# Finite Element Method Questions and Answers – Three Dimensional Trusses

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This set of Finite Element Method Multiple Choice Questions & Answers (MCQs) focuses on “Three Dimensional Trusses”.

1. In a 3-D truss element nodal displacement vector in a local co-ordinate is q’= ___
a) [q1]
b) [q2]
c) [q1,q2,q3]T
d) [q1,q2]T

Explanation: Local co-ordinates are measurement indices into a local co-ordinate system or local co-ordinate space. Nodes will have nodal displacements or degrees of freedom which may include translations, rotations, and for special applications, higher order derivatives of displacements.

2. Transformation between local and global co-ordinates is _____
a) q=Lq
b) q=L
c) q=L+q
d) q=$$\frac{L}{q}$$

Explanation: Transformations are frequently used in linear algebra and computer graphics, since transformations can easily be represented, combined and computed.

3. For a 3D truss element, transformation matrix L between local and global co-ordinates is given by ___
a) $$\begin{bmatrix}l &0&0 \\ 0&m&0\\0&0&n\end{bmatrix}$$
b) $$\begin{bmatrix}l &m&n \end{bmatrix}$$
c) $$\begin{bmatrix}l&0&n \\ 0&m&0 \end{bmatrix}$$
d) $$\begin{bmatrix}l&m&n&0&0&0\\ 0&0&0&l&m&n\end{bmatrix}$$

Explanation: A transformation matrix is a special matrix that can describe 2D and 3D transformations. Transformations are frequently used in linear algebra and computer graphics. Since transformations can be easily represented, combined and computed.

4. The direct cosines l, m, n are of local _____
a) z’- axes
b) x’- axes
c) y’- axes
d) None of the above

Explanation: Direction cosine refers to the cosine of the angle between any two vectors and three co-ordinate axes. Direction cosines are analogous extension of the usual notion of the slope to higher dimensions. In a truss element the direction cosines l, m, n are of local co-ordinate of x’- axes.

5. The direction cosines l, m, n with respect to ____ x-, y-, z- axes respectively.
a) Local
b) Local and global
c) Global
d) Transformation

Explanation: The direction cosines of a vector are the cosines of the angles between the vector and three co-ordinate axes. Direction cosines are analogous extension of the usual notion of the slope and higher dimensions. The direction cosines l, m, n are with respect to global x-,y-, z- axes .

6. In 3D truss, formula for direct cosine l = _____
a) x2-x1
b) $$\frac{x_2}{l_e}$$
c) $$\frac{x_1}{l_e}$$
d) $$\frac{x_2-x_1}{l_e}$$

Explanation: A truss is a two node element which allows arbitrary orientation in XYZ co-ordinate system. The 3D truss element can be treated as straight forward generalization of the 2D truss element.

7. The direct cosine m is given by formula ____
a) $$\frac{x_2-x_1}{l_e}$$
b) $$\frac{y_2-y_1}{l_e}$$
c) $$\frac{x_1-y_1}{l_e}$$
d) $$\frac{x_2-y_2}{l_e}$$

Explanation: A truss is a two node element which allows arbitrary orientation in XYZ co-ordinate system. The 3D truss element can be treated as straight forward generalization of the 2D truss element.

8. The direction cosine n is given by formula _____
a) $$\frac{x_2-x_1}{l_e}$$
b) $$\frac{y_2-y_1}{l_e}$$
c) $$\frac{z_2-z_1}{l_e}$$
d) Undefined

Explanation: A truss is a two node element. The three D truss element can be treated as straight forward generalization of the 2D truss element.

9. In 3D truss element, the nodal displacement vector in global co-ordinates is _____
a) q= [q1,q2]
b) q= [q1,q2,q3]
c) q= [q1,q2,q3,q4,q5,q6]
d) Undefined

Explanation: Nodes will have nodal displacements or degrees of freedom which may include translations, rotations, and for special applications, higher order derivatives of displacements.

10. In a truss element, element temperature load is ___
a) θe=EeAe
b) θe=EeAeε0
c) θe=EeAeε0$$\begin{Bmatrix}l \\ m \end{Bmatrix}$$
d) θe=EeAeε0$$\begin{Bmatrix}-l \\ -m \\l\\m\end{Bmatrix}$$