ASCE 7-10 Rigid Building or Other Structures, Rigid

[SteelPE]

I am currently trying to design a wood framed house in accordance with ASCE 7-10. The house is located hear a coast and is long, skinny and tall (3 floors of wood on top of a concrete foundation wall). The dimensions are 45' long x 16' wide x 42' tall. We are currently using wood shear walls on the upper 3 floors of the building (at least that is what we are proposing to do).

My question is in regards to wind loading. I am trying to calculate the wind loads in accordance with chapter 27 of ASCE 7-10 and I need to figure out what to use for G. I am able to use a G of 0.85 if I can calculate the building as being rigid. The problem is, all of the methods for calculating the frequency of a structure in ASCE 7-10 specifically reference steel, concrete or masonry. If I "shoe horn" wood shear walls into these equations I can calculate the building as being rigid (using equation 26.9-4 or possibly equation 12.8-7). How do you calculate the natural frequency for a building such as this one (keep in mind this is a single family residence not a 40 story building)?

 

[KootK]

Honestly, for a building of this sort, I've been just going straight to rigid without evaluating it in any way. For wind, I believe that "flexible" really means so damn flexible that building motion frequency is low enough that the building is interacting meaningfully with the wind to affect wind load, dynamic effects, and cross wind phenomenon. I just don't see it in a three story wood building.

 

[WARose]

The problem is, all of the methods for calculating the frequency of a structure in ASCE 7-10 specifically reference steel, concrete or masonry.

As far as I know, Eq. 12.8-7 (to figure period and (ergo) fundamental frequency) is good for whatever you want (including wood shear wall buildings). Alternatively, there are some equations (as you mentioned) specifically for moment frames, concrete/masonry shear walls, etc.....but 12.8-7 is still good to go for most stuff.

How do you calculate the natural frequency for a building such as this one (keep in mind this is a single family residence not a 40 story building)?

NDS (and most wood design texts) have shear wall deflection formulas. From that (combined, for all the walls) stiffness, you can figure the frequency: ω=√(k/m) [rad/sec]. Which is treating it as a single degree of freedom system......which is appropriate for low-rise, shear wall structures.

Considering the damping in wood framed buildings (not to mention the uncertainty in the shear wall deflection equations).....any estimate is going to be just that: an estimate. So 12.8-7 is probably as good as anything.

 

[SteelPE]

WARose,

I would agree with the statement regarding equation 12.8-7, however, the commentary of ASCE 7-10 specifically states that using these equations for wind loads is not recommended since wind and seismic impose their loads differently on structures.

 

[WARose]

I would agree with the statement regarding equation 12.8-7, however, the commentary of ASCE 7-10 specifically states that using these equations for wind loads is not recommended since wind and seismic impose their loads differently on structures.

I'd be curious to know where it says that. A building's natural frequencies are it's natural frequencies. (Regardless of loading.)

In any case, C26.2 says this:

When buildings or other structures have a height exceeding
four times the least horizontal dimension or when
there is reason to believe that the natural frequency is
less than 1 Hz (natural period greater than 1 s), the
natural frequency of the structure should be investigated.

Based on the dimensions you give above, sounds like you are rigid.

 

[bones206]

As a check on the natural frequency formula, you could model the structure to some reasonable level of detail and do a modal analysis to get the fundamental frequency. Similar to KootK, I tend to blow by this check without a second thought and use G = 0.85 for almost every kind of structure except those that are obviously flexible and could be dynamically “excited” by wind loading.

Someone did their PhD thesis on this subject if you really want to dig into it: Link

Anecdotally, I currently live in a skinny 2-story townhouse in a gusty coastal area, and I’ve definitely noticed some low amplitude vibration from strong wind at times. Probably in the 3-5 Hz range. Barely noticeable except when laying in bed and probably totally acceptable from a performance standpoint.

 

[SteelPE]

WARose,

My ASCE 7-10 C-26.9 has the following excerpt on page 520.

Most computer codes used in the analysis of structures would provide estimates of the natural frequencies of the structure being analyzed. However, for the preliminary design stages some empirical relationships for building period Ta (Ta = 1/n) are available in the earthquake chapters of ASCE 7. However, it is noteworthy that these expressions are based on recommendations for earthquake design with inherent bias toward higher estimates of fundamental frequencies (Goel and Chopra 1997 and 1998). For wind design applications these values may be non conservative because an estimated frequency higher than the actual frequency would yield lower values of the gust factor and concomitantly a lower design wind pressure.

 

[WARose]

However, it is noteworthy that these expressions are based on recommendations for earthquake design with inherent bias toward higher estimates of fundamental frequencies (Goel and Chopra 1997 and 1998). For wind design applications these values may be neoconservative because an estimated frequency higher than the actual frequency would yield lower values of the gust factor and concomitantly a lower design wind pressure.

If you look at the literature they cite, it almost exclusively deals with moment frames of reinforced concrete and steel. There I would see their point (as I have noticed the same thing).....but a low rise wood shear wall building? I'd just use the simple ratio I brought up earlier.

 

[JoshPlumSE]

The NDS Special Design Provisions for Wind and Seismic (SDPWS) gives equations for calculating the stiffness of a wood shear wall. If you know the mass of each floor and the stiffness of each wall, then you can calculate the natural frequencies if need be.

However, that being said, I feel like that it's going to come out rigid. If it were me, I'd assume it was rigid, maybe use the general equation to demonstrate it. And, only pull out the calculator for a better estimate if I get asked to justify my rigid assumption.