What is the distance of the resultant from point A on the beam?

In summary, the conversation is about calculating the resultant force and distance of a distributed load on a beam. The force is correctly calculated as 9.1877, but there is confusion about the distance which has been calculated as 2.0350 instead of (1/2*(43/10)). The correct distance is needed to accurately determine the moment caused by the resultant.
  • #1
tigertan
25
0
hi there,


I'm getting very very confused about distributed loads.

I am trying to figure out the resultant force of a distributed load on a beam. The function I've been given for q(x) is a polynomial (below x=0).

I have figured out the resultant for my function q(x)=x2-2x-4. I believe it is 9.1877 (positive being in the vertical direction). Length = 43/10

To find the distance of the resultant from point A on the beam, I have worked it out to be (1/2*(43/10).

I don't feel that the distance I have worked out it right and I'm not 100 percent sure about the resultant force either. Could someone please set me off in the right direction?

Thanks in advance.
 
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  • #2
Hi,

The force of 9.1877 is correctly calculated. It is the integral of the load.

Now to find the position of the resultant, we first calculate the moment around the point x = 0.
M = int (x * q(x)) dx between x = 0 and x = 4.3
= int (x^3 - 2x^2 - 4x) dx between x = 0 and x = 4.3
= - 4.1546
(negative because load works vertically)
This has to be equal to the moment caused by the resultant:
M = Fd
with d the distance from the point x = 0.
Hence
d = M/F = 2.0350

This is close to your (1/2*(43/10), but not exactly the same. How did you get there?
 

1. What is a distributed load force?

A distributed load force is a type of force that is spread out over a surface or area, rather than being applied at a single point. This can include forces like weight, pressure, or tension that are distributed across a structure or system.

2. How is a distributed load force different from a point load force?

A point load force is a force that is applied at a single point, while a distributed load force is spread out over an area. Point load forces can be represented by a single vector, while distributed load forces require a more complex representation, such as a load function.

3. What are some examples of distributed load forces?

Examples of distributed load forces include the weight of a person standing on a bridge, the pressure exerted by wind on the surface of a building, and the tension in a cable that is supporting a heavy object.

4. How do distributed load forces affect structures and systems?

Distributed load forces can have a significant impact on the stability and strength of structures and systems. They can create bending, shear, and torsion forces, which can cause deformation, stress, and ultimately failure if not properly accounted for in the design and engineering of the structure.

5. How do scientists and engineers calculate distributed load forces?

Calculating distributed load forces can be a complex process, as it involves determining the load function, which describes how the force is distributed across the surface or area. This can be done using mathematical equations and models, as well as through experimental methods, such as strain gauges and load cells.

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