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

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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Concept explainers

Mechanics of Solids

It is the study of the behavior of solid materials, their characteristics under various circumstances such as variation in external forces, temperature, and other internal factors. It is one of most important study in the field of engineering science, especially chemistry and mechanical engineering. In rigid body, the idealization of the solid body in which deformation is neglected. Deformation is known as the force acting on the solid state system which exerts change in its shape of the body but it continues to be at rest or in a uniform motion but it cannot accelerate. But those solid systems do have elasticity, compressibility and can be bent. This field is very vast since there are wide range of materials around us.

Question

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 2: (a) Degree of freedom

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Step 3: (b) Transformation matrix

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Step 4: (b) Transformation matrix

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Step 5: Find the Element stiffness matrix for all Elements

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Step 6: (c) Global stiffness matrix

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Step 7: d) System stiffness matrix (movable DOF)

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Step 8: d) Displacement under the action of P

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