Coplanar Parallel Force System
Parallel forces can be in the same or in opposite directions. The sign of the direction can be chosen arbitrarily, meaning, taking one direction as positive makes the opposite direction negative. The complete definition of the resultant is according to its magnitude, direction, and line of action.
For the beam loaded as shown in Fig. P-627compute the moment of area of the M diagrams between the reactions about both the left and the right reaction. (Hint: Resolve the trapezoidal loading into a uniformly distributed load and a uniformly varying load.)