GEOPHYSICALRESEARCH LETTERS, VOL. 13, NO. 6, PAGES589-592, STRUCTURAL John F. DAMAGE Hall IN and MEXICO James Earthquake Engineering Research Laboratory, L. JUNE 1986 CITY Beck California Institute of Technology damage in Mexico City caused by the September 19, bute the ductility demand throughout the building and avoid concentration of yielding in a single 1985 earthquake. story. Abstract. various This paper describes features cluded. the structural Photographs which illustrate of structural One explanation behavior is presented are Flat-plate in- forced as to why columns consisting and slabs of rein- without did not fare well in the earthquake. failure mode was caused by inadequate buildings with fundamental periods of elastic vibration considerably below the predominant twosecond period of the ground motion were most vulnerable construction, concrete beams, One type of shear strength in the slab-to-column connections which resulted in pancake failures of the slabs with the columns remaining upright in some cases (Figure 3). The use of unreinforced masonry to fill in to damage. Introduction exterior walls between reinforced concrete frames The September 19, 1985 earthquake caused considerable damage to modern construction in Mexico City, but only in those areas on the bed of an old lake because there the ground motion was is a common construction practice in Mexico City. The masonry panels, being stiff, attracted a considerably amplified brittle, About 1000 buildings, (Beck and Hall, large share of the earthquake load and, being 1986). from mostly of masonry and rein- failed. in Diagonal shear are cracks resulting a characteristic of such failures (Figure 4). In addition, use of masonry infills on three sides of a building, forced concrete, were destroyed. Many more suffered moderate, but repairable, damage. A brief look at the effect of the earth. quake on buildings in Mexico City is presented in this paper. Included is one explanation of why buildings with fundamental periods of elastic vibration considerably less than the predominant period of the lake-bed motions were damaged most severely. The intrusion of this paper into a journal of geo- while leaving the front open, created a nonsymmetric distribution of stiffness, causing a torsional response that increased the stress on the structural elements in the perimeter of the building. Steel construction is rare in Mexico City, yet one of the most spectacular examples of damage occurred to the complex of five steel-frame physical research is intended to round out this special issue on the Mexican earthquake and to promote interaction between civil engineers and geophysicists. Overview often an overstress buildings at Conjunto Pino Suarez. A 21-story tower overturned at the 3rd floor level and fell to the south onto another tower of 14 stories (Figure 5). A clue to the collapse mechanism was obtained after the neighboring identical 21-story of the Damage tower (background of Figure 5) was stripped reMost of the buildings that suffered full or partial collapses probably lacked ductility, that is, the ability to undergo considerable yielding without losing strength. Since even most wellbuilt buildings yield during strong ground shaking, ductility is essential to avoid collapse, especially for long-duration earthquakes when a number of yield cycles occur. In reinforced concrete construction, proper detailing and placement of the steel reinforcing bars is an important element in providing ductility. Perhaps with longer bar anchorages and extra hoops vealing buckled columns on its southern column line at the 3rd story. These were steel box columns, and their plates separated at the welds. An interesting characteristic of the damage in Mexico City is that a great number of buildings to confine •..:•..•:.•...:•,, . the concrete, the school shown in Figure 1 would have survived the shaking. In design, ductility is interrelated with strength because if the strength of a building is too low, then the ductility demanded by an earthquake is very high. In Mexico City, lack of strength was evident in the columns of many buildings principle principle stronger Copyright (Figure 2), a violation •,• •: •>•, •..:•..."..•.•. ..•,•'. .•. ,. , •. ..•..... .• ................ .•.::-.•::.,..•..:•..•:.• .......... ..•..:•'•:": ,, ............ ,.• ..:.... •:. .............. :..... • :•,:•....... •• .•::. :•:•. '•'•..•.. ß •...... ::......... •. :........ --.......... '"•:::.-::•:..• • •. ß .....•,•.:•:::•:. . ....-..:.:. ................. ..•.:::':: .•.•:...• ..-.:'7 " ...... , .:•>•.•.• .• .. .,.,•?•:• .... '• "".' ............ •,:- .: .•=================== ............. .> ::::::::::::::::::::::: "-•. :'>•-:,•:::•' .... =,•::.. ..:: .... :.....: ...... .................. ":: -.......... .,'"'.,•:-'? ................... .•: ........ •............... .............. •...... .............. '.. :::::::::::::::::::::::::::::: ?. :'-.::::' ':-.• .'.•.:-':. •:: :-•'•:•:•::...: "•:::" ..,?•::':•:'• ...... .... ' ..• .....-.-.... ... , ......... .. . ..,•,.•......•,..... : ....... •,•. •.. of an important .' .. ' •-•':"'".'" •-•::" . ':...:.:...,•.' :. ' .........::::".• .•:. :•'...... ,--':::. "',i:.. : :..:::' ••:•-._• '••..•:•:.•.. •,:... .•.-•.•-•.•..-. :, :•.. ,:........:-• of seismic resistant design. This states that proportioning columns to be than the girders is essential to distri1986 by the American Geophysical •-•:?:.•.•...• Union. ?.'• . . •...:•.. ..•.: •..:.....• :.... :.. .•. .'.. •::: Paper number 6L6089. 0094-827 6/86/006L-6 089503.00 Fig. 589 ..... ================== 1. Collapsed school. 590 Hall andBeck:Structural Damage in Mexico City. Fig. collapsed 2. in their Weak columns. upper stories, lower portion intact (Figure 6). leaving the One possible reason for this behavior is that designers tapered the column sizes severely in the upper stories, permissible if only gravity and wind loads act, but unwise for earthquake loads. Another possibility is through impact between two buildings of different heights, spaced closely together (Figure 7). Although most of the damage occurred to superstructures, there were some foundation failures. Those multistory buildings in Mexico City founde½ on piles that were not long enough to bear on th• firm stratum below the soft clay layer may have slipped downward during the earthquake. This may be why the building shown in Figure 8 tilted. Discussion 4. (begins to suffer damage), it softens, and its effective period of vibration of around two seconds should be par- creases. shorter On the other ..... ...,.. hand, period of elastic •.• •,,'• .,.,?.'..,,, •. ?•,- • . -.:•,---.----.. ...•..,•:•,•.,•.f•,•z% •,•,.• •,.•- ß lengthens. Thus, a building having an elastic period of two seconds or more may move away from being in resonance with the ground shaking as its response in- ticularly hard hit due to resonance. However, this is an oversimplification because most ........•,...... .?.-.•, •-• ?.,. •,•-.,-,..• -•,-'•,, .....•.,•.• ,.•-..• •.•..•... Cracked masonry infills. buildings do not behave elastically during strong ground shaking as economics prevents them from being designed to do so. As a structure yields of the Damage The predominant two-second period in the ground motion recorded at the SCT site on the lake bed (Beck and Hall, 1986) suggests that structures with fundamental periods of elastic vibration Fig. ,..,..,.,. ...• • .•.' . .,•,....,, . - . •, a building vibration '•'•?• ,,. •.•.•?.,•.. ...?..- -. ß. ,•..•- -., •..z-.... ß• having a may move into ..,•.•.,,, ,, ,-... ....... .,,. . • .h.• ,• ..•.....• •.-¾" .--•,,,.,.•,,•??' .'.•¾.•.-,-•,,..•,•....•,•.•.,. •.•-.•....•.. ..... •,•-•".••,'-•..•Ah.,....,•,...•--??•, •.•.• .•,•?•.;--.•?.,-¾,• '+-',"" ..... •"•"•'.-':,'?'?-/•"• "--"''"'?.'•'A.,'" ' A???•?"; "•"' •,?•,,•.A?•'f .,..•.'•'•.•"-•,' •., ,... •-•,':•;h,?' ......,............ ,,,..,...,-,-.•','.':• •---• ........ ,,""_•? ",', ?.?.•.•;•,_,•.,%. '"-.•.•""'•'•:'.•--.••,.,•-,•,•?•., '•,,,•:,,.•¾,•.. --..•..•......,.,............ .:•,•.;A.•, ,;,?•'"•,-. •;•.'• ..... ..:•:....:. ......... .... :...,,• •-." ,...... ,•..• ......... •...... . 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'•• • ....•..•..•..•••••••••••• '•' "•'••'•••••••' "7 ............... •..•'"'•'•..•,•.•,"',• '•'.,•",• ' •' ,...•'.-•,• '•'•"•-•., •..•f..•?--• ..... - ,•,...•,• • •,.,,•,. •...•..,•"•-'-.'• ...... •• ....... • %•.• -•..•. •.,.•.•..,..•--..•.•. • •,•,'.'• •% ......•- -.•,• ..... ........... ,/ •-.• •,•.-'•,, -•.,,,. ......... ,•,?•., ••,•,, ............... .• •-•+• ............ ...• ,,• • ,,,' - ?.•. ,.•<...h-•,.•.• ......•,.......... ? ß .... .•,•., .? .............. . •'.... • . .•.•..• -'•-•.L•..•.-.'•.,•..•' •.•'•...,-"•,•'•..,,.,,,,•..,., ,..,'•.. ?.•..• .-•',•, ' ..... ',, . •. "•A• .... •'A.•' •'"'•. -•'•'• .... '-•'•-•, -,•'•'•'•v• .... ,•. • ....., ............... •,.,.•,• .,.,•,.. ........... ....... •,•.. ...• ....... -•..• "•-.•,.• •-•.... ..•,, .•.... .• Fig. 3. - ..• •'" , ."•-.•'i•'??•'•:•..•'•" ,•"?•?•.?",'•, '-.-"•'•¾',.•'• '? plate construction. • .•.•..•• ,?.•?•",, •.,?,• .. ?• ,......... . •.•. ......... ................. •'• ,• -.•'•.•'•--• .• •.•.............. .' ,•,., ?-.,. ........ Fig. ••,.•""••.•' •". • • ..... •.... .•. ...•.......... •.... .....•.•..?•....?.?,, .'...•. •.•.-•.• ..... -•.•. •.•,•..... ....... ,,•-.. ,,•.•.-•'-. ' • ...•. .•-•v ....? • ,.... • .• .,-•,•,-, •'•.•.•.•,• .-•............................. •......................:•.,•..?' '• 5. • Toppled tower at Pino Suare•. Hall and Beck: Structural Damage in Mexico City. The effect attack that yielding a structure receives has on the seismic can be demonstrated by a time-history analysis using an elasticplastic, hysteretic model. Consider a set of buildings from 2 to 40 stories which meets the seismic provisions of the building code in Mexico City. By this code, the strength of the building must be sufficient to resist a set of forces acting at the floor levels equivalent to the inertia forces produced by vibration of the building in a linear deformation shape. The sum of these design forces equals the product of the building weight and a seismic coefficient of 0.06 (independent of N) and a design load factor of, say, 1.2. Assume the structure vibrates in a single, linear deformation shape with elastic period of vibration of N/10 seconds and elastic- .... -•:•-:•-,,..• '" -.......... '--'• '•>..• '•'....... '•- •-•-"....•..•..•.•..•.•-..•:.. ' ...... •.•..•-'.. •........ .•...... .¾..• .•-•-•• '• ....•'"":•""'• •' '•"""•<• ' '"•-'•'"'-• •'•'• force-displacementrelation. Introduce :?•.•.• ............. •:'•J<:•'"'? '" .... '•'•'•'•'"':"":•": •' .............................. .... • '•'•:• ••.......•?•.•..•.???•?• :•:•plastic an over•trength factor toenable atwo-•tory • -•.,•. ............... ..•L.•.....:•.•....:-..?.• building to behave elastically without yielding Fig. 6. Upper story collapse. these that were located in the area of damage either collapsed or were severely damaged. Since N-story buildings have, in Mexico City, a fundamental period of elastic vibration of about the most vulnerable buildings 1/2 to 1-1/2 seconds. • ..... ..... ..-.•½' ...,• 1986), periods of ranged roughly .-.,.--.• •'.:.r.':•: ....... .. this agrees with the evidence. shows that a factor 2.7 of will suffice Analysis when the input is taken as the SCT east-west ground motion. Postulate a decrease in the overstrength factor with building height according to 1 + 3.4/N. Such a relationship is reasonable because short buildings are often bearing wall structures which can be considerably stronger than the code requires, while tall buildings are beam-column frame strucures, often with masonry infills, which have relatively much less reserve strength. Results from time-history analyses for the SCT a resonance condition as it yields. Indeed, the most vulnerable buildings in Mexico City were those in the 6 to 15 story range; about 20% of N/10 seconds (Kobayashi et al., since from . .... ß ... ß •, --: .... :.....-• • .• •.. . -.. . • • ß .• 7• • • •:; ::• . • ::?'.'•,:'•-•.-.• ...........• •. ...:.•.•.•. ..•.• ...... •:'• •. ...........• ........... :..•.•.•...:?•. ../"•,,?:•'•:. •. ...•:.:".•...•,.•.• .., .• ..... . • •: .... •:.......--.-•.•.•: ' . . . •. . ,...•-i:..•:" .:: •-.-,•...•.-:.... . •:.... •.• : . •.: ..... •......... :.•:•-:•-•,:'• ..... :-. •..'".... ?........,,.ß. .-• . ..... . :., •::• ' .: . •.•.:•....:• ¾='•-.•' . ? ,.....• .-: ..• . :• . .... :........ ....... ....... .- ... • :•..-:.•.• --'•: .:=.... .•.:. •? .•.:.:?•<•:•--i ?. :.'............ . . .•.•=. ../-: :. ................... ß •",•...• '..i...... _...•.•.._..•...?•':..•....'•.......•.'•.'::- , -- . '.•: ? . .=" •... = ß . . .......... ....!..-.- .•..•. .....?•:-•..•.•..•.:.-•-•--..• • •....•....../?i?•:.• ....... ..• ................. ...... "?•...•. •:•.:::•.;•.•..•/•:'.•,•..'.:,. .... •.•.,:.•;:•..:•.•--.,..•:• .. ,•. . . ...... ........ ... ......... ................ . • . •'":........ :•:-..•-.L :: •....•..i,' ....." ' " '' .•"..'•;•::"..'•.•..•-..•.:',,.'-::" •?....•..•?• ..................... •. '...•'.•.: .•?•.. -• -..... .............. .•'•.::' ,, ',. . •. '..',....•. • - '".'•'?---•'•...•.:.'..:•..¾..:'.. .•":.•. •.--:...:.'. .... •,.?: :•.-. . . .. .• -•:• ..:•"•'?• ?•-:•i•--::"•..'•: ..... •.., ...... •- z,-..•,.•.•>': •.... •...•'-•. ..•:•..•? •.:•,.•.• ,...... •...' • ......... .•... ...... •...•?.. ß ............ .• ,,..•;•: .•..• •,. •.::•: ............. •.•.•, / .:.• -.:=•-.•..... i. :•.- . ... •... ..•:....•..•.... • ..... .•..:•.,.......•-.. .•.•::.:...• ........ Fig. 7. Impact damage. .... ...... •..•.•. '•' .• .... ' ' .."'•'•?.•..'i.•". .......'•'..•:.'• .................... ..----•.-• • • '- ."' ....... •'-.. •:• ".•'•• .'"' "? •-:.:...•-• •"... - • '•i•?.' '":•.--•::. •:•-• ..... :::::•'•::'" •.':'" •,•,.•.•.•.•.-•.•:...-•.. ........ ?........ •.:•-....•.•.....•...:-•.•?• .......... .•.•"?" ..•.•:...:•::..:.? -.?..... .•. • ....... .'...•.•?...-.: ?•..:?....•.-.•-•A•..•..•-...•.•.'.•.......:.•.: %.•.?': ':}' ...•.-'•-'•' •:: ..... • '•"-•::.::: ..• •'/'.•: ,...•. '..':":'-. ..• "S' .•: •:'-•".•?.•..' '• '.,.. •. :•':•:..' .... "•. •.......... ................. •.7•?•..::'-..> ...•...•"•:•....•...:.. •'•i•.••,.•-...•:•¾•;• ,..•.• •-.•??•,•,:'•. - . .-".....•:.•:..•::• ...-.,:.•.... -.,•,•:•'. ........... •:•...•:•-:•,"> ......... :,.' .... :•., -.... Fig. 8. Foundation failure. 592 Hall SEISMIC and Beck' Structural COEFFICIENT, C• =0.55 (elastic) C• = 0.06 BUILDING HEIGHT (NI•. Damage in Mexico City. long duration which produce many cycles of yielding. Increasing the seismic coefficient to 0.12 greatly reduces the ductility demand. The post-earthquake code in Mexico City now has es- sentially this seismic coefficient (Rosenblueth and Meli, 1986). Although the analysis correctly predicts the height range of the most vulnerable buildings, the ductility ratios given in Figure 9 and mentioned above should be interpreted with caution due to the many assumptions made. For example, soil-structure interaction and nonlinear soil softening have been neglected; the many degrees of freedom of a real structure have been replaced by a single, linear deformation shape; and uniform yielding throughout the building has been assumed. However, the analysis does capture an I•F 8TI•RIE$• essential characteristic of the nonlinear re- sponse, suggesting why the damage was concentrated in buildings with fundamental periods of elastic vibration significantly less than the two-second predominant period of the lake-bed motion. Concluding Remarks Even in the severely damaged areas of Mexico City, many buildings survived undamaged, some without even a broken pane of glass. Why did some buildings fare well while others suffered? Were building collapses due to gaps in engiBUILDING HEIGHT (N8• •IF $TSRIE$) Fig. 9. Building responses computed for east-west ground motion. the SCT east-west input are presented in Figure 9 (maximum roof displacement vs. building height and ductility ratio vs. building height) for three designs based on seismic coefficients of 0.06 (as in the Mexico City code), 0.12, and 0.55 (a value sufficiently high so that no yielding occurs). The ductility ratio, or ductility demand, is the maximum roof displacement experienced during the earthquake divided by the roof displacement at which yielding commences. If no yielding occurs, the ductility ratio is defined to be unity. The elastic response (Figure 9, top) shows a considerable resonance for buildings 20 to 25 stories in height due to the coincidence of their elastic vibration periods with the predominant period range in the ground motion input. For buildings designed with lower seismic coeffi- cients (0.06 or 0.12), this resonance disappears due to the lengthening of the building period as yielding takes place. The seismic attack on the building is best measured in terms of ductility demand (Figure 9, bottom). The demand is highest for buildings 6 to 15 stories in height. Apparently, yielding has moved the 6 to 15 story buildings into a resonance condition (relative to the yield displacement) and moved taller buildings away. The ductility ratio requirement of 5 to 7 as shown by the analysis can be met with good design and detailing practices, but could cause considerable trouble otherwise, especially for earthquakes of neering knowledge or to sloppy design or construction? Is the building code adequate? These questions remain partially unanswered. While general analyses such as presented in the previous section help, full resolution of these questions awaits studies of individual buildings. Unfortunately, a lack of detailed documentation of the damage following the earthquake, the subsequent demolition and removal of many buildings without inspection or material testing, and the difficulty of gaining access to the structural plans of the buildings may prevent these questions from ever being completely resolved. References Beck, J.L. and J.F. Hall, Factors contributing the catastrophe in Mexico City during the to earthquake of September 19, 1985, Geophys. Res. Letters, this issue. Kobayashi, H., K. $eo and S. Midorikawa, Report on seismic microzoning studies of the Mexico City earthquake of September 19, 1985, Part 2, Tokyo Institute of Technology, Yokohama, Japan, Feb. 1986. Rosenblueth, E. and R. Meli, The 1985 earthquake: causes and effects in Mexico City, Concrete International, American Concrete Institute, May 1986. J. L. Beck and J. F. Hall, neering Research Laboratory, Earthquake EngiCaltech, Pasadena, CA 91125 (Received February 28, 1986; accepted April 22, 1986.)