DYNAMIC VEHICULAR LOADING OF THE

NORTH FLOODWAY BRIDGES, 1975

by

Clyde E. Lee

conducted for

Texas Department of Highways and Public Transportation

in cooperation with the

U. s. Department of Transportation Federal Highway Administration

by the

CENTER FOR HIGHWAY RESEARCH

THE UNIVERSITY OF TEXAS AT AUSTIN

September 1975

The contents of this report reflect the views of the authors, who are responsible for the facts and the accuracy of the data presented herein. The contents do not necessarily reflect the official views or policies of the Federal Highway Administration. This report does not constitute a standard, specification, or regulation.

ii

PREFACE

This investigation was initiated on 1 July 1975 for the State Department

of Highways and Public Transportation by Sam Cox, District 21 (Pharr) through

Kenneth D. Hankins, D-10 Research (Austin) and Don W. McGowan, D-18, Main­

tenance and Operations Division (Austin). Field studies were conducted

on 9 July 1975 by Center for Highway Research personnel, Dr. Clyde E. Lee,

J. Leon Snider, and Randy Wallin, in cooperation with Mr. McGowan and per­

sonnel from the Resident Engineer's office in Raymondville.

Data reduction and analysis were performed at the Center by Dr. Hugh J.

Williamson, Research Engineer Associate IV; J. Leon Snider, Technical Staff

Assistant V; Randy Wallin, Computer Programmer I; Joe D. Word, Laboratory

Research Assistant II; Steven H. Golding, Laboratory Research Assistant II;

and other staff using facilities at the University and at the State Department

of Highways and Public Transportation and computer programs developed through

previous studies under the continuing Cooperative Highway Research Program.

Professor Emeritus Phil M. Ferguson, Department of Civil Engineering, The

University of Texas at Austin, contributed freely of his observations to the

study, also.

This is the third report dealing with bridge roughness that has been

prepared for the State Deparbnent of Highways and Public Transportation during

the past two years. All these investigations are direct examples of applying

the results of research in solving field design, maintenance, and operational

problems that are of immediate concern and of long-range interest.

Photographs were provided by Don W. McGowan.

iii

SUMMARY

The half-mile-long twin reinforced concrete bridges on U.S. 77 which

cross the North Floodway above Harlingen, Texas, were opened to traffic

in 1974. The 12-in. deck has developed an undulating longitudinal profile

with sags of 1/4 to 1/2 inch in most of the 25-ft spans; thus the riding

quality is impaired, vehicles using the highway are subject to extra wear, and

dynamic loads in excess of the static weight of traffic are induced.

In this study, a computer simulation technique was used to investigate

the complex interaction between the existing road surface profile and two

representative trucks in order to assess the magnitude and placement of the

potentially large dynamic wheel loads on the bridge structure. Maximum wheel

forces from 50 to 100 percent greater than static wheel weight were predicted

for the heavy vehicles operating at speeds between 40 and 55 mph.

Since these large dynamic loads occur in the normal speed range for

traffic, smoothing the surface profile with an overlay is recommended.

Speed-zoning can be used for temporary alleviation, but effective enforcement

will be very difficult on this particular highway.

iv

DYNAMIC VEHICULAR LOADING OF THE NORTH FLOODWAY BRIDGES, 1975

The North Floodway Bridges are located on U.S. 77 in Cameron County

some 8 miles north of Harlingen, Texas. Twin bridges, each approximately

one-half mile long, carry two lanes of traffic in each direction about 15 ft

above the floor of the broad, shallow floodway. The 44-ft wide deck of each

bridge, which includes the two 12-ft traffic lanes, a 12-ft right shoulder,

and a 6-ft left shoulder, consists of a 12-in. reinforced concrete slab

supported on 106 five-column concrete bents spaced nominally at 25-ft

intervals (see photos). The slab is dowelled to each bent cap, and armored

expansion joints are provided between the 200-ft, 125-ft, or 80-ft deck units.

A 20-ft approach slab is added at the ends of both bridges.

These structures, which were opened to traffic in 1974, were constructed

with a nominal 1/4-in. upward longitudinal camber in each span, but recent

profile surveys show that virtually all spans now have sag of this magnitude

or greater (see Appendix A). In some cases, elevation differences of up to an

inch or more in a 30-ft longitudinal distance exist. This undulating profile

extends over the full length of both bridges .and is consistent in the trans­

verse direction. The longitudinal profile of each shoulder is quite similar

to the profile of each traffic lane; therefore, traffic loading up to now has

apparently not had additional detrimental effects on the structure. Because

of this similarity in the longitudinal profiles of all the adjacent lanes, and

since the bridges are less than two years old, the cause of the sagging

profile is probably related more to construction technique or to concrete

shrinkage and creep than to traffic loading.

This irregular, undulating surface profile, regardless of its cause,

forces the wheels of vehicles crossing the bridges to translate vertically,

and at certain speeds, the sprung mass (body) of some vehicles is caused to

bounce, roll, and pitch severely. Under critical conditions when the vertical

movements of the vehicle are reinforced by each wave in the deck profile,

large dynamic wheel forces are produced. Previous research (Refs 1, 2, 3, and4)

1

View of southbound Harlingen North Floodway Bridge showing arrangement of bents.

View of northbound Harlingen North Floodway Bridge showing deck and support structure.

2

•

3

has shown that the resulting wheel impact forces can be more than twice the

corresponding static wheel weight. These severe dynamic loads need to be

minimized in order to prolong the service life of the structure, prevent

excessive wear or damage to vehicles using the bridges, and provide acceptable

riding quality.

There are several possible approaches to reducing or minimizing the

magnitude of dynamic loading caused by traffic operating on a rough surface

profile. An obvious solution is to smooth the profile. Sometimes, this is

undesirable or economically unfeasible. Speed control, when practical, tends

to reduce the effects of a rough surface and offers temporary alleviation if

properly enforced. Or, load-zoning can be applied in extreme cases to restrict

the magnitude of permissible static vehicle weight.

The Center for Highway Research at The University of Texas at Austin was

asked to analyze the nature and magnitude of dynamic loading that is resulting

from mixed traffic using the North Floodway Bridges and to suggest possible

remedial measures for controlling the loads. Through previous research,

computer simulation techniques which describe the complex dynamic behavior of

various types of vehicles traveling at different speeds over defined surface

profiles have been developed. Equipment for measuring the essential charac­

teristics of the road profile was available at the Center, and experience in

using the computer models was available. Therefore, the requested study was

undertaken.

Field Measurements

Longitudinal profile measurements in each wheel path of each lane of

interest on the bridges were required as input data to the computer simulation

program. The General Motors Road Surface Dynamics Profilometer operating

under Center for Highway Research Study No. 3-8-71-156 was used to obtain

these data on 9 July 1975. Preliminary tests showed that the best speed for

the profilometer to operate was at 20 mph. Profile waves up to 100 ft long

can be measured without significant distortion at this speed. It was found

that the profilometer vehicle pitched and oscillated excessively at 40 mph, a

speed at which somewhat longer waves could be measured. A cursory analysis of

the preliminary profile data and observation of traffic using the bridges

indicated that waves 100 ft or shorter would be of primary interest;

therefore, all profile measurements were made at 20 mph.

4

Profiles of the full length of each bridge were plotted and examined

visually to determine zones which included profile characteristics that are

likely to cause large impact loads. While it is possible to run the simulated

vehicles over the full length of the bridges, this was deemed unnecessary and

wasteful. Three sections, each about 350 ft long, were selected to be repre­

sentative of profile patterns that would probably cause large dynamic loads.

The first section, shown in Fig 1, includes about 125 ft of the approach in

the right traffic lane of the southbound bridge plus the first 125 ft of the

adjoining deck at the north end. This section includes a long wave on the

approach pavement, a sudden drop of about an inch onto the 20-ft approach

slab, and a series of 25-ft waves in the first few spans of the bridge.

The second section, shown in Fig 6, includes parts of two 200-ft deck

units near the center of the northbound bridge and contains the repeating

sawtooth pattern of 25-ft waves that are l/4 to 1/2-inch in amplitude found

throughout the length of both bridges. The third section (see Fig 12)

includes about 150 ft of the north end of the northbound bridge, the

tilted 20-ft approach (departure) slab, and some 150 ft of pavement just off

the bridge in the right traffic lane. An elevation difference of 1-1/2 inches

has developed in the 25-ft zone beyond the approach slab. All these profile

plots show only the left wheel path, but measurements were made and used in

the simulation model for both wheel paths. Visual examination and statistical

analysis of the relationship between right and left wheel path profiles

indicated great similarity; therefore, only the left wheel path profiles have

been illustrated in these figures. Plots of the right wheel path profiles in

the outside lane of both bridges are given in Appendix A.

In addition to the profile measurements, live-load deflection measure­

ments were made near the middle of a 200-ft unit of the southbound bridge. A

dial indicator with a least reading of 0.0001 inch was supported from the

ground under the outside traffic lane and allowed to contact the bottom

surface of the deck slab midway between two bents. The maximum live-load

deflection observed was approximately 0.060 inch. The dead-load-only

reading of the dial changed about 0.007 inch in the 4-hr period beginning

at 11:00 A.M. Deflections of this magnitude can be assumed to have negli­

gible effects on the dynamic behavior of vehicles on the bridge.

Vehicle Simulation

Although a wide variety of vehicles uses the bridges, critical dynamic

loading is most likely to result from a few truck configurations. Grain and

other agricultural produce are primary products hauled by the large trucks in

the area. A single-unit two-axle dual-rear-tire vehicle (Type 2D; see

5

Plate A) was chosen as representative of smaller trucks, and a five-axle

articulated tractor-semi-trailer (Type 3S-2; see Plate B) unit was selected to

represent the larger trucks. The parameters needed to characterize these

vehicles were available from previous research and are summarized in Table 1.

Other types of vehicles such as mobile homes, cars towing camping

trailers, and pickups with covers may experience adverse riding conditions on

these bridges at certain speeds, but since these lighter vehicles will

probably not create critical dynamic loads they were not included in this

study. Further analysis of the effects of bridge roughness on ride quality is

highly desirable, however.

The speed limit on U.S. 77 is normally 55 mph, and the bridges are

expected to accommodate at least this speed. Observation of traffic and

recent test rides over the North Floodway bridges by engineers in District 21

initiated the installation of advisory speed signs at 45 mph early in

July 1975. Vehicle speeds between 20 mph and 60 mph were therefore used in

the simulation study.

Analysis

Mathematical models of the two vehicles described above were, by computer

simulation, "driven" over the selected sections of the bridges at various

speeds. Tire forces that would result from the vehicles interacting with the

surface profile were plotted and examined.

Figures 2 through 5 show the wheel forces predicted from the simulated

vehicles operating over the profile shown in Fig 1. At 40 and 45 mph the

dynamic rear wheel force of the 2D type truck varied from its static weight

of 7,000 pounds by as much as 5,000 pounds (70 percent), and a similar

percentage variation in wheel force for the rear axles of the 3S-2 type

vehicle was produced at 50-55 mph (see Figs 4 and 5). The dynamic wheel

force variations were found to be less than this at lower and higher speeds

and the plots are therefore not included in this report.

Plate A. Schematic diagram of single-unit two-axle dual tire (Type 2D) vehicle model.

6

Plate B.

,, ,, ! I P

' I I' i'

Schematic diagram of five-axle tractor-semi-trailer articulated (Type 3S-2) vehicle model.

8

TABLE 1. VEHICLE CHARACTERISTICS

I. Two axle single unit (2D)

Body Mass 47.91 (lb-sec2

) I in.

Tread Width

Axle 1 74.0 in. Axle 2 70.0 in.

Axle Spacing 153 .o in.

Wheel Weights

1 Right 3139 lb. 1 Left 3012 lb. 2 Right 7780 lb. 2 Left 7103 lb.

Suspension System

Spring Stiffness

Axle 1 Right and Left 535 lb/in. Axle 2 Right and Left 3750 lb/in.

Damping

Axle 1 Right and Left 5 percent of critical Axle 2 Right and Left 3 percent of critical

Tires

Stiffness

Axle 1 Right and Left 4000 lb/in. Axle 2 Right and Left

(Duals) 8000 lb/in.

Damping

Axle 1 Right and Left 2 percent of critical Axle 2 Right and Left 2 percent of critical

(continued)

9

TABlE 1. (continued)

II. Five axle articulated (3S-2)

Cab Mass 40.5 2 .

(lb-sec ) I m.

Trailer Mass 143 (lb-sec2

) I in.

Tread Width

Axle 1 77 .o in. Axle 2 71.0 in. Axle 3 71.0 in. Axle 4 73.0 in. Axle 5 73.0 in.

Axle Spacing

Axle 1-2 147 .o in. Axle 1-3 196.0 in. Axle 1-4 472 .o in. Axle 1-5 523.0 in.

Wheel Weights

1 Right 6000 lb. 1 Left 6000 lb. 2 Right 8500 lb. 2 Left 8500 lb. 3 Right 8500 lb. 3 Left 8500 lb. 4 Right 8500 lb. 4 Left 8500 lb. 5 Right 8500 lb. 5 Left 8500 lb.

(continued)

10

TABLE 1. (continued)

Suspension System

SEring Stiffness

Axle 1 Right and Left 2000 lb /in. Axle 2 Right and Left 6000 lb /in. Axle 3 Right and Left 6000 lb /in. Axle 4 Right and Left 6000 lb /in. Axle 5 Right and Left 6000 lb /in.

DamEing

Axle 1 Right and Left 4.5 percent of critical Axle 2 Right and Left 3.0 percent of critical Axle 3 Right and Left 3.0 percent of critical Axle 4 Right and Left 1.5 percent of critical Axle 5 Right and Left 1.5 percent of critical

Tires

Stiffness

Axle 1 Right and Left 4500 lb/in. Axle 2 Right and Left 8000 lb/in. Axle 3 Right and Left 8000 lb/in. Axle 4 Right and Left 7500 lb/in. Axle 5 Right and Left 7500 lb/in.

DamEing

Axle 1 Right and Left 0.01 percent of critical Axle 2 Right and Left 0.50 percent of critical Axle 3 Right and Left 0.50 percent of critical Axle 4 Right and Left 0.25 percent of critical Axle 5 Right and Left 0.25 percent of critical

11

The dynamic wheel forces expected to result from the simulated vehicles

operating on the profile shown in Fig 6 are illustrated in Figs 7 through 11.

The repeating 25-ft waves in the bridge profile cause the 2D type truck to

oscillate most severely at 40 mph and produce dynamic wheel forces up to

about 50 percent greater than static wheel weight (see Figs 7 and 8). This

profile induced the greatest dynamic effects in the front axle and the trailer

axles of the 3S-2 type vehicle at 50 mph (see Figs 9, 10, and 11). In Fig 10,

it can be noted that the rearmost wheel almo.st leaves the surface and causes

downward loads nearly double the static wheel weight. At 45 and 55 mph, the

oscillations of the vehicle are not in phase with the waves in the profile,

damping occurs, and resulting dynamic wheel forces do not reach this same

magnitude.

Dynamic forces caused by the profile shown in Fig 12 are expected to be

quite large since traffic moves off the upward-tilted approach (departure)

slab and vehicle wheels fall into a 1-1/2-inch depression. Figures 13 and 14

show the predicted wheel forces for the 2D type vehicle running at 45 and

at 60 mph. The unsprung mass (wheels and axles) oscillate at a frequency of

about 10 to 12 Hz, as is typical, and the sprung mass (body and load) trans­

lates at about 2.5 Hz. The severe oscillations of the undercarriage caused by

the step-off bump damp out in about 40 ft, and the sprung mass goes through

about three cycles before its oscillations are damped. Wheel forces range

from about zero to some 70 percent greater than static wheel weight. It is

interesting that the peak predicted forces occur at 45 mph rather than

at 60 mph in this case. Oscillations of the sprung and unsprung masses were

in proper phase with each other and with the profile to cause a severe peak

load in the first cycle of the vehicle oscillation beyond the large profile

depression.

Individual wheel loads are of concern when considering local stress

conditions in the bridge deck, but the magnitude and position of the gross

dynamic load on a particular span must also be accounted for in design. The

gross dynamic force on the span is simply the accumulation of all the wheel

forces at a given instant. Figure 15 shows a plot of the gross dynamic load

that results from the 3S-2 vehicle operating over the sawtooth deck profile

near the middle of the northbound bridge (see Fig 6). The dynamic forces

produced by the simulated 80,000 pound vehicle varied more than 30 percent

from the static weight of the truck. This variation is of the same order as

the impact factor that is normally applied in the structural design of major

bridge elements.

Conclusion and Recommendations

12

The maximum dynamic wheel loads resulting from the simulation of two

representative trucks crossing the North Floodway bridges occurred in the

speed range between 40 and 55 mph. At these speeds, the undulating profile

which includes a repeating pattern of 25-ft waves excited the vehicles in the

range of 2.35 to 3.23 Hz, and caused the various vehicle components (sprung

masses, unsprung masses, tires, and suspension) to react in such a way that

the higher frequency oscillations of the undercarriage (around 12 Hz) were

added to the oscillations of the body/load masses (around 3 Hz) at critical

times to produce quite large dynamic wheel loads (50 to 100 percent greater

than static weight). This speed range is, of course, the normal operating

range for traffic on the bridges, and remedial measures that will reduce the

magnitude of dynamic loading are indicated.

Load-zoning nor speed zoning seems practical on this major highway;

therefore, smoothing the surface with an overlay to remove the sags between

bents and compensate for bent cap misalignment that may now exist appears to

be the best solution. The regular pattern of 25-ft waves in the profile (see

Appendix A) suggests that alignment of the bent caps is generally satisfactory,

but that the deck has sagged since construction. Special attention to the

finished grade of an overlay will be required in order to remove the waves

of 1/4 to 1/2-inch amplitude. Consideration should also be given to whether

sagging of the deck will continue.

In informal discussions with Professor Emeritus Phil M. Ferguson, he

pointed out that the pattern of longitudinal reinforcing steel used in these

bridge decks is efficient to resist bending moment but that it tends to cause

sagging between supports when the concrete shrinks or creeps. That is, the

volume change in the concrete due to these phenomena is resisted by the rein­

forcing steel. Heavier bottom steel at mid-span and heavier top steel over

the supports restrains the concrete in these zones from shrinking or creeping

as much as that in the respective top and bottom fibers of the slab where

lighter reinforcing is used.

13

A supplementary design criteria based on tolerable deflection should

probably be considered. Building codes for flat slabs set the minimum

thickness of the slab as L/28 for both ends continuous unless special

deflection checks are made. The 1-ft thick deck slab over the 25-ft supports

satisfies this criteria, but the 30-ft spans exceed it slightly. Even though

there may be no direct analogy between buildings and bridges, it is inter­

esting to note that the 30-ft spans which occur in the middle of the 80-ft

units do not meet the criteria and that each of these longer spans has more

sag than is generally seen in the 25-ft spans (see Appendix A, pp A-2, A-4,

A-7, A-8, A-11, A-13, A-16, and A-17). Perhaps this observation can be noted

for reference in future design of bridges of this type.

This study has dealt primarily with dynamic loading of the bridge

structure by traffic, but consideration of the riding quality and of the

effects of road roughness on vehicles is needed. At least one truck has

already experienced severe damage (frame of the trailer collapsed) while

traveling on one of these bridges, and complaints about a rough ride have been

voiced recently. Smoothing the riding surface will solve these problems.

z

I I

~-

1 1 ~!_j r-

·: 5C

c.oo

toJ _, ""r

25 ---- -----,- -

4 °- I t,: "': r; ~. - • f;:;, •· ~· r ~"i~ r: ~ ~ F I L t

1-fJRIZONTAL DISTANCE ( FT) 75 100 125 150 175 200 225 --r---- --,- -- -- - ~- --- -- ---.- - ------,---- ---- --r- -----~

c:::¢> SOUTHBOUND TRAFFIC

Fig 1.

r=~

0 20, !QR 25ft spocono typ

0 Approach Slob 105

Profile of left wheel path of outside lane, southbound bridge, bent no. 's 106 to 102.

250 - -.--

--r-----,-25 50

] ~000 ~

~"'~-------

R~QC ~ I

4000 r ~f,~

c

Fig 2.

------clO}S ~Ylt<!l'-L -- ?D gf>ifDlSIGNR'IC~-- SPl!C" 4G.QL r:P~ G•Lf - 5USP 3TlF SUSP DRMP- TIRL Sllf 1 IRl DAMP

1 ~3b LBS s.co 4:100 ~B~ : .oo ~ 3750 LBS 3.0D bCOO LAS 7.00

47 POINT MOVING AVEARGf Of PROFILE ·1 I I I I 75 100 125 150 175

HORIZONTAL DISTANCE (FT)

zo' Approach -·--1' Slob =-t-

0

Bent no 0

106 0

105 0

104

Left wheel forces on outside lane, southbound bridge, bent no. 's 106 to 102, 2-D truck at 40 mph.

I 225

0

103

- r 250

0 102

'\ I

l

50 75

¢Southbound

Fig 3.

100

20' Approoch Slab . ______ __t====::-:;i~--------- --~-----

Bent no' 106 105 104

Left wheel forces on outside lane, southbound bridge, bent no.'s 106 to 102, 2-D truck at 45 mph.

103

..

HORIZONTAL DISTANCE (FT) 50 75 00 125 150 -::o;=-------------.- -----,--------r---·------,-----

¢ South bound

12000

8000~~~~--~--~--~--~~~-~~/~~~~~~

'1000

~ooc.

llOOO r--~~~-~~.._..-_,.:,.._.,...;...,........,.,;",._,.....,..._,.__..

--------- ----

200 -r---

--~-

--- -- ·-- 1-- 2 9 Hz--l -----.

- ~--

Fig 4. Left wheel forces on outside lane, southbound bridge, bent no.'s 106 to 102, 3S-2 truck at 50 mph.

Fig 5. Left wheel forces on outside lane, southbound bridge, bent no.'s 106 to 102, 3S-2 truck at 55 mph.

...... CX>

•

r----- ---·----- -- --·

~--·-----,-- ---,-----,---- --,-25 50 75 100

~ NORTHBOUND TRAFFIC

-I Bent no

I 41 42 :o 0 43 44 0 0

45 0

I hl<c' -~ ._ ----~-~h~---- ,~;:-

4., ~ · .- /* ~'!\. ~ ... - ·-~HGf OF :-, >· ~ _:---,--- T- -- ---,--- -1 -- --r-- ---r- --~--- --,----,--- -~- - l-- ---~ -- - 1 125 150 175 200 225 250 275 300 325 350 375 400 425

46 0

Fig 6.

47 0

48 0

HORIZONTAL DISTANCE ( FT)

49 0

Profile of left wheel path of outside lane, northbound bridge, bent no. 's 41 to 58.

/

Fig 7. Left wheel forces on outside lane, northbound bridge, bent no.'s 41 to 58, 2-D truck at 40 mph.

N 0

Bent no 41 0

AXLE 2

42 0

..

43 0

44 0

45 0

Fig 8.

46 0

47 0

48 0

49 0

50 0

51 0

52 0

53 0

54 0

Left wheel forces on outside lane, northbound bridge, bent no.'s 41 to 58, 2-D truck at 45 mph.

400

57 0

58 0

N .....

.. •

CUlS5 5 v[HICLE-:-1'>i BfH OESIC,>,~·' lCN - SPU.O" '~.00 MPH ------------------+

~ --,-----

12000

8000~ ~ --./

1000 ~ c:::::C>Northbound 1;:ooo

BODO

-4000

'lXlf - SuSP ST .IF SUSP QI'>!1P - : l~E 51 Jf TIRE OR!"P

! ~§28 tR~ ~:~~ ~5~~ t§~ .~~ ·<:JU ~ 9~ 1 J;S BUOL LB!J . 50

I

oCJu LBS I .~J 7500 LB~ .25 5 6000 lBS J.SO 7500 LBS .25

47 P~;NT t'i)'II~G t;yf~FlGE OF PAOFILf

HORIZONTAL DISTANCE (FT) 100 125 150 175 200 · -,------r------r---- --'2stiz~--r ---

H!...

~ 53 54 0 0

------------------------------~

l200G

8000

1000

12000

8000 o.---=-=----=-~ ->v-o.if\

-4000

.~1--111.3Hz ~- - --~~--c;r-·- ·v---

XL' 1--113.2Hz r--2.5Hz---i

6000~~~, •• /::'\- 7~~ r·-\:._~-~':_ ·\--;~ ~-'\- ~~ ~~ E=-"V' 4C~G ~ "' ~'-/ __r--.i ~ v \_.J v

I ~

2 ~s~ b_,"- __,.,zdo~,.c~----,1~dc,..c ---cs-.!;dcr---.em---.1 *'dcrr~

Fig 9.

2 i c: ~-~-,.,,~~,., :"'.s---.,'l..tc~ c,c ----Ticr--"-'ce,_~~:I!I<~Chri<':L---""~'11f.l~c·!l'-~~1'-;;1 d-H~~e""· 2""s o-1-

1"::~ 4t>M~Jo ' lN. I

Left wheel forces on outside lane, northbound bridge, bent no. 's 41 to 54, 3S-2 truck at 45 mph.

Fig 10. Left wheel forces on outside lane, northbound bridge, bent no. 's 41 to 54, 35-2 truck at SO mph.

Fig 11. Left wheel forces on outside lane, northbound bridge, bent no. 's 41 to 54, 3S-2 truck at 55 mph.

-----,----- 1 ----- -r-- ------r

l 5C !-

- c·c ~Bent no' - ... , ~ 100

' 0

50 100

=::>NORTHBOUND TRAFFIC

101 0

102 0

103 0

104 0

Fig 12.

17 PDI~T nDiiN3 qvERRGt ~F PROFILE ------r- - --T- ---- -~ -- --r --- ---,-------- r---- -,--- ---- r---150 200 250 300

105

0

HORIZONTAL DISTANCE (FT)

106 0 20' ~pprooch.,.

1 doc i ~co 51~doo :1oo 24oo 2~cc

(lN. 1 HOR!ZO~TRL OlSTHNCE 1doo

Profile of left wheel path of outside lane, northbound bridge, bent no.'s 100 to 106.

I

l2GO a-. HU~ 75

I ~400

PL:J~ "'~- 2 ;Goo 16oo

350

6000

¢Northbound

Fig 13. Left wheel forces on outside lane, northbound bridge, bent no.'s 100 to 106, 2-D truck at 45 mph.

SO~·c ~ ¢Northbound ?SJ Approoch

Slab

I 1----i 10 2 Hz

~ 1--- 2 s Hz-------~ _ !' t\ 1_ \ (V \

'""' ~,~l~;l\J.LJ\'""A; ;\rJP,'.J'c,, "/'v'"F~/V \!t_~· -! t.I\ fv \

-,---- -- I -

300

l '

: ')QG f- ' I J \ I ! \! J v-'

'~XL~ 04 H'-1:, 7~ f-L. )T fl..;. 4 rJ!;.~6.lJi t

o __ _:_,·,..~d~n-~~,.,~d~a--~s,.,~d~a-~a'*'dc --rdno-17c.~--11Dc -----rt~aR?ffl'N~Rf~~--:,:;~t~cc <•pc;--~, p- -;-t~."---""T~:: --,-;Jo:------,--.c~ --m-~--,-g:JO- -"nt~- --:rL

Fig 14. Left wheel forces on outside lane, northbound bridge, bent no.'s 100 to 106, 60 mph.

., Q JC

D

., u ... 0 u..

120

060 ~

40

20

36% Heavy

Static

Wt.

IOL-------~----------J-----------~----------~------------~----------~----------~ 100 150 200 250 300 350 400

Fig 15.

Horizontal Distance (ft)

Total force exerted on bridge deck by 3S-2 vehicle traveling 50 mph over profile of Fig 6.

N 00

REFERENCES

1. Al-Rashid, Nasser I., Clyde E. Lee, and William P. Dawkins, "A Theoreti­cal and Experimental Study of Dynamic Highway Loading," Research Report 108-lF, Center for Highway Research, The University of Texas at Austin, May 1972.

2. General Motors Corporation, 'Tiynamic Pavement Loads of Heavy Highway Vehicles," National Cooperative Highway Research Program Report 105, Highway Research Board, 1970.

3. Lee, Clyde E., and Randy Machemehl, "Speed-Zoning to Reduce Dynamic Loads on the Port Isabel Causeway," Center for Highway Research, The University of Texas at Austin, March 1974.

4. Lee, Clyde E., and Randy Machemehl, 'Tiynamic Vehicular Loading of the Hubbard Creek Reservoir Bridge, 1975," Center for Highway Research, The University of Texas at Austin, April 1975.

29

APPENDIX A

APPENDIX A

The General Motors Road Surface Dynamics Profilometer operating under

Center for Highway Research Study No. 3-8-71-156 was operated at a speed

of 20 mph over the North Floodway bridges near Harlingen, Texas on 9 July 1975

to obtain the information presented herein. The analog records that were

recorded on magnetic tape were subsequently converted to digital form by

frequent sampling so that digital computer programs could be used in analysis.

The digitized raw data points have been plotted and connected by a solid line

in the following figures. For analysis purposes, each bridge was considered

in three 11,000-ft sections since standard computer programs were available to

operate in this format. The data were further separated into shorter frames

for convenience in presentation.

Most of the 1-1/4-inch-wide armored expansion joints show on the plots as

sharp spikes since the small road-following wheel of the profilometer dropped

into the joint under its 300-lb force. Approximate bent locations are shown

in the figures along with the length of the slab units between expansion

joints.

Because of certain limitation in the profilometer equipment, the road

elevations are not absolute with respect to a horizontal plane. Relative

elevations, however, over distances less than about 100 ft are fairly

accurate. Patterns of roughness can thus be determined and allowances made

for the fact that longer waves in the profile are not included precisely in

the raw data.

A special digital filtering program was used on the bridge profile data

to determine a running average of the amplitude of wavelengths between 15

and 35 ft. The dotted line in the figures shows the amplitude of the waves in

this range. A large portion of the total roughness of the bridge decks is

accounted for by these wavelengths, and a definite pattern of repeating waves

exists.

31

NORTHBOUND FIRST J100 FT.

CJ Lf)

HARLINGEN NORTH ~LOODWRY BRJOG[

U N F l L T E R E C -- S 0 L 1 0 L 1 N E FILTEREC -- C8TTED LINE

OUTSIDE LAi\JE:. RIGHT 'w'HEFLPPTH

CJ L;)

1-

CI:o > U) LLJ , _jC( LLJ.

0 a:o Ou; rr: .

r-1

I

0 Ul

c=> TRAFFIC

zo'Approad; 5/c.zb --f--A-~

I

FRRME 1

Zcx::> ~/\

2 3 4 5 7

N+-------~------~-------~------~--------~------1 o.oo 50-0D 150.00 zoo.oo 25C.OC1 300~00 3SO.OO 400.00

POSITI~N RLONG THE RJRC (fT. l

FILTER PRSSBRNC ~ 15.0 TO 35.0 FT. WRVE~ENGTHS

450.00

)).. I

0 '.J.) .

Zo 0

1-<I ./

0 > lJ)

w' _Jo

I 'u.J

0 <Io 0 li) a: .

....... !

0 UJ

HRRLlNGEN NORTH FLOOOwRY BRIDGE NORTHBOuND FIRST 1100 FT.

II

9 10

UNFILTERED - SOLID LINE F J L T ERE. D ·- D 0 T T E_ D L I N E.

eo . . ----- . ·--+--· 20C> I

II

'"

RIGHT wHEt:LPRTH ~RRME 2

zoo

II I Z I 3 14 I 5 16 I 7 18 19 20 2 I 2 2 23 24 25 Z6

N+-------~---------~------~------~---------~------~--------~------~------~ 1450.00 SOO. 00 550.00 E100. 00 650. O:J 700.00 750.00 800.00 800.00 900.00

POSITION RLONG THE RORD (FT.) FILTER PRSSBRNC 15.0 TD 35.0 FT. WAVELENGTHS ~

I N

:z

0 LJ)

N

0 If)

..__, 0 LJ) .

Zo 0

I­CC a > Ll) w.

0 ,_J !

w

0 ceo 0 ll) 0::: •

.......

HRRLJNGEN NORTH FLOODWRY BRIDGE NORTHBOUND FJR5T 1100 FT.

UNFlLTERED - 50LlD LINE RIGHT ~HEELPRTH

FllTERED - DOTTED LINE FRRME 3

zco'

-------------------------

I 27 ZB 29 :30 31 32 33 34

0 U)

N+-------~------~--------~-------~------~-------~~------~------~------~ 'goo. oo 950.00 l .0 0 0 . 0 0 l 0 S 0 . 0 0 1 1 0 0 . 0 0 1 1 S 0 . 0 0 1 2 0 0 . 0 0 1 2 E 0 . 0 0 1 3 0 0 . 0 0 1 3 f) 0 . 0 0

POSITION RLONG THE RORC (fT. l

FlLTER PRSSBRND . 15.0 TJ 35.0 FT. WRVELENGTHS )> I

w

HARLINGEN NORTH FLOODWRY BRIDGE NORTHBOUND SECOND 1100 FT.

z .........

0 0

0 <.D

0

'---' 0 N

Zo 0

0 cr.:o Oc.t::: a: .

0 I

UNFILTERED - SOLID LINE FILTERED - DOTTED LINE

;zoo' ____ .::..__ ______ ------··

r, I I

I r. I ' \ J '

I ,-{ I \

I

HIGHT WHE:f.LPFiTH FRAME J

, 2CX> ...... - .JL,

" I \

I I

I I

30 31 32 33 .34 35 36 37 38 39 40 41 42 43 44 45 40

0 0

....... -+------,-----10. 00

~----~-----,--

JDG.OO 1SO.OO 200.00 250.00

POSIT JON RLONG THE RORO FILTER PRSSBRND ~ 15.0 TO 3b.O

300.00 ( F T • J

350.00 400.00

FT. WAVELENGTHS

450.00

)>

' ~

CJ CJ

HARLINGEN NORTH FLOODWRY BRJDGE NORTHBOUND SECOND ))00 FT. UNFJLTERED - SOLJD LJNE FJLTERED - DOTTED LJNE

RJGHT WHEE.LPATH FRAML 2

~ r-------2~'--CJ

'I*" I

z '---" 0

N

Z:o 0

......_

G:o >N w.

CJ __ ..J I

w

0 a:CJ 0([) a: .

0 I

47 48 49 50 51 b-2 53 54 5£ 56 57 .58 59 60 61 b2 63 G4 6.5

0 0

~+-------~------~------~ 14SO. 00 soo.oo ~so.oo Roo.oo Rso.oo 1oo.oo 75o.oo aoo.oo a~o.oo

POSJTJON RLONG THE RORD (FT. l FJLTER PRSSBRNO ~ )5.0 TO 35.0 FT. WAVELENGTHS

900.00

z

0 0

0 (.C . 0

. Zo 0

1-

Cio >N LLJ •

0 ._I I

LLJ

0 CIO o(.!J a: .

0 I

0 0

HRRLINGEN NORTH FLOODWAY BRIDGE NORTHBOUND SECOND 1100 fT. UNFILTERED - SOLID LINE RIGHT WHELLP~TH

FILTERED- DOTTED LINE FRAME 3

200

T I

I I

6G ~7 68 69 70 71 72

r-1+----r-'goo.oo 950.00 1.000.00 1060.00 1 lOO.QO 1150.00 1200.00 !2SO.OO 1300.00 1350.00

POSITION RLONG THE RORO (FT. l

FILTER PRSSBRND ~ 15.0 TO 3S.O FT. WAVELENGTHS ~ I

0'

z

0 0

N

0 N

. Zo 0

1----­

Cia >..,­w. _jo

I w

0 Cia ON cr: . -I

0 0

HRRLINGEN NORTH FLOODWRY BRIDGE NORTHBOUND LR5T 1100 FT. UNFILTERED - SOLID LINE RIGHT WHEELPRTH FILTERED - DOTTED LINE FRRME 1

/ ao -- --- -- --- ------ --~--- ------ -- ---

2CJCJ

' I

69 70 71 72. 73 74 75 76 77 78 79 80 81 82. 84 85

N+-------~------~------~------~------~----~~----~~----~------~ 'o.oo so.oo 1oo.oo 1so.oo 2oo.oo 2so.oo 3oo.oo 3so.oo 4oo.oo 4So.oo

POSITION RLONG THE RORD (FT. l

FILTER PRSSBRND ~ 15.0 TO 35.0 FT. WAVELENGTHS ):> I

-..J

0 0

0 cr:o 0 C'-1 0:: •

...... I

0 0

HRRLINGEN NORTH FLOODWRY BRIDGE NORTHBOUND LRST 1100 FT.

I I

I 86 87

U ~J F I L T ERE D ·- S 0 L I 0 L I N E FILTERED - DOTTED LINE

89 90 91 9Z 93

._,. ...

94 96 97 98

RIGHT \.JHEELPRTH FRRME 2

/CO /01 /0.:2 103

N+-------~------~------~------~------~------~------~------~------~ 1450.00 500.00 S50. 00 600.00 650.00 700.00 750.00 800.00 850.00 900.00

POSITION RLONG THE RORD (FT.) FILTER PRSSBRND ; 15.0 TO 35.0 FT. WAVELENGTHS ~

I

00

0 0

N

0 N

HARLINGEN NORTH FLOODWRY BRIDGE NORTHBOUND LRST 1100 FT.

!25

UNFILTERED - SOLID LINE FILTERED - DOTTED LINE

~TRAFFIC

RIGHT WHEELPRTH FRRME 3

___., f\f'L--- ---- ---Pavement"

z

0 cr::o 0 C-J cr: •

..... I

0 0

I

104 105 /Q;

N+-------~------~-------~------~------~----~------~------~------~ 1900.00 950.00 1.000.00 1050.00 1100.00 1150.00 1200.00 1250.00 1300.00 1350.00

POSITION RLONG THE RORD (FT. l FILTER PRSSBRNO , 15.0 TO 35.0 FT. URVELENGTHS ~

I <..0

z

0 0

N

0 N

l­

ITo >v­w. _jo

I w

0 a:o 0 C'-l a: •

...... I

0 0

HARLINGEN NORTH FLOODWAY BRIDGE SOUTHBOUND FIRST 1100 FT. UNFILTERED - SOLID LINE FILTERED - DOTTED LINE

c::> TRAFFIC

RIGHT WHEELPRTH FRAME 1

I

/25' ~ t------· - ------ .I

1!1

II

Bent ,..yg /06 105 104- /03 102 /01

N+-------~------~------~------~------~----~~----~~----~------~ 'o.oo 5o.oo 1oo.oo 15o.oo 2oo.oo 25o.oo 3oo.oo 35o.oo 40o.oo 45o.oo

POSITION RLONG THE ROAD (fT. l FILTER PASSBAND : 15.0 TO 35.0 FT. WAVELENGTHS )>

I

0

z

0 0

0 ("

. Zo 0

l­ITo >v­w. _j~ w

0 ITO 0 C'-' a:: .

....... I

0 0

HARLINGEN NORTH FLOODWRY BRIDGE SOUTHBOUND FIRST 1100 FT.

I~ I I I I

U N F I L T E R E D -- S 0 L I 0 L I N E FILTERED - DOTTED LINE

t!!3t=>, .l- 200

I I '

ljl i

II

\ I ' l I j

v

RIGHT WHEELPRTH FRRME 2

200 -~------- ,L t_

N+-------~------~------~------~------~----~~----~------~------~ 1450.00 500.00 550.00 600.00 650.00 700.00 750.00 800.00 850.00 900.00

POSITION RLONG THE RORD (fT.) FILTER PASSBAND ~ 15.0 TO 35.0 FT. WAVELENGTHS }>

I

0 0

N

0 N .

HARLINGEN NORTH FLOODWRY BRIDGE SOUTHBOUND FIRST 1100 FT. UNFILTERED - SOLID LINE RIGHT WHEELPRTH FILTERED- DOTTED LINE FRAME 3

I 200 __..,+------ -------- ---------~

81 80 79 78 77 76 75

9 50 . 0 0 1 0 0 0 . 0 0 1 0 50 . 0 0 1 1 0 0 . 0 0 1 1 50 . 0 0 1 2 0 0 . 0 0 1 2 50 . 0 0 1 3 0 0 . 0 0 1 3 50 . 00

POSITION ALONG THE RORD (FT. J

FILTER PRSSBRND ~ 15.0 TO 35.0 FT. WAVELENGTHS > I

z

0 0 .

0 1..0

0

...._, 0 N

Zo 0

1-CI:o >N w. __jC( w

0 cr:o o([J a: .

0 I

0 0

HARLINGEN NORTH FLOODWRY BRIDGE SOUTHBOUND SECOND 1100 FT. UNFILTERED - SOLID LINE FILTERED - DOTTED LINE

RIGHT WHEfLPRTH FRAME 1

Bo' ' /1;1r---------:-----·-·-·-- ~- -------·- 200

I I ill

74 73

\ I '.../ I I

l I ·-

Iii I

Iii

72 7/

\ I I ,_,

70 69 69 67 E6 65 64- 63

' ' \ l

·~

-+-------~--------~------~------~--------~------~--------~------~------~

'o.oo so.oo 1oo.oo J5o.oo 2oo.oo 25o.oo 3oo.oo Jso.oo 4oo.oo 4So.oo POSITION RLONG THE RORD (FT, 1

FILTER PRSSBRND ~ 15.0 TO 35.0 FT. WAVELENGTHS

H g R L I N G E N N 0 R T H F L !J 0 0 \J A Y 8 R I 0 G E S 0 U T H B D U N 0 ~~ t C tJ N D 1 \ ll Cl ~ 1 .

0

z '-' 0

N

Zo 0

0 era Oc.c 0::: •

0 I

roz 6/

1450.00

UN F I L T ERE D -- 5 D L_ I D L I N E f' I l·~ I j l ' .· lf r r :' l ' 1 f I \ . ' \., I . . 1.. ' ri . '

FILTERED -DOTTED LINE

200

I I I \.!

t

I

I \ I I I

•'

59 58 57 56 55 54 53 52 51

~ H H "1 [' 2

--1

-,---- -··-----,.-----·---~- --,- . --·- ·---.,..-- ---··- -·~--,-- ..... ··-"""1___ ·-· "1

~~oo. oo :~.so. oo E) on. oo r;~.)o. oo ·,-on. oo 7~o. oo uno. OCJ FJ~;n. ou POS 1 ·r I CJN ALONG T Ht: tiCJHn l F T . 1

F I L T L R P R S S 8 R N 0 1 G . 0 T U :1 ~~ . lJ F r . W H V f L I . N (; r 11 J

I '111 f.l • !J u

l>

-.f:a.

z

c 0 .

0 c..c 0

'--" 0 N

Zo 0 1--t ..___

CI:o >N LLJ •

0 _ _j I

w

0 a:o Oc..c a: .

0 I

0 0

•

HARLINGEN NORTH FLOODWRY BRIDGe SOUTHBOUND SECOND 1100 FT. UNFILTERED - SOLID LINE FILTERED - DOTTED LINE

44 43 42 41 40

I

), ,,, I i \

~~- i! \ I : \ ( \

\ I ' ' I

'-'' '

RIGHT WHEELPRTH FRAME 3

~+-------~------~------~------~--------~------~------~------~------~ 'goo. oo 950.00 1 DOD. 00 1050.00 1100.00 11 SO. 00 1200.00 1250.00 1300.00 1350.00

POSITION RLDNG THE RORO (FT. 1

FILTER PRSSBRND ~ 15.0 TO 35.0 FT. WAVELENGTHS ~ I

•

HARLINGEN NORTH FLOODWRY BRIDGE SOUTHBOUND LRST 1100 FT.

z

0 0 .

0 CD

0

......., 0 N

Zo 0

1-0:o >N w. _Jo

I w

0 a:o Ow a:: .

0 I

0 0

'o .oo

UNFILTERED - SOLID LINE FILTERED - DOTTED LINE

\ ' \..J

.39 .38

; ' .. ---- -~-·· ·-- ------ - --

' ri, I 1

1 I I I I

\ I : ' / \ I I I J

\ J l \./ ' J '...-

I \

I ' I

37 3~ 35 34

I I

' I 'v

r. I '

I t \

I i 1

1

\ I I I I I \,

,, I l 1 \ I

32 31

l 'J I

" I I

I

so.oo 100.00 150.00

POSITION 200.00 250.00

RLONG THE RORD FILTER PASSBAND 15.0 TO 35.0

RIGHT WHEELPRTH FRAME 1

26 Z7 26 25 24 23

300.00 350.00 400.00 ( FT . l

FT. \JRVELENGTHS

450.00

z

0 0

0 (D

0

. Zo 0

l­ITo >w w .

0 _ _j i

w

0 ITO OLD cr:: .

0 I,

0 0

• •

HARLINGEN NORTH FLOODWRY BRIDGE SOUTHBOUND LRST 1100 FT. UNFILTERED - SOLID LINE FILTERED - DOTTED LINE

2CO'

22 21 20 19 18 17 It:. 15 14 13 12 II

r. I ~

I \ J \

I

/0 9

RIGHT WHEELPRTH FRAME 2

8

~

I> I I

I \ I I

zoo/

/\ I I

I I J \

7 cO s

~+-------~--------~------~------~~------~------~--------~------~------~ 1450.00 500.00 550.00 600.00 650.00 700.00 750.00 800.00 850.00

POSITION RLONG THE RORO (FT. J

FILTER PASSBAND ~ 15.0 TO 35.0 FT. WAVELENGTHS

900.00

):> I

•

HARLINGEN NORTH FLOODWRY BRIDGE SOUTHBOUND LRST 1100 FT.

z

0 0

·o

~ 0 N

Z:o C)

I-­cc 0 >N w.

0 _ _j I

w

0 cr::o OC.D a:: .

0 I

0 0

4 3

UNFILTERED - SOLID LINE FILTERED - DOTTED LINE

2

I I

~ !

0.0"

~ zo'Approach Slab

Bent Af£>

RIGHT WHEELPRTH FRAME 3

c:=> TRAFFIC

~+-------.-------~------~------~-------.-------.------~-------.------~

'soo. oo 950.00 1000.00 1 oso. 00 1100.00 1150.00 1200.00 1250.00 1300.00 1350.00

POSITION RLONG THE RORD (FT. J

FILTER PRSSBRND ~ 15.0 TO 35.0 FT. WAVELENGTHS ~ I