You need to take the sum of the horizontal reaction forces at each of the base nodes. So if, for example, you have a 10 storey building with three column members fixed at the base and you apply an earthquake in the x direction, you will need to take the force in the x direction at each of the supports of the column.

You could find the base shear from the accelerations also, but the way i described above is by far the simplest.

Dear Gerard

From my SIMULINK model, I'm getting, displacement, velocity and acceleration, how can I get the force at each of the supports of the column ?

and if I want to use the accelerations method how it will be ?

Best regards.

sum of horizontal force in x direction and sum of horizontal force in y direction you can get base shear in x and y direction respectively. or you can use max base shear and maximum displacement in push over analysis.

Dear Ahmed

how is that possible ? is there any equation or MATLAB code ?

I'm applying a ground motion on a structures to get, Displacement, Velocity and accelerations using a state space toolbox in SIMULINK, How can I get the forces ? or the base shear ?

regards.

Dear Mahdi,

Firstly you must say which analysis type you are performing? If you are doing time history analysis, you must determined  whether you are using modal method or direct method?

Also please answer the following questions so I can help you:

Can you get base reactions from SIMULINK?

Why you don't use popular softwares such as ETABS, SAP, PERFORM or OPENSEES?

Best regards,

Arjmandi.

Dear Seyyed Aliasghar

I'm doing a history analysis, using a state space resolution toolbox. 

I'm not getting any base reaction from my SIMULINK, I'm getting displacement, velocity and acceleration only.

the reason why I'm not using one of the software you just cited is that they are not offering any semi-active control device, I'm using a MR damper that I modelled in SIMULINK and also I'm controlling the MR damper using a Fuzzy logic toolbox available in SIMULINK.

Best regards.

Dear Mahdi

I'm not familiar with SIMULINK, so I won't be able to help you with a straight and simple solution. Reading the answers above, I guess there is not a syntax or toolbox available that you can use to extract outputs like storey forces or shear forces at different nodes straightly from software.

If this is the case, then I guess you're gonna have a rather complex solution ahead of you. If velocity, displacement and acceleration are the only outputs you can get from SIMULINK, you are gonna need to write a code that solves generalized equation of motion for structure in every step of acceleration time history, and then extract forces from that code. Then, you will be able to use the sum of shear forces at the base of columns as base shear of structure.

Also about the second part of your question, I have seen some examples that base shear of a structure is normalized to its weight. If this is also what you have in mind, the reason of normalizing base shear is to give a sense of lateral strength of structure compared to its own weight. This gives you a better understanding about the lateral strength of structure compared to only a number for shear force.    

Dear Behnam Ordoubadi

I found some code, calculating the base shear, based on the the accelerations of all the floors and also the ground acceleration, problem with that code is that it is not showing any significant reduction of the calculated base shear,  Mr. Gerard J. O'Reilly, who was the first to answer on my question mentioned something about this method, I would like to have more information if it possible.

Best regards.

Dear Mahdi

I could not follow what you mean by "significant reduction of the calculated base shear". Do you mean that the value of base shear does not show a reasonable variation in different steps of acceleration time history? Or do you mean that because of using a semi-active control system you were expecting a greater reduction in base shear value? 

Dear Behnam Ordoubadi

the maximum value of base shear does not show a reasonable variation between controlled and uncontrolled cases, and in some situation it is increasing, but I'm not sure if the method I'm using is correct or no.

According to most of the paper in the literature they are getting significant reduction up to 45% in some cases.

Regards.

Example using EC8

Dear Mahdi

If this is your problem, I think you will need to check your SIMULINK code first. In fact, first you need to make sure that the code itself has not a specific problem in calculation of base shear.

My suggestion is to verify the results of your SIMULINK code with another software, for example NONLIN. Fortunately, this software is easily accessible, and it is rather easy to use. Model a simple SDOF with it, and record the values of base shear. Then, without taking the control device into your code, record the values of base shear with SIMULINK.  with comparing these two, you can make sure that code is correct and then concentrate on any other aspect that is troubling your results.

Dear Behnam

my question was how to calculate the base shear from the out put (Displacement, velocity and acceleration) ? if I can calculate it (the base shear) then I can do what you are asking me to do, at this stage I'm not getting base shear at all and I'm asking how to calculate it.

Regards.

It depends on which software you are using. For example, in ETABS 2015, it is found Under Display menu>show tables, checkbox reactions/support reaction>Base Reactions.

Check the following reference Please.. it might's assist you in your question … Regards…

http://www.edwilson.org/book-wilson/17-model.pdf

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