EXAMPLE 6.0.2: RESULTANT COUPLE MOMENT FOR COPLANAR COUPLES

Determine the couple moment acting on the beam

Observe that the 10kN forces make a couple applied to the beam so using the couple moment resultant can be used

                                              

The magnitude of the force is already given as 10kN; however, what perpendicular distance between these forces is to the used.

Perhaps you would attempt to use trigonometry to solve for the distance between the two points where the loads are applied. But take note that you are not to solve the distance between those two points but to take the PERPENDICULAR distance between the lines of action of these two forces.

By taking the components of each force, you are going to create couples of the components with ease identifying the perpendicular distances between them.

The resultant moment of the moments from the vertical forces and the horizontal forces becomes

                                         

                                        

Take note that the moment of the vertical forces is positive because the couple rotates clockwise, the horizontal forces create a counterclockwise rotation making their moment negative. This is the reason why the resultant moment is solved using subtraction.

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