Proceeding the 6th Civil Engineering Conference in Asia Region: Embracing the Future through Sustainability ISBN 978-602-8605-08-3

WHY SHOULD DRIFT DRIVE DESIGN FOR EARTHQUAKE RESISTANCE? Mete A. Sözen1 1

School of Civil Engineering, Purdue University, West Lafayette, IN. E-mail: [email protected]

ABSTRACT It was the disastrous Messina Earthquake of 1908 that led the structural engineers in Italy to develop a procedure for earthquake-resistant design based on lateral forces. Considering the physics of structural response to earthquakes, this decision did not make sense. A structure cannot develop more lateral force than that limited by the properties of its components. An earthquake shakes a building. It does not load a building. A building loads itself during a strong earthquake depending on how stiff and strong it is. Nevertheless, the procedure based on force seemed to work in general. Besides it conformed to the thinking related to gravity loading and made it convenient to combine effects related to gravity and earthquake. Admittedly, an engineering design procedure can be good even if it is wrong. Because it worked, a whole near-science was built around the concept of lateral force. Today, it is not an exaggeration to claim that the peak ground acceleration is the focal point of almost all that governs earthquake-resistant design. In 1932, in a paper not filling a whole page in the Engneering News Record, Harald Westergaard (Westergaard, 1932) wrote that it was the ground velocity that was the driving factor for damage. His brilliant insight could have had the profession question whether force was the only issue for design, but it did not happen. Over the period 1967-1990, a series of earthquake simulation tests were carried out at the University of Illinois, Urbana. Although the tests were targeted at the problem of nonlinear dynamic analysis, the most useful results that emerged were that drift (lateral displacement) was the critical criterion for earthquake response of a structure, that strength made little difference for the drift response, and that maximum drift response could be related to peak ground velocity. The goal of the talk is to explain the changes in thinking inspired by what was observed in the laboratory and how developments on drift response are likely to affect preliminary proportioning of structures.

INTRODUCTION There are two simple design rules to achieve satisfactory earthquake resistance of a building structure. Both rules are related to geometry. Rule #1: Elevations of the floors must be at approximately the same level after the earthquake that they were before the earthquake and not as illustrated in Fig. 1. The object of the rule is to save lives. Rule #2: Geometry of the building on the vertical plane must not differ from its original geometry by more than a permissible amount on the order of a drift ratio 2 of 1.5% to 2% and not as illustrated in Fig.2. The object of the rule is to save the investment.

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Ratio of lateral relative displacement in a story to the height of the story.

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Fig. 1: After the Duzce, Turkey, earthquake of 1999 Rule #1 requires adequate detail, such as competent welding for structural steel or the proper amount of transverse reinforcement for reinforced concrete. It requires a minimum amount of analysis but considerable amount of knowledge from experience and experiment. The object is to achieve a fail-safe3 structure. Strictly, the engineer does not even need to know the characteristics of the ground motion. All the engineer needs to know is the finite possibility of the earthquake and be competent in the technology required to build a fail-safe structure. Rule #2 requires knowledge of the ground motion to occur and the response of the structure to that ground motion. Considering the lack of accuracy involved in estimating the ground motion in most localities, it requires a level of analysis consistent with the expected accuracy of the results in keeping with the tried and true engineering adage, “If one is going to be wrong anyway, one should be wrong the easy way.” This manuscript will focus on Rule #2

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Fig. 2: Chile 1985 As it can be inferred from the frequent use of PGA (Peak Ground Acceleration) for rating the intensity of strong ground motion in engineering design documents, equivalent lateral force tends to be the dominant driver in determining proportions of structural elements intended to serve as parts of a structural system resisting earthquake demand. G. W. Housner (Housner, 2002) attributes the use of lateral force in earthquake resistant design to M. Panetti of Torino Institute of Technology who was a member of the 14person committee formed by the Royal Italian Government after the disastrous earthquake of 28 December 1908. The committee was asked to develop design algorithms to help reduce the damage in 3

Meaning a structure that fails safely and not meaning a structure that does not fail although the no-fail option would be quite acceptable.

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later events. Panetti recognized the need for dynamic evaluation of the entire structure including its foundation but concluded that this was beyond the state of the art of his time and suggested design for equivalent static forces (Committee,1909). (Oliveto, 2004) has written that it was S. Canevazzi who suggested that the committee select buildings observed to have remained intact after the 1908 event and determine the maximum lateral static forces that they could have resisted, thus providing an observational basis for specifying lateral force requirements for design. The main concern of the committee members appears to have been two-story buildings. Studies by the committee resulted in a report requiring design lateral forces amounting to 1/8 of the upper-story weights and 1/12 of the first-story weight. Inasmuch as this method was modified after the Tokyo Earthquake of 1923 and re-modified countless times over the years by different groups in different countries, the main theme did not change. Except for rare instances, the dominant driver has remained as the equivalent lateral force despite changes in the amount and distribution of the forces assumed to act at different levels.

A SIMPLE METAPHOR FOR STRUCTURAL RESPONSE TO STRONG GROUND MOTION

Fig. 3A: Simple metaphor The response of the simple structural system in Fig. 3 does capture that of a large class of building structures. The two-dimensional “structure” in Fig.3a comprises one column fixed to Support A and, a rigid and strong girder resting on a frictionless roller on Support A. The girder is attached to a large mass. The flexural response of the column is assumed to be elasto-plastic (Fig. 3b). If Support A is moved rapidly to the right and if the mass is large enough, the column will develop its yield moment, My , at both ends (Fig. 3c). It will be subjected to a lateral shear force, V .

(1) My : limiting moment capacity of column h : clear column height V: shear force acting on the column. We ask a simple question. In the event of the idealized structure being subjected to a sudden horizontal movement of the foundation, what determines the maximum lateral force on the column?

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It is not unreasonable to assume that before the mass will have time to move, the columns will sustain a lateral deflection that will cause yielding. In that case, the base shear force is going to be that indicated by Eq. 1. Clearly, the driver is the moment capacity of the column. Now we need to modify our question. Who determines the base shear? The answer is the engineer. And that leads us to the next question. If the base shear is determined by the engineer, except in massive stiff structures, and not by the earthquake, why do we start the analysis with a crude estimate of the peak ground acceleration? We should be concerned with the drift and then, if needed, with the lateral force. This hypothetical conclusion may evoke an objection based on the fact that static design requires the force to determine the drift. What if the drift can be determined independently of the force or strength in most cases? Is it possible to determine the drift first and the strength later? Consideration of that possibility is the object of this discussion.

A BRIEF PERSPECTIVE OF THINKING ON EARTHQUAKE RESISTANT DESIGN IN THE SEVENTIES In the 1970’s professional thinking on earthquake-resistant design was dominated by at least four strong currents: (1) the concept of equivalent lateral forces as mentioned above, (2) theoretical considerations based primarily on experience and interests of mechanical engineers, (3) a response spectrum developed at the California Institute of Technology translated for design applications as “The Los Angeles Formula” that allowed lower base-shear coefficients for taller buildings, and (4) Newmark’s stroke of genius in expressing spectral acceleration response to strong ground motion in three period ranges: (a) nearlyconstant acceleration response, (b) nearly-constant velocity response, and (c) nearly-constant displacement response4 and then suggesting that energy absorption5 would reduce the calculated linear response either by the ductility ratio (ratio of yield to displacement capacity of the structure) or by a ratio based on the energy absorption capacity of the structure, with the reducing factor not exceeding five. In 1966, a simple experimental system (Sozen and Otani, 1970) to simulate one horizontal component of earthquake motion was assembled in structural laboratory of the University of Illinois, Urbana (Fig. 4). The experimental work was initiated by three engineers, Toshikazu Takeda, Polat Gűlkan, and Shunsuke Otani Their common goal was a reasonable explanation of the accepted reduction in the force response to earthquake demand. The first step appeared to be investigation and analytical reproduction of the forcedisplacement history of a reinforced concrete structure in an earthquake. Because almost all of the thinking about this problem had been in terms of a two-dimensional structure subjected to one horizontal component of the ground motion, experiments on the Simulator could answer some of the questions. Takeda had been dealing with the hysteresis problem for reinforced concrete structures at Tokyo University working with Professor Umemura (Takeda, 1962). At Urbana, he had the opportunity to test and polish his concept of nonlinear response of reinforced concrete in a dynamic environment.

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Much as it has been criticized for not being exact for every kind of ground motion, it is still an effective way of thinking of the ground-motion demand for proportioning structures. 5

It took some time to change the thinking from blast-resistant design where energy absorption was the issue to earthquake-resistant design where energy dissipation was the issue.

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Fig. 4: Elevation of the university of illinois earthquake simulator TAKEDA Using the University of Illinois Earthquake Simulator in 1967, a modest testing machine with a gravityload capacity not exceeding 45 kN and a double-amplitude displacement limit of 0.1 m., Takeda made a series of simple tests using single-degree-of-freedom specimens to determine the nonlinear response of reinforced concrete (Fig. 5). The specific object was to determine and formulate the hysteretic response of reinforced concrete in flexure as it was shaken to develop a series of displacements simulating those that might occur in an earthquake. The challenge was to calculate the lateral-force and drift response histories of a reinforced concrete structure throughout the duration of a base motion simulating one horizontal component of an earthquake motion. Takeda was successful in developing rules for hysteresis of reinforced concrete in the nonlinear range of response. The focus was on Newmark’s concept that the design force could be expressed as a fraction of the nonlinear-response force depending on the ductility of the structure. What Newmark accomplished virtually by intuition, Takeda was able to confirm by calculation based on properties of the structure and the ground motion.

Fig. 5: Test specimen type used by T. Takeda There was another aspect of Takeda’s test results that escaped notice, most likely because of the preoccupation with the magnitude of lateral force. The equivalent lateral force concept, that appeared to serve well as a design convention, had led to a contradiction between theory and observation. Analysis of the linear response of an arbitrarily damped structural model resulted in high lateral forces amounting to

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multiples of the structural weight, W. On the other hand, observations initiated in 1909, suggested that a lateral force of approximately W/12 might be sufficient. This created a wide intellectual chasm that focused attention on force response. The challenge to bring together linear dynamic response, observed nonlinear response, and a whole host of traditional safety factors led to overlooking Talbot’s dictum of “observation without preconception.”

Fig. 6: Results of test specimen T2 (Takeda) A simple example is provided by the results of one of Takeda’s test specimens that was subjected to two different levels of base motions with the same characteristics in successive test runs. Measured maximum force and drift responses are summarized in Fig.6 a and b in relation to maximum base acceleration measured in each test run. The maximum base acceleration was increased from 1.3g in test run 1 to nearly 2g in test run 2. The corresponding change in response acceleration was negligible (Fig. 6a). The observed maximum acceleration response of the mass (directly related to lateral force) was consistent with the concept of nonlinear (elasto-plastic) concept. Yielding of the column had already occurred in the first test run. Even though the maximum base acceleration in the second test run was some 60% higher than that in the first test run, the base shear would not be expected to increase. The maximum response acceleration would remain the same. Figure 6b shows the variation of the maximum drift (expressed as a ratio in relation to the column height) with increase in the maximum base acceleration. The increase in drift ratio of approximately 60% was comparable to the increase in the base acceleration of approximately 50%. It is, at best, awkward to explain this result in terms of force begetting drift. Could it be that drift begets force? This question which could have shortened the time toward a simple design concept was not asked.

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OTANI

Fig. 7: Variation of maximum roof drift with peak base velocity Otani’s main objective was to investigate whether Takeda’s hysteresis rules could be implemented in software to determine the response of multi-story reinforced concrete frames to strong ground motion (Otani, 1972). He developed the required software and tested its results using those from earthquakesimulation of tests of three-story frame structures. While he was doing that he also noted that there was a linear relationship between maximum drift and maximum base velocity. His penetrating observation ought to have clinched the idea that there was indeed a direct relationship between base velocity and drift response, but once again the emphasis on base shear as the driving factor resulted in not appreciating the importance of his observation.

GŰLKAN

Fig. 8: Gulkan's definition of substitute damping. In interpreting the results of single-bay single-story reinforced concrete frames tested using the simulator, Gűlkan maximum response in the range of nonlinear response, be it shear or drift, could be explained with a linear model using his definition of ”substitute damping” in period ranges that would fall within Newmark’s range of nearly constant velocity response and nearly constant displacement response (Gülkan, 1971). His results for substitute damping factors for the tests with base motions simulating earthquake motions are summarized in Fig. 8.

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Fig. 9: Acceleration response spectra at damping factors of 2 and 20% Gülkan observed the substitute damping to increase from 2% of critical at yield to approximately 15% at a defined ductility factor exceeding 4. Taking an extreme position, one could also interpret the damping data to suggest a sudden increase to 10% of critical and remain at that level. Linear acceleration response spectra are shown in Fig. 9 for the two bounding damping levels of 2 and 10 % of critical. Drift response spectra for the same conditions are shown in Fig. 10. The professional interest was on the implications of the substitute-damping idealization on force demand. If a structural system softened (increase in effective period) and developed increased damping under earthquake demand, the force demand would decrease. To cite a specific example in reference to Fig.9, if a system with an initial period of 0.5 sec softened to have an effective period of 1 sec. with effective damping increasing from 2 to 10% of critical, the response acceleration would decrease from 2g to 0.5g providing a rationale toward explaining the gap between linear-response analysis and design practice. Figure 10 shows the implications of the substitute-damping idealization on displacement response. Considering the system with an initial period of 0.5 sec. it is seen that, if the damping increases from 2 to 10 % of critical, the period could increase to 1 sec (a stiffness reduction to ¼ of initial) with no increase in the response displacement. A drift response calculated on the basis of a lightly damped linear system could be a good estimate of its nonlinear drift response.

Fig. 10: Displacement response spectra at damping factors of 2 and 10 % of critical ALGAN In the late seventies Algan (1982) started his work in search of a useful criterion by which to judge the safety and serviceability of a reinforced concrete structure in a seismic region. It still seems curious that at

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that time drift continued to be considered to be a minor consideration in design for earthquake resistance. This fact is captured very well in Appendix A. Algan’s compilation of data on damage revealed that, as long as brittle failure of the structure was avoided, the story drift ratio (a measure of the distortion of the building profile) was the best pragmatic indicator of intolerable damage especially because the structure amounted to a fraction of the cost of the building. His approach demanded a simple and yet realistic procedure for determining drift. To do that he went back to Gűlkan’s substitute damping, by that time expanded by Shibata (Shibata, 1974) into a fullfledged design method. The main conclusion from Algan’s work was that drift should control design rather than force and that the main concern for limiting drift was more often related to nonstructural elements than to the ductility of the structure. This was proposed explicitly during the seventh world conference on earthquake engineering in 1980 (Sozen,1980).

SHIMAZAKI In 1982, K. Shimazaki set out in search of an energy based criterion to determine the possible extent of response-force reduction (Shimazaki, 1984). While pursuing this goal he noticed that within Newmark’s range of nearly-constant velocity response, he could determine the nonlinear drift of reinforced concrete structures using linear analysis by assuming an amplified period of √2*T where T is the period based on uncracked state of the structure and a damping factor of 2% of critical. While this was a disturbing observation because his approach to drift response was insensitive to the area within the hysteresis loop as well as to strength it confirmed what Fig. 10 implied. Shimazaki reoriented his studies from acceleration to drift response to come up with a very simple and useful method for determining maximum drift response. He concluded that if TR + SR =>1

(2)

DR =