Question

In the analysis of a beam you are tasked to find the reaction forces on a loaded beam shown in the figure below Two slightly different free body diagrams on the same loaded beam are drawn: DIAGRAM 1 AGRAM 2 cos(9) ich statement regarding the two diagrams is correct? ct one: b. Ax =-C, and A,--C, d. The two diagrams do not represent the same system. e. Neither diagram represents the physical system.

Answer 1

Which statement regarding the two diagram is correct?

$\Rightarrow$ A_x = - C_x and A_y = - C_y

Option (b) : it will be correct.

Explanation : In Diagram 1, we have

A_x = horizontal force at point A to the rightward direction

A_y = vertical force at point A to the upward direction

In Diagram 2, we have

C_x = horizontal force at point A to the leftward direction

C_y = vertical force at point A to the downward direction

We can see in both diagram. Then, we get

A_x = - C_x and A_y = - C_y

We know that, | F | = _$\sqrt{}$F_x² + F_y²

where, F_x = horizontal force = F cos $\theta$   and   F_y = vertical force = F sin $\theta$