# Why buckling increases with depth of a beam?

"on increasing the depth unless the load is exactly on the right place the deep bar may bend by a process called buckling"

Why on increasing depth of a beam tendancy to buckle increases (only an intuitive explanation)? And what is the right place for the load to be in say a bridge such that no buckling whatsover occurs?

Shouldn't it be the opposite ie on increasing depth buckling should decrease because a thin ruler can buckle easily ?

I'm not sure where you got that quote, but it is very vague and not how it should be worded for the general case.

Buckling occurs due to eccentric loads, primarily on slender columns. Slenderness is the ratio of length to radius for a round column. A thin ruler is much more slender than a pop can, because a pop can is less length (shorter) and has a greater effective radius (ruler isn't as wide on any side).

That said: They may be talking about a situation closer to Lateral-Torsional Buckling similar to that pictured on the page:

If you were to increase the depth of the beam, it would be more prone to buckling in the middle in the fashion described there. This is quite a bit different from regular buckling though.

In this case, increasing the depth would be the same as increasing the slenderness ratio for the beam in the vertical direction. A big factor with this type of bucking has to do with the length of the beam though. When you apply the force far away from the supports of a beam it has a tendency to twist and bend (especially if it is more slender, the deeper it is, the bigger the moment you create around the middle when loading the top).

As far as your second question goes, real bridges have distributed loads. If you have to point load the bridge, do it near a support, preferably a very strong one.

If you're trying to build a bridge (sounds like it might be a project), consider that buckling wont be the only thing that can go wrong. Making the beams "deeper" will reduce the bending, but given some circumstances they will still easily buckle through the lateral-torsion.

Here is a (very bad MS paint) diagram I made of the forces.

Obviously in reality the angle would be a lot smaller, but you see if there's and eccentricity of the load, the deeper beam will have a bigger moment, because the force is the same, but $R \gt r$ so the moment on the deeper beam is greater, causing more twisting.

• Buckling and bending whats the difference? You said it would be more prone to buckling in the middle but isn't buckling caused due to compression at ends ? – Matt Mar 21 '17 at 21:01
• @RaghavSingal In Lateral-torsional buckling the beam would be twisting toward or away from us in that picture. Bending would make it bend up and down. The twisting is usually really bad for the beam even if it isn't noticeably bending up and down. – JMac Mar 21 '17 at 21:05
• Why when we apply force far away from supprt of beam it buckles more why does it even buckle when load is not providing longitudinal stress ? – Matt Mar 21 '17 at 21:14
• Basically what I am asking is where on a beam exactly and in what direction forve should be applied which causes the beam to buckle ? – Matt Mar 21 '17 at 21:15
• @RaghavSingal If you apply it near the middle of the beam it is free to twist more so this effect is worse. Even if you try to apply the force to the very middle of the beam, it still can develop more moment faster if it is deeper. I added a new (badly computer drawn with paint) picture of it. Also, you'll never get the load right in the middle, so there will be some moment, a "deeper" beam is worse for that. – JMac Mar 21 '17 at 21:30