure subjected to the following support movements: a beam-end settlement at Node #4; . a column base rotation at (Node #1). All members have a constant bending stiffness El and are considered as axially rigid. a) Determine the degree of kinematic indeterminacy (DKI) and show the independent DOFs. b) Assemble the structure stiffness matrix Kg. c) Assemble the structure fixed-end force vector Po. Then solve for nodal displacement vector Us based on the equations of...
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...
Please show work Answer shown below Problem 5: Consider the continuous beam structure shown below. For...
Please show work
Answer shown below
Problem 5: Consider the continuous beam structure shown below. For each node, state the force/moment and displacement/rotation boundary conditions required to properly set-up a solution by the stiffness method. Indicate unknown values with a "u 24 k 125 k-ft 200 k-ft Problem 5: M1 200k ft P1 24 k M2 0 k ft 1-u 0,- u Ma = 125k . ft 3-u
CE 160 Problem 1(15% 4 k B 12 ft AR 24 ft The statically determinate rigidly connected frame has a pin support at point A and a roller support at point C. The frame is subjected to a point load a...
CE 160 Problem 1(15% 4 k B 12 ft AR 24 ft The statically determinate rigidly connected frame has a pin support at point A and a roller support at point C. The frame is subjected to a point load at point B. The frame is rigidly con- nected at point B. If the bending stiffness of column AB is 40,000 k-ft and the bending stiffness for beam BC is 60,000 k-ft, find: I. (596) The bending moment diagram for...
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...
Ints) For the following mechanism: a. Determine the number of links in the mechanism b. Determine...
ints) For the following mechanism: a. Determine the number of links in the mechanism b. Determine the total joint order in the mechanism c. Determine the number of loops required for this mechanism d. Determine the mobility of this mechanism e. Draw an appropriate vector loop for this mechanism f. Write the vector loop equation(s) in vector form. g. Write the scalar components of the vector loop position equations. h. Determine any geometric constraint equations. i. Determine the scalar known(s)....
For the 3-D indeterminate (4-member) TRUSS structure shown in Figure 2A. Given that Px 10K (in...
For the 3-D indeterminate (4-member) TRUSS structure shown in Figure 2A. Given that Px 10K (in X-direction); Py none (in Y-direction); E 30,000 ksi; A 0.2 square inches. The nodal coordinates, the earth-quake displacement/settlement, and members' connectivity information are given aS Applied Load! Earth-Quake MEMBER #1 NODE # X node-i node-j 120.00" 160.00"| 80.00"| Px=-10 Kips none Py- none 120.00" 160.00"0.00"none 120.00"0.00" 0.00" none 0.00" 0.00"0.00" none 0.00" 0.00" 80.00" none none 2 none 4 4 none 4 +2.00" (in...
Use the stiffness method to analyse the elastic frame ABC shown below. Use a model made...
Use the stiffness method to analyse the elastic frame ABC shown below. Use a model made up of 2 the elements (AB and CB) and the axis indicated in the figure. All members have the following properties: E = 2 -10% kPa, A = 0.005 m², 1 = 1.5e - 4 m. Also the lengths of the elements are the same: AB = BC = L = 3.1 m and 6 = 45 kN/m. ות 0 B 3 2 x...
Use the stiffness method to analyse the elastic frame ABC shown below. Use a model made...
Use the stiffness method to analyse the elastic frame ABC shown below. Use a model made up of 2 the elements (AB and CB) and the axis indicated in the figure. All members have the following properties: E = 2 -10% kPa, A = 0.005 m², 1 = 1.5e - 4 m. Also the lengths of the elements are the same: AB = BC = L = 3.1 m and 6 = 45 kN/m. ות 0 B 3 2 x...
Use the stiffness method to analyse the elastic frame ABC shown below. Use a model made...
Use the stiffness method to analyse the elastic frame ABC shown below. Use a model made up of 2 the elements (AB and CB) and the axis indicated in the figure. All members have the following properties: E = 2 -10% kPa, A = 0.005 m², 1 = 1.5e - 4 m. Also the lengths of the elements are the same: AB = BC = L = 3.1 m and 6 = 45 kN/m. ות 0 B 3 2 x...
Problem 3 Analyze the frame structure subjected to the following support movements: a beam-end settlement at Node #4; . a column base rotation at (Node #1). All members have a constant bending stiffness El and are considered as axially rigid. a) Determine the degree of kinematic indeterminacy (DKI) and show the independent DOFs. b) Assemble the structure stiffness matrix Kg. c) Assemble the structure fixed-end force vector Po. Then solve for nodal displacement vector Us based on the equations of...
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...
Please show work
Answer shown below
Problem 5: Consider the continuous beam structure shown below. For each node, state the force/moment and displacement/rotation boundary conditions required to properly set-up a solution by the stiffness method. Indicate unknown values with a "u 24 k 125 k-ft 200 k-ft Problem 5: M1 200k ft P1 24 k M2 0 k ft 1-u 0,- u Ma = 125k . ft 3-u
CE 160 Problem 1(15% 4 k B 12 ft AR 24 ft The statically determinate rigidly connected frame has a pin support at point A and a roller support at point C. The frame is subjected to a point load at point B. The frame is rigidly con- nected at point B. If the bending stiffness of column AB is 40,000 k-ft and the bending stiffness for beam BC is 60,000 k-ft, find: I. (596) The bending moment diagram for...
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...
ints) For the following mechanism: a. Determine the number of links in the mechanism b. Determine the total joint order in the mechanism c. Determine the number of loops required for this mechanism d. Determine the mobility of this mechanism e. Draw an appropriate vector loop for this mechanism f. Write the vector loop equation(s) in vector form. g. Write the scalar components of the vector loop position equations. h. Determine any geometric constraint equations. i. Determine the scalar known(s)....
For the 3-D indeterminate (4-member) TRUSS structure shown in Figure 2A. Given that Px 10K (in X-direction); Py none (in Y-direction); E 30,000 ksi; A 0.2 square inches. The nodal coordinates, the earth-quake displacement/settlement, and members' connectivity information are given aS Applied Load! Earth-Quake MEMBER #1 NODE # X node-i node-j 120.00" 160.00"| 80.00"| Px=-10 Kips none Py- none 120.00" 160.00"0.00"none 120.00"0.00" 0.00" none 0.00" 0.00"0.00" none 0.00" 0.00" 80.00" none none 2 none 4 4 none 4 +2.00" (in...
Use the stiffness method to analyse the elastic frame ABC shown below. Use a model made up of 2 the elements (AB and CB) and the axis indicated in the figure. All members have the following properties: E = 2 -10% kPa, A = 0.005 m², 1 = 1.5e - 4 m. Also the lengths of the elements are the same: AB = BC = L = 3.1 m and 6 = 45 kN/m. ות 0 B 3 2 x...
Use the stiffness method to analyse the elastic frame ABC shown below. Use a model made up of 2 the elements (AB and CB) and the axis indicated in the figure. All members have the following properties: E = 2 -10% kPa, A = 0.005 m², 1 = 1.5e - 4 m. Also the lengths of the elements are the same: AB = BC = L = 3.1 m and 6 = 45 kN/m. ות 0 B 3 2 x...
Use the stiffness method to analyse the elastic frame ABC shown below. Use a model made up of 2 the elements (AB and CB) and the axis indicated in the figure. All members have the following properties: E = 2 -10% kPa, A = 0.005 m², 1 = 1.5e - 4 m. Also the lengths of the elements are the same: AB = BC = L = 3.1 m and 6 = 45 kN/m. ות 0 B 3 2 x...
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