Am I counting correctly? (Probably not)

[joakim_j]

Hello!

I am trying to figure out if a beam I have in mind (HEA200) is strong enough for the purpose I have in mind. I am not a structural engineer, but I still made some sort of attempt. The question is whether it is reasonable...

This concerns a beam that will be the support for an intermediate floor (only). The beam's length is 4.7 m, the total area of the intermediate floor is 38 sqm (the outer walls of the extension are 5x8 m, the beam is in the middle).

So... to my clumsy attempt at calculation...

Self-weight of floor: 0.5 kN/sqm
Imposed load: 2.0 kN/sqm

This gives a total distributed load of 2.5 * 38 = 95 kN, half of which is absorbed by the outer walls, and half by the beam, so the line load on the beam will be: 47.5 / 4.7 = 10.1 kN/m

The deflection will then be:

(5qL^4)/(384EI) where E = 210 GPa and I is 3692 * 10^4 mm^4, which gives about 8.3 mm deflection. That is approximately L/567, which can be considered acceptable.

Am I on the right track?

 

[Gabbe1]

I have not reviewed your entire calculation, but I did my own and found that the maximum deflection is 8.6mm.
So you seem to be in the right ballpark.

Edit.
When I check again, the difference is due to you calculating with 38m2 and I with 40. So we have calculated the same way and I can confirm that your calculation is correct.

 

[joakim_j]

I haven't reviewed your entire calculation, but I did my own and found that the max deflection is 8.6mm.
So you seem to be in the right area.

Edit.
When I check again, the difference is because you calculated with 38m2 and I with 40. So we actually calculated the same way, and I can confirm that your calculation is correct.

Thanks! Just to clarify, did you use any of my assumptions about loads etc., or did you do everything "from scratch"?

 

[Gabbe1]

Thanks! Just to clarify, did you use any of my assumptions about loads, etc., or did you do everything "from scratch"?

I usually use the same standard values you used, 50 kg/m2 dead weight and 200 kg/m2 load, as well as the assumption that half of the load impacts the beam (if it's in the middle). You usually get pretty close to the truth with these values even if there are things that can have an effect. For example, more than half of the load will impact the beam if the floor joists in the intermediate floor span uncut across the entire span. But mostly the above standard values and rules of thumb are enough to ensure you are on the right track when choosing a beam.