# The Equivalent

For analysis purposes in statics and dynamics, we will usually substitute in a single point force that is statically equivalent to the distributed load in the problem. This single point force is called the equivalent point load and it will cause the same accelerations or reaction forces as the distributed load while simplifying the math.

## What is an equivalent point load?

An equivalent point load is a single point force that will have the same effect on a body as the original loading condition, which is usually a distributed load.

## What is a distributed load in physics?

Basically: Distributed loads are a way to model forces in 2d. F = w d Sometimes called intensity, distributed loads have units of force over distance: N/m or lb/ft. Application: For a truck carrying a heavy uneven load, find where the center of the force is.

## How do you model a distributed load?

Distributed loads can be modeled as a single point force that is located at the centroid of the object. You can use straight-forward algebra, or use integration for more complex shapes. Then you replace the distributed load with the single point load acting at x distance.

## How do you replace a distributed load?

0:114:12(7C) Example: Replace a distributed load by a point force systemYouTubeStart of suggested clipEnd of suggested clipSo we have a 0 to L Q naught X over L DX dy so that’s just the integral of x squared. So we get QMoreSo we have a 0 to L Q naught X over L DX dy so that’s just the integral of x squared. So we get Q naught l squared.

## How do you find the equivalent force of a distributed load?

Finding the Equivalent Point LoadFinding the Equivalent Point Load. … The magnitude of the equivalent point load will be equal to the area under the force function. … Using the Area and Centroid in 2D Surface Force Problems: … The magnitude(Feq) of the equivalent point load will be equal to the area under the force function.

## How do you find the equivalent resultant force?

0:225:18Equivalent resultant force and couple moment – YouTubeYouTubeStart of suggested clipEnd of suggested clipSo the resultant force is equal to the sum of all the forces. We got two forces which is f1 plus f2MoreSo the resultant force is equal to the sum of all the forces. We got two forces which is f1 plus f2 f1 is equal to AI plus C R J minus 2k and sizzling kilonewtons f2 is equal to minus 2i.

## What is the force equivalent to the area under the distributed loading curve?

w ( x ) = Σ W i ℓ . This total load is simply the area under the curve , and has units of force.

0:044:58How to convert a UDL to Point Load – YouTubeYouTubeStart of suggested clipEnd of suggested clipSo how we achieve this is we multiply it by the length of the beam. So if we have 20 kilonewtons perMoreSo how we achieve this is we multiply it by the length of the beam. So if we have 20 kilonewtons per meter. Times 5 meters. You can see the units of meters cancel out.

## What is an example of a distributed load?

A continuously distributed external force is referred to as a distributed load. For example, the weight of a pile of snow on a roof is distributed over the area of the roof (Fig. 3.33). This means every unit of area bears some part of the total weight of the snow pile on the roof.

## How do you replace equivalent force couple system?

3:229:047.1 Replacing a Force with an equivalent Force-Couple systemYouTubeStart of suggested clipEnd of suggested clipAnd we have to replace this force P with an equivalent force couple system acting first at Point aMoreAnd we have to replace this force P with an equivalent force couple system acting first at Point a and then point B therefore we have to determine the magnitude. And direction of force RA.

## What is an equivalent force?

Two forces are said to be equivalent if they have the same magnitude and direction (i.e. they are equal) and produce the same moment about any point O (i.e. same line of action).

## How do you find the equivalent force couple system at point O?

0:008:34Equivalent Force Couple System example – YouTubeYouTubeStart of suggested clipEnd of suggested clipMoment you can draw at a which will behave dynamically equivalent to this okay. So to do that let meMoreMoment you can draw at a which will behave dynamically equivalent to this okay. So to do that let me reiterate you need to find the net force. And you need to find in that moment about point a.

## How do you solve a distributed load problem?

0:148:11Distributed loading on a beam example #2: triangular loadsYouTubeStart of suggested clipEnd of suggested clipAnd we also need to find out the location of the centroid of the shape of this distributed load.MoreAnd we also need to find out the location of the centroid of the shape of this distributed load. Because that will be important for us when we’re solving for the moment that it’s causing.

## How do you calculate uniformly distributed load on a beam?

The uniformly distributed load can be substituted by a concentrated load acting in the centre of gravity of the UDL. The total load on beam is the UDL multiplied by the length of the beam, i.e. 5 kN/m × 8.00 m = 40 kN.

## What is equivalent UDL?

EUDL (BM) The Equivalent Uniformly Distributed Load (EUDL) for Bending Moment (BM), for spans upto 10m, is that uniformly distributed load which produces the BM at the center of the span equal to the absolute maximum BM developed under the standard loads.

## How do you calculate uniformly distributed load?

The principle to calculate the reaction is similar to the example above. The uniformly distributed load can be substituted by a concentrated load acting in the centre of gravity of the UDL. The total load on beam is the UDL multiplied by the length of the beam, i.e. 5 kN/m × 8.00 m = 40 kN.

## How do you solve distributed load in statics?

0:148:11Distributed loading on a beam example #2: triangular loadsYouTubeStart of suggested clipEnd of suggested clipWe do solve for these we need two pieces of information we need the entire load that is beingMoreWe do solve for these we need two pieces of information we need the entire load that is being exerted on the object by the distributed load.

## What is distribution force?

A distributed force is a force that acts on a large part of a surface, not just on one place. The loading on the beam can be a distributed force or a force that acts at a single point. The intensity of a distributed force is the force per unit length, area, or volume.

## How to model distributed loads?

You can use straight-forward algebra, or use integration for more complex shapes. Then you replace the distributed load with the single point load acting at x distance. See in the truck example:

A distributed load is any force where the point of application of the force is an area or a volume. This means that the “point of application” is not really a point at all. Though distributed loads are more difficult to analyze than point forces, distributed loads are quite common in real world systems so it is important to understand how to model them.

## What is equivalent point load?

An equivalent point load is a single point force that will have the same effect on a body as the original loading condition, which is usually a distributed load . The equivalent point load should always cause the same linear acceleration and angular acceleration as the original load it is equivalent to (or cause the same reaction forces if the body is constrained). Finding the equivalent point load for a distributed load often helps simplify the analysis of a system by removing the integrals from the equations of equilibrium or equations of motion in later analysis.

## Why is distributed load important?

Looking ahead: Distributed load helps to model uneven loads. We’ll see it again as we do beam analysis

## How are magnitudes of distributed forces given?

It is also important to realize that the magnitudes of distributed forces are given in force per unit distance, area, or volume. We must integrate the distributed load over its entire range to convert the force into the usual units of force.

## Is pressure force over area?

While pressure is force over area (for 3d problems), intensity is force over distance (for 2d problems). It’s like a bunch of mattresses on the back of a truck. You can model it as 1 force acting at the center (an equivalent point load as in 3.3.2, or you can model it as intensity and divide the total force by the width of the truck bed (the distance that’s not visible in this image  ).

## Can we use the area/volume and the centroid/center of volume under the force function?

We can use the area/volume and the centroid/center of volume of the area or volume under the force function.