Is the Second Moment of Area a Universal Property of Beams?

[Iclaudius]

Hello my friends, so I am once again confused

Is the second moment of area a universal property of a beam i.e the beams cross section?
So what i mean to say is - if i have a beam and it is curved with a rectangular cross section, and take this same beam and ensure it to be now straight - will the second moment of area be the same in the two beams?

I = bd^(2)/2

where b =width
and d = depth

(let me know if my asking for help is poorly worded)

Appreciate the help,
Claudius

 

[Mech_Engineer]

Yes, the second moment of area is only dependent on a 2-D section of the beam. As long as the cross-section is uniform along the length of the beam, you should be good to go.

 

[SteamKing]

For a rectangular section, I = bd^3/12 about the centroidal axis. Second area moments have units of L^4.

 

[Studiot]

if i have a beam and it is curved with a rectangular cross section, and take this same beam and ensure it to be now straight

I'm confused about what you mean here.
Are you suggesting you apply some preload to straighten the beam longitudinally?

Your analysis will still be the same, with the same values for I so long as you remain within the conditions for engineering beam theory. That is a preload will not affect I.

The principal ones are:

Plane sections remain plane.
Deflections are small compared with the length.

And, of course, you add in the effect of any preload to your calculations.