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RE: ASCE 7-05 Diaphragm Design

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Gerard (and others),

First, Section 12.10.1.1 states that Rho is checked in SDC D, E and F only in Transfer elements, which are vertical elements such as shear walls that  move shear from diaphragms to foundations. They are not calculated in inertial elements and Eq. 12.10-1 is indicated which is the diaphragm design force that “distributes” shear through each diaphragm to the vertical components.

With that said, you still cannot assume Rho is 1.0 until you evaluate the structure using 2 possible methods (according to Breyer’s “Design of Wood Structures”). In Seismic Zones A-C. Zone A can be assumed Rho to be set to 1.0 but B and C must be verified to meet the first to checks in ASCE 7-05 Section 12.3.4.1. The first is whether or not you are in SDC B or C but the second is a requirement to check drift calculations and P-delta effects. There are no exceptions noted in section 12.3.4.1 for this.

 

In Seismic Design Category D, E and F, Breyer points to two methods that must be verified;

“In the first method (ASCE 7 Section 12.3.4.2, Item a), the user is asked to remove vertical resisting elements on at a time, and check to see if (1) the story strength is reduced by more than 33 percent OR (2) if an extreme torsional irregularity is created with the element removed. If either of these conditions exist, a Rho of 1.3 must be used; if it does not, Rho may be taken as 1.0. In shearwall structures, it is only shearwalls with a length shorter than the wall height that need be investigated. If all shearwalls have a length at least equal to their height, the structure will automatically qualify for Rho=1.0. Where removal of shearwall elements must be investigated, a rigid diaphragm analysis will be required, resulting in a significant analysis effort.

The Second method (ASCE 7 Sec. 12.3.4.2, Item b) applies only to buildings that are regular in plan at all levels (i.e., no irregularities are triggered). It requires that there be two qualifying shearwalls in the building perimeter at all sides in each evaluated story. For wood-frame shearwall buildings, the length of each shearwall is to be not less than one-half the story height. For other wall types, the length of each wall is required to be not less than the height of the story. If the required perimeter shearwalls are provided, the structure will qualify for Rho of 1.0; otherwise Rho will need to be taken as 1.3. This approach is much easier to apply in most simple buildings.”

 

“Design of Wood Structures – ASD/LRFD” by; Breyer, Fridley, Cobeen and Pollock – Sixth Edition, McGraw Hill Publishing Chapter 2 Page 2.48-2.49 Section: Redundancy/reliability factor.

 

I still have an issue with this in multi-story structures. The distribution of shear to each inertial element using Equation 12.10-1 is a distribution of the base shear to each level in proportion to the total base shear (the sum of the distributed story shears is equal to the base shear). In this case, Eq. 12.10-1 represents the percentage of shear distributed at each level Fx. According to Section 12.3.4.2 Rho in SDC D, E and F is equal to 1.3 unless the tests indicated in 12.3.4.2 (a) and (b) are satisfied. In;

“ (a) “Each story resisting more than 35 percent of the base shear in the direction of interest shall comply with Table 12.3-3 and (b) Structures that are regular in plan at all levels provided that the seismic force-resisting systems consist of at least to bays of seismic force-resisting perimeter framing on each side of the structure in each orthogonal direction at each story resisting more than 35 percent of the base shear. The number of bays for a shear wall shall be calculated as the length of shear wall divided by the story height or two times the length of shear wall divided by the story height for light-framed construction”  

 

This being the case, most multi-story structures below the roof will distribute through Fx or the diaphragm inertial shear, less than 35% of the base shear and thus qualify for Rho equal to 1.3.

 

I think we need to be cautious as to the intent of the code writers on this issue and look at the numbers. In most cases, light-framed structures will not develop large torsional distributions (where the distance from the center of mass to the center of rigidity is large), but the percentage of base shear distributed to lower levels (Fx and not Sum Fx which is the Vertical Element transfer) will be less than 35% in at least one of the levels.

 

Dennis

 

Dennis S. Wish, PE

 

Dennis S. Wish, PE

California Professional Engineer

Structural Engineering Consultant

La Quinta, CA 92253

760.564.0884 (Phone, Fax and Answering Machine)

dennis.wish(--nospam--at)verizon.net

http://structuralist.wordpress.com

http://www.structuralist.net

 

 

From: Gerard Madden, SE [mailto:gmse4603(--nospam--at)gmail.com]
Sent: Tuesday, April 22, 2008 1:57 PM
To: seaint(--nospam--at)seaint.org
Subject: ASCE 7-05 Diaphragm Design

 

The way I read section 12.10.1.1, it means that diaphragms shall only be design for the RHO factor when they are transfer diaphragms in Seismic Design Categories D, E, & F.

This seems logical (and OMEGA would kick in too due to the discontinuity).

This can be difficult to track if another frame line is taking load out of adjacent frame (even one that is not discontinuous) through the diaphragm (like unzipping it). This can happen say when you have say:

A 5 story braced frame from foundation to roof and then near bye a frame from foundation to 2nd floor. At the second floor diaphragm, force transfer can occur even though the 5 story frame is continuous.

Anyone beg to differ?

I guess the moral of the story is have RHO = 1.0 and get 2 frames per side...

--
-gm