Deflection Compatibility 1

[Quence]

Many structural textbooks such as Mcgregor's don't even have topics or words regarding "Deflection Compatibility".. what are other wordings or descriptions for it? Does it mean the strains of connecting elements have to be similar? Can you give example of elements with Deflection Incompability and compatibility?

 

[Agent666]

It doesn't mean the strains are similar, it means at any connected points the deflection must be similar to maintain deflection or deformation compatibility.

A example might be a pin based steel portal frame with a fixed base precast panel cladding panel on one side connected at the eave, the load carried by the portal or the panel will be such that at the eave the deflection must be compatible. You will find that due to the compatibility that there will be some load transfer between the two systems, for example under seismic loading the panel might resist a greater share of the total seismic load than the tributary load from the panel alone.

Another example might be a dual structure, with RC walls and RC moment frames, of which the two systems have quite a different fundamental behaviour on their own than when combined as part of a buildings lateral force resisting system. Put the two systems in series and the deflections at each level must be compatible, and forces develop between the two systems to maintain this compatibility.

Edit - like this image for second case

 

[Quence]

Any example of deflection incompatibility?

 

[Retrograde]

An example of deflection incompatibility would be joint slip. The fact that structures are incrementally constructed may also lead to deflection incompatibility.

One should note that the incompatibility is between the idealised structural model and the behaviour of real structures. Deflection compatibility is implied/necessary in the theoretical solution of any indeterminate system.

 

[Shu Jiang PEng SE]

for a continuous beam, the rotation angle of the beam at left of the intermediate support is equal to the rotation angle at right in magnitude, however one is clock wise and the other counter clock wise. This is deflection compatibility.

 

[BAretired]

Deflection compatibility refers to a method of solving statically indeterminate structures. For a determinate structure, reactions, moments and shears can be solved without considering deflection. For an indeterminate structure, compatibility of deflections must be considered.

For example, in the case of a propped cantilever, the structure is indeterminate to the first degree. There are too many reactions to solve with the equations of statics alone, but the problem can be solved by removing the prop, calculating the deflection of the cantilever at the location of the prop, then calculating the prop force required to restore the beam to its original position, or in other words, by using deflection compatibility.

BA

 

[Ron]

Another example of deflection incompatibility is with a wall under wind load. This is particularly true of cold formed steel (CFS) framing. Wood framing is usually overdesigned by default.

Consider a wall under lateral wind load with one or more windows in the wall. The corners of the wall are restrained by shear resistance, either through a 90 degree wall return or by termination of the wall into something more substantial such as a masonry or cast-in-place concrete intersection.

The studs for the wall are designed for stress, with only minor consideration for deflection, since that is moreso a serviceability issue. In an effort to create fewer problems for the contractor, the designer uses the same size/configuration/Section properties of the studs across the wall. When you get to a window opening, there is at least a doubling of the studs on either side of the window, sometimes a tripling or quadrupling of the studs considering the size and loading on the window.

Now consider that the face cladding on the wall is a rigid material such as stucco. Stucco has a typical maximum deflection criterion of L/360. This is commonly checked in one direction for the studs (individually), but is often not considered for the condition where the window framing creates a "hard spot" in the wall and the wall bends in two directions, not just one as the deflection check implies. The result is lack of consideration that bending occurs in the wall in a diaphragmatic condition, not just linearly as was checked. This leads to more potential for stucco cracking, water intrusion, and deterioration of the walls from this lack of appropriate consideration of deflection incompatibility. Leads to many thousands, perhaps millions, of dollars in damage to the structure.

Comments?

 

[271828]

Other wordings or descriptions that might be in your book:

Look for "Force Method," "Flexibility Method," or "Method of Consistent Deformations."

 

[BAretired]

Thanks 271828, I had forgotten those terms.

BA