Highlights from Chapter 12 of ASCE 7-16 Provisions for Linear Dynamic Analysis

Transcription

1 Highlights from Chapter 12 of ASCE 7-16 Provisions for Linear Dynamic Analysis Finley Charney, Ph.D., P.E. Professor of Structural Engineering, Virginia Tech Member of the ASCE 7-16 Seismic Subcommittee BSSC Webinar: September 28,

2 Linear Response History Analysis Background and Motivation Overview of the Procedure A Few Details Modeling Requirements Numerical Procedures Ground Motions Accidental Torsion, P-Delta Effects, and Load Combinations BSSC Webinar: September 28,

3 Linear Dynamic Procedures in ASCE 7-16: Modal Response Spectrum Analysis Linear Response History Analysis The motivation for moving Linear Response History (LRH) analysis from Chapter 16 to Chapter 12 was to allow Chapter 16 to be used exclusively for Nonlinear Response History (NLRH) analysis, and thereby to provide some simplification in LRH relative to NLRH. An alternate approach was to eliminate LRH analysis entirely. This was not done because LRH analysis provides the following advantages over Modal Response Spectrum (MRS) analysis: 1. The algebraic signs of all forces and deformations are retained in LRH analysis. The signs are lost in the modal combinations used in MRS analysis. 2. Concurrency of actions (axial force and bending moment) are retained in LRH analysis. Recovery of concurrent actions is not possible in MRS analysis. BSSC Webinar: September 28,

4 MRS analysis was developed in the 1960 s because LRH analysis, although theoretically available, was not feasible. Since then computer speed and storage capacity has increased by a factor of at least a million, and sophisticated analysis software is readily available. 2016: Vast majority of new building structures modeled using 3-D linear ELF or MRS analysis R, C d basically unchanged 1978: Vast majority of new building structures modeled using 2-D linear static analysis. R, C d first proposed in ATC ,000,000 Kb RAM 1,000,000 Mb Storage 6 Core dual GPU $4000 in 2016 dollars Mac Pro (2016) 1960 s: MRS Procedure Developed 64 Kb RAM 0.5 Mb Storage $4850 in 2016 dollars KayPro (1982) BSSC Webinar: September 28,

5 Modeling Requirements in LRH Analysis: The structure must be modeled in three dimensions. This is also required for MRS analysis and NLRH analysis in ASCE BSSC Webinar: September 28,

6 Modeling Requirements in LRH Analysis: The structure must be modeled in three dimensions. This is also required for MRS analysis and NLRH analysis in ASCE Where required, accidental torsion must be represented by use of mass offsets. This is necessary to retain algebraic signs and concurrency of force. BSSC Webinar: September 28,

7 Modeling Requirements in LRH Analysis: The structure must be modeled in three dimensions. This is also required for MRS analysis and NLRH analysis in ASCE Where required, accidental torsion must be represented by use of mass offsets. This is necessary to retain algebraic signs and concurrency of force. P-Delta effects must be included in the analytical model. This allows of the inclusion of P-Theta Effects (amplification of global torsional response) that is not possible by use of post-facto amplification of forces and displacements. BSSC Webinar: September 28,

8 Modeling Requirements in LRH Analysis: The structure must be modeled in three dimensions. This is also required for MRS analysis and NLRH analysis in ASCE Where required, accidental torsion must be represented by use of mass offsets. This is necessary to retain algebraic signs and concurrency of force. P-Delta effects must be included in the analytical model. This allows of the inclusion of P-Theta Effects (amplification of global torsional response) that is not possible by use of post-facto amplification of forces and displacements. Not less than three sets of Spectrum Matched ground motion must be used. The ground motions are tightly matched to the same spectrum used in MRS analysis, providing consistency with MRS analysis but at the same time allowing for the advantages described earlier. BSSC Webinar: September 28,

9 Creating an Accidental Mass Eccentricity 1. Relocate α times original floor mass to edge of building 2. Reduce all original floor masses by factor (1-α) 3. Determine alpha such that mass translates only in X direction a distance 0.05L. 0.05L Line of Mass Translation M Moved Y X L BSSC Webinar: September 28,

10 System Modeling for P-Delta and P-Theta Effects.25P 0.5P 0.5P 0.5P.25P 0.5P P P P 0.5P 0.5P P P P 0.5P Gravity Column 0.5P P P P 0.5P.25P 0.5P 0.5P 0.5P.25P Lateral System Column Apply ACCURATE spatial distribution of gravity loads. BSSC Webinar: September 28,

11 Ground Motions: Three sets (two orthogonal components) of spectrally matched ground motions are required. Each component of ground motion is matched over a period range 0.8T Lower to 1.2 T Upper Match is to + or 10% of the target spectrum based on average for three components Time domain methods of response spectrum matching consist altering the original acceleration series by the addition of wavelets at select times. The time domain method is more complex than the frequency domain method, but it possess better convergence properties and typically better conserves the nonstationary characteristics of the ground motion. Spectrum Matching tool Developed at Virginia Tech BSSC Webinar: September 28,

12 Amplitude Scaled Records 0.8T Lower 1.2T Upper 2.22s Match Point BSSC Webinar: September 28,

13 Spectrally Matched Records 0.8T Lower 1.2T Upper BSSC Webinar: September 28,

14 Comparison of Records Amplitude Scaled Spectrum Matched +/- 10% Match Significant record-to-record variability Generally above target at higher frequencies Converging on Mean Response requires many records Virtually no record-to-record variability Generally on target Converging on Mean Response takes relatively few records BSSC Webinar: September 28,

15 Numerical Procedures: Both Modal Response History analysis and analysis by Direct Integration of the equations of motion are allowed. Where Modal Analysis is used: The number of modes required in the analysis is the same as required for MRS analysis. 5% viscous damping is required in each mode. P-Delta effects are included in the computation of the mode shapes and frequencies (by use of an initial gravity-load only load case). Where accidental torsion is required, one set of analyses is performed for each mass offset. This generally requires combination of results among different runs, which is not convenient unless the analysis software accommodates such combinations. Modal analysis is extremely efficient, even when diaphragms are modeled as semi-rigid. Single ground motion analyses can be completed in a few minutes for even the most complex systems (with tens of thousands of DOF). BSSC Webinar: September 28,

16 Numerical Procedures: Both Modal Response History analysis and analysis by Direct Integration of the equations of motion are allowed. Where analysis by Direct Integration is used: A maximum of 5% damping is allowed in the dominant modes. P-Delta effects are included by using one of the following approaches: 1) By use of an initial geometric stiffness based on a gravity load analysis. This stiffness is held constant during the analysis, thus iteration is not required. This is consistent with the approach used in MRS analysis. 2) By updating the geometric stiffness at each time step and iterating on equilibrium. This is in fact a nonlinear analysis (but the materials remain linear elastic). Where accidental torsion is required, one set of analyses is performed for each mass offset. This generally requires combination of results among different runs, which is not convenient unless the analysis software accommodates such combinations. Direct integration analysis with constant geometric stiffness is computationally efficient. However significant disc storage may be required. Where the geometric stiffness is updated the time required to perform each analysis increases significantly, and may be a concern for large complex systems. BSSC Webinar: September 28,

17 Run Time and Storage Requirements: Computer Time 80-story SAP 2000 model with semirigid diaphragms 115,200 DOF Note: LRH uses CONSTANT geometric stiffness Storage Requirements BSSC Webinar: September 28,

18 LRH Analysis Approach (1) Compute elastic base shear in each direction using V=C s W. These are designated as V EX and V EY BSSC Webinar: September 28,

19 LRH Analysis Approach (2) Compute elastic base shear in each direction using V=C s W. These are designated as V EX and V EY Compute inelastic base shear in each direction: BSSC Webinar: September 28,

20 LRH Analysis Approach (3) Compute elastic base shear in each direction using V=C s W. These are designated as V EX and V EY Compute inelastic base shear in each direction: Run linear response histories for each ground motion component without accidental torsion BSSC Webinar: September 28,

21 Analysis Without Mass Eccentricity: E1_X E1_Y Basic Analyses Used to Determine Scale Factors and Two analyses (X and Y) are run independently for each each ground motion. This is required instead of simultaneous application of X and Y components because different scale factors may be required in different directions. Analyses are scaled by multiplying each set of results by I e /R, and then adjusted (if necessary) to provide a base shear in each direction that is not less than 100% of the ELF base shear. BSSC Webinar: September 28,

22 LRH Analysis Approach (4) Compute elastic base shear in each direction using V=C s W. These are designated as V EX and V EY Compute inelastic base shear in each direction: Run linear response histories for each ground motion component without accidental torsion Compute Force Scaled Factors for each ground motion in each direction of response BSSC Webinar: September 28,

23 LRH Analysis Approach (5) Determination of Scaled Force Histories The combined force response in the X direction shall be determined as I e X /R X times the computed elastic response in the X direction using the mathematical model with accidental torsion (where required) plus I e η Y /R Y times the computed elastic response in the Y direction using the mathematical model without accidental torsion. The combined force response in the Y direction shall be determined as I e η Y /R Y times the computed elastic response in the Y direction using the mathematical model with accidental torsion (where required), plus I e η X /R X times the computed elastic response in the X direction using the mathematical model without accidental torsion. BSSC Webinar: September 28,

24 LRH Analysis Approach (6) Determination of Scaled Displacement Histories The combined displacement response in the X direction shall be determined as X C dx /R X times the computed elastic response in the X direction using the mathematical model with accidental torsion (where required) plus η Y C dy /R Y times the computed elastic response in the Y direction using the mathematical model without accidental torsion. The combined displacement response in the Y direction shall be determined as η Y C dy /R Y times the computed elastic response in the Y direction using the mathematical model with accidental torsion (where required), plus η X C dx /R X times the computed elastic response in the X direction using the mathematical model without accidental torsion. EXCEPTION: Where the design base shear in the given direction is not controlled by Eq. (12.8-6), the factors η X or η Y, as applicable, are permitted to be taken as 1.0 for the purpose of determining combined displacements. BSSC Webinar: September 28,

25 Additional Analyses if Accidental Torsion is Required E1_X_+eY E1_X_-eY E1_Y_+eX E1_Y_-eX Four analyses required for each earthquake Analysis is performed by use of 5% building dimension mass offset in one direction (without amplification) A total of 18 analyses (6 for each earthquake) are required when accidental torsion is included BSSC Webinar: September 28,

26 Load Combinations for Each Ground Motion (E1_X_-eY) (E1_Y) (E1_Y_+eX) (E1_X) Combination 1 Combination 3 (E1_X_+eY) (E1_Y) (E1_Y_-eX) (E1_X) Combination 2 Combination 4 BSSC Webinar: September 28,

27 Values used for design and displacement Forces and displacements (story drifts) used for design are based on envelope quantities from all analyses. Envelope values in columns and walls (and in other instances where interaction of forces is important) consist, for example, of maximum positive bending moment and concurrent axial force, as well as maximum axial compressive force and concurrent bending moment. BSSC Webinar: September 28,

28 Linear Response History Analysis Summary Offers significant advantages over Modal Response Spectrum Analysis Based on CURRENT commercial software procedures, the method is more cumbersome than Modal Response Spectrum Analysis. However, the limitations in current software are related to post-processing. This issue can be easily resolved by software developers. Software developers should be encouraged to implement procedures that support the Chapter 12 LRH Analysis procedures. Some programs (such as ETABS) already provide much of the capability needed, including spectral matching of ground motions. The future of ASCE-7 Analysis Procedures? BSSC Webinar: September 28,

29 Run Time and Storage Requirements for 20-Story Building 18 Minutes for LRH Analysis (18 LRH Analyses) BSSC Webinar: September 28,

30 Run Time and Storage Requirements for 20-Story Building 135 Minutes for Direct LRH Analysis (18 LRH Analyses) BSSC Webinar: September 28,

31 Linear Response History Analysis: Level of effort required to run LRH vs MRS or ELF analysis: Choose Response History instead of Response Spectrum analysis Select Hazard Parameters: Site Class: A B C D E Latitude 37.2 Longitude Automatically selects ground motions and perform spectral matching Select Analysis Method: Equivalent Lateral Force Response Spectrum Response History Automatically sets up all required analyses cases (including accidental torsion), selects and matches ground motions, performs analysis, and post-processes results. BSSC Webinar: September 28,

32 Questions? BSSC Webinar: September 28,