Deep beam theory

[3dboy]

OK guys here is a real test. When analyzing a pulley sideplate it occurred to me that the behavior of it was analogous to a cantilever deep beam. That being so I pulled out the handy dandy roark's and found that there is a considerable stess increase (on the order of 6-10 times) depending on the geometry. It then occurred to me that this would also apply to shear tabs as well. This makes shear tabs get fairly thick or long. It seems that there is a flaw in my logic, but I'm not sure where.

Any ideas?

Jeremiah

 

[DaveAtkins]

A shear tab is not a true cantilever, and AISC looks at this type of connection two ways. First, for the design of the bolts, it is assumed that the connection plate is bolted to the supported beam with enough bolts so that it becomes part of the supported beam, and the welds to the supporting beam take only shear. Second, for the design of the welds, it is assumed that the connection plate is welded to the supporting beam with enough weld so that it becomes a cantilever off the supporting beam, and the bolts to the supported beam take only shear. Actual behavior is somewhere in between these two extremes.

DaveAtkins

 

[3dboy]

Ok that answers the weld and the bolts, but it still doesn't answer what the plate itself is designed for. If it is being treated as a cantilever, there is some moment in it. As such it is going to be a deep beam.

 

[flamby]

As you go on reducing the span, bending stresses reduce and a point will come when even 6 to 10 times of bending stresses will not be critical and shear will be the main criterion. Shear tabs have a very small span so I think bending, even magnified as per Roark, will not be the chief mode of failure.

So there must be a point where even deep beam stops being a depp beam and becomes shear tab. I have myself never checked it and shooting straight from the hip.

 

[ChipB]

Hmmmm.....Try AISCs connection design book. Go under coped beams. There are some plate buckling formulae they use in calculating the connections. I don't know them off the top of my head. Probably should as many times as I've had to do it. If I understand this correctly, you're pretty much talking about the same type of thing. The design process includes the effect of the connection's eccentricity. For a pulley's side plates, increase the load by at least 25% for impact.

I think DaveAtkins is talking more about clip angles being used as a type of shear tab. Typically, clip angle shear tabs are not welded along the top, making them "flexible". In other words, they may rotate slightly to alleviate transferring moment due to the connection to the supporting beam. Plate shear tabs are typically "semi-rigid". Some moment will be transferred.

 

[3dboy]

Ok,

I looked that up, those give me my allowable stresses based on limiting the failure mode to plate buckling. That does not affect my calculation of the actual stresses (which is what Roark's gives) I'm still left, according to Roark's with a 6 to 10 times increase in actual bending stresses due to "deep beam theory"

 

[DaveAtkins]

I was referring to single plate shear tab connections, not clip angles. Bending of shear tabs is not a design consideration, because it will not control (see page 4-53 of the 1989 ASD).

DaveAtkins