Formula to calculate height of sloshing wave above design height(E.7.2) 1

[TheEverest]

In equation E.7.2-1, 0.42 is taken whereas in some example problems I have seen 0.5 is taken. Can you please comment on this?

 

[HTURKAK]

If Af = 0.3483, for the tank D= 31.16 ft, there is something wrong !!!!
The sloshing period Tc should be around and less than 4.0 sec. Ks will be around 0.6 and if I =1.0

Sd1 =2.0 for Tc=3.5 sec ???

check your calculations and units...remember , the units shall be consistent ...

 

[TheEverest]

Yes, Tc is around 4 and Ks is around 0.6 but I=1.5 and
Sd1 = Q*Fv*S1 = 1*1.5*0.5 = 0.75 decimal %g.

Is the value of Sd1 incorrect?
Also to calculate Delta_S (Sloshing wave height), shall we use 0.42 or 0.5 in the formula?

 

[HTURKAK]

The formula Sd1 = Q*Fv*S1 is correct... but Q =2/3 .. if S1 =0.5 Fv=1.5 for site class D.

Apparently, you are in confusion for the seismic design . If you want a clear respond, provide more info regarding
Site seismic data, tank details..

Where is your site located when you look to E.4 ( E.4.1 thru E.4.3) ?..

You must look to the Table E-7— Minimum Required Freeboard.

If your Sd1 is correct and Sd1 =0.75 , Af=0.6*0.75* 1.5*(1/4)=0.169

and deltaS=0.5*31.16*0.169=2.6 ft.

 

[JStephen]

A couple of other notes here.
You can use the API-650 approach and calculate all those variables to 12 decimal places, but you're still dealing with a highly approximate design.
So in actuality, there's not a lot of difference between that 0.5 and 0.42 factor.
Note, for example, that the entire approach calculates the "ideal" elastic response, then divides it by 4 or 3.5 or 2 as the case may be because the actual response is nonlinear and inelastic and more highly damped, etc.
So some of those factors come out of committee votes, and people trying to decide if you want X percent probability of exceeding in Y years, or W percent probability in Z years or what.
The theoretical sloshing wave is a single uniform wave in one direction. But there are some swimming pool videos that illustrate the actual seismic waves, and they tend to be more chaotic and more 3-dimensional than you visualize. In this video, note especially the round pool at about 1:10.

https://www.youtube.com/watch?v=sjN-JBevGfg

I think you'd be hard put to even define what the sloshing wave height was in that pool.

 

[HTURKAK]

Mr JStephen , I fully agree with you. I looked to AWWA D100 . Still using the factor 0.5 (δs = 0.5DiIeSac )

and ASCE 7.16 δs = 0.42DiIeSac.

I looked also BS EN 1998-4:2006

dmax =0,84RSe (Tc1 )/ g

IMO , the code should be more specific for the small, fixed roof tanks ( since the roof should be designed for the associated uplift pressure ) rather than adopting 0.5 or 0.42 factor.

The following amazing video ,implies the rooftop swimming pool almost emptied.

https://www.youtube.com/watch?v=-x4DYktznbU