Analysis for torsion in multistorey buildings

Technical Abstract

Many structural designers in New Zealand are routinely using computer based analysis packages for carrying out three-dimensional spectral modal analyses of building structures, but output from such packages does not always produce results which are consistent with the requirements of the current New Zealand Loadings Code for buildings, NZS 4203:1984. Even greater difficulties arise for designers when dealing with eccentric structures which give significant torsional response. Therefore, the principal objective of this study is to prepare sound and reasoned guidelines as to how analysts and designers should most appropriately use existing convenient analysis packages to determine earthquake design actions for torsionally sensitive structures.

The requirements of design for torsion and the use of Spectral Modal Analysis techniques are closely related, because the analysis of torsionally unbalanced buildings is normally dealt with using the spectral modal analysis method. Much of the information and discussion in this report is therefore related to the spectral modal analysis method.

An important feature of the results from any spectral modal analyses, which often causes concern among designers, is that the member actions output are an envelope only, rather than an equilibrium set of actions, and no signs are available. A check on the envelope base shear can generally not be reconciled with the direction of the applied spectrum. In the past some designers have found it difficult to rationalize such results. This report investigates how the spectral modal analysis results for earthquake loading are being used by designers, and makes recommendations as to how torsion should most sensibly be dealt with.

Some practitioners believe that, where rigorous capacity design procedures are carried followed, such as in New Zealand, the specific details of torsional design procedures are not such an important issue.

0.2 Codes of Practice

Section 2 summarizes the seismic torsion provisions made by various international design codes, including those from New Zealand, USA, Canada, Mexico, the European Community and a proposed Australian code. Most codes stipulate similar requirements related to design for torsion, generally along equivalent static seismic load analysis for regular structures, but requiring spectral modal analysis for irregular or large buildings. The code equations for design torsional eccentricities to be used in static analyses are usually in the form of primary and secondary eccentricity expressions including terms to account for dynamic amplification of the static eccentricity and accidental eccentricity. The dynamic amplification of static eccentricity allows for the effect of coupling between translational and torsional modes of vibration. Amplification factors varying between 0.5 and approximately 2.5 are specified by various codes. The accidental eccentricity allows for uncertainties in the distributions of mass and stiffness and for possible torsional ground motion. Code allowances for this are generally either 5 percent or 10 percent of the buildings width. Where three-dimensional dynamic analyses are used, the dynamic eccentricity effects would normally be taken into account in the analysis but codes require that the accidental eccentricity effects are modelled by shifting the centres of mass at each floor level.

A detailed discussion of the NZS 4203:1984 provisions for torsion analysis is given. It would seem that the 1984 code provisions were written generally with only two-dimensional spectral modal analysis in mind, and that the analysis would only be used to derive an equivalent set of forces to be later applied to static analysis model.

The torsion provisions of NZS 4203:1992, which is a major revision of the New Zealand loadings code about to be issued, are discussed. These provisions appear to be generally appropriate and consistent with other international codes. However, there are some aspects which could be considered for revision in the future. Possible chance would be:

• The inclusion of amplification factors on the static eccentricity in the design torsional eccentricity expressions (some factors were included in the 1976 code but later deleted),
• Allowing the wider use of a modified equivalent static analysis method for the design of irregular buildings,
• Not allowing the beneficial effects of torsion to be taken in to account for elements on the stiff side of the building (already implemented in the Uniform Building Code) and possibly requiring further additional strength factors to be applied to these elements.
• To review the requirements for methods of scaling spectral modal analysis results to meet the principal objective of ensuring a minimum level of base shear strength.

0.3 Literature Review – Research on Torsion

An extension review of literature dealing with research on torsion is given in Section 3. This review addresses the following areas of research:

• Elastic response of single storey structures
• Inelastic response of single storey structures
• Elastic response of multi-storey structures
• Inelastic response of multi-storey structures
• Effects of diaphragm flexibility

The seismic torsional behavior of building structures is complex and far from being completely understood. Theoretical studies of the elastic and inelastic response of single storey structures are now quite numerous and the behavior of those systems should now be able to be dealt with some confidence. For multi-storey structures theoretical studies have been reported dealing with elastic torsional response, but information on the inelastic torsional response is only just starting to emerge. Some recent analytical studies to test the inelastic response of code designed multi-storey frame structures suggest that modifications may be necessary to code torsion provisions to ensure consistent and achievable levels of strength and ductility demand everywhere in the structure. A definitive understanding of the problem and adequately codified recommendations are necessary, but these are still not likely to be available until further study has been carried out.

Section 3 also summarizes information on research into diaphragm flexibility effects. The research highlights that it is important for designers to consider diaphragm forces in the design of buildings which have very irregular layouts of lateral load resisting framing, major re-entrant corners, diaphragm discontinuities or long narrow floors. Diaphragm flexibility effects are important to consider in the analysis of such buildings as they have major influence on the distribution of internal forces and actual forces generated in the floor diaphragms. Some analysis tools are available to designers to help predict the effects of diaphragm flexibility on the seismic response of multi-storey buildings.

0.4 Spectral Modal Analysis Methods

The spectral modal analysis technique is discussed in section 4. This technique combines the response spectrum analysis method for single degree of freedom structures with the modal analysis method for multi-degree of freedom systems. The background and details of various modal combination rules are discussed. All rules aim to give the envelope of structural response actions which would be predicted for an elastic time history analysis. The literature suggests that combination rules which allow for amplification and de-amplification effects caused by modal cross-correlation, can accurately predict the combined maximum response quantities. Several methods including the CQC method appear to give similar results. The CQC method is commonly used in dynamic analysis computer programs and appears to be as good as other alternative methods for use by designers.

It is universally agreed that whichever final response quantity is required, it must be obtained for each mode before and combination is carried out, and after modal combination no further combination of results should take place.

An alternative scaling procedure is suggested. This involves scaling according to the sum of combined spectral modal column shears rather than the combined spectral modal base shear. This may offer a more rational means of satisfying the intent of design codes for maintaining a minimum level of base shear strength in structures. The proposed method needs to be tested as part of further research before it can be confirmed as appropriate.

0.5 NZ Practice for Torsion and Spectral Modal Analysis

A summary is given of a recent informal survey of New Zealand designers conducted to find out how they carry out torsion design and spectral modal analysis in accordance with the loadings code. It is apparent that commercially available computer analysis packages are being used routinely in design offices. A practical discussion of the use the ETABS analysis package is included. Recommendations are made as to how analysts using computer analysis packages for the seismic analysis of building structures can include considerations of torsional effects.

Spectral modal analysis methods appear to be adequate to determine design actions for asymmetric multi-storey buildings in which seismic torsional effects are important.

Code requirements for accidental eccentricity are met by shifting the centres of mass at each level from the calculated positions. Rotational inertia about the centre of mass at each level is not normally adjusted. For most buildings, five separate spectral modal analyses will be required to meet the intent of the code. More analyses may be needed to determine the most unfavourable actions on elements where framing is irregular or skew.

Scaling of spectral modal analysis results is often necessary to satisfy the NZS 4203:1984 requirement that the combined spectral modal base shear is at least equal to 90 percent of the code equivalent static method base shear, and the combined spectral modal shear at every level is at least equal to 80 percent of the equivalent static method. The 1992 revision of NZS 4203 will require scaling of spectral modal analysis results to 100 percent of the code equivalent static method base shear generally, but to only 80 percent for structures satisfying certain regularity requirements. These code requirements should not be ignored by designers. The scaling should be carried out on every separate spectral modal analysis before the design force envelope is determined from the various individual analyses. It appears that designers using the ETABS package may not be scaling the spectral modal analysis results according to the code intended method. The way in which ETABS outputs base shear values is leading designers to scale according to the alternative scaling procedure suggested in Section 4 of this report. Most designers probably do not realize this.

The modal combination method employed should allow for modal cross-correlation effects between modes with closely spaced frequencies. The CQC method is considered satisfactory.

Many analysis packages assume that floor diaphragms are rigid in their own plane, but some are now including capabilities for modelling diaphragm flexibility effects. Special attention to modelling diaphragm flexibility effects should be considered when floor in-plane deformations may be important, or where there are significant discontinuities, holes or major re-entrant corners present in floors.

0.6 Capacity Design Procedures

The current code procedure given in the New Zealand concrete design code for the capacity design of concrete frames is based on using the results of the equivalent static force analysis of the New Zealand Loadings Code NZS 4203 and does not include provision for the use of a spectral modal analysis. The spectral modal analysis actions are an envelope; they do not occur simultaneously and they are not an equilibrium set of actions. A major question is therefore whether the present capacity design procedures can still be used, or how they should be modified, for the case where a spectral modal analysis has been carried out. Some people have suggested that the use of spectral modal analyses and capacity design procedures are incompatible. However, that is not a conclusion of this study. Section 6 suggests some minor adaptations to the capacity design procedure given in the New Zealand concrete design code for ductile concrete frames to allow satisfactory capacity design column actions to be derived from the envelope of spectral modal analysis actions. Further research should be carried out to rationalize the dynamic magnification factors to be used in the capacity design procedure for the case where code level actions are derived using spectral modal analysis methods rather than static analyses.

Earthquake damage reports often identify damage to floor diaphragms at re-entrant corners or adjacent to major structural discontinuities. The capacity design procedures used in New Zealand provide a rational method for determining beam and column design actions, but it is also important to extend the philosophy to ensure satisfactory performance of floor diaphragms. This section briefly addresses the issue. Methods are discussed for modelling diaphragm flexibility effects using computer analysis programs, so that in-plane design forces in floors can be estimated.

Recommendations for design and “detailing” for re-entrant corners are as follows:

• Provide edge beams to the floor either side of the corner. These should be continued through the corner and fully anchored in the adjacent floor panel, in the same way which steel stiffener plates would be designed in a steel portal knee joint.
• Diaphragm forces should be estimated and analysis for this should take account of diaphragm flexibility effects, that is, the tendency for re-entrant corner to “open” as adjacent wings of the floor to try respond out of phase with each other.
• The joint zone in the floor should be designed to resist the in-plane moment and shear in the floor diaphragm with adequate allowance for overstrength effects. Specific diaphragm design can be done by strut-and-tie design methods, for example.

0.7 Conclusions and Recommendations

A number of conclusions and suggestions for further research are made in Section 7. Extensive parametric analysis studies of inelastic multi-storey building systems are necessary to extend our understanding of the torsion problem.

0.8 Commentary Report

A draft of this report was sent to Dr A Chandler of University College, London and his commentary is reproduced in Appendix B of this report. Dr Chandler has published widely on the subject of analysis for earthquake induced torsion in buildings and is on the forefront of research on the subject.