Diaphragm-Rigidity Assumptions for
Distribution of Horizontal Forces in Light-Frame Construction
SEAOC Seismology Committee
The SEAOC Seismology Committee has received numerous inquires concerning the interpretation of current code provisions, which by strict interpretation could be taken to mean that extensive deflections calculations in conjunction with rigid diaphragm assumptions might be required for the design of all types of light-framed structures. In contrast, long-standing practice has been to design these types of structures using flexible diaphragm assumptions, which has resulted in structures that are generally regarded as capable of resisting earthquakes without unusual risk to occupants.
In response to these inquiries, the SEAOC Seismology Committee has reviewed applicable code provisions in conjunction with the extent to which any more elaborate or precise analysis might be able to provide any improvement or even real difference in the expected behavior of these structures.
Selected excerpts follow:
1605.2 Rationality. Any system or method of construction to be used shall be based on a rational analysis in accordance with well-established principles of mechanics. These words appeared in the 1976 UBC and subsequent editions.
1605.2.1 Distribution of Horizontal Shear. The total lateral force shall be distributed to the various vertical elements of the lateral-force-resisting system in proportion to their rigidities considering the rigidity of the horizontal bracing system or diaphragm. These words appeared in the 1961 UBC and subsequent editions.
1630.2.3 Simplified design base shear.
Sections 1630.1.2, 1630.1.3, 1630.2.1, 1630.2.2, 1630.5, 1630.9 and 1631 shall not apply when using the simplified procedure. (This section first appears in the 1997 UBC)
1630.6 (3rd paragraph) Horizontal
Distribution of Shear
Diaphragms shall be considered flexible for the purposes of distribution of story shear and torsional moment when the maximum lateral deformation of the diaphragm is more than two times the average story drift of the associated story… The “two times” rule first appears in the 1988 UBC.
1630.7 Horizontal Torsional Moments. Provisions shall be made for the increased shears resulting from horizontal torsion where diaphragms are not flexible. This language first appeared in the 1988 UBC. Very similar language, minus the “where diaphragms are not flexible” portion, appears in the 1961 through 1979 editions of the UBC. Only indirect language is present in the 1982 and 1985 editions.
2315.1 General. Particleboard vertical diaphragms and lumber and wood structural panel horizontal and vertical diaphragms may be used to resist horizontal forces in horizontal and vertical distributing or resisting elements, provided the deflection in the plane of the diaphragm, as determined by calculations, tests or analogies drawn therefrom, does not exceed the permissible deflection of attached distributing or resisting elements. See UBC Standard 23-2 for a method of calculating the deflection of a blocked wood structural panel diaphragm.
Permissible deflection shall be that deflection up to which the diaphragm and any attached distributing or resisting element will maintain its structural integrity under assumed load conditions, i.e., continue to support loads without danger to occupants of the structure. Except for renumbering of the UBC Standard, these same words are found in the 1973 UBC.
In summary, the current UBC provisions specify that a diaphragm may be considered flexible when the conditions of Section 1630.6 are met. However, it does not explicitly state that all diaphragms not meeting that condition must be considered as rigid.
The 1999 Blue Book, on pp. 257-259, presents a discussion of issues related to the determination of when a rigid versus flexible analysis may be more appropriate for the analysis of diaphragms. Briefly, it states that UBC Section 1630.6 defines a condition (diaphragm deflection greater than 2 times the average story drift) when a flexible diaphragm assumption must be used. For other conditions, it states “… UBC provisions require that the distribution of lateral forces be in proportion to the relative rigidity of the vertical resisting elements.” Note that diaphragms that are not classified as “flexible” are not necessarily “rigid.” They can have varying degrees of flexibility that must be considered. The Blue Book then goes on to discuss a number of pros and cons related to whether wood diaphragms should be assumed to be rigid. Notable statements include:
“For small, substantially regular buildings that have a good distribution of lateral resistance and are well tied together, earthquake performance to date suggests that design using flexible diaphragm assumptions is adequate for Life-Safe Performance. It has been suggested that one and two-family residences be given blanket exemption from consideration of the applicability of rigid diaphragm analysis. Such a blanket exemption does not, however, make sense from an engineering standpoint because many one and two-family residences have highly irregular configurations with low redundancy and significant discontinuities in the structural system.”
Further to this, the SEAOC Seismology Committee concluded during recent discussions that it should be acceptable to use flexible diaphragm assumptions for most one and two-family residences. For the relatively small diaphragm spans and complex interior partition layouts often found in residential construction, the inability to accurately calculate the rigidity of the various elements, including the rigidities contributed by finishes and nonstructural elements, can cause a wide disparity between the analysis results and the actual behavior. The results of an elaborate diaphragm analysis are not likely to be significantly better than that produced by the conventional “flexible” assumption. In comparison, a “flexible” assumption offers the benefit of often encouraging designers to locate vertical resisting elements in better proportion with the structure mass. When inelastic horizontal seismic deformations occur, a redistribution of forces between the vertical resisting elements will tend to produce relatively similar results, irregardless of the assumptions of rigidity that were used.
Engineers are cautioned that this presumption should not be arbitrarily extended to other, larger buildings. The engineer should review the particular circumstances of the structure at hand, including the overall shape and spans of diaphragms, the presence of stiffening attributes, and the relative accuracy of equations and methods available, to determine the method of analysis that is most appropriate. As a rule-of-thumb, if a diaphragm is considered “flexible” when the diaphragm deflections exceed 2 times the average story drift, then it might be considered “rigid” when the diaphragm deflections do not exceed ˝ the average story drift. The range between these values represents a “semi-rigid” behavior where more careful engineering judgement may be warranted.
Volume II, Examples 1 and 2 of the Seismic Design Manual present analyses which utilize “enveloping analysis” to consider the worst-case loads of both rigid and flexible assumption. These analyses are presented as examples that illustrate one approach to design, as well as the range of results from the two approaches. These examples are not intended to be definitive statements of “proper practice.” It should also be noted that the concept of an “enveloping analysis” is not mentioned anywhere in the building code, and therefore may be subject to varying interpretations. Engineers are encouraged to use independent engineering judgement in the interpretation of code provisions and their application to specific design situations - the use of an “enveloping analysis” approach is one method that may be used at the discretion of the design engineer.
The current pre-publication language of the 2000 IBC provisions defines a rigid diaphragm as being “a diaphragm that does not conform to the definition of flexible diaphragm.” The SEAOC Seismology committee disagrees with this definition as not considering a range of behavior defined as “semi-rigid.”