# Calculating Deflections of I-Beams with Varying Loads and Supports

• PTW
In summary, the conversation discusses the objective of being able to calculate the vertical deflection of I-Beams, using a pair of parallel beams with a single load and various lengths and load capacities. It is mentioned that a solid background in strength of materials is necessary and that there is no single simple formula for this calculation. Safety precautions are also mentioned. The conversation concludes with a suggestion to refer to a specific resource for more information.
PTW
My objective is to be able to calculate only vertical deflection of I-Beams (i.e. knowing which formula to use).

Constants:
Using a pair of I-Beams running parallel to each other with a single load being applied from directly above. The load sits on a steel plate across both Beams that are 4" apart. The Beams are pinned at each end with the single load centered half way (i.e. 12' beams with load applied at 6').
Variables:
The only two shapes of beams being used are S, and occasionally W. The most popular models being S10x35, S15x50, S18x70, and possibly a W12x40.
Beams will have a minimum rating of 50ksi (A992 or A572)
Beam lengths can vary from 8' long to 20'
Total loads vary from 120k to 260k (for the two beams to carry).

Thank you!

#### Attachments

• I-Beam Test.jpg
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Get a copy of Steel Construction Manual, by AISC. You need a solid background in strength of materials in order to understand it.

For the loading you show, you need to check for web buckling and shear in addition to bending. There is no one single simple formula. You need to do it right, or find somebody who knows how to do it right.

And do not stand near that setup when testing. If something let's loose, bad things can happen very fast.

@PTW -- your Profile page shows that you have a BSME and are working on your MSME. Can you say what courses you have taken that should help you to make this kind of calculation? Thanks.

PTW Profile Page said:
Location:
SW US
Occupation:
Field Engineering
University:
Mizzou
Education in Progress:
Masters
Completed Educational Background:
Favorite Area of Science:
Mechanical Engineering, Telecom

Last edited:
You may want to look at this summary too.

http://ruina.mae.cornell.edu/Courses/ME4735-2012/Rand4770Vibrations/BeamFormulas.pdf

Dale said:
You may want to look at this summary too.

http://ruina.mae.cornell.edu/Courses/ME4735-2012/Rand4770Vibrations/BeamFormulas.pdf
Thank you, Dale.

@PTW If you have completed a BSME as Berkeman indicates, surely you took a mechanics of materials course (not to mention a machine design course) in which you would have learned how to calculate the deflections of a uniform beam on simple supports. Is there something unusual about this case?

berkeman

## 1. What is I-Beam deflection?

I-Beam deflection is the amount of bending or sagging that occurs in an I-shaped steel beam when a load is applied to it.

## 2. How is I-Beam deflection calculated?

I-Beam deflection is calculated using the beam's material properties, dimensions, and the applied load. The most commonly used method is the Euler-Bernoulli beam equation, which takes into account the beam's cross-sectional area, length, and the modulus of elasticity of the material.

## 3. What is the formula for calculating I-Beam deflection?

The formula for calculating I-Beam deflection is: d = (5*W*L^4)/(384*E*I), where d is the deflection, W is the applied load, L is the length of the beam, E is the modulus of elasticity, and I is the moment of inertia.

## 4. What factors can affect I-Beam deflection?

The factors that can affect I-Beam deflection include the material properties of the beam, such as its modulus of elasticity and yield strength, the dimensions of the beam, and the type and magnitude of the applied load.

## 5. How can I reduce I-Beam deflection?

I-Beam deflection can be reduced by using a stiffer or stronger material for the beam, increasing the beam's dimensions, or by adding additional support, such as columns or braces, to the beam.

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