kleinlogel rigid frame VS Kinematic Method 4

[JonnoR]

Hi,

Im trying to assess the benefit of plastically analysing a portal frame against elastic analysis.
Therefore im currently trying to compare the difference between kinematic and kleinlogel for a simple portal frame analysis.

My thoughts are to assess the bending moments produced by each frame. Then compare the two against eachother with safety, cost ect as considerations.

Kinematic method should win as it will allow the use of a plastic hinge to form therefore giving the frame a higher bending moment capacity.
I have never used kleinlogel before but it seems the best option for an elastic comparison. I've found the formulas for kleinlogel but no formulas contain both a horizontal and vertical force similar to my current frame design.
The frame has two pinned feet and will assume two rigid connections for the connections between column and beam as to follow kleinlogel.

If someone could help to explain or even provide a calculation using kleinlogel for my frame and forces that would be great. (Visual learning is easier)

I have completed my kinematic analysis and have the bending moment capacity.

 

[BAretired]

Have you looked at Kleinlogel Case 39/2 and 39/7? Case 39/2 is for uniform load, but it should be easy enough to figure the case for a point load. Case 39/7 show results for a horizontal load at top left. The two cases can be combined by adding their results together.

Alternatively, work it out for yourself. It is pretty straightforward.

 

[JonnoR]

Thanks for that. I just analysed the frame using the method and then combined the two frames with superposition.
Kinematic Method finds the collapse load for a frame.
Kleinlogel finds the bending moment for a frame under a given load (not collapse load) so this might not of been the correct theorem to use. How would I find the collapse load for the elastic frame? On the positive I do now have the BM diagram.

As I'm trying to find the additional capacity plastic analysis I need some common ground for the two methods.

 

[bridgebuster]

nice to know I'm not the only one who still uses Kleinlogel.

 

[HTURKAK]

I agree with BARetired. You need to combine case 39/2 and 39/7..

He is like a man building a house, who dug deep and laid the foundation on the rock. And when the flood arose, the stream beat vehemently against that house, and could not shake it, for it was founded on the rock..

Luke 6:48

 

[BAretired]

How would I find the collapse load for the elastic frame?

You wouldn't. Elastic design does not give you the collapse load. That would come from a Plastic analysis.

Looks like the 14kN horizontal load didn't have much effect. Following are the results I found. The maximum positive moment occurs at the large 385kN gravity load, point E.

 

[JedClampett]

I'm surprised that anyone uses Kleinlogel. I've still got a Xerox copy, probably from 1976. 43.97 at Amazon. Hmmm? Man I'm tempted. It cost me $16 for an Old Fashioned!

 

[BAretired]

It was the go to reference for rigid frames in its day, but today, most engineers have frame programs which makes life a little easier. I find some of the Kleinlogel symbols a bit distracting.

 

[robyengIT]

I found different numbering but something similar. Furthermore it keeps in account the different values of "J" of column and horiz. beam

 

[StrEng007]

nice to know I'm not the only one who still uses Kleinlogel

I find some of the Kleinlogel symbols a bit distracting

I've got both books, rigid frames and multibay frames. I hate to say, I haven't even figured out how to navigate the multibay frames edition, it's so confusing.

 

[robyengIT]

as alternative solution you can dowload (free)this publication/manual

https://www.steelconstruction.info/images/9/9b/SCI_P292.pdf

 

[civeng80]

Pardon my ignorance but what is the kinematic (presume analysis) method ?

 

[BAretired]

I had never heard of it before either. It is just another name for Plastic Design.

 

[civeng80]

Ah yes kinematic as in the moving plastic hinges.

Thanks.

 

[HTURKAK]

Just for info.
The kinematic or collapse mechanism method is one of the plastic analysis methods. In this method , a collapse mechanism is assumed then with virtual work equations BMD calculated.

The other methods as far as i remember , incremental and statics method.

The OP states that he has completed kinematic analysis and have the bending moment capacity. I will suggest if he can post his calculation to see his approach.


Assuming constant section for beam and columns, ( the plastic moment is the same for all the frame elements ) , the plastic hinge develops at midspan of the beam ( at pt E at BAretired's second post, and a magenta big star for him ) but in order to get a collapse mechanism , at least two plastic hinges shall develop for the subject str. However , the second hinge location would at B but not with horizontal load 14 kN.




He is like a man building a house, who dug deep and laid the foundation on the rock. And when the flood arose, the stream beat vehemently against that house, and could not shake it, for it was founded on the rock..

Luke 6:48