ASCE 7-22 Fundamental Period for Non-Building Structures (15.4.4)

[trou33]

In ASCE 7-22 (and 7-16), equation 15.4-6 is used to find the fundamental period of a non-building structure, and by its inverse, the natural frequency. It's a simple enough calc for the 10'x10'x5' braced frame structure I'm designing for a piece of equipment that requires a maximum 20Hz limit. If I wasn't required to provide calculations for this, I could simply do an eyeball test and say it meets that limit.

I'm sure I'm overthinking it, but it's a bug in my brain now and I want to sort it out. I'm having trouble finding direction on the variable 'g' (I know, it's gravity). Section 11.3 doesn't provide units for g and if my deflection is measured in inches, it somehow makes sense to use g=386.4 in/s2 (=32.2ft/s2 * 12in/ft), but the inverse of equation 15.4-6 would be 32Hz which cannot be right. Using g=32 ft/s2, gets 9.2Hz which is more reasonable but having the conflicting units doesn't sit well with me. Does anyone know where ASCE gives direction on the units to be used for g throughout the code?

Further, this equation doesn't take into account the site specific conditions. It would make the most sense to me if SDS was used in this equation rather than g. Is there any rationale to this or am I overlooking something?

I appreciate the input. Thanks.

 

[HTURKAK]

Having worked with old versions of API standards , AFAIK the common practice is to use US customary units ( ft- lb-sec).
Regarding the subject formula ;
If you want to use US customary units;

wi, fi = lb
δi =foot
g = ft/sec² ( 32.2 feet/sec² )

Alternatively , you can use the same formula for SI units.

 

[ChorasDen]

Help paint the picture for me a little more, your units should fully cancel out, why are you getting different values based on assumed units used?

 

[ANE91]

This always messed with my head, back in Dynamics class. Units must be consistent throughout the expression. Recall that 386lb of force (or 1lbf) is equivalent to 1lb of mass (or 1lbm) subject to gravitational acceleration, or 386in/s². Thus, if using g expressed as inches per second squared, then w and f are in units of lbm*in/s². Also recall that 2pi is a radian.

Easy to screw up when doing the algebra.

 

[trou33]

I've been trying to figure out why I get different results using my calculator vs excel (might have found something to watch out for on my calculator). The resulting value using g=386.4 is what I was expecting - it's just odd in my mind to use that for g rather than 32.2 (assuming delta is measured in inches). Thanks everyone for the responses, but it seems to have been a user error.