Figure Q2 shows a 2-dimensional truss. The area of each member is equal to A. The modulus of elasticity for all members is the same and is equal to E. a) Label the elements, the movable and supported degrees-of-freedom (DOFs) in the figure. b) Determine the transformation matrix of all elements. c) Determine the global element stiffness matrix of all elements (indicate the corresponding DOFs) in terms of EA. d) Assemble the system stiffness matrix (movable DOFs only) ! 2 m 2 m Figure Q2 e) Determine the displacements under the action of P in terms of P and EA. f) Determine the axial force on each member in terms of P. D 1 m
Figure Q2 shows a 2-dimensional truss. The area of each member is equal to A. The modulus of elasticity for all members is the same and is equal to E. a) Label the elements, the movable and supported degrees-of-freedom (DOFs) in the figure. b) Determine the transformation matrix of all elements. c) Determine the global element stiffness matrix of all elements (indicate the corresponding DOFs) in terms of EA. d) Assemble the system stiffness matrix (movable DOFs only) ! 2 m 2 m Figure Q2 e) Determine the displacements under the action of P in terms of P and EA. f) Determine the axial force on each member in terms of P. D 1 m
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:Figure Q2 shows a 2-dimensional truss. The area of
each member is equal to A. The modulus of elasticity
for all members is the same and is equal to E.
a) Label the elements, the movable and supported
degrees-of-freedom (DOFs) in the figure.
b) Determine the transformation matrix of all
elements.
c) Determine the global element stiffness matrix of
all elements (indicate the corresponding DOFs)
in terms of EA.
d) Assemble the system stiffness matrix (movable
DOFs only)
B
2 m
2 m
Figure Q2
e) Determine the displacements under the action of P in terms of P and EA.
f) Determine the axial force on each member in terms of P.
P
1 m
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Step 1: Data given
VIEWStep 2: (a) Degree of freedom
VIEWStep 3: (b) Transformation matrix
VIEWStep 4: (b) Transformation matrix
VIEWStep 5: Find the Element stiffness matrix for all Elements
VIEWStep 6: (c) Global stiffness matrix
VIEWStep 7: d) System stiffness matrix (movable DOF)
VIEWStep 8: d) Displacement under the action of P
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