Final answer:
The replacement of distributed loading with an equivalent resultant force involves calculating the force's magnitude and location from a pivot point, using moments and equilibrium conditions.
Step-by-step explanation:
To replace the distributed loading with an equivalent resultant force, we must find the magnitude of the force and its location from the point O. The magnitude of the resultant force is equal to the area under the distributed loading curve. To find its location, we use the concept of the center of gravity of this area, which represents the point at which the entire load could be concentrated and have the same moment (rotational effect) about a pivot point.
Considering the pivot and leveraging the perpendicular components of the forces, we apply equilibrium conditions for forces in both the x and y directions and employ the equilibrium condition for torques to solve for the unknown forces. Through the free-body diagram, this systematic approach reveals the locations and magnitudes of the forces acting on a structure.
The process involves calculating the moments about the pivot and setting the sum of the moments due to individual distributed loads equal to the moment due to the resultant force at its specific location from the pivot to maintain equilibrium.