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RE: ACI 350.3-01 - seismic design of liquid detention tank

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I am a member of the ACI committee that developed ACI 350.3. (I am more
familiar with the use of US Customary units vs metric units, but I have used
metric units on occasion.)

I believe that you are correct regarding the units for m, m(i), and m(w)
under Section 1.2. As shown in R9.2.4, the unit mass is multiplied by
(length)^2, so both the metric units and the US Customary units shown should
have been multiplied by (length)^2 (i.e., resulting in kN.s^2/m^2 or
lb-s^2/ft^2). 

However, I am not sure that there is a problem with the units for 'k' in
Equation 9-9. Since 1 kPa = 1 kN/m^2, it seems that 'kN' cancels out, and
there is no '1000' conversion factor to contend with. However, I think your
derivation for 'm' resulting in units of kg/m is incorrect - that conversion
should have included a factor of 1000 to convert kN to 1000-kg. (I suspect
that the reason the mass is defined in terms of kN instead of kg is to avoid
problems handling the 1000 conversion factor, although I was not involved in
the unit conversions.) 

The committee is just finalizing the next version of ACI 350.3 (for
publication in early 2005), and this error had not yet been detected. I will
forward this to the committee chairman to see if we can get it corrected
now. 


William C. Sherman, PE 
(Bill Sherman) 
CDM, Denver, CO
Phone: 303-298-1311
Fax: 303-293-8236
email: shermanwc(--nospam--at)cdm.com


> -----Original Message-----
> From: Derek [mailto:derekh(--nospam--at)krahn.com] 
> Sent: Friday, April 02, 2004 11:57 AM
> To: seaint(--nospam--at)seaint.org
> Subject: ACI350.3-01 - seismic design of liquid detention tank
> 
> 
> Is anybody familiar with this code. I am new to this 
> particular code and a couple of things have caught my 
> attention. Any comments would be appreciated.
> 
> 1. I'm sure this is a typo, but under section 1.2-Notation 
> the SI units given for m, mi and mw are kNs2/m4. I am as 
> convinced as can be that these units should be kg/m. If the 
> units are correct then the equations for mw and mi given in 
> the commentary R9.2.4 are dimensionally inconsistent. It 
> could also be that the dimensions for rho (mass density) 
> given in section 1.2 are incorrect, however the units given 
> there are kNs2/m4 which is equivalent to kg/m3 and would seem 
> correct. Anyone?
> 
> 2. Onto something more concerning. Equation 9-9 states that 
> omega_sub_i = sqrt(k/m). k being the flexural stiffness of 
> the tank wall and m being the mass of the wall and impulsive 
> component of the stored liquid.
> 
> Lets assume that section 1.2 is indeed correct and I am 
> incorrect in my statement above. k is in units of kPa and m 
> is in units of kNs2/m4 then equation 9-9 is dimensionally 
> inconsistent as the units for sqrt(k/m) come out at m/s 
> whereas omega_sub_i is in units of rad/s.
> 
> Lets assume that section 1.2 is incorrect. k in units of kPa 
> and m in units of kg/m. Dimensionally now the equation is 
> correct, however, because k is in units of kPa (ie 10^3 Pa) 
> then there is a factor of sqrt(1000) that has to be taken 
> into account. In other words the equation should be sqrt(k/m*1000).
> 
> Can anyone help, does any of this even make sense?
> 
> PS: sorry for using SI units but having a background in 
> Australia, these are the only units I understand.
> 
> thanks
> Derek

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