Dynamic Studies of the AASHO Road Test Bridges

S. J . F E N V E S , A . S . V E L E T S O S , and C . P . S I E S S Respectively, Assistant Professor, Professor, and Professor of

Civil Engineering, University of Illinois

A brief description of the objectives and scope of the dynamic studies performed on the bridges of the A A S H O Road Test is presented. The relationship of these studies to previous field tests is pointed out, and the general method of attack used is discussed briefly, together with the types of measurements taken and the analytical studies conducted. Finally, the highlights of some of the more important results obtained and of the conclusions drawn are presented. The details of the analyses and the intermediate steps leading to the conclusions presented are omitted, and only the most important findings are discussed.

This paper is offered as a synopsis or digest of the detailed account of the investigation previously presented (1, 2) and is intended to serve both as an introduction to the study for persons desiring further informa­tion and as a concise summary for those interested only in the major findings.

• This paper gives a brief review of the program of dynamic tests conducted on the AASHO Road Test bridges, and presents some of the major results of the investigation. The test bridges involved have been described in other papers (?, U). The planning of the test program and the analysis and interpretation of the data were conducted at the University of Illinois as a cooperative research project with the Highway Research Board.

The broad objective of the research program was to study the dynamic effects produced by moving vehicles and to relate the observed be­havior to theoretical predictions. A special effort was made to obtain reliable, carefully controlled data and to collect information of value in the planning and interpretation of future field tests on actual bridges. The scope of the project was restricted by the special nature of the test bridges, which were simple-span, single-lane structures, specifically de­signed to study their behavior under repeated applications of overstress. Because of their special design, the test bridges were consider­ably more flexible than bridges of the same span designed according to current specifica­tions. Furthermore, because of their narrow­ness, the test bridges were expected to and actually did behave essentially as a single simply-supported beam. Finally it must be em­phasized that no consideration was given in the design and construction of the bridges and ap­proaches to any of the particular requirements of the dynamic studies. Because of these limi­tations, no attempt was made to obtain an "im­pact formula" for the bridges tested much less for a general class of bridges.

The experimental setup at the AASHO Road Test consisted of 18 test bridges and a large number of vehicles of various sizes and dimen­sions, together with instrumentation and ex­periment control facilities normally found only in the best laboratory experiments. Thus, even though the test bridges were simplified models not directly representative of those designed for more conservative stress levels, the program served as a transition between laboratory model tests and full-scale field tests on actual bridges.

Although the primary interest of the study was the dynamic behavior of the bridges, a large portion of the project was concerned with obtaining comprehensive data on the character­istics of the test bridges and the vehicles.

In the bridge studies, loading tests were per­formed with stationary and slowly moving vehicles to determine the stiffness of the bridges and the lateral distribution of moments and deflections. Frequencies and damping char­acteristics were measured several times during the test period for comparison with computed values. For a few bridges, forced vibration tests were performed with a mechanical oscil­lator. Finally, the profiles of the approaches and bridges were measured at several dates, and the effect of the profile irregularities on the oscillations of the vehicles were investigated.

Vehicle studies consisted of static loading tests designed to determine the load-deflection relationship and frictional characteristics of the axles, and a large number of dynamic tests with the vehicles running over various pave­ments and obstructions. In the latter, the var­iation of the interacting force between the

83

84 C O N F E R E N C E ON T H E AASHO ROAD T E S T

vehicle and the roadway and the deformation of the suspension springs were measured. From this information, the frequencies of the vehicles and the damping characteristics of the tires and suspension springs were inferred.

The dynamic tests proper involved 15 of the 18 test bridges and 14 test vehicles. Over 1,800 dynamic test runs were performed, with vari­ous combinations of bridges and vehicles, and with speeds ranging from 10 to 50 mph. Several bridges were retested at various dates to determine the effects of changes in bridge properties occurring under the test trafflc. In several groups of tests, additional variables were introduced to study the effect of certain unusual conditions, such as vehicles with blocked springs, induced initial oscillations in both the vehicles and the bridges, eccentric loading, and sudden braking on the bridges. The results of the tests were analyzed and interpreted in the light of the available theo­

retical background. For a number of test runs, both the detailed characteristics of the response and the absolute maximum effects were com­pared with the corresponding theoretical predictions.

The details of the test setup, control, and instrumentation will not be discussed here. It is sufficient to say that comprehensive and re­liable data on the response of the birdges and vehicles have been obtained. Of particular interest was the special equipment developed by the Road Test staff to measure the dynamic vehicle loads (5).

P A R A M E T E R S OF B R I D G E - V E H I C L E S Y S T E M

The dynamic behavior of a bridge under the passage of a moving vehicle can best be introduced by means of a simple example. Figure 1 shows the simply-supported beam

DIRECTION OF MOVEMENT

SPAN L

T O T A L DYNAMIC R E S P O N S E

CRAWL R E S P O N S E

MAX. DYNAMIC MAXIMUM RESPONSE - AMPLIFICATION

PACTOR

MAXIMUM CRAWL = 1.00

RESPONSE

VARIATION OF MOMENT AT MIDSPAN

DYNAMIC INCREMENTS FOR MOMENT AT MIDSPAN

Figure 1.

B R I D G E R E S E A R C H 85

traversed by a single load of magnitude P mov­ing from left to right. The variation of the moment at midspan of the beam is plotted against the position of the load. The variation of the moment consists of a crawl curve, repre­senting the effect of the load moving slowly across the bridge (shown by the dashed line), and a "wavelike" component superimposed on the crawl curve. The maximum dynamic mo­ment at midspan, that is the peak value of the curve shown, does not necessarily occur when the load is at midspan, but depends on the "fre­quency" of the dynamic component.

In this study, the maximum dynamic effect for a section, whenever and wherever it occurs, expressed as a percentage of the corresponding effect produced by a stationary or slowly crawl­ing vehicle, will be denoted as the maximum amplification factor. This is equivalent to set­ting the peak ordinate of the crawl curve to unity, and expressing the ordinates of the dynamic curve in terms of this value (Fig. 1). The maximum amplification factor is directly related to the commonly used impact factor by the expression:

Impact Factor = Maximum Amplification Factor - 1.00 (1)

This manner of studying dynamic effects in terms of the corresponding static or crawl effects requires that additional emphasis be placed on the study of the static response of the bridges.

A second quantity useful in the detailed study of dynamic effects is the dynamic incre­ment, defined as the difference betAveen the in­stantaneous value of a dynamic effect at a point and the corresponding crawl effect at the same point, expressed in terms of the maximum value of the crawl effect. The bottom plot (Fig. 1) shows the history curve of dynamic incre­ments, or simply the dynamic increment curve, for midspan moment for the described example.

In attempting to determine the factors affect­ing the dynamic response, apparently the be­havior must depend on such items as the span, weight and stiffness of the bridge, and the speed, weight, size, and type of suspension of the vehicle. A great deal of confusion can be avoided, and much useful information gained if these properties are combined into dimen-sionless bridge-vehicle parameters. The four most significant parameters determined from previous studies (6) are given below.

(a) The speed parameter a is defined as

a = —— 2 L

in which

( 2 )

Although a is used as a measure of speed, it in­corporates the span L and the other bridge properties embodied in the period Ti. Thus the same speed v may correspond to different values of a for different bridges of the same span. The period of the wavelike component of the response curves is approximately equal to the natural period of the unloaded bridge, and consequently there are approximately l / ( 2 a ) complete cycles of oscillations during the time of transit of an axle over the span. This relationship is only approximate because the "period" of the bridge-vehicle system is a vari­able quantity.

(b) The weight ratio, R, is defined as _ Total weight of vehicle ~ Total weight of bridge

(c) The frequency ratio 4> is defined as _ Natural frequency of an axle

Natural frequency of bridge

( 3 )

( 4 )

V = vehicle speed; Ti, = fundamental natural period of vibra­

tion of the bridge; and L = span length of bridge.

The axle frequency used in computing ^ is de-tremined from the effective stiffness of the suspension system of an axle and the static load on the axle.

(d) The axle spacing ratio s/L, where s is the axle spacing and L is the span.

In addition to the above parameters, any effect which tends to excite vertical oscillations in the vehicle will produce changes in the force transmitted by the vehicle to the bridge, and thus affect the bridge response. These effects come from two sources:

1. Initial vehicle oscillations, produced by irregularities in the approach pavements, in­cluding any discontinuities at the bridge en­trance; and

2 . Any deviation of the bridge profile from a straight line, which induces additional oscilla­tions in the vehicle, and thus affects the forces exerted by the vehicle on the bridge.

P R O P E R T I E S OF B R I D G E S AND V E H I C L E S

Figure 2 (top) shows the variation of strain at midspan of the three beams of bridge 3 B (with composite steel beams) as a function of the position of a 2-axle test vehicle moving over the bridge at a crawl speed of approximately 3 mph. The ordinates are given in terms of the mean value of the maximum strains in the three beams. The three curves are in good agreement with each other. Since the section moduli of the three beams are essentially equal, it can be concluded that the live load was dis­tributed almost equally to the three beams. The bottom plot shows the excellent agreement be­tween the average measured curve and the corresponding computed curve for a prismatic beam. These figures are typical of a large

86 C O N F E R E N C E ON T H E AASHO ROAD T E S T

B R I D G E 3 B ( C O M P O S I T E S T E E L ) V E H I C L E 91

NTERIOR B E A M C E N T E R B E A M E X T E R I O R BEAM

O « 0 4

y>«-AVERA6E MEASURED C O M P U T E D FOR BEAM

0 2 2 0 0 4 0 8 1 0 P O S I T I O N O F D R I V E A X L E / S P A N

Figure 2. Comparison of crawl curves, strain at mid-span.

number of crawl curves studied, and show that, as expected, each test bridge regardless of the type of construction behaved essentially as a single simply-supported beam.

In general, the magnitudes of the crawl effects, as well as those produced by stationary vehicles, and the natural frequencies deter­mined from free-vibration records agreed closely with computed values, or, where dis­crepancies existed, these could be accounted for. As an example, in the earliest tests the reinforced concrete bridges appeared stifFer than predicted by a cracked-section analysis; however, as the tests progressed the agreement

between computed and measured values im­proved rapidly. In this connection, it was ob­served that, for the noncomposite steel bridges and for the prestressed and reinforced concrete bridges, the stiffness of the bridges after the vehicle left the bridge was not representative of the stiffness corresponding to the case in which the vehicle was on the span. This differ­ence is due to the fact that in the bridges de­signed for noncomposite action, a certain amount of composite action was restored as soon as the vehicle left the span. For the con­crete bridges, the explanation lies in the differ­ent degree of crack opening while the vehicle was on the span and after the passage of the vehicle. Inasmuch as the bridge period Tj, enters in the speed parameter a, it follows that, even if the speed of the vehicle were constant, the actual value of a while the vehicle was on the span would vary with the position of the load.

During the period of the test traffic, there was some increase in permanent deflections and loss of stiffness caused by increased appli­cations of overstress, but in general the bridge properties did not change appreciably in the 3-yr period.

The profiles of some of the approach pave­ments and bridges were far from smooth (Fig. 3). Disregarding the small irregularities, the profile shows "waves" having lengths of 10 to 30 ft, which, for the vehicle speeds considered, influenced significantly the vertical oscillations of the vehicle.

The range of the principal characteristics of the bridges are summarized in Table 1.

In contrast to the bridge properties, which could be determined to a reasonable degree of accuracy and replication, the vehicle properties were generally subject to larger experimental

< to z o <n UJ o

o Q: u.

z o I -< > UJ

0 5

0

-0 5

-10

-15 1.0

0 5

0

- 0 5

10

V B R I D G E 2 B

^^-BEGINNING OF T E S T S / END OF T E S T S

BRIDGE 7A / ^^•^"'^O-X

' V * f— ' '•

/ v/ / / / /

/ , 1 I

80 6 0 4 0 2 0 0 2 0 DISTANCE FROM L E F T ABUTMENT, F E E T

4 0 5 0

Figure 3. Variation of approach and bridge profiles.

B R I D G E R E S E A R C H 87

28.0

VEHICLE 415 DRIVE AXLE

a.

Q

tiJ - I X

<

20.0h

12.0

T IRES SUSPENSION SPRINGS

1 1 1 1 1 1

0.2 0.4 0 0.4 AVERAGE DEFLECTION, INCHES

Figure 4. Typical vehicle load-deflection curves.

0.8

T A B L E 1

BRIDGE CHARACTERISTICS

Quantity- Range Span 50 ft Width 15 ft Total weight 73 to 104 kips Avg. measured

73 to 104 kips

natural frequency 3 2 to 6.9 ops

Avg. measured 3 2 to 6.9 ops

damping coeiiicient 0.8 to 4.5 pel cent of critical

Avg. midspan 0.8 to 4.5 pel cent of critical

deflection +1.2 in. (camber) to — 1 2 in. (sag)

uncertainties. Under static loading the vehicle tires behaved essentially as linear springs, al­though the loading and unloading paths did not coincide exactly. Figure 4 shows a typical load-deflection plot for a test on the drive axle of a truck-semitrailer. The leaf-type suspension springs could be represented by a model con­sisting of a linear spring and a frictional damper in parallel (9). A complete cycle of loading and unloading results in a residual de­flection in the system (Fig. 4). However, the single curve is somewhat misleading, since in several tests, especially those involving the axles of semitrailers, significant discrepancies between duplicate tests were observed.

From the load-deflection characteristics, the natural frequencies of the vehicles were com­puted for two conditions: (a) the vehicle vibrating on its tires only, and (b) the vehicle vibrating on the combined tire-suspension sys­tem. In addition, the limiting value of the frictional force in the suspension springs was evaluated. As long as the variation in the in­teraction force is less than the limiting fric­

tional force, the springs remain "locked" and the vehicle vibrates on the tires only. An increase in the interaction force beyond this limiting value causes the springs to become active and, during the corresponding- period, the vehicle vibrates on the combined tire-spring system.

Some of the most valuable information from the entire test program was obtained from con­tinuous records of the variation in the tire pressure and spring deformations taken in tests with vehicles running over pavements and various obstructions. The frequencies of the dominant oscillations in the tire pressure rec­ords were generally lower than those predicted on the basis of the static load-deflection tests. This was true even when the vehicle springs were blocked, and is believed to reflect the additional flexibility of the vehicle frame. The damping in the tires, determined from drop tests of vehicles with blocked suspension springs, could be considered to be viscous, and was of the order of 1 percent of critical. In test runs with normal suspension, comparison of the relative magnitudes of the variation of the force in the tires and the force transmitted by the springs showed that the limiting fric­tional force was generally lower than that determined from static tests. Careful exami­nation of a number of test records showed that the suspension springs deflected only occasion­ally, and that under severe excitation the fric­tional force seemed to disappear entirely. Fig­ure 5 shows the response of the left tire and spring on the drive axle of a three-axle vehicle in a run over a rough pavement; in the middle portion the amplitudes of the tire and spring response are essentially equal, indicating that no energy is dissipated by friction in the sus­pension system.

88 C O N F E R E N C E ON T H E AASHO ROAD T E S T

THREE-AXLE VEHICLE 513 ROUGH PAVEMENT

0 0 SPEED 2 0 mph

o a: o u. z o I -o < 111

\.0 Q

L 2 o 0.8 H

V) 1-0

LEFT PRIVE WHEEU T|RES

L E F T DRIVE WHEEL SUSPENSION SPRING

2.0 4.0 TIME , S E C O N D S

Figure 5. Variation of interaction force in test on pavement.

6.0

The average single amplitudes of the varia­tion in the interacting force ranged up to one-quarter of the static load for vehicles with nor­mal suspension running over pavements with Present Serviceability Index (PSI) (7) ratings of 2.0. Although the variations of the forces in the tires of the vehicles could be correlated approximately with the major irregularities of the pavement surface, there appeared to be no correlation between these force variations and the PSI rating.

The principal characteristics of the 14 test vehicles used are summarized in Table 2.

The dimensionless bridge-vehicle parameters were determined from the described bridge and vehicle characteristics. Table 3 shows the range of the significant parameters for 32 com­binations of bridges and vehicles. For the

T A B L E 2

CHARACTERISTICS OF TEST VEHICLES

Quantity Range

Total weight Maximum axle load Axle spacing Spring stiffness of tires

(2 or 4 tires per axle) Spring stiffness of suspension

springs Limiting frictional force Axle frequency, springs blocked Axle frequency, springs acting

8.0 to 56.4 kips 6.0 to 23.6 kips 10.5 to 24.2 ft

8 9 to 29 0 kips per in.

3.6 to 24.0 kips per in. 8 to 20% of axle load 3.5 to 4.6 cps 1.8 to 2.9 cps

speed parameter a only the maximum values are shown. Because the tests dealt with a lim­ited number of bridges and vehicles with fixed

T A B L E 3

RANGES OF BRIDGE-VEHICLE PARAMETERS

Parameter Composite Steel

Number of subseries: 2- axle vehicles 3- axle vehicles

Maximum value of speed parameter, Weight ratio, R:

2- axle vehicles 3- axle vehicles

Frequency ratio, springs blocked, <t>i: 2- axle vehicles 3- axle vehicles

Frequency ratio, springs acting, ^ i , : 2- axle vehicles 3- axle vehicles

Type of Bridge Construction

Noncomposite Steel

Prestressed Concrete

Reinforced Concrete

2 1 1 1 12 4 4 7

0 18 0 19 0 11 0 22

0 28 0 26 0 21 0 21 0 38-0 66 0 52-0 61 0 28-0 44 0 28-0 49

0 78-0 91 0 97 0 56 1 18 0 64-0 91 0 84-1 04 0 56-0 78 0 90-1 23

0 43-0 51 0 63 0 36 0 76 0 37-0 47 0 24-0 54 0 26-0 38 0 45-0 63

UJ

o o

0 6

1.0

- I 1.4

M 0 . 6

B R I D G E R E S E A R C H

B R D G E 3 B ( C O M P O S I T E S T E E L ) V E H I C L E 9 1

89

««C = 0 . I 3 8

1.0

1.4 - 0 . 6

/ Z V X '

D R I V E A X L E T I R E S " V R I G H T " W H E E L /

-L E F T W H E E L — /

D R I V E A X L E S P R I N G S . 1 1

, ^ R I V E A X L E E N T E R S

1 1 1 — 1 - 0 . 4 0 0 . 4 0 . 8

P O S I T I O N O F D R I V E A X L E / S P A N

Figure 6. History curves of interaction forces.

1.0

properties, the parameters are given by bridge type and by vehicle type {i.e., 2-axle and 3-axle). The range of parameters for groups of tests involving different types of bridges and vehicles are usually exclusive of each other. Considering all tests, weight ratios ranged from 0.21 to 0.66; frequency ratios, with vehi­cle springs acting, ranged from 0.27 to 0.76; and the maximum value of the speed param­eter a was 0.22. The upper limits of the weight and frequency ratios, as well as the maximum value of a, are considerably higher than those corresponding to 50-ft span bridges of conven­tional design; however, the ranges of the parameters are representative of those for bridges of different spans {8).

It must be emphasized that, because the experimentally determined properties of the test bridges and vehicles were subject to vary­ing degrees of uncertainty, the dimensionless bridge-vehicle parameters also involve certain approximations.

DYNAMIC BEHAVIOR O F B R I D G E S AND V E H I C L E S

In order to understand the details of the dynamic behavior of the bridge-vehicle sys­tem during the passage of a vehicle over the bridge, a large number of records were studied in detail. Results for a typical test involving composite steel bridge 3B, a two-axle dump truck, and a speed of 44.5 mph, are shown in Figures 6 through 8. The vehicle response is shown (Fig. 6) in terms of the measured varia­tion in the interaction force and the spring de­flection of the drive axle. The vehicle had a vertical motion on its tires before entering the bridge, and this oscillation continued while the vehicle was on the bridge; with the springs en­gaging only occasionally. The bridge response

is shown in terms of the total deflection and the total strain at midspan of the center beam (Fig. 7). For comparison, the corresponding response curves obtained for a vehicle moving at crawl speed are shown by dashed lines. The curves correspond closely to the schematic sketch pre­viously presented.

It is apparent that the curves for deflection and strain, although similar in appearance, show differences in detail. This difference is eliminated when the respective crawl effects are subtracted from the total effects when the effects are expressed in terms of dynamic in­crements (Fig. 8, top). This experimental ob­servation, confirming a theoretical prediction postulated several years ago(P), has the imme­diate implication that in future tests a consid-

b J in V) i § UJ a. 1 - ( O

iij 5

i ^

o < iZ Z a. S <

0 0

0 4

0 8

I 2 0

0 4

0 8

1 2

BRIDGE 3 B V E H I C L E 91 oC = 0 1 3 8

^75—

- V DEFLECTION AT MIDSPAN _ \ / /

\ / ^ - V /' X . A -CRAWL -

- Y>.

- ^ STRAIN AT MIDSPAN ,^->o^

- ^ ACRAWL - X y^OYNAMIC

- \ ^•"'f 1 ' '

0 4 0 8 1 0 POSITION OF DRIVE A X L E / S P A N

Figure 7. History curves of response.

90 C O N F E R E N C E ON T H E AASHO ROAD T E S T

BRIDGE 3B VEHICLE 91 » 0.138

iij

o

i

O

(0 s u I -

I -z Ul 2 UJ

g

MIDSPAN RESPONSE OF CENTER BEAM

DEFLECTION STRAIN

THIRD POINT STRAINS

MIDPOINT THIRD POINT TWO THIRD POINT

DEFLECTION AT MIDSPAN

CENTER BEAM INTERIOR BEAM EXTERIOR BEAM

0.22 0 0.4 0.8 SPEED PARAMETER «

Figure 8. Comparison of dynamic increments.

1.0

erably smaller number of measurements may be used to determine the bridge response. The same relationship holds for dynamic incre­ments at different points on the same beam (Fig. 8, center), and, for the particular bridges considered, at midspan of the three parallel beams (Fig. 8, bottom). In all of the response curves shown, the oscillations correspond to the fundamental period of vibration of the bridge and there are no noticeable components corresponding to the "period" of variation of the interacting force. These results and the general trends subsequently summarized are in agreement with theoretical predictions {9, 10, 11).

The effect of increased speed parameter a is to shift the peak response to the right, as well

as to increase the peak dynamic increment. Figure 9 repeats the dynamic increment curve for deflection at midspan, together with curves corresponding to speeds of 24.7 and 33.7 mph. However, from a design standpoint only the maximum total response, or maximum ampli­fication factor, is of interest. Figure 10 plots the maximum amplification factors for the bridge-vehicle combination against the speed parameter a. Each point represents the maxi­mum response for a particular run, regardless of when in the time-history the particular maximum occurred. Such a plot is known as a spectrum curve. Three salient features are as follows:

1. Whereas the increase in dynamic incre­ments is practically linear with increased a, the

B R I D G E R E S E A R C H 91

_ , - 0 2 u. iij o

CO

BRIDGE 3 B VEHICLE 91

- A /"A / \ ! ' V L / A \ / y V . >

• < = 0 oTifc \ y / v^'^ 7 'V/ • < = 0 I 0 5 - ^ ^ A / •c = 0 1 3 8 — /

1 1 1 1

- 0 2 2 0 0 4 0 . 8

P O S I T I O N O F DRIVE A X L E / S P A N

Figure 9 . Variation of dynamic increment witli «.

I 0

1.4

BRIDGE 3B (COMPOSITE STEEL) VEHICLE 91

1 u

L2

< 1.0 1.4

I 2

1.0

DEFLECTION

STRAIN

0.05 0.10 SPEED PARAMETER «K

0.15

Figure 10. Variation of maximum amplification factors with speed; midspan response, center beam.

spectrum curve for the total effects is not linear, but consists of several peaks of increas­ing magnitude. This is because the maximum values of the dynamic increment and the cor­responding static effect do not generally coin­cide. For example, the total response at a — 0.11 is less than that at a = 0.08, even though the peak dynamic increment is twice as large. This is because the peak dynamic incre­ment at a = 0.11 combines with a lower crawl ordinate, while a smaller dynamic increment at a = 0.08 occurs almost exactly when the crawl ordinate is maximum.

2. Even though the dynamic increment curves for strain and deflection are essentially equal, the spectrum curves for total effects are different. This is again due to the differences in the shape of the crawl curves. For a two-axle vehicle, the crawl curve for strain is sharply peaked, and thus the maximum values of the dynamic mcrements away from midspan combine with low crawl ordinates. However, exactly the reverse is true for a 3-axle vehicle, where the crawl curve for strain is relatively flat for a length equal to the axle spacing.

3. There is considerable experimental scat­ter due to the variations in the properties of the bridges and the vehicles, to the unavoidable errors in measurement and in reduction of the data, and to the fact that the test conditions were not completely controlled. Of all these, the condition of the vehicle as it entered the span, which was not regulated and which was not even measured in the majority of the tests, appears to have been the most significant single factor contributing to the experimental scatter. These oscillations were present in essentially all tests. The average single amplitude of the variation of the axle load on the approach, pavement ranged from practically zero to one-sixth of the static load.

The effect of these uncertainties on the bridge response can again be studied in two ways: (a) by comparing the detailed features of the time-histories for dynamic increments, or (b) by comparing the absolute maximum amplification factors. Figure 11 shows a spec­trum curve for a series of tests comprising more than 70 runs. The experimental points fall in a broad band with a width of the order of 20 percent of the maximhm static response. However, when the dynamic increment curves for the two most widely spaced points are com­pared (Fig. 12), this spread does not involve a difference in bridge behavior or a lack of replication in the detailed characteristics of the response. Therefore, the dispersion must be considered the normal experimental error.

COMPARISON B E T W E E N E X P E R I ­M E N T A L AND T H E O R E T I C A L

R E S U L T S

One of the principal objectives of the dy­namic studies was to relate the observed effects to theoretical predictions. In particular, it was desired (a) to investigate the degree of accu-

i <

1.4

1.2

S,.o

I " 10

DEFLECTION

• • •

STRAIN

0.05 0.10 0.15 SPEED PARAMETER

0.20

Figure 11. Replication of amplification factors; mid-span response, center beam.

92 C O N F E R E N C E ON T H E AASHO ROAD T E S T

B R I D G E 3 B { C O M P O S I T E S T E E L )

Ul -O.H

O H 0

u

V E H I C L E 4 1 5

oC » 0 . 1 4 7

D E F L E C T I O N A T M I D S P A N

+ 0 . 4

1 1 1 - 1

P O S I T I O N O F R E A R A X L E / S P A N

Figure 12. Replication of dynamic increment curves.

racy with which existing theories could predict the behavior of the test bridges and vehicles, and (b) to account for any differences that might exist between the observed and com­puted behavior. It should be obvious that the uncertainties in the measured properties affect significantly the degree of agreement that can be achieved, especially since the measured data enter twice into the comparison: once as the measured response used as a basis of compari­son, and again, as the experimentally deter­mined parameters used in the analytical solu­tions. The degree of agreement cannot be ex­pected to be better than the reliability of the field measurements.

The theory (S) used in this study represents the culmination of ten years of impact studies at the University of Illinois and is believed to be the most comprehensive and accurate analy­sis of the problem that has been developed to date. In the analysis, the bridge-vehicle system is idealized as shown in Figure 13. The bridge is represented by a weightless prismatic beam supporting five concentrated masses. The vehi­cle is represented by two rigid masses, corre­sponding to the tractor and semitrailer, inter­connected at the "fifth-wheel" and supported by three axles. Each axle is represented by two springs in series, corresponding to the tires and springs, respectively, and a frictional damper, representing the frictional resistance of the suspension system, in parallel with the top spring. The limiting frictional force in the damper for either direction of deformation is assumed to be constant.

The numerical solutions for the analytical

TRAILER MASS TRACTOR MASS FRICTIONAL DAMPER SUSPENSION SPRING TIRE

MASSLESS PRISMATIC BEAM I' l ^ ^ J<= CONCENTRATED MASSES

Figure 13. Analytical model.

model were obtained on the I L L I A C , a high­speed digital computer, by means of a com­puter program which was a slight modification of that previously reported (9) in that the bridge was represented by a simple beam. A distinction must be made between the general method of analysis and the much more limited version embodied in the computer program. For example, whereas the general method per­mits the consideration of any initial condition of the vehicle as it enters the span, such lati­tude was not provided for in the computer pro­gram. Therefore, these initial conditions could generally not be accounted for adequately. Similarly, whereas the general method allows for any variation of the bridge deck profile, the computer program used could handle only a second-degree parabola. Because of these and similar restrictions, certain test conditions could not be represented adequately in the solu­tions obtained. Furthermore, due to time limi­tations, it was not possible to modify signifi­cantly the computer program and carry out the comparisons to the point where all experi­mental uncertainties were accounted for.

The comparisons herein constitute a small fraction of those actually made. Starting first with the time-histories of the response and con­sidering the case where the experimental un­certainties were the smallest. Figure 14 shows the result for a run on a composite steel bridge and a vehicle with blocked springs, with a value of a = 0.11. In this case, the major un­certainties concerning the characteristics of the suspension springs of the vehicle were eliminated, and the agreement between the measured and computed response for both the vehicle and the bridge is excellent.

The comparisons for tests involving vehicles with normal suspension have been hampered primarily by the uncertainties regarding the load-deformation relationship of the vehicle suspension system and by the difficulties in accounting for the initial oscillations in the vehicle as it entered the bridge. These diffi­culties are due primarily to the impossibility of determining with any degree of accuracy

B R I D G E R E S E A R C H 93 B R I D G E 3 B

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1 1 1 1 - 0 . 2 2 0 0 . 4 0 . 8 1.0

P O S I T I O N O F D R I V E A X L E / S P A N

Figure 14. Comparison of history curves; test with blocked vehicle springs.

- 0 . 2

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Figure 15. Comparison of history curves; 2-axle vehicle, normal suspension.

from the available test data the values of the various parameters involved. However, for the composite steel bridges, it was generally pos­sible to approximate the portion of the experi­mental curves for which the effects were the largest. A typical example for bridge 3B tra­versed by a 2-axle vehicle at a speed corre­sponding to a value of a = 0.12 is shown in Figure 15. The dashed and dotted curves cor­respond to analytical solutions obtained, re­spectively, for a smoothly rolling vehicle and for the case with approximate initial conditions. A similar example, involving a 3-axle vehicle

and a value of a = 0.13 is shown in Figure 16. Even in this rather complex case, the bridge behavior is accurately predicted up to the time when the drive axle leaves the span at X/L = 0.6.

The detailed comparisons obtained to date for the prestressed concrete and the reinforced concrete bridges have generally been unsatis­factory. As pointed out, the cracking in these bridges changed their natural fi-equencies as the vehicle moved across the span, and this effect could not be duplicated with the existing theory based on a beam with constant proper-

94 C O N F E R E N C E ON T H E AASHO ROAD T E S T

BRIDGE 3 B

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I N I T I A L O S C I L L A T I O N S 1 1 1

POSITION O F R E A R A X L E / S P A N

Figure 16. Comparison of history curves; 3-axle vehicle, normal suspension.

ties. Although this factor is believed to be the principal cause of discrepancy, it should be noted that within the time available it did not prove possible to study these records as criti­cally as those for the composite steel bridges.

As would be expected, the agreement be­tween the computed and measured values of the absolute maximum effects, which are the quantities of interest in design, was consider­ably better than the agreement in the details of the history of the dynamic increment curves.

A representative comparison (composite steel bridge 2B and a 3-axle vehicle) of spec­trum curves for maximum amplification fac­tors is shown in Figure 17 (top). The ana­lytical curve was obtained for a smoothly rolling vehicle. Since the particular test series shown was conducted before the beginning of the road test traffic, the approach pavement was relatively smooth (Fig. 3). The larger

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BRIDGE 3 B VEHICLE 415

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a 2 0

Figure 17. Comparison of spectrum curves; deflection at midspan of center beam.

scatter in the experimental data occurs at the lower speeds for which the computed curve is fairly sensitive to small variations in the speed parameter.

Figure 17 (bottom) shows a comparison for bridge 3B (composite steel) for which the ap­proach pavement was quite irregular at the time these tests were conducted. The large dis­crepancies between the measured and computed results are attributed to the effect of initial oscillations. The theoretical curve based on a smoothly rolling vehicle represents essentially a lower bound to the experimental results.

These comparisons represent only the high­lights of those studied critically. Admittedly, perfect agreement was not obtained for every detail of every curve studied. However, for those cases where the properties of the bridges and vehicles were subject to relatively few uncertainties, the theory used was found to predict reliably the salient features of the be­havior of the system. This category includes the composite steel bridges and essentially all the test vehicles. In the other cases, the experi­mental uncertainties as to the actual bridge behavior and certain limitations of the avail­able computer program precluded further com­parisons. In general, the agreement obtained must be considered more than satisfactory and provides complete confidence in the ability of the theory to predict the observed response.

R E V I E W OF E X P E R I M E N T A L FINDINGS The major features of the experimental find­

ings can be reviewed in the light of the results of extensive numerical solutions obtained by the application of the theory (5, 9,10,11). Con­sidering first the effect of individual bridge-vehicle parameters, it was usually not possible to vary one parameter over a significant range while keeping the other parameters constant (Table 3). Figure 18 shows one of the mean­ingful comparisons obtained. The spectrum

B R I D G E R E S E A R C H

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BRIDGE 2 B V E H I C L E C • B R I D G E 3 B V E H I C L E 4 1 5 • - - B R I D G E 3 B V E H I C L E 5 1 3 • BRIDGE 9 B V E H I C L E 4 1 5

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95

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Figure 19. Effect of vehicle characteristics; deflection at midspan of center beam.

curves pertain to four series of tests, involving three different bridges and three different vehi­cles, in which all parameters except the speed parameter a were nearly the same. The gen­eral increase of the maximum amplification factors with increased a is essentially as pre­dicted by theory. The scatter of points is not larger than that observed in a single series of tests. The bridge type is not shown since it is directly reflected in the pertinent bridge-vehi­cle parameters, and all studies indicate that within the uncertainties involved there is no reason to expect, for example, a reinforced concrete bridge to behave differently from a steel beam bridge with the same parameters.

The majority of comparisons were made by studying the spectrum curves for different bridges using the same vehicle and by compar­ing the response of the same bridge under the passage of different vehicles. In the first case, no meaningful comparisons could be made, owing to the large variations in the bridge properties. In the second case, however, it was observed that different vehicles carrying their rated loads produced essentially similar effects, even when the weight ratio changed by a factor of two. One of these comparisons, composite steel bridge 3B and three truck-semitrailer vehicles, is shown in Figure 19. These observa­tions confirmed that the weight ratio was a relatively unimportant parameter.

Because of the large dissimilarities in the properties of the test bridges of different types of construction and the magnitude of the ex­perimental scatter under seemingly identical conditions any over-all curve of the variation of the maximum dynamic effects with the speed parameter a would be meaningless. Fig­ure 20 shows the cumulative percentages of amplification factors in 533 tests, involving six bridges and four 3-axle vehicles. The largest amplification factors for these tests were 1.63 for deflection and 1.41 for moment. Only 5 percent of the tests had amplification factors for deflection in excess of 1.40, and in only 2

percent of the runs was the amplification fac­tor for moment larger than 1.30.

In addition to the tests described, special tests were conducted to investigate the effects of certain unusual conditions. These included tests in which the suspension springs of the vehicles were blocked, tests with induced ini­tial oscillations of the vehicles or the bridges, and tests with eccentric loads. Blocking of the vehicle suspension springs resulted in essen­tially doubling the interacting forces as com­pared to vehicles with normal suspension sys­tems, and, as a consequence, the maximum dynamic increments were similarly doubled. Initial vehicle oscillations, induced by allowing the vehicle to drop from a ramp placed on the approach pavement, resulted in large local effects as the vehicle "bottomed" after the drop; however, because of the large frictional damping in the vehicle, the effects at midspan were essentially of the same order of magni-

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Figure 20. Cumulative percentages of amplification factors; 3-axle vehicles, all bridges.

96 CONFERENCE ON T H E AASHO ROAD TEST

tude as those in the regular tests. Similarly, induced bridge oscillations, simulating continu­ous traffic of heavy vehicles, had no significant influence. Finally, in eccentric tests designed to produce maximum effects in the edge beam, the maximum amplification factors for the edge beam were for all practical purposes the same as the corresponding effects in the center beam under the application of concentric loads.

In general, it can be stated that the effects of the various bridge-vehicle parameters, wher­ever they could be isolated, were in agreement with those predicted by theory, that no new significant parameter was discovered, and that not even a rearrangement in the order of im­portance of the parameters was deemed neces­sary on the basis of the results of the tests.

SUMMARY AND CONCLUSIONS In a short summary of an extensive investi­

gation extending over three years, some sweep­ing generalizations must be made. The tests yielded valuable information on the actual be­havior of the bridges and vehicles, as well as of the combined bridge-vehicle system. Simi­larly, the experience gained in this study pro­vides many new guidelines for the conduct of future field tests.

The most significant result, however, was the confidence gained in the value and reli­ability of the theoretical analysis. It is fair to say that this study has removed the analysis from the realm of theoretical and model studies and proved its applicability to actual tests. This fact alone has considerable economic sig­nificance. The analytical solutions presented took about 15 minutes of I L L I A C time per problem at a cost of approximately $20 each, including preparation of data and plotting of results. This amount is to be compared with the cost of instrumenting, testing and reduc­tion of data for an actual field test.

The results also suggest a different approach to be taken in future tests. Undoubtedly, tests of utmost reliability for detailed comparison with theory will still be needed in the future, especially for bridges that are more complex and at the same time more typical than the simplified models that were available on the AASHO Road Test, However, the majority of

the tests in the future will have to be aimed at obtaining values or ranges of values of the per­tinent parameters to be used in conjunction with analytical studies. These data, as demon­strated by the current investigation, can often be obtained economically from reasonably sim­ple tests on the bridges and vehicles.

R E F E R E N C E S 1. "Dynamic Studies of Bridges on the

AASHO Road Test." HRB Special Report 71 (1962).

2. "AASHO Road Test Report Four: Bridge Research." HRB Special Report 61D (1962).

3. F I S H E R , J . W . , AND V I E S T , I . M., "Behavior of Road Test Bridge Structures Under Re­peated Overstress. ' HRB Special Report 73 (1962).

4. ViEST, I . M., "Summary Report on Bridge Research." HRB Special Report 73 (1962).

5. F I S H E R , J . W . , AND H U C K I N S , H . C , "Meas­uring Dynamic Vehicle Loads." HRB Spe­cial Report 73 (1962).

6. W E N , W . K . , AND V E L E T S O S , A. S., "Dy­namic Behavior of Simple-Span Highway Bridges." HRB Bull. 315, 1-26 (1962).

7. C A R E Y , W . N. , J R . , AND I R I C K , P. E . , "The Pavement Serviceability-Performance Con­cept." HRB Bull. 250, 40-58 (1960).

8. W A L K E R , W . H . , AND V E L E T S O S , A. S., "A Method for Estimating the Dynamic Re­sponse of Simple Span Highway Bridges." To be published as Civil Engineering Studies, Structural Research Series, Uni­versity of Illinois (1962).

9. HUANG, T . , AND V E L E T S O S , A. S., "Dynamic Response of Three-Span Continuous High­way Bridges." Civil Engineering Studies, Structural Research Series No. 190, Uni­versity of Illinois (1960).

10. "Tenth Progress Report, Highway Bridge Impact Investigation." Department of Civil Engineering, University of Illinois (1960) .

11. "Eleventh Progress Report, Highway Bridge Impact Investigation." Department of Civil Engineering, University of Illinois (1961) .