Determine the resultant moment produced by forces F_BF B ​ and F_CF C ​ about point O. Express the result as a Cartesian vector.

 Determine the resultant moment produced by forces 

$F_B$ and $F_C$ about point O. Express the result as a Cartesian vector.

Image from: Hibbeler, R. C., S. C. Fan, Kai Beng. Yap, and Peter Schiavone. Statics: Mechanics for Engineers. Singapore: Pearson, 2013.

Solution:

To solve this question, we will be using part 1 and part 2 from the previous questions. Please refer to them if any part is confusing.

From part 1, we know that the moment produced by $F_B$ is:

$M_{O1}=\left\{-1800i\right\}N\cdot m$

 

From part 2, we know that the moment produced by $F_C$ is:

$M_{O2}=\left\{1080i+720j\right\}N\cdot m$

 

The resultant moment is then $M_{O1}+M_{O2}$:

$M_{resultant}=M_{O1}+M_{O2}$

$M_{resultant}=\left\{-1800i\right\}+\left\{1080i+720j\right\}$

$M_{resultant}=\left\{-720i+720j\right\}N\cdot m$