Question $1$

Consider the structure in the nccompanying sketch that is subjected to the given horizontal and wertical forces al $A.B$ and $C$ are pin connections in the same plane; the distance between the two points is variable.

Ournim in this proltem is to see how the resultant force at $A$ is distrilutrat between the eonnecting members $AB$ and $AQ$ under specified cireumstances $T$ thi tis equivalent to finding components along specifired dinectons.

$1$: Determine the magnitude $R$ of the$-$restltant $R$ of the $450kN$ and $6n0kN$ force and sperify the direction of $R.$

$1$:$2$ Caleulate the components of $R-$along the members in the following circumstances and interpret youlr reztits graphically.

$($a$)$ Member $AB$ is vertical. Ealculate the components along $AB$ and $AC.$

$($b$)$ Member $AB$ has a lengtt of $5$ m $.$ Galculate the components along $AB$ and $AC.$

$($e$)$ Member $AB$ is vertical; a third member is connected from $A$ to the midpoint of $B$ and $C,$ call this point $D.$ Calculate the components along $AB,AD$ and $AC.$