# Calculating Weight Savings with Rectangular Section Beam

• MMCS
In summary, the question is asking for the minimum dimensions of a square section cantilever beam to carry a concentrated load of 10 kN at its free end without exceeding a maximum bending stress of 30 MPa. The answer to this question is 182mm. For the second question, the percentage savings in weight when using a rectangular section beam with a depth equal to twice its width is 29.6%. However, this would also result in a reduction in load bearing capability, so there would need to be an increase in depth for the same load bearing capacity. The formula used for the first question is x*x^3/12, but for the second question, the breadth and depth (b and d) must be used
MMCS
Here is the original question, i know the first answer as 182mm

A square section cantilever beam, 3 m in length, carries a concentrated load of 10 kN at its free end. If the maximum bending stress is not to exceed 30 MPa determine the minimum dimensions of the section.

Ans 182mm,

What would be the percentage saving in weight if a rectangular section beam, having a depth equal to twice its width, were to be used instead?

Intuitively it seems there would be a weight reduction of 50% if the width dimension was halved however I have the answer to be 29.6%, does somebody know how i would get to this?

Thanks

Why don't you show some calculations and see if the answer pops out.

MMCS said:
Intuitively it seems there would be a weight reduction of 50% if the width dimension was halved
Equally intuitively, it would have half the load bearing capability. There would have to be a corresponding increase in depth.

How would i use this in the fomula? To solve the first question i used I to be x*x^3/12, but now because it is of rectangular cross section i would use b and d, however this gives me two uknowns

You know a relationship between breadth and depth. From the OP, assume D = 2*B

Here is my working, i am a few percent off, can you see any mistakes?

#### Attachments

• working.png
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## What is a rectangular section beam?

A rectangular section beam is a structural member that has a cross-section in the shape of a rectangle. It is commonly used in construction and engineering projects, such as bridges and buildings.

## Why is weight savings important in beam design?

Weight savings is important in beam design because it can reduce the overall weight of a structure, leading to cost savings and improved performance. It also allows for more efficient use of materials and can make construction easier and faster.

## How do you calculate weight savings with rectangular section beam?

To calculate weight savings with a rectangular section beam, you first need to determine the weight of the original beam using its dimensions and material properties. Then, you can calculate the weight of the new beam using different dimensions or materials. The weight savings is the difference between the two weights.

## What factors affect weight savings in beam design?

The factors that affect weight savings in beam design include the dimensions and shape of the beam, the material used, and the support conditions. Other factors to consider are the load and stress distribution, as well as the desired strength and stiffness of the beam.

## How can weight savings impact the structural integrity of a beam?

Weight savings can impact the structural integrity of a beam by reducing its load-carrying capacity and stiffness. This can lead to deflection, bending, and ultimately failure of the beam. Therefore, it is important to carefully consider weight savings in the design process and ensure that the beam can still meet the required structural requirements.

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