# Finite Element Method Questions and Answers – Plane Frames

This set of Finite Element Method Multiple Choice Questions & Answers (MCQs) focuses on “Plane Frames”.

1. Plane frame members have only 2 degrees of freedom at each of its node.
a) False
b) True

Explanation: Plane frame members have a total of 3 degrees of freedom at each of its node. They are Axial deformation, Vertical deformation, and Rotation. Therefore, while calculating the Member stiffness matrix, all the 3 degrees of freedom have to be considered.

2. In case of a plane frame member, all the elements lie on different planes.
a) False
b) True

Explanation: The given statement is false. All elements of any plane frame member lie on a singular plane. These elements are interconnected by rigid joints. For calculation purpose, these rigid joints are considered to be frictionless.

3. What type of frame is depicted in the figure below?

a) Elements
b) Nodes
c) Plane frame
d) 3D frame

Explanation: Plane frame is depicted in the given figure. Figure shows a two dimensional beam acting upon by axial, shear, and rotational forces. These three forces correspond to the 3 degrees of freedom of every node of a plane frame member.

4. What are the type of stresses induced by the cross section of a plane member?
a) Axial, Bending and Tensile stresses
b) Compressive, Torsional and Tensile stresses
c) Linear, dynamic and static stresses
d) Axial, Shear and Bending stresses

Explanation: The type of stresses that are generally induced by the cross section of a plane member are Axial, Shear and Bending stresses. These arise due to the application of Axial, shear, and bending loads respectively. As the plane frames are of two dimensional geometry, these are the limited resultant stresses arising in the same.

5. “In a plane frame, the stiffness matrix is transformed from a local to global co ordinate system.” Why is this so?
a) The members in a plane frame are oriented in different directions
b) The members in a plane frame are oriented in same direction
c) The members in a plane frame are orthogonal to one another
d) The members in a plane frame are parallel to one another

Explanation: In a plane frame, the members are oriented in different directions; hence it is necessary to transform the stiffness matrix of the individual members from local to global co ordinate system before the formulation of global stiffness matrix.
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6. What is the generalized expression for the nodal vector of a plane frame member when subjected to axial and transverse loads?
a) q = [q1 q2 q3 q4 q5]
b) q = [q1 q2 q3 q4 q5 q6]
c) q = [q1 q2 q3 q4]
d) q = [q1 q2 q3]

Explanation: The generalized expression for the nodal vector of a plane frame member when subjected to axial and transverse loads is given by q = [q1 q2 q3 q4 q5 q6]. Each node will have 3 degrees of freedom, 2 displacements and 1 rotation. This is with respect to the local co ordinate system.

7. Which of the following can be treated as a plane frame for analysis?
a) Aerospace composite structures
b) Lattice Domes
c) A simple bridge
d) Transmission towers

Explanation: A simple bridge can be treated as a plane frame for analysis. This is because, for a simple bridge, the members can be projected onto a single plane; whereas, lattice domes, transmission towers, and aerospace composite structures cannot be projected onto any singular plane.

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