Rakesh K. Goel

Seismic Analysis of Buildings to Recorded Motions

Rakesh K. Goel — Tue, 21 Sep 2010 08:19:41 PDT

This investigation focused on developing an improved understanding of challenges associated with computation of nonlinear response of three-dimensional building to recorded ground motions, and if the base shear estimated from recorded motions, denoted as “estimated base shear” in this report, is an accurate indicator of the true base shear. For this purpose, three-dimensional models of two buildings – one reinforced-concrete building and one steel building – are developed in OpenSees and Perform3D¬. The analysis of these models included pushover analysis for lateral force distribution proportional to the first mode in each of the two principle directions, and nonlinear response history analysis (RHA) to compute response for 30 ground motions recorded during past earthquakes. It was found that modeling assumptions as well as different software may lead to significantly different pushover curves: concentrated plasticity model leads to lower strength, early initiation of yielding, and post yielding strength loss in pushover curves compared to spread plasticity model, strength loss model for beams/columns leads to significant post yielding strength loss in the pushover curve, and differences in solution schemes and convergence criteria available in different software programs also affect the pushover curves. It was also found that there prediction of median peak response from different software can differ from 10% to 40%. Finally, the median estimated base shear exceeds the true base shear by 10% to 20% with the value exceeding by as much as 50% for individual earthquake. Therefore, estimated base shear should be used with caution as an estimate of the true base shear.

Base Shear Estimated from Floor Accelerations and Column Shears

Rakesh K. Goel — Mon, 20 Sep 2010 17:46:41 PDT

This paper compares base shear computed from floor accelerations (inertial base shear) and column shears (structural base shear) for several single-degree-of-freedom (SDF) systems and two mid-rise, multi-story buildings due to a suite of 30 earthquake ground motions. The presented results show that the inertial base shear is close to structural base shear in short-period (<1>sec) SDF systems but may significantly exceed the structural base shear for individual ground motions in longer period (> 1 sec) SDF systems. Furthermore, the inertial base shear exceeds the structural base shear in the median by 10% to 20% and may exceed the structural base shear by as much as 70% for individual ground motions in multi-story buildings. Therefore, it is concluded that the inertial base shear should be used with caution to estimate the structural base shear in buildings with long fundamental vibration period whose motions are recorded during individual earthquake ground shaking.

Simplified Procedures for Seismic Analysis and Design of Piers and Wharves in Marine Oil and LNG Terminals

Rakesh K. Goel — Mon, 20 Sep 2010 17:45:19 PDT

Simplified Procedure for Seismic Evaluation of Piles with Partial-Moment Connection to the Deck in Marine Oil Terminals

Rakesh K. Goel — Mon, 17 May 2010 15:37:54 PDT

This paper presents development of a simplified procedure for seismic evaluation of piles with partial-moment connection typically used in marine oil terminals. The current seismic evaluation procedure of the piles in marine oil terminals includes monitoring material strains specified in the Marine Oil Terminal Engineering and Maintenance Standard (MOTEMS) during the nonlinear static pushover analysis to estimate the displacement capacity of piles. This investigation developed closed-form formulas for estimating the displacement capacity of piles by using a simple pile-deck connection system. The displacement capacity estimated from these formulas ensures that the material stain limits specified in the MOTEMS is not exceeded. These formulas are demonstrated to be "accurate" by comparing results from these formulas against those from the nonlinear finite-element analysis. The formulas developed in this investigation utilize the curvature ductility capacity of the pile section and rotation ductility capacity of the connection at the selected seismic design level, along with the parameter β which depends on the relative stiffness of the pile and the connection and the parameter η which depends on the relative strength of the connection and the pile.

EVALUATION OF NONLINEAR STATIC PROCEDURES USING STRONG-MOTION RECORDS OF BUILDINGS

Rakesh K. Goel — Thu, 07 Jan 2010 14:24:27 PST

The objective of this investigation is to evaluate the FEMA-356 Nonlinear Static Procedure (NSP) and a recently developed Modal Pushover Analysis (MPA) procedure using recorded motions of four buildings that were damaged during the 1994 Northridge earthquake. For this purpose, the motions at non-instrumented floors are “derived” from the motions at instrumented floors by using cubic spline interpolation procedure. Analytical models of the four buildings are developed using the computer program D2DX and calibrated by matching the computed vibration periods and the “elastic” periods identified form the recorded motions. Accuracy of the computer model is evaluated by comparing the computed displacement histories with the recorded motions. Finally, the displacement and drifts from the FEMA-356 NSP and the MPA procedures are compared with the values “derived” from the recorded motions.

It is found that the FEMA-356 NSP typically underestimates the drifts in upper stories and overestimates them in lower stories when compared to the recorded motions. Among the four FEMA-356 distributions considered, the “Uniform” distribution led to the most excessive underestimation or overestimation indicating that this distribution may be unnecessary. Furthermore, FEMA-356 distributions failed to provide accurate estimates of story drifts for buildings that satisfied the FEME-356 criterion for detecting the presence of higher mode effects indicating the need to carefully re-examine this criterion. The MPA procedure, in general, provides much-improved estimates of the response compared to the FEMA-356 NSP. In particular, the MPA procedure, unlike the FEMA-356 NSP, is able to capture the effects of higher modes. The error noted in few responses from the MPA procedure appears to be due to limitations associated with application of the modal combination rule, which is developed for response spectrum type applications, to peak responses from a single ground motion. For a building that exhibits dominant effects of “soft” first story, such as the Sherman Oaks 13-story building, however, neither the MPA procedure nor the FEMA-356 NSP led to reasonable estimate of the response; the MPA procedure provided reasonable estimates for the Los Angeles 19-story building that exhibited “soft” first story but this effect did not dominate the overall behavior of the building.

EVALUATION OF CURRENT NONLINEAR STATIC PROCEDURES FOR CONCRETE BUILDINGS USING RECORDED STRONG-MOTION DATA

Rakesh K. Goel et al. — Thu, 07 Jan 2010 14:24:08 PST

This study evaluates current Nonlinear Static Procedures (NSPs) specified in the FEMA356, ASCE-41, ATC-40, and FEMA-440 documents using strong-motion data from reinforced-concrete buildings. For this purpose, three-dimensional computer models of five reinforced concrete buildings – Imperial County Services Building, Sherman Oaks Commercial Building, North Hollywood Hotel, Watsonville Commercial Building, and Santa Barbara Office Building – are developed. When appropriate, springs at the building’s base are included to account for the soil-structure interaction effects. These buildings are selected because they were strongly shaken, several deformed beyond their linear-elastic range, during past earthquakes and their recorded motions are available. The recorded motions are interpolated to obtain motions at non-instrumented floors. These motions are used to derive seismic demands – peak roof (or target node) displacement, floor displacements, story drifts, story shears, and story overturning moments. The pushover curves are developed from nonlinear static analysis of computer models of these buildings and various demands estimated from the NSP methods.

A comparison of peak roof (or target node) displacements estimated from the NSPs with the value derived from recorded motions shows that: (1) the NSPs either overestimate or underestimate the peak roof displacement for several of the buildings considered in this investigation; (2) the ASCE-41 Coefficient Method (CM), which is based on recent improvements to the FEMA-356 CM suggested in FEMA-440 document, does not necessarily provide a better estimate of roof displacement; and (3) the improved FEMA-440 Capacity Spectrum Method (CSM) generally provides better estimates of peak roof displacements compared to the ATC-40 CSM. However, there is no conclusive evidence that either the CM procedures (FEMA-356 or ASCE-41) or the CSM procedure (ATC-40 or FEMA-440) lead to a better estimate of the peak roof displacement when compared with the value derived from recorded motions.

A comparison of the height-wise distribution of floor displacements, story drifts, story shears and story overturning moments indicates that the NSP provides: (1) reasonable estimate of floor displacements; (2) poor estimate of drifts in upper stories due to its inability to account for higher mode effects; (3) very poor, and possibly unreliable, estimates of story shears and story overturning moments.

A comparison of pushover curves from various computer programs using different modeling assumptions led to significantly different pushover curves. This indicates significant sensitivity of pushover curves to modeling assumptions which may potentially lead to different results and conclusions from the NSP.

Evaluation of Code Period Formula for Concrete MRF Buildings

Rakesh K. Goel et al. — Tue, 23 Jun 2009 15:19:03 PDT

The empirical formula specified in US building codes for fundamental vibration period of concrete moment resisting frame buildings is evaluated using periods of buildings measured from their strong motion records. The presented results show that the current code formula may lead to fundamental periods that are much shorter than the measured periods. In order to obtain better correlation between measured and computed periods, regression analysis technique has been used. The results indicate that the value of C, in the current code formula should be increased from its present value of 0.030 to 0.035.

Response to B. Maison's Discussion of "Evaluation of Modal and FEMA Pushover Analyses: SAC Buildings"

Rakesh K. Goel et al. — Tue, 23 Jun 2009 15:19:02 PDT

Seismic Control of Asymmetric Structures

Rakesh K. Goel — Tue, 23 Jun 2009 15:19:01 PDT

Control of Earthquake Induced Vibrations in Asymmetric Buildings Using Passive Damping

Rakesh K. Goel — Tue, 23 Jun 2009 15:18:59 PDT

This paper summarizes the results of a recent investigation on the dynamic response of asymmetric-plan buildings with supplemental viscous damping to harmonic ground motion using modal analysis techniques. It is shown that most modal parameters, except modal damping ratios and dynamic amplification factors, are affected very little by the plan-wise distribution of supplemental damping in the practical range of system parameters. The first modal damping ratio increases while the second decreases as CSD moves from right to left of the system plan, and their values increase with larger plan-wise spread of the supplemental damping. Trends for the dynamic amplification factors are reversed, as they are inversely influenced by the damping ratio, i.e., higher the damping lower the dynamic amplification factor. The largest reduction in the flexible edge deformation occurs when damping in the first mode is maximized.

Capacity and Stiffness of Bridge Abutments During Earthquakes

Rakesh K. Goel — Tue, 23 Jun 2009 15:18:59 PDT

Evaluation of a Modified MPA Procedure Assuming Higher Modes as Elastic to Estimate Seismic Demands

Anil K. Chopra et al. — Tue, 23 Jun 2009 15:18:58 PDT

The modal pushover analysis (MPA) procedure, which includes the contributions of all significant modes of vibration, estimates seismic demands much more accurately than current pushover procedures used in structural engineering practice. Outlined in this paper is a modified MPA (MMPA) procedure wherein the response contributions of higher vibration modes are computed by assuming the building to be linearly elastic, thus reducing the computational effort. After outlining such a modified procedure, its accuracy is evaluated for a variety of frame buildings and ground motion ensembles. Although it is not necessarily more accurate than the MPA procedure, the MMPA procedure is an attractive alternative for practical application because it leads to a larger estimate of seismic demands, improving the accuracy of the MPA results in some cases (relative to nonlinear response history analysis) and increasing their conservatism in others. However, such conservatism is unacceptably large for lightly damped systems, with damping significantly less than 5%. Thus the MMPA procedure is not recommended for such systems.

Improved Direct Displacement-Based Design Procedure for Performance-Based Seismic Design of Structures

Rakesh K. Goel et al. — Tue, 23 Jun 2009 15:18:57 PDT

Direct displacement-based design requires a simplified procedure to estimate the seismic deformation of an inelastic SDF system, representing the first (elastic) mode of vibration of the structure. This step is usually accomplished by analysis of an “equivalent” linear system using elastic design spectra. In this paper, an equally simple procedure is developed that is based on the well-known concepts of inelastic design spectra. This procedure provides: (1) accurate values of displacement and ductility demands, and (2) a structural design that satisfies the design criteria for allowable plastic rotation. In contrast, the existing procedure using elastic design spectra for equivalent linear systems is shown to underestimate significantly the displacement and ductility demands. The existing procedure is shown to be deficient in yet another sense; the plastic rotation demand on structures designed by this procedure may exceed the acceptable value of the plastic rotation, leaving an erroneous impression that the allowable plastic rotation constraint has been satisfied.

Evaluation of Modal and FEMA Pushover Procedures Using Strong-Motion Records of Buildings

Rakesh K. Goel — Tue, 23 Jun 2009 15:18:56 PDT

The objective of this investigation is to evaluate the FEMA-356 Nonlinear Static Procedure (NSP) and a recently developed Modal Pushover Analysis (MPA) procedure using recorded motions of four buildings that were damaged during the 1994 Northridge earthquake. For this purpose, displacements and drifts from the FEMA-356 NSP and the MPA procedures are compared with the values “derived” from the recorded motions. It is found that the FEMA-356 NSP typically underestimates the drifts in upper stories and overestimates them in lower stories when compared to the recorded motions. Among the four FEMA-356 distributions considered, the “Uniform” distribution led to the most excessive underestimation or overestimation indicating that the need to carefully reevaluate the usefulness of this distribution in the FEMA-356 NSP. Furthermore, FEMA-356 distributions failed to provide accurate estimates of story drifts for a building that satisfied the FEMA-356 criterion for detecting the presence of higher mode effects indicating the need to carefully re-examine this criterion. The MPA procedure, in general, provides estimates of the response that are much closer to the values from the recorded motion compared to those from the FEMA-356 NSP. In particular, the MPA procedure, unlike the FEMA-356 NSP, is able to capture the effects of higher modes. For a building that exhibits dominant effects of “soft” first story, however, neither the MPA procedure nor the FEMA-356 NSP led to reasonable estimate of the response.

Evaluation of Modal and FEMA Pushover Analyses: SAC Buildings

Rakesh K. Goel et al. — Tue, 23 Jun 2009 15:18:55 PDT

This paper comprehensively evaluates the Modal Pushover Analysis (MPA) procedure against the ‘‘exact’’ nonlinear response history analysis (RHA) and investigates the accuracy of seismic demands determined by pushover analysis using FEMA-356 force distributions; the MPA procedure in this paper contains several improvements over the original version presented in Chopra and Goel (2002). Seismic demands are computed for six buildings, each analyzed for 20 ground motions. It is demonstrated that with increasing number of ‘‘modes’’ included, the height-wise distribution of story drifts and plastic rotations estimated by MPA becomes generally similar to trends noted from nonlinear RHA. The additional bias and dispersion introduced by neglecting ‘‘modal’’ coupling and P-Δeffects due to gravity loads in MPA procedure is small unless the building is deformed far into the inelastic range with significant degradation in lateral capacity. A comparison of the seismic demands computed by FEMA-356 NSP and nonlinear RHA showed that FEMA-356 lateral force distributions lead to gross underestimation of story drifts and completely fail to identify plastic rotations in upper stories compared to the values from the nonlinear RHA. The ‘‘Uniform’’ force distribution in FEMA-356 NSP seems unnecessary because it grossly overestimates drifts and plastic rotations in lower stories and grossly underestimates them in upper stories. The MPA procedure resulted in estimates of demand that were much better than from FEMA force distributions over a wide range of responses—from essentially elastic response of Boston buildings to strongly inelastic response of Los Angeles buildings. However, pushover analysis procedures cannot be expected to provide satisfactory estimates of seismic demands for buildings deforming far into the inelastic range with significant degradation of the lateral capacity; for such cases, nonlinear RHA becomes necessary.

Energy Based Approach to Earthquake Response of Asymmetric Systems

Rakesh K. Goel — Tue, 23 Jun 2009 15:18:54 PDT

Extension of Modal Pushover Analysis to Compute Member Forces

Rakesh K. Goel et al. — Tue, 23 Jun 2009 15:18:53 PDT

This paper extends the modal pushover analysis (MPA) procedure for estimating seismic deformation demands for buildings to compute member forces. Seismic demands are computed for six buildings, each analyzed for 20 ground motions. A comparison of seismic demands computed by the MPA and nonlinear response history analysis (RHA) demonstrates that the MPA procedure provides good estimates of the member forces. The bias (or error) in forces is generally less than that noted in earlier investigations of story drifts and is comparable to the error in the standard response spectrum analysis (RSA) for elastic buildings. The four FEMA-356 force distributions, on the other hand, provide estimates of member forces that may be one-half to one-fourth of the value from nonlinear RHA.

Direct Displacement-Based Design Using Inelastic Design Spectrum

Rakesh K. Goel et al. — Tue, 23 Jun 2009 15:18:52 PDT

Role of Higher-"Mode" Pushover Analyses in Seismic Analysis of Buildings

Rakesh K. Goel et al. — Tue, 23 Jun 2009 15:18:50 PDT

The role of higher-“mode” pushover analyses in seismic analysis of buildings is examined in this paper. It is demonstrated that the higher-“mode” pushover curves reveal plastic hinge mechanisms that are not detected by the first-“mode” or other FEMA-356 force distributions, but these purely local mechanisms are not likely to develop during realistic ground motions in an otherwise regular building without a soft and/or weak story. Furthermore, the conditions necessary for “reversal” of a higher-“mode” pushover curve are examined. It is shown that “reversal” in a higher-“mode” pushover curve occurs after formation of a mechanism if the resultant force above the bottom of the mechanism is in the direction that moves the roof in a direction opposite to that prior to formation of the mechanism. Such “reversal” can occur only in higher-“mode” pushover analyses but not in the pushover analyses for the first-“mode” or other FEMA-356 force distributions. However, the “reversal” in higher-“mode” pushover curves was found to be very rare in several recent investigations that examined behavior of many moment-resisting frame buildings. Included are guidelines for implementing the Modal Pushover Analysis for buildings that display “reversal” in a higher-“mode” pushover curve.

Evaluation of US Seismic Code Provisions for Asymmetric-Plan Systems

Rakesh K. Goel et al. — Tue, 23 Jun 2009 15:18:49 PDT

The effects of plan asymmetry on the earthquake response of code-designed, one-story systems are identified with the objective of evaluating how well these effects are represented by torsional provisions in US building codes. The earthquake-induced deformations and ductility demands on resisting elements of asymmetric-plan systems, are compared with their values if the system plan were symmetric. The presented results demonstrate that the design eccentricity in US building codes should be modified in order to achieve the desirable goal of similar ductility demands on asymmetric-plan and symmetric-plan systems. The design eccentricity should be defined differently depending on the design value of the reduction factor R.