Effects of Low-Cycle Fatigue on a Ten-Story Steel Building

Navid Nastar1, James C. Anderson

2, Gregg E. Brandow

3, Robert L. Nigbor

4

1 Ph.D., P.E., Lecturer, Dept. of Civil & Env. Engrg., University of Southern California

Project Engineer, Brandow & Johnston, Inc.

2 Ph.D., Professor, Dept. of Civil & Env. Engrg., University of Southern California

3 Ph.D., S.E., President, Brandow & Johnston, Inc.

Adjunct Professor, Dept. of Civil & Env. Engrg., University of Southern California

4 Ph.D., P.E., Research Engineer, Dept. of Civil & Env. Engrg, University of California, Los

Angeles

Abstract

Following the Northridge Earthquake (1994), the SAC steel project was initiated to investigate

the causes of widespread damage observed in the connections of steel moment frame buildings.

The published results of these studies concentrated on local connection defects that potentially

initiated the observed cracks. It was also considered that much of the observed connection

damage was the result of yielding of the material in the connection region and the formation of

plastic hinges. However, damage to some buildings could not be reconciled by the use of these

failure mechanisms. This has led to a renewed interest in the effects of low-cycle fatigue on the

members and connections in steel buildings that are either elastic or have been driven into the

weakly nonlinear range.

The current paper is focused on the effect of low-cycle fatigue in the connection damage

observed in a ten-story steel building after the Northridge Earthquake. A comprehensive fatigue

analysis procedure is developed based on the Palmgren-Miner method and S-N curves

established for the high-cycle fatigue range are extended to the low-cycle region using the

limited test results that are available. Fatigue analysis is performed at critical locations of a

representative moment frame using the established procedure. Finally, the pattern of cumulative

fatigue at critical connections and the observed damage are compared. Results of this analytical

study indicate that the effect of low-cycle fatigue may be significant in evaluating and predicting

various types of connection damage similar to that observed in the steel moment frames during

the Northridge Earthquake.

Introduction

Although structural steel is an excellent building material that has positive characteristics which

make it behave well in many conditions, there are still concerns with its fatigue behavior and

possible cyclic fatigue failures of steel components in the scientific community. One of the major

consequences of the Northridge Earthquake of January 17, 1994, was the widespread connection

damage that posed an essential question regarding the behavior of Pre-Northridge steel moment

frame connections. Before the Northridge Earthquake, steel moment resisting frames were

believed to have ductile behavior that would achieve high-cycle fatigue. As a result, fatigue was

not considered to be a failure mode for these connections during a seismic event. Observations

after the Northridge Earthquake indicated that these connections essentially failed at relatively

low stress levels with only a few high-stress cycles of vibration.

As a result of these failures, many researchers tried to gain a better understanding of the causes

of damage observed in the connections of the steel moment frames. Due to the complexity of the

problem, the SAC steel project was initiated by FEMA. The majority of published results of this

nationwide project concentrated on local connection defects that potentially initiated the

observed cracks. It was also considered that much of the observed connection damage was the

result of yielding of the material in the connection region and the formation of plastic hinges.

Although remarkable research under the SAC project was performed to address the above issues,

damage to some buildings could not be reconciled by use of these failure mechanisms. This led

to a renewed interest in studying the effects of low-cycle fatigue that can potentially justify the

observed connection failures.

Several factors have been identified that can contribute to potential low-cycle fatigue failure in

steel buildings. Fatigue is primarily a function of stress level and number of stress cycles.

Conditions that could cause a stress level that is at or just below yield include moderate to strong

earthquake ground motions and the geometry of the connections with localized stress

concentrations. Factors increasing the number of stress cycles experienced in the building

include the frequency of occurrence of moderate to strong earthquakes, low structural damping,

and the contribution of higher modes of vibration with their increased number of stress cycles.

The contribution of higher modes can also be increased by structural framing that incorporates

vertical setbacks. Nastar (2008) discusses the contribution of higher modes in cumulative fatigue

analysis in details.

The current study uses a comprehensive analysis procedure for low-cycle fatigue that is based on

the Palmgren-Miner method. Although fatigue curves relating cyclic stress to number of cycles

to failure (S-N) are readily available for conditions of high-cycle fatigue, there is only a limited

amount of experimental data available for low-cycle fatigue. Using this limited experimental

data, the authors have extended the S-N curves for the high-cycle fatigue range into the low-

cycle range for use in this study. A series of linear and non-linear time history analyses is

conducted on a ten-story building damaged by the Northridge Earthquake. The building was

instrumented at the roof and had a lateral load resisting system consisting of steel moment

frames in both directions. The method of rainflow cycle counting, developed by Prof. T. Endo

(Matsuishi and Endo, 1968), is used to evaluate the highly irregular variations of load with time

and permit the use of the Palmgren-Miner Method for estimating the fatigue life that has been

expended during the seismic event. Finally, the pattern of cumulative fatigue at critical locations

in the building will be evaluated and compared with the observed damage during Northridge

Earthquake.

Fatigue Analysis Procedure

In order to evaluate the effect of fatigue under seismic loading, it will be necessary to consider

stress amplitudes that change in an irregular manner. A simple rule for doing this that is widely

used in civil engineering was suggested by A. Palmgren in 1924. However, the procedure was

not widely used until the publication of a paper by M. A. Miner (Miner, 1945). The results of this

paper are generally referred to as the Palmgren-Miner Rule which is represented by the following

equation:

1 2

1 2

1j

f f fj

NN N

N N N ! !"

A stress amplitude is applied for a number of cycles, N1 where the number of cycles to failure

corresponding to this stress level from the S-N curve is Nf1. The fraction of the fatigue life used

is then N1/Nf1. This procedure is applied for another stress level and another fraction of the

fatigue life, N2/Nf2 is used. The rule states that fatigue failure is expected when such life fractions

sum to unity which implies that 100% of the structural life is exhausted. In order to utilize this

rule in a seismic analysis, it will be necessary to select a cycle-counting procedure for converting

the number of cycles of irregular time history response into an equivalent number of uniform

cycles. It will also be necessary to establish a fatigue life curve for Pre-Northridge moment

connections. This curve is technically known as the S-N curve and indicates the stress level

versus the number of cycles to failure.

Dowling (Dowling, 2007) has noted that in prior years, there was considerable uncertainty and

debate concerning the proper procedure for cycle counting and a number of different methods

were proposed and used. It now appears that a consensus has emerged and that the best approach

is a procedure called “rainflow cycle counting” that was developed by Professor T. Endo in

Japan. This procedure is also discussed in more detail by Dowling (2007). Relevant computer

programs for this operation are available in MATLAB (2005) and were used for this in the

current study.

In order to apply the Palmgren-Miner Rule, it is necessary to have a procedure for estimating the

number of cycles to failure at each stress level (Nj). Since in this analysis, it is anticipated that

the stress level will be either elastic or just weakly nonlinear, the use of a stress based approach

is suggested. This also works well since previous work for civil engineering structures is based

on this approach and therefore the current study builds on the body of previous experimental

research.

Bertero and Popov (1965) conducted tests on rolled steel sections under large alternating strains

in a special test fixture in which no welding was required. They discuss the potential of low-

cycle fatigue as a failure mechanism, noting that the fatigue life cannot be estimated solely from

the fatigue characteristics of the material but depends on other factors that include size and type

of member and in particular, the states of stress and strain along the critical region of a member.

This indicates that the use of stress concentration factors may lead to a procedure for estimating

the fatigue life of different sections. In particular, their tests indicated that local buckling of the

beam flanges can cause a rapid reduction in the number of stress cycles to failure.

Tests by Fisher et al. (1977) on rolled beams, welded beams and beams with end welded cover

plates were mainly concerned with the fatigue strength in the high-cycle region (105 to 10

7 cycles

to failure). The results of these tests have been widely used in establishing the fatigue design

criteria currently used in the United States. Since high-cycle fatigue is significant for bridge

structures, the criteria developed from these tests are widely used in the design and assessment of

steel bridges. In another document published later, Fisher, et al. (1998) present additional test

results in the high-cycle region. The current study uses appropriate stress concentration factors to

extend these test results to the Pre-Northridge connection detail.

A series of low-cycle fatigue tests on welded joints with high-strength steel members were

conducted in Japan by Kawamura and Suzuki (1992). The test specimen was a relatively small,

H-shaped steel beam (Fy = 62.5 ksi) mounted vertically to a 1.6 inch steel plate with backup bars

removed for all tests. For comparison with the results of low-cycle fatigue tests conducted in Los

Angeles (Partridge et al., 2000), the stress values are normalized relative to the yield stress of the

material as shown in figure 1. From the results of these tests, it was concluded that fatigue failure

occurred for all test specimens; however, it was also noted that the size of the beam test

specimen was very small.

Ten full scale connection specimens were tested under cyclic loads in the low-cycle region (2-

100 cycles) of the S-N Curve (Partridge et al., 2000). The connection specimens consisted of

W18x40 beams connected to W14x155 stub columns. With the adjustment described in the

previous paragraph, the results of these tests on full size specimens showed good agreement with

the tests in Japan on small size specimens, as shown in Figure 1.

Figure 1. Comparison between the available low-cycle fatigue tests.

It is convenient to relate all of these test results through the use of a stress concentration factor

(SCF). The SCF for the rolled beam is assumed to be 1 as done in the AISC Specification,

Appendix K, and all other configurations are relative to this value. Since the buildings of

particular interest are built prior to the Northridge Earthquake (1994) the beam to column

connections will have the backup bar in place. The SCF for the backup bar as determined from

the tests conducted by Partridge, et al. is estimated to be 1.3. A finite element model of a typical

Pre-Northridge exterior joint was developed and used to determine stress concentrations and to

estimate the SCF for the connection geometry, as shown in Figure 2. Relative to that of a rolled

beam SCF was found to be approximately 1.75. Finally a SCF for welded vs. rolled beams is

determined to be 2.4. Combining these three SCF’s leads to an SCF for the connection of 5.5

relative to a rolled section.

Figure 2. Stress concentration study in a typical Pre-Northridge connection with continuity plates.

The established S-N Curve for the exterior, Pre-Northridge connection is shown in Figure 3. In

the high cycle region, it is anchored to the tests conducted by Fisher, et al. In the low cycle

region it is anchored to the tests conducted by Partridge, et al. including both with and without

backup bars.

Figure 3. Established S-N curve for the Pre-Northridge connection.

The equation of this curve that is used for the fatigue analysis is given as follows:

For S > 19.7 ksi (N < 36175); S [ksi] = 69.3N-0.1198

For S < 19.7 ksi (N > 36175); S [ksi] = 658.4N-0.326

where N is the number of cycles to failure and S is the flexural stress. This procedure is

described in details by Nastar (2008).

Case Study Building

The ten-story steel building selected for this study is located in the San Fernando Valley,

California. The lateral load resisting system consists of steel moment frames with Pre-Northridge

field-welded field-bolted connections in both major directions (North-South and East-West). The

gravity system comprises concrete filled metal deck supported by steel wide flange beams and

columns. Figure 4 shows a view of the building and Figure 5 shows a typical floor plan (4th

-8th

).

Figure 4: Investigated ten-story building.

One the prominent characteristics of this building, is the vertical set back that could potentially

increase the higher mode effects and result in higher cumulative fatigue at critical elements

(Nastar, 2008). This was one of the major reasons for the selection of this building for the current

study. In addition, the building was instrumented by California Department of Mines and

Geology (CDMG) at the roof level. The recorded data is used to calibrate and validate the

analytical model and to verify some of the dynamic parameters such as viscous damping and

period of vibration.

Investigations after the Northridge Earthquake performed by Brandow and Johnston, Inc.

revealed that the building experienced significant damage at the steel moment frame

connections. A careful study of the observed damage after the Northridge Earthquake indicates

that the moment frames on lines D and F.5 are representative of the typical damage observed in

the building. Figure 6 illustrates the elevation of the investigated frames. Thick lines show the

beam and columns of the connections under investigation.

NORTH

Figure 5: Typical floor (4th-8th) framing plan.

Figure 6: Investigated frames of the ten-story building.

Observations after the Northridge Earthquake showed that no major damage occurred in the

moment frame on gridline F.5. Also, they demonstrated that gridline 10 of moment frame D

could be a representative of the typical damages that occurred in this building. As shown in

Figure 6, the moment connections on gridline 10 from 2nd

floor through the 9th

floor are studied

carefully for the level of stress they experience. Furthermore, fatigue analysis is performed on

the calculated stress histories to evaluate the cumulative fatigue at these locations.

Figure 7 shows the typical damage observed in Pre-Northridge steel moment frame connections

after the Northridge Earthquake. Post-Northridge inspection results show that most of the

damage in Frame D gridline 10 happened at 5th

, 6th

, and 7th

floors. The 6th

floor experienced the

most severe damage represented by types 2 and 3 in the bottom of the connection. This means

the connection had cracks that went through the weld and column flange (Types 2b and 3b). The

5th

floor experienced only type 2 damage in the bottom of the connection, and cracks were just

observed in the bottom flange weld (Type 2b). The damage at the 7th

floor was minor, and only

small cracks in the weld root zone of the bottom flange were observed (Type 1b).

Figure 7: Typical moment frame connection damage observed in the ten-story building.

Analytical Study

In order to study the behavior of the ten-story building during the Northridge Earthquake and to

get a better understanding of what the frame beams and columns went through during the event,

a series of modal analyses for mode shapes and frequencies, linear modal time-history, and

nonlinear direct integration time-history analyses is performed on a two dimensional model using

SAP 2000. The 10-story building is almost symmetrical in both North-South and East-West

directions. Lateral load-resisting system in each direction consists of four steel moment frames.

The two selected moment frames for this study, are part of the lateral system in East-West

direction which in fact is the longitudinal direction of the building. These two frames together

are assumed to approximately support half of the total seismic forces in East-West direction. As

a result, half of the building seismic mass was assigned to the model at each level. Also, in order

to make the two frames work together, weightless link elements with high axial stiffness were

used to connect the frames together and to represent axial stiffness of floor slabs. These members

had pinned connections at the ends.

Since the earthquake record plays a major role in the results of a time-history analysis, a

thorough investigation is performed to select the best available earthquake record for the

purposes of the current study which has been explained in details by Nastar (2008).

Study of the available earthquake records in the area using United States Geological Survey

(USGS), California Department of Mines and Geology (CDMG), University of Southern

California (USC), and Department of Water and Power (DWP) networks, indicates that the

closest usable record to the site was recorded at USC 03 station. This earthquake record is

selected to be used for time-history analyses explained later in this paper. USC 03 is located at

17645 Saticoy Street, Northridge, California, with a latitude and longitude of 34.209 and

-118.517 degrees, respectively. Figure 8 shows the record.

Base Acceleration (East)

-4

-3

-2

-1

0

1

2

3

0 10 20 30 40 50 60

Time (sec)

Ac

c.

(0.1

g)

Base Velocity (East)

-40

-30

-20

-10

0

10

20

30

0 10 20 30 40 50 60

Time (sec)

Ve

loc

ity

(c

m/s

ec

)

Base Displacement (East)

-10

-8

-6

-4

-2

0

2

4

6

8

0 10 20 30 40 50 60

Time (sec)

Dis

pla

ce

me

nt

(cm

)

Figure 8: Corrected acceleration, velocity, and displacement records in East direction, Northridge main

event recorded at USC 03 station.

Modal analysis for mode shapes and frequencies is performed and periods obtained from the

SAP building model for the first three modes are calculated to be 2.70, 1.07 and 0.63 seconds

using only the mass of the dead loads.

A series of linear modal time-history analyses is performed on the model. The main objective of

the linear modal time-history analysis is to plot the stress histories at the critical locations of the

frames as identified in Figure 6. In order to do that, it is necessary to have a reasonable degree of

confidence in the model and calibrate it by adjusting the values of damping and mass assigned

according to the behavior of the actual building. Time history responses obtained from the

computer model are compared with those recorded in the building. The calibration process

results in the value of 1% for damping for all modes. In addition, study of the assigned frame

masses indicates that the original masses (masses indicated in the original design documents),

which result in the first mode period of 2.7 seconds, seem to create the best match with the roof

response. Figure 9 shows the roof response recorded by CDMG.

Roof Accel. (CDMG Record)

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0 10 20 30 40 50 60

Time (sec)

Accel. (g

)

Roof Displ. (CDMG Record)

-15

-10

-5

0

5

10

15

0 10 20 30 40 50 60

Time (sec)

Dis

pl. (in

)

Figure 9: Roof acceleration and displacement (East) recorded by CDMG station.

It is shown that a moving-window Fourier analysis of the CDMG roof record indicates the first

mode period of 2.5 seconds. This shows reasonable agreement with first mode period of 2.7

seconds calculated from the model. Figure 10 shows the results of the moving-window Fourier

analysis. This indicates that the first mode period of the building did not change during the

Northridge event and as a result there have not been significant nonlinearities in the building

during the earthquake.

0

0.5

1

1.5

2

2.5

3

5 10 15 20 25 30 35 40 45 50

Time (sec)

Fir

st

Mo

de P

eri

od

(s

ec

)Figure 10: Moving-window Fourier analysis of the CDMG roof acceleration record (10-sec windows with

5-sec shifts).

This observation is well justified by studying the maximum stresses (M/S) at the investigated

beams and columns. This study has been performed on maximum stresses resulting from the

linear modal time-history analysis. As shown in Figure 11, the maximum stresses are not

significantly larger than the yield value. This combined with the fact that higher than yield

stresses happened in very few cycles (Figures 13 and 14), validates the use of the linear modal

time-history analysis. It is concluded that building nonlinearities have not been significant during

the Northridge Earthquake and use of the linear modal time-history analysis is adequate for the

purposes of this study. Low maximum demand to capacity ratios for the lateral seismic loads

resulting from the linear analysis as shown in Figure 12, also indicate that the behavior is

primarily linear-elastic and confirms the previous observations.

Beam Maximum Stress/Yield Stress

0

0.5

1

1.5

9th 8th 7th 6th 5th 4th 3rd 2nd

Floor

Max.

Str

ess/Y

ield

Str

ess

Column Maximum Stress/Yield Stress

0

0.5

1

1.5

9th 8th 7th 6th 5th 4th 3rd 2nd

Floor

Max.

Str

ess/Y

ield

Str

ess

Figure 11: Maximum stress (M/S from linear analysis) to yield ratio at the investigated beams and

columns.

A series of non-linear direct integration time-history analyses was performed on the same model

used for the linear modal time-history analysis. The purpose was to study the effect of

nonlinearities in the behavior of the frames. According to the original design documents, the

steel used in the structure was specified as A36 for the beams and A572 GR.50 for the columns

of the moment frames. Following the Northridge earthquake (1994), it was noted that the actual

yield stress of A36 steel is generally higher than the specified minimum of 36 ksi. Also, the

available mill test results indicate that the average values of the beam and column yield stress are

50 and 52 ksi respectively. The non-linear analysis as explained by Nastar (2008), studies the

effect of variation in yield stress of beams and columns and concludes that the response is not

sensitive to the yield stress used. Comparison between the results of the linear and non-linear

analyses confirms that the building behavior appears to be mainly linear-elastic.

Figure 12: Maximum demand to capacity ratios for the lateral seismic loads result of linear modal time-

history analysis.

Results

Stress histories in the investigated beams and columns on line 10 resulting from the time-history

analysis is shown in Figures 13 and 14 respectively. The stress values plotted are calculated by

dividing the moment at the end of each member (M) by the elastic section modulus (S). The

plotted stress histories for the beams at different floors indicate that the maximum beam stresses

are at or slightly above yield and do not show significantly higher stress values at the floors with

severe connection damage (5th

, 6th

, and 7th

floors). In other words, maximum stress values are not

high enough to justify the connection damages caused by the Northridge Earthquake and don’t

explain variation in damage over height of building. Similarly, the column stress histories do not

appear to justify the severe column damage observed at the 6th

floor. Similar to beams, it is

concluded that the maximum column stress values are not high enough to justify the connection

damages caused by the Northridge Earthquake.

Following the fatigue analysis procedures outlined previously, the rainflow method is used to

count the number of cycles that occurred at intervals of 5 ksi. Figures 15 and 16 illustrate the

rainflow histograms for the investigated beams and columns respectively.

-80

-60

-40

-20

0

20

40

60

80

0 10 20 30 40 50 60

Time (sec)

Str

es

s (

ks

i)9th

8th

7th

6th

5th

4th

3rd

2nd

Figure 13: Beam stress histories at different floors of frame D line 10.

-80

-60

-40

-20

0

20

40

60

80

0 10 20 30 40 50 60

Time (sec)

Str

es

s (

ks

i)

9th

8th

7th

6th

5th

4th

3rd

2nd

Figure 14: Column stress histories at different floors of frame D line 10.

Using the Palmgren-Miner equation, the cumulative fatigue damage is computed for the beams

and columns. Figure 17 shows the calculated cumulative fatigue at beams and columns. This

figure indicates that the beam at the 6th

floor has the highest cumulative fatigue of 0.41. It also

shows that 7th

floor column (column between 6th

and 7th

floors) has the highest cumulative

fatigue of 0.75. This observation appears to be in accordance with the most severe connection

damage observed at the 6th

floor. Due to effect of potential defects and principal stresses that are

not included this study, cumulative fatigue values of 0.41 and 0.75 are believed to be high

enough to be potentially considered the cause of observed damages. Here it can be seen that due

to the Northridge Earthquake the fatigue life of the 6th

floor beam has been reduced by about

41% and the fatigue life of the 7th

floors column (between 6th

and 7th

) has been reduced by about

75%. In other words, 41% and 75% of the fatigue life of these members have been theoretically

used by the Northridge Earthquake.

2nd floor 3rd floor

4th floor 5th floor

6th floor 7th floor

8th floor 9th floor

Figure 15: Rainflow histograms for investigated beams.

The analytical study described in this paper only considers the effect of one earthquake on the

fatigue life of the ten-story building elements. Since the cumulative fatigue created by past

events is remembered by the connection, it appears that low-cycle fatigue damage will be more

2nd floor 3rd floor

4th floor 5th floor

6th floor 7th floor

8th floor 9th floor

Figure 16: Rainflow histograms for investigated columns.

significant for the buildings that have experienced two or more earthquakes in their life. In other

words, the behavior of the building during an earthquake depends on the fatigue accumulated in

the elements from all the past major seismic events. This indicates the significance of the

cumulative fatigue values calculated earlier for beams and columns. Studies currently in progress

consider the effect of multiple earthquakes.

Cumulative Fatigue at Columns

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

9th Floor 8th Floor 7th Floor 6th Floor 5th Floor 4th Floor 3rd Floor 2nd Floor

Cu

mu

lati

ve F

ati

gu

e

Cumulative Fatigue at Beams

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

9th Floor 8th Floor 7th Floor 6th Floor 5th Floor 4th Floor 3rd Floor 2nd Floor

Cu

mu

lati

ve F

ati

gu

e

Figure 17: Cumulative fatigue at the investigated beams and columns.

It is noted that the cumulative fatigue at the column above, the column below, and the beam at

each joint can contribute directly to the connection damage. Figure 18 illustrates the sum of

cumulative fatigue values at the column above, the column below, and the beam at each

connection. It can be observed that the 5th

, 6th

, and 7th

floors have the highest cumulative fatigue

values in Figure 18. These floors are the floors that experienced significant connection damage

during the Northridge Earthquake. A closer look at Figure 18 indicates that the cumulative

fatigue distribution at the investigated connections match the observed damage during the

Northridge Earthquake. The damage indicator used in this comparison for quantifying the

connection damage in the ten-story building shows the number of damaged locations in the

beams and columns adjacent to the joints at each level in all the moment frames in the

investigated direction (East-West) of the building.

SUM of Cumulative Fatigue at Column Above, Column Below, and Beam at Each Floor

0.0

0.5

1.0

1.5

2.0

2.5

9th 8th 7th 6th 5th 4th 3rd 2nd

SU

M o

f C

um

ula

tive

Fa

tig

ue V

alu

es

-80

-60

-40

-20

0

20

40

Dam

ag

e I

nd

icato

r

SUM of Cumulative Fatigue Values Connection Damage Indicator

Figure 18: Comparison between cumulative fatigue distribution and connection damage observed during

the Northridge Earthquake.

Conclusions

Investigations of the damage pattern in the ten-story building indicate that the cumulative fatigue

distribution at the investigated connections reasonably match the observed damage during the

Northridge Earthquake. They also clarify that stress histories at the investigated beams and

columns do not show stress values significantly higher than yield and as a result do not justify

the observed connection failures. The results of this study show that low-cycle fatigue can have a

significant effect on the damage potential to certain steel buildings located in active seismic

regions. Applying the developed fatigue analysis procedure to any similar instrumented steel

building located in active seismic region indicates that even a moderate earthquake ground

motion may cause a significant reduction in the fatigue life without any indication of serious

damage. It also offers a means of identifying the condition of buildings that have experienced a

limited number of earthquake ground motions with little or no visible damage.

The general conclusions of the current study on the ten-story building can be summarized as

follows:

1. Beam and column stress histories resulting from the linear time-history analysis do not

indicate the occurrence of stress values significantly higher than yield. Additionally, yield

and slightly above yield stress levels occur only in a few cycles and as a result do not

justify the observed connection failures. This conclusion is also confirmed by the low

values of demand to capacity ratio in the structure.

2. Low-cycle fatigue is significant at all the investigated members. As expected, high-cycle

fatigue was not important during the Northridge Earthquake.

3. Cumulative fatigue distribution at the investigated beams and columns reasonably

matches the observed damage during the Northridge Earthquake.

4. This study shows that the following wording from the “AISC Steel Construction

Manual”, appears to be incorrect for the steel buildings similar to the investigated ten-

story building:

“Fatigue shall be considered in accordance with Appendix 3, Design for Fatigue, for

members and their connections subject to repeated loading. Fatigue need not be

considered for seismic effects or for the effects of wind loading on normal building

lateral load resisting systems and building enclosure components.”

On the contrary, fatigue may play a major role in the behavior of structures during

seismic events and needs to be further investigated and carefully considered in the

seismic design of certain structures. The result of the current research emphasizes that

low-cycle fatigue may be the cause of connection damage in the investigated building

similar to that observed during the Northridge Earthquake.

5. As described earlier, low damping and vertical irregularity (set-back) are the

characteristics of the investigated ten-story building which contributed to the results. It

appears that other steel buildings having these characteristics might need some additional

analyses. Anderson et al. (2009) describes the results of a similar study on a sixteen-story

building with these characteristics.

6. The low damping may be important in the results of this study. One way to improve this

is to include supplemental damping.

7. Response data does not support the existence of plastic hinges at failure locations.

Recorded data and calculations indicate pre-dominate elastic response. Hence, fatigue

(low-cycle) must be significant in explaining the overall behavior (damage).

8. This study does not directly include the effect of defects in the connection life cycle. The

tests used to develop S-N curves in the low-cycle region are mostly comprised of

specimens that are built at the fabrication shops with higher quality control measures.

Considering the defects due to variations in construction quality specifically in regards to

field welding can significantly reduce the fatigue life cycle (Nj) of the Pre-Northridge

connection which will result in higher cumulative fatigue values.

9. The building used in this study has experienced only one earthquake. Since the

cumulative fatigue created by past events is remembered by the connection, it appears

that low-cycle fatigue damage will be more significant for the buildings that have

experienced two or more earthquakes in their life. In other words, the behavior of the

building during an earthquake depends on the fatigue accumulated in the connections

from all the past major seismic events. Studies currently in progress consider the effect of

multiple earthquakes.

10. The results of earlier studies (Nastar, 2008) indicate that the contribution of higher modes

significantly affects the results. The effects of the cycles experienced by the frame

caused by all modes of vibration are captured in the analysis presented.

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