Finite Element Method Questions and Answers – Plane Trusses

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

1. Plane trusses are also known as _____
a) One–dimensional trusses
b) Two-dimensional trusses
c) Three-dimensional trusses
d) Poly dimensional trusses

Explanation: Truss elements are two- node members which allow arbitrary orientation in XYZ co-ordinate system. Truss transmits axial force only. Planar truss is one where all members and nodes lie within Two dimensional plane.

2. A truss structure consists only ___ force members.
a) Only one
b) Two
c) Three
d) Poly

Explanation: Truss elements are two node members which allow arbitrary orientation in XYZ co-ordinate system. Truss transmits axial force only, in general, three degree of freedom element. A truss structure consists only 2 truss members.

3. Plane truss element can be shown in _____
a) Local coordinate system
b) Global coordinate system
c) Local and global coordinate systems
d) Dimensional structure

Explanation: Truss is one where all members and nodes lie within two dimensional plane. Truss is that elements of a truss have various orientation. These different orientations can be shown in local and global coordinate system.

4. The truss element is a _____ when we see it in a local co-ordinate system.
a) Three dimensional
b) One dimensional
c) Two dimensional
d) Thermal component

Explanation: Truss is one where all members and nodes lie within two dimensional plane. Truss is that elements of a truss have various orientations. When we see a truss in local co-ordinate system, the element of a truss can be seen as one dimensional element.

5. Where l and m are direct cosines, then transformation matrix L is given by ___
a) $$\begin{bmatrix}l & 0 \\ m & 0\\0 & l\\0 & m \end{bmatrix}$$
b) $$\begin{bmatrix}l & 0 \\0 & m \end{bmatrix}$$
c) $$\begin{bmatrix}l & m \end{bmatrix}$$
d) $$\begin{bmatrix}l & m & 0 & 0\\0 & 0 & l & m \end{bmatrix}$$

Explanation: The direct cosines l and m are introduced as l = cos θ and m=cos ф. These direction cosines are the cosines of the angles that the local x’-axis makes with the global x-, y- axes.

6. Formula for direct cosine l=cosθ= ______
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. Planar truss is one where all the members and nodes lie within two dimensional plane.

7. The direct cosine m is given by formula cosф= ____
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: The direct cosines l and m are introduced as l=cosθ and m=cosф. These direction cosines are cosines of the angles of that local x’- axis makes with global x- and y- axes. Let (x1,y1) and (x2,y2) be the co-ordinates of nodes 1 and 2.

8. Strain energy (U) in global co-ordinates can be written as ____
a) q’ T kq
b) q’ T k
c) k q
d) $$\frac{1}{2}$$ q’ T kq

Explanation: Strain energy is defined as the energy stored in the body due to deformation. Strain energy per unit volume is known as strain energy density and the area under stress- strain curve towards the point of deformation.

9. The stress σ in a truss element is given by ____
a) σ=E
b) σ=ε
c) σ=Eeε
d) σ=α

Explanation: Stress is a physical quantity that expresses the internal forces that neighboring the particles of a continuous material exert on each other. Expression for element stresses can be obtained by noting that a truss element in local co-ordinates is simple two- force member.

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$$\begin{Bmatrix}-l \\ -m \\l\\m\end{Bmatrix}$$