Finite Element Method Multiple Choice Questions 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
Answer: b
Clarification: 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
Answer: b
Clarification: 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
Answer: c
Clarification: 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
Answer: b
Clarification: 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})
Answer: d
Clarification: 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})
Answer: d
Clarification: 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})
Answer: b
Clarification: 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 k’q’
b) q’ T k’
c) k’ q’
d) (frac{1}{2}) q’ T k’q’
Answer: d
Clarification: 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
Answer: c
Clarification: 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\mend{Bmatrix})
Answer: d
Clarification: In a truss, temperature effect is arised then thermal stress problem is considered here. Since the element is simply a one dimensional element when viewed in local co-ordinate system, the element temperature load in the local co-ordinate system.