T3B1 Static and Dynamic Behavior of a Pultruded FRP Truss

STATIC AND DYNAMIC BEHAVIOR OF A PULTRUDED FRP TRUSS FOOTBRIDGE

T. Kumada1, Seishi Yamada2, E. Johansen3 and R. Wilson3 1 Hirose & Co. Ltd., Japan

2 Dept of Architecture and Civil Engrg, Toyohashi University of Technology, Japan 3 E.T. Techtonics Inc., USA

ABSTRACT For a last decade, long-lived FRP materials have been used in bridges in the world but very few applications were in Japan. The reason would be mainly the lack of practical data of real, large-scale bridges for structural design engineers and bridge owners. In this study, the static and dynamic experiments of pultruded FRP truss footbridge system has been performed. The adopted specimen is of a pony truss type footbridge with bolted joints and its length and width are 18.223m and 2.0m, respectively. The bridge slab was statically loaded using water tanks. The ratio of the center deflection to the span was 1/610 at a static 3.5 kN/m2 loading level and it has been suggested that the present FRP footbridge system has very high rigidity for static loading. On the other hand, various dynamic loading tests were also performed; jumping, running, repeated stepping by pedestrians or horizontally impact force was subjected to the specimen. Consequently, the acceleration responses in all the loading cases have been shown to be relatively small due to high damping system rather than steel bridges. The first natural frequency was 3.7 Hz for the mode having a mixed torsion and sway mode and the second was 6.4 Hz for the mode having a vertical vibration mode. The present paper suggests that the adopted pultruded FRP truss bridge system has good performances for the practical use of pedestrians. KEYWORDS FRP, truss footbridge, large scale experiment, deflection, natural frequency, damping coefficient. INTRODUCTION The glass FRP (fiber reinforced polymer) materials have a good comparison with steel because of the lightweight, high strength per weight and high durability under the corrosive environment. From these aspects, the FRP materials increase gradually to be applied to the main structure members of bridges. In the early 1990s, FRP bridges started to be constructed in the Europe and the US, however, the first Japanese FRP bridge located at the Ikei-Tairagawa road park in Okinawa Prefecture, was constructed in 2000. After that, an application of the FRP materials to the bridge did not expand. In 2008, two FRP footbridges were constructed on Hakui City in Ishikawa Prefecture, and on Takayama City in Gifu Prefecture. The context of these applications includes that the simple implementation of the update and the repair becomes urgent works. In Japan there are now many old bridges whose age exceeds 50 years; therefore the expectations of the FRP bridges are now rising. However, there have been very few applications in Japan. The reason would be mainly the lack of practical data for real, large-scale bridges and structural designers or bridge administrators hesitate to adopt FRP. In this study for the pultruded FRP truss footbridge system originally developed in 1996 in the US, the static and dynamic experiments using an around eighteen meter span specimen have been carried out and the various useful practical data for this large scale model have been in comparison to the permissible quantities of Japanese conventional guidelines for steel bridges. OVERVIEW OF EXPERIMENTAL FOOTBRIDGE Design of Footbridge The structure type of this experimental footbridge is the lattice type half-through truss structure as shown in Figure 1. Each member was connected by the bearing-type bolt connection. There are the double splice joints at bottom-chord and top-chord members. All the truss members were of pultruded glass FRP using the unsaturated-polyester. The design specification of this footbridge is shown in Table 1. The bridge length is 18.223 m (60ft),

355

the span 17.805 m and the width 2.0 m. A design criterion of this footbridge was adopted to be based upon the Japanese Technical Standard for Pedestrian Crossing Bridges (1979). A cross section profile is shown in Figure 2; the FRP decks were connected with the bolt to bottom chords and stringers and FRP hand rails (channel section 76x22x6 mm) were installed for the falling prevention to the vertical posts in 0.2 m interval of each rail. It is noted in the above technical standard that the serviceability limiting value of the deflection during the live load must be not exceed 1/600 of a span length. However, this limitation may reduce to 1/400 when the matter of vibration is specifically considered. Therefore, the deflection limiting value in this specimen was adopted 1/400 under the confirmation that the lowest natural frequency is over 2.4 Hz. The above standard specifies that the frequency (1.5 - 2.3 Hz), which gives pedestrians an unpleasant feeling, must be avoided. The safety factors were determined referring to the recommendation of US pultrusion companies, and are generally accepted by the structural engineering community in US. The safety factors for beam strength and Young's modules were adopted as 2.5 and 1.0, respectively. The structural analysis has been used three-dimensional frame analysis program (STAAD ver.2004). The maximum deflections for the dead load and the live load were computed to be 9.1 mm and 43.4 mm, respectively; these satisfy the limitation (1/400). In addition, the natural frequencies were computed to be 6.6 Hz and 5.1 Hz for vertical and horizontal directions, respectively; these were higher than the lower bound limit value 2.4 Hz published in the Standard 1979.

Figure 1. Side elevation Table 1. Design specification Figure 2. Cross section Member Properties Table 2. Material properties The channel members C205 was used for bottom and top chords, top caps, and stringers; the channel members C150 for crossbeams, and the pipe members SP50 for horizontal braces and vertical posts. The mechanical properties of these pultrusion materials listed in Table 2 are from the catalogue specification of the pultrusion company and from the present new coupon testing. The present material tests have been performed based on the JIS K 7054 (Testing Method for Tensile Properties of Glass Fiber Reinforced Plastics). Three specimens for each series were prepared; however, some collapses were of the pulling-out mode at tab section. Therefore, the minimum tensile strength values obtained through the present tests are listed in Table 2. The elastic tensile modulus was calculated from the inclination of the stress-strain relation based upon the difference of strain between 0.0005 and 0.0025; each average for present test results is listed in Table 2. The tensile modulus of coupon tests was not used in the present design; the adopted modulus, 19.2 GPa, has been commercially provided from the pultrusion companies.

Movable End

18,288 mm (60 ft)

(South Side)

Fixed End

(North Side)

No.1No.2No.3No.4No.5No.6

No.7

Splice Section

Tensile Mem.

Top Chord(Splice Sec.)

Compre

ssive

Mem

.

Bottom Chord(Splice Sec.)

: Strain Gauges: Survey Points

Top Chord(Center Sec.)

Bottom Chord(Center Sec.)

17,805 mm

(+)

(-)

CH1 CH3CH2 CH4

z

y

(East Side)(West Side)

(+)

(-)

(+) (+)(-)

: Acceleration Meter (Vertical): Acceleration Meter (Horizontal)

(-)

3,505 mm

Vertical Posts Handrails

FRP DeckingStringerBottom Chords

Bridge Length (Girder Length) 18.288m (60 ft)

Span 17.805m (58 ft 5 in) Width 2m (6 ft 7 in)

Live Loads (Pedestrian Live Loads)

5.0kN/m2 (Supporting Floor Systems) 3.5kN/m2 (Main Supporting Members)

Seismic Loads Horizontal Seismic Coefficient kH=0.25 Lateral Force= kH x(Dead Loads+1.0kN/m2)

Wind Loads Windwaed 2.0kN/m2 Leeward 1.0kN/m2

Snow Loads Live Loads + 1.0 kN/m2 Temperature Loads 24 deg.C (75 deg.F)

Deflection 1/400 of the span Vibration 2.4Hz Greater

Items C205 C150 SP50

Dimension (mm)

Catalogue Data 228 228 228 Tensile Strength （MPa） Test Results 283 Exceed 325 351 Exceed

Catalogue Data 17.2 17.2 17.2 Tensile Modulus （GPa） Test Results 20.4 23.9 30.8

203

56

10

152

43

1051

51 6

356

Figure 3. View of water tanks at 100%

STATIC TESTING Static vertical uniform-loading 3.5 kN/m2 was loaded as the equivalent design live load. Twenty water tanks for uniform loading were set-up on the entire of FRP decking. Each tank has the length 1.844m, the width 0.91 m and the height 0.91m and consists of wooden boards and a polyethylene sheet. Water was stored into these tanks for loading and was drained from tanks for unloading. The measurement was executed at five steps, 25% (0.875 kN/m2), 50% (1.75 kN/m2), 75% (2.625 kN/m2), 100% (3.5 kN/m2) and 100% (the 2nd) of the maximum load (3.5 kN/m2). The view of water tanks at the 100% load step is shown in Figure 3. The water depth of each water tank controlled the loaded weight. The total weight of water tanks was 5.52 kN, though it was not included in the loaded weight; the initial loading condition was set on the state after installing all the water tanks on the deck. In the second lording 100%, at unloading step, the deflections were measured after removing all the water tanks; therefore, the apparent negative load occurred. In the loading procedure, water was stored from the center to the end of the bridge; water was drained from the end of the bridge to center at unloading. Concerning the measurement, the deflection of the bottom chord was measured by the levels. The measurement points shown in Figure 1, was No.1 to No.7 in interval 3 m of the longitudinal direction. The benchmark of deflection was selected as that of No.1 in the west side of the fixed-end. The vertical deflection was adopted to be positive in the upward direction; therefore, deflection is expressed at the negative value. Strain gauges were pasted at each side (east side and west side) of top chords and bottom chords, of the center of beam and nearest splice section (Figure 1). The locations of the strain gauges were at surface and backside of the top chord and bottom chord. And concerning the diagonal member, the strain gauges were attached at top face and bottom face. RESULTS OF STATIC TESTING The measured vertical deflection curves along the bottom chords after applying the 100% loading are shown in Figure 4. These deflection values are the displacements at the 100% load step from the datum values which were measured

after removing all the water tanks, the displacements are shown to be approximately equal between in east side and in west side. The design displacement for the live load was calculated 43.4 mm at the bridge center; the measured displacements were 31 mm in the east side, and 29 mm in the west side, and they are smaller than the design displacement. This means that the experimental footbridge is stiffer than the design model. At design, the attached members (FRP decks and rails) are not considered to be structural members.

The relations between the displacement and the vertical loads at the midpoint of the bottom chord, are shown in Figure 5. Before applying 25% loading, preliminary loading (3.5 kN/m2) was subjected to 4.5m area of the centre of bridge span, then some residual deformation occurred. After installation of the experimental footbridge, the camber height of the bottom chords was 45 mm. After the testing, the camber heights of bottom chord at east side and west side decreased to be 11mm and 16mm, respectively. It means that the residual displacement occurred around 30 mm. As load steps proceed, the residual

?0 ?0 ?0 0 10 20 30 40 50

0

1.75

3.5 Bottom Chord (West Side) No.4

Surc

harg

e q　

(kN

/m2 )

Displacement (mm)

Loading

Unloading

29mm

?0 ?0 ?0 0 10 20 30 40 50

0

1.75

3.5 Bottom Chord(East Side) 　No.4

Sur

char

ge q　

(kN

/m2 )

Displacement　(mm)

Loading

Unloading

31mm

Figure 4. Deflection along the bottom chord member

Notice Points Design Stress (MPa)

Design Strain (x 10-6)

Splice Section -10.2 -531 Top Chord Center Section -12.4 -646 Splice Section 14.6 760 Bottom Chord Center Section 17.6 917

Tensile Member 19.6 1021 Diagonal member Compressive Member -28.2 470

Table 3. Analytical stress and strain on design calculation

(a) Chord of west side (b) Chord of east side Figure 5. Vertical loads versus displacement

18.288 15.240 12.192 9.144 6.096 3.048 0.000

?0

?0

?0

0

Survey Point　(m)Movable EndNo.2No.3No.4No.5No.6

Fixed End

Def

lect

ion　

(mm

)

Bottom Chord(West)

Bottom Chord(East)31mm

29mm

No.1No.7

357

displacement increased. At the 100 % loading step, FRP member stresses were still within elasticity limits, so that the cause of the residual displacement was supposed to be the slip of bolt joints. Almost the same manner of the residual displacements was shown in the first and the second 100% loading steps; it would be possible to be pointed out that the slip of bolt joints occurs hardly when the same maximum load has been experienced once. Therefore, the displacement due to slip of the bolt joint at erection, needs to be considered in design.

In this experimental footbridge, there are two splice sections along the bridge axis. It has to be considered that the about 15 mm residual displacement per splice joint. Analytical stress and strain on design calculation at 100% loading step are shown in Table 3. In calculation, Young's modulus for the compressive diagonal members and the other members were adopted as 60 GPa and 19.2 GPa, respectively. The designed stress is very small compared with FRP material strength. In case of the FRP footbridge design, the deflection criteria of chord members are generally serious rather than those of the material strength. The measurement of strain gauges near a splice joint section and the center of the chord, in each load phase, are shown in Figure 6. The strain data indicate the average of measurement. The strain gauges were pasted to the surface and backside of members. It is shown that the relation between the strain and the load is roughly linear. In the design calculation, the stress of the top-chord is smaller than the stress of the bottom chord. However, the measurement result is not clearly different between the top-chord and the bottom chord. In addition, the calculated strain is larger than the measurement strain. It means that the stiffness of the experimental footbridge was higher than the analytical model. The measured strain data of the diagonal members in each load phase are shown in Figure 7. The axial and bending stress were calculated from the measured data. The strain gauges were pasted at top face and bottom face of the member. The axis stress increases as the load increases. The bending stress of the compressive diagonal member did not increase, on the other hand, the bending stress of the tensile member increased. Each compressive and tensile member is crossed at the center of member, so the associated deflection is restrained. Therefore, the bending stress of the tensile member whose flexural rigidity was very small, occurred negligibly. (a) Splice section (b) Center section Figure 7. Axial strain and bending Figure 6. Axial strains versus vertical loads strain in a diagonal member DYNAMIC TESTING In the dynamic experiment, vertical and horizontal direction accelerometers were installed on the location No.4 of Figure 1. The accelerometers were pasted on the top flange surface of both sides of the center of bottom chords. As shown in Figure 2, concerning vertical accelerometers of CH1 and CH3, positive acceleration indicate upper direction. And concerning horizontal accelerometers of CH2 and CH4, positive acceleration indicate east direction. Sampling interval is 0.002 seconds and whole measurement time is 30 seconds. The experimental cases are four kinds of seven cases as listed in Table 4. Each case was attempted three times. In the impact excitation experiment of CASE 1 to 3, a man whose weight was approximately 800N, jumped once on the FRP decking to charge excitation force. After getting down the decking floor, the man kept a resting state until the end of measurement to avoid the influence of the free-oscillation. These three cases of an experiment were practiced at the different impacted point, which was at the center, the west side and the east side,

Table 4. Experimental cases in dynamic testing Load

Cases Excitation Methods

Excitation Force

Excitation Direction Excitation Points

CASE 1 Shock by Jumping

Experimenter (0.8kN) Vertical Bridge Axis: Center

Width Direction: Center


Experimenter (0.8kN) Vertical Bridge Axis: Center

Width Direction: West


Experimenter (0.8 kN) Vertical Bridge Axis: Center

Width Direction: East

CASE 4 Random Vibration

by Running

Experimenter (0.55 kN) - Bridge Axis: From North to South

Width Direction: Zigzag

CASE 5 Sympathetic

Vibration by Stepping

Experimenters (3.5 kN) Vertical Bridge Axis: Center

Width Direction: overall width

CASE 6 Shock by Hit

Hit by Timber

Rod Lateral

Bridge Axis: Center Width Direction:

Crossbeam (West Side) 1 spot

CASE 7 Thrust

by Manpower

Push by 3 People Lateral

Bridge Axis: Center Width Direction:

Crossbeam (West Side) 3 spots

0 1.75 3.5

?00

?00

0

200

400

Surcharge q (kN/m2)

Axia

l Stra

in ε

a (μ

)

Splice Section

Bottom Chord(West)

Bottom Chord(East)

Top Chord(West)

Top Chord(East)

0 1.75 3.5

?00

?00

0

200

400

Surcharge q (kN/m2)

Axia

l Stra

in ε

a (μ

)

Center Section

Bottom Chord(West)

Bottom Chord(East)

Top Chord(East)

Top Chord(West)

0 1.75 3.5

?00

?00

0

100

200

300

400

?0

0

50

100

Surcharge q (kN/m2)

Axi

al S

train

εa

(μ)

X뺹race

Ben

ding

Stra

in ε

b (μ

)

Tensile Member(Bend)

Tensile Member (Axis)

Compressive Member(Axis)

Compressive Member(Bend)

358

Figure 9. Typical result of CASE 3

on center of bridge axis direction. In the random excitation of CASE 4, the man, whose weight was approximately 550N, ran zigzag from the north side to the south side of the bridge with acceleration and deceleration. And the average speed was around 3m/s. In the resonance experiment of CASE 5, five men whose total weight was approximately 3.5kN, marched in place at the center of the bridge to generate resonance vibration. It continued approximately 7 seconds. After a stop, they kept the resting states until the end of measurement. In the horizontal excitation (CASE 6 and 7), crossbeams were excited from the horizontal direction to make the vibration of the horizontal direction. The experiment way of CASE 6 was an excitation by hitting the crossbeams with wooden square lumbers. The experiment way of CASE 7 was an excitation by pushing three of crossbeams with three men power. RESULTS OF DYNAMIC TESTING As a typical result of dynamic testing, results of five cases (CASE 1, 3, 4, 5, and 7) are selected in the present discussion. In each case, the time history of acceleration, the power spectrum and the phase diagram of acceleration are shown in Figures 8 to 12. In addition, about the vertical acceleration, upward directions are plotted by positive sign, and about horizontal acceleration, westward positive sign plot directions.

In CASE 1 (Figure 8), the maximum acceleration measured about 600 gal. Just as the experimenter got down a floor, the wave profile indicated high frequency and high damping effect. As for the power of Fourier’s spectrum, the vertical direction is stronger compared with the horizontal direction. It would be seen that high frequency includes, but the dominant frequency is 6.4 Hz. The phase diagram of the vertical direction shows a positive correlation, and there are very few vibration ingredients of the twist and the horizontal direction in the phase diagram of horizontal direction.

In CASE 2 and 3 (Figure 9), the maximum acceleration measured about 400 gal. It is observed that wave profile includes high frequency same as that in CASE 1. The power of the vertical direction is stronger compared with the horizontal direction, in Fourier’s spectrum. The dominant frequencies are 6.4 Hz in the vertical direction and 3.6 Hz and 8.8 Hz in the horizontal direction. Some of the negative correlation and phase difference are seen in the phase diagram of vertical direction. The phase diagram of horizontal direction shows a positive correlation; it means that the twist or horizontal vibration accompanies the vertical vibration.

In CASE 4 (Figure 10), the random excitation was generated by the running. This is stronger load compared with usual walking. The maximum acceleration measured about 200 gal. According to Fourier’s spectrum, the dominant frequencies are 6.5Hz and 3.7Hz in the vertical direction and in the horizontal direction, respectively. It seems that the waves of vertical direction are not correlated in phase diagram. The phase diagram of horizontal direction shows positive correlation though a few phase differences are seen; it means that the twist or horizontal vibration accompanies the vertical vibration.

In CASE 5 (Figure 11), it is attempted to amplify the acceleration by response vibration. However, the amplification stayed within about 200 gal and the associated high amplification was not observed. According to Fourier’s spectrum, the dominant frequencies are 3.6 Hz and 7.2 Hz in the vertical direction. The reason is seemed that the marched period was a little different from target period though the experimenters tried to fit the half of the natural period. In the phase diagram of vertical direction, it is observed that the positive correlation includes a few phase differences. The phase diagram of horizontal direction shows a positive correlation. It seems that the torsion mode vibration is generated. This observation indicates that the torsion mode occurred due to experimenter's stamping of same direction (left foot, right foot). In CASE 6 and 7, the dominant frequency of

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CASE 3?

: CH3: CH1

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rum

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: CH1: CH3

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600

After Shocked

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H3)

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Vertical Acceleration(CH1) (gal) Upper（＋）

CASE 3?

?00 ?00 ?00 0 100 200 300

?00

?00

?00

0

100

200

300After Shocked

Hor

izon

tal A

ccel

erat

ion(

CH

4) (g

al)

Wes

t（＋）

Horizontal Acceleration(CH2) (gal) West（＋）

CASE 3?

100 101 102

0

15

30

45

60

Frequency (Hz)

Pow

er S

pect

rum

(gal

2 /sec

)

CASE3?

: CH2: CH4

Horizontal Acceleration

(a) Time history of acceleration

(b) Power spectrum

(c) Phase diagram


(b) Power spectrum

(c) Phase diagram

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: CH1 : CH3

?00 ?00 ?00 0 200 400 600

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?00

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400

600 After Shocked

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tical

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eler

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(gal

)

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pper（＋）


CASE 1?

?00 ?00 ?00 0 100 200 300

?00

?00

?00

0

100

200

300

Hor

izon

tal A

ccel

erat

ion(

CH

4) (g

al)

Wes

t（＋）


After Shocked

CASE 1?

100 101 102

0

100

200

300

Frequency (Hz)

Pow

er S

pect

rum

(gal

2 /sec

)

CASE1?

: CH1: CH3


100 101 102

0

2

4

6

8

10

Frequency (Hz)

Pow

er S

pect

rum

(gal

2 /sec

)

CASE1?

: CH2: CH4



359

horizontal vibration is 3.7 Hz as shown in Figure 12. The time history of acceleration indicates an opposite phase in the vertical direction. It means that the vibration with torsion mode occurs. The damping constants were calculated using filtering wave of CASE 1 in the vertical direction. On the other hand, they were calculated from data of CASE 7 concerning the horizontal direction. The mask frequency for filtering is from 5.5 to 8.5 Hz in CASE 1. And the mask frequency is from 2.5 to 4.5 Hz in CASE 7. The damping constants of vertical direction and horizontal direction are 1.2 % and 1.5 %, respectively. It would be evaluated that the damping coefficients of this experimental bridge were relatively higher than those of conventional steel girder footbridges for around 20m span whose damping coefficients were obtained to be less than 1% in the literature. Therefore, the FRP footbridge would have good characteristic concerning the damping. CONCLUSIONS In this study, the static and the dynamic load testing on 18 m of pultruded GFRP truss footbridge has been carried out. These may be summarized as follows: 1) It has been discussed that the ratio of the deflection into the span length was about 1/600 in 100 % loading and was much smaller than the design limitation of 1/400. The deflection of this bridge is almost same as maximum deflection of 1/600 by live load in the steel truss road bridge; the stiffness of GFRP truss footbridge is shown to be comparatively high. 2) It has been pointed out that the slip of the bolted joints affects the deflection increases and needs to be considered for the evaluation in design. 3) The natural frequency is approximately 3.7 Hz and 6.4 Hz for a dominated twist and horizontal vibration mode and for a dominated vertical deflection mode, respectively. Both have been confirmed to be quite high rather than the design criteria range of 1.5 to 2.3 Hz. 4) The acceleration responses have not been amplified by the various excitation ways; it suggests that there is no problem in the usability as a footbridge. The present GFRP truss footbridge system is made clear to have a good structural performance as much as the conventional steel footbridges on the static and dynamic loadings. REFERENCES Japan Road Association. (1979). “Japanese Technical Standard for Pedestrian Crossing Bridges”, (in Japanese) AASHTO. (2009). “Standard Specifications for Structural Supports for Highway Signs, Luminaires, and Traffic

Signals”, Section 8 Fiber-Reinforced Composites Design.

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CASE 5?

?00 ?00 0 200 400

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?00 ?00 ?00 0 100 200 300

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?00

0

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200

300


Hor

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tal A

ccel

erat

ion(

CH

4) (g

al)

Wes

t（＋）

Stepping

CASE 5?

100 101 102

0

30

60

90

120

150

Frequency (Hz)

Pow

er S

pect

rum

(gal

2 /sec

)

CASE5?

: CH2: CH4


100 101 102

0

200

400

600

Frequency (Hz)

Pow

er S

pect

rum

(gal

2 /sec

)

CASE5?

: CH1: CH3



(b) Power spectrum

(c) Phase diagram

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CASE 4?

?00 ?00 0 200 400

?00

?00

0

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400Running

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H3)

(gal

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CASE 4?

100 101 102

0

250

500

750

1000

1250

Frequency (Hz)

Pow

er S

pect

rum

(gal

2 /sec

)

CASE4?

: CH1: CH3


100 101 102

0

100

200

300

400

Frequency (Hz)

Pow

er S

pect

rum

(gal

2 /sec

)

CASE4?

: CH2: CH4


?00 ?00 ?00 0 100 200 300

?00

?00

?00

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200

300


Hor

izon

tal A

ccel

erat

ion(

CH

4) (g

al)

Wes

t（＋）

Running

CASE 4?


(b) Power spectrum

(c) Phase diagram Figure 10. Typical result of CASE 4 Figure 11. Typical result of CASE 5

5 6 7?00?0

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100


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CASE 7?

：CH1 ：CH3

5 6 7?00?0

050

100

Hor

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tal

Acc

eler

atio

n　(g

al）


CASE 7?

：CH2 ：CH4

100 101 102

0

40

80

120

160

Frequency (Hz)

Pow

er S

pect

rum

(gal

2 /sec

)

CASE7?

: CH2: CH4


100 101 102

0

25

50

75

100

Frequency (Hz)

Pow

er S

pect

rum

(gal

2 /sec

)

CASE7?

: CH1: CH3



(a) Time history of acceleration (Vertical)

(b) Time history of acceleration (Horizontal)

(c) Power spectrum

360

United States Department of Agriculture Forest Service. (2006). “A Guide to Fiber-Reinforced Polymer Trail Bridges”, http://www.fs.fed.us/t-d/pubs/htmlpubs/htm06232824/index.htm.

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Documents

T3B1 Static and Dynamic Behavior of a Pultruded FRP Truss