Question

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) \(\begin{bmatrix}l & m & 0  & 0\\0 & 0 & l & m \end{bmatrix}\)

This question was posed to me in a national level competition.

Origin of the question is Plane Trusses topic in division Trusses of Finite Element Method

Answer 1

The correct answer is (d) \(\begin{bmatrix}l & m & 0  & 0\\0 & 0 & l & m \end{bmatrix}\)

The best 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.