Dynamic response of highway trucks due to road surface roughness

Cornpurrs & Structures Vol. 49, No. 6. pp. 1055-1067. 1993 0 1994 Elswier Science Ltd Printed in Great Britain. 0045-7949/93 56.00 + 0.00

Pergamon

DYNAMIC RESPONSE OF HIGHWAY TRUCKS DUE TO ROAD SURFACE ROUGHNESS T. L. WANG,? M. SHAHAWY$ and D. Z. HUANGt tDepartment

of Civil and Environmental Engineering, Florida International University, Miami, FL 33199, U.S.A. $Structures Research and Testing Center, Florida Department of Transportation, Tallahassee, FL 32310, U.S.A. (Received 1 April 1992)

Alastrati-Vehicle characteristics, vehicle speed and road surface roughness are major factors influencing bridge dynamic response.. In order to improve the previous vehicle model studies, vehicle models with seven or twelve degrees of freedom were developed for H20-44 and HS20-44 trucks, respectively. Vehicle models were validated by comparisons with the real truck dynamic systems. The road surface roughness was generated from power spectral density (F’SD) functions for very good, good, average, and poor roads. The impact factors of suspension and tire forces were obtained for vehicle models running on different classes of roads at various speeds. A comparison of computed and experimental impact results was also made.

1. INTRODUCTION

Vehicle characteristics, vehicle speed and road surface roughness are some of the major factors that influence the dynamic response of a bridge due to moving

loads. In reality, a truck is a very complex mechanical system because of its suspension. Some assumptions need to be made in order to simplify the vehicle characteristics in mathematical modeling analysis. The dynamic analysis of highway vehicles has been studied since the middle of this century. Brief reviews of the literature can be found in [l-6]. Most of the previous studies have assumed that (1) the vehicle frames are rigid, (2) the interleaf friction forces are considered in a suspension system, (3) spring forces and damper forces are proportional to displacements and a single point. However, all vehicle models were limited to pitch mode vibration and road surface profiles were obtained from field measurement in most of these studies. Even though Whittemore et al. [6] used frequency domain prediction techniques to simulate pavement load, the techniques were established only for linear systems excited by stationary random inputs. In this study, the numerical road surface roughness spectrum is generated by using the random number based on the power spectrum density functions. Vehicle nonlinearity can be admitted when the generated road surface roughness is treated as an input function directly. In addition, the new vehicle models will include the roll vibration. 2.

VEHICLE MODELS

H20-44 and HS20-44 trucks are two major design vehicles in the American Association of State Highway and Transportation Oflicials (AASHTO)

Specification [7l. Two nonlinear vehicle models with seven and twelve degrees of freedom were developed according to the H20-44 and HS20-44 trucks, respectively. Figures 1 and 3 illustrate the side and front views of the H20-44 vehicle model. Three rigid masses represent the truck, front wheel/axle set, and rear wheel/axle set, respectively. In the model, the truck was assigned three degrees of freedom, corresponding to the vertical displacement (JJ), rotation about the transverse axis (pitch or O), and rotation about the longitudinal axis (roll or 4). Each wheel/axle set is provided with two degrees of freedom in the vertical and roll directions. The total degrees of freedom in the model are seven. Similarly, another vehicle model (refer to Figs 2 and 3) with twelve degrees of freedom was developed to represent an HS20-44 truck, consisting of five rigid masses as tractor, semi-trailer, steer wheel/axle set, tractor wheel/axle set, and trailer wheel/axle set. Tractor and semi-trailer were assigned three degrees of freedom (y, 0, and 4) individually. Two degrees of freedom (y and 0) were assigned for each wheel-axle set. The tractor and semi-trailer were interconnected at the pivot point (so-called fifth wheel point, see Fig. 2). Suspension force consists of the linear elastic spring force and the constant interleaf friction force [8]. The load-displacement relationships for friction force, suspension spring force, and combination of these two forces are shown in Fig. 4. The tire springs are assumed to be linear. Since the truck is a complex physical system, certain assumptions were made to simplify the model. These assumptions are as follows: 1. The vehicle runs at a constant speed.

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Fig. 1. Side view of an H20-44 vehicle model. 2. All components move with the same velocity in the longitudinal direction. 3. Provision is made in the model for wheel lift. Under this condition, the vertical tire stiffnesses are taken as zero. 4. Each tire contacts the road at a single point. 5. Force inputs are limited to the vertical direction. 6. In suspension systems, damping elements were assumed to be linear and to be of the viscous type. Damper force is proportional to the velocity. Ten per cent of the critical damping value was used for damping coefficient [6]. In the tires, the damping forces were neglected.

and relative displacements, whereas the dissipation energy, D = ZDi,of the system is obtained from the damping forces. The total kinetic energy, T = Xl;, of the system is calculated using the mass, mass moment of inertia, and translational as well as rotational velocities, of the system components. The moment of inertia of all components is assumed to be constant and the weight of each component is considered as the external force on that component. The equations of motion of the system are derived, using Lagrange’s formulation, as follows:

8%

_dT+dv+aD=o,

The total potential energy, V = Xvi, of the system is then computed from the spring stiffnesses ‘6

Ir

I

N

k

a4i

Is

4 _

‘I

I_

15 I I

‘2

*1-

\

1

I-

t-

‘4

Fig. 2. Side view of an HSZO-44vehicle model.

$3+

a4

(1)

Dynamic response of highway trucks

1057 18”

tr

-I

c

0t1

f

h

YII

Fig. 5. Side view of step bump used in vehicle validation.

3. VEHICLE MODEL VALIDATION

d.

Fig. 3. Front view of H20-44 and HS20-44 vehicle models.

where qi and di are the generalized displacements and velocities. Details of derivation are presented in 191. The equations of motion were solved by using a fourth-order Runge-Kutta scheme [lo, 111, with an integration time step of 0.005 sec. Such a small time step was necessary to avoid numerical instability. The real percentage of impact acquired from the study is defined as

sm 1

4-

Imp(%) =

[

1 x 100%

(2)

in which R, and R, are the absolute maximum responses for dynamic and static studies respectively.

(a) Friction force

In order to check that the mathematical vehicle models properly simulate a real truck dynamic system, it is necessary to validate the models. The 3/4 in-high x 18 in-long and l/2 in-high x 18 in-long step bumps were taken to generate a vertical input for H20-44 and HS20-44 vehicle models respectively, as shown in Fig. 5. The appropriate data used in dynamic simulation of the models was adopted from [8] and is given in [9]. The experimental data was available in [6]. Both damped and undamped suspensions were considered, but tire damping was neglected in this study. Typical tire force histories for H20-44 and HS20-44 vehicle models are shown in Figs 6-9. Impact factors of suspension and tire forces for wide range of vehicle speeds are given in Tables 1 and 2 for H20-44 and Tables 3 and 4 for HS20-44. It may be seen that the impact factors of suspension forces were reduced when a damped suspension system was considered in most cases. However, for tire forces, the impact factors did not change significantly between damped and undamped suspension systems. The comparisons of computed

(b) Suspension spring force 6

(c) Combination of friction and suspension spring forces Fig. 4. The relationship between the force and displacement in the suspension system.

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0’

0.3

0.6

1.2

0.9

1.5

0’ 0.3

1.6

0.6

SIMULATION TIME (SEC)

vehicle with undamped suspension system running at 3/4 inhigh step bump and 55 mph.

1.3

1.6

2.3

2.6

3.3

I 1.6

1.5

1.2

SIMULATION TIME (SEC)

Fig. 6. The tire force history of the rear axle of an H20-44

01 0.6

0.9

3.6

Fig. 7. The tire force history of the rear axle of an H20-44 vehicle with damped suspension system running at 3/4 inhigh step bump and 55 mph.

0’ 0.6

4.3

SIMULATION TIME (SEC)

I

1.3

1.6

2.3

2.6

3.3

3.6

4.3

SIMULATION TIME (SEC)

Fig. 8. The tire force history of the tractor axle of an HS20-44 vehicle with undamped suspension system running at l/2 in-high step bump and 35 mph.

Fig. 9. The tire force history of the tractor axle of an HS20-44 vehicle with damped suspension system running at l/2 in-high step bump and 35 mph.

and experimental impact results of tire forces in different axles are illustrated in Figs 10-13. The agreement between computed and experimental results was found to be very good. The computed impact factors of tire forces almost cover all experimental results.

4. ROAD SURFACE ROUGHNESS

The typical road surface may be described by a periodically modulated random process. The power spectral density (PSD) is a useful tool for analyzing the periodically modulated random process. The PSD

Table 1. Maximum suspension forces and impact factors of an H20-44 vehicle running at 3/4 in-high step bump for different suspension damping conditions and vehicle soeeds Damped suspension

Undamped suspension Maximum static force &ins)

Vehicle speed (mph) 15

Front axle

Rear axle

3.704

13.440

Maximum dynamic force tkins)

Impact factor (%1

Maximum dynamic force (kit&

Impact factor f%)

20 25 30 35 40 45 SO 55

5.361 5.074 4.877 4.721 4.648 4.513 4.506 4.444 4.324

44.74 36.99 31.67 27.46 25.49 21.84 21.65 19.98 16.74

5.164 5.048 4.865 4.705 4.624 4.516 4.494 4.452 4.306

39.42 36.29 31.34 27.02 24.84 21.92 21.33 20.19 16.25

15 20 25 30 35 40 45 SO 5s

24.158 24.097 24.499 24.321 24.449 23.438 22.193 22.638 22.196

79.7s 79.29 82.28 80.96 81.91 74.39 65.13 68.42 65.15

24.163 23.990 24.051 24.129 24.489 23.405 22.093 22.622 22.189

79.78 78.50 78.95 79.53 82.21 74.14 64.38 68.32 65.10

Dynamic response of bigbway trucks

1059

Table 2. Maximum tire forces and impact factors of an H20-44 vehicle running at 3/4 in-high step bump for different suspension damping conditions and vehicle speeds Damped suspension

Undamped suspension Maximum static force

(kips)

Front axle

5.260

Rear axle

functions developed

for highway

15.040

surface roughness

by Dodds

Maximum dynamic force

Impact factor

Maximum dynamic force

Impact factor

6ph)

(kips)

(%)

Wps)

W)

15

20 25 30 35 40 45 50 55

9.313 8.926 8.946 8.888 8.950 8.942 8.892 8.964 8.952

78.19 69.70 70.08 68.97 70.15 70.00 69.05 70.42 70.19

8.882 8.882 8.940 8.878 8.918 8.940 8.893 8.965 8.961

68.86 68.86 69.96 68.78 69.54 69.96 69.07 70.44 70.36

15 20 25 30 35 40 45 50 55

29.330 29.480 28.874 29.758 29.107 28.392 29.585 29.310 29.156

95.01 96.01 91.98 97.86 93.53 88.78 96.71 94.88 93.86

29.714 29.644 28.614 29.704 29.158 28.626 29.689 29.200 28.827

97.57 97.10 90.25 97.50 93.87 90.33 97.40 94.15 91.67

Vehicle speed

have been

S(f#l)=A

and Robson [123. They are

shown as

S(r$)=A

02 --, 90

(3)

(b
2

--“2,

f#J>$

0 90

‘O’

where S(4) is the PSD (m*/cycle/m), b, is the wave number (cycle/m), A is the roughness coefficient (m3/cycle), and 4. is the discontinuity frequency = 1/(2n) (cycle/m).

Table 3. Maximum suspension forces and impact factors of an HS20-44 vehicle running at l/2 in-high step bump for different suspension damping conditions and vehicle speeds Undamped suspension Maximum static force (kips)

Steer axle

Tractor axle

Trailer axle

2.915

14.193

14.573

Vehicle speed (mph)

(4)

Maximum dynamic force (kips)

Damped suspension

Impact factor W)

Maximum dynamic force (kips)

Impact factor (%)

15 20 25 30 35 40 45

4.470 4.241 4.069 3.860 3.848 3.735 3.651

53.34 45.47 39.60 32.42 31.99 28.12 25.26

3.971 3.941 3.878 3.835 3.764 3.659 3.697

36.23 35.19 33.04 31.57 29.12 25.52 26.82

15 20 25 30 : 45

25.133 25.538 23.441 22.148 21.845 21.852 22.131

77.08 79.93 65.16 56.05 53.92 53.96 55.93

23.279 22.484 22.203 23.338 20.124 21.005 21.557

64.02 58.42 56.44 64.43 41.79 48.00 51.89

I5 20 25 30 35 40 45

23.463 22.878 22.966 22.257 21.677 21.712 22.614

61.01 56.99 57.59 52.73 48.75 48.99 55.18

23.218 23.218 22.908 22.816 22.347 33.351 23.012

59.32 59.32 57.19 56.57 53.34 53.37 57.91

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Table 4. Maximum tire forces and impact factors of an HS20-44 vehicle running at l/2 in-high step bump for different suspension damping conditions and vehicle speeds Undamped suspension Maximum static force (kips)

Steer axle

Tractor axle

Trailer axle

Maximum dynamic force (kips)

Vehicle speed (mph)

suspension Maximum dynamic force (kius)

Impact factor (%)

Impact factor (%)

3.995

15 20 25 30 35 40 45

6.891 6.524 6.482 6.458 6.501 6.405 6.426

72.49 63.13 62.25 61.65 62.72 60.32 60.84

6.518 6.488 6.499 6.470 6.455 6.358 6.476

63.15 62.40 62.69 61.96 61.57 59.16 62.09

15.994

15 20 25 30 3s 40 45

28.741 26.660 25.591 25.971 25.717 26.387 26.003

79.71 66.69 60.01 62.38 60.79 64.98 62.58

29.598 27.915 25.993 26.502 25.841 25.990 25.682

85.06 74.54 62.52 65.70 61.57 62.50 60.58

16.012

15 20 25 30 35 40 45

25.381 25.242 25.801 25.889 25.845 25.931 25.411

58.51 57.64 61.13 61.68 61.41 61.95 58.70

25.623 25.602 25.320 25.978 25.828 25.955 25.790

60.02 59.89 58.13 62.24 61.30 62.09 61.06

120 i? 0:

0

100

UNDAMPED SUSPENSION DAMPED SUSPCNSION CXPCROIENTU-:-IDATA

60 0

h-~.

0

“NDAYPCD SUSPCNSlDN DMPCD SUSPENSION CXPCRlYCNTAL DATA

d

60.

g 2

40.

z?i

20.

0

0 0 0

0

0

0

0 20

50

40

30

60

VEHICLESPEED (MPH)

100

-g

60

’ iz

60

0

t

20

30

40

50

VEHICLESPEED (MPH)

Fig. 10. The comparison of computed and experimental impact results for tire forces of the rear axle of an H20-44 vehicle running at 3/4 in-high step bump.

i?

10

Fig. 11. The comparison of computed and experimental impact results for tire forces of the steer axle of an HS20-44 vehicle running at l/2 in-high step bump.

UNDAMPED SUSPENSION DUPED SUSPENSION EXPERIMENTAL DATA

k-. -.

_----

- ---_ 8

20

30

I

40

I 50

VEHICLESPEED (MPH) Fig. 12. The comparison of computed and experimental impact results for the tire forces of the tractor axle of an HS20-44 vehicle running at l/2 in-high step bump.

20

30

40

VEHICLESPEED (MPH) Fig. 13. The comparison of computed and experimental impact results for the tire forces of the trailer axle of an HS20-44 vehicle running at l/2 in-high step bump.

Dynamic response of highway trucks

!c:,:t 0

WI

,.

.

.

64

128

192

I

256

3 2

1 -4.0 0

64

125

182

I 256

DISTANCE

DISTANCEALONGTHE ROAD(M) [ai *mt s&s

ALONGTHE ROAD(Id) (a) ni+t LLmz

E

2.0

z”

1.0

g

0.0

s

-1.0

2 -2.0 s\

gj m

256

0

D&k

DISTANCEALONGTHE ROAD(M) @a)Iam \ina Fig. f4. Vertical highway surface pro&s road.

1:::t.1 ALO: THE ROE (N) ib) Lett line

in a very good

Fig. 16, Vertical highway surface profiles in an average road.

The values of wi and w, varied from 1.36 to 2.28 [I2]. In order to simplify the description of road surface roughness, both wi and w, are assumed the value of two. Equations (3) and (4) are converted as follows:

It was found that the comparison between nume~cal and analytical PSDs agreed fairly well [9]. The random numbers which have approximate white noise properties were generated first [ 131.Then, these random numbers were passed through the first order recursive filter [14]. Finally, the output function will be the road surface roughness. The detail of the procedure has been discussed by Wang [lo]. In this study, the values of 5 x 10m6, 20 x 10m6, 80 x lo-‘* and 256 x lOA m*/cycle were used according to Intemational Organization for Standardization (ISO) specifications [15] as the roughness coefficient A for the classes of very good, good, average, and poor roads, respectively. The sample length was taken as 256m (839.9 ft) and 2048 (2”) data points were generated for this distance. The average vertical highway surface profiles of right and left lines from five simulations are shown in Figs 14-17 for very good, good, average, and poor roads respectively.

S(gl)=A

2

2.0

2 ii

1.0

s

0$ -2. 0

iz

0.0

s w

-1.0

5:

2 VI

-2.0 0

84

128

182

258

DISTANCEALONGTHE ROAD(M) ,a> Righr‘in* 5. SUMMARY

2

2

0

256

DIST:CE ALOZTHE ROE(M) (b, I&r line Fig, IS. Vertical highway surface profdes in a good road.

AND CONCLUS?ONS

According to the real H20-44 and HS20-44 trucks, two nonlinear vehicle models with seven and twelve degrees of freedom were developed and validated by the experimental data. Four different classes of road surface roughness were generated for very good, good, average, and poor roads. The maximum dynamic forces and entire force histories were recorded in 800-B simulation length when vehicle models with damped suspension system were running on the different classes of roads. Typical force histories of suspension and tire for H20-44 and HS20-44 vehicles

T. L. WANGet al.

1062

u

4.0

E E

2.0

6 3 0 E

-2.0

0.0

u" -4.0 iz 5 -6.0 VI 0

64

128

192

256

VI

Ol 1.2

2.2

3.2

SIMULATIONTIME (SEC)

DISTANCEALONGTHE ROAD(Id) (oi)HlqhtLine 52

5

6.0 ,

Fig. 20. The suspension force history of the tractor axle of an HS20-44 vehicle with damped suspension system running at 75 mph and average road surface condition.

-1

L

2 -6.0 3. 0 0-l

25R

DIST:CE ALOETHE (b)Left line

ROE(M)

Fig. 17. Vertical highway surface profiles in a poor road. 1.2

2.2

3.2

4.2

6.2

5.2

7.2

SIMULATIONTIME (SEC) Fig. 21. The tire force history of the tractor axle of an HS20-44 vehicle with damped suspension system running at 75 mph and average road surface condition.

O-0 VERYGOODROADSWRPACE A-.& GOODROAG SURFACE 0-o AVRRAGEROAD SURFACE o-----v

m

0.6

1.6

2.6

3.0

4.6

5.6

POOR ROM

SURFACE

6.6

SIMULATIONTIME (SEC) Fig. 18. The suspension force history of the rear axle of an H20-44 vehicle with damped suspension system running at 75 mph and average road surface condition.

0’

10

20

30

40

50

60

70

60

VEHICLESPEED (MPH) Fig. 22. Impact results of suspension forces for the front axle of an H20-44 vehicle with damped suspension system.

25,

I

140 -

z a 5 2 ?? 2cr

20 R 15 10

; E

5

2

120

O-0

d--a O--O o-----v

100. 60.

VERY GOOD ROAD SURFACE GOOD ROAD SURFACE AVERAGE ROAD SVRFACE POOR ROAD SURFACE ~c.p_.._---

v... -.._,v

60.

0 0.6

1.6

2.6

3.6

4.6

5.6

6.6

SIMULATIONTIME (SEC) Fig. 19. The tire force history of the rear axle of an H20-44 vehicle with damped suspension system running at 75 mph and average road surface condition.

t;

40.

d 2

20.

x--._s

.o/-,...

..‘.

o----o F:

.v...

p ,./’

,-I+-o-_-O

o/ e__-4-__‘L-----9----e---~---r~

0 10

20

30

40

50

80

70

60

VEHICLESPEED (MPH) Fig. 23. Impact results of suspension forces for the rear axle of an H20-44 vehicle with damped suspension system.

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Dynamic response of highway trucks

Table 5. Maximum suspension forces and impact factors of front axle of an H20-44 vehicle with damped suspension system for different road surface conditions and vehicle speeds Road surface conditions Good Average

very good Maximum static force (kips)

3.704

VehiCle speed (mph) 15 25 35 45 55 65 75

Orips)

Impact factor (“/I

Maximum dynamic force (kips)

Impact factor (“/I

Maximum dynamic force (kipsl

4.008 3.996 4.947 4.064 4.054 4.102 4.084

8.20 7.87 9.26 9.71 9.43 10.73 10.24

4.146 4.166 4.183 4.199 4.296 4.370 4.368

11.92 12.46 12.93 13.36 15.99 17.98 17.91

4.444 4.421 4.847 4.950 4.954 5.170 5.660

Maximum dynamic fOW2

Poor

Impact

Maximum dynamic

Wl

(kips)

rmpact factor Wl

19.97 19.34 30.84 33.63 33.74 39.57 52.79

5.050 5.188 6.l65 6.244 6.182 5.739 5.995

36.32 40.06 66.44 68.57 66.89 54.94 61.85

factor

force

Table 6. Maximum suspension forces and impact factors of rear axle of an H20-44 vehicle with damped suspension system for different road surface conditions and vehicle speeds Road curface conditions

very good

Maximum static

Vehicle

force fkiP@

speed (mph)

IJ.440

15 25 35 45 :: 75

Average

Good

Poor

&bsl

factor <“/of

Maximum dynamic force fkips)

Impact factor @f

Maximum dynamic force &ips)

Impact factor W-t

Maximum dynamic force Rips>

Impact factor (%I

17.274 17.275 17.561 17.518 17.435 17.463 17.570

28.53 28.53 30.67 30.34 29.72 29.93 30.73

17.804 17.840 17.976 18.003 18.057 18.290 18.859

32.47 32.74 33.75 33.95 34.36 36.08 40.32

18.679 20.203 20.241 21.442 21.336 21.161 21.264

38.98 50.32 50.60 59.54 58.75 57.45 58.21

22.553 21.271 23.304 24.976 25.586 27.657 25.771

67.81 58.26 73.39 85.83 90.37 105.78 91.75

Maximum dynamic force

Impact

Table 7, Maximum tire forces and impact factors of front axie of an H20-44 vehicle with damped suspension system for different road surface conditions and vehicle speeds Very good Maximum static force (kipsl

5.260

Road surface conditions Good Average

Poor

Vehicle speed (mph)

Maximum dynamic force tkipsl

Impact factor WI

Maximum dynamic force
Impact factor (“Al

Maximum dynamic force Ikipsf

Impact factor (%f

Maximum dynamic force (kipsl

Impact factor WI

:: 35 45 55 65 75

5.462 5.516 5.525 5.588 5.627 3.636 5.643

4.87 3.83 5.04 6.23 6.98 7.15 7.29

5.660 5.823 5.940 5.978 6,199 6.183 6.261

10.70 7.69 12.92 13.64 17-67 17.54 19.03

6.230 6.442 7.183 7.480 7.729 9.046 9.384

22.47 18.43 36.55 42.20 46.94 71.97 78.40

7.544 8.412 9.863 9.960 9.71 I 9.6i8 10.265

43.42 59.92 87.51 89.36 84.61 82.85 95.16

YeBY GO00 RDAD SURFACE *--a GDOB ROAD SURFACE 4---o AYERAGS RDAD SURFACE (I -... P POOR ROAO SURFACE l . FXPERMXTAL DATA

O--O

.=--~..,_~_..~-~-

_,d..V

,’

Fig. 24. Impact results of tire forces for the front axle of an H20-44 vehicle with damped suspension system.

Fig. 25. The comparison of computed and experimental impact results of tire forces for the rear axle of an H20-44 vehicle with damped suspension system.

T. L.

1064 140

.

o-

et ai.

160

0 VERY DOOD RQAD SUfWACL

O--P

10

WANG

G ;

POOR ROAD SURFACE

20

30

50

40

60

70

o-0 A-.4 O---o v----v

140 120

50

10

WRY GOOD ROAD SURFACE Gooll ROAD SumwE AW$RAGE ROAD SURFACE POOR ROAD SURFACE

20

V~HIC~SP~~D(MPH)

30

40

50

80

70

80

VEHIC~SP~ED(MPH)

Fig. 26. Impact results of suspension forces for the steer axle of an HS20-44 vehicle with damped suspension system.

Fig. 27. Impact results of suspension forces for the tractor axle of an HS20-44 vehicle with damped suspension system.

Table 8. Maximum tire forces and impact factors of rear axle of an H20-44 vehicle with damped suspension system for different road surface conditions and vehicle speeds Very good

static force (hips)

IS.040

Vehicle speed (mph) 1.5 25 35 45 55 65 75

Maximum dynamic force &ipsl

Impact factor (%I

15.799 15.967 16.018 16.066 16.138 16.306 16.227

6.50 6.82 7.30 8.42 7.89

Road surface conditions Good Average ~Maximum Maximum dynamic Impact dynamic Impact force force factor factor WI Chips) @ripsI (%I 16.407 16.783 17.083 17.306 17.592 17.681 18.543

9.09 11.59 13.58 15.07 16.97 17.56 23.29

17.673 19.408 19.906 21.421 20.759 21.596 22443

17.51 29.04 32.35 42.42 38.02 43.59 49.22

Poor Maximum dynamic

Impact

force

factor

(k&N

(“,I

22.165 20.809 23.165 26.091 25.358 25.894 26.853

47.37 38.36 54.02 73.47 68.60 72.17 78.55

Table 9. Maximum suspension forces and impact factors of steer axle of an HS20-44 vehicle with damned _ suspension _ for different

road surface

conditions

Road surface conditions Average Good

Very good Maximum static force

Vehicle speed

Maximum dynamic force

Impact factor

&ins)

(mph)

&ins)

2.915

15 25 35 45 55 65 75

3.350 3.373 3.360 3.433 3.379 3.385 3.411

Poor

Maximum dynamic

Impact

Maximum dynamic

Impact

Maximum dynamic

Impact

WI

force &ins)

factor (%)

force @ins)

factor W)

force (kins)

factor WJ)

14.93 15.72 15.28 17.78 15.92 16.12 17.03

3.479 3.551 3.677 3.683 3.510 3.576 3.593

19.35 21.81 26.15 26.33 20.41 22.67 23.24

3.680 3.881 4.045 4.063 4.875 4.504 4.365

26.25 33.15 38.76 39.37 67.24 54.52 49.76

4.625 4.505 5.028 5.318 6.069 5.508 N/A

58.67 54.53 72.50 82.42 108.20 88.95 WA

Table 10. Maximum suspension forces and impact factors of tractor axle of an HS20-44 vehicle with damned system for different

Very good Maximum static force (hips)

14.193

Vehicle tsm% 15 25 35 45 55 65 75

system

and vehicle speeds

road surface

conditions

suspension

and vehicle speeds

Road surface conditions Good Average

Poor

Maximum dynamic force (hips)

Impact factor Wl

Maximum dynamic force (hips)

Impact factor W)

Maximum dynamic force (hips)

Impact factor W)

19.083 19.142 19.499 19.252 19.221 19.024 19.033

34.45 34.87 37.38 35.65 35.42 34.04 34.11

19.763 19.353 20.000 20.222 20.311 20.773 20.087

39.25 36.36 40.91 42.48 43.11 46.36 41.53

20.798 20.719 20.63 I 22.300 23.371 22.340 22.211

46.54 45.98 45.36 57.12 64.67 57.40 56.50

Maximum dynamic

Impact

force @ins)

factor W)

22.856 23.435 25.662 28.500 28.324 26.323 WA

61.04 65.12 80.81 100.80 99.56 85.47 N/A

Dynamic response of highway trucks

01 10

1065

1

’

20

30

40

60

60

70

80

VEHICLESPEED (YPH)

VEHICLESPEED (MPH) Fig. 28. Impact results of suspension forces for the trailer axle of an HS20-44 vehicle with damped suspension system.

Fig. 29. Impact results of tire forces for the steer axle of an HS20-44 vehicle with damped suspension system.

Table 11. Maximum suspension forces and impact factors of trailer axle of an HS20-44 vehicle with damped suspension system for different road surface conditions and vehicle speeds Very good Maximum static force otips)

14.573

Vehicle ?ms 15 25 35 45 55 65 75

Maximum dynamic force otips) 18.862 19.059 19.178 19.152 18.972 19.433 19.273

Impact factor (%) 29.43 30.79 31.60 31.42 30.18 33.35 32.25

Road surface conditions Average Good Maximum dynamic force (kips) 19.342 19.849 20.476 19.988 19.711 20.176 20.832

Impact factor (%) 32.73 36.20 40.51 37.16 35.26 38.45 42.95

Poor

Maximum dynamic force (kips)

Impact factor (%)

Maximum dynamic force (kips)

Impact factor

21.560 20.991 22.221 23.344 22.818 22.301 22.87 1

47.95 44.04 52.48 60.19 56.58 53.03 56.94

26.376 24.079 31.295 26.473 28.589 29.283 N/A

80.99 65.23 114.74 81.66 %.I7 100.94 N/A

W)

Table 12. Maximum tire forces and impact factors of steer axle of an HSZO-44 vehicle with damped suspension system for different road surface conditions and vehicle sneeds Very good Maximum static force (kips)

3.995

Road surface conditions Good Average

Vehicle speed (mph)

Maximum dynamic force (kips)

Impact factor (%)

Maximum dynamic force otips)

Impact factor (%)

Maximum dynamic force (kips)

15 25 35 45 55 65 75

4.294 4.365 4.348 4.422 4.475 4.521 4.562

7.49 9.25 8.84 10.68 12.00 13.17 14.18

4.474 4.612 4.912 4.845 4.960 5.035 5.033

11.99 15.43 22.96 21.28 24.15 26.02 25.99

4.893 5.314 5.443 6.074 6.703 6.023 6.822

Poor

factor (%)

Maximum dynamic force Orips)

Impact factor (%)

22.48 33.01 36.25 52.03 67.79 50.76 70.76

6.461 6.821. 7.040 8.774 8.455 8.572 N/A

61.73 70.74 76.22 119.62 111.64 114.56 N/A

Table 13. Maximum tire forces and impact factors of tractor axle of an HS20-44 vehicle with damped suspension system for different road surface conditions and vehicle speeds Very good Maximum static force (kivs)

15.994

Vehicle

15 25 35 45 55 65 75

Road surface conditions Good Average

Poor

Maximum dynamic force (kius)

Impact factor (%)

Maximum dynamic force (kips)

Impact factor (%)

Maximum dynamic force (kips)

Impact factor (%)

Maximum dynamic force fkins)

17.804 17.874 18.377 18.613 18.892 18.402 18.441

11.32 11.76 14.90 16.38 18.12 15.06 15.30

19.507 19.524 20.991 21.919 21.552 21.730 20.608

21.97 22.08 31.25 37.05 34.76 35.87 28.85

21.910 21.549 22.724 25.667 26.469 25.530 25.746

36.99 34.74 42.08 60.48 65.50 59.63 60.98

24.960 29.212 28.563 39.058 33.769 29.674 N/A

Impact factor I%) 56.06 82.65 78.59 144.21 111.14 85.54

VA

o----o VRRY woo ROAO SuRFACL F

A-

100

-d

O----o v-.-.0

GOOD ROM SURFACE AVERAGE ROAD SURFACE POOR ROAU SURFACE

_-0-_---a--

___o----_&-

10

20

30

40

50

60

70

0

80

10

20

VEHICLE SPEED (MPH)

70 o---o

i? w

50

80

70

Fig. 31. Impact results of tire forces for the trailer axle of an HS20-44 vehicle with damped suspension system.

70 0-o A---A

40

VEHICLE SPEED (MPH)

Fig. 30, The comparison of computed and experimental impact results of tire forces for the tractor axle of an HS20-44 vehicle with damped suspension system.

60

30

SIBElI AXLE TRACTORAXLE TRAILER AXLE

G

0-o .%---A O--o

SD

SCEER AXLE TRACTOR AXLE TRAILER AXLE

507

01

12

14

18

,

18

20

22

24

’

28

28

’

12

30

14

16

18

20

22

24

26

28

30

L2 W')

Lz @T)

Fig. 32. Impact results of suspension forces in an HS20-44 vehicle with damped suspension system running at 55 mph and good road surface condition for different L, values.

Fig. 33. Impact results of tire forces in an HS20-44 vehicle with damped suspension system running at 55 mph and good road surface condition for different L, values.

running at 75 mph and average road surface condition are shown in Figs 18-21. A summary of the impact factors of suspension and tire forces for different road surface conditions and vehicle speeds is given in Tables 5-14 and ill~trat~ in Figs 22-31. The different distances between the tractor and trailer axles (L,) of an HS20-44 vehicle have also been studied. The results are shown in Table 15, Figs 32 and 33. The conclusions of this study are summarized as follows:

suspension and tire forces. However, the vehicle speeds influence the impact factors significantly in average and poor roads. 3. The impact factors of both suspension and tire forces obtained from the poor road are the highest among these four different road surface conditions for speed varied from 15 to 75 mph. The lowest impact factors are always found in the very good road. 4. In Tables 13 and 14, it may be seen that the impact factors of tire forces of tractor axle are much higher than those of trailer axle in HS20-44 vehicle. 5. When values of L, changed, the impact factors of all three axles of HS20-44 vehicle varied slightly. However, Figs 32 and 33 show that the highest

1. The impact factors of both suspension and tire forces increased with vehicle speed in most cases. 2. The impact factors were affected slightly by the vehicle speeds in very good and good roads for both Table 14. Maxims

tire forces and impact factors of traiier axle of an HS20-44 vehicle with damped suspension system for different road surface conditions and vehicle speeds Very good

Maximum static force (kipsl

16.012

Vehicle speed (mph) 15 25 35 4.5 55 65 75

Maximum dynamic force (hips) 17.059 17.470 17.401 17.450 17.588 17.823 17.801

Impact factor (%l 6.54 9.10 8.67 8.98 9.84 11.31 11.17

Road surface conditions Good Average Maximum dynamic force Chips) 17.743 17.952 18.673 18.482 19.164 18.970 19.863

Impact factor (%l 10.81 12.11 16.61 15.42 19.68 18.47 24.05

Maximum dynamic force @ipsl 19.007 19.959 20.308 22.922 21.423 21.476 21.720

Impact factor W) 18.70 24.65 26.83 43.15 33.79 34.12 35.64

Poor Maximum dynamic force Wpsl 25.085 22.258 28.01 I 25.813 27.585 28.116 N/A

Impact factor Wl 56.66 39.00 74.93 61.21 72.27 . 75.59 N/A

Dynamic response of highway trucks

1067

Table 15. Maximum suspension forces, tire forces, and impact factors of an HS20-44 vehicle with damped suspension system running at 55 mph and good road surface condition for different L, values Tire

Suspension

JG* (ft)

Steer axle

14 16 18 20 22 24 26 28

Tractor axle

14 16 18 20 22 24 26 28

Trailer axle

14 16 18 20 22 24 26 28

Maximum static force (kips)

2.915

14.193

14.573

Maximum dynamic force (kips)

Impact factor (%)

3.510 3.510 3.548 3.574 3.501 3.506 3.541 3.539

20.41 20.40 21.72 22.61 20.11 20.29 21.48 21.40

20.311 20.648 20.639 19.531 20.120 20.578 20.070 19.904

43.11 45.48 45.42 37.61 41.76 44.99 41.41 40.24

19.711 19.768 19.754 19.613 19.746 19.788 19.770 19.786

35.26 35.65 35.56 34.58 35.50 35.79 35.66 35.77

Maximum static force (kips)

3.995

15.994

16.012

Maximum dynamic force (kips)

Impact factor (%)

4.960 4.960 4.861 4.870 4.821 4.867 5.007 5.026

24.15 24.15 21.68 21.90 20.67 21.84 25.33 25.80

21.552 21.744 21.323 20.332 20.957 21.181 21.955 21.093

34.76 35.96 33.32 27.13 31.03 32.44 37.28 31.89

19.164 19.019 18.929 19.097 18.924 18.869 19.105 19.014

19.68 18.78 18.21 19.26 18.18 17.84 19.32 18.74

*L2 is the distance between the tractor and trailer axles. impact factors were obtained when L, = 14-16 ft and 26-28 ft for both suspension and tire forces. 6. Some experimental data obtained by Whittemore et al. [6] were used to compare with computed data. A comparison of computed and experimental impact results for tire forces is presented in Figs 25 and 30. It can be seen that the computed impact values agree very well with the experimental data. REFERENCES

1. S. J. Fenves, A. S. Veletsos and C. P. Siess, Dynamic studies of bridge on the AASHO road test. Highway Research Board, Report 71, National Academy of Scienses, Washington, DC (1962). 2. S. J. Fenves, A. S. Veletsos and C. P. Siess, Dynamic studies of the AASHO road test bridge. Hiahwav Research Board, Report 73, National Academy of Sciences, Washington, DC (1962). 3. S. Levy and J. P. D. Wilkinson, The Component Element Merhod in Dynamic. McGraw-Hill, New York (1976). 4. G. R. Potts and H. S. Walker, Nonlinear truck ride analysis. J. Engng for Industry, Trans. ASME, May, 597-602 (1974). 5. A. S. Veletsos and T. Huang, Analysis of dynamic response of highway bridges. J. Engng Mech. Div., AXE %, 593620 (1970). 6. A. P. Whittemom, J. R. Wiley, P. C. Schultz and D. E. Pollock, Dynamic pavement loads of heavy highway

10. 11.

12. 13.

14. 15.

vehicles. National Cooperative Highway Research Program Report, Washington, DC (1970). Standard Specifications for Highway Bridges, 14th Edn. American Association of State Highway and Transportation Officials, Washington, DC (1989). T. Huang, Dynamic response of three-span continuous highway bridges. Ph.D. dissertation, University of Illinois, Urbana, IL (1960). T. L. Wang and D. Z. Huang, Computer modeling analysis in bridge evaluation. Final research report prepared for Florida Department of Transportation under Contract No. C-3394 (WPI-0510542), Tallahassee, FL (1991). T. L. Wang, Ramp/bridge interface in railway prestressed concrete bridges. J. Struct. Engng, AXE 116, 1618-1659 (1990). T. L. Wang, V. K. Garg and K. H. Chu, Railway bridge/vehicle interaction studies with a new vehicle model. J. Struct. Engng, AXE 117, 2099-2116 (1991). C. J. Dodds and J. D. Robson, The description of road surface roughness. J. Sound Vibr. 31, 175-183 (1973). J. Moshman, Random number generation. In Mathematical Methods for Digital Computers (Edited by A. Ralston and H. S. Wilf), Vol. II, Chap. 12, pp. 249-263. John Wiley, New York (1967). R. K. Otnes and L. Enochson, Digital Time Series Analysis. John Wiley, New York (1972). C. J. Dodds, BSI proposals for generalized terrain dynamic inputs to vehicles. ISO/TC/l08/WG9, Document No. 5, International Organization for Standardization (1972).