# I-Beam deflection

1. Mar 9, 2005

### hedons

Hi,

I am working on a project where I have an I-Beam supporting a cantilevered load.

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For ease of fabrication, I need change the cross section of this I-beam.

Due to other limitations:
1. I cannot increase the web thickness.
2. I cannot increase the I-beam height.

My options are to :
1. Increase the upper flange width.
2. Increase the lower flange width.
3. Increase the upper flange thickness.
4. Increase the lower flange thickness.

In order of their benefit, which of those four parameters, if increased in equal amounts, will help to minimize the beam deflection while under load?

I was not sure if there are general rules of thumb to apply here or If I actually need to determine the Moment of Inertia for each proposed cross section to carry out the beam deflection calculations.

Thanks!

Last edited: Mar 9, 2005
2. Mar 9, 2005

### FredGarvin

Does the cross section of the beam have to be constant for the entire length of the beam?

What do you consider a benefit? A smaller deflection? Since you are limited in the real beneficial changes you can make (short of material change which you did not mention) I would simply do my best to maximize your moment of inertia. If you set up a spread sheet, you can easily calculate the values with various geometry.

3. Mar 10, 2005

### hedons

Hi Fred,

It is a concentrated load at the end.

The beam doesn't have to be of a constant cross section, however there is nothing to be gained (except extra fabrication costs) by tapering it as the arm increases.

I'll set up the spreadsheet and start plugging in numbers.

Thanks again.

4. Mar 10, 2005

### minger

Yes, off the top of my head, the moment of interia of a rectangle is (bh³)/12 + Ad² where d is distance from CG???? Either way it's close I think, haha. based on this, I would think your best bet is to increase the flange thickness. Not only is moment of interia a function of h³, but it will also increase the CG of that rectangle slightly which will increase the distance from it's CG to the CG of the beam.........if I'm not mistaken.

5. Mar 10, 2005

### cincirob

"My options are to :
1. Increase the upper flange width.
2. Increase the lower flange width.
3. Increase the upper flange thickness.
4. Increase the lower flange thickness.

In order of their benefit, which of those four parameters, if increased in equal amounts, will help to minimize the beam deflection while under load?"

Assuming you're looking for lower stess or reduced deflection, adding material as far away from the centerline is the most desirable. One thing to beware of: If you make the beam asymmetrical, you can raise stress. For instance, if you made a t beam by taking the bottom flange off and adding that material to the top flange, your moment of inertial would probably decrease. The distance from the neutral axis to the edge where the bottom flange was will increase and that will result in higher stress.

You mentioned tapering the beam. For the load case stated you can reduce weight significantly. Basically you can have a small thickness at the end (enough to sustain the shear load) and the rest of the beam can be tapered so that it is at the maximum allowable stress for the material.

6. Mar 10, 2005

### Staff: Mentor

Also consider that the top of the beam is in tension while the bottom of the beam is in compression. So it would be ideal to have a thicker or wider flange at the top as opposed to the bottom.

7. Mar 11, 2005

### PerennialII

Yeah, if you're free to work with the profile even with the dofs you've given creating a changing profile from the tip would be optimal.