Chapter 6: Analytical Studies 
ductility demand has, in general, only a small effect on TakedalO oscillators having DDD = 2. Collapse of the 
displacement demand applies equally to the standard damaged oscillators (whether the corresponding 
Takeda oscillator and to Takeda oscillators that exhibit undamaged oscillator collapsed or not) is indicated by a 
pinching. The Takeda5 oscillators with initially reduced ratio equal to six, and collapse of the undamaged 
strength, given by RSR = 0.6, tended to have a response oscillators is indicated by a ratio equal to zero. 
amplified to a much greater extent than is observed for Approximately 10% of the oscillators having DDD = 2 
the TakPinch model, reflecting the more dramatic form collapsed with no prior damage. This indicates that 
of strength degradation that was implemented in the structures characterized by negative post yield 
Takeda5 model. stiffnesses must remain nearly elastic if collapse is to be 
avoided. Prior ductility demand may cause 
6.4.3.3 Response of TakedalO Model displacement response to either increase or decrease for 
The TakedalO model is a Takeda model having post those oscillators that do not collapse. 
yield stiffness equal to 10% of the yield point secant 
Figure 6 54 plots the displacement time history of a
stiffness. As has been found previously by others, mod one second oscillator having DDD = 8 and PDD
with negative post yield stiffness are prone to collapse 
ranging from 0 (undamaged) to 8, subjected to the NS, where collapse is defined as the point at which component of the 1940 El Centro record. It can be
the displacement is large enough that the force resisted observed that prior ductility demand helps to avoid
by the oscillator decreases to zero. Comparisons of peak collapse in some cases, and may cause collapse in
displacement response are of limited value when collapse 
occurs. Instead, the likelihood of collapse is used others. 
to assess the impact of prior damage on response for the 6.4.4 Response Statistics
TakedalO models. 
Summary response statistics were prepared to identify 
Figures 6 51 to 6 53 plot the ratio, d dldd, of damaged general trends in the data. 
and undamaged peak displacement response for the 
Records=SD; DDD=2; PDD=1; RSR=1; Model=Takedal0 
oscillator
6 Amplitude of 6 identifies collapse of damaged oscillator; 0 identifies collapse of only the undamaged Excludes cases where prior damage (PDD) exceeds undamaged response 5 S. A SP88GUKA.360 
4 V LP89CORR.090 
NR94CENT.360 
IV79ARY7.140 
br 3 e V 00 Vzh & nV 
0 O 4 0 I2 3 4 
Period Ratio, TIT, 
Figure 6 51 Effect of Cracking on Displacement Response of TakedalO Model for Short Duration Records (DDD= 8 and PDD=1) 
DDD = Design Displacement Ductility; PDD = Prior Ductility Demand; RSR = Reduced Strength Ratio 151 
Technical Resources 
FEMA 307 Technical Resources 151 
Chapter 6: Analytical Studies 
Mean (d d dd), TakPinch, RSR=1 
S.a a. Mean + SD (d dldd), TakPinch, RSR=1 
8 116 rv 6 6Ea) 
a 4 E 4. 1:2 115 
4 727. 
1 
0 
0 
0 
2 
0 
8 
1 I 1:0 0.9 b O09 
l; D00 o i1; 0 i i.E 1 2 3 4 5 6 7 8DesignDisplacementDuctility (
DDD) Mean (d dldd), TakPinch, RSR=0.8, 
0 a. a. 
2 1.43 1.22 1:16 
1:23 1 22.11 1101 
00 10 0 100 10 
1 2 3 4 5 6 7 8 
Design Displacement Ductility (DDD) 
Mean + SD (d dldd), TakPinch, RSR=0.8 
86 0 6. E 
0) a 4 E 0a 
j.44 ll5 
2 2 1S4 1.l I. 
a 0 1:071.O8.100 0.98 
0e M; 37 1.40 1 17 > z1 
0 II 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 
a. Design Displacement Ductility (DDD) Design Displacement Ductility (DDD) 
EL E, 8 
Mean (d d dd), TakPinch, RSR=0.6 
S a Mean + SD (dd dd), TakPinch, RSR=0.6 
8. 1:24 a r0 6 4 0 
1.0. `4 4, 111 s1, 02 
Ca E0 a 6 4 a. i.i < 1.45. 1; 20 
a) 2 I1.21 1.08 1.04 
11ii1 1:17 10; 7 1.. 03 
2 1.<72 1A2; 1.55 
1:48h6 64; 1A3 1.26 
0 0 0 1 2 3 4 5 6 7 8 A. 1 2 3 4 5 6 7 8 
Design Displacement Ductility (DDD) Design Displacement Ductility (DDD) 
Figure 6 56 Mean and Standard Deviation Values of d d dd for TakPinch Model. 
damaged structure to a given earthquake varies relative 
to the response in the initially undamaged state. 
However, this variability is insignificant in the context 
of variability arising from other sources. For example, 
the hysteresis model and earthquake ground motion 
have a greater effect on response displacements than the 
variability arising due to prior damage. Figures 6 32 to 
6 34 indicate how different the peak displacement 
response of undamaged Takeda and bilinear models can 
be to a given earthquake. 
Figure 6 57 shows the percentage of TakedalO 
oscillators that reached their collapse displacement. It 
can be observed that 10% or more of those structures 
designed to achieve a displacement ductility of two 
collapsed. This indicates the need to ensure that 
structures having negative post yield stiffnesses remain 
nearly elastic if collapse is to be avoided. Strength 
reduction tends to increase the tendency of the 
oscillators to collapse. No clear trend emerges as to the 
effect of PDD on the tendency of these oscillators to 
collapse. 
6.5 Nonlinear Static Procedures 
6.5.1 Introduction 
Nonlinear static analysis is used to estimate inelastic 
response quantities without undertaking the effort 
required for inelastic dynamic analyses. Several 
methods are presently in use. No consensus has 
emerged as to the applicability and relative accuracy of 
the methods, which are collectively known as nonlinear 
static procedures (NSP) These procedures each focus 155 
Technical Resources 
FEMA 307 Technical Resources 155 
Chapter 6: Analytical Studies 
Collapse Percentage for RSR=1 
X 8, v > 8O2 6 6; E.
O 4. 65% 869 
I ?. 2 21% 58% 909M 
0% 10% 55% 859% 
0 070l% 5, %, i 9s 
0. 1 2 3 4 5 6 7 8 
Design Displacement Ductility (DDD) 
Collapse Percentage for RSR=0.8 
0. 8: 
I E. 6j. 4. 
7 1 9 4n.
2242%: 
69%G. 9 6% 
a0.66% 98
I 1 2 3 4 5 6 7 8 
Design Displacement Ductility (DDD) 
Collapse Percentage for RSR=0.6 
8 6.>4. s pt sa E o 2 9. 
n4t t 8X% 6
A 98% c.
j j t I
O 1 2 3 4 5 6 7 8 
Design Displacement Ductility (DDD) 
Figure 6 57 Percent of Takeda10 Oscillators that Collapsed 
on different parameters for determining estimates of NSP are compared with values computed from dynamic 
peak displacement response. Consequently, NSP analyses in Section 6.6. 
displacement estimates may be affected to different 
degrees by differences in hysteretic model, initial 6.5.2 Description of Nonlinear Static 
stiffness, lateral strength, and post yield stiffness. Procedures 
Section 6.5.2 describes three nonlinear static methods; The methods are briefly described in this section for 
displacement coefficient, secant, and capacity spectrum cases assumed to correspond most closely to the 
methods. Differences among the methods and the dynamic analysis framework of Section 6.3.3, 
implications for estimating displacements are discussed representing wall buildings at the collapse prevention 
in Section 6.5.3. Assumptions made to extend the performance level. The reader is referred to FEMA 273 
methods to cases with prior damage are discussed in for greater detail on the displacement coefficient 
Section 6.5.4. Displacement estimates obtained using method, and to ATC 40 for greater detail on the secant 
and capacity spectrum methods. The displacement 
FEMA307 
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Technical Resources FEMA 307 
Chapter 6: Analytical Studies 
coefficient method described here is the same as in 
FEMA 273. 
6.5.2.1 Displacement Coefficient Method 
The displacement coefficient method estimates peak 
inelastic displacement response as the product of a 
series of coefficients and the elastic spectral 
displacement. The peak displacement estimate, dd, is 
given by dd = COCIC2C3Sa@); (6 2) 
where coefficients C0 through C3 modify the spectral 
displacement, given by the product of the elastic 
spectral acceleration, Sa, and (Te 21t) 2, where T, is an 
effective period based on the effective stiffness 
determined using the construction of Figure 6 58. 
In the above, C0 relates the spectral displacement and 
the expected roof displacement, and is set at 1 for 
SDOF systems. The coefficient C1 accounts for the 
amplification of peak displacement for short period 
systems, is set at 1 for T, > Tg, and is computed as 
follows for T, < Tg: 
Cl = 1 + (1 1 Tg (6 33 
where R = the strength reduction factor, given by the 
ratio of the elastic base shear force and the effective 
Fye Fye 0.6 Fye 
Pushover ye yI Displacement 
yield strength, Fyes illustrated in Figure 6 58. An 
optional limit of 2 on C1 was not applied in the analyses 
described here. 
The coefficient C2 accounts for the type of hysteretic 
response. At the collapse prevention performance level, 
C2 varies linearly between 1.5 at 0.1 sec and 1.2 at Tg. 
and remains at 1.2 for T, greater than Tg. 
The coefficient C3 accounts for increases in 
displacements that arise when P A effects are significant. 
Because the dynamic analyses did not include 
second order effects, C3 was assigned a value of 1. 
However, the Takeda 10 models had a negative post 
yield stiffness of 10 percent, which approximates P A 
effects 
6.5.2.2 Secant Method 
The secant method assumes that the peak displacement 
response of a nonlinear system can be estimated as the 
peak response of an elastic system having increased 
period. An idealized lateral force displacement curve 
for the structure is developed using a static pushover" 
analysis. The elastic response of the structure is 
computed using a response spectrum analysis, using 
initial component stiffness values. The resulting elastic 
displacements are used to obtain revised stiffness values 
for the components, set equal to the secant stiffness 
defined at the intersections of the component force 
displacement curves and the elastic displacements 
obtained from the response spectrum analysis. Using 
these revised stiffness values, another response 
spectrum analysis is performed, and iterations continue 
Force I y PDDAy 
Displacement 
Figure 6 58 Construction of Effective Stiffness for use with the Displacement Coefficient Method 
FEMVA 307 Technical Resources 
Chapter 6: Analytical Studies 
Force Ax PDDAy Displacement 
Figure 6 59 Initial Effective Stiffness and Capacity Curves Used in the Secant and Capacity Spectrum Methods 
Force or Spectral 
Pseudo Acceleration 
5% Damped 
Elastic Spectrum 
Pushover Curve Peak Displacement Estimate 
Displacement or Spectral 
Displacement 
Figure 6 60 Schematic Depiction of Secant Method Displacement Estimation 
until the displacements converge. All response stiffness. This stiffness may be used to obtain a revised spectrum analyses are made for 5% damping in the estimate of peak displacement response. These secant method, as described in ATC 40. iterations continue until satisfactory convergence 
For SDOF structures, the secant method can be occurs. This is shown schematically in Figure 6 61. 
implemented in spectral pseudo acceleration spectral 
displacement space, much like the capacity spectrum 6.5.2.3 Capacity Spectrum Method 
method. The force displacement curve may be Like the secant method, the capacity spectrum method 
determined using the constructions of Figure 6 59 for assumes that the peak displacement response of a 
both the undamaged and damaged oscillators. This nonlinear system can be estimated by an elastic system 
curve is plotted together with the elastic response having reduced stiffness. The difference is that the 
spectrum for 5% damping in Figure 6 60. An estimate elastic spectral response values are modified to reflect 
of peak displacement is indicated in the figure. For the increases in damping associated with inelastic response. 
undamaged oscillators, an initial estimate of peak A lateral force pushover" curve is developed for the 
displacement response is the peak response of an elastic structure and plotted on spectral pseudo acceleration 
oscillator having stiffness equal to the initial stiffness of spectral displacement coordinates. The structure is 
the oscillator. The intersection of the previous assumed to displace until it reaches an elastic demand 
displacement estimate with the idealized force curve that has damping that corresponds to a value 
displacement curve of the structure defines a new secant based on the current displacement estimate. 
Technical Resources FEMA 307 
Chapter 6: Analytical Studies 
5% Damped 
Elastic Spectrum 
Pushover Curve 
Peak Displacement Estimate 
10. 
Displacement or Spectral 
Displacement 
Figure 6 61 Schematic Depiction of Successive Iterations to Estimate Displacement Response Using the Secant 
Method for Single Degree of Freedom Oscillators 
The method may be implemented by successively 6.5.3 Comments on Procedures 
iterating displacement response. The initial 
displacement is estimated using the initial stiffness of From the above descriptions, it is clear that there are 
the structure and assuming elastic response for damping fundamental differences among the various NSPs. The 
equal to 5% of critical damping. The intersection of the displacement coefficient method primarily relies on the 
displacement estimate and the idealized force initial effective stiffness to determine a baseline spectral 
displacement curve determines a revised estimate of the displacement, and it considers strength to a lesser extent 
secant stiffness. Effective viscous damping is revised for short period structures. 
prescriptively, based on the displacement estimate. This 
calculation represents the increase in effective damping The secant and capacity spectrum methods are 
with increased hysteretic losses. The iterations continue insensitive to initial stiffness (for structures that yield) 
until satisfactory convergence is obtained. Figure 6 62, and displacement estimates depend primarily on yield 
illustrates the application of the method. strength and post yield stiffness. Effective damping 
varies with displacement amplitude in the capacity 
Spectral Pseudo 5% Damped Elastic Spectrum 
Acceleration 2 10, 15, and 20% Damped Spectra 
Pushover Curve 
Peak Displacement F Estimate 
Displacement or Spectral 
Displacement 
Figure 6 62 Schematic Depiction of Successive Iterations to Estimate Displacement Response Using the Capacity 
Spectrum Method 
FEMA 307 Technical Resources 
Chapter 6: Analytical Studies 
spectrum method, while it is invariant in the secant 
method. In the form presented in ATC 40, secant 
method displacement estimates are independent of 
hysteretic model. Through changes in coefficient C2, 
changes in the force displacement model may be 
incorporated in the displacement coefficient method. 
Differences in hysteresis model are accounted for in the 
capacity spectrum method adjusting effective damping 
for three structural behavior types." 
6.5.4 Application of Procedures to 
Undamaged and Damaged 
Oscillators 
Each procedure presumes that a smoothed, elastic 
design response spectrum is to be used in practice. To 
avoid uncertainties in interpretation of results, the actual 
pseudo acceleration spectra were used in place of a 
smoothed approximation in this study. For the capacity 
spectrum method, the actual pseudo acceleration 
spectra were computed for a range of damping levels, 
and the spectral reduction factors that are prescribed for 
use with smoothed design spectra were not employed. 
These modifications introduce some scatter in the 
resulting displacement estimates that would not occur if 
smoothed spectra had been used. Thus, some 
smoothing" of the data may be appropriate when 
interpreting the results. 
The NSPs were developed for use with undamaged 
structures. In this study, the NSPs were applied to the 
initially damaged structures using the assumptions 
described below, representing one of many approaches 
that can be taken. Recommended procedures for 
estimating displacements are described in Section 4.4 of 
FEMA 306. 
For the displacement coefficient method, the capacity 
curve was obtained by the procedure described in 
FEMA 273. For the uncracked oscillators, a bilinear 
curve was fit, crossing at 60% of the bilinear curve yield 
strength. For the damaged oscillators, the effective 
period of vibration was set at the initial period of the 
damaged oscillators. Displacements were amplified by 
the factor Cl without imposing the optional limit of 2 
specified in the provisions. 
The secant method was applied iteratively. For 
undamaged oscillators, the initial stiffness was the 
yield point secant stiffness. For damaged oscillators, it 
was set at the secant stiffness obtained at the 
displacement imposed by prior ductility demands. The 
initial stiffness of the damaged oscillators therefore 
reflected the previous damage. 
The capacity spectrum method was also applied 
iteratively, beginning with the same initial oscillator 
stiffness used in the secant method. Effective damping 
was determined by using the yield point of the 
undamaged oscillators. The capacity spectrum method 
was implemented for an intermediate building 
characteristic, identified as Type B. This type is 
considered to represent average existing buildings 
subjected to short duration motions and new buildings 
subjected to long duration motions. For this type, 
effective damping is limited to 29% of critical damping. 
For both the capacity spectrum and the secant stiffness 
methods, 10 iterations were performed for each 
structure. These iterations generally converged on a 
single result, and differences in successive 
approximations were typically less than 1%. On 
occasion, differences in successive approximations 
were large, suggesting a lack of convergence due to the 
jagged nature of the actual (not smoothed) spectra. 
Where these differences occurred, the displacement 
estimate at the tenth iteration was retained. 
6.6 Comparison of NSP and 
Dynamic Analysis Results 
6.6.1 Introduction 
In evaluating the utility of the NSPs, attention may be 
directed at two estimates. The first is peak displacement 
response; it could be expected that an acceptable 
procedure would estimate the peak displacement 
response, dd, of a nonlinear system within acceptable 
limits of accuracy. Second, it is possible that a 
procedure may be systematically biased, and hence may 
estimate displacement response poorly while providing 
reasonable estimates of displacement ratio; that is, the 
ratio of damaged structure displacement to undamaged 
structure displacement, d dldd. These response indices, 
dd and d d dd, are examined in detail in the following 
sections for Takeda oscillators designed for bilinear 
DDDs of 8. 
6.6.2 Displacement Estimation 
Peak displacement response of the undamaged Takeda 
oscillators was estimated for each earthquake record. 
The ratio of the peak displacement estimate from NSP 
Technical Resources FEMA 307 
Chapter 6: Analytical Studies 
and the value computed for each Takeda5 oscillator, at 
each period and for each ground motion record, is 
plotted in Figure 6 63 for DDD = 8 and RSR = 1. The 
log scale plots the ratio of estimated and computed 
displacement, ddNsp dd. Plots are presented for each 
ground motion category and for each NSP. 
In Figure 6 63, it can be observed that the ratio of the 
estimated and computed displacements, ddNspldd, can 
vary significantly, ranging from less than 0.3 to more 
than 100. At any period ratio, the ratio ddNsp dd may 
approach or exceed an order of magnitude. Because the 
trends tend to be consistent for each ground motion 
record, the jaggedness of the actual spectra does not 
appear to be the source of most of the variability. 
Figure 6 64 plots mean values of ratios dd NSPldd 
determined for each NSP, for all ground motions and all 
DDD values. Results for short and long period 
Takeda5 oscillators are plotted separately. In 
Figure 6 64, it can be observed that the NSP procedures 
tend to overestimate, in a mean sense, the displacements 
computed for the short period Takeda5 oscillators for 
all DDD. Takeda oscillators having DDD = 1 often 
displaced less than their bilinear counterparts because 
the Takeda oscillators had initial stiffness equal to twice 
that of their bilinear counterparts. The difference in 
initial stiffness explains the tendency of the NSP 
methods to overestimate displacements for low DDD. 
This is particularly true for the secant method estimates 
of short period oscillators, for which mean ratios 
exceeded six for DDD greater than 1. The period ratio, 
Te Tg, marking the boundary of the elevated estimates 
tends to be less than one, possibly reflecting the 
effective increase in period of Takeda5 oscillators as 
their stiffness reduces (Figure 6 63) 
Figure 6 64 indicates that each NSP tends to 
overestimate the displacement response of short period 
oscillators and that the capacity spectrum method is 
most accurate for long period Takeda5 oscillators, in a 
mean sense. Nevertheless, Figure 6 63 indicates the 
substantial variability in displacement estimates and the 
potential to overestimate or underestimate 
displacements with all methods. A single estimate 
cannot capture the breadth of response variability that 
may occur at a given site. 
Based on Figures 6 63 and 6 64, the coefficient and 
capacity spectrum methods appear to be reasonably 
accurate and to have the least scatter. The secant method 
tended to overestimate displacement and exhibited more 
scatter in values of ddNSPdd 
6.6.3 Displacement Ratio Estimation 
The ratio of damaged oscillator displacement, d d, and 
the displacement of the corresponding Takeda oscillator 
having no initial damage, dd, was estimated using the 
NSP methods for each Takeda oscillator earthquake 
pair, as described in Section 6.5.4. This estimated 
displacement ratio is compared with the ratio computed 
from the dynamic analyses in Figures 6 65 through 
6 73. 
It can be observed that simple application of the 
displacement coefficient method using the initial 
stiffness of the undamaged oscillator to calculate dd and 
using the reduced stiffness of the damaged oscillator to 
calculate d d almost always overestimates the effects of 
damage for the cases considered. 
Application of the secant and capacity spectrum 
methods, using the initial and reduced stiffness values, 
typically led to nearly identical displacement estimates: 
estimates of d dldd were often approximately equal to 
one. Figures 6 68 through 6 73, which might appear to 
testify to the success of the methods, instead tend more 
to represent the inverse of the d dldd as computed for the 
Takeda models. Figures 6 38 through 6 40 indicate that 
computed values of ddld d should tend to be around one, 
decreasing slightly for small periods. 
The preceding plots examine the effectiveness of the 
methods, as implemented here, for estimating the 
consequences of prior ductility demand. It is also of 
interest to examine the effectiveness of the methods in 
accounting for strength loss. To do this, the ratio of the 
displacement obtained with RSR = 0.6 to that with 
RSR = 1.0 was evaluated for the nonlinear Takeda5 
oscillators having DDD = 8 and PDD = 1, in order to 
compare the NSP estimates of the displacement ratio 
with the displacement ratio computed for the nonlinear 
Takeda5 oscillators. The upper plots in Figures 6 74 
through 6 82 show the estimated displacement ratio for 
one of the three NSPs, and the lower plots of these 
figures normalize this displacement ratio by the 
displacement ratio computed for the Takeda5 
oscillators. It can be observed that the NSP methods 
tend to account correctly for the effect of strength 
reduction on displacement response, in a mean sense. 
(Text continued on page 177) 
Technical Resources 
Technical Resources
FEMA 307 n (0) 1 C. 
Short Duration Long Duration 
Forward Directive 
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Figure 6 64 Mean values of ddNspldd for all ground motions for each NSP method, for short and long period 
Takeda5 Models. See text in Section 6.6.2. 
Records=SD; DDD=8; PDD=8; RSR=1; Model=Takeda5 
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Figure 6 65 Coefficient Method Estimates of Ratio of Damaged and Undamaged Oscillator Displacement 
Normalized by Computed Ratio, for Short Duration Records 
DDD = Design Displacement Ductility; PDD = Prior Ductility Demand; RSR = Reduced Strength Ratio 
FEMA 307 Technical Resources 
Chapter 6: Analytical Studies 
Records=LD; DDD=8; PDD=8; RSR=1; Model=Takeda5 
Excludes cases where prior damage (PDD) exceeds undamaged
response Ah o [I0CH85LLEO.010 
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Figure 6 66 Coefficient Method Estimates of Ratio of Damaged and Undamaged Oscillator Displacement 
Normalized by Computed Ratio, for Long Duration Records 
DDD = Design Displacement Ductility; PDD = Prior Ductility Demand; RSR = Reduced Strength Ratio Records=FD; DDD=8; PDD=8; RSR=1; Model=Takeda5 
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Figure 6 67 Coefficient Method Estimates of Ratio of Damaged and Undamaged Oscillator Displacement 
Normalized by Computed Ratio, for Forward Directive Records 
DDD = Design Displacement Ductility; PDD = Prior Ductility Demand; RSR = Reduced Strength Ratio 
Technical Resources FEMA 307 
Chapter 6: Analytical Studies 
Records=SD; DDD=8; PDD=8; RSR=1; Model=Takeda5 response
Excludes cases where prior damage (PDD) exceeds undamaged 
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Figure 6 68 Secant Method Estimates of Ratio of Damaged and Undamaged Oscillator Displacement Normalized by 
Computed Ratio, for Short Duration Records 
DDD = Design Displacement Ductility; PDD = Prior Ductility Demand; RSR = Reduced Strength Ratio Records=LD; DDD=8; PDD=8; RSR=1; Model=Takeda5 
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Figure 6 69 Secant Method Estimates of Ratio of Damaged and Undamaged Oscillator Displacement Normalized by 
Computed Ratio, for Long Duration Records 
DDD = Design Displacement Ductility; PDD = Prior Ductility Demand; RSR = Reduced Strength Ratio 
FEMA 307 Technical Resources 
Chapter 6: Analytical Studies 
Records=FD; DDD=8; PDD=8; RSR=1; Model=Takeda5 5 
Excludes cases where prior damage (PDD) exceeds undamaged response 
o LN92LUCN.250 LO O IV79BRWY.315 
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Computed Ratio, for Forward Directive Records 
DDD = Design Displacement Ductility; PDD = Prior Ductility Demand; RSR = Reduced Strength Ratio 
Records=SD; DDD=8; PDD=8; RSR=1; Model=Takeda5 
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Figure 6 71 Capacity Spectrum Method Estimates of Ratio of Damaged and Undamaged Oscillator Displacement 
Normalized by Computed Ratio, for Short Duration Records 
DDD = Design Displacement Ductility; PDD Prior Ductility Demand; RSR = Reduced Strength Ratio 
Technical Resources FEMA 307 
Chapter 6: Analytical Studies 
Records=LD; DDD=8; PDD=8; RSR=1; Model=Takeda5: 
Excludes cases where prior damage (PDD) exceeds undamaged response 
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Figure 6 72 Capacity Spectrum Method Estimates of Ratio of Damaged and Undamaged Oscillator Displacement 
Normalized by Computed Ratio, for Long Duration Records 
DDD = Design Displacement Ductility; PDD = Prior Ductility Demand; RSR = Reduced Strength Ratio 
Records=FD; DDD=8; PDD=8; RSR=1; Model=Takeda5 
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Figure 6 73 Capacity Spectrum Method Estimates of Ratio of Damaged and Undamaged Oscillator Displacement 
Normalized by Computed Ratio, for Forward Directive Records 
DDD = Design Displacement Ductility; PDD = Prior Ductility Demand; RSR = Reduced Strength Ratio 
FEMVA 307 Technical Resources 167 
Chapter 6: Analytical Studies 
Records=SD; DDD=8; PDD=1; Model=Takeda5 
3 Excludes cases where prior damage (PDD) exceeds undamaged response 
a) (, 2 (: EC, 0 co 01 II 
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having DDD= 8 and PDD= J 
DDD = Design Displacement Ductility; PDD = Prior Ductility Demand; RSR = Reduced Strength Ratio 
FEMA 307 
Technical Resources
Technical Resources FEMA 307 
Chapter 6: Analytical Studies 3 
Records=LD; DDD=8; PDD=1; RSR=0.6; Model=Takeda5 
Excludescases where prior damage (PDD) exceeds undamaged response 
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DDD = Design Displacement Ductility; PDD = Prior Ductility Demand; RSR = Reduced Strength Ratio FEMA 307 Technical Resources 169 
Chapter 6: Analytical Studies 
Records=FD; DDD=8; PDD=1; Model=Takeda5 4 
Excludes cases where prior damage (PDD) exceeds undamaged response 
o LN92LUCN.250 
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having DDD= 8 and PDD= 1 DDD = Design Displacement Ductility; PDD = Prior Ductility Demand; RSR = Reduced Strength Ratio 
Technical Resources FEMA 307 
Chapter 6: Analytical Studies 
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Excludescases where prior damage (PDD) exceeds undamaged 
response 
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Figure 6 77 Secant Method Estimates of Displacement Ratio of RSR=0.6 and RSR=1.0 Takeda5 Oscillators having 
DDD= 8 and PDD= 1 
DDD = Design Displacement Ductility; PDD = Prior Ductility Demand; RSR = Reduced Strength Ratio 
FEMA 307 Technical Resources 
Chapter 6: Analytical Studies 
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3 Excludes cases where prior damage (PDD) exceeds undamaged response 
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Figure 6 78 Secant Method Estimates of Displacement Ratio of RSR=0.6 and RSR=1.0 Takeda5 Oscillators having 
DDD= 8 and PDD= 1 
DDD = Design Displacement Ductility; PDD = Prior Ductility Demand; RSR = Reduced Strength Ratio 
172 Technical Resources FEMA 307 
Technical Resources FEMVA 307 
Chapter 6: Analytical Studies 
Records=FD; DDD=8; PDD=1; Model=Takeda5 
3 Excludes cases where prior damage (PDD) exceeds undamaged response 
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Figure 6 79 Secant Method Estimates of Displacement Ratio of RSR=0.6 and PSR=1.0 Takeda5 Oscillators having 
DDD= 8 and PDD= 1 
DDD = Design Displacement Ductility o PDD = Prior Ductility Demand; RSR = Reduced Strength Ratio 
FEMA 307 Technical Resources 173 
Chapter 6: Analytical Studies 
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3 Excludes cases where prior damage (PDD) exceeds undamaged response 
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Figure 6 80 Capacity Spectrum Method Estimates of Displacement Ratio of RSR=0.6 and RSR=1.0 Takeda5 
Oscillators having DDD= 8 and PDD= 1 
DDD = Design Displacement Ductility; PDD = Prior Ductility Demand; RSR = Reduced Strength Ratio 
17 174 Technical Resources FEMA 307 
Chapter 6: Analytical Studies 
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3 Excludes cases where prior damage (PDD) exceeds undamaged response 
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0 0.5 1 1.5 2 Period, T (sec) Figure 6 81 Capacity Spectrum Method Estimates of Displacement Ratio of RSR=0.6 and RSR=1.0 Takeda5 Oscillators having DDD= 8 and PDD= t DDD = Design Displacement Ductility; PDD = Prior Ductility Demand; RSR = Reduced Strength Ratio FEMA 307 Technical Resources 
Chapter 6: Analytical Studies Records=FD; DDD=8; PDD=1; Model=Takeda5 
3 Excludes cases where prior damage (PDD) exceeds undamaged response o1LN92LUCN.250 Q A O IV79BRWY.315 CX0U. 
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Z5 Excludes cases where prior damage (PDD) exceeds undamaged response = LN92LUCN.250 O IV79BRWY.315 
A LP89SARA.360 V NR94NWHL.360
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Period, T (sec) [Figure 6 82 Capacity Spectrum Method Estimates of Displacement Ratio of RSR=0.6 and RSR=1.0 Takeda5 Oscillators having DDD= 8 and PDD= 1 
DDD = Design Displacement Ductility; PDD = Prior Ductility Demand; RSR = Reduced Strenqth Ratio Technical FEMA 307
4, 7 It (o Chapter 6: Analytical Studies 
6.7 Conclusions and Implications 
The analyses presented indicate that the displacement 
response characteristics of the ground motions generally 
conform to expectations based on previous studies. 
Forward directivity motions may have larger displacement 
response in the long period range than would be 
predicted by the equal displacement rule. The strength 
reduction factor, R, appropriate for forward directivity 
motions may need to be reduced somewhat relative to 
other classes of motion if ductility demands are to be 
held constant. 
The displacements of the Takeda oscillators were 
sometimes several fold greater or less than those of the 
bilinear oscillators. Although it is fundamentally 
important to consider displacements in seismic 
response, variability of the response estimates as 
affected by ground motions and hysteresis model must 
also be considered. 
Previous damage, modeled as prior ductility demand, 
did not generally cause large increases in displacement 
response when the Takeda models with positive post 
yield stiffness were exposed to performance level 
earthquakes associated with life safety or collapse prevention. 
Prior ductility demands were found to cause 
mean changes in displacement response ranging from 
3% to +10% for the Takeda5 and TakPinch oscillators 
having no strength degradation (Figures 6 55 and 6 56) 
PDDs of 8 often caused a slight decrease in the 
displacement response computed using the Takeda5 and 
TakPinch models; response infrequently was 20% to 
30% or more higher than that for the undamaged 
oscillator. 
For oscillators having cyclic strength degradation, 
represented by the TakPinch oscillators, the effect of 
strength degradation was generally to increase the mean 
displacement response, but only by a few percent. The 
mean increase was larger for the structures having lower 
DDD, reaching as much as 21% for oscillators having 
RSR = 0.6. This result merely indicates that strength 
degradation tends to cause displacement response to 
increase relative to undamaged or nondegrading systems. 
Further examination revealed that increasing PDD 
increases or decreases the mean response of TakPinch 
systems with strength degradation by only a few percent 
(Figure 6 56) The weaker oscillators, represented by 
larger DDD, are more likely to exhibit damage in a real 
earthquake, and to have smaller increases in 
displacement due to prior ductility demands. 
While prior damage causes relatively small changes in 
mean displacement response relative to undamaged 
structures, it also introduces some variability in 
displacement response. Variability in response is 
inherent in earthquake resistant design, and the 
variability introduced by prior damage should be 
considered in the context of variability arising from 
different ground motions, choice of hysteretic models, 
modeling assumptions, and other sources. For example, 
Figures 6 32 to 6 34 illustrate the degree to which 
different earthquakes can cause bilinear and Takeda 
oscillators of equal strength to have substantially 
different peak displacement response. Thus, the 
variability in response introduced by prior damage is 
not considered significant. 
Three NSPs for estimating peak displacement response 
were applied to the Takeda oscillators. Significant 
variability in the estimated displacements, when 
compared with the values calculated from nonlinear 
dynamic analysis, underscores the difficulty in 
accurately estimating response of a SDOF system to a 
known ground motion. The accuracy of the NSP 
estimates is compared in Figure 6 63. In Figure 6 64 it 
can be observed that the capacity spectrum and 
coefficient methods are more accurate, in a mean sense, 
than the secant method, and that all methods tend to 
overestimate the displacement response of short period 
Takeda5 oscillators. 
The NSPs were also used to estimate the change in 
displacement caused by a prior earthquake. Given the 
relatively small effect of damage on peak displacement 
response, it appears that damaged structures should be 
modeled similar to their undamaged counterparts, in 
order to obtain identical displacement estimates for 
performance events that are stronger than the damaging 
event. This results in damage having no effect on the 
displacement response, which closely approximates the 
analytical results. 
The accuracy with which an NSP accounts for strength 
reduction was explored. It was found that each NSP was 
reasonably able to capture the effect of strength 
reduction. 
The above findings pertain to systems characterized by 
ductile flexural response having degrading stiffness, 
with and without pinching. Systems with negative post 
yield stiffness were prone to collapse, even with DDD 
of 2. Such systems should remain nearly elastic if their 
collapse is to be avoided. 
FEMA 307 Technical Resources 
Chapter 6: Analytical Studies 
6.8 References 
Araki, H Shimazu, T and Ohta, Kazuhiko, 1990, On 
Residual Deformation of Structures after Earthquakes, 
Proceedings of the Eighth Japan Earthquake 
Engineering Symposium 1990, Tokyo, Vol. 
2, pp. 1581 1586. (In Japanese with English 
abstract.) 
ATC, 1996, Seismic Evaluation and Retrofit of Concrete 
Buildings, Applied Technology Council, ATC 40 
Report, Redwood City, California. 
ATC, 1997a, NEHRP Guidelines for the Seismic Rehabilitation 
of Buildings, prepared by the Applied 
Technology Council (ATC 33 project) for the 
Building Seismic Safety Council, published by the 
Federal Emergency Management Agency, Report 
No. FEMA 273, Washington, D.C. 
ATC, 1997b, NEHRP Commentary on the Guidelines 
for the Seismic Rehabilitation of Buildings, prepared 
by the Applied Technology Council (ATC 33 
project) for the Building Seismic Safety Council, 
published by the Federal Emergency Management 
Agency, Report No. FEMA 274, Washington, D.C. 
Boroschek, R.L 1991, PCNSPEC Manual, (Draft), 
Earthquake Engineering Research Center, University 
of California at Berkeley. 
Cecen, H 1979, Response of Ten Story Reinforced 
Concrete Model Frames to Simulated Earthquakes, 
Doctoral Thesis, Department of Civil Engineering, 
University of Illinois at Urbana. 
Fajfar, P. and Fischinger, M 1984, Parametric Study 
of Inelastic Response to Some Earthquakes 
Recorded in Southern Europe, Proceedings of the 
Eighth World Conference on Earthquake Engineering, 
Vol. 4, pp. 75 82. 
Humar, J 1980, Effect of Stiffness Degradation on 
Seismic Response of Concrete Frames, Proceedings 
of the Seventh World Conference on Earthquake 
Engineering, Vol. 5, pp. 505 512. 
Iwan, W.D 1973, A Model for the Dynamic Analysis 
of Deteriorating Structures, Proceedings of the 
Fifth World Conference on Earthquake Engineering, 
Vol. 2 pp. 1782 1791. 
Iwan, W.D 1977, The Response of Simple Stiffness 
Degrading Systems, Proceedings of the Sixth 
World Conference on Earthquake Engineering, Vol. 
2, pp. 1094 1099. 
Kawashima, K Macrae, G Hoshikuma, J and 
Nagaya, K 1994, Residual Displacement 
Response Spectrum and its Application, Journal of 
Structural Mechanics and Earthquake Engineering, 
Japan Society of Civil Engineers, No. 501, pp. 183192. 
(In Japanese with English abstract.) 
Lepage, A 1997, A Method for Drift Control in Earth 
quake Resistant Design of RC Building Structures, 
Doctoral Thesis, Department of Civil Engineering, 
University of Illinois at Urbana. 
Mahin, S.A 1980, Effects of Duration and Aftershocks 
on Inelastic Design Earthquakes, Proceedings 
of the Seventh World Conference on 
Earthquake Engineering, Vol. 5, pp. 677 679. 
Mahin, S.A and Lin, J 1983, Construction of Inelastic 
Response Spectra for Single Degree of Freedom 
Systems Computer Program and Applications, 
Earthquake Engineering Research Center, University 
of California at Berkeley, Report No. UCB 
EERC 83 17, Berkeley, California. 
Mahin, S.A and Boroschek, R 1991, Influence of 
Geometric Nonlinearities on the Seismic Response 
and Design of Bridge Structures, Background 
Report to California Department of Transportation, 
Sacramento, California. 
Minami, T and Osawa, Y 1988, Elastic Plastic 
Response Spectra for Different Hysteretic Rules, 
Earthquake Engineering and Structural Dynamics, 
Vol. 16, pp. 555 568. 
Miranda, E 1991, Seismic Evaluation and Upgrading 
of Existing Buildings, Doctoral Thesis, Department 
of Civil Engineering, University of California, Berkeley. 
Moehle, J.P Browning, J Li, Y.R and Lynn, A 1997, 
"Performance Assessment for a Reinforced Concrete 
Frame Building, (abstract) The Northridge 
Earthquake Research Conference, California Universities 
for Research in Earthquake Engineering, 
Richmond, California. 
Nakamura, T and Tanida, K 1988, Hysteresis Model 
of Restoring Force Characteristics of Reinforced 
Concrete Members, Proceedings of the Ninth 
World Conference on Earthquake Engineering, 
Paper 6 4 7, Vol. VI. 
Nasser, A.A and H. Krawinkler, H 1991, Seismic 
Demands for SDOF and MDOF Systems, John A. 
Blume Earthquake Engineering Center, Stanford 
University, Report No. 95, Stanford, California. 
FEMA 307 
Technical Resources
Technical Resources FEMA 307 
Chapter 6: Analytical Studies 
Newmark, N.M and Riddell, R 1979, A Statistical 
Study of Inelastic Response Spectra, Proceedings 
of the Second U.S. National Conference on Earthquake 
Engineering, pp. 495 504. 
Otani, S 1981, Hysteresis Models of Reinforced Concrete 
for Earthquake Response Analysis, Journal 
(B), Faculty of Engineering, University of Tokyo, 
Vol. XXXVI, No. 2, pp. 125 159. 
Palazzo, B and DeLuca, A 1984, Inelastic Spectra 
for Geometrical and Mechanical Deteriorating 
Oscillator, Proceedings of the Eighth World Conference 
on Earthquake Engineering, Volume IV, pp. 
91 98. 
Parducci, A and Mezzi, M 1984, Elasto Plastic 
Response Spectra of Italian Earthquakes Taking 
into Account the Structural Decay, Proceedings of 
the Eighth World Conference on Earthquake Engineering, 
Volume IV, pp. 115 122. 
Paulay, T, and Priestley, M.J.N 1992, Reinforced Concrete 
and Masonry Buildings: Design for Seismic 
Resistance, Wiley & Sons, New York. 
Qi, X and Moehle, J.P 1991, Displacement Design 
Approach for Reinforced Concrete Structures Subjected 
to Earthquakes, Earthquake Engineering 
Research Center, Report No. UCB EERC 91 02, 
University of California at Berkeley, Berkeley, California. 
Rahnama, M and Krawinkler, H 1995, Effects of P 
Delta and Strength Deterioration on SDOF Strength 
Demands", Proceedings of the 1 0 th European Conference 
on Earthquake Engineering, Vol. 2, pp. 
1265 1270. 
Riddell, R 1980, Effect of Damping and Type of 
Material Nonlinearity on Earthquake Response, 
Proceedings of the Seventh World Conference on 
Earthquake Engineering, Vol. 4, pp. 427 433. 
Saiidi, M 1980, Influence of Hysteresis Models on 
Calculated Seismic Response of R C Frames, Proceedings 
of the Seventh World Conference on 
Earthquake Engineering, Vol. 5, pp. 423 430. 
Sewell, R.T 1992, Effects of Duration on Structural 
Response Factors and on Ground Motion Damage 
ability, Proceedings of the SMIP92 Seminar on 
Seismological and Engineering Implications of 
Recent Strong Motion Data, pp. 7 1 to 7 15. 
Shimazaki, K and M.A. Sozen, M.A 1984, Seismic 
Drift of Reinforced Concrete Structures, Research 
Reports, Hasama Gumi Ltd Tokyo (in Japanese), 
and draft research report (in English) 
Somerville, P.G Smith, N.F Graves, R.W. and Abrahamson, 
N.A 1997, Modification of Empirical 
Strong Ground Motion Attenuation Relations to 
Include the Amplitude and Duration Effects of Rupture 
Directivity, Seismological Research Letters, 
Vol. 68, No. 1. 
Takeda, T Sozen, M.A and Nielsen, N.N 1970, 
"Reinforced Concrete Response to Simulated 
Earthquakes, Journal of the Structural Division, 
American Society of Civil Engineers, Vol. 96, No. 
ST12, pp. 2557 2573. 
Wolschlag, C 1993, Experimental Investigation of the 
Response of RIC Structural Walls Subjected to 
Static and Dynamic Loading, Doctoral Thesis, 
Department of Civil Engineering, University of Illinois 
at Urbana. 
Xie, L. L and Zhang, X 1988, Engineering Duration 
of Strong Motion and its Effects on Seismic Damage, 
Proceedings of the Ninth World Conference 
on Earthquake Engineering, Vol. 2, Paper 3 2 7. 
FEMA 307 Technical Resources 
Example Application
7. 7.1 Introduction 
This section gives an example of the use of FEMA 306 
recommendations to evaluate earthquake damage in a 
two story reinforced concrete building. The example is 
meant to be as realistic as possible and is based on an 
actual structure. 
7.1.1 Objectives 
The example is intended to help evaluating engineers 
understand such issues as: 
the overall process of a FEMA 306 evaluation. 
accounting for pre existing damage. 
how both observation and analysis are used in the 
evaluation procedures. 
determining and using the applicable FEMA 306 
Component Damage Classification Guides, 
including cases where an exactly applicable damage 
guide is not provided. 
foundation rocking of walls, which may be a 
prevalent behavior mode in many structures. 
some of the ways engineering judgment may need to 
be applied. 
how restoration measures can be determined based 
on either the direct method or the performance 
analysis method. 
aspects of using a nonlinear static procedure of 
analysis (pushover analysis) 
establishing displacement capacities and demands. 
Reading through the example could be the best introduction 
to an understanding of the FEMA 306 evaluation 
process. References to the applicable sections of 
FEMA 306 or 307 (or to other sources) are given in 
"bookmark" boxes adjacent to the text. Because the 
example is meant to be illustrative, it contains more 
description and explanation than would normally be 
contained in an engineer s evaluation report for an 
earthquake damaged building. 
It should be clear from this example that the FEMA 306 
recommendations for evaluating earthquake damage 
must be implemented under the direction of a knowledgeable 
structural engineer, particularly when a performance 
analysis is carried out. The responsible engineer 
should have a thorough understanding of the principles 
behind the FEMA 306 recommendations and should be 
familiar with the applicable earthquake research and 
post earthquake field observations. FEMA 307 provides 
tabular bibliographies and additional information 
on applicable research. 
A fundamental tenet of the component evaluation methods 
presented in FEMA 306 is that the severity of damage 
in a structural component may not be determined 
without understanding the governing behavior mode of 
the component, and that the governing behavior mode is 
a function not only of the component s properties, but 
of its relationship and interaction with surrounding 
components in a structural element. In the following 
sections, the evaluation of the example building emphasizes 
the importance of this principle. There may be a 
temptation among users of FEMA 306 to use the damage 
classification guides as simple graphical keys to 
damage, and to complete the analysis by simply matching 
the pictures in the guides to the observed damage. 
The example is intended to show that this is not the 
appropriate use of the guides. It is organized to emphasize 
the importance of the analytical and observation 
verification process that is an essential element of the 
evaluation procedure. 
7.1.2 Organization 
The example is organized as shown in the flow chart of 
Figure 7 1. This organization follows the overall evaluation 
procedure outlined in FEMA 306, beginning with 
a building description and observations of earthquake 
damage. 
The building has been subjected to a previous earthquake. 
The damage investigation establishes the preexisting 
conditions so that the loss from the recent 
earthquake can be evaluated. The preliminary classification 
of component types, behavior modes, and damage 
severity are made by observing the structure. It is 
shown, however, that classification of behavior modes, 
and hence damage severity, may be unclear when based 
on observation alone. Simple analytical tools provided 
in the material chapters of FEMA 306 are used to verify 
the expected component types and behavior modes, and 
damage severity is assigned accordingly. The steps 
required to estimate the loss by the direct method are 
FEMA 307 Technical Resources 
Chapter 7: Example Application 
00 Nl 04.l 4 Evaluation by 
Performance Analysis 
3vlainb h 4.1 4.2 Performance Objectives 
Nonlinear static analysis 
4.3 Pushover capacity curve 
4.4 Estimate of d9, the 
displacement caused by the 
damaging earthquake 
4.5 Displacement demand 
4.6 Analysis of the restored structure 
4.7 Performance restoration measures 
Figure 7 1 Flowchart for example 
FEMA 307 Resources FEMA 307
182Technical Technical Resources
182 Chapter 7: Example Application 
illustrated, and a relative performance analysis is carried 
out. It is emphasized that the direct method provides 
only loss estimation information, and that a 
relative performance analysis is required in order to 
make performance based design decisions. 
Damage records for all of the structural walls of the 
building are included. The damage records for two of 
the walls are discussed in detail. Damage records for the 
remaining walls are given at the end of the example. 
7.2 Investigation 
7.2.1 Building Description 
The example building is a two story concrete building 
located on a sloping site. The building is aT" shape in 
plan with the stem of the T on the downhill side, containing 
a partial lower story below the other two stories. 
The building was designed and constructed in the late 
1950s. The building is located about 3.6 miles from the 
epicenter of the damaging earthquake. 
The overall plan dimensions of the building are 362 feet 
in the North South direction by 299 feet in the East 
West direction. The floor slabs cantilever about 6 feet 
from the perimeter columns forming exterior sun 
screens balconies. The building facade along the perimeter 
is set back 8 feet from the edge of the slab. For the 
typical floor, the interior floor area is about 62, 600 
square feet, and the total slab area is about 70, 400 
square feet. The lower level encompasses about 20, 200 
square feet. Floor plans are shown in Figure 7 2 and an 
elevation is shown in Figure 7 3. The roof of the building 
supports mechanical equipment.
The floors and roof are constructed with waffle slabs 
comprised of a 4 % inch thick slab and 14 inch deep 
pans (18 2 inches total depth) Columns supporting the 
slabs are typically spaced at 26 feet in each direction. 
The interior columns are 18 inch square and the perimeter 
columns are 18 inch diameter. The columns are supported 
on spread footings. 
Reinforced concrete walls in both directions of the 
building resist lateral forces. The walls are 12 inches 
thick and are cast monolithically at each end with the 
gravity load carrying columns. The walls are typically 
located along corridors, and the corridor side of the wall 
has a 1 inch thick plaster coat. The typical solid wall 
configuration and reinforcement are shown in 
Figure 7 4. 
In the lower level there are several reinforced concrete 
masonry (CMU) walls that are framed between the 
ground and the first floor slab (basement level) in the 
three story section of the building. The CMU walls are 
attached to the first floor slab. However, these walls 
were not designed as shear resisting elements. Because 
the first floor slab is anchored to the foundation in the 
two story portion of the building, the contribution of the 
CMU walls to the lateral force resistance, particularly in 
the east west direction, is minimal. 
Several of the reinforced concrete walls have door 
openings, 7 feet 3 inches tall by 6 feet 6 inches wide, in 
the middle of the wall, creating a coupled wall. The typical 
coupled wall configuration and reinforcement are 
shown in Figure 7 5. In the three story section of the 
building (the stem of the T), the walls are discontinued 
at the lower level. This lower level contains a single 
reinforced concrete wall in the north south direction 
centered between the two walls above. 
7.2.2 Post earthquake Damage
Observations 
Following the damaging earthquake, Visual 
the engineers performed a post earth observation, 
quake evaluation of the building. The GuideNDE1, 
initial survey was conducted one Section 3.8 
month after the damaging earthquake. of FEMA306 
The structural drawings for the building were reviewed. 
The follow up investigations were conducted about 
three months following the earthquake. 
The post earthquake evaluations were conducted using 
visual observation techniques on exposed surfaces of 
the structural elements. The sections of wall above the 
ceiling were typically observed only where the suspended 
ceiling tiles had fallen during the earthquake. 
Crack widths were measured at selected locations using 
magnifying crack comparators for most of the significant 
cracks in each wall. 
7.2.2.1 Pre Earthquake Conditions 
The building had experienced some l 
cracking prior to the damaging earth vs. new 
quake. The pre existing damage is cracks, 
judged to have been caused by a previous Section 3.4 
earthquake. The heaviest damage of FEMA306 
appeared to have been in the coupling 
beams. The wall cracks above the ceiling line were 
observed to have been repaired by epoxy injection. 
183 Technical Resources 
FEMA 307 Technical Resources 183 
Chapter 7: Example Application 
T (yP) a) First and Second Floor Plan 
Reinforced 
Edge of 
Floor Slab 
b) Basement Floor Plan 
Figure 7 2 Floor Plans 
1 844 Technical Resources FEMA 307 
Chapter 7: Example Application 
I 11 I I I, 12nd I 
r E r r 1l T 1 list If 
Figure 7 3 Building Cross section 
13 f ars (13in. 
1 6 IL. H 1 8 in. S q Column 
41 I I II E second 
I t 11 @ First 1G 5" 
I l t v R rad1
lg X ff 4 8arq k Slab On 
P3 6 11 IIfI I I 90r (Type
I 1 1 1 Hook at Otto Footing
26 0" Figure 7 4 Example Solid Wall Detail (Condition at Line 7) 
FEMA 307 Technical Resources 18 
FEMA 307 Technical Resources 185 
as PRELIMINARY CLASSIFICATION 
BY OBSERVATION 
FINAL CLASSIFICATION 
BY ANALYSIS 
(Building Name: 
Element Component Damage Record 
Project ID: Prepared by: 
I COMPONENT TYPE 
0. Concrete Shear Wall Building 
Location Within Building: 
ATC 43 Example ATC 
Date Inspected: 
Floor 2nd Column: 2 24 Sep 97 
Sketch and Description of Component and Damage: 
Roof LJ C, 0 I | BEHAVIOR MODE I I BEHAVIOR MODE as 0 m 0 I I :a (p 0 0 i AS82, g , 1 Second B, C, H or M IM M (Overturning) x ITI 5. 01 L 1Ll 7L r Lr fi First I DAMAGE SEVERITY I Legend: 
Crack (Width< 0.030 inch) Spall 
Crack Width in Mils (0.00l Inch) Not Accessible 
Crack Previously Filled with Epoxy 
Crack at Pre existing Surface Patch Partition Moderate If H 
Insignificant If 
Key Plan B, C, or M 
A Tr L CD AIn 0 N. 
N PRELIMINARY CLASSIFICATION FINAL CLASSIFICATION 
BY OBSERVATION BY ANALYSIS 
0 COMPONENT TYPE I I COMPONENTTYPE I 
I I I I RC3 I 0 CD I IF. I II I I I CD RC3 lb RC3 RCI RCt RC1 RC1 I I1I II lil rn C) S I BEHAVIOR MODE II BEHAVIOR MODE I 4
CD CD m 5 i x rH CD
I ISor 1 C I11 I A 0 co w H N I H j S.
o 0 11 iII III li I DAMAGE SEVERITY I I DAMAGE SEVERITY I m I I m I
i Ea KLI U D.; 2 alI I a =I E I I
9 0S III IIrIII m 0 4

Chapter 7: Example Application 
observed to have horizontal cracks along the interface between the top of the wall and the floor slab above.
7.2.3 Preliminary Classification (by Observation) of Component Types, Behavior Modes, and Damage Severity 
The first critical step in interpreting o component damage records is to identify - types, the components within the structural - Table5-1 of element under investigation. In FEMA 306 this case, the example building is reinforced concrete, so the summary of relevant component types is found in Sections 2.4 and 5.2.1 of FEMA 306.
7.2.3.1 Component Types 
The first pass in the identification process is conducted by observation, keeping in mind that the definition of a component type is not a function of the geometry alone, but of the governing mechanism of lateral deformation for the entire element or structure. Thus the identification of structural components requires consideration of the wall element over multiple floor levels. Complete diagrams showing the crack pattern over multiple floor levels such as the ones shown in the attached damage records shown in Figures 7-6, 7-7 and Damage Records D1 through D19 (Appendix A) are essential.
For the typical coupled wall elements of the example building, shown in Component Figure 7-7, a survey of the element identification, geometry and the general pattern of FEMA 306 damage suggests that the beams over the openings may be classified as weaker coupling beams (RC3), and that the wall piers flanking the openings will behave as two-story cantilever components (RC 1). The thought process that leads to this conclusion includes the recognition that the beam elements are likely to be weaker than the walls on either side of the coupling beams, as well as a mental visualization of the lateral deformation of the walls and the attendant large deformation demands on the beams. As shown in Figure 7-6, the solid reinforced concrete wall component is type RCL.
7.2.3.2 Behavior Modes and Damage Severity 
Once the component types have been identified, an initial classification of the Behavior modes and damage severity modes, Table 5-2 of may be made by inspecting the visible FEMA 306 damage with reference to the component damage classification guides. Tables 5-1, 5-2, and 5-3 of FEMA 306 are also helpful in identifying behavior modes appropriate to the identified components.
For the typical coupled wall shown in Figure 7-7, the coupling beam component (RC3) on the second floor is observed to have light diagonal (shear) cracking, with little or no evidence of flexural cracking. As is typical of a building designed in the late 1950s, the coupling beam does not contain diagonal reinforcement, or even sufficient stirrup reinforcement, so mode A (ductile flexure) may be safely eliminated. The diagonal cracks then suggest that the behavior mode may be either mode B (flexure/diagonal tension) or mode H (preemptive diagonal tension). At the first floor coupling beams, the damage is more severe, but the behavior mode still appears to be either B or H.
In the first floor coupling beam, identification of the damage severity is relatively - Component straightforward: the observed Guides, Section 5.5 damage would be classified as Heavy of FEMA 306 regardless of the behavior mode. In many cases, however, the damage severity level may depend on the behavior mode. In the second floor coupling beam, for example, the damage would be classified as Insignificant if the behavior mode is identified as B (flexure followed by diagonal tension), but as Moderate if the behavior mode is identified as H (preemptive diagonal tension).
Similarly, the wall piers of the coupled walls (RC1) have light diagonal cracking, which may be indicative of early stages of mode B (flexure/diagonal tension), early stages of mode C (flexure/diagonal compression) or more advanced stages of mode H (preemptive diagonal tension). In the first two cases, damage would be classified as Insignificant, while in the last case, damage would be classified as Moderate.
It is often not possible to distinguish between the different behavior modes, and hence the damage severity, with- out some analysis. This is particularly important for lower levels of damage Verification Loop 1, 3 f EMA 306 where different modes may look very much alike, but which have different response at higher levels of damage.
Consider, for example, modes B and H. The flexural cracks that initiate mode B response may have closed and become nearly invisible. The light diagonal cracking that occurs at the outset of both modes B and H will then be indistinguishable from one another, and only analysis of the section will differentiate the two modes, and hence the severity of damage. In other cases, the differences between modes are of less importance - FEMA 307 Technical Resources Chapter 7: Example Application Modes B and C are physically different, but have a similar effect on the stiffness, strength, and deformation capacity of the component at all levels of damage severity.
7.2.4 Final Classification (by Analysis) of Component Type, Behavior Mode and Damage Severity 
In the previous section, component type, behavior mode, and damage severity were preliminarily defined based only on observation. In this section, those definitions are verified by calculation. In practice, iterations between observation and analysis may be needed to interpret correctly the seismic response and damage.
7.2.4.1 Expected Strength 
The expected pre-earthquake strengths for each of the components were calculated - Expected using the FEMA 306 strength, Section 3.6 Section 3.6 procedures. The design of FEMA 306 concrete strength was shown on the drawings to be 3000 psi. According to the discussion in FEMA 306, Section 5.3.2, expected concrete strengths ranging from 1.0 to 2.3 times the specified strength are not unrealistic. In the example building, concrete strength was suspect, so tests were conducted which revealed that expected strength was, in fact, near the specified strength. For the purposes of the following analysis an expected strength of 3000 psi was assumed.
Based on the drawing notes, reinforcing bars had a specified yield strength of 40 ksi. The expected strength of the reinforcing bars was assumed to be greater than the nominal yield strength by a factor of 1.25, so a value of 50 ksi was used for the yield strength in all calculations.
If, during the course of the analysis, it becomes difficult to reconcile analytically determined behavior modes with observed damage, assumed values for material strength may need to be re-evaluated or verified through tests.
There are two typical element types in the lateral-force- resisting system, solid walls and coupled walls. The following sections describe the details of the calculations and methodology used to classify the components of these elements.
7.2.4.2 Example 1 -Solid Wall (28-2C) 
Once a preliminary damage classification has been made by visual observation, it will generally be necessary to perform some analysis to distinguish between behavior modes that are different but visually similar.
As a first example, consider the damage record for the wall shown in Figure 7-6. The wall is 12 inches thick with 18-inch square boundary elements at each end.
The wall length from center to center of the boundary elements is 26 feet, and the story height is 13 feet-6 inches. Note that the wall is L-shaped in plan and has a 26-foot return along line B.
Component Type. 
The definition of this wall as a single RC 1 component (isolated wall or stronger wall pier) is easily and intuitively verified by sketching the inelastic deformation mechanism for the wall and its surrounding structure. The slabs framing into the wall clearly do not have the stiffness or strength to force a "weaker wall" type of behavior. The wall is therefore a single component with a height of 27 feet.
Behavior Mode. 
The preliminary classification identified four possible Component behavior modes for this component guides, that were consistent with the component - and RC2H, type and the observed damage: Section 5.5 mode B (flexure/diagonal tension), of FEMA 306 mode C (flexure/diagonal compression), mode H (preemptive diagonal tension), and mode M (foundation rocking). For each of these behavior modes, Component Guides provide, in addition to the visual description of the different behavior modes, guidance in the analytical steps required to verify a particular behavior mode. See for example the Component Damage Classification Guide RClB under "How to distinguish behavior mode by analysis". Based on the recommendations of the guide, the shear associated with the development of the maximum strength in flexure, diagonal tension, web crushing, and foundation rocking were calculated. Calculation results are summarized in Table 7-1. Selected details of the calculations are provided in the box on page 192.
The relationship between capacities of the different potential behavior modes defines the governing component behavior mode. Initially, consider the first five modes listed in Table 7-1, temporarily neglecting the overturning (foundation rocking) response. Because the wall is flanged, its response depends op the direction of seismic force, and the flexural capacity must be calculated for each direction. It is possible that a different behavior mode will govern in each of the two different loading directions. In this example, the diagonal tension strength at low ductility is less than the flexural strength Technical Resources FEMA 307 Chapter 7: Example Application Table7-1 Capacity of Potential Behavior Modes for Typical Solid Wall (2B-2C) Behavior Mode Shear FEMA 306 Comments Capacity Reference (kips) Flexure (modes A & B) -flange 1570 Sect. 5.3.5 All distributed reinforcement is included in compression in the calculation of flexural strength, as is the contribution of the flange reinforcement - Me = 31, 300 k-ft.
Flexure (A & B) -flange in tension 2230 Sect. 5.3.5 Me =44, 600 k-ft Diagonal Tension (B & H) -at 1350 Sect. 5.3.6b Low ductility implies yu< 2 and high ductility low flexural ductility implies y 2 5, but for this example the exact displacement ductility is not Diagonal Tension (B) -at high Sect. 5.3.6b important. Capacity at high ductility does flexural ductility not govern, since flexural yielding does not occur.
Web crushing (C) 2560 Sect. 5.3.6c Overturning (M) -flange in compression - 343 Sect. 5.2.6 When the flange is in tension, the vertical Me = 6, 860 k-ft load includes dead load contribution of flange.
Overturning (M) -flange in tension -923 Sect. 5.2.6 Me= 18, 000 k-ft Shear associated with development of the moment strength in either loading direction, so mode H (preemptive restoring force. However, the overturning value calculated diagonal tension) appears to be the governing the is sufficiently less than the other behavior modes behavior mode. In either direction, web crushing can be to suggest that damage will be limited by rocking on the eliminated as a potential behavior mode since its capacity -foundation. Mode M is therefore the behavior mode for is greater than that of all of the other modes. In the wall.
absence of overturning, mode H would therefore be selected as the behavior mode for this component. Damage Severity L. The identification of the rocking behavior mode is important, because the damage severity - Additional calculations indicate, however, that foundation - is different for mode M than for mode H. While rocking (overturning of the wall and its foundation) there is no explicit Component Damage Classification will occur before the other failure modes can develop. Guide provided for the rocking mode-the component This is indicated in the last two rows of Table 7-1, may be considered as roughly analogous to the portion where overturning capacity with the flange in compression -of a flexural wall (mode A) above the plastic hinge is shown to be less than other behavior modes. As region-there is a ductile fuse in the structure below the shown in the example calculations (see sidebar), the component in question that will prevent the development - foundation rocking capacity is based on the static over- of the brittle, force-controlled behavior mode H turning force associated with all tributary gravity loads. by limiting the development of additional seismic force.
In reality, there are a number of factors that would Using this analogy, and Component Guide RC1A, the increase the force required to overturn the wall, so the damage severity is classified as Insignificant. Without calculated value may be a lower bound. For example, as the rocking mechanism, the behavior mode would be the foundation lifts, it will pick up an increasing tribu-classified as H, and the damage severity would be Moderate tary area of the surrounding slabs, thus increasing the rather than Insignificant. It is important to note FEMA 307 Technical Resources 
Chapter 7: Example Application 
EXAMPLE CALCULATIONS FOR DIFFERENT BEHAVIOR MODES EXAMPLE CALCULATIONS FOR DIFFERENT BEHAVIORMODES EXAMPLE 1 -SOLID WALL 
Flexure: The boundary elements at each end of the wall have 4-#10 and 7-#1 1 bars. The vertical wall reinforcement is #4 bars at 13" on center in each face. An approximation of the flexural capacity with the flange in compression may be made, assuming that all the steel in the tension boundary and all the wall vertical steel is yielding, as follows: Boundary Wall Verts. Dead Load Me (comp.) = Agfye 'wal + Asvfye, wall/2 + PDL (wall}) Ia.l /2 = (15.3) 50 (26) + (9.2) 50 (13) + (419) 13 = 31, 300k-ft With the flange in tension the capacity increases because of the yielding of the wall vertical reinforcing in the effective flange width assumed to be one half the effective wall height (M/V) plus the wall thickness, or about ten feet. The capacity also increases because of the additional dead load resistance of the flange. An approximation of the flexural capacity with the flange in tension is then: Flange Verts. Flange Dead Load Me (ten.) = Me (comp.) + Asvfye I wall + PDL flange) I wall = 31, 317 + (3.8) 50 (26) + (320) 26 = 44, 600 k-ft These approximations for moment capacities were checked using strain compatibility calculations and found to be acceptable. Using an M/V ratio of 20 ft the shear forces associated with the moment capacities are 1570 k (flange in compression) and 2230 k (flange in tension).
Diagonal Tension (Shear Strength) : In order to include the effect of axial load on shear strength, and the potential degradation of the shear in plastic hinge zones, the equations recommended in Section 5.3.6b of FEMA 306 were used to calculate the diagonal tension strength.
V =V+V+V p it C An M/V ratio of 20 feet was used (approximately 0.75 times the component height) based on the analysis results for shear and moment.
As=41.2 in2 A = 4176in 2 Ps = 0.0098 Thus Equations 5-3 and 5-4 of FEMA 306 yield a= 1.5 krc = 3.5 (low ductility) P= 0.7 krc= 0.6 (high ductility) and the concrete contribution (Equation 5-2) becomes ge Vc = kc/krfc b. (0. 81 ) Vc= 605 kips at low ductility demand Vc = 104 kips at high ductility demand - The steel contribution is given by Equation 5-5: S= pnfyef b h where Pn=.00256, fye = 50 ksi, bw = 12", and hd is limited by the component height of 27'-0". Thus V, =498kips The axial load contribution is given by Equation 5-6. Considering only the structure dead load tributary to the wall (419 kips) VP becomes (I -c) N = (iM I) V = 264 kips (flange in compression) = 249 kips (flange in tension) NOTE: c = 16.8 in. (flange in compression), c = 33 in.
 (flange in tension) Therefore, Equation 5-1 for the diagonal tension strength gives a value of 1352 kips at low ductility demand, and 851 kips at high ductility demand, both with the flange in tension.
Diagonal Compression (Web Crushing) : The web crushing strength is given by Equation 5-7. This equation requires an estimate of the drift ratio to which the component is subjected, with increasing drift corresponding to a decrease in capacity. An upper bound estimate of 1 percent drift is assumed, to get a lower bound on the web crushing strength: 1.8f'b (0.81, ) 2560 kips 1+ (600 -2000 A) 4 Asf' Foundation Rocking (Overturning) : The static overturning calculation includes not only the dead weight of the wall and tributary slabs at the 2nd floor and roof, but also a tributary area of the slab on grade (496 kips total) and the foundation weight (16 kips per footing).
When the wall flange is in tension, the weight of the flange and additional DL are included.
1 I V, = Mo, =- (496k (26' 1 2) + 16k (26') ) (M/V) 20 = 343 kips (flange in compression) 1 (M /V) 1 =- (496k (26' / 2) + 446k (26') +16k (26') ) 20 923 kips (flange in tension) Technical Resources FEMA 307 Chapter 7: Example Application that the damage severity is not a function of the observed crack pattern alone -the governing behavior mode must be known before a judgement of the damage severity can be made.
7.2.4.3 Example 2 -Coupled Wall (7L-7M) 
As an example of the second typical wall element type, consider the damage record for the coupled wall shown in Figure 7-7. Like the solid wall example, the wall is 12 inches wide with 18-inch-square boundary elements at each end. However, there is a 6'-6" wide by 7-3" tall opening in the center of the wall at each floor. The wall length from center to center of the boundary elements is 26 feet, and the story height is 13'-6". The coupled wall has an L-shaped plan with a 26-foot flange along line M. The coupling beam and wall are similar to the example shown in Figure 7-5, except that this particular coupled wall is discontinuous below the first floor and is supported on 24-inch-square reinforced-concrete columns at the basement.
Component Type. 
Visual observation leads to the division of this structural element into two RC1 wall piers and two RC3 coupling beams. Analysis will verify that the beams are weaker than the walls, and thus that the initial classification is valid.
Behavior Mode. 
In the preliminary classification, the coupling beams were designated by observation as mode B (flexure / diagonal tension) or mode H (preemptive diagonal tension), and the wall piers were designated as mode B (flexure / diagonal tension), mode C (flexure / diagonal compression), mode H (preemptive diagonal tension), or mode N (individual pier rocking).
As in the first example, the shears associated with the development of the maximum strength in flexure, diagonal tension, and web crushing were calculated, with results summarized in Tables 7-2 and 7-3. Selected details of the calculations are provided for reference on pages 196 through 198.
Looking first at the RC3 coupling beam component, the calculation results shown in Table 7-2 indicate that the shear strength will be reached before the development of the moment strength, even at low ductility levels, so the behavior mode H (preemptive diagonal tension) governs.
For the RC1 wall pier components, the calculations and discussions that follow show that behavior mode N, individual pier rocking, governs the seismic response.
For the piers of the coupled wall, which discontinue below the first floor and are supported on basement columns, this behavior mode involves the yielding in flexure of the basement columns and the coupling beams reaching their capacity in shear. The wall pier rotates about the supporting column in a manner similar to Table 7-2 Capacity of Potential Behavior Modes for Typical Coupling Beam Coupling Beams RC3 Behavior Mode Limiting Component Shear (kips) FEMA 306 Reference Comments Flexure (mode A) Me=1210 k-ft 373 Sect. 5.3.5 Note that slab reinforcement was ignored in the calculation of the beam flexure capacity. Since preemptive shear governs (242 < 373), this is irrelevant.
A more accurate calculation would be warranted if the capacities in the different modes were similar.
Diagonal Tension (B and H) -242 Sect. 5.3.6b Governing capacity at low flexural ductility Diagonal Tension (B) -at high flexural ductility 137 Sect. 5.3.6b This capacity does not govern since flexural yielding does not occur.
Sliding Shear (D) 150 Sect. 5.3.6c This mode is unlikely since it typically occurs after flexural yielding. Such yielding is not expected since preemptive diagonal tension governs over flexural response.
 Component shear in beam associated with development of the component moment strength Technical Resources FEMA 307 Technical Resources Chapter 7: Example Application Table7-3 Shear Capacities for Potential Behavior Modes of Wall Pier (RC1) Components in Coupled Wall Potential Behavior Mode Limiting FEMA 306 Notes Component Reference Shear (kips) Flexure (mode A) See notes Sect. 5.3.5 In example calculations, moment capacities are compared to moment demands corresponding to mode N. Flexure is shown not to govern.
Diagonal Tension (mode B and H) at Low Flexural Ductility Sect. 5.3.6b Limiting shears are compared to those for RC1 @7L-load to east 690 behavior mode N. To consider redistribution - RCl @7L-load to west 311 of lateral forces, the sum of shears RCI @7M-load to east 328 for the two wall piers is considered.
RC1@7M-load to west 692 Diagonal Tension (mode B) at High Flexural Ductility Sect. 5.3.6b These capacities do not govern, since RC 1 @ 7L-load to east 470 flexural yielding does not occur.
RC1 @7L-load to west 163 RCI @7M-load to east 166 RCI @7M-load to west 472 Web Crushing (mode C) Sect. 5.3.6c Web crushing not applicable for low axial RC1 @7L-load to east 1710 load or tension.
RC1 @7M-load to west 1810 Rotation about Column Shear in piers is limited by capacity of (mode N) coupling beam (RC3) components.
RC1 @7L-load to east 330 RC1 @7L-load to west 300 RC1 @7M-load to east 300 RC1 @7M-load to west 330 foundation rocking. Free body diagrams corresponding The limiting component shears associated with possible to this mechanism and behavior mode are shown in the behavior modes for the wall piers are summarized in example calculations that follow. Table 7-3. The table verifies that the web crushing (diagonal compression) can be eliminated as a possible Comparison of the moment demands corresponding to behavior mode because the capacity is much higher the behavior mode N to moment capacities of the wall than that corresponding to other behavior modes.
pier sections is shown in the example calculations. The Behavior mode H, preemptive diagonal tension, is moment demands are well below the moment capacity investigated by comparing the limiting shears to those ties, indicating that flexural yielding will not occur. This of mode N eliminates modes B (flexure/diagonal tension) and C (flexure/diagonal compression) as possible behavior Diagonal tension capacities at high ductility are only modes. relevant for the combined flexure/diagonal tension behavior mode, which will not occur since flexural 194 Technical Resources FEMA 307 Chapter 7: Example Application yielding and the consequent degradation of the V, component of shear strength does not occur. The relevant diagonal tension capacities are those at low ductility.
The diagonal tension capacities of 31 1k (RCl @7L-load to west) to 328k (RC 1@7M-load to east) for the wall piers subject to axial tension are similar to the shear demands in the pier rotation mode after failure of the coupling beams; however, there is significant capacity of 690k (RC1 @7L-load to east) to 692k (RC1 @7M load to west) in diagonal tension on the corresponding compression sides of the wall. A diagonal tension failure cannot fully develop on one side of the coupled wall without transferring lateral forces to the other side of the wall. Considering that shear can be transferred as axial forces in the coupling beam and slab according to the stiffness and strength of each wall pier, the sum of wall pier component strengths on each side of the coupled wall can be used to determine the governing behavior mode. For the individual pier rotation behavior, the associated total shear demand is 630k on the coupled wall element. For a diagonal tension behavior mode occurring in both wall piers, the associated shear capacity is 1003k to 1018k. Diagonal tension failure will not govern, since the pier rotation behavior mode occurs at a lower total lateral load. Thus, the results of the analytical calculations indicate the pier rotation (N) is the governing behavior mode for the RC1 components.
This analytical conclusion agrees with field observation.
The degree of diagonal cracking observed in the wall pier RC1 components is consistent with substantial shear stress, but less than that which might be expected for diagonal tension failure.
Damage Severity. 
For the RC3 components behaving in mode H, the damage classification guides indicate that the observed damage is moderate in the second story and heavy in the first story coupling beam. In the wall piers, the protection of the element by a ductile mode (similar to mode N, Foundation Rocking) in surrounding components places them in an insignificant damage category.
7.2.5 Other Damage Observations 
Several of the walls were observed to have horizontal cracks just below the roof slab and/or the second-floor slab. In addition to new cracks of this type, a few walls had pre-existing horizontal cracks below the slabs, which had been repaired by epoxy injection. The widest of these horizontal cracks occurred under the roof slab of the wall on column lines 7C-7D, as shown in the Component Damage Record D3. The engineer in the field indicated that joint movement occurred at this crack and suspected that sliding shear behavior may have occurred.
Subsequent thinking by the evaluating engineers about this observation, however, weighed against the conclusion of sliding shear behavior. The crack was not observed to extend into the boundary columns of the wall, and there was no evidence of lateral offset at the boundary columns. While the crack is located near a likely construction joint where poor construction practice can exacerbate sliding shear behavior, the crack is not located in the maximum moment region of the wall.
As is indicated in FEMA 306, sliding shear behavior is most likely to occur after flexural yielding has occurred.
For this wall, flexural yielding would initiate at the base of the wall where moments are at a maximum, not at the top. In any case, foundation rocking preempts flexural yielding for the typical solid wall, as indicated previously in this example. A quick calculation of sliding shear strength shows that the behavior mode is not expected to govern the wall's response.
Given this information, the damage observations are reconsidered, and it is judged that sliding movements did not occur at the horizontal crack. Therefore, the most likely explanation is that these horizontal cracks are caused by earthquake displacements in the out-of- plane direction of the wall. It is judged that the horizontal cracks, whose widths are less than 0.03 inches, do not significantly affect seismic response.
7.2.6 Summary of Component Classifications 
7.2.6.1 Solid Walls 
All wall components of the building are evaluated in a similar manner, as described in the preceding sections.
In total, the building has six coupled walls plus five solid walls acting in the North-South direction, and two coupled walls plus six solid walls acting in the East- West direction. The damage records for these walls can be found in Component Damage Records D1-D19 (Appendix A).
Each solid wall is a single structural component (RC 1), while each coupled wall has four components: two coupling beams (RC3) and two wall piers (RC1). Thus there are a total of 43 structural wall components in the building, as indicated in Tables 7-4 and 7-5. For each of these, the component type, behavior mode and damage severity is established as described below and shown in the tables.
195 Technical Resources FEMA 307 Technical Resources 195 Chapter 7: Example Application EXAMPLE CALCULATIONS FOR DIFFERENT BEHAVIOR MODES EXAMPLE 2 -COUPLED WALL (7L-7M) COUPLING BEAMS The total diagonal tension strength is then 242 kips at low ductility, and 137 kips at high ductility.
RC3 Flexure: RC3 Sliding (Sliding Shear) : The moment strength of the coupling beams is calculated as discussed in FEMA 306, Section 5.3.5 using expected values -FEMA 306 Section 5.3.6d gives the sliding shear strength for material properties (f'ce = 3 000 psi, fye = 50 ksi). The for coupling beams at moderate ductility levels as beams are 6'-3" deep, with 3 -#9 bars at top and bottom and #4 bars @ 13" on center at each face. The calculated moment capacity is 1210 k-ft. This capacity is determined using strain compatibility calculations that demonstrate that sliding = 3h) Vfebwd = 150 kips all longitudinal bars yield. The MN ratio for the coupling beam is 3-3", so the shear associated with development of This failure mode is generally associated with beams that the moment capacity at each end of the beam is 373 kips. are well reinforced for diagonal tension, and that undergo Note that slab reinforcement is ignored in the calculation of multiple cycles at a moderate ductility level. Since the pre- the beam flexure capacity. It will be shown below that pre-emptive shear failure mode governs, the sliding shear mode emptive shear clearly governs, so this is irrelevant. How-is not a potential failure mode.
ever, a more accurate calculation would be warranted if the capacities in the different modes were similar. WALL PIERS RC3 Diagonal Tension (Shear Strength) : RC1 Flexure: The equations for diagonal tension strength in The figures below show the free body diagrams of the wall Section 5.3.6b of FEMA 306 may be used for coupling for lateral forces toward the east and toward the west. In beams. For beams, the axial load is not significant, thus both cases it is assumed that the coupling beams and first Vp = 0 and Equation 5-1 becomes: floor slab have reached their capacities. It is also assumed that the columns beneath the first floor are yielding in flexure.
These assumptions define a potential inelastic lateral V =V +1V mechanism for the wall. If the assumed lateral mechanism for the coupled wall is correct, the flexural capacity of the Using an M/V ratio of 3-3" (half the clear span of the coupling - RC 1 components must be sufficient to generate the diagonal beams) Equations 5-3 and 5-4 of FEMA 306 yield tension failure in the RC3 coupling beams. The moment a= 1.5 Pg= 0.0 0 5 9 demand diagrams for the RC 1 pier components are also Krc 3.5, 0.6 shown below.
, B=0.61 F = 55 psi The boundary elements in the wall piers at lines L and M each contain 8-#1 1 vertical bars. The vertical wall reinforcing comprises #4 bars at 13" on center in each face. Using and the concrete contribution Equation 5-2 becomes strain compatibility calculations, the moment capacities at the top and bottom of the piers (between the first floor and ba/3krc.
the top of the door opening) corresponding to the appropriate - Vc= bW (0.81w) axial loads are calculated.
V4 = 127 kips at low ductility The moment capacity and demand for the RC1 components must be determined with respect to the same axis. For RC1 @L the elastic centroid is selected. For RC1 @M the V, = 22 kips at high ductility elastic centroid of the component neglecting the return wall is used as the axis. When the return wall is in compression it The steel contribution is given by Equation 5-5 contributes little to the flexural strength of the wall pier.
However, when in tension, the reinforcement in the return V = Pnfyebwh d increases moment strength. Therefore, in the capacity calculations, the vertical reinforcement in approximately 10 ft.
where pn =.00256 is based on the vertical (stirrup) reinforcement - of return is included. This distance is estimated in accordance with FEMA 306 Section 5.3.5b as 50% to 100% of, he = 50 ksi is the expected steel yield strength, the MIV for the entire wall.
bw = 12", and hd = 75" is the horizontal length over which vertical stirrup reinforcement contributes to shear strength, The flexural demand and capacity of the RC 1 components in this case the length of the coupling beam. Thus are summarized in the following table: V, = 115 kips - 196 Technical Resources FEMA 307 Chapter 7: Example Application CALCULATIONS FOR EXAMPLE 2-COUPLED WALL (continued) Component Load Direction Location on Pier Axial Load (k, comp.+) Moment Capacity (k-ft) Moment Demand (k-ft) Top 773 6470 1650 East Bottom 773 6470 3960 RCWLs Top -265 2190 428 Bottom -265 2190 1660 East Top -215 2400 618 East @M Bottom -215 7120 1480 RC1@M Top 823 6660 1850 West Bottom 823 6660 4160 I9 26' Return wall on Return wall on Line M 3k Line M (Coupling bm. DL) 220 k 201 k 201 k 1 /220i -g-= I 106k 11 13.5' 106k 113.5' (Column DL) 119k. (Column DQ 119k 110k 99Zk 99 k 9110k 13.5' 106k 13.5' 106 k 143k 143 k 330 k 300 k 3< I -I K5 K5 ' 33 K 443ft-k 280 ft-k (Col. moment capacity 248ft-k 431 ft-k (Col. moment capacity axial load) @associated t at associated axial load) 773 kf AxialforcesinRC1 215k Axial forces in RC1 823k 265 4; components I (comp.) (comp.) components T (ten.) (ten.) Free Body Diagram for Seismic For to East : West Roof i Roof i 244 i Second i Second 21 i i M/V=1F2.6' i \v 1 First i3960 t1482 Moment Diagram (@ centroid of i i Moment Diagram (Q centroid of piers) for Load to East Moment Diagram (d centroid of piers) for Load to West (plotted on tension side ink-ft) (plotted on tension side in k-ft) j FEMA 307 Technical Resources Chapter 7: Example Application CALCULATIONS FOR EXAMPLE 2 -COUPLED WALL (continued) 26' 12" 18" :01 'z im wall 126" I flange) Plan Distance to the elastic centroid from gridline: / [126 (12) +2 (18) 3] X= ([1 26 (12) 126/2+2 (18) 3 (9) ] 1-9 = 50.2" or 4.2' Comp. Load Axial Load Reduce Net Tot. Duct.
Direct. (k) vc for Ten. VC VS VP V (k) (k) (k) (k) East 773 265 1.0 265 133 292 690 low RC1 @L (comp.) 45 45 470 high West -265 265 0.67 178 133 0 311 low (ten.) 45 30 163 high East -215 265 0.74 195 133 0 328 low RC1@M (ten.) 45 33 166 high West 823 265 1.0 265 133 294 692 low (comp.) 45 45 472 high RC1 Diagonal Tension (Shear Strength) : V, = 133 kips The equations in Section 5.3.6 of FEMA 306 were again The compressive axial load contribution is given by used to calculate the diagonal tension strength. Equation 5-6.
V.= v, + +v,, v, = ( (I, -c) NM Using the component M/V values from the moment diagrams - (2 -M), Equations 5-3 and 5-4 yield V ax= 1.5 fl=0.76 p = 0.0013 Considering all of the above contributions the diagonal tension - g strengths of the RC 1 components are summarized in the and the concrete contribution from Equation 5-2 becomes table above: Vc =-ocskrc+/ f'bw (0 8hw) RC1 Diagonal Compression (Web Crushing) : V, Iaflk,.Vrf, beW The web crushing strength is given by Equation 5-7. This = 265 kips at low ductility equation requires an estimate of the drift ratio to which the component is subjected, with increasing drift decreasing the V, = 45 kips at high ductility capacity. An upper bound estimate of 1% is assumed to get a lower bound on the web crushing strength: When the component experiences net axial tension ACI 318-95, eqn. 11-8 specifies the the concrete contribution to 18fbW (08lw) shear strength, Vc, be reduced by the factor 1-[N, / (500 V. N. 1710psfbRCI 7L load to East Ag) ]. 1+ 600-2000 A Lj The steel contribution is given by Equation 5-5 = 1807 kips foRC RO 7Mload to West V, = pnfyewihd Web crushing is not typically an issue for low axial loads or where pn =. 0 0 2 56 'fye = 50 ksi, bw = 12", and hd is limited net tension.
by the height of the door 7'-3". Thus Technical Resources FEMA 307 Chapter 7: Example Application The typical solid walls were calculated to behave in a foundation rocking (or overturning) mode (type M).
There are no damage guides for this behavior mode.
However, component behavior description in FEMA 306 considers this mode to have moderate to high ductility.
The damage associated with this behavior mode may not be apparent based on the observations of the walls. Damage to other structural and nonstructural elements, such as damage to the floor slab at the base or to the beams framing into the ends of the walls, should be used to assess the severity of the mode. Since there was no significant damage to the adjacent structural and nonstructural elements, the damage severity is judged to be Insignificant.
7.2.6.2 Coupling Beams 
Based on calculations, the behavior mode of the coupling beams is Preemptive Diagonal Tension (Type H).
Based on the damage observations and the component guides, the damage for the coupling beams with spalling, bar-buckling, and/or significant cracking was classified as Heavy. For the coupling beams with shear cracking, but no bar-buckling or significant spalling, the damage is Moderate.
7.2.6.3 Wall Piers 
The walls adjacent to the coupling beams are expected to behave in a mode of individual pier rocking (type N).
There are no Component Guides for this behavior mode.
However, the component behavior description for this mode of behavior considers this mode to have moderate to high ductility. Similar to the solid shear walls, the lack of damage to the adjacent structural and nonstructural elements was used to classify the damage as Insignificant.
7.3 Evaluation by the Direct Method The effects of damage are quantified by the costs associated with potential Hypothetical repairs (component restoration measures -repairs for), which if implemented, would method, restore the components to their pre- Section 4.6 event condition. In the direct method, of FEMA 306 restoration measures are considered on a component-by-component basis without an analysis of global performance. It is intended to be a simple and approximate approach. The Component Damage Classification Guides in FEMA 306 are used to determine the appropriate potential repairs to restore each component.
The potential repairs required to restore the structural performance and nonstructural functionality of the building include both structural and nonstructural (e.g., cosmetic) measures for each damaged component.
7.3.1 Structural Restoration Measures 7.3.1.1 Coupling Beams As shown in Tables 7-4 and 7-5, three of the coupling beams were classified Damage as component type RC3, behavior guide for mode H, having Heavy damage. As Table 5-2 of recommended for this component FEMA306 type, behavior mode, and damage severity, the component restoration measure chosen is to replace these components. The proposed repair would be to remove the concrete at the coupling beam and a portion of the floor slab, install new reinforcing bars, and cast new concrete for the wall. The new reinforcing steel in the coupling beams would be detailed in accordance with the current provisions of the governing building code for coupled shear walls, as shown in Figure 7-8.
The coupling beams with Moderate damage could be repaired by epoxy injection of all diagonal shear cracks greater than 10 mils wide, since epoxy injection is recommended for structural restoration using the damage guide for RC3H. Although it is possible to inject smaller cracks, the additional cost does not justify the marginal benefit. Since cracks as large as 12 mils can be tolerated in normal concrete structures (ACI, 1994), the unrepaired cracks should not be detrimental. The length of the cracks to be injected is estimated as 100 feet.
7.3.1.2 Solid Walls The remaining wall components are type N or M. There are no Component Guides for these modes to indicate the appropriate repairs directly. As discussed earlier, these modes have moderate to high ductility capacity.
Conservatively, the damage guide for Type B, flexure / diagonal tension, is used since this is a moderate ductility mode, analogous to the actual behavior mode. The Component Guides for the type RC1B components indicate that if cracks are less than 1/16 inch, the damage can be classified as Insignificant, and therefore structural repairs are not necessary. Two of the shear wall components had cracks that exceeded 1/16 inch.
This amount of cracking would be classified as Moder- FEMA 307 Technical Resources Chapter 7: Example Application Table 7-4 Summary of Component Type, Behavior Mode, and Damage Severity for Wall Components (North-South Direction) Column Floor Wall Type Component Type and Damage Severity Line Behavior Mode B / 2-3 First-Second Coupled RC1N Insignificant Coupled First t 0 First-Second Coupled RC1N Insignificant B I 5-7 First-Second Coupled RC1N Insignificant First Coupled RC3H Moderate First-Second Coupled RC1N Insignificant B /10-12 First-Second Coupled RClN Insignificant First Coupled RC3H Moderate First-Second Coupled RClN Insignificant Second> Coupled" j CH" Moderate B /14-15 First-Second Coupled RC1N Insignificant E /2-3 First- Second Coupled RC 1N Insignificant E / 2-3 First-Second Coupled RC1N Insignificant irt Second Coupled RC3H Insignificant E 1-5 Second Coupled RC3H Insignificant First-Second Coupled RC1N Insignificant G I 7-8 First-Second Solid RC1M Insignificant G / 9-10 First-Second Solid RC1M Insignificant M / 7-8 First-Second Solid RC1M Insignificant M / 9-10 First-Second Solid RC1M Insignificant M / 8-9 Ground Solid RC1B Insignificant 200 Technical Resources FEMA 307 200 Technical Resources FEMA 307 Chapter 7: Example Application Table 7-5 Summary of Component Type, Behavior Mode, and Damage Severity for Wall Components (East-West Direction) Column Floor Wall Type Component Type and Damage Severity Line Behavior Mode 7 /L-M First-Second Coupled RC1N Insignificant First-Second Coupled RC1N Insignificant 10/ L-M First-Second Coupled RC1N Insignificant First-Second Coupled RC1N Insignificant 2/ B-C First-Second Solid RC1M Insignificant 2/ D-E First-Second Solid RC1M Insignificant 7/ C-D First-Second Solid RC1M Insignificant 10/ C-D First-Second Solid RC1M Insignificant 15 /B-C First-Second Solid RC1M Insignificant 15 / D-E First-Second Solid RC1M Insignificant ate for type B behavior. Epoxy injection is recommended -In addition, many of the suspended ceiling tiles became in the Component Damage Classification dislodged and fell during the earthquake. The nonstructural - Guides for these cracks. Thus, for performance restoration - repairs would include replacing the ceiling tiles.
by the direct method, these walls would have all of the cracks exceeding 1/16 inch repaired by injection 7.3.3 Restoration Summary and Cost with epoxy. The total length of crack to be injected is Table 7-6 summarizes the performance restoration measured estimated at 22 feet. Tbe 76 performance restoration estimated at 22 feet and estimated costs. Additional costs related to Spalls (other than at the coupling beams that are being inspection, evaluation, design, management and indirect placed) could be repaired by application of a concrete costs may also be involved repair mortar to restore the visual appearance. The total volume of concrete spalls is estimated to be 3 cubic 7.4 Evaluation by Performance feet.
Analysis 7.3.2 Nonstructural Restoration 
The use of the direct method is limited to an estimate of Measures the loss associated with the damaging earthquake. It wall components with visible cracks could be cannot be used to evaluate actual performance. For repaired by patching the cracks with plaster, and then these purposes, relative performance analysis as painting the entire wall. This repair is only intended to described in FEMA 306 is used. The basic procedure restore the visual appearance of the wall. Restoration of comprises a comparison of the anticipated performance other nonstructural characteristics, such as water tight-of the building in future earthquakes in its pre-event, ness and fire protection, are not necessary in this damaged, and repaired conditions. This comparison instance. may be made for one or more performance objectives.
FEMA 307 Technical Resources 201 Chapter 7: Example Application Remove & Replace Existing Concrete Coupling Beam #4 Hoops @ 2 1/2 inches Diagonal Bars in a Existing 3-#9 Bars 6 inch x 8 inch Cage to Remain Epoxy Dowel 38 inches into Existing Wall #4 Bars @ 12 inches Elevation #4 Stirrups @ Floor Slab Joists Section Figure 7-8 Detail of Coupling Beam Replacement Table 7-6 Restoration Cost Estimate by the Direct Method Item Unit Cost Quantity Cost (1997 dollars) (1997 dollars) Epoxy Injection $25.00 ft 122 ft $ 3, 050.
Coupling Beam Removal and Replacement $74.00 /cu ft 122 cu ft $ 9, 028.
Patch and paint walls $0.60 /sq ft 10, 175 sq ft $ 6, 105.
Replace ceiling tiles $2.00 /sq ft 15, 000 sq ft $30, 000.
General Conditions, Fees, Overhead & Profit (@ 30%) $14, 455.
Total $62, 638.
7.4.1 Performance Objectives return period (10 percent probability of exceedance in Two performance objectives are 50 years) for this site. The response spectrum for this considered in this example. The first is Performance earthquake is shown in Figure 7-9. The soil at the site objectives, was determined to be type S,. Using the available the life safety performance level, as Section 4.2 seismic data, the spectral response at short periods (T = defined in FEMA 273, for an of FEMA306 0.2 sec) for this site is 1.0 g and the spectral response at earthquake associated with a 475-year 1 second is 0.56 g.
202 Technical Resources FEIVA 307 Chapter 7: Example Application 1.2 0.
0 0 0.6 0 0 1 -E 0.4 I.
4'0.2 CO) 0 I 0 0.5 1 1.5 2 2.5 3 Period (Sec) Figure 7-9 Response Spectra for Selected Performance Levels The building was also checked for immediate occupancy performance level using an earthquake with a 50 percent probability of exceedance in 50 years. For this earthquake, the spectral response at short periods at this site is 0.68 g and the spectral response at 1 second is 0.35 g. The response spectra for the immediate occupancy performance level is also shown in Figure 7-9.
It should be noted that these performance objectives do not necessarily correspond to the original criteria used for design of the building.
7.4.2 Nonlinear Static Analysis 
7.4.2.1 Computer Model 
The building is analyzed in its pre-event, post-event and repaired conditions using a three-dimensional computer model. Modeling of the building is done using the recommendations of FEMA 273 and FEMA 306. The model is subjected to a nonlinear static (pushover) analysis to assess its force/displacement response. For this example, the analysis is run only in the East-West direction, which is the direction that experienced the most significant damage.
The computer analysis program SAP2000 (CSI, 1997) is used to model the structure. The reinforced concrete walls and coupling beams are modeled using beam elements. The beam elements are located at the center of gravity of each wall section, and are given properties that represent the wall section stiffness. Rigid end offsets are used to model the joint regions in the coupled walls as shown in Figure 7-10. Small models of individual walls are used to verify that the beam elements used to model the walls have approximately the same stiffness and shear distribution as a model using shell elements for the walls. A three dimensional view of the global model is shown in Figure 7-11. The horizontal floor and roof diaphragms are modeled using beam elements, as shown in Figure 7-11, with lumped masses at the nodes.
The pushover analysis is conducted by applying static loads at the locations of the lumped masses in a vertical distribution pattern as described in the second option of Section 3.3.3.2 C, of FEMA 273. Sixty percent of the total lateral force is applied to the roof, thirty percent is applied at the second floor, and ten percent is applied at the first floor. The nodal loads are increased proportionally in progressive iterations. When elements reach their strength limit, their stiffness is iteratively reduced to an appropriate secant stiffness and the model is rerun at the same load level until no elements resist loads in excess of their calculated capacities. (Secant stiffness method, see side bar.) The pushover analysis is continued to cover the displacement range of interest, which is based on a preliminary estimate of the maximum displacement demand.
A global pushover curve is then produced.
FEMA 307 Technical Resources Chapter 7: Example Application I I I I I I I I I I I I Figure 7-10 Mathematical Model of Coupled Shear Wall 7.4.2.2 Component Force-Displacement Behavior Component force-displacement curves are developed for each of the typical wall components using the generalized force-displacement curves from Figure 6-1 of FEMA 273.
The acceptance limits for the coupling beam components are based on Table 6-17 of FEMA 273 for the case of Component force- displacement relations, FEMA 273 and Sections 4.3 and 4.4 of FEMA 306 "nonconforming", transverse reinforcement, and shear exceeding 6twAwr-. The pre-event shear-strength-to- I I L L.
I I chord-rotation relationship is shown in Figure 7-12 (a).
Also shown in this figure are the points representing the displacement limits for immediate occupancy and life safety performance.
The initial slope of the component force/deformation curves is based on modeling for the initial elastic stiffness of the com-pre-event. The pre-event structure is condition, modeled using the effective initial Section 4.4.3.1 of stiffness values recommended in Table 6-4 of FEMA 273. Walls and coupling FEMA 306 COEFFICIENT Either of two methods are recommended for establishing displacement demands for a nonlinear static analysis: the coefficient method and the capacity spectrum method. A description of these methods is included in ATC 40. The coefficient method is also described in FEMA 273, and the coefficient and capacity spectrum methods are described in FEMA 274. Although either method may be used, it is essential for a valid comparison that the same method be used to assess the performance of the pre-earthquake, post-earth- quake, and repaired structure, as outlined in FEMA 306.
In this example, the coefficient method is used. In this method, a target displacement, dt is calculated and compared to the displacement of a control node, generally located at the roof. The target displacement is determined by multiply- AND CAPACITY SPECTRUM METHODS ing a set of coefficients times a function of the effective building period and the spectral acceleration.
T2 =CoCiC 2C3Sa 4 2 g t 4, r To use the coefficient method, the nonlinear static analysis must be conducted in order to construct the pushover curve.
The pushover curve can be presented as spectral acceleration versus spectral displacement or as base shear versus roof displacement. Once the pushover curve is constructed, an equivalent bilinear curve is fitted to approximate the actual curve. The equivalent bilinear curve is then used to obtain the effective stiffness of the building and the yield base shear needed for calculating the target displacement.
Technical Resources Technical Resources FEMA 307 Chapter 7: Example Application Beam Elements Representing Solid Wall Figure 7-11 Mathematical Model of Full Building beams are given a flexural rigidity of 0.5Ecg. The basement columns of the structure, which support the discontinuous walls, are given a flexural rigidity of 0.7Eclg. As recommended in FEMA 273, the shear rigidities of all components are set equal to gross section values.
The post-event structure is modeled with stiffness values multiplied by the Ak factors recommended in FEMA 306. Heavily damaged coupling beams have their stiffness reduced to 20 percent (ok = 0.2) of the pre-event value. Moderately damaged coupling beams have their stiffness reduced to 50 percent (o'k = 0.5) of the pre- event value. For the solid shear walls, where damage is classified between Insignificant and None, stiffness is reduced to between 80 percent to 100 percent of the pre- event stiffness depending on the amount of cracking.
The horizontal plateau of the component force/deformation curves is based on the strength of the governing behavior mode. For the pre-event structure, the strength Beam Elements Representing Floor Slab Nodes Where Lateral Loads are Applied is based on calculations as illustrated in Section 7.2.4 of this example. For the post-event structure, the pre-event strength is multiplied by the IQ factors recommended in FEMA 306. Heavily damaged coupling beams have their strength reduced to 30 percent of the pre-event value. Moderately damaged coupling beams have their strength reduced to 80 percent of the pre-event value.
For components where damage is classified either Insignificant or None, the strength is not reduced.
Figure 7-12 (b) shows the force-deformation curves for the moderately and heavily damaged coupling beams.
7.4.2.3 Foundation Rocking 
Since the governing behavior mode of the solid concrete walls is identified to be foundation rocking, this behavior is incorporated into the pushover analysis. To model the rocking, the stiffness of the lower story wall elements is reduced when the shear force in those elements reaches the shear force that causes rocking. Once the wall element in the model had started to overturn in the analysis, the stiffness is adjusted so that the wall FEMA 307 Technical Resources Chapter 7: Example Application NONLINEAR ANALYSIS USING LINEAR ANALYSIS COMPUTER PROGRAMS 
Currently, there are few commercially available computer programs for direct implementation of the nonlinear analysis required for a pushover analysis. Many of the nonlinear pro- grams available are sophisticated but can be expensive and difficult to use. For many buildings, a linear elastic analysis program can be used to assess iteratively the nonlinear behavior of the building.
There are two ways to implement a nonlinear static analysis using a linear computer program. Both methods are based on adjusting the stiffness of an element once the analysis indicates that the element has reached its yield level. One method uses the tangential stiffness of the element at the dis placement level above yield; the other uses a secant stiff- ness. The figures below depict the difference between the two methods.
Model #4 Models Model #2, a) C.
L o ILL fo el #1 / Sum of models gives final forces and displacements Displacement Figure i -Tangential Stiffness Method The tangential stiffness method is described in detail in ATC 40 (ATC, 1996). Lateral forces are applied to the building and proportionally increased until an element reaches its yield level. A new model is then created in which the yielding component has its stiffness reduced to zero or a small post-yield value. An incremental load is applied to the new would resist about 10 to 20 percent more shear force than that calculated to cause overturning. This adjustment is made to account for the additional dead weight of the structure that the wall would pick up once it started to uplift. The amount of additional overturning resistance in the wall is based on the shear and moment capacity of the beams framing into the wall.
Model #3 M Model #2 Mo/e/ / Model #1 ILL Model #4 gives forces and displacements Displacement A Xs #lk-A i ls.-%-.M-Jlt4X 16t model until another component reaches its yield level. The process continues until a complete mechanism has formed or until the maximum displacement level of interest has been reached. The sum of forces and deformations of each of the incremental models then represent the global behavior of the structure.
In the secant stiffness method, lateral forces are applied to the building and proportionally increased until a component reaches its yield level. A new model is then created in which the yielding element has its stiffness reduced by a value chosen to produce the correct post-yield force in the component.
The new model is then rerun at the same force level, and components are checked to verify that the force in the component has not exceeded, or reduced significantly below, its yield level. If necessary, the stiffness of the yielding element may need to be adjusted so that the force in that element is approximately equal to the post-yield force level. Other elements need also be checked since they may be resisting additional load no longer resisted by the yielding element.
After iterating until all elements are at approximately the correct force level, a new model is created at a larger lateral force level. The process is repeated at each force level. The behavior of the structure and each element at a given force level is represented directly by the behavior of the appropriate model, rather than combining the results of several models.
7.4.3 Force-Displacement Capacity (Pushover Analysis) Results 7.4.3.1 Pre-Event Structure The results of the pushover analysis indicate the progression of displacement events to be as follows for East-West loading (See Figure 7-2 for wall locations) : o Initially the two solid walls on lines 7 and 10 between lines C and D reach their rocking capacity.
FEMA 307 Technical Resources Technical Resources FEMA 307 Chapter 7: Example Application 250.-.2 200150 1 -l1 & I1 '.1l I -I 1S-I I I.1 (n 100 50 0 ltI -Ir L I-I1z; II IT t I 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 300 Rotation (Radians) a) Pre-event 300 1 1I I I 250 1- co 'W1W -+Moderate CL 200 W =11 -Heavy " 150 I s1 100 Cl) 50 0 -U = I 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 Rotation (Radians) b) Post-event In I c 300 250 4-co.2 200 -150 a4 100 50 0 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 Rotation (Radians) I c) Replacement Coupling Beam with Diagonal Reinforcement Figure 7-12 Component Force-Displacement Curves for Coupling Beams FEMA 307 Technical Resources 207 Chapter 7: Example Application Comparison of Pre-event and Post-event Pushover Curves 9, 000 8, 000 - 7, 000 - -6, 000- 0.
X 5, 000 t) 4, 000- o 1 m 3, 000 -Post-event 2, 000 - 1, 000 0 4 0 0.5 1 1.5 2 2.5 Roof Displacement (Inches) Figure 7-13 Comparison of Pre-event and Post-event Pushover Curves When the solid walls between lines C and D are As shown in Figure 7-13, the pushover analysis softened, the solid walls on lines 2 and 15 between indicates that global nonlinearity begins at a base shear lines B and C, and between D and E at the first floor of approximately 5000 k. As lateral displacements pick up additional force and reach their rocking increase, the base shear climbs to about 8000 k. Since capacity. 10% of the total is applied at the first floor and is transmitted directly into the foundation, the force As the solid walls are softened, the coupled walls on resisted by the structure above the first floor prior to lines 7 and 10 between lines L and M resist more global nonlinearity is about 4500 k. Allowing for some force. The first floor coupling beam picks up more increase in capacity to reflect rocking behavior more force than the second floor coupling beam and accurately (see Section 7.4.2.3), this agrees well with reaches its shear capacity first. the hand-calculated capacities of the walls summarized in Tables 7-1 and 7-3. The applied load in excess of the Additional coupling beams reach their capacity and capacity of the walls is resisted by the columns. The solid walls continue to rock as the displacement magnitude of the increased load is compatible with the of the structure is increased. capacity of the columns. In the analysis, the first story coupling beams are the first element to reach the The approximate target roof displacement is reached immediate occupancy and life safety acceptability after the coupling beams have exceeded their limits. The component deformation limit for immediate collapse prevention acceptability limit, requiring a occupancy occurs when the roof displacement reaches reduction in their capacity. about 0.65 inches and that for life safety is reached at FEMA307 Technical Resources Technical Resources FEMA 307 Chapter 7: Example Application about 0.88 inch. These displacements are taken as the displacement capacity d^, as defined in FEMA 306.
The progression of damage shown in the analysis is consistent with the observed damage.
7.4.3.2 Post-Event Condition 
For the post-event structure, the progression of displacement events is modeling of essentially the same as that outlined condition, for the pre-event structure. The results Section 4.4.3.2 of the post-event pushover analysis of FEMA306 are shown in Figure 7-13. In this analysis, the first story coupling beams reach the immediate occupancy acceptability limit at a roof displacement of 0.47 inches; the beams reach the life safety limit at a roof displacement of 0.66 inches. These values are used for d'.
7.4.3.3 Comparison of Force-Displacement Capacity Curves (Pushover Curves) The performance of the post-event building was slightly different than the pre-event performance; the overall building is softer since more deflection is obtained for the same magnitude of applied load. The reduced stiffness of the damaged components causes the global reduction of stiffness of the post-event structure. The Moderate and Heavy damage to some of the components corresponds to a reduction in their strength. At 1.2 = co.0 I0.8 o 0.6 a XO.4 u.
0.2 (0 0.0 0 0.5 1 larger displacements (greater than about 1.5 inches) the response of the pre-event and post-event structures are essentially the same.
7.4.4 Estimation of Displacement, de, Caused by Damaging Earthquake The accuracy of the structural model of the building can be verified by estimating the maximum displacement, de, that was caused by the damaging event. This is done in two ways. If the data were available, actual ground motion records could be used to predict displacement analytically. Secondly, the pushover curve in conjunction with component capacity data could be used to estimate displacements from the observed damage.
In this case, a spectrum from recorded ground motion at a site approximately 1.5 mi. from the building was available (see Figure 7-14). FEMA 273 (equation 3-11) uses the displacement coefficient method to estimate maximum displacement from spectral acceleration as follows: 2 de= CoCiC2C3Sa g (7-1) In this expression the coefficients C0 to C3 modify the basic relationship between spectral acceleration and 1.5 2 2.5 3 Period (Sec.) Figure7-14 Response Spectra from Damaging Earthquake FEMA 307 Technical Resources Chapter 7: Example Application placement for an elastic system as a function of the effective period of the structure, The effective period for the pre-event structure is approximately 0.3 sec. The spectral acceleration for this period from Figure 7-14 would be approximately 0.5 to 0.6 g producing an elastic spectral displacement between 0.4 and 0.5 in.
The coefficient C0 converts spectral displacement to roof displacement and has an approximate value of 1.25 for two- and three-story buildings.
For short-period buildings, the maximum inelastic displacement often is greater than the elastic. FEMA 273 provides the following expression Cl to adjust conservatively from elastic to inelastic: 01.0+ (R -1.0) To Cl = R e where R = Sa 1 (7-2) W In these expressions, the effective base shear at yield as a portion of the building weight, or about 0.28 in this case. This would result in an R-factor of approximately 1.4 to 1.7. The point where the spectral acceleration transitions from the acceleration to velocity controlled zone occurs at a period of around 0.5 to 0.6 sec. These values would combine to result in a coefficient Cl of around 1.2 to 1.4.
The coefficient C2 accounts for the shape of the hysteresis curve and is equal to 1.0 in this case. The coefficient C3 accounts for dynamic P-A effects and is also equal to 1.0 for this case.
Combining all of the coefficients and the elastic spectral displacement results in an estimate for the maximum displacement at the roof, de, of between 0.6 to 0.9 in.
From the damage observations, one of the first-floor coupling beams in the east-west direction appeared to reach its capacity, since a severe crack had developed and a transverse bar had buckled. Shear cracking had also developed in the wall piers adjacent to the coupling beams.
From the pushover analysis, at displacement demands between 0.3 inches and 0.5 inches, the coupling beams reach their capacity. The pushover analysis also indicates that the first floor coupling beam would be the first to reach its capacity, which is verified by the observations.
Since only the first floor beams were heavily damaged, the displacement demand of the damaging event should not have been much greater than 0.5 in.
The difference between the analytical estimate of and the estimate from the model and observed damage is not large. The difference is acceptable because the building is farther away from the epicenter than the site where the motion was recorded, and actual recorded building response is usually less than that which is predicted analytically.
Based on the comparison there is no need to adjust the structural model.
7.4.5 Displacement Demand 7.4.5.1 Estimate of Target Displacement Estimating the target displacement can be an interactive process. The nonlinear static analysis produces a force- displacement pushover curve covering the displacement range of interest. Based on the procedures of FEMA 273, an equivalent bilinear curve is fitted to the pushover curve and a yield point is estimated.
Using this yield point and the associated effective period, the target displacement is calculated using the coefficient method. Given the calculated target displacement, the equivalent bilinear curve can be refitted, adjusting the yield point, and giving a new target displacement.
The revised target displacement is close to the original estimate so further iteration is not needed.
EXAMPLE CALCULATIONS FOR PRE-EVENT AND POST-EVENT DISPLACEMENT DEMANDS Section 5.4 of FEMA 306 describes the procedures for calculating the displacement demand for both the pre-event and the post-event structures. The pre-event and post-event pushover curves for this example are shown in Figure 7-13.
For this example, the coefficient method is used to calculate the target displacements and FEMA 306 procedures are used to determine the corresponding displacement demands.
Pre-Event Target Displacement, dd An idealized bi-linear capacity curve for the pre-event structure is developed to approximate the actual pushover curve. Based on this idealized curve, the yield level base shear V. is 6000 kips and the yield level displacement Dy is 0.31 inches. The effective stiffness Ke then becomes 19, 400 kips/inch.
Technical Resources FEMA 307 Chapter 7: Example Application EXAMPLE CALCULATIONS FOR PRE-EVENT AND POST-EVENT DISPLACEMENT DEMANDS (continued) aU, 0.
10, 000 : 8, 000 M 6, 000 Pushover curve U) 4, 000 idealized curve U) CD 2, 000 m 0 0 0.5 1 1.5 2 Roof Displacement (Inches) Comparison of idealized bilinear curve to pushover the pre-event effective stiffness and the post-yield stiffness curve for the post-event curve to calculate a target displacement.
In this example, the slopes of the post-yield curves for the The initial period 0.25 seconds taken from the initial pre-event and post-event conditions are similar. Therefore, structural model. The effective period is calculated to be the target displacements will be essentially the same. The 0.30 seconds using the ratio of the initial to the effective value for d'd1 will be taken as the pre-event demand displacement - stiffness., which is 1.68 inches.
K. 27900 T  A = 0.25 = 0.30 Post-Event Target Displacement, d'd2 K 19400 Considering the post-event pushover curve, the effective stiffness Ke, with V. = 5600 and D. = 0.32 is 17, 500. The spectral acceleration Sa, based on the life safety earth- initial and effective periods are 0.25 seconds and 0.31 seconds - quake response spectra at the effective period is 1.0 g..
The coefficients are: The damping coefficient 13 for the post-event structure is calculated = 1.25 for a 2-to-3-story building to be 0.06 based on Equation 5-3 of FEMA 306, due to the change in the post-event effective stiffness. The Cl = 1.58 using the equation for T, in the constant damping adjustments for the response spectrum (B, and BI), acceleration region of the spectrum interpolating from Table 2-15 in FEMA 273, are 1.06 and 1.04 respectively. This changes the spectral acceleration for C2 = 1.0 the post-event structure to 0.97.
C3= 1.0 The value for Cl becomes 1.55, and the other coefficients Thus the target displacement from Equation 3-11 of FEMA are the same as for the pre-event condition. Using these val273 is: the new target displacement is calculated as: dt = 1.25 (1.58) (l.Og) (386 in/sec2g) (0.30) 2/4it2 dt= 1.71inches = 1.68 inches This value is assigned as dd, the maximum displacement in This value is assigned as d'd2.
its pre-event condition. The displacement demand from the damaging earthquake de was estimated to be 0.6 inches. Since d'dl is greater than de, Post-Event Target Displacement, d'dl the displacement demand for the post-event structure d'dis There are two values for the post-event displacement equal to d'dl, which is 1.68 inches.
demand that need to be calculated. The first value, d'd, uses 211 Technical Resources FEMA 307 Technical Resources 211 Chapter 7: Example Application The target displacement dd for the d pre-event structure for life safety performance -demand, against the 475-year-Section 4.4.4 return-period earthquake, based on of FEMA306 the coefficient method calculations, is 1.68 inches. The displacement demand for immediate occupancy after the 100-year earthquake is 0.97 inches.
Calculations (see sidebar on previous page) indicate that displacement demand for the post-event structure is essentially the same as for the pre-event structure.
7.4.5.2 Effects of Damage on Performance 
The changes in displacement capacity and displacement demand caused by the effects of damage are summarized in Table 7-7. The Performance Indices, P and PF in Table 7-7 are the ratios of the displacement capacity, d, or dc', to displacement demand, dd or id, as defined in FEMA 308. The displacement capacities calculated in Section 7.4.3 are based on the assumption that the coupling beams are primary components. FEMA 273 allows coupling beams to be treated as secondary members.
Since the global capacity is controlled by the acceptability of the coupling beams, the displacement capacities are determined again assuming that the coupling beams are secondary components and the results are included in Table 7-7. The global displacement capacity, although higher for Life Safety, is still controlled by the coupling beams. The relative change in Performance Index is similar in both cases, indicating that the effects of damage are the same.
The Performance Indices for both the pre-event and post-event structures are less than one for both performance objectives, indicating that the objectives are not met. The effects of damage can be quantified by identifying restoration measures to return the Performance Index to its pre-event value, as outlined in the following sections. The actual course of action to accept, restore, or upgrade the damaged building is a separate consideration for the owner and the local building authority.
7.4.6 Analysis of Restored Structure 7.4.6.1 Proposed Performance Restoration Measures The primary difference between the pushover models of the pre-event building and the post-event building is the performance of the coupling beams. In their post-earth- quake condition, the coupling beams were considered to have less stiffness and strength than in their pre-event condition. The displacement limits were also reduced by the A'D factor of 0.7. This resulted in the overall reduced stiffness, strength, and displacement capacity of the structure.
To restore the overall performance of the building, various schemes could be investigated, for example, the addition of new concrete walls without repairing damaged components. In this case however, the most straightforward repair appears to be the same component-by-component restoration considered in the direct method. This principally involves the repair of the damaged coupling beams. The coupling beams would be repaired as suggested by the Component Guides in FEMA 306 for the RC3H components. The moderately Table7-7 Performance Indices for Pre-event and Post-event Structures Displacement Capacity (inches) Displacement Demand (Inches) Life Immediate Safety Occupancy; dd =1.68 dd =0.97 dd'= 1.68d, '= 0.47 dd'= 0.97 0. s Gondar comj0 & d, = 0.65 dd =1.68 dd =0.97 d' = 0.47 dd' = 1.68 dd' = 0.97 Performance Index (Capacity/Demand) Life Immediate Safety Occupancy P =0.52 P =0.67 P'= 0.39 P'= 0.48 P =0.60 P =0.67 P' = 0.45 P' = 0.48 Life Safety b g..
treated Coupling beams treated Pre-event d, =0.88 Post-event dj= 0.66 Coupling be ins treated Pre-event d, =1.00 Post-event d' = 0.76 Immediate Occupancy 0 S primary, = 0.65 FEMA 307 Technical Resources Technical Resources FEMA 307 Chapter 7: Example Application damaged coupling beams are repaired by injecting the cracks with epoxy. The heavily damaged coupling beams are repaired by removing the damaged coupling beams and replacing them with new coupling beams.
Each new coupling beam will be designed using the provisions of the current building code, which requires diagonal reinforcing bars be installed as the primary shear resistance. A detail of the potential repair is shown in Figure 7-8.
7.4.6.2 Analysis Results The moderately damaged coupling beams are "repaired" in the model by revising their stiffness and strength based on the Component Damage Classification Guides. The heavily damaged coupling beams that were replaced are given stiffness values for initial, undamaged elements and displacement capacities as in FEMA 273 for flexure-governed beams with diagonal reinforcement, as shown in Figure 7-12 (c). The stiffness of the moderately damaged coupling beams is restored to 80 percent of the pre-event stiffness. The strength and displacement limits are restored to the pre-event values.
The strength and stiffness of the other components in 9, 000 - 8, 000 - -7, 000- = 6, 000-, 5, 000- #-4, 000 - 1) 3, 000 M 2, 000 co 1, 000 0- 0.5 the model are unchanged from their post-event condition.
The pushover analysis is then conducted using the same procedures and load patterns.
The progression of displacement events for the repaired structure is similar to that for the pre-event structure except that the replaced coupling beam does not reach its collapse prevention displacement limit. Figure 7-15 shows the pushover curve for the repaired structure.
Also shown on this curve is the pre-event pushover curve. The overall behavior of the repaired structure closely matches that of the pre-earthquake structure, as it was designed to do. The ratio of displacement capacity to demand, d2 I dd, is 0.53 for the life safety performance level and 0.66 for immediate occupancy, which are the same as those for the pre-event performance.
The displacement capacity for the repaired structure is governed by the component deformation limits of the coupling beams that were not replaced. Note that an effective upgrade measure might be to replace all coupling beams, as this would greatly increase global displacement capacity.
1 1.5 2 Roof Displacement (Inches) Figure 7-15 Comparison of Pre-event and Repaired Pushover Curves FEMA 307 Technical Resources Chapter 7: Example Application 7.4.7 Performance Restoration 7.5 Discussion of Results Measures 7.5.1 Discussion of Building 7.4.7.1 Structural Restoration Measures Performance Based on the relative performance analysis, replacing the three heavily Hypothetical repairs for damaged coupling beams and injecting relative the cracks in the moderately dam-performance aged coupling beams restores the method, Section 4.5 of performance of the structure. The volume of reinforced concrete coupling FEMA 306 beams to be removed is estimated to be about 41 cubic feet per coupling beam. The length of shear cracks to be injected in the moderately damaged coupling beams is estimated to be 100 feet.
7.4.7.2 Nonstructural Restoration Measures The Component Guides for the type RC1B components indicate that if cracks are less than 1/8 inch, the damage can be classified as Insignificant, and therefore structural repairs are not necessary. Two of the wall components had cracks that exceeded 1/16 inch. These wall components will have all of the cracks exceeding 1/16 inch repaired by injection with epoxy. The total length of these cracks is estimated to be about 22 feet.
The wall components with visible cracks will be repaired by patching the cracks with plaster and painting the entire wall. This repair is only intended to restore the visual appearance of the wall. Restoration of other nonstructural characteristics, such as water tightness and fire protection, is not necessary.
7.4.7.3 Summary of Restoration Measures and Costs Table 7-8 summarizes the repairs and estimated costs.
Additional costs related to inspection, evaluation, management, and indirect costs may also be involved.
The example building contains some typical features found in older concrete wall buildings, such as lightly reinforced concrete elements and discontinuous wall elements. Although the building was designed adequately according to the building code at the time, the design would not be appropriate by current building codes. Because of the improvement in seismic design provisions over the years, it is expected that the building, in its pre-event condition, would not meet the life safety performance level of FEMA 273.
The weak link in the building, as determined by analysis and confirmed with the field observations, is the shear capacity of the coupling beams. Although the analysis indicates that foundation rocking of the solid walls is probably the initial nonlinearity in the building, the rocking of the walls is not detrimental to the global behavior under the anticipated seismic demands.
In the section of the building in which the coupling beams were damaged, the coupled shear walls are discontinuous and are supported by columns at the ends of the walls. Normally, columns supporting discontinuous walls are susceptible to high compressive stresses, and consequently reduced ductility capacity, as the wall overturns. During the pushover analysis, the forces in the columns supporting the coupled walls remained within their capacity. The reason the columns were not overstressed is that the coupling beams acted as fuses for the coupled wall element. The overturning force in the columns could not be greater than the shear capacity of the coupling beams. If the strength of the replaced coupling beams is too large, the overturning force generated could cause failure of the columns below the Table7-8 Restoration Cost Estimate by the Relative Performance Method Item Unit Cost (1997 Dollars) Epoxy Injection $25.00 /lin ft Coupling Beam Removal and Replacement $74.00 / cu ft Patch and paint walls $0.60 /sq ft Replace ceiling tiles $2.00 /sq ft General Conditions, Fees, Overhead & Profit (@ 30%) Total Quantity 122 ft 122 ft3 10, 175 ft2 15, 000 ft2 Cost (1997 Dollars) $3, 050.
$9, 028.
$6, 105.
$ 30, 000.
$ 14, 455.
$ 62, 638.
FEMA 307 Technical Resources 
FEMA 307 Technical Resources Chapter 7: Example Application wall, resulting in a partial collapse of the building. For this reason, the capacity of the repaired coupling beam was designed to be similar to that of the previous coupling beam.
One of the advantages of the relative performance analysis is the ability to assess the behavior of structure and the influence of the behavior of the individual components on the overall behavior. Strengthening a single component may not produce a significant improvement in the overall performance if the progression of failure shifts to a less desirable mode. The pushover analysis of the repaired structure needs to consider the change in overall behavior caused by the repairs.
Because of the improved performance of the first story coupling beams that were replaced, these beams no longer control the global displacement limit of the structure. The force/displacement capacity of the second story coupling beams in their repaired condition is the same as in the pre-event condition. The displacement demand at which the second story coupling beams reach their acceptability limit is very close to the limit at which the first story coupling beams in the pre-event condition reached their limit. Therefore, the overall performance of the building is not improved substantially.
The information gained from these analyses can be used to assess whether an upgrade of the building to improve its performance may be cost effective.
7.5.2 Discussion of Methodology and Repair Costs This example has illustrated some of the important aspects in the FEMA 306 approach to assessing the earthquake damage to concrete and masonry wall buildings.
The example building represents an actual building that experienced a damaging earthquake.
FEMA 306 presents two methods for calculating the loss associated with earthquake damage, the direct method and the relative performance method. These methods are used to determine the loss, which is measured as the cost associated with returning the building to its pre-event performance. In this example, the cost of restoring the performance using the two methods produce the same result, principally because the repairs chosen in the relative performance method match those suggested by the direct method. In other buildings, there can be differences between the results obtained by the two methods.
The Nonlinear Static Procedure described in FEMA 273 is used in the relative performance method to assess the performance of the building in the pre-event, post-event and repaired conditions. This analysis method is relatively new and is still subject to further refinements.
This procedure can be time-consuming to implement properly. As the method and the analytical tools become further developed, this method should be easier to implement.
7.6 References ACI Committee 201, 1994, "Guide for Making a Condition Survey of Concrete in Service," Manual of Concrete Practice, American Concrete Institute, Detroit, Michigan.
CSI, 1997, SAP2000: Integrated Structural Design & Analysis Software, Computers and Structures Inc, Berkeley, California ATC, 1996, The Seismic Evaluation and Retrofit of Concrete Buildings, Applied Technology Council, ATC-40 Report, Redwood City, California.
Technical Resources FEMA 307 Technical Resources Appendix A. Component Damage Records for Building Evaluated in Example Application FEMA 307 Technical Resources Component Damage Records for Building Evaluated in Example Application Component Damage Record DI Building Name: Project ID: Prepared by: Concrete Shear Wall Building ATC 43 Example ATC Location Within Building: Date: Floor: 1st/ 2nd Column Line: 2 Component Type: 24-Sep-97 Sketch and Description of Damage: Legend: Crack Spall Z Crack Width in Mils (0.001 Inch) LNA 2 Crack Previously Filled with Epoxy ( Not Accessible Crack at Pre-existing Surface Patch Partition FEMA 307 Technical Resources Technical Resources FEMA 307 Component Damage Records for Building Evaluated in Example Application Component Damage Record D2 Building Name: Project ID: Prepared by: Concrete Shear Wall Building ATC43 Example ATC Location Within Building: Date: Floor: 1st/ 2nd Column Line: 2 Component Type: 24-Sep-97 Sketch and Description of Damage: X Legend: Crack Spall 0 Crack Width in Mils (0.001 Inch) [NA.
x<; Crack Previously Filled with Epoxy o Not Accessible Crack at Pre-existing Surface Patch WA/ Partition FEMA 307 Technical Resources 219 

Component Damage Records for Building Evaluated in Example Application 
Component Damage Record D3 
Building Name: Project ID: Prepared by: 
Concrete Shear Wall Building IATC 43 Example ATC 
Location Within Building: Date: 
Floor: 1st/ 2nd Column Line: 7 Component Type: 24-Sep-97 
Sketch and Description of Damage: 
Legend: 
Crack zD Spall
-Z Crack Width in Mils (0.001Inch) LNA | 
X, Crack Previously Filled with Epoxy / Not Accessible 
Crack at Pre-existing Surface Patch 
k},AI Partition 
FEMA 307 
Technical Resources 
220 Technical Resources FEMA 307 
Component Damage Records for Building Evaluated in Example Application 
Component Damage Record D4 
Building Name: Project ID: Prepared by: 
Concrete Shear Wall Building ATC 43 Example ATC 
Location Within Building: Date: 
Floor: 1st/ 2nd Column Line: 7 Component Type: 24-Sep-97 
Sketch and Description of Damage: 
Legend: 
Crack Spall 
Crack Width in Mils (0.001 Inch) LNA 4 
Crack Previously Filled with Epoxy ' Not Accessible 
Crack at Pre-existing Surface Patch 
I/I Partition 
FEMA 307 Technical Resources 
Component Damage Records for Building Evaluated in Example Application 
Component Damage RecordD5 
Building Name: Project ID: Prepared by: 
Concrete Shear Wall Building ATC 43 Example ATC 
Location Within Building: Date: 
Floor: 1st/ 2nd Column Line: 10 Component Type: 24-Sep-97 
Sketch and Description of Damage: 
Legend: 
Crack Spall 
I-Crack Width in Mils (0.001Inch) KNA 1 
X X Crack Previously Filled with Epoxy Not Accessible 
Crack at Pre-existing Surface Patch 
I/i Partition 
FEMA 307 Technical Resources
Technical Resources FEMRA 307 
Component Damage Records for Building Evaluated in Example Application 
Component Damage Record D6 LL 
Building Name: Project ID: Prepared by: 
Concrete Shear Wall Building ATC43 Example ATC 
Location Within Building Date: 
Floor: 1st/ 2nd Column Line: 10 Component Type: 24-Sep-97 
Sketch and Description of Damage: 
Legend: 
Crack Spall 
Crack Width in Mils (0.001Inch) LNAJ 
Crack Previously Filled with Epoxy Not Accessible 
Crack at Pre-existing Surface Patch P 
J of Partition 223 
Technical Resources 
FEMA 307 Technical Resources 223 
Component Damage Records for Building Evaluated in Example Application 
Component Damage Record D7 
Building Name: | Project ID: Prepared by: 
Concrete Shear Wall Building I ATC 43 Example ATC 
Location Within Building: Date: 
Floor: lst/ 2nd Column Line: 15 Component Type: 24-Sep-97 
Sketch and Description of Damage: C Legend: -Crack Spall 0 Crack Width in Mils (0.001 Inch) LNA. 
y y Crack Previously Filled with Epoxy Not Accessible 
Crack at Pre-existing Surface Patch Partition 
Technical Resources FEMA 307 
Component Damage Records for Building Evaluated in Example Application 
Component Damage RecordD8 
Building Name: Project ID: Prepared by: 
Concrete Shear Wall Building ATC 43 Example ATC 
Location Within Building: Date: 
Floor: 1st/2nd Column Line: 15 Component Type: 24-Sep-97 
Sketch and Description to Damage: 
Legend: 
Crack A Spall 
Crack Width in Mils (0.001Inch) [LNA. 
X; Crack Previously Filled with Epoxy Not Accessible 
Crack at Pre-existing Surface Patch Partition I 
FEMA 307 Technical Resources 225 
Component Damage Records for Building Evaluated in Example Application 
Component Damage Record D9 
Building Name: Project ID: Prepared by: 
Concrete Shear Wall Building ATC 43 Example ATC 
Location Within Building: Date: 
Floor: 1st/2nd Column Line: B Component Type: 24-Sep-97 I
Sketch and Description of Damage: 
Legend: -Crack M Spall 
Crack Width in Mils (0.001 Inch) LNA | 
X.X Crack Previously Filled with Epoxy Not Accessible 
Crack at Pre-existing Surface Patch 
Partition 
Technical Resources FEMIA 307 
Component Damage Records for Building Evaluated in Example Application 
Component Damage Record D10 
Building Name: 
Concrete Shear Wall Building 
Location Within Building: 
Floor: 1st 2nd Column Line: B 
Sketch and Description of Damage:
Legend: -Crack Project ID: ATC 43 Example 
Component Type: 
4M Spall Prepared by: 
ATC. Date: 24-Sep-97 
3P Crack Width in Mils (0.001 Inch) 
LNA.E X, Crack Previously Filled with Epoxy Not Accessible 
Crack at Pre-existing Surface Patch 
307 Technical Resources 227 Partition
FEMA 307 Technical Resources 227 
Component Damage Records for Building Evaluated in Example Application 
Component Damage Record Dll 
Building Name: Project ID: Prepared by: 
Concrete Shear Wall Building ATC 43 Example ATC 
Location Within Building': Date: 
Floor: lst/2nd Column Line: B Component Type: 24-Sep-97 
Sketch and Description of Damage: 
Legend: 
Legend: Crack Spall 
Crack Width in Mils (0.001 Inch) LSNA N 
Crack Previously Filled with Epoxy Not Accessible 
X Crack at Pre-existing Surface Patch 
Partition 
228 FEMA 307
Technical Resources 
Component Damage Records for Building Evaluated in Example Application 
Component Damage Record D12 
Building Name:, Project ID: Prepared by 
Concrete Shear Wall Building ATC 43 Example ATC 
Location Within Building: Date: 
Floor: lst/2nd Column Line: B Component Type: 24-Sep-97 
Sketch and Description of Damage: 
Legend: 
Legend: Crack Spall
2 i.O Crack Width in Mils (0.001 Inch) LNA | 
Crack Previously Filled with Epoxy Not Accessible 
X; Crack at Pre-existing Surface Patch 
Partition 
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Component Damage Records for Building Evaluated in Example Application 
Component Damage Record D13 
Building Name: Project ID: Prepared by-
Concrete Shear Wall Building ATC 43 Example ATC 
Location Within Building* Date: 
Floor: 1st/2nd Column Line: E Component: 24-Sep-97 
Sketch and Description of Damage: 
Legend: 
Crack Spall 
Crack Width in Mils (0.001 Inch) [NA 
Crack Previously Filled with Epoxy Not Accessible 
Crack at Pre-existing Surface Patch 
Partition 
Technical Resources FEMA 307 
Component Damage Records for Building Evaluated in Example Application 
Component Damage Record D14 
Building Name: Project ID: prepared by: 
Concrete Shear Wall Building I ATC 43 Example ATC 
Location Within Building: Date: 
Floor: 1st/ 2nd Column Line: E Component Type: 24-Sep-97 
Sketch and Description of Damage: 
Legend: 
Crack Spall 
;0. Crack Width in Mils (0.001 Inch) [ NA| 
Crack Previously Filled with Epoxy Not Accessible 
)( X Crack at Pre-existing Surface Patch 
Partition 
FEMA 307 Technical Resources 
Component Damage Records for Building Evaluated in Example Application 
Component Damage Record D15 
Building Name: Project ID: Prepared by: 
Concrete Shear Wall Building ATC 43 Example ATC 
Location Within Building: Date: 
Floor: 1st/2nd Column Line: G Component Type: 24-Sep-97 
Sketch and Description of Damage: j 
Legend: 
Crack A Spall 
30 Crack Width in Mils (0.001 Inch) [NA| 
Crack Previously Filled with Epoxy Not Accessible 
Crack at Pre-existing Surface Patch 
Partition 
Technical Resources FEMA 307 
Component Damage Records for Building Evaluated in Example Application 
Component Damage Record D16 
Building Name: Project ID: Prepared by: 
Concrete Shear Wall Building ATC 43 Example ATC 
Location Within Building: Date: 
Floor: lst/2 nd Column Line: G Component Type: 24-Sep-97 
5ketch and 
Legend: 
Crack Spall 
30 Crack Width in Mils (0.001 Inch)
Crack Previously Filled with Epoxy Not Accessible 
Crack at Pre-existing Surface Patch l: Partition 
FEMA 307 Technical Resources 233; 
Component Damage Records for Building Evaluated in Example Application 
FEMA 307
Technical Resources FEMA 307
Component Damage Records for Building Evaluated in Example Application 
Component Damage Record D18 
Building Name:- Project ID: Prepared by: 
Concrete Shear Wall Building ATC 43 Example ATC 
Location Within Building: Date: 
Floor: lst/2nd Column Line: M Component Type: 24-Sep-97 
Sketch and Description of Damage: 
Legend: 
Crack Spall 
Crack Width in Mils (0.001 Inch) 
Crack Previously Filled with Epoxy Not Accessible 
A X Crack at Pre-existing Surface Patch 
l5/ Partition 
FEMA 307 Technical Resources 
Component Damage Records for Building Evaluated in Example Application 
Component Damage Record D19 
Building Name: Project ID: Prepared by: 
Concrete Shear Wall Building ATC 43 Example ATC 
Location Within Building: Date: 
Floor: lst/2nd Column Line: M Component Type: 24-Sep-97 
Sketch and Description of Damage: 
First 
I XI 
Ground 
Legend: 
Crack 
Crack Width in Mils (0.001 Inch) 
Spall
Crack Previously Filled with Epoxy Not Accessible 
Crack at Pre-existing Surface Patch 
Partition 
236 
Technical Resources 
Technical Resources FEMA 307 
ATC-43Project Participants 
ATC MANAGEMENT 
Mr. Christopher Rojahn, 
Principal Investigator 
Applied Technology Council 
555 Twin Dolphin Drive, Suite 550 
Redwood City, CA 94065 
Technical Management Committee 
Prof. Dan Abrams 
University of Illinois 
1245 Newmark Civil Eng'g. Lab., MC 250 
205 North Mathews Avenue 
Urbana, IL 61801-2397 
Mr. James Hill 
James A. Hill & Associates, Inc. 
1349 East 28th Street 
Signal Hill, CA 90806 
FEMA/PARR Representatives 
Mr. Timothy McCormick 
PaRR Task Manager 
Dewberry & Davis 
8401 Arlington Boulevard 
Fairfax, VA 22031-4666 
Mr. Mark Doroudian 
PaRR Representative 
42 Silkwood 
I Aliso Viejo, CA 92656 
Mr. Craig Comartin, 
Co-PI and Project Director 
7683 Andrea Avenue 
Stockton, CA 95207 
Mr. Andrew T. Merovich 
A.T. Merovich & Associates, Inc. 
1163 Francisco Blvd., Second Floor 
San Rafael, CA 94901 
Prof. Jack Moehle 
Earthquake Engineering Research Center 
University of California at Berkeley 
1301 South 46th Street 
Richmond, CA 94804 
Prof. Robert Hanson 
FEMA Technical Monitor 
74 North Pasadena Avenue, CA-1009-DR 
Parsons Bldg., West Annex, Room 308 
Pasadena, CA 91103 
FEMA 307 Technical Resources 
Materials Working Group 
Dr. Joe Maffei, Group Leader 
Consulting Structural Engineer 
148 Hermosa Avenue 
Oakland California 
Mr. Brian Kehoe, Lead Consultant 
Wiss, Janney, Elstner Associates, Inc. 
2200 Powell Street, Suite 925 
Emeryville, CA 94608 
Dr. Greg Kingsley 
KL&A of Colorado 
805 14th Street 
Golden, CO 80401 
Analysis Working Group 
Prof. Mark Aschheim, Group Leader 
University of Illinois at Urbana 
2118 Newmark CE Lab 
205 North Mathews, MC 250 
Urbana, IL 61801 
Project Review Panel 
Mr. Gregg J. Borchelt 
Brick Institute of America 
11490 Commerce Park Drive, #300 
Reston, VA 20191 
Dr. Gene Corley 
Construction Technology Labs 
5420 Old Orchard Road 
Skokie, IL 60077-1030 
Mr. Edwin Huston 
Smith & Huston 
Plaza 600 Building, 6th & Stewart, #620 
Seattle, WA 98101 
Prof. Richard E. Klingner 
University of Texas 
Civil Engineering Department 
Cockbell Building, Room 4-2 
Austin, TX 78705 
ATC-43 Project Participants 
Mr. Bret Lizundia 
Rutherford & Chekene 
303 Second Street, Suite 800 North 
San Francisco, CA 94107 
Prof. John Mander 
SUNY at Buffalo 
Department of Civil Engineering 
212 Ketter Hall 
Buffalo, NY 14260 
Prof. Mete Sozen, Senior Consultant 
Purdue University, School of Engineering 
1284 Civil Engineering Building 
West Lafayette, IN 47907-1284 
Mr. Vilas Mujumdar 
Office of Regulation Services 
Division of State Architect 
General Services 
1300 I Street, Suite 800 
Sacramento, CA 95814 
Dr. Hassan A. Sassi 
Governors Office of Emergency Services 
74 North Pasadena Avenue 
Pasadena, CA 91103 
Mr. Carl Schulze 
Libby Engineers 
4452 Glacier Avenue 
San Diego, CA 92120 
Mr. Daniel Shapiro 
SOH & Associates 
550 Kearny Street, Suite 200 
San Francisco, CA 94108 
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Technical Resources FEMA 307 
ATC-43 Project Participants 
Prof. James K. Wight Mr. Eugene Zeller 
University of Michigan Long Beach Department of Building & Safety 
Department of Civil Engineering 333 W. Ocean Boulevard, Fourth Floor 
2368 G Brown Long Beach, CA 90802
Ann Arbor, MI 48109-2125
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Applied Technology Council Projects And Report 
Information 
One of the primary purposes of Applied Technology 
Council is to develop resource documents that translate 
and summarize useful information to practicing engineers. 
This includes the development of guidelines and 
manuals, as well as the development of research recommendations 
for specific areas determined by the profession. 
ATC is not a code development organization, 
although several of the ATC project reports serve as 
resource documents for the development of codes, standards 
and specifications. 
Applied Technology Council conducts projects that 
meet the following criteria: 
1. The primary audience or benefactor is the design 
practitioner in structural engineering. 
2. A cross section or consensus of engineering opinion 
is required to be obtained and presented by a neutral 
source. 
3. The project fosters the advancement of structural 
engineering practice. 
A brief description of several major completed projects 
and reports is given in the following section. Funding 
for projects is obtained from government agencies and 
tax-deductible contributions from the private sector. 
ATC-1: This project resulted in five papers that were 
Published as part of Building Practices for Disaster 
Mitigation, Building Science Series 46, proceedings of a 
workshop sponsored by the National Science Foundation 
(NSF) and the National Bureau of Standards 
(NBS). Available through the National Technical Information 
Service (NTIS), 5285 Port Royal Road, Springfield, 
VA 22151, as NTIS report No. COM-73-50188. 
ATC-2: The report, An Evaluation of a Response Spectrum 
Approach to Seismic Design of Buildings, was 
funded by NSF and NBS and was conducted as part of 
the Cooperative Federal Program in Building Practices 
for Disaster Mitigation. Available through the ATC 
office. (Published 1974, 270 Pages) 
ABSTRACT: This study evaluated the applicability 
and cost of the response spectrum approach to seismic 
analysis and design that was proposed by various 
segments of the engineering profession. 
Specific building designs, design procedures and 
parameter values were evaluated for future application. 
Eleven existing buildings of varying dimensions 
were redesigned according to the procedures. 
ATC-3: The report, Tentative Provisions for the Development 
of Seismic Regulations for Buildings (ATC-3-
06), was funded by NSF and NBS. The second printing 
of this report, which includes proposed amendments, is 
available through the ATC office. (Published 1978, 
amended 1982, 505 pages plus proposed amendments) 
ABSTRACT: The tentative provisions in this document 
represent the results of a concerted effort by a 
multi-disciplinary team of 85 nationally recognized 
experts in earthquake engineering. The provisions 
serve as the basis for the seismic provisions of the 
1988 Uniform Building Code and the 1988 and subsequent 
issues of the NEHRP Recommended Provisions for 
the Development of Seismic Regulation for 
New Buildings. The second printing of this document 
contains proposed amendments prepared by a 
joint committee of the Building Seismic Safety 
Council (BSSC) and the NBS. 
ATC-3-2: The project, Comparative Test Designs of 
Buildings Using ATC-3-06 Tentative Provisions, was 
funded by NSF. The project consisted of a study to 
develop and plan a program for making comparative 
test designs of the ATC-3-06 Tentative Provisions. The 
project report was written to be used by the Building 
Seismic Safety Council in its refinement of the ATC-3-
06 Tentative Provisions. 
ATC-3-4: The report, Redesign of Three Multistory 
Buildings: A Comparison Using ATC-3-06 and 1982 
Uniform Building Code Design Provisions, was published 
under a grant from NSF. Available through the 
ATC office. (Published 1984, 112 pages) 
ABSTRACT: This report evaluates the cost and technical 
impact of using the 1978 ATC-3-06 report, 
Tentative Provisions for the Development of Seismic 
Regulations for Buildings, as amended by a joint 
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committee of the Building Seismic Safety Council 
and the National Bureau of Standards in 1982. The 
evaluations are based on studies of three existing 
California buildings redesigned in accordance with 
the ATC-3-06 Tentative Provisions and the 1982 
Uniform Building Code. Included in the report are 
recommendations to code implementing bodies. 
ATC-3-5: This project, Assistance for First Phase of 
ATC-3-06 Trial Design Program Being Conducted by 
the Building Seismic Safety Council, was funded by the 
Building Seismic Safety Council to provide the services 
of the ATC Senior Consultant and other ATC personnel 
to assist the BSSC in the conduct of the first phase of its 
Trial Design Program. The first phase provided for trial 
designs conducted for buildings in Los Angeles, Seattle, 
Phoenix, and Memphis. 
ATC-3-6: This project, Assistance for Second Phase of 
ATC-3-06 Trial Design Program Being Conducted by 
the Building Seismic Safety Council, was funded by the 
Building Seismic Safety Council to provide the services 
of the ATC Senior Consultant and other ATC personnel 
to assist the BSSC in the conduct of the second phase of 
its Trial Design Program. The second phase provided 
for trial designs conducted for buildings in New York, 
Chicago, St. Louis, Charleston, and Fort Worth. 
ATC-4: The report, A Methodology for Seismic Design 
and Construction of Single-Family Dwellings, was published 
under a contract with the Department of Housing 
and Urban Development (HUD). Available through the 
ATC office. (Published 1976, 576 pages) 
ABSTRACT:
This report presents the results of an 
in-depth effort to develop design and construction 
details for single-family residences that minimize 
the potential economic loss and life-loss risk associated 
with earthquakes. The report: (1) discusses 
the ways structures behave when subjected to seismic 
forces, (2) sets forth suggested design criteria 
for conventional layouts of dwellings constructed 
with conventional materials, (3) presents construction 
details that do not require the designer to perform 
analytical calculations, (4) suggests 
procedures for efficient plan-checking, and (5) presents 
recommendations including details and schedules 
for use in the field by construction personnel 
and building inspectors. 
ATC-4-1: The report, The Home Builders Guide for 
Earthquake Design, was published under a contract 
with HUD. Available through the ATC office. (Published 
1980, 57 pages) 
ABSTRACT: This report is an abridged version of 
the ATC-4 report. The concise, easily understood 
text of the Guide is supplemented with illustrations 
and 46 construction details. The details are provided 
to ensure that houses contain structural features 
that are properly positioned, dimensioned and 
constructed to resist earthquake forces. A brief 
description is included on how earthquake forces 
impact on houses and some precautionary constraints 
are given with respect to site selection and 
architectural designs. 
ATC-5: The report, Guidelines for Seismic Design and 
Construction of Single-Story Masonry Dwellings in 
Seismic Zone 2, was developed under a contract with 
HUD. Available through the ATC office. (Published 
1986, 38 pages) 
ABSTRACT: The report offers a concise methodology 
for the earthquake design and construction of 
single-story masonry dwellings in Seismic Zone 2 
of the United States, as defined by the 1973 Uniform 
Building Code. The Guidelines are based in 
part on shaking table tests of masonry construction 
conducted at the University of California at Berkeley 
Earthquake Engineering Research Center. The 
report is written in simple language and includes 
basic house plans, wall evaluations, detail drawings, 
and material specifications. 
ATC-6: The report, Seismic Design Guidelines for 
Highway Bridges, was published under a contract with 
the Federal Highway Administration (FHWA). Available 
through the ATC office. (Published 1981, 210 
pages) 
ABSTRACT: The Guidelines are the recommendations 
of a team of sixteen nationally recognized 
experts that included consulting engineers, academics, 
state and federal agency representatives from 
throughout the United States. The Guidelines 
embody several new concepts that were significant 
departures from then existing design provisions. 
Included in the Guidelines are an extensive commentary, 
an example demonstrating the use of the 
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Guidelines, and summary reports on 21 bridges 
redesigned in accordance with the Guidelines. 
The guidelines have been adopted by the American 
Association of Highway and Transportation 
Officials as a guide specification. 
ATC-6-1: The report, Proceedings of a Workshop 
on Earthquake Resistance of Highway Bridges, was 
published under a grant from NSF Available 
through the ATC office. (Published 1979, 625 pages) 
ABSTRACT: The report includes 23 state-of-the-
art and state-of-practice papers on earthquake 
resistance of highway bridges. Seven of the 
twenty-three papers were authored by participants 
from Japan, New Zealand and Portugal. 
The Proceedings also contain recommendations 
for future research that were developed by the 45 
workshop participants. 
ATC-6-2: The report, Seismic Retrofitting Guidelines 
for Highway Bridges, was published under a 
contract with FHWA. Available through the ATC 
office. (Published 1983, 220 pages) 
ABSTRACT: The Guidelines are the recommendations 
of a team of thirteen nationally recognized 
experts that included consulting engineers, 
academics, state highway engineers, and federal 
agency representatives. The Guidelines, applicable 
for use in all parts of the United States, 
include a preliminary screening procedure, 
methods for evaluating an existing bridge in 
detail, and potential retrofitting measures for the 
most common seismic deficiencies. Also 
included are special design requirements for various 
retrofitting measures. 
ATC-7: The report, Guidelines for the Design of 
Horizontal Wood Diaphragms, was published under 
a grant from NSF. Available through the ATC 
office. (Published 1981, 190 pages) 
ABSTRACT: Guidelines are presented for designing 
roof and floor systems so these can function 
as horizontal diaphragms in a lateral force resisting 
system. Analytical procedures, connection 
details and design examples are included in the 
Guidelines. 
ATC-7-1: The report, Proceedings of a Workshop 
of Design of Horizontal Wood Diaphragms, was 
published under a grant from NSF. Available 
through the ATC office. (Published 1980, 302 pages) 
ABSTRACT: The report includes seven papers on 
state-of-the-practice and two papers on recent 
research. Also included are recommendations 
for future research that were developed by the 35 
workshop participants. 
ATC-8: This report, Proceedings of a Workshop on 
the Design of Prefabricated Concrete Buildings for 
Earthquake Loads, was funded by NSF. Available 
through the ATC office. (Published 1981, 400 pages) 
ABSTRACT: The report includes eighteen state-
of-the-art papers and six summary papers. Also 
included are recommendations for future 
research that were developed by the 43 workshop 
participants. 
ATC-9: The report, An Evaluation of the Imperial 
County Services Building Earthquake Response and 
Associated Damage, was published under a grant 
from NSF. Available through the ATC office. (Published 
1984, 231 pages) 
ABSTRACT: The report presents the results of an 
in-depth evaluation of the Imperial County Services 
Building, a 6-story reinforced concrete 
frame and shear wall building severely damaged 
by the October 15, 1979 Imperial Valley, California, 
earthquake. The report contains a review 
and evaluation of earthquake damage to the 
building; a review and evaluation of the seismic 
design; a comparison of the requirements of various 
building codes as they relate to the building; 
and conclusions and recommendations pertaining 
to future building code provisions and future 
research needs. 
ATC-10: This report, An Investigation of the Correlation 
Between Earthquake Ground Motion and 
Building Performance, was funded by the U.S. Geological 
Survey (USGS). Available through the ATC 
office. (Published 1982, 114 pages) 
ABSTRACT: The report contains an in-depth analytical 
evaluation of the ultimate or limit capacity 
of selected representative building framing 
types, a discussion of the factors affecting the 
seismic performance of buildings, and a sum-
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summary and comparison of seismic design and seismic 
risk parameters currently in widespread use. 
ATC-10-1: This report, Critical Aspects of Earthquake 
Ground Motion and Building Damage Potential, was 
co-funded by the USGS and the NSF. Available 
through the ATC office. (Published 1984, 259 pages) 
ABSTRACT: This document contains 19 state-of-
the-art papers on ground motion, structural 
response, and structural design issues presented by 
prominent engineers and earth scientists in an ATC 
seminar. The main theme of the papers is to identify 
the critical aspects of ground motion and building 
performance that currently are not being 
considered in building design. The report also contains 
conclusions and recommendations of working 
groups convened after the Seminar. 
ATC-11: The report, Seismic Resistance of Reinforced 
Concrete Shear Walls and Frame Joints: Implications 
of Recent Research for Design Engineers, was published 
under a grant from NSF. Available through the 
ATC office. (Published 1983, 184 pages) 
ABSTRACT: This document presents the results of 
an in-depth review and synthesis of research reports 
pertaining to cyclic loading of reinforced concrete 
shear walls and cyclic loading of joint reinforced 
concrete frames. More than 125 research reports 
published since 1971 are reviewed and evaluated in 
this report. The preparation of the report included a 
consensus process involving numerous experienced 
design professionals from throughout the United 
States. The report contains reviews of current and 
past design practices, summaries of research developments, 
and in-depth discussions of design implications 
of recent research results. 
ATC-12: This report, Comparison of United States and 
New Zealand Seismic Design Practices for Highway 
Bridges, was published under a grant from NSF. Available 
through the ATC office. (Published 1982, 270 
pages) 
ABSTRACT: The report contains summaries of all 
aspects and innovative design procedures used in 
New Zealand as well as comparison of United 
States and New Zealand design practice. Also 
included are research recommendations developed 
at a 3-day workshop in New Zealand attended by 16 
U.S. and 35 New Zealand bridge design engineers 
and researchers. 
ATC-12-1: This report, Proceedings of Second Joint 
U.S.-New Zealand Workshop on Seismic Resistance of 
Highway Bridges, was published under a grant from 
NSF. Available through the ATC office. (Published 
1986, 272 pages) 
ABSTRACT: This report contains written versions of 
the papers presented at this 1985 Workshop as well 
as a list and prioritization of workshop recommendations. 
Included are summaries of research 
projects being conducted in both countries as well 
as state-of-the-practice papers on various aspects of 
design practice. Topics discussed include bridge 
design philosophy and loadings; design of columns, 
footings, piles, abutments and retaining structures; 
geotechnical aspects of foundation design; seismic 
analysis techniques; seismic retrofitting; case studies 
using base isolation; strong-motion data acquisition 
and interpretation; and testing of bridge 
components and bridge systems. 
ATC-13: The report, Earthquake Damage Evaluation 
Data for California, was developed under a contract 
with the Federal Emergency Management Agency 
(FEMA). Available through the ATC office. (Published 
1985, 492 pages) 
ABSTRACT: This report presents expert-opinion 
earthquake damage and loss estimates for industrial, 
commercial, residential, utility and transportation 
facilities in California. Included are damage 
probability matrices for 78 classes of structures and 
estimates of time required to restore damaged facilities 
to pre-earthquake usability. The report also 
describes the inventory information essential for 
estimating economic losses and the methodology 
used to develop loss estimates on a regional basis. 
ATC-14: The report, Evaluating the Seismic Resistance 
of Existing Buildings, was developed under a grant from 
the NSF. Available through the ATC office. (Published 
1987, 370 pages) 
ABSTRACT: This report, written for practicing 
structural engineers, describes a methodology for 
performing preliminary and detailed building seismic 
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evaluations. The report contains a state-of-
practice review; seismic loading criteria; data collection 
procedures; a detailed description of the 
building classification system; preliminary and 
detailed analysis procedures; and example case 
studies, including nonstructural considerations. 
ATC-15: The report, Comparison of Seismic Design 
Practices in the United States and Japan, was published 
under a grant from NSF. Available through the ATC 
office. (Published 1984, 317 pages) 
ABSTRACT: The report contains detailed technical 
papers describing design practices in the United 
States and Japan as well as recommendations emanating 
from a joint U.S.-Japan workshop held in 
Hawaii in March, 1984. Included are detailed 
descriptions of new seismic design methods for 
buildings in Japan and case studies of the design of 
specific buildings (in both countries). The report 
also contains an overview of the history and objectives 
of the Japan Structural Consultants Association. 
ATC-15-1: The report, Proceedings of Second U.S.-
Japan Workshop on Improvement of Building Seismic 
Design and Construction Practices, was published 
under a grant from NSF. Available through the ATC 
office. (Published 1987, 412 pages) 
ABSTRACT: This report contains 23 technical 
papers presented at this San Francisco workshop in 
August, 1986, by practitioners and researchers from 
the U.S. and Japan. Included are state-of-the-practice papers and case studies of actual building 
designs and information on regulatory, contractual, 
and licensing issues. 
ATC-15-2: The report, Proceedings of Third U.S.-
Japan Workshop on Improvement of Building Structural 
Design and Construction Practices, was published 
jointly by ATC and the Japan Structural Consultants 
Association. Available through the ATC office. (Published 
1989, 358 pages) 
ABSTRACT: This report contains 21 technical 
papers presented at this Tokyo, Japan, workshop in 
July, 1988, by practitioners and researchers from 
the U.S., Japan, China, and New Zealand. Included 
are state-of-the-practice papers on various topics, 
including braced steel frame buildings, beam-column joints in reinforced concrete buildings, summaries 
of comparative U. S. and Japanese design, 
and base isolation and passive energy dissipation 
devices. 
ATC-15-3: The report, Proceedings of Fourth U.S.-
Japan Workshop on Improvement of Building Structural 
Design and Construction Practices, was published 
jointly by ATC and the Japan Structural Consultants 
Association. Available through the ATC office. (Published 
1992, 484 pages) 
ABSTRACT: This report contains 22 technical 
papers presented at this Kailua-Kona, Hawaii, 
workshop in August, 1990, by practitioners and 
researchers from the United States, Japan, and Peru. 
Included are papers on postearthquake building 
damage assessment; acceptable earth-quake damage; 
repair and retrofit of earthquake damaged 
buildings; base-isolated buildings, including Architectural 
Institute of Japan recommendations for 
design; active damping systems; wind-resistant 
design; and summaries of working group conclusions 
and recommendations. 
ATC-15-4: The report, Proceedings of Fifth U.S. Japan 
Workshop on Improvement of Building Structural 
Design and Construction Practices, was published 
jointly by ATC and the Japan Structural Consultants 
Association. Available through the ATC office. (Published 
1994, 360 pages) 
ABSTRACT: This report contains 20 technical 
papers presented at this San Diego, California 
workshop in September, 1992. Included are papers 
on performance goals/acceptable damage in seismic 
design; seismic design procedures and case studies; 
construction influences on design; seismic isolation 
and passive energy dissipation; design of irregular 
structures; seismic evaluation, repair and upgrading; 
quality control for design and construction; and 
summaries of working group discussions and recommendations. 
ATC-16: This project, Development of a 5-Year Plan 
for Reducing the Earthquake Hazards Posed by Existing 
Nonfederal Buildings, was funded by FEMA and was 
conducted by a joint venture of ATC, the Building Seismic 
Safety Council and the Earthquake Engineering 
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Research Institute. The project involved a workshop in 
Phoenix, Arizona, where approximately 50 earthquake 
specialists met to identify the major tasks and goals for 
reducing the earthquake hazards posed by existing non-
federal buildings nationwide. The plan was developed 
on the basis of nine issue papers presented at the workshop 
and workshop working group discussions. The 
Workshop Proceedings and Five-Year Plan are available 
through the Federal Emergency Management Agency, 
500 "C" Street, S.W., Washington, DC 20472. 
ATC-17: This report Proceedings of a Seminar and 
Workshop on Base Isolation and Passive Energy Dissipation, 
was published under a grant from NSF. Available 
through the ATC office. (Published 1986, 478 
pages) 
ABSTRACT:
The report contains 42 papers describing 
the state-of-the-art and state-of-the-practice in 
base-isolation and passive energy-dissipation technology. 
Included are papers describing case studies 
in the United States, applications and developments 
worldwide, recent innovations in technology development, 
and structural and ground motion issues. 
Also included is a proposed 5-year research agenda 
that addresses the following specific issues: (1) 
strong ground motion; (2) design criteria; (3) materials, 
quality control, and long-term reliability; (4) 
life cycle cost methodology; and (5) system 
response. 
ATC-17-1: This report, Proceedings of a Seminar on 
Seismic Isolation, Passive Energy Dissipation and 
Active Control, was published under a grant from NSF. 
Available through the ATC office. (Published 1993, 841 
pages) 
The 2-volume report documents 70
ABSTRACT: 
technical papers presented during a two-day seminar 
in San Francisco in early 1993. Included are 
invited theme papers and competitively selected 
papers on issues related to seismic isolation systems, 
passive energy dissipation systems, active 
control systems and hybrid systems. 
ATC-18: The report, Seismic Design Criteria for 
Bridges and Other Highway Structures: Current and 
Future, was published under a contract from the Multidisciplinary 
Center for Earthquake Engineering 
Research (formerly NCEER), with funding from the 
Federal Highway Administration. Available through the 
ATC office. (Published 1997, 152 pages) 
ABSTRACT: This report documents the findings of a 
4-year project to review and assess current seismic 
design criteria for new highway construction. The 
report addresses performance criteria, importance 
classification, definitions of seismic hazard for 
areas where damaging earthquakes have longer 
return periods, design ground motion, duration 
effects, site effects, structural response modification 
factors, ductility demand, design procedures, foundation 
and abutment modeling, soil-structure interaction, 
seat widths, joint details and detailing 
reinforced concrete for limited ductility in areas 
with low-to-moderate seismic activity. The report 
also provides lengthy discussion on future directions 
for code development and recommended 
research and development topics. 
ATC-19: The report, Structural Response Modification 
Factors was funded by NSF and NCEER. Available 
through the ATC office. (Published 1995, 70 pages) 
ABSTRACT: This report addresses structural 
response modification factors (R factors), which are 
used to reduce the seismic forces associated with 
elastic response to obtain design forces. The report 
documents the basis for current R values, how R 
factors are used for seismic design in other countries, 
a rational means for decomposing R into key 
components, a framework (and methods) for evaluating 
the key components of R, and the research 
necessary to improve the reliability of engineered 
construction designed using R factors. 
ATC-20: The report, Procedures for Postearthquake 
Safety Evaluation of Buildings, was developed under a 
contract from the California Office of Emergency Services 
(OES), California Office of Statewide Health 
Planning and Development (OSHPD) and FEMA. 
Available through the ATC office (Published 1989, 152 
pages) 
ABSTRACT: This report provides procedures and 
guidelines for making on-the-spot evaluations and 
decisions regarding continued use and occupancy 
of earthquake damaged buildings. Written specifically 
for volunteer structural engineers and building 
inspectors, the report includes rapid and detailed 
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evaluation procedures for inspecting buildings and 
posting them as "inspected" (apparently safe), "limited 
entry" or "unsafe". Also included are special 
procedures for evaluation of essential buildings 
(e.g., hospitals), and evaluation procedures for non-
structural elements, and geotechnical hazards. 
ATC-20-1: The report, Field Manual: Postearthquake 
Safety Evaluation of Buildings, was developed under a 
contract from OES and OSHPD. Available through the 
ATC office (Published 1989, 114 pages) 
ABSTRACT:
This report, a companion Field Manual 
for the ATC-20 report, summarizes the 
postearthquake safety evaluation procedures in 
brief concise format designed for ease of use in the 
field. 
ATC-20-2: The report, Addendum to the ATC-20 
Postearthquake Building Safety Procedures was published 
under a grant from the NSF and funded by the 
USGS. Available through the ATC office. (Published 
1995, 94 pages) 
ABSTRACT:
This report provides updated assessment 
forms, placards, and procedures that are based 
on an in-depth review and evaluation of the widespread 
application of the ATC-20 procedures following 
five earthquakes occurring since the initial 
release of the ATC-20 report in 1989. 
ATC-20-3: The report, Case Studies in Rapid 
Postearthquake Safety Evaluation of Buildings, was 
funded by ATC and R. P. Gallagher Associates. Available 
through the ATC office. (Published 1996, 295 
pages) 
ABSTRACT: This report contains 53 case studies 
using the ATC-20 Rapid Evaluation procedure. 
Each case study is illustrated with photos and 
describes how a building was inspected and evaluated 
for life safety, and includes a completed safety 
assessment form and placard. The report is intended 
to be used as a training and reference manual for 
building officials, building inspectors, civil and 
structural engineers, architects, disaster workers, 
and others who may be asked to perform safety 
evaluations after an earthquake. 
ATC-20-T: The report, Postearthquake Safety Evaluation 
of Buildings Training Manual was developed under 
a contract with FEMA. Available through the ATC 
office. (Published 1993, 177 pages; 160 slides) 
ABSTRACT: This training manual is intended to 
facilitate the presentation of the contents of the 
ATC-20 and ATC-20-1. The training materials consist 
of 160 slides of photographs, schematic drawings 
and textual information and a companion 
training presentation narrative coordinated with the 
slides. Topics covered include: posting system; 
evaluation procedures; structural basics; wood 
frame, masonry, concrete, and steel frame structures; 
nonstructural elements; geotechnical hazards; 
hazardous materials; and field safety. 
ATC-21: The report, Rapid Visual Screening of Buildings for 
Potential Seismic Hazards: A Handbook, was 
developed under a contract from FEMA. Available 
through the ATC office. (Published 1988, 185 pages) 
ABSTRACT: This report describes a rapid visual 
screening procedure for identifying those buildings 
that might pose serious risk of loss of life and 
injury, or of severe curtailment of community services, 
in case of a damaging earthquake. The 
screening procedure utilizes a methodology based 
on a "sidewalk survey" approach that involves identification 
of the primary structural load resisting 
system and building materials, and assignment of a 
basic structural hazards score and performance 
modification factors based on observed building 
characteristics. Application of the methodology 
identifies those buildings that are potentially hazardous 
and should be analyzed in more detail by a 
professional engineer experienced in seismic 
design. 
ATC-21-1: The report, Rapid Visual Screening of 
Buildings for Potential Seismic Hazards: Supporting 
Documentation, was developed under a contract from 
FEMA. Available through the ATC office. (Published 
1988, 137 pages) 
ABSTRACT: Included in this report are (1) a review 
and evaluation of existing procedures; (2) a listing 
of attributes considered ideal for a rapid visual 
screening procedure; and (3) a technical discussion 
of the recommended rapid visual screening procedure 
that is documented in the ATC-21 report. 
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ATC-21-2: The report, Earthquake Damaged Buildings: 
An Overview of Heavy Debris and Victim Extrication, 
was developed under a contract from FEMA. 
(Published 1988, 95 pages) 
ABSTRACT: Included in this report, a companion 
volume to the ATC-21 and ATC-21-1 reports, is 
state-of-the-art information on (1) the identification 
of those buildings that might collapse and trap victims 
in debris or generate debris of such a size that 
its handling would require special or heavy lifting 
equipment; (2) guidance in identifying these types 
of buildings, on the basis of their major exterior features, 
and (3) the types and life capacities of equipment 
required to remove the heavy portion of the 
debris that might result from the collapse of such 
buildings. 
ATC-21-T: The report, Rapid Visual Screening of 
Buildings for Potential Seismic Hazards Training Manual 
was developed under a contract with FEMA. Available 
through the ATC office. (Published 1996, 135 
pages; 120 slides) 
ABSTRACT: This training manual is intended to 
facilitate the presentation of the contents of the 
ATC-21report. The training materials consist of 
120 slides and a companion training presentation 
narrative coordinated with the slides. Topics covered 
include: description of procedure, building 
behavior, building types, building scores, occupancy 
and falling hazards, and implementation. 
ATC-22: The report, A Handbook for Seismic Evaluation 
of Existing Buildings (Preliminary), was developed 
under a contract from FEMA. Available through the 
ATC office. (Originally published in 1989; revised by 
BSSC and published as the NEHRP Handbook for Seismic 
Evaluation of Existing Buildings in 1992, 211 
pages) 
ABSTRACT: This handbook provides a methodology 
for seismic evaluation of existing buildings of 
different types and occupancies in areas of different 
seismicity throughout the United States. The methodology, 
which has been field tested in several programs 
nationwide, utilizes the information and 
procedures developed for and documented in the 
ATC-14report. The handbook includes checklists, 
diagrams, and sketches designed to assist the user. 
ATC-22-1: The report, Seismic Evaluation of Existing 
Buildings: Supporting Documentation, was developed 
under a contract from FEMA. (Published 1989, 160 
pages) 
ABSTRACT: Included in this report, a companion 
volume to the ATC-22 report, are (1) a review and 
evaluation of existing buildings seismic evaluation 
methodologies; (2) results from field tests of the 
ATC-14 methodology; and (3) summaries of evaluations 
of ATC-14 conducted by the National Center 
for Earthquake Engineering Research (State University 
of New York at Buffalo) and the City of San 
Francisco. 
ATC-23A: The report, General Acute Care Hospital 
Earthquake Survivability Inventory for California, Part 
A: Survey Description, Summary of Results, Data Analysis 
and Interpretation, was developed under a contract 
from the Office of Statewide Health Planning and 
Development (OSHPD), State of California. Available 
through the ATC office. (Published 1991, 58 pages) 
ABSTRACT: This report summarizes results from a 
seismic survey of 490 California acute care hospitals. 
Included are a description of the survey procedures 
and data collected, a summary of the data, 
and an illustrative discussion of data analysis and 
interpretation that has been provided to demonstrate 
potential applications of the ATC-23 database. 
ATC-23B: The report, General Acute Care Hospital 
Earthquake Survivability Inventory for California, Part 
B: Raw Data, is a companion document to the ATC23A 
Report and was developed under the above-mentioned contract from OSHPD. Available through the 
ATC office. (Published 1991, 377 pages) 
ABSTRACT: Included in this report are tabulations 
of raw general site and building data for 490 acute 
care hospitals in California. 
ATC-24: The report, Guidelines for Seismic Testing of 
Components of Steel Structures, was jointly funded by 
the American Iron and Steel Institute (AISI), American 
Institute of Steel Construction (AISC), National Center 
for Earthquake Engineering Research (NCEER), and 
NSF. Available through the ATC office. (Published 
1992, 57 pages) 
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ABSTRACT: This report provides guidance for most 
cyclic experiments on components of steel structures 
for the purpose of consistency in experimental 
procedures. The report contains recommendations 
and companion commentary pertaining to loading 
histories, presentation of test results, and other 
aspects of experimentation. The recommendations 
are written specifically for experiments with slow 
cyclic load application. 
ATC-25: The report, Seismic Vulnerability and Impact 
of Disruption of Lifelines in the Conterminous United 
States, was developed under a contract from FEMA. 
Available through the ATC office. (Published 1991, 440 
pages) 
ABSTRACT:
Documented in this report is a national 
overview of lifeline seismic vulnerability and 
impact of disruption. Lifelines considered include 
electric systems, water systems, transportation systems, 
gas and liquid fuel supply systems, and emergency 
service facilities (hospitals, fire and police 
stations). Vulnerability estimates and impacts 
developed are presented in terms of estimated first 
approximation direct damage losses and indirect 
economic losses. 
ATC-25-1: The report, A Model Methodology for 
Assessment of Seismic Vulnerability and Impact of Disruption 
of Water Supply Systems, was developed under 
a contract from FEMA. Available through the ATC 
office. (Published 1992, 147 pages) 
ABSTRACT:
This report contains a practical methodology 
for the detailed assessment of seismic vulnerability 
and impact of disruption of water supply 
systems. The methodology has been designed for 
use by water system operators. Application of the 
methodology enables the user to develop estimates 
of direct damage to system components and the 
time required to restore damaged facilities to pre-
earthquake usability. Suggested measures for mitigation 
of seismic hazards are also provided. 
ATC-28: The report, Development of Recommended 
Guidelines for Seismic Strengthening of Existing Buildings, 
Phase I: Issues Identification and Resolution, was 
developed under a contract with FEMA. Available 
through the ATC office. (Published 1992, 150 pages) 
ABSTRACT:
This report identifies and provides resolutions 
for issues that will affect the development of 
guidelines for the seismic strengthening of existing 
buildings. Issues addressed include: implementation 
and format, coordination with other efforts, 
legal and political, social, economic, historic buildings, 
research and technology, seismicity and mapping, 
engineering philosophy and goals, issues 
related to the development of specific provisions, 
and nonstructural element issues. 
ATC-29: The report Proceedings of a Seminar and 
Workshop on Seismic Design and Performance of 
Equipment and Nonstructural Elements in Buildings 
and Industrial Structures, was developed under a grant 
from NCEER and NSF. Available through the ATC 
office. (Published 1992, 470 pages) 
ABSTRACT:
These Proceedings contain 35 papers 
describing state-of-the-art technical information 
pertaining to the seismic design and performance of 
equipment and nonstructural elements in buildings 
and industrial structures. The papers were presented 
at a seminar in Irvine, California in 1990. Included 
are papers describing current practice, codes and 
regulations; earthquake performance; analytical and 
experimental investigations; development of new 
seismic qualification methods; and research, practice, 
and code development needs for specific elements 
and systems. The report also includes a 
summary of a proposed 5-year research agenda for 
NCEER. 
ATC-29-1: The report, Proceedings Of Seminar On 
Seismic Design, Retrofit, And Performance Of Non-
structural Components, was developed under a grant 
from NCEER and NSF. Available through the ATC 
office. (Published 1998, 518 pages) 
ABSTRACT:
These Proceedings contain 38 papers 
presenting current research, practice, and informed 
thinking pertinent to seismic design, retrofit, and 
performance of nonstructural components. The 
papers were presented at a seminar in San Francisco, 
California, in 1998. Included are papers 
describing observed performance in recent earthquakes; 
seismic design codes, standards, and procedures 
for commercial and institutional buildings; 
seismic design issues relating to industrial and hazardous 
material facilities; design, analysis, and testing 
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and seismic evaluation and rehabilitation of 
conventional and essential facilities, including hospitals. 
ATC-30: The report, Proceedings of Workshop for Utilization 
of Research on Engineering and Socioeconomic 
Aspects of 1985 Chile and Mexico Earthquakes, was 
developed under a grant from the NSF. Available 
through the ATC office. (Published 1991, 113 pages) 
ABSTRACT: This report documents the findings of a 
1990 technology transfer workshop in San Diego, 
California, co-sponsored by ATC and the Earthquake 
Engineering Research Institute. Included in 
the report are invited papers and working group recommendations 
on geotechnical issues, structural 
response issues, architectural and urban design considerations, 
emergency response planning, search 
and rescue, and reconstruction policy issues. 
ATC-31: The report, Evaluation of the Performance of 
Seismically Retrofitted Buildings, was developed under 
a contract from the National Institute of Standards and 
Technology (NIST, formerly NBS) and funded by the 
USGS. Available through the ATC office. (Published 
1992, 75 pages) 
ABSTRACT: This report summarizes the results from 
an investigation of the effectiveness of 229 seismically 
retrofitted buildings, primarily unreinforced 
masonry and concrete tilt-up buildings. All buildings 
were located in the areas affected by the 1987 
Whittier Narrows, California, and 1989 Loma Prieta, 
California, earthquakes. 
ATC-32: The report, Improved Seismic Design Criteria 
for California Bridges: Provisional Recommendations, 
was funded by the California Department of Transportation 
(Caltrans). Available through the ATC office. 
(Published 1996, 215 Pages) 
ABSTRACT: This report provides recommended 
revisions to the current Caltrans Bridge Design 
Specifications (BDS) pertaining to seismic loading, 
structural response analysis, and component design. 
Special attention is given to design issues related to 
reinforced concrete components, steel components, 
foundations, and conventional bearings. The recommendations 
are based on recent research in the 
field of bridge seismic design and the performance 
of Caltrans-designed bridges in the 1989 Loma Prieta 
and other recent California earthquakes. 
ATC-34: The report, A Critical Review of Current 
Approaches to Earthquake Resistant Design, was developed 
under a grant from NCEER and NSF. Available 
through the ATC office. (Published, 1995, 94 pages) 
This report documents the history of U.
ABSTRACT. 
S. codes and standards of practice, focusing primarily 
on the strengths and deficiencies of current 
code approaches. Issues addressed include: seismic 
hazard analysis, earthquake collateral hazards, performance 
objectives, redundancy and configuration, 
response modification factors (R factors), 
simplified analysis procedures, modeling of structural 
components, foundation design, nonstructural 
component design, and risk and reliability. The 
report also identifies goals that a new seismic code 
should achieve. 
ATC-35: This report, Enhancing the Transfer of U.S. 
Geological Survey Research Results into Engineering 
Practice was developed under a contract with the 
USGS. Available through the ATC office. (Published 
1996, 120 pages) 
ABSTRACT: The report provides a program of recommended 
"technology transfer" activities for the 
USGS; included are recommendations pertaining to 
management actions, communications with practicing 
engineers, and research activities to enhance 
development and transfer of information that is 
vital to engineering practice. 
ATC-35-1: The report, Proceedings of Seminar on New 
Developments in Earthquake Ground Motion Estimation 
And Implications for Engineering Design Practice, 
was developed under a cooperative agreement with 
USGS. Available through the ATC office. (Published 
1994, 478 pages) 
ABSTRACT: These Proceedings contain 22 technical 
papers describing state-of-the-art information on 
regional earthquake risk (focused on five specific 
regions California, Pacific Northwest, Central 
United States, and northeastern North America); 
new techniques for estimating strong ground 
motions as a function of earthquake source, travel 
path, and site parameters; and new developments 
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specifically applicable to geotechnical engineering 
and the seismic design of buildings and 
bridges. 
ATC-37: The report, Review of Seismic Research 
Results on Existing Buildings, was developed in conjunction 
with the Structural Engineers Association of 
California and California Universities for Research 
in Earthquake Engineering under a contract from the 
California Seismic Safety Commission (SSC). Available 
through the Seismic Safety Commission as 
Report SSC 94-03. (Published, 1994, 492 pages) 
ABSTRACT. This report describes the state of 
knowledge of the earthquake performance of 
nonductile concrete frame, shear wall, and 
infilled buildings. Included are summaries of 90 
recent research efforts with key results and conclusions 
in a simple, easy-to-access format written 
for practicing design professionals. 
ATC-40: The report, Seismic Evaluation and Retrofit 
of Concrete Buildings, was developed under a contract 
from the California Seismic Safety 
Commission. Available through the ATC office. 
(Published, 1996, 612 pages) 
ABSTRACT. This 2-volume report provides a 
state-of-the-art methodology for the seismic 
evaluation and retrofit of concrete buildings. 
Specific guidance is provided on the following 
topics: performance objectives; seismic hazard; 
determination of deficiencies; retrofit strategies; 
quality assurance procedures; nonlinear static 
analysis procedures; modeling rules; foundation 
effects; response limits; and nonstructural components. 
In 1997 this report received the Western 
States Seismic Policy Council "Overall 
Excellence and New Technology Award." 
ATC-44: The report, Hurricane Fran, South Carolina, 
September 5, 1996: Reconnaissance Report, is 
available through the ATC office. (Published 1997, 
36 pages.) 
ABSTRACT: This report represents ATC's 
expanded mandate into structural engineering 
problems arising from wind storms and coastal 
flooding. It contains information on the causative 
hurricane; coastal impacts, including storm 
surge, waves, structural forces and erosion; 
building codes; observations and interpretations 
of damage; and lifeline performance. Conclusions 
address man-made beach nourishment, the 
effects of missile-like debris, breaches in the 
sandy barrier islands, and the timing and duration 
of such investigations. 
ATC-R-1: The report, Cyclic Testing of Narrow Plywood 
Shear Walls, was developed with funding from 
the Henry J. Degenkolb Memorial Endowment Fund 
of the Applied Technology Council. Available 
through the ATC office (Published 1995, 64 pages) 
ABSTRACT: This report documents ATC's first 
self-directed research program: a series of static 
and dynamic tests of narrow plywood wall panels 
having the standard 3.5-to-1 height-to-width 
ratio and anchored to the sill plate using typical 
bolted, 9-inch, 5000-lb. capacity hold-down 
devices. The report provides a description of the 
testing program and a summary of results, 
including comparisons of drift ratios found during 
testing with those specified in the seismic 
provisions of the 1991 Uniform Building Code. 
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FEIVA 
ATC BOARD OF DIRECTORS (1973-Present) 
Milton A. Abel (1979-85) : John F. Meehan* (1973-78) 
James C. Anderson (1978-81) Andrew T. Merovich (1996-99) 
Thomas G. Atkinson* (1988-94) David L. Messinger (1980-83) 
Albert J. Blaylock (1976-77) Stephen McReavy (1973) 
Robert K. Burkett (1984-88) Bijan Mohraz (1991-97) 
James R. Cagley (1998-2001) William W. Moore* (1973-76) 
H. Patrick Campbell (1989-90) Gary Morrison (1973) 
Arthur N. L. Chiu (1996-99) Robert Morrison (1981-84) 
Anil Chopra (1973-74) Ronald F. Nelson (1994-95) 
Richard Christopherson* (1976-80) Joseph P. Nicoletti* (1975-79) 
Lee H. Cliff (1973) Bruce C. Olsen* (1978-82) 
John M. Coil* (1986-87, 1991-97) Gerard Pardoen (1987-91) 
Eugene E. Cole (1985-86) Stephen H. Pelham (1998-2001) 
Edwin T. Dean (1996-99) Norman D. Perkins (1973-76) 
Robert G. Dean (1996-2001) Richard J. Phillips (1997-2000) 
Edward F. Diekmann (1978-81) Maryann T. Phipps (1995-96) 
Burke A. Draheim (1973-74) Sherrill Pitkin (1984-87) 
John E. Droeger (1973) Edward V. Podlack (1973) 
Nicholas F. Forell* (1989-96) Chris D. Poland (1984-87) 
Douglas A. Foutch (1993-97) Egor P. Popov (1976-79) 
Paul Fratessa (1991-92) Robert F. Preece* (1987-93) 
Sigmund A. Freeman (1986-89) Lawrence D. Reaveley* (1985-91) 
Barry J. Goodno (1986-89) Philip J. Richter* (1986-89) 
Mark R. Gorman (1984-87) John M. Roberts (1973) 
Gerald H. Haines (1981-82, 1984-85) Charles W. Roeder (1997-2000) 
William J. Hall (1985-86) ArthurE. Ross* (1985-91, 1993-94) 
Gary C. Hart (i975-78) C. Mark Saunders* (1993-2000) 
Lyman Henry (1973) Walter D. Saunders* (1975-79) 
James A. Hill (1992-95) Lawrence G. Selna (1981-84) 
Ernest C. Hillman, Jr. (1973-74) Wilbur C. Schoeller (1990-91) 
Ephraim G. Hirsch (1983-84) Samuel Schultz* (1980-84) 
William T. Holmes* (1983-87) Daniel Shapiro* (1977-81) 
Warner Howe (1977-80) Jonathan G. Shipp (1996-99) 
Edwin T. Huston* (1990-97) Howard Simpson* (1980-84) 
Paul C. Jennings (1973-75) Mete Sozen (1990-93) 
Carl B. Johnson (1974-76) Donald R. Strand (1982-83) 
Edwin H. Johnson (1988-89, 1998-2001) James L. Stratta (1975-79) 
Stephen E. Johnston* (1973-75, 1979-80) Scott Stedman (1996-97) 
Joseph Kallaby* (1973-75) Edward J. Teal (1976-79) 
Donald R. Kay (1989-92) W. Martin Tellegen (1973) 
T. Robert Kealey* (1984-88) John C. Theiss* (1991-98) 
H. S. (Pete) Kellam (1975-76) Charles H. Thornton* (1992-99) 
Helmut Krawinkler (1979-82) James L. Tipton (1973) 
James S. Lai (1982-85) Ivan Viest (1975-77) 
Gerald D. Lehmer (1973-74) Ajit S. Virdee* (1977-80, 1981-85) 
James R. Libby (1992-98) J. John Walsh (1987-90) 
Charles Lindbergh (1989-92) Robert S. White (1990-91) 
R. Bruce Lindermann (1983-86) James A. Willis* (1980-81, 1982-86) 
L. W. Lu (1987-90) Thomas D. Wosser (1974-77) 
Walter B. Lum (1975-78) Loring A. Wyllie (1987-88) 
Kenneth A. Luttrell (1991-98) Edwin G. Zacher (1981-84) 
Newland J. Malmquist (1997-2000) Theodore C. Zsutty (1982-85) 
Melvyn H. Mark (1979-82) 
John A. Martin (1978-82) * President 
ATC EXECUTIVE DIRECTORS (1973-Present) 
Ronald Mayes (1979-81) Roland L. Sharpe (1973-79) 
Christopher Rojahn (1981-present) 
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Sponsors, Supporters, and Contributors 
Sponsors 
Structural Engineers Association of California 
James R. & Sharon K. Cagley 
John M. Coil 
Burkett & Wong 
Supporters 
Charles H. Thornton 
Degenkolb Engineers 
Japan Structural Consultants Association 
Contributors 
Lawrence D. Reaveley 
Omar Dario Cardona Arboleda 
Edwin T. Huston 
John C. Theiss 
Reaveley Engineers 
Rutherford & Chekene 
E. W. Blanch Co. 
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