Lateral Deflection of Rigid Frame with Bracing

[Tygra_1983]

Dear all,

I am wishing to do preliminary analysis on the horizontal deflections at the top of tall structures. Below, though it is not a tall structure shows the configurations of a rigid frame with bracing. I would like to calculate the deflection for a similar structure, just that, I use 15, 20, 30 plus storeys.

Thus far, I have found formulas to calculate the deflections of a rigid frames alone. These come in the form of:

deltaf = w*H^4/(8*E*I) for the flexural deflection of the whole building

deltaS = V*h^3/(sumC*12*E*Ic) + V*h^2*L/(sumB*12*E*Ib) for the shear deflection for each storey

Where:

w = horizontal uniform load
H = building height
h = storey height
L = is the beam length
E = modulus of elasticity
I = second moment area of the frame system
V = average cumulative shear
Ic = second moment area of the columns
Ib = second moment of area of the beams
sumC = number of columns per storey
SumB = number of beams per storey

Total deflection at top = deltaf + deltaS*(number of storeys)

So, I am sorted with deflection of rigid frames alone, but now I want to calculate the deflection if bracing is added - which will obviously reduce the deflection. I feel I have exhausted
my search on the internet for papers and in text books, and cannot find anything that will help me with this specific problem. Thus, I am really hoping someone on here can assist me on this? Is there an amendment to the above formulas I can make? Or is there any other formula/method that someone here could reveal to me?

Best wishes

 

[driftLimiter]

Look at Chopra Dynamics of Structures. You need to understand how the rigidity of diagonal and x braces effects the stiffness of each floor and then the whole building. Those forumlas you posted are for one element only, the structure you show has many elements all contributing to the response.

Also Hibbeler Structural Analysis!

The problem is super general, you could try to approximate the building as a cantilever column. But the deflections you get are going to be based on whatever assumption of stiffness you have for the members. Its a big assumption to do just generally. If you had a more detailed structural model you could get better results.

Could also solve it out in terms of the column and brace stiffness.

It isn't an easy ask but certainly possible to compare the effect of different configurations.

 

[Tygra_1983]

I am doing a static analysis, not a dynamic analysis.

Is not any further help could give me?

Best wishes

 

[driftLimiter]

I know that your doing a static analysis but Chopra gives a good explanation of how braces effect lateral stiffness.

It sounds to me like you really need to hit the books. Hibbeler Statics and Hibbeler Structural Analysis is more than enough to get you off an running on solving this problem.


Before you use those deflection equations you aught to understand what they mean, what does each term signify.

Also if I understood more about what you are getting at with this question (self-research, school project, homework, design hope its not design) then I and others could offer more guidance.

It is a very general question Deflections at the top of tall structures is a huge and important field of design. Not all buildings are created equally, the deflection at the top is a function of the unique properties of that building, as well as the actual loading.

Unfortunately answering anything about the deflection of the top of a tall building is going to require deep understand to make the required simplification or a more complete design/analysis so you can actually put numbers on it.

The general principle is that rigid frames are more flexible than braced frames of any kind. X braces vs Diagonal braces depends on what type of braces are selected, how the connections look, etc. For example if the braces are exactly the same stiffness then an X-braced configuration is twice as stiff but this is assuming that both braces can resist lateral load, the normal case is that a compression brace buckles and is not effective against load.

I suggest learning how to do frame analysis and even direct stiffness analysis method of structural analysis, then make a sample structural model that you can solve by whatever means, then make multiple versions of the model with different brace/moment frame configurations and study the results.