James O. Malley

Senior Principal, Degenkolb Engineers

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*RSA procedure developed in 1950’s (or earlier) as a means of addressing dynamic characteristics of the structural through modal analysis approach

*Code History * 1985 UBC – only mentioned for irregular structures, with no direction * 1988 UBC – first time dynamic provisions introduced. Many of the concepts

in ASCE 7-10 date back to this time * Required for irregular buildings

* Reduced forces when compared to ELF designs for regular buildings

* 90% rule for mass participation

*A lot has changed since 1988 (or 1950)! * Computing power * Better understanding of structural response, especially in the nonlinear

range

**Issue – 90% Mass Participation Rule

* Instituted many years ago when computing power was fraction of present

*This may result in not properly capturing local demands on stiff elements * Not a major issue for overall response in most cases

*Approach – Follow ASCE 4 Procedures *Capture all modes down to T=0.05 seconds

*Calculate “Residual Mass” for shorter period modes

*Apply Sa at T=0.5 sec to Residual Mass * Sa=Sds(0.4 + 0.15/Ts )

*Exception allows old 90% rule to be used

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*Result – All mass is included in the design *Avoids underestimating design forces on some elements

*Implication – Better captures full dynamic response of structures *Not critical for most building structures

*May apply more for non-building structures

*Modern software already can perform Residual Mass calculations

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Revise Section 12.9.1 as follows:

12.9.1 Number of Modes

An analysis shall be conducted to determine the modes of vibration for the structure. The analysis shall include sufficient modes to capture participation of 100% of the structures mass. For this purpose, It shall be permitted to represent all modes with periods less than 0.05 seconds in a single rigid body mode having a period of 0.05 seconds.

EXCEPTION: Alternatively, the analysis shall be permitted to include a sufficient number of modes to obtain a combined modal mass participating of at least 90 percent of the actual mass in each orthogonal horizontal direction of response considered in the model.

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*Issue – Existing Commentary is out of date *Missing updated references

*Does not include updated procedure (CQC3)

*Approach – Reflect updates and new procedure *CQC3 Method (Menun and Der Kiureghian, 1998)

provides critical orientation of structure *Endorsed by Wilson for multi-component analyses

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*Result – Brings commentary up to date with modern software applications that incorporate this approach for modal combination

**…. The SRSS or CQC method is applied to loading in one

direction at a time. Where Section 12.5 requires explicit consideration of orthogonal loading effects, the results from one direction of loading may be added to 30 percent of the results from loading in an orthogonal direction. Wilson et al. (20001995) suggested that a more accurate approach is to use the SRSS method to combine 100 percent of the results from each of two orthogonal directions where the individual directional results have been combined by SRSS or CQC, as appropriate. Menun and Der Kiureghian (1998) proposed an alternate method, referred to as CQC3, that provides the critical orientation of the earthquake relative to the structure. Wilson (2000) endorsed the CQC3 method for combining the results from multiple component analyses.

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*Issue – 85% Rule for Scaling to ELF Base Shear *Instituted many years ago to encourage use of RSA *Thought to provide better distribution of forces,

and therefore better performing structures

*Recent studies by ATC for FEMA P695 and NIST GCR10-917-8 and NIST GCR10-917-20 indicate increased collapse probability for RSA design when compared to ELF *Effect exacerbated for long period structures

*Equivalent performance indicated when scale to 100%

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*Approach – Scale to 100% of ELF for both forces and drifts

*Result *ELF design will be used more often (RSA still required for irregular structures)

*More uniform collapse probability

*Implication – May drive the more use of NLRH analyses to reduce structural frame costs

*Revise Section 12.9.4 as follows: 12.9.4 Scaling Design Values of Combined Response A base shear (V) shall be calculated in each of the two orthogonal horizontal directions using the calculated fundamental period of the structure T in each direction and the procedures of Section 12.8. 12.9.4.1 Scaling of Forces Where the calculated fundamental period exceeds CuTa in a given direction, CuTa shall be used in lieu of T in that direction. Where the combined response for the modal base shear (Vt) is less than 100 percent of the calculated base shear (V) using the equivalent lateral force procedure, the forces shall be multiplied by V/Vt, where: V = the equivalent lateral force procedure base shear, calculated in accordance with this section and Section 12.8 Vt = the base shear from the required modal combination 12.9.4.2 Scaling of Drifts Where the combined response for the modal base shear (Vt) is less than CsW, and where Cs is determined in accordance with Eq. 12.8-6, drifts shall be multiplied by CsW/Vt.

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*Issue – Use of 3D Models for RSA *Modern analysis tools can pick up 3D effects automatically

*Use of rigid and semi-rigid diaphragms to capture 3D response

*Approach – Requires 3D model for all RSA designs, either rigid or semi-rigid diaphragms

*Result – Better overall representation of structural response *Use of 2D models limited to ELF or preliminary analyses

*Implication – May result in more use of ELF for simple structures

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12.9.8 Structural Modeling A mathematical model of the structure shall be constructed in accordance with Section 12.7.3, except that all structures designed in accordance with this Section shall be analyzed using a 3-D representation. Where the diaphragms have not been classified as rigid in accordance with Sections 12.3.1, the model shall include representation of the diaphragm’s stiffness characteristics and such additional dynamic degrees of freedom as are required to account for the participation of the diaphragm in the structure’s dynamic response. Proposed new Commentary: Using modern software, it often is more difficult to decompose a structure into planar models than it is to develop a full three-dimensional model. As a result, three-dimensional models are now commonplace. Increased computational efficiency also allows efficient modeling of diaphragm flexibility. As a result, when modal response spectrum analysis is used, a three-dimensional model is required for all structures, including those with diaphragms that can be designated as flexible.

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*Divide only T1 response by R (other modes respond elastically)

*Adjust Cs in the short period range to account for higher displacement demands (equal displacement rule doesn’t apply)

*Should we scale only to base shear? (also to OTM, e.g.)

*Should a factor be applied to account for multi-mode effects?

*Revise spectra development to multi-point approach

*Incorporate accidental torsion into procedure

*Modify to better approximate 1% in 50 year collapse probability

*Should RSA be re-worked to allow de-coupling from ELF?

*Should RSA be replaced by LRHA??? *Another proposal was also approved to update LRHA Provisions to

make them more widely applicable.