Fixed connections formulas 1

[Quence]

I need reference for the moments and reactions if the connections are all fixed instead of pinned (see attached image)

 

[Agent666]

I assume the following might be what you are discussing, though the terms you use are confusing my poor brain.

Etabs has the ability to define a rigid offset for the joint regions, and you can use a factor between 0 and 1 to select the degree of 'rigid end offset' used to represent the joint regions. At 100% (1.0 ratio) the joint region is connected by infinitely rigid members out to the face of the joint region for any intersecting members, essentially accounting for no deformation in the joint region during the analysis.

Set the ratio to zero assumes that the members and their stiffness carries through to the node location. Setting it to an intermediate value sets a rigid region equal to the ratio of the joint width in a given direction and then the remainder of the joint region is set to the equivalent stiffness of the incoming member.

I believe the treatment of joint regions during the analysis is covered in the help, so check there just to make sure I've got it right as not sitting in front of Etabs at the moment!
Something like this will be in the help file

Why don't you provide a model and/or a markup/sketch of exactly what you are asking, as I'm confused when you talk about neither fixed or pinned and then talk about moment connections and reactions when you perhaps imply internal design actions, etc, etc.

 

[Quence]

Simply.. when designing a simple beam connection to 2 columns at the end.. do you use the formula of the moments of the beam fixed at both ends and uniformly distributed load...

M max (at ends) = wl^2 / 12
M (at center) = wl^2 / 24
Mx = w/12 (6Lx-l^2-6x^2)

Or do you use the formulas for beam pinned at both ends and uniformly distributed load....
M (at center) = w l^2 /8
Mx = wx/2 (l-x)

??

 

[BridgeSmith]

"...do you use the formula of the moments of the beam fixed at both ends and uniformly distributed load..."

Unless the columns are infinitely rigid (which they never are), the ends are not fixed. If the connection can carry moment, the ends are partially restrained based on the stiffness of the columns - it's a frame.

"Or do you use the formulas for beam pinned at both ends and uniformly distributed load..."

If the ends are pinned or are configured to allow rotation of one member relative to the other with minimal resistance, modeling them as pinned should approximate the behavior.

It's really very simple; the model has to reflect the reality of the actual structure to be built.

 

[BAretired]

Simply.. when designing a simple beam connection to 2 columns at the end.. do you use the formula of the moments of the beam fixed at both ends and uniformly distributed load...

M max (at ends) = wl^2 / 12
M (at center) = wl^2 / 24
Mx = w/12 (6Lx-l^2-6x^2)

Or do you use the formulas for beam pinned at both ends and uniformly distributed load....
M (at center) = w l^2 /8
Mx = wx/2 (l-x)

If you were analyzing it by hand, you could start with either of those cases. Depends on which method you choose.

Using moment distribution, you would start with fixed end moments and distribute according to stiffness of members, correcting for side sway if necessary.

Using slope deflection method consistent deformations, you would calculate the rotation at each end of the beam, then determine the moments required to equalize the slope of each column and beam.

Using ETABS (or any other frame program), you would input the geometry, degrees of freedom of each joint, member properties and load. You would not input any moments. You would allow the program to analyze the structure and output the final moments. Finally, you would do a sanity check to ensure you were in the ballpark.

BA

 

[ThomasH]

Quence:

I assume that you are trying to understand how Etabs handles flexible connections.

Try this:

A simple continous beam (2 spans). Run it with a fixed (rigid) connection and with a free (pinned). Those are the two extremes and you should know the correct results.
Next, try with a flexible connection and see how you input the flexibility and how the results change.

In some software's the connection is defined as a spring, in others the connection is defined in fractions or percent. And the latter can from a mathematical point of view be strange.

Good Luck

Thomas

 

[Quence]

If you were analyzing it by hand, you could start with either of those cases. Depends on which method you choose.

Using moment distribution, you would start with fixed end moments and distribute according to stiffness of members, correcting for side sway if necessary.

Using slope deflection method, you would calculate the rotation at each end of the beam, then determine the moments required to equalize the slope of each column and beam.

BA. May I know what structural books gave such details about slope deflection method and moment distribution in designing structures for those who want to refresh themselves with these after forgetting early college lessons on statics? Mcgregor Reinforced Concrete Mechanics and Design and even Dolan Design of Concrete Structures and others only focus on nomimal flexural strength of beams using pinned support examples. Integrated frames actions and computations were not detailed a bit.

 

[IDS]

Recommended reference book: Reynold's Reinforced Concrete Designer's Handbook:

https://www.crcpress.com/Reinforced...nolds-Steedman-Threlfall/p/book/9780419258308

It's UK code focussed, but the analysis and detailing is applicable anywhere.

Regarding your original query, I think some of the responses are misleading.

If you do a frame analysis, modelling the complete structure, then the distribution of moments at the joints is automatically included. You can adjust the model to take account of the increased stiffness from the face of columns to the centre line, but that will normally only make a small difference.

If you are modelling a single line of beams as a continuous beam with point supports, then you have to adjust the model to account for the rotational restraint provided by the columns. You can do that by adding a spring restraint equal to the rotational stiffness of the columns at each beam end.

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[BAretired]

Happy to oblige, Quence.

IDS has already recommended one book. I am not familiar with it, but the book I used in the early fifties was "Statically Indeterminate Structures" by C.K. Wang. I thought that possibly it was no longer available, but I checked on the internet and found that it still is. It is considered one of the best books on the subject. It covers the two methods mentioned and several others.

Also, make friends with Google. If you Google "Moment Distribution Method" or "Slope Deflection Method" you will find a number of articles written about these two methods. I took a quick look and thought they appeared pretty good, but I can't say that I studied any of them long enough to recommend any particular article.

https://www.google.com/search?q="Moment+Distribution+Method"&ie=utf-8&oe=utf-8&client=firefox-b-ab

https://www.google.com/search?q="Slope+Deflection+Method"&ie=utf-8&oe=utf-8&client=firefox-b-ab

BA