Using the stiffness method, determine the axial forces within members and the displacements of joints of the truss shown in the Figure 1. The truss was built using 50 mm x 50 mm x 3 mm SHS with E= 200 GPa (approx). (Cross members BD and CE are not connected at the middle)
(a) Show local stiffness matrices for each member and the assembled global stiffness matrix. Show your step by step solution. (30 Marks)
(b) Use an appropriate method
to solve the matrix if necessary (e.g. inverse matrices). (20
marks) and tabulate the results
Homework Answers
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Using the stiffness method, determine the axial forces within members and the displacements of jo...
Q2. Statically determinate or indeterminate truss analysis by the stiffness method. (50 marks) a) Determine the stiffness matrix of the whole truss given in problems 14.9 and 14.10 (p. 583). Indicate...
Q2. Statically determinate or indeterminate truss analysis by
the stiffness method. (50 marks)
a) Determine the stiffness matrix of the whole truss given in
problems 14.9 and 14.10 (p. 583). Indicate the degrees-of freedom
in all the stiffness matrices. (18 marks)
b) Calculate all the nodal displacements and all the member forces
for the truss.
(16 marks)
14-9. Determine the stiffness matrix K for the trus Take A 0.0015 m2 and E 200 GPa for each member. 2 12 4...
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...
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...
Using the stiffness method, Calculate the stiffness matrix of the frame and show all displacements and reactions at node #2. Assume that all joints are fixed. Calculate the all bending moments and sho...
Using the stiffness method, Calculate the stiffness matrix of
the frame and show all displacements and reactions at node #2.
Assume that all joints are fixed.
Calculate the all bending moments and show in a diagram.
E=200GPa, I=300(106) & A=10(103)
24 kN/m 4m 8m 20 kN 4m
24 kN/m 4m 8m 20 kN 4m
2. For the pin-jointed truss shown in Figure Q2.1 applied at node 4. The Young's modulus E(GPa) is the same for...
2. For the pin-jointed truss shown in Figure Q2.1 applied at node 4. The Young's modulus E(GPa) is the same for the three truss vertical downward force P(kN) is a members. The cross sectional area of each of the truss members is indicated below and expressed in terms of a constant A. By using the stiffness method: (a) Compute the reduced stiffness matrix Kg [5 marks [10 marks (b) Calculate the global displacements of node 4 in terms of P,...
Use stiffness method to find the axial force for all members in the truss. *Note: the...
Use stiffness method to find the axial force for all members
in the truss.
*Note: the drawing is not to scale.
8 1259.8mm 5 7 3 2 10 Р pin support roller support 300mm 300 mm 360mm P=300N ,E= 2500N/mm², A=250mm² member 3 is perpendicular to member 1 and 4 member 9 is perpendicular to member 8 and 11
tatically determinate or indeterminate frame analysis by the stiffness method (45 marks) a) Determine the stiffine...
tatically determinate or indeterminate frame analysis by the stiffness method (45 marks) a) Determine the stiffiness matrix of the frame of problems 16.5 and 16.6 (p. 619). Indicate the degrees-of freedom in all the stiffness matrices. b) D Q4. S (10 marks) etermine all the displacement components at node 2 and all the reactions including the reactions at node 2. Show all calculations. c) (18 marks) of the frame on the compression side showing all the salient values (5 marks)...
Analyse the beam shown in Figure 4 using the stiffiness method. Node D is fixed and...
Analyse the beam shown in Figure 4 using the stiffiness method. Node D is fixed and node 2 and 3 are rollers. A uniform distributed load of 1 kN/m is acting on member 1 . And a load of 10 kN is acting at the middle of member2. EI is constant for all members a) Identify the force vector of the structure; [4 marks] b) Identify the displacement vector of the structure; [2 marks] c) Determine the stiffness matrices 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...
Q2. Statically determinate or indeterminate truss analysis by
the stiffness method. (50 marks)
a) Determine the stiffness matrix of the whole truss given in
problems 14.9 and 14.10 (p. 583). Indicate the degrees-of freedom
in all the stiffness matrices. (18 marks)
b) Calculate all the nodal displacements and all the member forces
for the truss.
(16 marks)
14-9. Determine the stiffness matrix K for the trus Take A 0.0015 m2 and E 200 GPa for each member. 2 12 4...
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...
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...
Using the stiffness method, Calculate the stiffness matrix of
the frame and show all displacements and reactions at node #2.
Assume that all joints are fixed.
Calculate the all bending moments and show in a diagram.
E=200GPa, I=300(106) & A=10(103)
24 kN/m 4m 8m 20 kN 4m
24 kN/m 4m 8m 20 kN 4m
2. For the pin-jointed truss shown in Figure Q2.1 applied at node 4. The Young's modulus E(GPa) is the same for the three truss vertical downward force P(kN) is a members. The cross sectional area of each of the truss members is indicated below and expressed in terms of a constant A. By using the stiffness method: (a) Compute the reduced stiffness matrix Kg [5 marks [10 marks (b) Calculate the global displacements of node 4 in terms of P,...
Use stiffness method to find the axial force for all members
in the truss.
*Note: the drawing is not to scale.
8 1259.8mm 5 7 3 2 10 Р pin support roller support 300mm 300 mm 360mm P=300N ,E= 2500N/mm², A=250mm² member 3 is perpendicular to member 1 and 4 member 9 is perpendicular to member 8 and 11
tatically determinate or indeterminate frame analysis by the stiffness method (45 marks) a) Determine the stiffiness matrix of the frame of problems 16.5 and 16.6 (p. 619). Indicate the degrees-of freedom in all the stiffness matrices. b) D Q4. S (10 marks) etermine all the displacement components at node 2 and all the reactions including the reactions at node 2. Show all calculations. c) (18 marks) of the frame on the compression side showing all the salient values (5 marks)...
Analyse the beam shown in Figure 4 using the stiffiness method. Node D is fixed and node 2 and 3 are rollers. A uniform distributed load of 1 kN/m is acting on member 1 . And a load of 10 kN is acting at the middle of member2. EI is constant for all members a) Identify the force vector of the structure; [4 marks] b) Identify the displacement vector of the structure; [2 marks] c) Determine the stiffness matrices 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...
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