Name: finding the resultant of distributed loads
Uploaded: 2023-09-22T11:49:32.000Z
Duration: 1 min 13 s
Channel: JoVE

In engineering applications, it is important to consider the loading distribution along the line.
The net force applied due to the distributed load is represented as a single vector, called the resultant force.
Consider an arbitrary-shaped flat plate subjected to uniform loading.
The force acting on an infinitesimal area on the plate has a magnitude equivalent to the differential volume element.
The resultant force acting on the plate is calculated by summing all the differential forces acting on the entire plate surface.
Integrating over the plate&#39;s area gives us an expression for calculating the magnitude of the resultant force, which is also equal to the total volume underneath the distributed-loading diagram.
The location of the resultant force is determined by comparing the moments of the resultant force with those of all the differential forces about their respective axes.
The obtained expressions imply that the force&#39;s line of action passes through the geometric center or centroid of the volume under the distributed-loading diagram.

resultant of a general distributed loading

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.

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 ...

resultant-of-a-general-distributed-loading

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Mechanical Engineering

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Center of Gravity and Centroid

KEY TERMS AND CONCEPTS

finding the resultant of distributed loads

Distributed loads create a force that is spread over a surface instead of acting at one point. To analyze this kind of loading, engineers use a single resultant force. That force represents the net effect of the entire load.

This idea is important in structures that face non-uniform loads. Wind can push on buildings and towers with changing speed and direction, so the load is not evenly spread. Bridges also experience non-uniform loading from vehicles, and some parts of the bridge can feel more stress and strain than others.

To find the resultant force, the small forces acting on tiny areas are added together with integration over the load-bearing surface. The size of the resultant force equals the total area under the distributed-loading diagram. Its location is found by comparing moments, which means the turning effects of the force about an axis.

The line of action of the resultant passes through the geometric center, or centroid, of the volume under the load diagram. Knowing both the size and location of the force helps engineers judge whether a structure has enough strength and rigidity. Because loading can change, these calculations help support safe and reliable design for buildings, bridges, and other structures.

Finding the Resultant of Distributed Loads

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Distributed loads create a force that is spread over a surface instead of acting at one point. To analyze this kind of loading, engineers use a single resultant force. That force represents the net effect of the entire load. This idea is important in structures that face non-uniform loads. Wind can push on buildings and towers with changing speed and direction, so the load is not evenly spread. Bridges also experience non-uniform loading from vehicles, and some parts of the bridge can feel...

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key terms and concepts

Learn how engineers combine non-uniform loads into one resultant force, find its location with moments, and apply the idea to bridges and buildings.

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Finding the Resultant of Distributed Loads

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