FINAL REPORT
APPLICATION CLOSE-RANGE OF TERRESTRIAL PHOTOGRAMMETRY TO
STRUCTURES BRIDGE
by
Hilton Marvin H.
Research Scientist Senior
(Photogrammetry by Bales, F. B.
Engineer) Photogrammetric
(The findings, expressed opinions, conclusions this and in
necessarily of the author those and those of report
not
are
agencies.) sponsoring the
Highway Vir.ginia Transportation Council Research &
(A Sponsored by Cooperative Organization Jointly Virginia the
Highways Department Transportation of and &
Virginia) University the of
Cooperation with Transportation Department the of S. U. In
Highway Federal Administration
1985 June
85-R40 VHTRC
COMMITTEE RESEARCH ADVISORY BRIDGE
Bridge Engineer, MISENHEIMER, Chairman, VDH&T District L. L.
Bridge Supervisor, Engineer ANDREWS, Design VDH&T E. J.
Bridge Engineer, CHAMBERS, FHWA Division C. L.
Div., GARVER, Administrator Division VDH&T JR., D. Construction C.
HILTON, Research Scientist, Senior H. VH&TRC M.
Engineer, MCGEE, VDH&T G. G. Assistant Construction J.
Engineer, MENEFEE, Structural Steel JR., F. VDH&T M.
Bridge Engineer, MORECOCK, District H. VDH&T R.
Engineer, NASH, JR., A. District VDH&T C.
Bridge PREWOZNIK, Engineer, District VDH&T F. L.
Bridge •Engineer, SELLARS, VDH&T District W. L.
Bridge Engineer, SUTHERLAND, G. F. VDH&T
University Engineering, Old Prof. Civil Dominion WANG, of R. L. L.
Engineer, WILLIAMS, Materials P. District VDH&T C. ii
SUMMARY
photogrammetry close-range application terrestrial of field A to
displacements magnitude structural and of order small of the measurement
10/1318
conducted. A elevation Jena UMK differences in camera was was
photographs evaluations. used the in take the used to
bridges girders several steel deflections of of the Measurements on
i/8
achieved with be
of the in order that accuracies
suggest
can on
0MK
10/1318 close-range addition,
using the In normal
camera. care
applications bridge be other photogrammetry used for terrestrial
can
technique condi- using
for this By deck for condition such
surveys. as
preparing taking and hand need for the tion
measurements surveys,
provide photographs eliminated. The field sketches the is in perma- a
potential
evaluate reference be used
which
record to nent
as a can
structural
of deck changes the condition the in movements. to
gage or
desirable, of bridge the
evaluations records of Where permanent use
are
considered. should photogrammetry close-range be
10/1318 satisfactory during produced results the The UMK
camera
Highways of by Virginia purchased and Department the study has been and
applications. terrestrial close-range Transportation for It is
recom-
capabil- of bridge made the engineers highway be and that mended
aware
photogrammetry. close-range of ities iii
CONVERSION SI FACTORS
Multiply To To Convert By
Length:
2.54 in--- cm
0.025 in 4 m
0.304 8 ft m
yd 0.914 4 m
609 344 kin- ml
Ares
2 2
6.451 600 E+O0
in.
cm_-
z z
9.290 304 ft E-02
m
2 2
yd 8.361 274 E-01
m
9
2.589 988 E+O2 mi-: Hectares
(a) 4.046 856 E-Of •ectares------acre
3
353 E-05 2.957
oz m
3
4.731 765 E-04 pt
m
3
9.463 529 E-04 qt
m 3
706 1.638 E-05
m
3
ft 2.831 685 E-02
m
3 3
yd 549 7.645 E-Of m
3
1.,000 lm NOTE: L
Volume
Unit per
Time:
ft•31mln
3
m3/sec 4.719 E-04 474
m3/sec ft•/s 685 E-02 831 2.
m31
In•/ml. E-07 2.731 177
sec
/
E-02 258 1.274 •/rain
yd
s ec------
m
3
/s•c
E-05 gal/min-.------6.309 029 m
E-02 kg 2.834
952
oz
E-03 kg 174 1.555 dwt
4.535 924 E-01 kg ib
847 E+02. 9.071 kg Ib) (2000 ton
Mass per
Unit
Volume:
Ib/yd2•- 2
kg/m E+01 4.394 185
3
Ira3--
in• E+04 990 kg 2.767 / lb
kg/m lb/ft.• 846 E+OI 1.601
3
kglm E-Of 5.932 Iblyd•= 764
Velocity:
(Includes
Speed)
m/s E-01 3.048 000 ft/s
mls E-Of 4.470 400 .•.lh
m/s E-OI 144 444 5. knot
km/h E+O0 344 1.609 ml/h•-•------
Force Per
Unit Ares
2
E+03 757 lbf/In 6.894 Ps
2
E+OI 026 lbf/ft 788 4. Pa
Viscosity:
2/
E•06
1.000 000
cS s m
t E-Of Pa's l.O00 000 p
5/9
°F-32) °C Temperature
CLOSE-RANGE TERRESTRIAL PHOTOGRAMMETRY APPLICATION OF TO
BRIDGES TO HIGHWAY
by
Hilton Marvin H.
Research Scientist Senior
(Photogrammetry by Bales, F. B.
Engineer) Photogrammetric
INTRODUCTION
obtaining Photogrammetric surveying information involves in
an
by photographs object. taking of from indirect measurements
an manner
usually procedures surveying where Unlike conventional measurements
are
object photogrammetry directly field, involves of the the in made
photographs required recording these the obtain using the and
to area on
photogrammetric office. the later When time in measurements at
a
general required. techniques operations used, These three
are are are
photography, photographs, taking and, planning, the processing the and
photographs finally, desired using the obtain The the measurements. to
products example, produce photographs, be such
for used other to as can
topographic maps.
photogrammetry. for broad number of
There
it In
are uses a a sense
(interpretative) qualitative quantitative well be for
used
as as can
(metric) diversity, photogrammetry has been work. of found this Because
beyond applications of fields useful number be
its in most to
common a
forestry, mapping. fields include surveying these of all and Some in
physics, biomedical, transportation engineering, and of astronomy, types
(I) planning. urban
photogrammetry aerial
be divided into and Metric two
areas: can
high photogrammetry precision
which terrestrial. aerial is In
camera, a
photograph airplane, plane the flies
used mounted
is in to
area an as an
photographs photogrammetry, taken terrestrial from fixed
For
over. are
earth's positions majority surface. either the While the of
or on near
photogrammetry highway transportation conducted work the the and in
presented work field been of the aerial this the has is in type, report
applications potential evaluation of concerned of with
terres-
an some
bridges. highway photogrammetry trial to
particular photogrammetry study The this of be further
in
can use
close-range photogrammetry. terrestrial defined these In type
as
object applications relatively the mounted close be the is to to camera
close-range the when Photogrammetry be considered photographed. is to
4 330 approximate of camera-to-object in the distance is in to range
(2) fields where direct Photogrammetry used this is in ft. in
many range
impractical,
costly, diffi-
object either of is measurement very or an
impossible obtain cult if otherwise. to not
of
number highway engineering be there transportation and In
may a
photogrammetry. These close-range applications for terrestrial
may
significant measuring historically documenting from structures to range
structural of deflections structural small distances such movements,
as
of structural positions changes relative other members, the in or
elements.
SCOPE PURPOSE AND
applicability
the study
evaluate of primary this The to
purpose was
small of photogrammetry the close-range for of terrestrial measurement
Several bridge members. of deflection structural such the movements
as
study follows: secondary of the
purposes as were
background precedents for of the
and the i. Review
use some
obtaining close-range photogrammetry for terrestrial
bridges. engineering of measurements
used general of in the classification 2. Review
cameras
applications. terrestrial
accomplish particular the 3. used Evaluate the to
camera
study. primary of the purpose
photogrammetry close-range terrestrial 4. Evaluate of the
use
bridge recording deck condition for surveys.
technique ability small define Evaluate the of the 5. to
the associated with such that differences elevation in as
bridge decks. surface of texture
work office study field and limited the
of the The to
scope was
bridges, Several accomplish objectives. which the above to necessary
study. were-selected field An for later, detail described
in
more are
photogrammetry by resulting photography analysis the made of the
was
Transportation. Highways Virginia and of Department of the section
BACKGROUND
relatively long photogrammetry used Close-range has been
over a
beginning of period nineteenth the middle the time, of In in century.
by photographs
applications terrestrial used earliest the
surveyors were
point-by-point technique. develop
from
intersection It to maps
was
a
photographs. identify however, difficult, different point the
to
same on
by problem of resolved the the This invention comparator, stereo was
independent Pulfrich work 1901 of which resulted from the in
(3) possible the simultaneous 1903. made This device Fourcade and in
photograph
of different setting measuring marks identical of two
s
on
point-by-point by method, Succeeding calculations made the views.
were
subsequently work automated. been but this has
applied photogrammetry close-range architecture when 1885 In
to
was
(3) began photogrammetric Meydenbower Germany. archive the in monument
widely photogrammetry aid Architectural used reconstruction in is to now
damage related for other restoration efforts after and to
measurements
glaciers.
photogrammetry The used 1889 work. In to
survey pos-
was
technique changes sibility the and using observe of in size the to
recognized, glaciers velocity thus
dimension the and of time
was was
early analysis photogrammetric Other of added the measurements. to
close-range photogrammetry applications the of of the century at turn
images evaluation X-ray taken of for medical included the purposes.
1920's development photogrammetry dealt with the the of Up
to
Subsequently, photographs ground however, the taken from main stations.
photography development placed emphasis the of both the aerial
was on
stereoplotting produce instrume.nts useful that used data and the to
are
applica- photographs. given With from aerial attention recent to
more
photogrammetry of
variety technical of terrestrial it in tions
areas,
a
obtaining recognized being for be used again method that
is
can a as
legis- objects for Federal of documentation and measurements purposes.
example, placed
for the has
restrictions lation in recent years,
use on
engineering federal for that of funds and other activities construction
historically significant When
site affect
sites structures. may or •a or
eligible inclusion for the either
included is is structure
on, on, or
Places, be Register effort made of National Historic prevent to must an
only alternative demoli- where harm the
the is site. In to
cases some
required removal, often records of the
that it is tion structure
or
or
acquired. object of kind often require This could be documentation
subsequent field the laborious time-consuming and and measurements
bridge, drafting drawings. addition, inventory of of In structures
an
encouraged department transportation that within each
is
state so now
historically significant identified. be is It apparent structures
can
photogrammetry close-range could be used terrestrial in assist that to
applicability approach satisfying using of requirements. this The these
historically objects significant and associated document structures to.
Virginia
transportation evaluated in projects with in
recent
a was
by Spero.(4) work that by documentation this concluded in It report
was
sufficiently and photogrammetric is methods is cost- accurate
very
photo- by obtaining data field that effective. also noted It
was
of traditional labor-intensive,
the whereas is grammetry not
more use
recommended further normally
labor- It methods intensive. is
very was
photo- terrestrial close-range could be used that that
for
camera a
Subsequently, the purchased. used that
be the grammetry
was on
camera
presented this being study by
Spero work and the in report
was
on
Transportation. Highways purchased and by Virginia of Department the
later. described This is camera
photogrammetry and distortion
of terrestrial The to
measure use
deflection bridges precedent. and Distortion without in is not movement
by
monitoring
determined be function of of
time
structure
on as a can a
photogrammetry regular Accordingly, of of
the basis.
account
use an a
by presented
bridge girder in Scott
box
in movement
to was measure a
by
1978.(5) the caused arch of of The the distortion measurement
an
described.(3)
this bridge also In been railroad has of settlement
a
of develop the photogrammetry the used latter instance contour to
was
and fit constructed lining could be distorted that arch armored
to so
an
10/1318
UMK instance, another Jena it. In support
two recent cameras
of
bridge the Germany determine used in
measurements exact to
a were on
bearings could be bearings that
structural elements the the at
new so
required
rail- the would techniques have of fabricated. The other
use
would have unacceptable periods of and bridge time for be closed road
to
Williamsburg costly.(6) the
still
been
In
recent
case,
more a more
photo- surveyed
using City
York Bridge the East River in New
was across
corroded of techniques the condition grammetric the determine
.to suspen-
profile during
load bridge cables and sion tests. get to
accurate
an
First, bridge cited. technique
advantages this using of the Two
were on
only few bridge for
closed
considerable the and saved time
a was
was
required
techniques would have hours, the other whereas of many
use
be considerable that Secondly, data stereophotos days. the record can
information. additional reexamined obtain time to at any
CAMERAS PHOTOGRAMMETRIC CLOSE-RANGE
General Classification
photo- total the used initial in the instrument The is
camera
surveying function instruments grammetric similar is and in to system
object.
Whereas
about used obtain information since is it
to a an
only for provide direction
information in theodolite
transit
one can or
virtually. yield
sighting, information photograph
in given
a can
a a
the point identified Therefore,
unlimited of number directions. any on
photograph
would different with direction the represent respect to
a
position.
The important good
thus is instrument since camera camera an
quality photographs
metric to necessary are accuracy. assure
should be that photo- noted the It used for terrestrial cameras
differ those from aerial used for Since grammetry in
surveys.
photogrammetry terrestrial the stationary used from positions, is
camera
design simpler than is its that of for
aerial used
surveys. a camera
(phototheodolite) The combined, effect,
is in theodolite with
camera a
photographs and used obtain object is of from fixed control to
an
overlapping points. photographs obtain phototheodolite order In the to
be from
another, moved
station mounted must to two at one or cameras a
rigid distance known of the ends base
could be used obtain apart
to
on a
photographs. the pairs of
hand, Aerial the other stereo
cameras,
on
being
during
good lens, in require motion fast shutter
exposure, a a
mechanism
short for high-speed times, film and with
emul- exposure
a a
photogrammetry, project sion. this Since concerned with terrestrial was
aerial will be further. discussed not cameras
close-range that The used photo-
for terrestrial cameras are
designated either
metric nonmetric. Nonmetric grammetry are as or
have
that interior unknown and orientation often is is
cameras
an
principal unstable; i.e., principal point the and illustrated distance
Figure unknown 1
in unstable. hand,
other the Metric cameras, are or on
fixed assumed have
With the interior orientation. to were once a
development having focusable of tolerable radial distortion and
cameras
stability, adequate longer only designate it
the
to
was no cameras
having being fixed suggested
orientation been has that metric. It
a as
simplest
classify being the by
the metric is to way
camera a as
(3) of existence fiducial marks.
normally designed specifically
Nonmetric for
not cameras are
photogrammetric
they calibrated work
and be if
in must to way
some are
be for such work. used combination Used appropriate with in data
an
reduction highly provide
nonmetric results system, accurate cameras can
costly less and
than Several metric reduction data schemes
are cameras.
Karara.(3)
by reported general have been
In nonmetric
sense, a camera a
obtained be for low
but expensive evaluation cost, system
can an
sophisticated requiring
required. would be The computer
program a
costly, photographs but metric the is taken with the instru-
camera more
analogue plotters. availability restituted be with The the of ments
can
plotters
logical would make the the
metric choice to appear
camera more
for projects require that that be from derived the most measurements photographs.
Fiducial
Marks Negative
Perspective
center
(Lens)
Principal
Point
Principal
Object
Distance
principal distance, showing Illustration Figure i.
(From fiducial principal marks. point, and
3.) Ref.
"cartographic"
and
called work used for metric Cameras
cameras are
geometric
for highly corrected by usually lenses characterized are
distortion.
10/1318 The UMK Camera
by reported study earlier study and the used this The in
camera
10/1318. Spero(4) single (Jena)
metric This model the UMK Zeiss was
the of UMK device. views Two mounted
its orientation in is
own camera
10/1318 tripod shown in
device mounted orientation its in are a on
3. Figures and 2
(Jena) Figure 2. Front of view the 10/1318 Zeiss UMK
Photogrammetric Universal Camera.
Figure
10/1318 3. UMK being
placed
tripod camera on
for field use.
10/1318 wide-angle efficiently where field used
The be UMK
a or can
taking large focusing required. Objective picture allows the size is
a
infinity. photographs between l.Sm of and The less than of distances
large objective
lens, focusing the
offers of continuous range
a camera
horizontal vertical
stop-settings, of of and choice
times exposure
or a
photographic format, The vertical horizontal and of
choice axis.
a or
handling separated facilitate and substructure be
and its to
can camera
high Angles degree precision operation. of with with be measured
can a
include of
the Other features the orientation system. an camera
electromagnetic illumination of the shutter electrical release and
10/1318 universal
fiducial of with marks. second the Use UMK
camera a
possible configuration of the double-mourrted where erection in is
two
a
10/1318 probably single tripods of difficult.. be would The is UMK one
close-range versatile available the of for the in
most
cameras use
photogrammetric applications. of features the of terrestrial main Some
I, either film Table the noted Table
in i. summarized in As
camera are
photographs.
plates taking of this the for used be
For
purpose or can
plates study, glass image that
distortion eliminate the used
to can were
shrinkage changes film. with with associated and temperature occur
being photogrammetric photographs be defined
the studies In
as
can
by horizontal, oblique of vertical, the the of orientation
nature or
optical Accordingly,
the
of the when is axis axis
camera camera.
and
horizontal, being photographs
horizontal be defined will the
so as
analyzed photographs with vertical be
Horizontal and stereo-
can on.
photogra- commonly plotting aerial for used scopic instruments that
are
photographs require phy Oblique study. available for and the
were
analytical stereoplotters for A restitution. universal accurate
or
only study. stereoplotter for this However, available universal
not was
accomplish photographs
the vertical horizontal and to necessary were
objectives work. of the main
Table i
10/1318 (Jena) Model of UMK Summary of the Main Features Zeiss
Single Terrestrial Camera
Photographic Principal Position Format Nominal Tilt Minimum Format
(ram) material of focal rotation distance
range
range
(deg) (m) principal length
(ram) P0,int
Central Plates 4 130x180 -30 I00 I. Yes Variable or
film in steps
to
+90
Source" 3. Ref.
•_ASUREMENTS FROM PHOTOGRAPHS
photogrammetry photographs normally the In taken that such
are
overlap 60% object there will be
the being in observed. Thus, if
a
area
adjacent photographs
pair of
objects from viewed positions,
two a are
lying overlapped the seen in
be three dimensions. in area can
develop overlapping the photographs of To stereoplotter geometry a
high-precision used. is is
It instrument that be used obtain
to a can
three-dimensional information photographed object. the about accurate
accomplished This overlapping photographs placed when is the in two are
relationship device the that such between field the stations is
camera
reproduced precisely.
Basically, photographs correctly the
very
are
aligned stereoplotter the when optical in the positioned
axes are as
they photographs when
optical the taken.
The for axis
were were a
photograph by (shown located is of four the fiducial marks earlier
use
i)
Figure in that recorded image the
the of time at
are exposure. on
through The lines of intersection opposite drawn the fiducial marks will
(Figure principal I). locate the point principal the When point is
directly optical
the of axis of each projectors the of the
two
over
stereoplotter overlapping the interior photograph orientation for •each
is recovered. With the light recovered, interior orientation the
rays
through plates passing replica the be will those that of entered the
a
photographs when
the taken. The position relative and camera were
duplicate will orientation the existing situation the of time not
at
photography, however, the until exterior elements orientation have. been
photographs recovered. Each of stereoplot?.. the in the be posi- must
with tioned the X, Y, result, degrees and
As Z six respect to axes.
a
freedom, of which include three translations three and rotations, have
overlapping be photograph. for recovered each accomplish order In to
to
this adequate orientation,
number of points control be must survey an
provided.
Relative orientation solves for five elements orientation and
can
accomplished by manipulating be the such model that estab- is it stereo
arbitrary lished
effect, scale. It, pair in each of at
an
causes
corresponding by point intersect recovering relative the to at rays
a
other.
tilts projectors the of with Absolute each respect two to
solves orientation for by accomplished elements orientation and is
seven
scaling leveling scaling, and model. the horizontal For control
two
plotted points drawing the
scale the be used. The at to are map on or
points control make used the horizontal between distance the
to
are
corresponding
photographic equal points model the distance the
to on
drawing by
changing This done is model the base the in instru- map. or
leveling, least three For points control vertical needed ment. at
are
plane.
establish
The four of the models quite often to stereo a corners
used, however, front back and side and
side rotations to to are are
scaling operations model conducted make the level. of The
stereo to two
leveling alternately repeated and
refine the
to
necessary are re- as
sults, adjustment
affect the other. since may one
recovered, resulting the When the exterior orientation is stereo-
by scopic be model table which tracing be moved measured
can a can
through
all All model three three the directions. motions in
space can
automatically. manually be monitored When either and recorded
or
stereoscopically through viewing spectacles model colored attached the
table, tracing, the circular the model within the
operator to a sees
floating white which differences ele- dot be used determine in to
can
accomplished by floating vertical- This moving the white dot vation. is
ly object. Thus,
point until be the with it
in to contact appears a on
sloping if the wanted elevation terrain, the elevation of
to
trace a one
floating continuously changed of the dot would have be maintain to to
plot line with of surface. the
To apparent contour, contact
a a con-
floating elevation, question fixed the the elevation dot in is at stant
stereoplotter tracing table horizontal and of the the the moved in
keeping plane. By surface, line the dot the with terrain in contact
a
model points elevation of the
be traced.
Discrete constant can can on
time-dependent of be elevation. determine measured the their In to case
photographs distortion of of
deflection structures, measurement are or
photographs object, taken additional of the latter and
time
at
are a
durinK Changes taken occurring the locations. the elevation in at same
photogra- interval thus before and after from the be time measured can
phy.
ACCURACY
the engineers of
Accuracy of in the
is main measure-
one concerns
structural distances, elevation, differences of in movements. ment or
particularly structural of This of the is the in
measurement true
case
magnitude. only expected of deflections of small order that be
to a are
techniques photogrammetric from
that obtained The be
accuracy can
quality depends of
of the factors number and such the
nature
upon
a as
camera-to-object quality photographic materials, of the the the camera,
distance, disposition few. points, just and the of control
the to
name a
Consequently, possible will that be accuracies it is
not to state
Generally, applicable directly however, all is situations. to
accuracy
having photograph. given related of the the scale
For
to
camera a a
length, photo camera-to-object focal of the scale the function is
a
usually expressed function distance. of the Hence,
is
accuracy as a
photo-taklng conditions, _+0.01%
of of distance. For
accuracy average an
Accordingly, camera-to-object the achieved. distance be
at a can i0
1/16
ft, within 50 could obtain of distance in. to
accuracy an one
only technique, Normally, of order the the the minimize in to
cost
sought. degree has been of that indicated is is accuracy It
necessary
applications photogrammetry
for industrial of that aim
most accuracy an
(3) photo-taking _+0.02% of of about the is distance. At it rate, any
close-range remarkable obtained with that be accuracies apparent
can
techniques. photogrammetric measuring
APPLICATIONS RESULTS OF FIELD
Bridge Condition Survey Deck
photogrammetry application possible close-range terrestrial of One
photo•raphically recording bridge deck These condition is in surveys.
bridge repaired,
decks be conducted that recondi-
to surveys are are on
replaced.
degree repair the of tioned, determine order
In to or or
bridge
decks of the rehabilitation on-site examinations necessary, are
mapping involve the conducted.
The the examinations on-site areas on
surface where located. of deck Areas distress various types
are
by usually example, of delamination, for detected the chain
of
a use
are
drag, sounding hammer, of delamination both. the The
is extent
or a
scaling, Patches, sketches. deck off recorded and marked the also
on on
of also located recorded and other evidences deterioration and
are on
addition, sketches. taken from locations the
certain In cores are on
laboratory decks and the determine chloride examined in to contents.
information, be regions the deck Using all this the distressed of
on can
along calculated, results using information the the of this with and
replacing analyses, rehabilitating bridge the chloride decision
or on a
deck be made. can
close-range photogrammetry bridge of for the deck evaluate To use
bridge
evaluation that scheduled for condition
surveys, a was was
bridge study. 33 located selected for The of is Harrison- Rte. east
on
simple composed burg of 81. four and is Interstate It
spans overpasses
spans), (two approach 6 68 ft ft 7 and and has 52 in in
center two spans
regular bridge roadway ft deck 39.5 curbs. between width of The a
laying fashion,
the work usual conducted condition in its
survey crew
marking grid delaminated off the off deck and and dis- .in pattern a
they several of detected. the
tressed After
spans
areas as were were
photography begun, surveyed traffic marked that the the
and
was so
by photogrammetry well deck control used could be the the
party as as
bridge deck of the established
line the such base
A survey
crew. was on
width
photograph. that each could Targets the be covered entire in were
26-ft for the laid deck intervals based needs the the
at
out
on on
length. height mounting of focal Three lines of the and its
camera
placed bridge deck, each of the the side and
targets were on one on ii
closed that lanes approximately of the the to in another two center were
operation. during the traffic
bucket of the attached plywood frame
mounted in
The to
a camera was
he±ght 36 operated of ft (Figure 4).
The boom llft at a
was camera a
allow moved bucket the truck bridge and deck. The the above to were
total
A reference the above of the positioning targets. center
camera
taken. bridge deck A photographs overlapping the of of eleven
were
gives through 8, which photographs Figures 5 shown in these of is mosaic
end. bridge from beginning the
complete deck of the of the view west
a
marked distressed
f±gures,
the these from be noted As were areas can
which determ±ne used chalk white blue
dark and A with to
were crayon. a
Probably color darker is
the photos. the
the
easiest to see on was
acceptable. either best, but is
boom for lift of bucket
mounting the 4. Figure Camera
a on
bridge deck. photographing of close-range a 12 13
edges of of the All the delaminated by
measured the areas were
deck information this and
recorded sketches. their Thus, survey crew on
the data recorded could be later used calculate the of dis- to
area
tressed that would material require deck the removal if be
to
were
rehabilitated. photographed,
deck If the however,
these
were measure-
would be field, have taken the in the of the since not ments to
area
distressed could material photographs. be determined 9, from the Figure
example, (Figure for shows 7) distressed the regions plotted of 3 span
photographs. scale from the
The of feet in each dis- to
square
area
region
plat. tressed shown the interesting is is It that the
to note
on
lighter
patches colored deck the Figure
shown 7 in had that spots
on are
repaired been earlier rehabilitation Although of the in deck. these
an
patches deck, outlined they the easily plotted
shown not
were on were
as
by patches marked broken the lines with Figure 9. in Several of these
patches their and measured
calculated compared and the w•th were areas
photographs. the determined from values
The close in areas very were
likely but photo- that the it determined is from the agreement,
areas
graphs
precise than
those calculated the from direct more are measure-
because deck level it is difficult sometimes define ments, at
to more
edges patches the photographs. of of than the from the is it some
close-range photogrammetry The bridge of for deck condition use
developing eliminate the for need sketches of deck the surveys can
taking
for and linear addition, of
In type. measurements any perma- a
of deck surface record the available future for reference is and nent
information Visual
that such
described above be obtained use. as
can
photographs from the needed, possible if and future structural settle-
changes other elevation
position in relative
be measured ment
or
or can
making by
photographic of the initial
Having record. permanent
use a
might for record future be primary close-range the
using for
use reason
photogrammetry bridge for
deck
condition While the of survey. a
use
technique
could reduce of the work thus the and required
some manpower
for the by photogrammetry would be this offset the for need survey,
personnel lift bucket and truck and operator. a 17
• o
• o
o •, o
Surface in.Elevation Irregularities C.rscks Differences of and
bridge points Several the described the deck of above
on were
determining selected of the for differences small elevation. in purpose
photogrammetric locations depth the At three engineer the of measured
highest joint filler the surface of relative deck level the the
to
(Figure i0). immediately adjacent joint the points, four other At to
depth made similar pitting he the of of small the in measurements
some
Finally, deck cracks surface. widest of he the widths three measured
bridge joints. deck several of the
of All these
measurements
near were
1/16
by straightedge taken field using the the in and in
to nearest
a
photogrammetric independently The engineer rule. the determined dis-
subsequently 0.01 the ft. field The tances to nearest measurements were
compared 0.01 the converted ft with those determined from and to nearest
photographs the selected Table shown 2. the Of in ten measurement
as
by comparisons, four ft,
0.01 differed the five
and same, were one
by 0.02 differed ft. the All of vertical comparisons
measurement
were
1/8
photogrammetric less. only within The
taken in
measurements or were
I/8 (i.e. in), approximately 0.01 ft but the is it to nearest apparent
exacting close-range that obtained be with the
measurements
very can
I/8 photogrammetric technique. of within the Measurement actual in
sufficiently highway value bridge for and
accurate most are applications.
depression Figure i0. joint Relative filler. of 19
Table 2
and Comparison Selected Field of Some
Photogrammetric Measurements
Measurements
Difference, Description Field, tric, of Pho togramme
Ft Ft Location Ft
depth 0.00 0.06 0.06 I Joint
depth .01 .06 2 .05 Joint
depth .00 .05 3 .05 Joint
.01 .02 pit .03 Surface 1
.00 .03 .03 pit Surface 2
.01 .02 3 Surface .03 pit
.01 4 pit .02 .03 Surface
.02 .07 Crack .05 width 1
.01 .06 Crack .05 width 2
0.08 0.00 3 Crack 0.08 width
developed irregularities bridge surface deck also be The of
can a
photographs. showing the from small deviations of the in One
very way
spaced bridge develop
close surface of deck is at contours to
a a
bridge 64 technique, interval. this the the of Rte. Rte. For test
over
Allegheny study. 0.05-ft County 639 for selected in A contour was
defining for surface interval used evaluate of
the contours to
was use
roughness photographs, Figure Ii. shown from the results in the and
are
rightward pointing by of The of deck shown the the the is contours
crown
perfectly Ideally, figure.
of smooth the the at trans- center
upper a
slope bridge by straight represented
deck would
be
contour a verse a on
edge deck. Furthermore, line horizon- the from the the the of to
crown
for spacing would be the all tal between lines the the contour same
Thus, and the shown. the in nonlinear lines variation contours contour
roughness, adjacent between the width surface, show contours or 20
irregularities, the surface in of deck. linearity the Deviations from
along the lines show degree relative the roughness of these contour
at
points.
spacing wider between A
in of the certain deck contours
a
area
indicates low closer high
spacing
high Adjacent spot;
and spot.
a a a
relatively low bumpy reveal region. spots a
The cracks of extensive the bridge deck the 64
Rte. mapped
on
were
photographs from taken from help above deck. the define cracks the To
they readily that
be could photographs, identified the in so two
proce-
dures used. first The involved wetting the deck with down
were
water.
the evaporated
As it longer remained cracks the in than the water
on
surface, clearly thereby
and defined cracks period the for of time
a
that prevailing with varied the ambient conditions. procedure This did
entirely satisfactory be
the since not of in the to
prove
water
some
cracks evaporated photography before the could be and initiated
completed. The procedure chalking second involved they cracks the
so
readily could be photographs. the in procedure This well, worked
seen
people
could mark the
cracks photographing ahead well of the two
as
so
that there delay.
Considerable effort additional and manual
was no
labor, however,
required
mark cracks. the plan Figure 12 is to
are
a
of the view cracking of network the close-range that by be shown
can
photogrammetry. terrestrial particular this lengths deck On the total
of the cracks 2,625 measured 1,344 total, ft. this Of ft cracks
were
measuring less than 1 width. in
kind this While mapping of would
not
mm
ordinarily bridge be done deck,
results close-range the show that
on a
photogrammetry
be extremely used conduct intricate to can surveys.
Figure ii. spaced Contours 0.05-ft intervals reveal deck surface at
irregularities. 21
bridge 64 Rte. deck of cracks Rte. Plan of Figure 12. in view over
639.
Bridges of Deflection
photo- terrestrial close-range applicability of evaluate the To
bridges structural measuring small for movements, two grammetry
were
could be and the bridges time under construction Both studied. at
were
placement of the subsequent photographed the prior and concrete to
to
steel
of the deflection girders. Thus, load dead the deck steel the
on
measured. The could be weight deck girders of the the under concrete
495 bridge
in 66
bridges Rte. the Metro first of the Rte.
two over
was
29) (alternate the Rte. 5th County; the Fairfax. second Street
was
Lynchburg. railroads in Southern Norfolk and crossing of the and Western
be could that
land bridges
has least of Each these at
open span over
one
opposed
Thus,
the under position the used to structure. to as camera
earlier, the described the
of the the above
structure,
as camera use
photographs being of taken with beneath the used
structure, camera was
bridge of underside the the superstructure. 22
Bridge 495 Metro Rte. over
bridge simply composed 495 supported of The ii Rte. is
spsns.
Deflection 7,
long tsken ft which 107
is measurements
span.
were
on
bearing composed between points and, like remaining all of the is spans,
girders. box steel The vertical each webs box of connected two
two are
by
plste, flsnge bottom the but steel hss esch
web similar top st
to
a
a
regular plste bridge, that girder. of effect, The deck for the in s
completes box the for The rails outbound the inbound section. snd Metro
tracks girder.
centered each box are over
positions, bridge, Three located
the transverse to
camera were
ground established
beneath the mld-span that 7 such its maximum
span
on
deflection could approximately be positions measured. The
camera were
ft below girders. 21 bottom the of mid-span, the box 12 Near
paper.
glued plates girders. bottom the the steel of box From targets to
were
each of overlapping positions, photographs the
taken
to
camera were
photograph typical pairs. the taken from A the create stereo center
position beneath the Figure 13. shown be is noted As in structure
can
photograph, forming place. from the wood for the deck the is in concrete
triangulation approach A used establish hor±zontal the and to was
positions vertical the of of each the
end From targets structure.
on a
65-ft ground, located baseline both horizontal the and vertical on
angles turned the of elevations for each the Two targets. to were
calculated--one baseline. of from each end the Good targets were
between these elevations indicated the control for that the agreement
close-range photogrammetry subsequent making adequate. the In was
triangulation deflection
used than rather
measurements,
program a was
photographic setting stereoplotter. the models The in
measurements
a
original plates glass made from 422F
the using Mann
were
a mono-
principal digitizer and the point located the and rotated comparator,
analysis, the coordinates. positions the the established In target
ground from
the be assumed and fixed the measurements to perspec- were
actually tive assumed The
but the is center true, to was move. reverse
vertical of the this determined be
in movement structure
can manner
displacement bridge the computed of the since
be from apparent can an
perspective of the movement center.
field, by the elevation the the of In base determined
camera was
leveling. differential adding this By elevation the the distance to to
perspective the elevations perspective of the center, true
centers at
the analytical three triangu- determined.
the stations From camera were
lation the elevation perspective of the apparent program, center
was
calculated for each of positions. the difference The between
camera
the the and elevations perspective of the each true apparent
at center
position bridge resulting of the of the from amount movement
gave camera
load girders the subjected. which the to were 23
girder Figure 66 13. Underside of box 7 of Rte. Metro
span
bridge placement. deck prior Twelve for targets to
photogrammetry the shown. are 24
photography.was during conducted
the The when solar
summer, ra-
substantial differential girder diation steel in temperatures can
cause
bridges. girders results of shown The have other steel studies that
flanges during day upward deflect will the the when hotter than top
are
lower.(8,9)
objectives study the of this the of
Since to
one was
photogrammetry close-range measuring for evaluate the of small use
photographed structural several the under times movements, at span was
placed, condition, the unloaded deck before the i.e. the
to
was measure
thermally deflection. induced
photographs bridge eight-day of taken All of the the
were over an
period, photographs period during During the latter of this June. part
placed before taken three the deck
and times times at at two were was
two-day afterwards. taken initial three of The
data
sets
over were a
thermally period provide of reference and the
induced to measurement
a a
period occurring of hours. deflection The last
several
two sets
over a
(after
single during day of data the deck recorded had
concrete were a
used
placed), load deflection been and
of the the dead to
were measure
photographs
approxi- The of these last of taken two sets at span. were
mately day initial the data that the time of the
to same as ensure
reasonably environmental would be conditions the same.
given 3 4. Tables obtained The 3 and Table in measurements are
gives deflection station, the taken from each and measurements camera
photographs taken these listed with reference initial the
June to
are on
A, three positions 23. ground the and the Points
C
B
camera were on
position points beneath the
the and Point A B center span. was camera
approximately 4 located Table 7 side. ft shows the and either C to
were
photography of occurring between deflection the times. span 25
23 and 2:00 June between that indicate The
measurements p.m.
on
by mid-span downward
deflected morning, the the 8:10 at next
span
a.m.
4). order, (Table be result in This
0.011 ft of to
appears average an
higher 2:00 due expected be would have been the since to
at
to p.m.
span
24), (June
morning thermally the 8:10 By induced the next moment.
a.m.
girders would the flanges would, and cooler of be the top
course,
of the 2:00 position downward their with deflect at respect to p.m.
differential
10:08 8:10 and previous afternoon. Between
a.m., a.m.
develop
the would flanges lower and between the temperatures
as upper
girders deflect began flanges the heat, would and to top to
cause
girders the that indicate 4, the upward. Table shown As in measurements
strongly results upward
0.016 These ft. of suggest deflected
average an
only direction showing the technique capable of that the is correct not
magnitude well. of order but their structural small of movements, as
4 the Table shown in of The series
measurements two next
are
weight resulting of the the mid-span from the deflections of span
10:40
24
June and 10:08 deck.
June Between concrete
on a.m.
on a.m.
10:40 0.252 ft. mid-span
30, deflection Between the
a.m. average
was
upward ft by 0.011 deflected 30, however, the
2:22 and June
span p.m. on
3),
(Table 2 about
0.236 ft yield
of deflection final
to or average
a
13/16 once differential again upward indicates deflection This in.
a
lower. being the flanges than effect, with the top temperature warmer
girders steel of the
plan deflection for the calculated value The
6here
1/16
While is weight given in. 2
of the under the
concrete as was
values, 3/4-in be plan it measured and between the difference cannot
a
Slight varia-
photogrammetric results in the that assumed error. are
explain of could
of steel the the dimensions tions in concrete
some or
developed of each from photogrammetric difference. The the measurements
showing differ- reasonably consistent, positions
the three camera are
i/8 but
all for less the order of
in
measurements one
or
ences on
i/4 could be difference this of by less than differed Some in. which
during occurring the bridge the small in thermal attributed movements
to
another.
position from required
the
timed to to one camera move 26
3 Table
(Span Photogrammetric Mid-span Deflection 7, Measurements
at
495) Bridge 66 Rte. Metro Rte. over
Deflection, Relative Ft*
Time Condition Average Point Date Point A Point B C
6-23 00 Unloaded 2- Reference Reference Reference p.m.
6-24 8"10 Unloaded 0.018 0.001 0.011 0.015 a.m.
6-24 10:08 0.001 Unloaded 0.014 0.002 0.005 + + + a.m.
6-30 10"40 0.259 Loaded 0.239 0.242 0.247 a.m.
6-30 22 0.246 2- 0.230 Loaded 0.236 0.232 p.m.
Downward deflection with the reference respect to measurement
Upward deflection reference with the respect to measurement
4 Table
Mid-span Photography Deflection Occurring Between Times
(Span 495) 7, Bridge 66 Rte. Metro Rte. over
Deflection, Ft*
Poin fl Point, B..P.o.in.t. .A.verage Period Time C t
6/23 6/24 2:00
8:10 0.001 0.018 0.0015 0.011 p.m. a.m.
6/24 6/24 8"10 10"08 0.015
0.017 0.016 0.017 + + + + a.m. a.m.
6/24 6/30 -10:40 10-08
0.253 0.244 0.258 0.252 a.m. a.m.
6/30-
6/30
10-40 0.013 0.009 0.010 2"22 0.011 + + + + p.m. a.m.
Downward deflection
Upward deflection 27
Bridge Railroads 5th and Southern Street & W N over
plate bridge three-span, 5th steel of The continuous Street is
a
girder design. study, during under the Since it construction it
was
close-range photogrammetry provided the opportunity
to to
measure an use
deflection
girders weight resulting deck. of of from the concrete a
long
bridge 147 The 5th of ft end and the the Street two
spans are
long.
bridge 170 of the ft continuous is is Because center
span a
design, by girders deflection the of of influenced the is steel
any span
loading bridge the unlike the 5th other therefore Street is
span; any on
simple availability bridge the earlier. the discussed Metro Due to span
bridge, Figure of shown beneath the 170 ft land the in center
open span,
placed 14, targeted being study. Figure for shows
the 15 targets was on
composed of the the of haunched steel five underside which is
span, girders.
procedures photogrammetric taken for used The the
measurements on
bridge bridge. this those the similar used
Three
Metro to
rows were on
right applied angles of girders centerline the the targets to to at
were
before,
portion and the middle of the three
As
span. camera near
positions ground of established
beneath the the
center
row were on
bridge. right angles Elevations and the determined targets at to
were
girders mid-span. the addition points all the and In
target to at at on
engineer's
photogrammetric level take the used
measurements, to
was an
girders points elevations before after all the both the and target at
photogrammetric check loaded the with the deck
concrete were as a on
photographs All of the elevation and measurements. measurements
were
placed September deck before taken occasions; the
and
in two
was on one
completed. April following another
of the deck the after in year was
Finally, the before used after elevation and to measurements were
girders calculate of the the deflection each of the steel target at
o
placed bridge points. skewed 27 but the Since the is targets at at
are
angles right bridge, additional the deflection
measurements at to
mid-span photographs. taken from the were
leveling by taken comparison with deflection of the A
measurements
•from photogrammetry presented those Table deflections The 5. in is at
according the 5 from from i listed 15 numbered and
targets to to are row
of each the deflection measured side the the The of to
east
west
span.
leveling by by given photogrammetry point determined that
and
are as
along points difference with the of there the 7 15 the between For two.
of 15 the differed difference
the between Five measurements. two
was
no
by by ft, Therefore, 0.01 by of 0.02 0.03 ft. 15 12 the ft and
two
one
I/8
by
ft, points The 0.01 about differed
than in.
average or no more
difference techniques 0.01 between ft. the less than two was 28
steel
continuous
three-span,
the of the of
span 14. center View Figure
bridge. girder 5th Street
5th
of Street
the placed
center being span Targets 15. on Figure
bridge. 29
girder the determined from mid-span of each The deflection
at
as
slight upward noted, photographs 6. be given
Table As in is a can
0.07.
ft downward the With measured which did deflection not
agree was
from either
plans. values provided bridge The deflection the average on
mid-span resulted deflection
6 little Table Table that 5 suggest
very
or
investigat±on, placement Upon it deck. of the the from concrete was
for continuous calculation of deflections for the found that
span
bridge placed the bridges entire that the assumed is is it concrete
on
The br±dge
this constructed in
the However, not at manner.
was once.
placed of end the positive
the in two
moment spans concrete
areas was
region of placed positive date, first; the later in
it moment at
a was
regions later, negative still the and the in moment
center over span,
that entirely from of different actual piers. The situation the was
plastic
the all the deck assuming that at structure concrete
one was on
example,
for the placed end the When is time. two concrete spans,
on
end the upward. the will deflect After sets concrete center on span
with composite the action due of the inertia increases to moment spans
of the deflection downward increased the steel. This resistance to
pos•tlon placed deck
its the when moment concrete
center span
on was
placed subsequent the weight Thus, of the region. the to
concrete
only girders back placement the deflected have initial center span
may
Consequently, deflection the position. approximate unloaded their to
leveling
by
checked by photogrammetric and obtained data
very
are means
interesting
actually likely occurred. is It what of accurate
measures
plan calculations deflection the which assumption that the
note to up.on
engineer photo.grammetric when the known the based
not to
was were
made. leveling photogra•metric and measurements were 30
Table 5
by Photogrammetric Comparison the Deflections the of Measured
Engineer's Technique those Using with Obtained Level
an
(Span Virginia) Lynchburg, Bridge, 2, 5th Street
Deflection, Ft* Measured
Leveling Photogrammetry ,,T.arg,et Difference No.
0.00 0.02 0.02
0.01 0.02 0.01 + +
0.02 0.02 0 + +
0.03 0.02 0.01 + +
0.01 0.02 0.03 +
O.O3 O.O3 0
0.01 0.01 0
0.01 0.02 0.01 + +
0.01 0.00 0.01 +
0.00 0.00 0
0.02 0.01 0.03 +
0.01 0.01 0
0.00 0.00 0
0.01 0.01 0
,,0,..03
0.01 0.02 .-
Average -0.002 0.009 -0.001
deflection Downward
Upward deflection 31
Table 6
Photogrammetric Mid-Span Deflection Measurements
at
(Span Virginia) 2, Lynchburg, Bridge, 5th Street
Deflection, Girder Number Ft
0.002 1 +
0.015 2 +
0.024 3 +
4 0.005 +
0.00 5
Average 0.009 +
CONCLUSIONS
following study The conclusions from be this close- of drawn
can
applied
photogrammetry
highway terrestrial of
to measurements range as bridges.
pho£ogrammetry developments I.
50 60 last the Over in
years,
or
photography stereoplotting. mainly been have aerial and in
During close-range however, few the last terrestrial
years,
photogrammetry being has been rediscovered for used and is
applications disciplines.
of various wide in Some
range a
applications highway bridges have demonstrated the
recent to
ability technique of difficult this otherwise to meet
measure-
and evaluation requirements using less lower cost, ment at
time, causing disruption less traffic be and would the than to
with methods. other many case
close-range 2. study The results of that the terrestrial show
photogrammetry be the of for used small measurement
can
magnitude displacements of order structural and
differences elevation. deflection the of The in measurements
girders of loading steel under that suggest concrete
i/8 accuracies achieved the be of with order
in
on can
10/1318 normal using that
utilized the
UMK
care camera was
study. field technique the thus The in could used be
to
indirectly general magnitude determine of the of order loads
imposed
structural members whenever their deflections upon
can
be measured.
10/1318
3. The satisfactory UMK results for the gave
camera
during taken study. the within Accuracies measurements
were
the desirable being for of the types
measurements range
taken. preferred This
because others
of
camera was over some
large, Consequently, 5 its format. 7 in, in be could it
x
used distances closer object required the and fewer
at to
photographs having than smaller formats.. cameras
Close-range photogrammetry 4. bridge be useful
deck
can on
by eliminating condition the for need sketches field
surveys
by reducing and the of field required.
amount measurements
addition, photographs the In be obtain used additional to can
information if needed
used be reference
to
gauge or
a as
potential changes future condition, elevation, in relative
or
advantages position. might These primary the be
reason
close-range
photogrammetry using for bridge for deck
a
condition savings the since field in work and
survey,
by photogrammetry offset the is personnel for need manpower
llft and bucket truck and operator. a
5. of small elevation,-such Measurements differences in those
as
bridge irregularities, associated with deck surface be
can
i/8 accomplished within using accuracies normal in to care.
probably could Greater accuracies obtained be if
necessary.
irregularities Surface by developing also be shown
can
close-interval photographs. from the contours
Extremely 6. bridge intricate
deck condition such
surveys, as
cracks, the mapping accomplished of be with close- can
photogrammetry. While this of would type range
not survey
ordinarily
conducted, study be this did in it
to serve
capabilities demonstrate technique. the of the of some 33
RECOMMENDATIONS
preliminary results by the Spero, work results of the the Based
on
engineer, photogrammetric it study, of the opinion the and of this
was
Transportation Highways of Virginia & Department the recommended that
Subsequently, 10/1318 study. the the purchase used in the UMK
camera
making capability
of
purchased, the giving Department the
use
was camera
the need in arises the photogrammetry when close-range terrestrial of
Recently, disciplines.
other transportation well in field
an
as as
Department's
the purchased, adds which analytical stereoplotter to
was
photogrammetry terrestrial Close-range capabilities. photogrammetric
might problems that
solving difficult approach offers measurement
to
an
rehabilitation. It repair, and bridge maintenance, with associated be
of the engineers made be bridge highway and that recommended is
aware
technique. capability availability of this and 34
ACKNOWLEDGEMENTS
study could This have been conducted without the of services F. not
photogrsmmetry Habel, Bales snd of the of G. W. the section B. Jr.
Highways Virginis Department Transportation. of snd cooperation The of
Misenheimer, Prewoznik, bridge Sellars and W. rL. district F. L. L. L.
Lynchburg, Culpeper engineers the districts, Staunton, and in
respec-
tively, indispensable conducting French, the field studies. in J.W. was
supervisor, technician assisted work with 66 the field the Rte. Metro
on
gratefully acknowledges bridge. by The suthor the rendered assistance
individuals. all of these 35
REFERENCES
Raymond I Davis, E., Foote, Anderson, Francis S. James J. and Edward
Mikhail, Theory Surveying M. Practice, ed., and 6th McGraw-Hill,
1981.
Moffitt, Mikhail, H., Photogrammetry, and F. E. M. Harper Row, and
York, 1980, 648 New pp.
Atkinson, Dev.e.lopment .Close Photogrammetry..-•..l, ..R.an•e B., K. in
Applied Publ•shers, Ltd., Science London, 1980.
"The Spero, Photogrammetric Paul A.C., Recording
of Historic
Transportation
.VHTRC 83-R35, Sites, " Highway Virginia and
Council,'
Transportation Charlottesville, Research Virginia, June
1983.
"S
Scott, P.J., tructural Deformation Measurement of Model Box
a
Brldge," Photogrammetric
Girder
9, Record, Vol. 51, 361-76, No. pp.
1978.
.phot.o.g.raphy, ! F.unct.i0.n.a Publishing Company, 18, PTN 2, Vol.
No.
March/April 1983, 41. p.
"Mapping Eng..i.neering. Record Test," Speeds Bridge New April 19, s
1984, 27. p.
"Factors Hilton, Affecting H., M.
Deflections Girder During Bridge
Highwa
Deck 40.0, Construction, h
"
Re Record 55-68 • .rc
s pp. ea
Washington, C., 1972. D.
"Deflections Camber and in Loss Heat-Curved
Girders,"
Transportation.
950, Research Record Bridge No. Second
'•o'l'.'
'D. Engineering Conference, Washington, 2, 1984. C., 37