Crack on a Steel S-Beam

[Eigenvalue4]

Hi,

There is a situation where there is a carbon steel S-beam in bending. There is a vertical load in the middle of the length of the beam. Thus, the beam is in bending. The beam has a low ductility but has no cracks.

If a crack appears, what is the most likely place where it will appear on the bottom flange? Will it be most likely at the extremity of the bottom flange or in the middle of the bottom flange? The flanges of S-beams are tapered.

 

[BridgeSmith]

The most likely place for a crack due to overloading is wherever the steel reaches its strain limit after yielding and strain hardening first. This would be somewhere within the region that has necked down.

Cracks due to cyclic loading leading to fatigue would most likely occur in the region where the fatigue range in tension is the highest, specifically wherever there was an imperfection (damage, corrosion, rolling defects, etc.) that creates a stress riser.

In either case, it would be very difficult to predict the location where a crack would occur. In the case of overloading failure, it would be obvious that the beam was failing well before it cracks. Even a low ductility steel beam will strain noticeably before fracturing.

 

[JStephen]

This sounds suspiciously like homework.
My guess is that a crack is mostly likely to form at a place where there is some defect due to physical damage, arc strike, corrosion, etc.
In your diagram, you have a point load and pointy supports, and therefore have infinite stresses at each of those three points, which makes them rather suspect if there is no ductility.
In real life, there would likely be some sort of stiffener or welding or bolting at that center load, which would also be a good candidate.
I suppose the proper homework approach is to calculate bending and shear at each of those points, then use the failure theory of your choice to estimate failure. Which, come to think of it, means the answer would also require the beam length and beam properties to actually get results.

 

[Eigenvalue4]

This would be somewhere within the region that has necked down.

What do you mean by "region that has necked down"?

This sounds suspiciously like homework.

This is not a homework, I have graduated a while ago and I work as a structural engineer.

 

[BridgeSmith]

What do you mean by "region that has necked down"?

Watch around the 7 minute mark of this video:

https://duckduckgo.com/?hps=1&q=ten...&atb=v375-1&iax=videos&ia=videos&iai=https://

http://www.youtube.com/watch?v=fpKn8Sxk5WI