How to find a beam for my (simple) application

Question

I have a spanof 9m that I bridge with a (as yet unspecified) beam. From this beam hangs a load (a pipeline), right in the middle, of 4.295 kN. The beam is simply supported. I want to use an IPE steel beam. How do I go from here to specifiying the exact size? I'd appreciate a specific answer, but more importantly a walkthrough.

I understand I have a bending moment of 5.163 kNm. Now I need to divide this moment by the moment of inertia (that I can find in the right table) and I arrive at a stress. So my question is, which specific of the many moments of inertia my Lölner Stahlbautabellen list is the right one, and what is a decent assumption for max stress, and what margin of safety to apply.

The purpose of this question is a) to arrive at a size that's no too far off, for puprpose of a drawing and maybe cost estimates, and b) to educate myself a bit. Before the structure is built, we will run this by a structural engineer, which brings me to purpose c) not to look ridiculous with a horribly under- or oversized beam.

Answer 1

Depending upon your region, codes, safety factors can change. In essence, someone else typically comes up with the safety factor, while we come up with the maximum stress. However, you are performing one of the many functions of newly graduated engineers who do not have a license and need to perform work outside school before they can be licensed. The order of operations here is simple. You will usually want a spreadsheet.

1. Guess a safety factor. For steels, use 2.2 for this step.
2. Take the load and multiply the load by a safety factor before beginning (due to non-linear effects, it is considered better practice to increase the load instead of reducing the allowable stress, though for your beam it will not matter).
3. Calculate the moment for this setup as described. You calculated incorrectly, the maximum moment in the middle would normally be $\frac{PL}{4}$, where L is the span of the entire beam (9m), so the moment is 9,663.75 Nm. With 2.2 multiplies it is 21,260.25 N*m (round in last step).
4. Divide by the yield stress for the steel you intend to use (290 MPa is typical for this kind of beam).
5. Glance at your list of beams that are near this value (the IPE 160 and the IPE 180 are close. The IPE 160 is a bit light, but we had a lot of safety.)
6. Record in your spreadsheet the 3-4 sizes that work closely. Go a bit above and a bit below. You also need to record the kg/m for the beam.
7. Calculate the load from the dead weight. This works out to $\frac{9.81*w*L^2}{8}$, where w is the kg/m for the beam, L is the full span.

8. Using this information, now calculate the actual factor of safety when using this beam.

   1. Multiply the dead load by 1.1 and the pipe weight by a safety factor in a cell.
   2. Determine the stress by dividing by the actual beam section and compare to the yield strength (290 MPa).
   3. Setup a solver in the spreadsheet to change the safety factor until it finds a safety factor such that the stress in the beam is equal to the yield stress.

With the various factors of safety, you now know how these beams perform. 1.6 can be used for light loading, 1.8 is typical for most loading, and some people will ask for factors of safety of 2 or greater in unusual circumstances. For this application, finding a beam that meets a minimum of 1.8 will probably be satisfactory. Show all work, including the spreadsheet printout to your structural engineer, who can best advise on what the code says is allowed and what yield strength to use.

Answer 2

You could use this to calculate moment of inertia:

https://www.amesweb.info/SectionalPropertiesTabs/SectionalPropertiesIbeam.aspx

Assuming you put the beam like an I, you use the Ixx in your stress calculation.

Factors of safety are application specific so I cannot reasonably suggest one. Important factors determining a factor of safety are:

How sure you are the load is the stated load, temperature, dynamic loads that cause fatigue,stress concentrations,how the beam was made and many other factors can change material properties.

You can be really conservative and put a factor of safety of 4-6 times if you don't know what you are doing and chances are, it "might" be okay.

Another thing to think about is that the beam will also need to support it's own weight, so that should also be in your calculations in the form of a load at the center of mass of the beam.

You can also learn from "structurefree" in youtube who teaches these kinds of things.

And at the end of the day these calculations are "ballpark" calculations, so they aren't absolute, it might work or it might not.