Question

34 Chapter 2 Force Systems Representative Problems 2/11 The two structural members, one of which is in tension and the other in compression, exert the indi- cated forces on joint O. Determine the magnitude of the resultant R of the two forces and the angle e which R makes with the positive x-axis. 3 kN 2 kN 4 30° Problem 2/11

Use and identify the steps of the graphical/semi-graphical method

(parallelogram law) to find:

i. The vector expression of the resultant

ii. The magnitude and angle (with respect to the x axis) of the resultant

b. Use and identify the steps (from problem 1b) of the algebraic method to find:

i. The vector expression of the resultant

ii. The magnitude and angle (with respect to the x axis) of the resultant

Answer 1

We have to find resultant magnitude and direction.

Parallelogram method: - R rightarrow = A rightarrow + B rightarrow, R rightarrow = squareroot A^2 + B^2 + 2AB cos 90 degree = 3.6 KN R rightarrow = A rightarrow + B rightarrow = (2 cos 30 degree + 3 cos 60 degree) i + 2(sin 30 degree - 3 sin 60 degree)j (i) R rightarrow = 3.23 i - 1.6 j (ii) Vertical-bar R rightarrow Vertical-bar = 3.6/K N rightarrow Resultant magnitude tan theta = 1.6/3.23 = 0.5 theta = 26.35 degree rightarrow counter - clock wise from +ve x - axis.