Resultant of a General Distributed Loading

While designing structures exposed to non-uniform loads, it is crucial to consider the resultant force and its location. This resultant force is a single vector representing the net force applied due to the distributed load.

Examples such as load distribution due to wind and load distribution on a bridge illustrate how this concept is used to analyze and design safe, reliable structures under variable loading conditions. Most structures, such as residential buildings, bridges, and towers, are designed to withstand non-uniform wind loading, which varies with the wind speed and direction. Similarly, bridges are designed to withstand the weight of vehicles passing over them. However, the weight distribution of vehicles is not uniform, and some parts of the bridge may experience more stress and strain than others. It is necessary to calculate the resultant force acting on the buildings or bridges, which is a non-uniform load distribution problem.

To determine this force, the magnitude of each differential force acting on infinitesimal areas must be summed and integrated over the load-bearing surface area. The magnitude of this resultant force is equal to the total volume under the distributed-loading diagram. The location of this resultant force can be determined by comparing its moments with the moments of all the differential forces about their respective axes. This implies that the line of action of this force will pass through the geometric center or centroid of the volume under consideration.

Knowing where and how much force is applied to a structure allows engineers to ensure sufficient strength and rigidity for the structure to be fit for purpose. These values may also change based on variable loading conditions, so it is essential to consider these potential changes in order to design a safe and secure structure.