Question

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) \(\frac{x_2-y_2}{l_e}\)

I got this question by my college professor while I was bunking the class.

This key question is from Plane Trusses topic in portion Trusses of Finite Element Method

Answer 1

Right choice is (b) \(\frac{y_2-y_1}{l_e}\)

To explain: 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.