Estimate of base shear coefficient

[zsherliza]

Dear Vesna,

I have conducted pushover analysis to plot capacity curve (base shear-displacement) of a MDOF bridge. I applied lateral loads to lumped masses at the deck and pier. There are 27 piers in the bridge structure and I have input lateral loads to all the lumped masses. My lateral load profile was determined by multiplying mass with modeshape value, and introduced P-delta by using the P-delta geometric transformation in piers. I run the analysis and my curve is similar to that obtained in the Laura Eads example i.e. after the curve reached maximum force at 20 mm displacement, it descended (post yield having negative stiffness). Then I tried to get the base shear coefficient and the value at yielding is 1.07 g ( base shear at yielding/ [the sum of mass x modeshape]). I feel that this value is too big, i.e to recommend this value for the design of a new bridge is ridiculous. Laura Eads example, on the other hand, gave the base shear coefficient as (weight/base shear).

Would you mind telling me what I did wrong? Why did the example by Laura Eds suggest that base shear coefficient is weight/base shear, and not (base shear/weight)?

I would also like to check if I have used the wrong recorder for base shear. To get base shear, I used the Node recorder to record reactions at the pier bases. Since I would like to get base shear in the transverse direction, I have summed up the reactions in DOF 3 in each pier at every time step. Then I plotted these values against the displacement at monitoring node.

In dynamics analysis, how do I determine the base shear in each column? What I have done is, find the reaction at maximum displacement response. Is this correct? Or do I have to sum up the reactions from time 0.0 sec to the time where maximum displacement response is observed?

Thank you Vesna, for your attention. I really need to get some answers very soon, since I am running short of time for thesis submission.

Regards,
zsherliza

[oleviuqserh]

As far I know, the base shear coefficient is computed just as described… dividing the base shear of the structure with its weight. However, according to your post, it sounds like you are dividing the maximum base shear (calculated by means of a static-pushover analysis) with the weight of the bridge. The base shear at yielding, however, should be preferably taken at the moment in which the first plastic hinge is generated within the structure. This value is then divided by the total weight of the bridge to obtain the base shear coefficient at yielding.

> In dynamics analysis, how do I determine the base shear in each column?

By "base shear", what do you mean? Maximum base shear that each column can carry on, or the base shear at section yielding.

[zsherliza]

Dear oleviuqserh (sorry if this not your name),

Thank you very much for your answer.
My thesis is on evaluation of a seismic coefficient value for low seismicity countries. As the title may suggest, I am not using any developed response spectrum to conduct pushover analysis. What I have done is get some information from dynamic analysis and input them in my pushover program. This is so I can get the largest base shear that the bridge can withstand without collapsing. Then by using the same base shear-displacement curve, I will determine yielding and by using that value, I hope to recommend a seismic coefficient value (base shear/weight) to use in my thesis. This is the reason for asking these questions.

By 'base shear' at each column, what I meant was the base shear at section yielding. Is this the same as looking at the time when steel yields, and then pick up the base shear value (from node recorder for reaction) at that period. If yes, let's say a column did not experience yielding, is it right to sum all the reactions (say in transverse direction) recorded throughout the simulation period to get the base shear in that column?

Thank you very much for your time.

Regards.

[oleviuqserh]

Would you tell me what kind of information derived from your dynamic analysis are you inputting in the analysis of pushover (I presume you are performing a static-pushover analysis). In other words, are you performing a seismic simulation with a representative set of earthquakes to get an intermediate value of the base shear or just solving an eigen-problem (consisting of obtaining the eigenvectors and their corresponding eigenvalues) to generate the shape of the pushing-load?

Moreover, I do not know any useful indicator which consists of summing all transverse reactions recorded throughout the simulation to get a preview of the base shear at yielding. In fact, because of the nonlinearity of the problem, you cannot infer it by any means. Additionally, if rebars did not experience yielding in tension, I would suggest that crushing in the concrete is also monitored or checked at the other face of the section, since this action could be controlling the failure of the section.

[zsherliza]

I was using the dynamic analysis to get the eigenvectors (from ''eigen" recorder) to input as my lateral load profile in pushover analysis. I read from the message board that the base shear is the sum of horizontal reactions (transverse or longitudinal) at the base, and this is why I have assumed the value of base shear as I have described. Looks like this is questionable....

My work consists of examining the seismic performance of a bridge to a few ground motions and I am trying to determine the base shear due to each excitation. What then is the base shear, from dynamic analysis? I am trying to plot these base shear-displacement pairs on the pushover curve to see the reliability of pushover analysis in predicting yielding and so on.

Thanks again

[oleviuqserh]

Sorry, I misunderstood you. Yes, you are right. The base shear of the bridge is computed as the summation of all transverse reactions recorded _at every time step_ throughout the simulation. This is the same no matter if you are performing a pushover analysis or a seismic simulation. I thought you were suggesting of doing an accumulative summation of all transverse reactions recorded from time t0 to time tf… So yes, you are right and this is the correct way to do it…

The following is a document which I strongly recommend to clear up doubts about static nonlinear analysis procedures: "ATC-40. Seismic Evaluation and Retrofit of Concrete Buildings, Volume 1, by Applied Technology Council." Another useful document is the study recently conducted by the PEER team: "Modeling and acceptance criteria for seismic design and analysis of tall buildings." Although, the document is mainly focused on analysis of tall buildings, there is a chapter dealing with nonlinear analysis procedures.

[zsherliza]

Dear oleviuqserh,

I should thank you for clearing things up for me. Thanks again for the references, I will try to search and read them soon.

Regards,
zsherliza