# Solve Simple Loading System: Express Resultant Force in i & j

• Lmck33
In summary, the question asks you to express the 6.25kNm resultant force at the 2m mark using the unit vectors i and j.

## Homework Statement

The question is fairly easy, however the way they want the answer displayed is doing my head in.. Anyways the questions states

"replace the loading system by an equivalent resultant force (express your answer in terms of the unit vectors i and j)"

The question is a simple beam with forces along different sections, refer to the image I've uploaded to see what I'm talking about.

## The Attempt at a Solution

I know that the resultant Force lies along the beam at the 2metre mark and the force at this particular point, is 6.25kN I believe...

Any help is greatly apprechiated, I'm a little new to the whole vector thing, so forgive me. Thanks in advance

Lmck33

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• F4-31.jpg
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Well if you move a load to the centroid, you get the force at the centroid and a resulting moment.

So if you move the 2.5kN to the 2m mark, you will get a clockwise moment of 6.25kNm.

Understand?

But I too am not sure about how they want the answer expressed. (with respect to the i component that is)

Hi thanks for the reply, I understand that if I move 2.5kN to the 2m mark, I will get a clockwise moment of 6.25kNm. However the question asks me to "Express my answer using the unit vectors i and j" How would I express 6.25kNm into its appropriate unit vectors?

The 6.25 is in the j direction

Ah Thank you so much. The answer was j(6.25) kN. Life savers :D

what was the answer to this question? j(6.25) doesn't seem right to me

the answer to this was Fr = vector J (-6.25)kN.

didn't u need to express a value for i? like 0i-6.25j?

I suppose you could... Are you doing the same question in mastering engineering or mastering physics?

mastering engineering

all my answers are getting rejected for some reason, is there something I'm missing? :S

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Have a look at that attached image of mine... Maybe that can help you.

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• a.png
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Nvm i got it, was entering unit wrong.

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hahah no worries man, should of mentioned that you needed to select the vector button :S. Module 3 is looking fun ay :D

## 1. What is a simple loading system?

A simple loading system is a structural system where the external forces acting on the system are applied at only one point or in one direction. This means that the forces are either parallel or perpendicular to the surface of the structural element.

## 2. How do you express the resultant force in i and j components?

To express the resultant force in i and j components, you must first determine the magnitude and direction of the forces acting on the system. Then, you can use vector addition to find the resultant force, and finally, resolve the resultant force into its horizontal (i) and vertical (j) components using trigonometry.

## 3. What is the purpose of expressing the resultant force in i and j components?

Expressing the resultant force in i and j components allows us to break down a complex force system into simpler components. This makes it easier to analyze and understand the effects of the forces on the system, as well as calculate the resulting displacement and deformation of the structure.

## 4. What are the units for the i and j components of the resultant force?

The units for the i and j components of the resultant force are the same as the units for the original force components. For example, if the original force components are given in Newtons (N), then the i and j components of the resultant force will also be in Newtons (N).

## 5. Can the resultant force be expressed in i and j components for any type of loading system?

Yes, the resultant force can be expressed in i and j components for any type of loading system, as long as the external forces acting on the system can be represented as vectors. This includes systems with multiple forces acting at different angles, as well as systems with forces acting in three dimensions.