# Finite Element Method Questions and Answers – One Dimensional Problems – Properties of K

This set of Finite Element Method Multiple Choice Questions & Answers (MCQs) focuses on “One Dimensional Problems – Properties of K”.

1. Dimension of global stiffness matrix is _______
a) N X N, where N is no of nodes
b) M X N, where M is no of rows and N is no of columns
c) Linear
d) Eliminated

Explanation: A global stiffness matrix is a method that makes use of members stiffness relation for computing member forces and displacements in structures. The dimension of global stiffness matrix K is N X N where N is no of nodes.

2. Each node has only _______
a) Two degrees of freedom
b) One degree of freedom
c) Six degrees of freedom
d) Three degrees of freedom

Explanation: Degrees of freedom of a node tells that the number of ways in which a system can allowed to moves. In a stiffness matrix each node can have one degree of freedom.

3. Global stiffness K is a______ matrix.
a) Identity matrix
b) Upper triangular matrix
c) Lower triangular matrix
d) Banded matrix

Explanation: A banded matrix is a sparse matrix whose non zero entities are confined to a diagonal band, comprising the main diagonal and zero or more diagonals on either side. A global stiffness matrix K is a banded matrix. That is, all the elements outside the band are zero.

4. The dimension of Kbanded is _____ (Here NBW is half bandwidth)
a) [N X NBW ]
b) [NBW X N]
c) [N X N]
d) [NBW X NBW]

Explanation: K can be compactly represented in banded form. As Kbanded is of dimension [N X NBW] where NBW is the half band width.

5. In many one-dimensional problems, the banded matrix has only two columns. Here NBW=____
a) 6
b) 3
c) 7
d) 2

Explanation: NBW means half bandwidth. Many of the One- dimensional problems banded matrix has only 2 columns then NBW=2. We know that
NBW=max(Difference between dof numbers connecting an element)+1
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6. Stiffness matrix represents a system of ________
a) Programming equations
b) Iterative equations
c) Linear equations
d) Program CG SOLVING equations

Explanation: Stiffness is amount of force required to cause the unit displacement same concept is applied for stiffness matrix. The stiffness matrix represents a system of linear equations that must be solved in order to ascertain an approximate solution to differential equation.

7. Stiffness matrix is _____
a) Non symmetric and square
b) Symmetric and square
c) Non symmetric and rectangular
d) Symmetric and rectangular

Explanation: Stiffness matrix is a inherent property of the structure. The property of a stiffness matrix, as the stiffness matrix is square and symmetric.

8. In stiffness matrix, all the _____ elements are positive.
a) Linear
b) Zigzag
c) Diagonal
d) Rectangular

Explanation: Stiffness matrix represents system of linear equations that must be solved in order to ascertain an approximate solution to the differential equation. The stiffness matrix is an inherent property of a structure. In stiffness matrix all the diagonal elements are positive.

9. The size of global stiffness matrix will be equal to the total ______ of the structure.
a) Nodes
b) Degrees of freedom
c) Elements
d) Structure

Explanation: For a global stiffness matrix, a structural system is an assemblage of number of elements. These elements are interconnected to form the whole structure. The size of global stiffness matrix will be equal to the total degrees of freedom of the structure.

10. Element stiffness is obtained with respect to its ___
a) Degrees of freedom
b) Nodes
c) Axes
d) Elements

Explanation: A stiffness matrix represents system of linear equations that must be solved in order to ascertain an approximate solution to the differential equation. Element stiffness is obtained with respect to its axes.

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