Basis of T-Beam effective width

[Enhineyero]

I was wondering, why is the T-beam effective width a function of the span length? or to be more precise for relevant codes a function of the points of contraflexure for sagging bending moments.

Hope someone could help

 

[KootK]

It's instructive to think about this in strut and tie terms. The compression in the flange originates down at the tension face and spreads out laterally as it makes it's way up. It takes a bit of beam length in order for that load spreading to kick in.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[Enhineyero]

Hi Kootk, interesting answer, (on plan) what is the angle of distribution of the compression component of the strut

 

[hokie66]

KootK may have good insight into how the flange actually reacts, but I doubt that was the basis for the ACI Code provisions, which go back at least 60 years, before we began to talk about strut and tie.

 

[KootK]

While the term "strut and tie" is a fairly recent addition to the structural lexicon, the underlying concept of the truss analogy dates back to Ritter and Morsch at the turn of the 19th centurary. Engineers have been thinking critically about the disposition of compression in RC members for just about as long as there have been RC members.

Regardless, it was not my intent to suggest that the effective flange width provisions were based on strut and tie analyses. Rather, I was merely suggesting the use of strut and tie visualization as a device for understanding the need for a span based limit on effective flange width.

The code provision would seem to imply a load spread of about 1:4. For comparison, other code provisions (walls) in ACI imply load spread of 1:2 and, were strut and tie methods to be used in earnest, one could conceivably bump that up to around 1:1.5.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[rapt]

Kootk,

And we always thought your answers were based on deep thinking theory!

It is due to the fact that the compression stress in the slab drops off as you move away from the web due to shear lag. The effective width is an attempt to define a width over which the stress assuming constant stress over the flange width would give a reasonable estimate of this drop off. It is related to span length (and distance between points of contra-flexure) in many codes because the dispersion width will be greater in a longer span length. Those rules are based on UDL's however. For major concentrated loads it should be related to the distance from the maximum +ve moment point to the point of contra-flexure of the concentrated load is not at mid span.

 

[KootK]

Whether you're talking STM or shear lag, the issue du jour is load spread. With shear lag, you're usually considering a parabolic drop off based on an assumed linearly elastic material. With STM, you're assuming that the concrete crushes locally and the compression forces get redistributed. I don't know that either view gives a much "truer" picture of load spread than the other. I'd like to think that the ACI provisions were based on testing done at some point in time but, at present, I'm not aware of any such testing.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.