# Finite Element Method Questions and Answers – Beams on Elastic Support

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This set of Finite Element Method Multiple Choice Questions & Answers (MCQs) focuses on “Beams on Elastic Support”.

1. Which of the following is a class of applications formed by beams supported on soil?
a) Soil foundation
b) Winkler foundation
c) Elastic Beam foundation
d) Reinforced foundation

Explanation: Winkler foundation is a class of applications formed by beams supported on soil. There are many engineering applications where the beams are supported on elastic members.

2. Single row bearings can be considered by a node at each bearing location.
a) True
b) False

Explanation: Single row bearings can be considered by a node at each bearing location. Also for single row bearing, bearing stiffness can be added to the vertical degree of freedom.

3. Which of the following statements is not correct about beams on elastic supports?
a) Rotational stiffness has to be considered for journal bearings
b) Single row bearings can be considered by a node at each bearing location
c) In wide journal bearing stiffness per unit length has to be considered
d) Rotational stiffness need not be considered for roller bearings

Explanation: Rotational stiffness has to be considered for roller bearings. Also in wide journal bearings stiffness per unit length has to be considered.

4. Which of the following statements are correct regarding beam elements?
a) Beam elements can resist force and moment about x and y axis
b) Beam elements can resist only force about x and y axis
c) Beam elements can resist only force about x, y, and z axis
d) Beam elements can resist force and moment about x, y, and z axis

Explanation: Beam elements can resist force and moment about x, y, and z axis.

5. Rod elements cannot resist shear force applied on the element.
a) True
b) False

Explanation: Rod elements cannot resist shear force applied on the element. Rod element does not have the required vertical degree of freedom to resist shear force.

6. Which of the following expressions must be added to the element stiffness matrix for beams supported on elastic supports, where l is length of beam element, and s is the stiffness per unit length of element?
a) $$\frac{sl}{420}\begin{bmatrix}156&22l&54&-13l\\22l&4l^2&13l&-3l^2\\54&13l&156&-22l\\-13l&-3l^2&-22l&4l^2\end{bmatrix}$$

b) $$\frac{EI}{l^2}\begin{bmatrix}12&-6l&-12&6l\\-6l&4l^2&6l&2l^2\\-12&6l&12&6l\\6l&2l^2&6l&4l^2\end{bmatrix}$$
c) $$\frac{EI}{l^3}\begin{bmatrix}12&-6l&-12&6l\\-6l&4l^2&6l&2l^2\\-12&6l&12&6l\\6l&2l^2&6l&4l^2\end{bmatrix}$$
d) $$\frac{EI}{420}\begin{bmatrix}156&22l&54&-13l\\22l&4l^2&13l&-3l^2\\54&13l&156&-22l\\-13l&-3l^2&-22l&4l^2\end{bmatrix}$$

Explanation: The value of stiffness matrix to be added for beams with elastic support is
$$\frac{sl}{420}\begin{bmatrix}156&22l&54&-13l\\22l&4l^2&13l&-3l^2\\54&13l&156&-22l\\-13l&-3l^2&-22l&4l^2\end{bmatrix}$$
Here l is length of beam element, and s is the stiffness per unit length of element. The stiffness matrix of the beam element affects the displacement of the nodes and their interpolation in the beam element.

Sanfoundry Global Education & Learning Series – Finite Element Method. 