Retrofitting Steel Joist Supported Footbridges for Improved

Vibration Response

Onur Avci, Ph.D., P.E., M.ASCE1

1Structural Project Engineer, AECOM, Specialty Practices Group, 20 Exchange

Place, 12th

Floor, New York, NY, 10005, USA. Email: onur.avci@aecom.com

ABSTRACT

The main objective of this paper is to determine the possible increase in natural

frequencies of the two joist supported laboratory footbridges when bottom chord

extensions are installed in an attempt to reduce annoying floor vibrations. The results

with bottom chord extensions installed after the concrete placement are compared to

results when the bottom chord extensions are installed prior to concrete placement.

Results from the static and dynamic tests on the single span footbridge indicate that

installing the bottom chord extensions to the joists after concrete placement and with

the center of the span jacked up increases the flexural stiffness and fundamental

natural frequency considerably, but not as much as installing the bottom chord

extensions before the concrete placement. For the three span footbridge, installing

the bottom chord extensions also increases the flexural stiffness and fundamental

natural frequency considerably, but there is no distinctive advantage of installing the

bottom chord extensions before the concrete placement. For both of the footbridges,

the magnitude of the increases in natural frequencies is sufficient to consider the

installation of bottom chord extensions as a remedy to stiffen (and retrofit) a floor and

reduce floor vibrations due to occupancy movements.

INTRODUCTION

Strength and deflections were the two common limit states being considered for the

design of steel framed floor systems. With the use of high strength steel, lighter

sections and low inherent damping, floor vibration serviceability has become a

governing factor for the design of steel framed floor systems. In the presence of

annoying floor vibrations in joist supported floor systems, sometimes bottom chord

extensions are installed in an attempt to stiffen the floor system and correct the

annoying vibrations problem by increasing the fundamental natural frequency.

However, the effect of bottom chord extensions on the joist behavior is not very well

known. There have been recommendations on strengthening the bottom chord

elements (Fisher 2005, Broekemeier and Fisher 2007); however, the writer was

unable to find any published document on extending joist bottom chords in an attempt

to improve floor stiffness, which in turn will improve the vibration response. The

study presented in this paper focuses on the effect of bottom chord extensions on the

fundamental frequency of two laboratory footbridges. Experimental and analytical

studies were conducted on single span and three span joist supported laboratory

footbridges with different bottom chord extension (BCE) configurations. Three

dimensional finite element computer models were created to simulate and compare

the results of stiffness and dynamic tests with the philosophy of testing the

footbridges and updating the finite element models, trying to minimize the

discrepancies between the test results and the FE model for better behavior prediction.

TEST SETUPS

A single span footbridge (Figure 1) and a three span footbridge (Figure 2) were

constructed at the Thomas M. Murray Structural Engineering Laboratory, Virginia

Tech, Blacksburg, Virginia. The single span footbridge of dimensions 2.13 m by 9.14

m (7 ft by 30 ft) was built inside the laboratory, while the three span footbridge 2.13

m by 27.43 m (7 ft by 90 ft) was built outside. Both of the footbridges were

constructed using 1.5VL Vulcraft deck with depth of 38 mm (1.5 in.) and a normal

weight concrete slab with a depth of 114 mm (4.5 in.); with a total slab depth of 152

mm (6.0 in.) supported on two parallel lines of 30K7 x 9.14 m (30 ft) span Vulcraft

joists at 1.22 m (4 ft) on center. Elco Grade 8 Stand-off screws with 102 mm (4 in.)

of stand-off and spaced at 305 mm (12 in.) on center were used to connect the cold-

formed steel decks to the joist top chords before the concrete was placed. The 28-day

concrete compressive strengths are 29.8 MPa (4320 psi) for the single span footbridge

and 34.2 MPa (4960 psi) for the three span footbridge.

Fig. 1. Single Span Footbridge, 2.13 m by 9.14 m (7 ft x 30 ft)

Fig. 2. Three Span Footbridge, 2.13 m by 3 @ 9.14 m (7 ft x 3 @ 30 ft)

Concrete walls were used as supports for the single span footbridge and exterior

supports for the three span footbridge. Built-up steel H-cross sections were used for

interior supports for the three span footbridge (Figure 3). The joist seats were welded

to the bearing plates located on the concrete walls at exterior supports. At the interior

supports, the two top chords were welded to each other using a steel bar to provide

top chord continuity. The joist seats at the interior supports were also welded to the

continuity plates located on the built-up sections. Bottom chord continuity was

provided by HSS 38 mm x 38 mm x 4.8 mm (1.5 in. x 1.5 in. x 3/16 in.) bottom chord

extensions. The BCE’s were instrumented as load cells so that the axial force in the

member could be monitored and recorded (Figure 4). Two of the four BCE’s of the

single span footbridge (S1 and S2 in Figure 5) and all twelve BCE’s of the three span

footbridge (Figure 6) were instrumented as load cells. For the three span footbridge,

the exterior BCE’s were connected to the concrete walls of the two exterior supports

(Extensions N1, S1, N6 and S6 in Figure 6). Interior BCE’s were connected to the

interior supports (Extensions N2, S2, N3, S3, N4, S4, N5 and S5 in Figure 6).

Exterior Support

Interior Support

Interior Support

Fig. 3. Three Span Footbridge Supports

(a) At Exterior Support (b) At Interior Support

Fig. 4. Bottom Chord Extensions

Note: 1 ft = 0.305 m

Fig. 5. Bottom Chord Extension Locations- Single Span Footbridge

Note: 1 ft = 0.305 m

Fig. 6 Bottom Chord Extension Locations- Three Span Footbridge

In the experimental program, static flexural stiffness tests were conducted first to

understand the flexural stiffness behavior of the footbridges. Both single span and

three span footbridges were tested with different BCE configurations (Figures 7 and

8). The three stages of the single span footbridge and the five stages of the three span

footbridge construction are the BCE configurations needed to determine the relative

effect of installing BCE’s after the concrete is placed.

a) Stage 1: Bottom Chord Extensions In Place

b) Stage 2: Bottom Chord Extensions Removed

c) Stage 3: Bottom Chord Extensions Re-installed

Fig. 7. Bottom Chord Extension Configurations for Single Span Footbridge

a) Stage 1: All Bottom Chord Extensions In Place

b) Stage 2: Exterior Bottom Chord Extensions Removed

c) Stage 3: All Bottom Chord Extensions Removed

d) Stage 4: Interior Bottom Chord Extensions Re-installed

e) Stage 5: All Bottom Chord Extensions Re-installed

Fig. 8. Bottom Chord Extension Configurations for Three Span Footbridge

Static flexural stiffness test protocol, finite element modeling technique and stiffness

test results are shown in detail by Avci (2005) and Avci and Murray (2011); therefore

will not be repeated here in this paper.

MODAL TESTING

The objective of vibration testing conducted in this study was to experimentally

determine the natural frequencies, modal damping ratios, and the corresponding mode

shapes of the laboratory footbridges and to determine the effect of BCE’s for each

configuration. For that purpose, chirp, sinusoidal, heel drop and walking excitations

were applied on the footbridges, while the acceleration response of the footbridges

was measured. A shaker placed on a force plate was used to generate and measure

the chirp and sinusoidal excitations. Heel drops were conducted on a force plate as

well. For all excitations, frequency response functions (FRF) were measured and

recorded. The collected FRF data was input and curve fitted in the ME’ScopeVES

software (Vibrant Technology, Inc. 2003) and natural frequencies, modal damping

ratios, and the corresponding mode shapes were approximated per the input data.

Single Span Laboratory Footbridge

The shaker and force plate assembly was placed at the inside and outside quarter

points on the single span footbridge, and chirp signals were used to sweep a

frequency range of 4-20 Hz for the three BCE configurations. The first bending

frequency was the main interest since it is in the range of human sensitivity for the

single span footbridge. Acceleration response data was collected at the points shown

in Figure 9. The first bending mode shape of the SAP2000 FE model and curve fitted

ME’ScopeVES model are shown in Figure 10. The FRF plots at the drive point are

shown in Figure 11(a) while the results of the accelerometer placed at the footbridge

center are displayed in Figure 11(b).

Fig. 9. Accelerometer Locations – Single span Footbridge

a) SAP2000 b) ME’ScopeVES

Fig. 10. First Bending Mode Shape – Single span Footbridge

Stage 1

Stage 3

Stage 2Stage 1

Stage 3

Stage 2

a) Accelerometer at Outside Quarter Point b) Accelerometer at Center Point

Fig. 11. Chirp FRF’s for Quarter Point Excitation - Single Span Footbridge

ME’ScopeVES approximated natural frequency and modal damping ratios are shown

in Table 1.

Table 1. Natural Frequencies and Damping Ratios for Single Span Footbridge

FE Model

fn (Hz)

Modal

Damping

Ratio (%)

fn (Hz)

Stage 1 8.08 0.451 7.99

Stage 2 6.95 0.448 7.03

Stage 3 7.65 0.409 7.99

MEScope Results

It is shown that removing the BCE’s from the system (Stage 2) resulted in a 14% drop

(8.08 Hz to 6.95 Hz) in the natural frequency of the footbridge. Re-installing the

BCE’s after jacking up the footbridge (Stage 3) increased the natural frequency of

Stage 2 configuration about 10% (6.95 Hz to 7.65 Hz). Note that the Stage 3 (retrofit)

natural frequency (7.65 Hz) is slightly less than the as-built condition (Stage 1) of

8.08 Hz. Both Stage 1 (as-built) and Stage 3 (retrofit) natural frequencies are higher

than the Stage 2 natural frequency which means the BCE’s do stiffen the footbridges.

As the floor systems with higher natural frequencies would be less vulnerable to

annoying vibrations, the magnitude of increase in natural frequencies of the single

span footbridge is sufficient to consider the installation of BCE’s as a remedy to

stiffen the footbridge and reduce vibrations.

The FE model natural frequency predictions are also shown in Table 1. It is noted

that the curve fitted ME’ScopeVES and FE model frequency predictions are within

1% with each other for Stages 1 and 2, while the FE model natural frequency is 4%

higher than the ME’ScopeVES predictions for Stage 3. It is also observed from Table

1 that there is not any consistent effect of BCE’s on modal damping ratios.

Three Span Laboratory Footbridge

The excitation forces applied to the single span footbridge were repeated for the three

span footbridge. The shaker and force plate assembly were placed at several

locations in the three spans. Acceleration response data was collected at the 75 points

shown in Figure 12. The first three bending modes were the main concern since they

were in the range of human sensitivity for the three span footbridge. The torsional

modes did not play an important role in the acceleration response. The first three

bending modes were determined using the SAP2000 FE model and curve fitted

ME’ScopeVES model as shown in Figure 13 (SAP2000 mode shapes on the first row

and ME’ScopeVES mode shapes on the second row).

Fig. 12. Accelerometer Locations- Three Span Footbridge

a) Mode 1 b) Mode 2 c) Mode 3

Fig. 13. Bending Modes - Three Span Footbridge

The chirp FRF results for central Bay 2 and central Bay 3 excitation points are shown

in Figures 14, 15 and 16. In each figure, the FRF magnitudes are at the drive points

since they have the best coherence values consistently for all measurements.

The results of the central Bay 2 chirp excitations are shown in Figure 14. For this

excitation location it was not possible to excite the second bending mode since the

shaker location is at the node point. Thus, the peaks in Figure 14 are the peaks of

bending modes 1 and 3. The results of the central Bay 3 chirp excitations are shown

in Figures 15 and 16. At this excitation location it was possible to excite all the first

three bending modes. Results of the first two modes are shown in Figure 15 with

third mode results shown in Figure 16.

Stage 1

Stage 5

Stage 3

Stage 3

Stage 2Stage 2 Stage 1

Stage 4

Stage 5

Stage 4

Figure 14 Chirp FRF’s for Bay 2 Central Point Excitation- First and Third

Bending Modes- Three Span Footbridge

Stage 1

Stage 5

Stage 3

Stage 3

Stage 2

Stage 2Stage 1

Stage 4

Stage 5

Stage 4

Figure 15 Chirp FRF’s for Bay3 Central Point Excitation- First and Second

Bending Modes- Three Span Footbridge

Stage 3

Stage 2

Stage 1

Stage 4

Stage 5

Figure 16 Chirp FRF’s for Bay3 Central Point Excitation- Third Bending

Mode- Three Span Footbridge

The collected FRF data for the three span footbridge was also input and curve fitted

in the ME’ScopeVES software. The approximated natural frequency and modal

damping ratios are shown in Table 2.

Table 2. Bending Mode Natural Frequencies and Damping Ratios for Three

Span Footbridge

FE Model FE Model FE Model

fn (Hz)

Modal

Damping

Ratio (%)

fn (Hz) fn (Hz)

Modal

Damping

Ratio (%)

fn (Hz) fn (Hz)

Modal

Damping

Ratio (%)

fn (Hz)

Stage 1 7.76 0.265 7.76 8.11 0.255 7.88 8.93 0.332 9.76

Stage 2 7.51 0.272 7.49 7.90 0.361 8.10 8.81 0.539 9.63

Stage 3 7.49 0.281 7.49 7.81 0.402 7.78 8.37 0.213 8.70

Stage 4 7.60 0.273 7.49 8.14 1.440 8.10 8.78 0.203 9.63

Stage 5 7.80 0.178 7.76 8.13 0.235 7.88 8.89 0.571 9.76

First Bending Mode Second Bending Mode Third Bending Mode

MEScope Results MEScope Results MEScope Results

It is shown in Table 2 that the first bending natural frequency of Stage 1 (7.76 Hz)

decreased to 7.51 Hz (3% drop) when the exterior BCE’s were removed from the

system (Stage 2). The second bending natural frequency of Stage 1 (8.11 Hz)

decreased to 7.90 Hz (again about a 3% drop) when the exterior BCE’s were removed

from the system (Stage 2). Also, the third bending natural frequency of Stage 1 (8.93

Hz) decreased to 8.81 Hz (a drop of less than 2%) when the exterior BCE’s were

removed from the system (Stage 2). Removing the interior BCE’s (Stage 3) did not

affect the first bending mode frequency (a slight change from 7.51 Hz to 7.49 Hz);

however, it decreased the second bending mode frequency from 7.90 Hz to 7.81 Hz

(about 1% drop), it also decreased the third bending mode frequency from 8.81 Hz to

8.37 Hz (5% drop). Re-installing the interior BCE’s (Stage 4) increased the first

bending mode natural frequency from 7.49 Hz to 7.60 Hz (about 1.5% increase), the

second bending mode frequency from 7.81 Hz to 8.14 Hz (4% increase) and the third

bending mode natural frequency from 8.37 Hz to 8.78 Hz (5% increase). Re-

installing the exterior BCE’s (Stage 5) increased the first bending mode natural

frequency from 7.60 Hz to 7.80 Hz (about 3 % increase) and the third bending mode

natural frequency from 8.78 Hz to 8.89 Hz (1% increase). The second bending mode

remained almost the same (a slight change from 8.14 Hz to 8.13 Hz).

The trend in Table 2 is very similar to the one in Table 1. The presence of BCE’s is

stiffening both of the footbridges. Like the single span footbridge, the magnitude of

increase in natural frequencies of the three span footbridge bending modes is

sufficient to consider the installation of BCE’s as a remedy to stiffen the footbridge

and reduce vibrations.

The FE model natural frequency predictions are also shown in Table 2. The curve

fitted ME’ScopeVES and FE model frequency predictions are within 1% of each

other for the first bending mode and 3% for the second bending mode for all stages.

For the third bending mode, the FE model predictions are 4-to-10% higher than the

ME’ScopeVES natural frequencies. It is also observed from Table 2 that there is not

any consistent effect of BCE’s on modal damping ratios.

CONCLUSIONS

The goal of this paper was to determine the possible increase in natural frequencies of

the joist supported footbridges when bottom chord extensions are installed in an

attempt to reduce annoying floor vibrations. Extensive analytical and experimental

studies are performed on two laboratory footbridges with different bottom chord

extension configurations. Results from static stiffness testing and modal testing on

both of the footbridges indicate that installing the bottom chord extensions to the

joists increases the flexural joist stiffness and fundamental natural frequency

considerably. The magnitude of the increases in natural frequencies is sufficient to

consider the installation of bottom chord extensions as a remedy to stiffen (and

retrofit) the footbridges and reduce annoying vibrations.

REFERENCES

Avci, O. (2005). “Effects of Bottom Chord Extensions on the Static and Dynamic

Performance of Steel Joist Supported Floors", Ph.D. Dissertation, Virginia

Polytechnic Institute and State University, Blacksburg, Virginia.

Avci, O. and Murray, T. M. (2011), "Effect of Bottom Chord Extensions on the Static

Flexural Stiffness of Open-Web Steel Joists", Journal of Performance of Constructed

Facilities, ASCE , doi:10.1061/(ASCE) CF.1943-5509.0000262

Broekemeier, M. W. and Fisher, J.M. (2007). Evaluation and Modification of Open-

Web Steel Joists and Joist Girders, North American Steel Construction Conference,

NASCC 2007 Proceedings, New Orleans, LA.

Computers and Structures, Inc. (2003). "SAP2000 - Linear and Nonlinear Static and

Dynamic Analysis and Design of Three-Dimensional Structures", Berkeley,

California.

Fisher, J.M. (2005). Strengthening Open-Web Steel Joists, Engineering Journal,

Fourth Quarter, pp 247-259.

Vibrant Technology, Inc. (2003). "ME’ScopeVES 4.0", Scotts Valley, California.