analogy of a cantilever 3

[biheja43]

Hi,
Anybody got an idea about analogy of a cantilever to estimate the moment and a deflection in a sway frame which is statically indeterminate I need to know the procedure for this method Regards

 

[OldPaperMaker]

biheja43,
If you are referring to the Column Analogy method for finding the moments, shear and deflection of indeterminate structures you will have to dig up the text book that you used for that undergraduate class in indeterminate structures.

 

[ishvaaag]

Well, it comes to my mind a method that uses substructures taking floors separately with hinges at midheight of the columns at typical floors and at some other point at the 1st floor (2/3 of height column to zero level?). Essentially you were determining results for each substructure, starting atop, since the fixed moments to be relaxed were chosen proportional to the inertiae of the columns.

Note that such approach can become grossly inaccurate when precisely like a cantilever the lateral deformation puts entire levels of columns in single curvature. So no deal for tall buildings.

This notwithstanding I may have a book by Takabeya (surely in some closet I don't open but maybe twice a year) that calculated tall structures by akin simplified methods, and in fact know of 1 building about 100 m tall calculated by Takabeya's rule (I think it had some kind of mega-structure setup, with main frame sustaining a number of smaller inset frames).

Also, of course, one could presently engage in a work of matching the lateral deformations of particularly tuned cantilevers to those of frames. This is surely more long than difficult today with structural analysis packages.

 

[Lion06]

The short-hand methods I learned were the portal frame method and the cantilever method. Neither of them, however, are helpful for finding the deflection of a sway frame - they are really for determining shears, moments, and axial forces.

I don't know of a way to estimate the deflection of a sway frame. You might just have to bite the bullet and use something like the slope-deflection method or Castigliano's theorem (personally, I'm a big fan of Castigliano).

 

[Qshake]

And keep in mind that estimates from the portal method or the cantilever method can, in cases, greatly overestimate shears and moments. Also know that along with not providing deflections, if the EI or rigidity changes within the make up of the frame or frames, the results will be less accurate than with constant EI.

Regards,
Qshake

Eng-Tips Forums:Real Solutions for Real Problems Really Quick.

 

[cap4000]

Can you get the Linton Grinter book called the "Theory of Modern Steel Structures" published in 1949. On pages 140 & 141 it has an approx' way to determine the deflection of a frame. It has an angular distortion of the frame and its deflection based on the end moments of the column. Grinter has a 6 story building totally worked out.

 

[paddingtongreen]

Is this a simple portal frame?

Michael.
Timing has a lot to do with the outcome of a rain dance.

 

[biheja43]

Yes its simple portal frame.
are the centroidal distance method and cantilever analogy same method? what confuse me is that in centroidal distance method assume the area of the internal columns are double the exterior columns which I don’t think the analogy of cantilever have this assumption!!!

 

[OldPaperMaker]

biheja43,
We may be experiencing a language problem here. My old text, in USA english, referres to one of the classic methods for solving indeterminate structures as "Elastic Center and Column Analogy Methods". It is like Moment Distribution, Slope Deflection, Work & Energy, etc. They all start with the differential equation of bending.These are not processes like the Portal Method. They are real different.

As in my original suggestion, if the Elastic Center & Column Analogy is what you are referring to that you get out a text book on indeterminate structures and start refreshing your self on these methods. It is not rocket science but it is also not something that one can explain in a forum like this.

I have never heard of something called the "cantilever analogy".

 

[Lion06]

OldPaperMaker-

The cantilever method is very similar to the portal method. The portal method assumes pins at mid-height of the columns and you start with shears to determine axial loads and moments. The cantilever method starts with axial loads to determine shears and moments.

 

[paddingtongreen]

Here is a monograph by Professor Hardy Cross on Column Analogy.

http://cobweb.ecn.purdue.edu/~ce474/Docs/ColumnAnalogy_HardyCross.pdf

Michael.
Timing has a lot to do with the outcome of a rain dance.

 

[BAretired]

The cantilever analogy is not a technique I have used, but here is a PDF on the subject:

http://www.google.ca/url?sa=t&source=web&cd=10&ved=0CFsQFjAJ&url=http://

http://www.wpi.edu/Pubs/ETD/Availab...LNss3TK4Q&sig2=2n3QInpVpWXwOXT1rWiMNw&cad=rja

BA

 

[Splitrings]

This can be solved by virtual work methods fairly easily. This is really the same as Castigliano's method, but is easier for me to follow. If it is simple 2-D portal frame without axial deformations the flexibility or stiffness methods can be used.

 

[paddingtongreen]

If this is a simple portal, and the columns are of the same stiffness, and if the horizontal load is applied at the beam level, the problem is statically determinate. There will be a point of inflection, or contraflexure if you prefer, at midspan. You can place a hinge there and the moments can easily be calculated. It is not difficult then to calculate the rotation of the joint and the deflection of the column due to this rotation and to it's own bending.

Michael.
Timing has a lot to do with the outcome of a rain dance.