The dynamic properties of wood shearwall buildings were evaluated, such as modal frequencies, damping and mode shapes of the structures. Through analysis of recorded earthquake response and by forced vibration testing, a database of periods and damping ratios of woodframe buildings was developed. Modal identification was performed on strong-motion records obtained from five buildings, and forced vibration tests were performed on a two-story house and a three-story apartment building, among others. A regression analysis is performed on the database to obtain a period formula specific for woodframe buildings. It should be noted that all test results, including the seismic data, are at small drift ratios (less than 0.1%), and the periods would be significantly longer for stronger shaking of these structures. Despite these low amplitudes, the equivalent viscous dampings for the fundamental modes were usually more than 10% of critical during earthquake shaking

Beck, J. L.

Camelo, V. S.

Hall, J. F.

English

Caltech Authors - Main

Dynamic Characteristics of Woodframe Buildings

 
 
 
DYNAMIC CHARACTERISTICS OF WOODFRAME BUILDINGS 
 
 
V. S. Camelo1, J. L. Beck2 and J. F. Hall3 
 
 
ABSTRACT 
 
 The dynamic properties of wood shearwall buildings were evaluated, such as 
modal frequencies, damping and mode shapes of the structures.  Through analysis 
of recorded earthquake response and by forced vibration testing, a database of 
periods and damping ratios of woodframe buildings was developed.  Modal 
identification was performed on strong-motion records obtained from five 
buildings, and forced vibration tests were performed on a two-story house and a 
three-story apartment building, among others.  A regression analysis is performed 
on the database to obtain a period formula specific for woodframe buildings.  It 
should be noted that all test results, including the seismic data, are at small drift 
ratios (less than 0.1%), and the periods would be significantly longer for stronger 
shaking of these structures. Despite these low amplitudes, the equivalent viscous 
dampings for the fundamental modes were usually more than 10% of critical 
during earthquake shaking. 
 
  
Introduction 
 
 Current building codes prescribe a design earthquake load based on the characteristics of 
the building and site under evaluation.  These codes specify simplified formulas to approximate a 
building’s fundamental period, which can help describe how it will behave during an earthquake. 
 Recent research has shown that the 1997 Uniform Building Code period formulas substantially 
underestimate the fundamental periods for concrete and steel moment-resisting frame buildings, 
as well as those for concrete shearwall buildings (Goel and Chopra 1997, 1998).  An important 
objective of this research is to evaluate and improve upon the current code period formulas for 
woodframe structures. 
 
 Much research has been done on the dynamic and cyclic characteristics of wood 
subsystems and connection panels, but full-scale testing of woodframe buildings had been sparse 
until the CUREE-Caltech Woodframe Project (CUREE 2001).  A database of periods, dampings 
and mode shapes of woodframe buildings has been obtained under Task 1.3.3 of this project; this 
was accomplished by analyzing available seismic data and performing forced vibration tests.  A 
                     
1Graduate Research Assistant, Dept. of Civil Engineering, California Institute of Technology, Pasadena, CA 91125  
2Professor of Applied Mechanics and Civil Eng., California Institute of Technology, Pasadena, CA 91125 
3Professor of Civil Engineering, California Institute of Technology, Pasadena, CA 91125 
 
period formula specific for woodframe structures is obtained by regressing on appropriate 
structural characteristics using this database, providing a descriptive parameter for the dynamic 
behavior of these buildings. 
 
  
Available Seismic Records 
 
 Eight sets of earthquake records were obtained from five woodframe buildings 
instrumented by the California Strong Motion Instrumentation Program.  The earthquake data 
were analyzed using the Caltech program MODE-ID, which uses a well-established system 
identification procedure to estimate the modal parameters of the dominant contributing modes for 
the building being evaluated (Beck 1978, Beck and Jennings 1980).  The periods and dampings 
obtained are summarized in Table 1.   
 
Table 1.     Summary of building dynamic characteristics from earthquake records. 
 
Building Location San Bernardino Parkfield Bishop Indio Eureka 
Building Height (top of roof) 29.9’ 13.2’ 17’ 13.7’ 26.0’ 
No. of Stories 3 1 1 1 2 
Building Type Motel School Fire-Station Hospital Office 
Length:  (Longit.) 180.5’ 48’ 62’ 298’ 80’ 
 (Transv) 132’ 30’ 50’ 148’ 54’ 
Date of Earthquake 6/28 1997 
7/26 
1997 
3/11 
1998 
4/4 
1993 
12/20 
1994 
5/17 
1993 
7/25 
1997 
2/8 
1995 
Magnitude (ML) 4.2 3.7 4.5 4.2 4.7 6.0 4.9 3.9 
Peak Roof Acceleration 9.2%g 7.8%g 7.1%g 12.3%g 20.1%g 4.4%g 8.2%g 6.2%g 
Total Drift (mm):  (Longit.) 0.7 0.7 0.8 0.5 0.9 1.2 0.4 0.4 
(Roof w.r.t. Base) (Transv) 0.6 0.7 0.7 0.5 1.5 0.3 0.2 0.5 
Periods (sec): (Longit.) 0.22 0.20 0.23 0.14 0.15 0.11 0.13 0.17 
(First Mode) (Transv) 0.19 0.21 0.18 0.11 0.13 0.18 0.14 0.20 
Frequency (Hz): (Longit.) 4.6 5.0 4.4 7.3 6.6 8.7 7.9 5.8 
(First Mode) (Transv) 5.4 4.8 5.6 8.7 8.0 5.6 7.1 4.9 
Damping Ratio: (Longit.) 13.6 % 14.1 % 7.7 % 11.6 % 10.8 % 12.2 % 8.9 % 16.5 % 
(First Mode) (Transv) 17.3 % 6.9 % 11.7 % 14.2 % 15.3 % 7.0 % 6.3 % 14.9 % 
 
 
 The high damping levels from the modal identification of the seismic records are 
consistent with the damping levels exhibited in the shaking table tests of a 2-story woodframe 
house performed at the University of California at San Diego (Fischer et. al. 2001).  The 
fundamental frequency estimates from different earthquakes for buildings with multiple 
earthquake recordings are quite consistent, since the drifts are at similar levels.  (It is known from 
experience that the uncertainty in the estimates of the fundamental frequencies is relatively small 
if the drift levels are comparable from test to test.)  On the other hand, the fundamental damping 
estimates vary significantly for the San Bernardino 3-story motel.  This may be partly because the 
instrumentation layout does not allow the excitation of the structure to be well captured.  
However, experience has shown that the uncertainty in the damping estimates is relatively large 
even when the excitation is well defined; it is thought that this is partly because the assumed 
linear viscous damping is not a good model for the actual damping mechanisms and partly 
because the seismic response of the model is not very sensitive to changes in the damping level, 
and therefore the error measure in the program MODE-ID is more sensitive to frequency than to 
damping.  The damping ratios for the model averaged 11.8% and ranged from 6.3% to 17.3% 
during earthquake shaking of the five buildings. 
 
 Detailed analysis of the earthquake records showed a gradual elongation in the natural 
periods of vibration over each record, which was longest at the time of strongest shaking and 
which gradually returned to the original value.  Similarly, the damping ratios gradually increased 
during the course of the earthquake and were highest at the time of strongest shaking, after which 
they gradually returned to their original values.  See Fig. 1 for a plot of the detailed analysis 
results for the 1-story Bishop fire-station. 
 
Bishop Fire Station
(5/17/93)
4
6
8
10
0 6 12 18 24
Time during earthquake (sec.)
Fr
eq
ue
nc
y 
(H
z)
EW (longitudinal) NS (Transverse)
 
Bishop Fire Station
(5/17/93)
0
5
10
15
0 6 12 18 24
Time during earthquake (sec.)
Eq
ui
va
le
nt
 V
is
co
us
 
D
am
pi
ng
 R
at
io
s 
(%
)
EW (longitudinal) NS (Transverse)
 
 
Figure 1.    Bishop fire station MODE-ID analysis details.  Note that peak earthquake shaking 
occurs within 6-12 second window. 
 
 
Forced Vibration Tests 
 
 The forced vibration tests were performed to supplement the dynamic characteristics 
database, since currently only a limited number of earthquake records have been obtained in 
woodframe buildings.  These tests measured harmonic vibrations induced by a shaking machine 
in the buildings being tested.  The force delivered by the shaking machine is generated by the 
centrifugal acceleration of the weights, so it is proportional to the square of the frequency of 
rotation of these weights and also to their eccentricity around the rotating shafts (see Fig. 2).   
 
 
 
Figure 2.    Harvey Mudd College shaker:  detail of shaft 
with weights at 2.5% eccentricity 
 
 
 Ranger seismometers and/or force balance accelerometers were used for recording the 
building response at each driving frequency, then sinusoidal curves were fitted to the recorded 
time histories from each output channel in order to determine their amplitude and relative phase. 
 Only seismometer results are presented here.  After calculating the frequency-response curves 
for all data channels, the modal frequencies and corresponding damping ratios were computed by 
using a curve-fitting approach involving nonlinear least-squares matching of the model and 
measured frequency response amplitudes.  Results are shown in Table 2 for a 3-story apartment 
building and a 2-story house. 
 
 
Table 2.     Summary of building dynamic characteristics from forced vibration tests. 
 
Building Location Catalina Ave.,  Pasadena 
Del Mar Blvd.,  
Pasadena 
Building Height (top of roof) 20’ 30’ (above garage) 
No. of Stories 2 3 + garage 
Building Type House Apartments 
Peak Total Drift (mm): 
(Roof w.r.t. Base)    0.54 0.52 
Shaking Direction Shaker Eccentricity 
Period 
(Sec) 
Freq 
(Hz) 
Damp. 
(%) 
Period 
(Sec) 
Freq 
(Hz) 
Damp. 
(%) 
2.5% 0.175 5.7 5.0% 0.189 5.3 4.7% 
10% -- -- -- 0.192 5.2 4.6% NS (Longitudinal) 
20% -- -- -- 0.196 5.1 4.9% 
2.5% 0.182 5.5 2.9% 0.227 4.4 4.7% 
10% 0.196 5.1 2.9% -- -- -- EW (Transverse) 
20% 0.204 4.9 2.7% 0.238 4.2 5.1% 
2-Story House (Pasadena) 
 
This two-story house, owned by the California Institute of Technology and located in the 
vicinity of the campus, was being used as an undergraduate dormitory.  It is built on cripple 
walls, and constructed circa 1940, with first floor plan area nearing 2000 square feet.  It has two 
brick fireplaces, which have been seismically retrofitted and anchored to the roof.  The building 
has wood shingle siding, the interior finish is plaster, and the original hardwood floors are still in 
place.  The shaker was placed at the second floor of this house, on the top of the main stairway 
over a sheet of plywood and secured in place by planks of wood that were fastened to the 
plywood and squeezed between the walls to provide maximum force transfer to the building.  
The intent was to avoid any damage to the building, so the assembly was not bolted to the floor.  
See Fig. 3 for picture of test site, Fig. 4 for shaker setup, and Fig. 5 for channel locations. 
 
 
  
 
Figure 3.    2-Story House (Pasadena) Figure 4.    Experimental setup. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 5.    Seismometer locations 
N 
S.
 C
at
al
in
a 
Av
e 
 
  
LIVING   
 
 
ROOM  
 
  
KITCHEN   
 
 
BA
TH
 
 
BEDROOM   
 
 
  
  
 
  
LIVING   
 
 
ROOM  
 
 
FIREPL.   
 
 
    1st FLOOR PLAN       
FI
R
EP
L.
 
 
  
5 
(a
tti
c)
 
2nd FLOOR PLAN       
1   
 
 
3   
 
 
2   
 
 
4   
 
 
BATH   
 
 
BEDROOM   
 
 
 
  
FI
R
EP
L.
   
FIREPL.   
 
 
BEDROOM   
 
 
 
  
BEDROOM   
 
 
 
  
BEDROOM   
 
 
BATH   
 
BA
TH
 
  6  (attic) 
  
 
 
SHAKER   
 
 
N 
A set of frequency response curves is shown in Fig. 6 for shaker force oriented in the EW 
direction.  The EW and NS fundamental modes of the 2-story house are coupled to the torsional 
response; all channels are excited in both modes as observed from the double peaks, one at each 
resonant frequency.  The identified EW and NS fundamental frequencies are 5.5 Hz and 5.7 Hz 
at 2.5% eccentricity.  Also, note from the figure the downward shift in fundamental frequencies 
as the eccentricity increases (larger shaker force).  Maximum total drift was 0.54 mm for EW 
shaking at 20% eccentricity. 
 
 
 
Figure 6.    2-Story House (Pasadena):  Forced vibration tests on 6/27/00.  The amplitudes are 
normalized by the square of the frequency.  Odd numbered channels face North and 
even numbered channels face West. 
 
 
 
3-Story Apartment Building (Pasadena) 
 
This apartment building is owned by the California Institute of Technology and is located 
in the vicinity of the campus.  It was built circa 1960, and it is currently being used as graduate 
student apartments.  There is a partially underground parking garage with concrete block walls 
around three sides and the East side of the garage is open.  The first floor plan area is 
approximately 5000 square feet, with an aspect ratio of approximately 3:1.  The student 
ch6 
ch4 
ch2 
ch3 
ch5 
ch1 
ch6 
ch4 
ch2 
ch3 
ch5 
ch1 
ch3 
ch5 
ch1 
ch6 
ch4 
ch2 
apartments are located at the first and second floor levels, and there is a penthouse apartment 
occupying the third floor.  The exterior wall finish is stucco, the interior finish is drywall, and the 
flooring is a soundproofing topping (probably lightweight concrete) over sheathing.  The shaker 
was placed at the third floor, over a sheet of plywood and wedged between wood planks.  Screws 
were driven through the planks, plywood and floor deck below to secure the shaker assembly.  
See Fig. 7 for picture of test site, Fig. 8 for shaker setup, and Fig. 9 for channel locations. 
 
 
 
   
 
Figure 7.    3-Story Apt. Bldg. (Pasadena) Figure 8.    Experimental setup. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 9.    Seismometer locations. 
 
 
 
1st FLOOR PLAN 
E. Del Mar Blvd.   
  5  
3rd FLOOR PLAN 
1 
6  3  
2  
7  SH
A
K
E
R
 
N 
  E. Del Mar Blvd. 
UNDERGROUND GARAGE 
Concrete 
Block 
Walls 
Concrete 
Block 
Walls 
4   
2nd FLOOR PLAN 
A set of frequency response curves is shown in Fig. 10 for the shaker force oriented in the 
NS direction.  The 3-story apartment building showed strong torsional behavior when shaken in 
this direction due to the lack of walls on the East side of the parking garage.  The average NS 
motion amplitude (channels N6 and N7) at resonance is similar to the EW motion amplitude at 
the ends of the building (channels E1 and E2, which are out of phase).  The identified 
fundamental resonant frequency is 5.3 Hz at 2.5% eccentricity; the value for EW shaking is 4.5 
Hz (results not shown).  Note from the figure that the fundamental frequency of this building 
decreased as the shaking amplitude increased.  Maximum total drift was 0.52 mm for NS shaking 
at 20% eccentricity. 
 
 
 
Figure 10.    3-Story Apartment Building (Pasadena):  Forced vibration tests on 7/10/00.  
Amplitudes normalized by the square of the frequency. 
N7
E1
E2
N6
N7
E1
E2
N6
N7
E1
E2
N6
Period Formula by Regression 
 
 The data obtained from the analysis of the earthquake records and the forced vibration 
tests was used to perform a regression analysis for the periods with respect to the height of the 
buildings.  A Maximum Likelihood estimation method was chosen based on a lognormal 
probability distribution for the periods at each value of the selected regressor.  The best-fit curve 
for the median period T̂  can be represented by the following formula: 
 
 0.55h032.0T̂ =  (1) 
 
where h is the height of the building.   
 
 Fig. 11 shows a comparison between the periods found from regression on data and the 
period formula prescribed by the 1997 UBC.  The 16- and 84-percentile curves are also shown, 
where the standard error in lnT is 0.129 (Camelo, Beck and Hall 2001).  
 
 
0.10
0.12
0.14
0.16
0.18
0.20
0.22
0.24
0.26
0.28
0.30
10 15 20 25 30
Height (ft)
Pe
rio
d 
(s
ec
.)
  EQ Data
  Forced Vibration
Data
UBC 1997
Median Period
(Eqn. 1)
16th Percentile
84th Percentile
UBC 1997
T=0.032 h0.55
T=0.020 h0.75
EQ Data
Forced Vibration Data
il
Eqn. 1
 
 
Figure 11.    Period by Regression vs. 1997 UBC Period Formula. 
 
 
Conclusions 
 
 The database compiled during this research has provided valuable insight regarding the 
dynamic characteristics of woodframe buildings, which showed fundamental natural periods 
between 0.11 and 0.24 sec (4.2 and 8.7 Hz), and damping ratios averaging 7.2% and ranging 
from 2.9 to 17.3%.  This database was used to develop a period formula that can be compared to 
the current UBC formula, but it must be noted that the database was derived from low-amplitude 
shaking (inter-story drifts less than 1.5 mm), since strong shaking data is not currently available.  
The periods are expected to be significantly longer for stronger shaking of these structures, as 
suggested by the frequency shortening shown in Figs. 6 and 10.  It should be noted that the 
damping values obtained from the forced vibration tests were much lower than those obtained 
from the analysis of the earthquake data even though the drift levels were similar.  This may be 
due to differences between the buildings being tested and those from which the earthquake 
records were obtained, but at this time the cause of this variation is not clear.   
 
 The authors are currently testing other woodframe buildings to examine the effect of 
increased motion amplitude on the building’s natural frequencies and to investigate the floor 
diaphragm behavior of these structures.  These future studies are expected to assist in 
establishing sound design and construction guidelines. 
 
 
Acknowledgments  
 
 Funding for the research detailed in this report was provided by the Consortium of 
Universities for Research in Earthquake Engineering (CUREE) as part of the CUREE-Caltech 
Woodframe Project, under a grant administered by the California Office of Emergency Services 
and funded by the Federal Emergency Management Agency.  The authors are also grateful for 
Professor Ziyad Duron’s generosity in lending the Harvey Mudd shaker.  His expertise and that 
of his research assistants were invaluable. 
 
 
References 
 
Beck, J. L.  (1978).  Determining Models of Structures from Earthquake Records. EERL Report No. 78-
01, California Institute of Technology, Pasadena, Calif. 
 
Beck, J. L., and P. C. Jennings (1980).  Structural Identification Using Linear Models and Earthquake 
Records,  Earthquake Engineering and Structural Dynamics, 8, 145-160 
 
Camelo, V. S., J. L. Beck, and J. F. Hall (2001).  Dynamic Characteristics of Woodframe Buildings.  
CUREE-Caltech Woodframe Project Report,  Richmond, Calif. 
 
CUREE (2001).  http://www.curee.org/projects/woodframe_project/woodframe_intro.html 
 
Fischer, D., et al.  (2001). Shake Table Tests of a Two-Story Woodframe House.  CUREE-Caltech 
Woodframe Project Report,  Richmond, Calif. 
 
Goel, R. K., and A. K. Chopra (1998).  Period Formulas for Concrete Shear Wall Buildings,  Journal of 
Structural Engineering - ASCE 124:  (4) 426-433. 
 
Goel, R. K., and A. K. Chopra (1997).  Period Formulas for Moment Resisting Frame Buildings,  Journal 
of Structural Engineering - ASCE 123:  (11) 1454-1461. 
 
Uniform Building Code  (1997).  International Conference of Building Officials, Whittier, Calif. 


Determining Models of Structures from Earthquake Records.

Period Formulas for Concrete Shear Wall Buildings,

Period Formulas for Moment Resisting Frame Buildings,

Shake Table Tests of a Two-Story Woodframe House. CUREE-Caltech Woodframe Project Report,

Structural Identification Using Linear Models and Earthquake Records, Earthquake Engineering and Structural Dynamics,

Uniform Building Code

http://authors.library.caltech.edu/34247/1/2001Camelo.pdf

Dynamic Characteristics of Woodframe Buildings

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