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Acceleration time equation for design spectrum plot


Suveksa shrestha
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Hello all,

This might be a minor  question to ask .But then I have some queries on the design spectrum plot as per Chopra."Dynamics of Structure"(3rd edition), response spectrum chapter 6.After the plot is made by amplifying given peak acceleration,velocity and displacement.The same is plotted in the tripartite graph ,from where the values corresponding to T=1/33 sec,1/8 sec ,10 sec and 33 sec.why are  those coordinate points  and the value corresponding to it are noted for obtaining pseudo acceleration or displacement from the relation given ,ie A=omegaVelocity,V=omegaDisplacement?I know how to plot but I am not getting any physical idea about the science of plotting at these points.After this,for each intervals and in place where acceleration governs ,velocity governs  and time governs,an equation ,Acceleration(A)=xT^y(where,time is time of consideration of the occurence of acceleration 'A') is used ..Please kindly give me thoughtful insights on why this equation would work to determine the variance of acceleration with the time period of actual structure.

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On 3/23/2017 at 3:51 PM, Rana said:

You question to me is unclear. Could you clarify what you wanna ask (may be in bullet points)? 

  • My assignment was to construct a design response spectrum using  Newmark and Hall method for 5% damping for a given peak acceleration 0.25g.The question stated that the peak velocity of 122 cm/sec,peak displacement of 91 cm are consistent with a peak acceleration of 1g. Related to that I had to plot the design response spectrum for 0.25 g.Can you explain,what is meant by consistent?we have been given a formula to to find out peak velocity and displacement in relation to the consistency with 1g but  what is it actually?
  • I solved the tripartite graph from the formula given and I plotted the pseudovelocity design spectrum from which  at different time instance where after amplification and at time instance 1/33,1/8,10 and 33 sec ,I was able to plot acceleration vs time graph by equation as (A=xTy where,A=acceleration,T=time,x and y comes from solving two equation as example when T=0.02,A=1g,T=0.5,A=5g,from which x and y values were determined).I wonder why are we using this empirical formula.
  • The Spectrum obtained by Newmark and Hall method was then compared with IS 1893 -2000 fig .2 (for hard rock) and was compared.When we plotted the above mentioned acceleration ie 0.25g we didnot know the site condition so maybe ,the plot was different to IS 1893-2002? Noted that the IS 1893 -2000 was for 1g ,we scaled it to 0.25g and was compared.(Please refer to Clause.6.4.2  from IS 1893-2002  and the excel sheet attached herewith )
  • During this whole process,I don't know why we used a consistent acceleration(as mentioned above) to get a plot for 0.25g? and when we compared it with IS 1893-2000 .Does this means that the consistent acceleration we compared were the available data from previous earthquakes?or is it just empirical assumption?

I would be very glad to have insights on the doubt I am actually having.Thankyou

tutorial31893&newmarkcomparison.xlsx

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By consistent, it means that in order to draw the ‘design’ response spectrum you got to know the PGA, PGV and PGD. Usually when these are unknown, PGA is taken as 1g. PGD and PGV are estimated by the relationships given by Newmark and Hall (see Chopra book). However, in your case, you already got PGV and PGD for PGA=1.0g, right? Now you have to make the pseudo-accelration/velocity/deformation spectrums based on this. After that, you have to scale the calculated response spectrums for 0.25g simply by multiplying them by 0.25. For more on this refer to Chopra book (4th edition) section 6.9.

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  • 2 weeks later...

 

We are interested in the acceleration the building observed not the ground vibration.. 

1. This response of a building with respect to acceleration vs time period is plotted in Building acceleration/ Pseudo acceleration graph. 

2. Damping: Higher the damping % faster the building will loose energy & it will cum to stable state. 

3. Mode shapes: The collective motion of a building when subjected to shaking.. 

4. Base shear: Its the forces acting at the base of the building.

5. Displacement: Max. displacement is always at the top storey. 

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