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PUBLIC ROADS 


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UNITED STATES DEPARTMENT OF AGRICULTURE 









BUREAU OF PUBLIC ROADS 





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Vib See Nels We) Vv DECEMBER, 1928 


1 eet 





THE YADKIN RIVER BRIDGE 


U.S. GOVERNMENT PRINTING OFFICE: 1928 


epovbiks 


iad _—> ne 


ROADS 


A JOURNAL OF HIGHWAY RESEARCH 


U. 8S. DEPARTMENT OF AGRICULTURE 
BUREAU OF PUBLIC ROADS 


CERTIFICATE: By direction of the Secretary of Agriculture, the matter contained herein is published as administrative information and is required 
for the proper transaction of the public business 


obtained. 


The reports of research published in this magazine are necessarily qualified by the conditions of the tests from which the data are 
Whenever it is deemed possible to do so, generalizations are drawn from the results of the tests; and, unless this is done 


the conclusions formulated must be considered as specifically pertinent only to the,described conditions 


VOL. 9, NO. 10 


TABLE OF 


Loading Tests on a Reinforced Concrete Arch 


THE U. S. BUREAU 


DECEMBER, 1928 


R. E. ROYALL, Editor 


CONTENTS 


Page 


185 


OF PUBLIC ROADS 


Willard Building, Washington, D. C. 


REGIONAL HEADQUARTERS 
Mark Sheldon Building, San Francisco, Calif. 


DISTRICT 


DISTRICT No. I, Oregon, Washington, and Montana. 
Box 3900, Portland, Oreg. 


DISTRICT No. 2, California, Arizona, and Nevada. 
Mark Sheldon Building, San Francisco, Calif. 


DISTRICT No. 3, Colorado, New Mexico, and Wyoming. 
301 Customhouse Building, Denver, Colo. 
DISTRICT No.4, Minnesota, North Dakota, South Dakota, and 
Wasconsmn, 410 Hamm Building, St. Paul, Minn. 
DISTRICT No. 5, Iowa, Kansas, Missouri, and Nebraska. 
8th Floor, Saunders-Kennedy Bldg., Omaha, Nebr. 


DISTRICT No. 6, Arkansas, Oklahoma, and Texas. 


1912 Fort Worth National Bank Building, Fort 
Worth, Tex. 


OFFICES 


DISTRICT No. 7, Illinois, Indiana, Kentucky, and Michigan. 
South Chicago Post Office Building, Chicago, III. 
DISTRICT No. 8, Louisiana, Alabama, Georgia, Florida, Mississippi, 


South Carolina, and Tennessee. 
Box J, Montgomery, Ala. 
DISTRICT No. 9, Connecticut, Maine, Massachusetts, New Hamp- 
shire, New Jersey, New York, Rhode Island, and Vermont. 
Federal Building, Troy, N. Y. 
DISTRICT No. 10, Delaware, Maryland, North Carolina, Ohio, Penn- 
sylvania, Virginia, and West Virginia. 
_ Willard Building, Washington, D. C. 
DISTRICT No. 11, Alaska. 
. Goldstein Building, Juneau, Alaska. 
DISTRICT No. 12, Idaho and Utah. 
Fred J. Kiesel Building, Ogden, Utah. 


Owing to the necessarily limited edition of this publication it will be impossible to distribute it free to any persons or 
institutions other than State and county officials actually engaged in planning or constructing public highways, instructors 


in highway engineering, periodicals upon an exchange basis, and Members of both Houses of Congress. At the present 


time names can be added to the free list only as vacancies occur. 


Others desiring to obtain Pustic Roaps can do so 


by sending 10 cents for a single number or $1 per year to the Superintendent of Documents, U.S. Government Printing 


Office, Washington, D. C. 








' 
: 





LOADING TESTS ON A REINFORCED CONCRETE ARCH 


REPORT ON TESTS MADE ON YADKIN RIVER BRIDGE IN NORTH CAROLINA 


Reported by ALBIN L. GEMENY, Senior Structural Engineer, Bureau of Public Roads, and W. F. HUNTER, Designing Bridge Engineer, North Carolina Highway 
Commission 


tests it 1s desired to discuss briefly some of the 
assumptions which are made in arch-bridge 
design. 
The hingeless, reinforced-concrete arch rib is a 
statically indeterminate structure which can be ana- 


one describing the details of these particular 


by expansion joints at one or more points. It may be 
rigidly attached to the tops of the spandrel columns or it 
may have movable bearings on the columns. In prac- 
tically all cases the columns are integral with the rib. 

In designing, the effect of the superstructure on the 
deformation of the rib is generally neglected even 


lyzed only by considera- 
tion of the elastic prop- 
erties of the concrete 
and steel of which it is 
constructed. In apply- 
ing the theory of elastic 
structures to the anal- 
ysis of an arch rib, it 
is assumed that the 
modulus of elasticity 
of the concrete is con- 
stant for all parts of 
the arch and at all 
intensities of stress up 
to the working stress 
for which the arch is 
designed. It is further 
assumed that a plane 
section of the rib re- 
mains plane after the 
rib has been deformed. 

In open-spandrel 
arch construction, the 
floor system is sup- 
ported by the spandrel 
columns through which 
the loads are transmit- 
ted to the ribs. In cur- 
rent design practice it 
is assumed that the 
loads are distributed 
only to adjacent panel 
points and are applied 
as vertical forces at the 
points of the rib at 
which the columns are 
attached, although it is 
apparent that a con- 


STATEMENT BY THE ADVISORY COMMITTEE! 


HE NORTH CAROLINA STATE HIGHWAY COMMIS- 
SION built in 1922, asa Federal-aid project, a 3-span concrete 
arch bridge over the Yadkin River, also known as the Pee 

Dee River, between Albemarle and Mount Gilead. In 1926 the 
Carolina Power & Light Co. began the construction of a dam on a 
site about 9 miles downstream from the bridge. The water of the 
river, upon the closing of the dam, was to be backed up to such a 
height as to submerge the bridge and necessitate its replacement by 
a new bridge at a higher elevation. Between the time of completion 
of the new bridge and the closing of the dam, a period of several 
months, the old bridge was to be demolished so as to offer no ob- 
struction to the flow of water in the river. 

These circumstances presented a unique opportunity to test a 
modern, full-size, reinforced concrete arch bridge with moderately 
long spans. In recent years the popularity of the arch bridge has 
increased greatly because of its superior esthetic value and, in this 
country, millions of dollars are spent annually on this type of bridge 
alone. Consequently, there is a widespread tendency on the part 
of bridge engineers to embrace any idea which may lead to more 
economical or more satisfactory arch design without sacrificing 
safety. In departing from current practice, the judgment of the 
engineer is based more and more on data developed by the various 
research agencies of the world. 

The North Carolina State Highway Commission, recognizing the 
opportunity to make this test, and desiring to make it as complete 
as the available time and money permitted, requested the coopera- 
tion of the Bureau of Public Roads. 

The bureau acceded to the State’s request, and the two agencies 
then jointly issued to various technical and scientific societies and 
colleges invitations to participate in the experiment by appointing 
one or more of their members to serve on an advisory committee. ! 
The purpose of this committee was to formulate general plans for 
the test, and, by meeting from time to time, assist those in active 
charge in the solution of problems which would certainly be en- 
countered during the period of the test, and assist in interpreting 
the results. The advisory committee first met in April, 1927, and 
formulated general plans; several meetings were held during the 
course of the test, and at a final meeting on November 8, 1928, this 
report was approved by the committee. Acknowledgments by 
the committee are given below. ? 


though it isobvious that 
this effect may be of con- 
siderable importance. 
The degree to which the 
rib deformation is mod- 
ified by the superstruc- 
ture depends upon the 
number of breaks in the 
continuity of the floor 
system, the method of 
connecting it to the col- 
umns, and upon the 
stiffness of the columns. 
In the case of an arch 
with the floor system 
continuous over the 
whole span and rigidly 
attached to the tops of 
the columns, we have, 
in fact, a fixed, spandrel 
braced arch in which 
the diagonals are omit- 
ted and their functions 
performed by the rigid 
joints at the ends of the 
columns. In the case 
of an arch with expan- 
sion joints at each panel 
point and with the floor 
system supported onex- 
pansion bearings, the 
condition would ap- 
proach those assumed 
in designing. Usually 
the conditions lie some- 
where between these 
two extreme _ cases. 
The free rib is three 


tinuous floor system distributes the loads to panels be- 
yond those in which they are applied, thus rendering 
indeterminate the distribution of the load to the rib. 
The floor system may be continuous or it may be broken 





1 Membership of the advisory committee formed as a result of invitations issued 
by the Bureau of Public Roads and the North Carolina Highway Commission was 
as follows: University of North Carolina represented by Dean G. M. Braune; North 
Carolina State College represented by Dean W. C. Riddick; American Association 
of State Highway Officials represented by Searcy B. Slack, bridge engineer of the 
Georgia State Highway Board; American Society of Civil Engineers represented by 
Prof. Clyde T. Morris of Ohio State University; American Railway Engineering 
Association represented by J. B. Hunley, engineer of structures of Cleveland, Cin- 
cinnati, Chicago & St. Louis Ry. Co.; American Concrete Institute represented by 
A. B. Cohen, consulting engineer, New York, N. Y.; Highway Research Board rep- 
resented by A. T. Goldbeck, director of the bureau of engineering, National Crushed 
Stone Association; U. S. Bureau of Standards represented by D. E. Parsons, 
associate engineer; American Society for Testing Materials represented by F. E. 
Schmitt, editor, Engineering News-Record; U. 8S. Bureau of Public Roads repre- 
sented by E. F. Kelley (chairman), chief, division of tests; O. L. Grover, principal 
bridge engineer; H. M. Westergaard, professor of theoretical and applied mechanics, 
University of Illinois; and L. W. Teller, senior engineer of tests; North Carolina 
State Highway Commission represented by L. R. Ames, State highway engineer; 
Wm. L. Craven, bridge engineer; M. M. Trumbull, assistant bridge engineer; and 
E. H. Kivett, engineer of tests. 


24135—28——1 


times indeterminate and the complete arch, in the 
present case, thirty-nine times indeterminate. 








2 The instruments and scientific apparatus used in this test were furnished by the 
following organizations: The American Society of Civil Engineers and the Bureau 
of Standards furnished the electric telemeters. The Bureau of Standards furnished 
the Berry strain gauges and temperature coils. The Bureau of Public Roads fur- 
nished the radiusmeter, weighing cells, thermometers and deflection wires. The 
committee on concrete and reinforced concrete of the American Society of Civil 
Engineers furnished the clinometers. 

The installation of instruments and making of field observations were under the 
direction of G. W. Davis of the Bureau of Public Roads, assisted by W. F. Hunter 
and W. M. Price of the North Carolina Highway Commission and Albin L. Gemeny 
and E. C. Sutherland of the Bureau of Public Roads. The electric telemeters were 
calibrated and installed by O. 8. Peters of the Bureau of Standards. All computations 
were made by W. F. Hunter and Albin L. Gemeny. The preliminary model analysis 
was made by D. H. Overman of the Ohio State Highway Department under the direc- 
tion of Prof. Clyde T. Morris of Ohio State University. The brass wire model analysis 
was made by G. W. Davisand E. C. Sutherland. The final model analysis was made 
by Prof. J.T. Thompson of Johns Hopkins University and Albin L. Gemeny, using a 
model constructed by the Bureau of Public Roads. The bridge maintenance depart- 
ment of the North Carolina Highway Commission made available one of its forces 
during the entire period of the test to do all construction work and operate the ferry. 
The foreman of this force was J. P. Beach under the general direction of C. B. 
Taylor. Success in the prosecution of the test was due in large measure to the 
enthusiastic cooperation of the North Carolina Highway Commission through 
Messrs. Craven, Trumbull, and Hunter of the bridge department. 


185 





PUBLIC ROADS 


Vol.9 No 10 






























pe 125 


Tz 











A method of analyzing indeterminate structures, 
developed comparatively recently by Professor Beggs, 
of Princeton University, consists in studying the elastic 
action of a model, each member of which is of the same 
relative stiffness as the corresponding member of the 
structure. By the application of the Maxwell theorem 
of reciprocal deflections, and Miller Breslau’s principle 
that any influence line is a deflection diagram, the 
moment, thrust, and shear at any section may be 
found and the stresses computed. 


OBJECTS OF THE TESTS OUTLINED 


The North Carolina bridge tests were conducted for 
the following specific purposes: 


(1) To compare the measured deformations of a full-size, 
reinforced concrete arch rib with the deformations as determined 
by the theory of elastic structures, when the rib carried loads 
producing stresses of moderate intensities, and was as free as 
practicable from the restraining action of the superstructure. 

(2) To make the same comparisons when the rib carried loads 
which produced stresses of high intensities. 

(3) To determine the effect of the superstructure on rib de- 
formations by comparing deformations measured when the 
superstructure was intact and the measured and computed 
deformations of the rib free from restraint by the superstructure.’ 





3 Further references will be made simply to the “free rib.” 


“ 
RIB REINFORCEMENT 6-% ROUND 
BARS TOP AND BOTTOM 








EXPANSION JOINT 


EXPANSION JOINT 





CENTER LINE 


“ ” 


18-0 
















BEARING PLATES 


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PLAN 
Fic. 1.—Detaits or Test SPAN 


(4) ‘To compare the measured deformations of the rib, both 
with and without the restraining action of the superstructure, 
and the deformations as determined from an analysis made by 
the use of an elastic model. 


TEST BRIDGE DESCRIBED 


The test bridge consisted of three 2-rib open-spandrel 
arch spans of 146 feet 3 inches clear span and 28 feet 
3 inches rise with seven 42-foot 6-inch deck-girder ap- 
proach spans at each end. The floor system of the 
arches rested on sliding bearing plates at each panel 
point. These plates were found to be badly corroded 
and probably had ceased to function freely as sliding 
bearings. The intermediate arch piers below the 
springing line were of hollow construction, the hollow 
space being filled with field stones. The end arch piers 
had buttresses on the shore side to increase their resist- 
ance to overturning under the unbalanced thrust. 
The piers were founded on solid rock. Details of the 
test span are shown in Figure 1. 

The bridge was built by contract, using cement and 
reinforcing steel furnished by the State highway 
commission. ‘The coarse aggregate consisted of crushed 
field stones found in the vicinity of the bridge site. 
Inspection of the aggregate in cores taken from the 








December, 1928 PUBLIC 








187 


ROADS 














bridge disclosed several varieties of stone, all of which 
were apparently hard, sound, and durable. The fine 
aggregate consisted of a mixture of 5 parts of sand to 1 
of stone screenings. <A well-known brand of Portland 
cement was used. 

The concrete for the piers below the springing line 
was mixed in the proportions 1:2'4:5 and, for the 
remainder of the bridge, in the proportions 1:2:4. 
Tests of 6 by 12 inch cylinders of the 1:2:4 concrete 
made at 28 days showed strengths of 2,140, 1,900, 
1,655, and 1,258 pounds per square inch. Each of these 
strengths is for a single cylinder representing about 50 
cubic yards of rib concrete and are arranged in the 
order of location of the batch from springing line to 
crown. Inspection records do not show clearly which 
of the arch spans is represented by these cylinders. 

The reinforcing steel consisted principally of round, 
deformed bars of intermediate grade steel. Some of 
the minor reinforcing consisted of square, deformed 
bars. Tension tests on the steel showed an average 
yield point of about 48,000 pounds per square inch and 
an average ultimate strength of 75,300 pounds per 
square inch. 

Cuts made in the concrete for installing instruments, 
taking test specimens and destroying the continuity of 
the superstructure showed dense, hard concrete ap- 
parently of good quality. The steel, where the cover- 
ing of concrete was stripped off, showed clean surfaces, 
free from all signs of corrosion. 


PRELIMINARY EXPERIMENTS MADE 


Various possible methods of measuring vertical de- 
flections of the rib and horizontal movements of piers 
were considered and it was decided to use suspended 
wires. ‘The wires for measurement of pier movements 
were to be fixed at the far piers of the adjacent spans 
on the assumption that temperature movements of 
any point on the wire would be vertical, the position of 
such point horizontally remaining fixed. In order to 
test this assumption, a wire was stretched between two 
firmly planted posts at the Arlington Experiment Farm 
and observations made of the movements of a number 
of points fixed on the wire over a period of time during 
which there was a considerable change in temperature. 
It was observed that no appreciable horizontal move- 
ments of the points took place. 

The deflection wires (described in detail on p. 192) 
were installed in June, 1927. At the same time ther- 
mometers were placed in holes drilled in the ribs at 
different distances from the surfaces of the concrete. 
The holes were filled with cup grease and closed with 
corks through which the stems of the thermometers 
passed. Temperature movements at the crown of both 
ribs of the center arch span were observed daily over a 
period of several months. The observations showed an 
average movement of one-fortieth of an inch for a 
change of 1° C. in average rib temperature. 


TANKS FILLED WITH WATER USED FOR TEST LOADS 


The test span was loaded with tanks of water, filled 
by pumping from the river. The tanks were 12 feet 
6 inches wide by 20 feet long and 18 feet high, inside 
dimensions, and were built of timber with structural 
steel underframes. The length was such as to permit 
supporting the load at two adjacent panel points. 
Rollers were provided so that the empty tanks could 
be easily moved into any desired position on the bridge. 
After being placed in position, the tanks were jacked 








up and allowed to rest symmetrically on four bearing 
blocks located over the center of the columns at which 
the loads were to be applied, as shown in Figure 2, page 
190. The tanks were leveled by the use of plumb bobs 
suspended at each end and then filled with water. The 
tanks were moved while empty to avoid overstraining 
the floor system. 

Force to move the tanks 
was applied by a truck 
through a block and tackle 
arrangement anchored to the 
solid handrails on each side 
of the bridge. At ordinary 
temperatures the tank could 
be rolled over the rock as- 
phalt surface of the bridge 
floor but at high tempera- 
tures it was necessary to use 
plank runways to prevent the 
rollers from sinking into the 
asphalt. 

It was not possible to weigh the tanks by ordinary 
methods and a special weighing cell was used for the 
purpose. This device makes use of a small copper 
cylinder, specially heat-treated and of fixed size, which 
when compressed under load, is permanently deformed 
according to a fixed law. 

The complete weighing cell consists of a hollow steel 
cylinder into which a steel piston fits closely. On the 
inside of the cylinder head is a hardened steel face or 
anvil with a plane, smooth surface. On the entering 
end of the piston is a corresponding hardened steel 
face. The copper cylinder, one-half inch in diameter 
by one-half inch high, is placed on end in the steel 
cylinder on the smooth surface and the piston is allowed 
to rest on it. The load whose magnitude is desired is 
then applied to the piston and its entire weight is 





LOADING TANK 


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PuMPING PLANT FoR FILLING TANKS 


transmitted to the copper cylinder. The length of the 
copper cylinder is measured with a micrometer caliper 
before and after the load is applied. The weight corre- 
sponding to the deformation of the cylinder is taken 
from a calibration curve which has been previously 
determined in the laboratory for the particular size 
and quality of copper cylinder used. 

The empty tank was weighed by placing a cell under 
each corner of one end and two cells with an equalizer 
under the center of the opposite end. The total weight 
of the tank was the sum of the four weights indicated 
by the cells. The weight of the tank was also calculated 
from the unit weights of the timber determined by 


188 





weighing specimens of the material used in constructing 
the tanks. The weights determined by the two 
methods checked within 1 per cent. The weight of 
each empty tank was found to be approximately 
47,000 pounds and this figure was used in the computa- 
tions. The water capacity of each tank was 4,500 
cubic feet, 33,750 gallons, or 281,250 pounds. The 
increments of water load at each panel point were 
22,750, 45,500, and 68,250 pounds. 








Two WEIGHING CELLS IN PLACE AT ONE END or TANK 
TESTS DIVIDED INTO THREE PHASES 


The test was divided into three phases which, for 
convenience, are designated as series 1, 2, and 3. 

In series 1 a single tank was placed so as to apply its 
load at two adjacent panel points and deformations 
observed over the entire rib from springing line to 
springing line with the superstructure intact. The 
series of loadings began at a pier and continued suc- 
cessively to the crown. The tank was also placed on 
one of the adjacent spans in a panel next to the crown, 
and deformation readings were taken on the span 
under observation. . 

In series 2, the same procedure was followed except 
that the deck and railings were cut at each panel 
point and supported on new, greased bearing plates 
so as to destroy, as far as practicable, the continuity 
of the floor system and its restraining action at the 
tops of the columns, and the curtain wall near the 
crown was broken out. In this series, the load at 
panel points 1 and 2 (fig. 2) was omitted because of 
the small deformations caused by the load in this 
position . 

In series 3, two tanks were placed in the position to 
produce the maximum stress in the rib and the de- 
formations were measured as in series 1 and 2, with 
the superstructure in the same condition as in series 2. 


PUBLIC ROADS 


Vol. 9, No. 10 


Four increments of load were applied at each posi- 
tion of loading: The empty tank, the tank filled with 
91,000, 182,000, and 273,000 pounds of water. 

In destroying the continuity of the superstructure for 
series 2 and 3 the slab, girders, and handrail over each 
cross beam were cut through with air drills and the steel 
severed with an oxyacetylene flame. The ends of the 
oirders were then jacked up and new, well-greased bear- 
ing plates inserted at each girder bearing. The girder 
ends on the entire east half of the span were shattered 
by the cutting operation to such an extent as to make 
the bearings on the cross beam unsafe. To relieve 
these bearings of the tank loads, holes were cut through 
the deck at the panel points and timber bearing blocks 
placed directly on the cross beams. In two panels 
it was thought necessary to support the dead weight 
of the floor system on timbering built up from the ribs. 
This was done in such a way that the arch was not 
stiffened. 

DEFORMATIONS MEASURED 


In order to measure completely the deformation of 
the rib under live load, the following six measurements 
were made: 

(1) Deformations of the concrete on the extrados 
and the intrados at nine sections of the rib spaced 18 
feet 6 inches apart along the axis. 

(2) Deformations of the reinforcing steel near the 
springing lines and at the crown. 

(3) Rotation of the arch axis at nine points spaced 
18 feet 6 inches along the axis. 

(4) Deflections of the rib at nine columns, no meas- 
urements being taken at the column next to each pier. 

(5) The change in length of mid-ordinates of each 
of the 31 consecutive 5-foot arcs of the axis. 








ScAFFOLD FrRoM WHICH OBSERVATIONS WERE MADE 





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December, 1928 PUBLIC 











CuttTinc THROUGH THE FLOOR System AT A PANEL Point 
To Destroy CONTINUITY 





Cut THroucH HANDRAIL, CURB, AND FLOOR 


(6) Rotation and horizontal movements of the piers. 
The locations of the instruments are shown in Figure 
2. It was decided that deformations under load 
should be measured only on the north rib of the middle 
arch span. This span, including the piers, was sym- 
metrical; the north rib was somewhat protected from 
the direct rays of the sun except in the early morning 
and was, therefore subject to more uniform tempera- 
ture conditions than the south rib. 


MEASURING INSTRUMENTS DESCRIBED 


TELEMETERS USED TO MEASURE DEFORMATIONS OF CONCRETE 
AND STEEL 


Deformations of the concrete at the extrados and 
intrados and deformations of the steel were measured 
by means of McCullom-Peters electric telemeters.* 


‘ For a complete description of the McCullom-Peters electric telemeter see Tech- 
nologic Paper No. 247 of the Bureau of Standards entitled ‘‘A New Electric Tele- 
meter,’’ by Burton McCullom, and O. S. Peters. 


189 


ROADS 








The electric telemeter consists of a stack of carbon 
disks held under pressure. A change of length of the 
stack 1s accompanied by a change of pressure and 
electrical resistance, the stack of disks acting as an 
elastic body. Suitable terminal pieces or mountings 
for the stack are supplied which can be attached to a 
structural member at two points spaced some distance 
apart. Changes in length between these points will 
change the length of the stack and also the electrical 
resistance which can readily be measured at any con- 
venient point by running wires from the terminals of 
the carbon resistor to a suitable measuring instrument. 





TELEMETERS SECURED TO CONCRETE AND REINFORCING 
STEEL ON THE ExtTrRapos NEAR THE SPRINGING LINE 





CENTRAL STATION IN PrER WHERE TELEMETER READINGS 
WERE TAKEN 


The 2-element type of telemeter with 8-inch gauge 
length was used in these tests. The terminals were 
fixed to the concrete by means of screws threading 
into steel plugs which were grouted in the concrete. 
Telemeters were placed on the steel by stripping off 
about a foot of the concrete cover, drilling into the 
steel and attaching the instrument. 


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190 





December, 1928 PUBLIC 


L9a 


ROADS 

















Instruments were placed on the concrete at the in- 
trados and extrados at each of nine normal sections 
of the rib which were spaced 18 feet 6 inches along the 
axis and also on the steel in the intrados and extrados 
near the two springing lines and at the crown. Wires 
were carried from each of the instruments to a Wheat- 
stone bridge in the east pier of the center span of the 
arch where the resistances were read. The Wheat- 
stone bridge was energized by a 6-volt battery and the 
a was kept constant by a variable resistance 
coil. 

It was found necessary to make temperature correc- 
tions for the instruments. This was first attempted 
in series 1 by removing two of the instruments from 
the steel and placing them on members of the bridge 
which were not subjected to direct stress, one at the 
crown and one at the springing line. The readings 
on these neutral telemeters were used as corrections 
for the stress-measuring telemeters which were divided 
into two groups, each having temperature conditions 
apparently the same as those of one of the neutral 
telemeters. Recognizing the possibility of inaccuracy 
in this assumption, it was decided to use a more accurate 
method in series 2 and 3. A pair of resistance-coil 
thermometers was placed at each of the telemeters for 
measuring deformations of concrete, one embedded 
in the concrete near the instrument and the other 
fixed to the instrument itself. Wires were carried 
from the coils to a measuring instrument in the pier 
where the resistances were read each time a set of 
readings was taken on the telemeters. The difference 
in temperature between the instrument and the con- 
crete, multiplied by the thermal coefficient of expansion 
of the metal of the instrument was applied as a correc- 
tion to the unit deformation calculated from the direct 
reading on the telemeter. 

The method of making this correction is illustrated 
by the following example. The telemeter considered 
is 12A, located on the extrados near the springing line. 
The empty tank was placed at panel points 2 and 3. 
It is desired to measure the stress produced by the 
weight of water in the full tank. 

Resistance reading with empty tank=13.1 ohms, in this case 
indicating tension. 

Tension calibration factor for telemeter 12A—0.0000222 inch 
per inch per ohm. 

Telemeter reading = 0.0000222 & 13.1=0.0002910 inch per inch 
elongation. 

The resistance coil thermometers indicated that the tempera- 
ture of the telemeter was 3° C. lower than that of the concrete 
thereby increasing the tension reading due to deformation of 
the concrete. 

Correction due to temperature=0.0000110 3=0.0000330 
inch per inch elongation. 

Corrected reading = 0.0002580 inch per inch elongation. 

This process is repeated with the tank full and the result is 
0.0005018 inch per inch elongation. 

The difference between corrected readings for empty and full 
tank = 0.0005018 — 0.0002580 = 0.0002438 inch per inch. 

Stress produced by added load=0.0002438 x 4,000,000 = 975.2 
pounds per square inch. 

In the above calculation the thermal coefficient of 
expansion of the metal of the instrument is 0.0000110 
per degree centigrade and it is assumed to be approxi- 
mately the same for the concrete. The same process 
was used for deformations of the reinforcing steel which 
was considered as taking the temperature of the sur- 
rounding concrete since only a small surface was 
exposed to the air. 

When the resistance coils were installed, two were 
placed at the neutral telemeter at the crown in order 





to find the relation between the temperature correc- 
tions as determined by the neutral telemeters and by 
the resistance coils. It would have been desirable to 
have placed coils at the neutral telemeter at the 
springing line but none was left for this purpose. It 
was found that the difference in temperature between 
the neutral telemeter at the crown and the adjacent 
concrete changed by about the same amount as in 
the case of the instruments on the rib, although the 
actual temperatures varied from point to point of the 
rib. It was, therefore, decided that the reading on 
this one neutral telemeter would be a more accurate 
correction than that which had been determined by 
erouping the telemeters. All of the stress curves of 
series 1 are, accordingly, based on telemeter readings 
corrected in this manner. 

When it was found necessary to correct the telemeter 
readings for temperature it was decided to attempt 
check measurements with a 20-inch Berry strain gauge. 
Because of the small strains to be measured and 
physical obstacles to careful manipulation of the gauge, 
the results were not satisfactory. 





TAKING A ROTATION MEASUREMENT WITH A CLINOMETER 


MEASUREMENT OF ROTATION OF ARCH AXIS 


The rotations of the arch axis were measured by 
means of a clinometer or level bar. The clinometer 
consists of a square bar of steel supported horizontally 
on two pointed steel legs set vertically and spaced 20 
inches apart. One of these legs is fixed while the other 
is adjustable vertically by a fine screw thread and 
hand nut. The amount of vertical adjustment neces- 
sary to level the bar is indicated by a suitable microm- 
eter dial in contact with the adjustable leg. A sensi- 
tive level bubble is placed horizontally on the upper 
face of the steel bar. 


192 


PUBLIC 








Two steel plugs containing gauge holes were grouted 
in the inner side of the rib 1n such a manner that they 
were 20 inches apart and approximately in the same 
horizontal plane and the line between the gauge holes 
was bisected by a plane normal to the axis at the 
point at which it was desired to measure the rotation. 
To measure the rotation under any increment of load, 
the points of the clinometer were placed in the gauge 
holes of the plugs and the level bubble brought to the 
center of the bubble tube by use of the adjusting screw 
and#the micrometer dial read. After the load was 
applied, another reading was taken. The difference in 
the two readings was the relative vertical movement 
of the two plugs in thousandths of an inch, and this 
change In relative elevation divided by the gauge length 
gave the rotation In radians. 








MEASURING A Mip-ORDINATE WITH THE RADIUSMETER 
t 
RIB DEFLECTIONS 


Deflections of the rib were measured from a wire 
stretched between the tops of the piers, over the cen- 
ters of the spandrel columns. ‘This wire was fixed at 
one end and passed over a pulley at the other end and 


had attached a weight of about 100 pounds for the 


purpose of maintaining a constant tension and thus a 
constant sag in the wire. Small metal plates contain- 
ing gauge holes were fixed in the tops of the columns 
directly under the wire. Deflections were measured 
with a scale graduated to fortieths of an inch and pro- 
vided with a pointed metal shoe which was placed in the 
gauge holes in the plates. Measurements were made 
before loading and after each increment of load. 


MEASUREMENT OF MID-ORDINATES OF CHORDS 


Changes in length of the mid-ordinates of 5-foot 
chord lengths of the axis were measured with a radius 
meter. The radius meter consists of a steel tube to 
which is attached two hardened steel points set at 
right angles to the axis of the tube and 5 feet apart. 
One of these points is rigidly fixed to the tube and the 
other has a flexible joint permitting a slight variation 


ROADS Vol. 9, No. 10 


_ 











in the distance between the points. Midway between 
these points and on the side of the tube opposite to 
that to which the points are attached a micrometer 
dial, reading to one ten-thousandth of an inch, is 
mounted. ‘The dial stem is provided with an extension 
passing through a clearance hole in the tube. This 
tube is encased in a larger tube, to which it is attached 
only at the support points, so that, in manipulating 
the instrument, no force can be applied to the inner 
tube which would deflect it and affect the readings on 
the dial. The readings in series 1 were taken with the 
stem extension free to bend a small amount laterally. 
It was found that this lateral movement of the stem 
extension gave appreciable readings on the dial, and 
in series 2, a close-fitting sleeve bearing was provided 
for the extension so as to prevent lateral movement. 

Round steel plugs containing gauge holes were 
grouted into the inner side of the rib on the axis so as 
to mark off consecutive 5-foot chords. Midway 
between each pair of these plugs a square plug was 
erouted into the rib so that its upper surface and the 
line between the gauge holes were in parallel planes 
normal to the face of the mb. In measuring mid- 
ordinate changes, the two steel points of the instrument 
were set in the gauge holes of a pair of plugs and the 
stem extension of the dial was allowed to rest on the 
square plug. On the back of the dial case was an 
arm which rested against the side of the rib and main- 
tained the dial in a plane parallel to and at a constant 
distance from the face of the mb. The difference 
between readings before and after the application of 
the load gave the change in mid-ordinate. 





CLINOMETER AND RADIUSMETER GAUGE PLUGS IN INNER 
Face or Ris 


MEASUREMENT OF PIER MOVEMENT 


Provision was made for measuring pier movements in 
two ways. Clinometer plugs were placed on top of 
each end of each pier and on a line parallel to the axis 
of the bridge. Readings on these points gave rotations 
of the top of the pier but not displacements parallel 
to the bridge axis. Provision for measuring these 
displacements was made by stretching two wires on 
each side of the bridge fixed to points on the far piers 
of the spans adjacent to that being loaded. The 
wires were stretched so that they just cleared the ends 
of the piers and each pair of wires was spaced 5 feet 
apart vertically. Metal gauge plugs were fixed in 
the piers opposite a copper reference mark fixed to 
each wire. Horizontal movement of the points on 
the piers with reference to the fixed points on the 
wires were measured with a scale. Differences of 
movements of the upper and lower points on the piers 
gave an additional measure of the pier rotation. 








PUBLIC 


December, 1928 











MODULUS OF ELASTICITY OF THE CONCRETE DETERMINED 


In order to determine the modulus of elasticity of 
the concrete for use in the preliminary computations, 
one specimen was cut from a curtain wall in each pier 
of the span under observation. Two 6 by 12 inch 
cylinders were drilled from each of these specimens 
and tested. Compression tests gave an average value 
of 4,500,000 pounds per square inch for the modulus 
of elasticity. These specimens were taken from an 
unimportant part of the structure which was not under 
stress and it was thought advisable to make further 
determinations of this value. 

A more representative value of the modulus of clas- 
ticity was obtained after the completion of the field 
observations. Specimen blocks were taken from the 
rib at the sections where the telemeters had been 
attached. Nine of the specimens were taken with the 
intention of drilling two test cylinders from each block. 
Because of defects in the specimens only seven suitable 
test cylinders were obtained. These cylinders were 6 
inches in diameter with an average length of 10 inches. 

The stress-strain curves obtained with a mirror exten- 
someter of the Martens type ® are shown in Figure 3. 
The curves show an average value of the proportional 
limit of 1,111 pounds per square inch, an average ulti- 
mate strength of 4,293 pounds per square inch and an 
average modulus of elasticity of 3,930,000 pounds per 
square inch. 


MATHEMATICAL ANALYSIS MADE OF THE FREE RIB 


Field measurements were taken of the dimensions of 
the arch rib. The rib was analyzed by dividing the 
span into 20 equal horizontal divisions and applying 
the theory of elastic structures by the method of sum- 
mations. It was assumed that the superstructure pro- 
duced no effect on the deformation of the rib other than 
the effect as dead load. Since field observations 
showed no measurable movements of the piers, a con- 
dition of perfect fixity of the rib at the springing lines 
was assumed. 

A value of 4,000,000 pounds per square inch was used 
for the modulus of elasticity of concrete and 30,000,000 
pounds per square inch for that of steel which resulted 
in a value of 7.5 for n in the beam and column formulas. 
The coefficient of expansion for concrete was taken as 
0.00001 per degree centigrade. 


TasBLE 1.—Calculated horizontal thrusts, vertical shears, and 
moments at the springing line, and calculated moments at the 
telemeter points for unit loads of 1 pound at the columns } 























Loadatcolumn); Ho Vo Mo | Ma My M. Ma | M, 

Pounds| Pounds| Ft.-lbs. ; Ft.-lbs. | Ft.-lbs. | Ft.-lbs. | Ft.-lbs. | Ft.-lbs. 
se 0.082} 0.990 | —9.35 | —6.04 | +1.31 | +0.57 | +0.09 | —0. 25 
2 a 349 »953 |—12.86 —10,32 | +1.59 | +2.79 | +. 48 Son! 
SS ae . 720 soe | — 19,80) | —2.57 | 6.92 | +1.85 | —1.28 
Cie ee 1.132 2607) —O.c5)) —9. 00 | —3, 88") 1.55 | +4. 90 Se 
as eee 1, 434 -600 | 41.60) +.20 | —3.05 | —1.82 | +4.01} -++1.56 
OL ae ern 1. 550 «000 | +-7.75 | 15.46 | —-1.29 | —3.41 | —.75 | -+6,42 
0 eee 1. 434 ~ 350 ;|+10.96 | +8.51 | +.45 | —3.48 | —3.03 | +1.56 
eee 1, 132 221 |4+-10.80 | +8.61 | +1.37 | ~2.69 | —3. 35 = 16! 
.,  ——_— 420 116 | +7.90 |} --6.30 | +1.40 | —1.60 | —2.50}; —1.28 
Baim ass . 349 oa | +-4.10)) -F5.40 | -+-.85 | =271 | --1.28 —. 84 
vet ee . 082 me) LOD | ee ietazo | 17 | —. 82 —. 25 

| 





1 Letters a, b,c, d, and e designate the points along the axis at which the telemeters 
were attached to the rib, the point a being near the springing line and the others in 
order toward the crown where the point e is located. 


§ For a complete description of the mirror extensometer see Handbook of Testing 
materials by Adolph Martens, Pt. I, vol. 1, pp. 67 to 76. 


24135—28——2 


ROADS 





A tabulation of the ordinates of the influence lines 
thus computed is shown in Table 1. From _ these 
influence lines moment diagrams were drawn and 
stresses, rotations, deflections, and mid-ordinate 
changes were computed. 


MODEL ANALYSES MADE 


A preliminary analysis was made with Beggs deform- 
eter gauges using a paper model. This analysis was 
not complete owing to the difficulty of placing the 
gauges on the rib in panels near the crown, where the 
superstructure interfered with the placing of the plugs 
used to produce displacements in the model. 

Next an attempt was made to analyze the arch by 
the use of a brass wire model, applying the principles 
used in the Beggs method. The thrust, shear, and 
moment at the end were accurately determined by 
displacing the brass plates used to represent the piers. 
However, when an effort was made to produce displace- 
ments near the piers and crown with the piers fixed, 
difficulty was experienced in getting sufficiently large 
deflections to be accurately measured by the means 
used because of the stiffness of the model.® 

The results of the above analyses were finally dis- 
carded and an analysis was made with the Beggs gauges 
and a model cut from sheet celluloid 0.08 inch thick. 
This model included the two spans adjacent to the 
span under observation. It was first analyzed with 

























































3200 ee ees ey a ee ee | 2 i alee ae ee eeeeeee Rt 
sais | ek eB ee | ‘oi 
2400 |——,—_--——- -- rae = 
ee Boks oi: 
POINT NO 3. POINT NO 4,/<POINT NO 7 
eon a ooo ame | 
| ; |_| _ 
| | POINT| MODULUS 
! 4 NO [OF ELAST 


4,960,000 
3,950,000] |, 
3,880,000} |, 


9A | 3,350,000 


ssf hc 











VIE 
































UNIT LOAD-POUNDS 





3200 











2400 














1 
OINT NO.9 
CORE B. t 


POINT NO.II 








1600 














PPTL. 
LIMIT | 

LBS PER.SQ INCH 
98 |3,410,000] 1,100] 4,590 


1,300 | 3,490 
700 | 4,780 
(@) 4 


40 60 80 100 120 140 (60 








OINT; MQDULUS 
NO j|OF ELAST. 











800 



































DEFORMATION - HUNDRED THOUSANOTHS OF AN INCH PER INCH 


Fic. 3.—STRESS-STRAIN CURVES FOR 6-INCH CorRES DRILLED 
FROM Nortu ArcH Ris at CLINOMETER Points. CoRES 
TESTED IN Dry ConpiTIon. Damp Cores (NOT SHOWN) 
LoADED up To 700 Pounps PER SquaRE INcH SHOWED 
Mopvu.Li APPROXIMATELY 5 PER CENT LESS THAN WHEN DRy 


6 A description of this method applied to end conditions for statically indeterminate 
frames may be found in an article entitled ‘‘ Brass Wire Models Used to Solve Inde- 
terminate Structures” by A. Bull, Engineering News-Record, Dec. 8, 1927. 








194 PUBLIC ROADS | Vo.9, No 10 


ee a A A 
= — Seen = ———— SIR eae SS - - ~ = --- — 











the columns integral with the floor system but with a LOAD ON COLUMNS | AND 2 

cuts in the deck at sections corresponding to the miami analianuaes 

expansion joints in the actual structure. Influence a Le ee ae 
lines for thrust, shear, and moment were determined 


in each panel at sections of the model corresponding as | MEASURED STRESSES: 
nearly as practicable to the sections of the nb at which aS itil Pagal: 
the telemeters were placed. 

Then the model was modified in an effort to simulate 
the condition of fixity which obtained at the tops of 
the columns in the test bridge. The floor system was 
cut loose from the columns and connected again by 
welding flexible webs of celluloid across the cuts. The 
size of these.connecting pieces was arbitrarily chosen 
as there was no means of determining the flexibility T.C.I2A. T.C:BA. TIC.6A. TCA. TC.2A. T.C10. T.C.8. T.C.6: “TC.4. 
which would produce the same degree of fixity as that 
existing in the bridge. The analysis was repeated 
with the model in this condition. The entire super- 
structure was next removed and the analysis made on 
the free rib. For convenient reference, the analyses 


with the model in the three foregoing conditions are 0 re : + 
tivel iA 4° ae 


designated as A, B, and C, respectively. A complete |. lee ee : 
; ‘ | | | i 
400 \ ‘ 


TENSION 


THEORETICAL STRESSES:~ 
CONCRETE TAKING TENSION. 





COMPRESSION 


INTRADOS 








TENSION 








description of this analysis, with detailed results, will 
appear in an early issue of PuBLic Roaps. 

From the influence lines thus determined, the moment Meg ene ae 
diagrams for all conditions of loading were drawn. In [Pees SE oc 
cases A and B, moments were calculated at each side of a | 
each column and at the springing line. Rotations were — CONCRETE TAKING TENSION. 
determined from these moment diagrams. 

Stresses were computed on the extrados and intrados 
at each telemeter point. 


COMPRESSION 











800 
T.C.9A. T.C.7A. T.C.SA. T-C.3A. T.CAl.  T.C.9. T.C.7. TCS. F.C... 


LOAD ON COLUMNS 2 AND 3 
EXTRADOS 


800 


COMPUTED AND MEASURED DEFORMATIONS COMPARED 


The loading of the bridge was begun in September, 
1927, and observations were taken day and night until 
December, 1927, with only two interruptions; one 
when the ferry broke down and the loading tanks had to 
be moved from the bridge to allow traffic to pass, and 
the other during the time required to cut the deck in 
preparation for series 2 and 3 loadings. Night as well as 
day observations were made so as to take advantage of 
the more uniform atmospheric conditions at night. 

The data were compiled and compared as soon as 
they were observed. In this way any obviously incon- 
sistent data were discovered and those due to instru- 








400 


TENSION 








STRESSES - POUNDS PER SQUARE INCH. 

















400 \— MEASURED STRESSES:~ 
AVERAGE OF THREE SETS 

OF TELEMETER READINGS. 
a ; oe 
THEORETICAL STRESSES:~ 


COMPRESSION 











mental imperfections were eliminated as far as prac- : CONCRETE TAKING TENSION. 

ticable. “ia T.CA2A. T.C.8A. T.C.6A. TC.4A. T.C.2A, T.C.10. T.C.8, T.C.6. T1.C.4, 
The computed and measured results are compared 

by means of charts showing the deformations of the Pass pula | 

rib for the conditions of continuity of superstructure MEASURED STRESSES: | 


and positions of load as described above. This com- La ioaun wernce or ree evs | 
. . ‘ : OF TELEMETER READINGS. 

parison is made for deformations as measured by fiber io /\ | ee ie 
stresses, rotations of axis, deflections, and changes in 400 J) AN CONCRETE TAKING TENSION. 
lengths of mid-ordinates of 5-foot arcs of the axis. In | y 
addition, the measured and theoretical stresses and rota- , 
tions are compared with values computed from the 

results of the analysis of the structure with the Beggs 





TENSION 























- 
— — 
t 
—t— = 8 Qi xX 
N 
=O" o> 











| 
3 

deformeter gauges. N \ ; OS 

A full tank load on an adjacent span produced no : a / Z 
measurable deformations in the span under observa- a a | 
tion and no measurable pier movement occurred during od co" a 
the test. Therefore, all computed results are based on é is a | 
fixity of the rib at the pier. All deformation curves — “ie 
are plotted with abscissas measured along the axis of * 
the rib. _ T.C.9A. T.C.7A. T.C.5A. T.C.3A. Toe) LS les esl 

The deformations are shown for loads exclusive of LOCATION OF TELEMETER POINTS ALONG RIB AXIS 
the weight of the tank. In this manner, the effects of Fic. 4«=SenaseeRin. Ue Tee 


temperature changesjare reduced to a minimum in wit Deck Intact (szrizs 1) 








December 1928 


TENSION 


COMPRESSION 


TENSION 


COMPRESSION 


STRESSES- POUNDS PER ‘SQUARE INCH. 
TENSION 


COMPRESSION 


TENSION 


COMPRESSION 


Pre. 


LOAD ON COLUMNS 3 AND 4 
© MODEL ANALYSIS-A 
© MODEL ANALY SIS-8 
@ 1ST. DAY. XNIGHT. 


+2NO. DAY. EXTRADOS 


W = 68,250 POUNDS. 
















MEASURED STRESSES:- . 
(= AVERAGE OF THREE SETS \ 
OF TELEMETER READINGS. 





T.CA2A. T.C.8A. TC.6A. TC.4A. TC2A, TCIO. T.C.8. T.C.6. T.C.4. 
INTRADOS 


MEASURED STRESSES - 
\-— AVERAGE OF THREE SETS 




















400 
; V 
THEORETICAL STRESSES:- 
ONCRETE TAKING TENSION. 
800 
EGGA, VGTA. TESA, TESA. TCI TE.9) TG? 1.6.5. T:C.t 
LOAD ON COLUMNS 44ND 5 
EXTRACOS 
i?) Hd 
400 
MEASURED STRESSES'- 
800 AVERAGE OF THREE SETS 


OF TELEMETER READINGS. 


| 
THEORETICAL STRESSES:- 
CONCRETE TAKING TENSION. 






T.CA2A. T.C.6A. TC.6A. TCAA. T.C2A. TCO. T.C.8. T.C.6. T.C.4. 





INTRADOS 
800 
AVERAGE OF THREE SETS 
“OF TELEMETER READINGS. 
400 
t¢) 
400 
THEORETICAL STRESSES:+ 
CONCRETE TAKING TENSION. 
800 
TOA eG. TAME SATINIGOA. TGS TEES. TG? TE... aC. I- 
LOCATION OF TELEMETER POINTS ALONG RIB AXIS 
5.—STRESSES IN ARCH RiB UNpbeER 1-TANK 


Loapine with Deck INTacT (sERIES 1) 


PUBLIC ROADS 


195 








LOAD ON COLUMNS 5 AND 6 
o MODEL ANALYSIS-A 
o MODEL ANALY SIS-B 
@ 1ST. DAY xXiST. NIGHT. 


+2ND.DAY. 42ND. NIGHT. EXTRACOS 


W= 686,250 POUNDS 














z 
5 400 
7) 
ra 
uJ 
= 
fe) 
z 
° 
a 400 
“ 
WW 
x 
SS MEASURED STRESSES :- 
9 AVERAGE OF FOUR SETS 


800 
THEORETICAL STRESSES :~ 


CONCRETE TAKING TENSION. 





TC.12A. T.C.8A. T.C.6A. T.C-4A.T.C.2A. TCIO. TC.8. TCS. T.C.4. 
INTRADOS 


ny 
@ 
oO 
oO 





THEORETICAL STRESSES — 
CONCRETE TAKING TENSION —7 


STRESSES ~POUNDS PER SQUARE INCH. 


TENSION 
da 
° 
Oo 











COMPRESSION 


MEASURED STRESSES:- 
AVERAGE OF FOUR SETS 
OF TELEMETER READINGS 





800 


CIA TeTAS (TGSAmEG oA, PCll seo. G7. dmGe5. 7:¢. 1. 


LOCATION OF TELEMETER POINTS ALONG RIB AXIS 


Fig. 6.—StTRESSsEsS IN ArcH Ris UNpsr 1-Tanx LOADING 
with Deck InrTact (seRIzs 1) 


making comparisons. The tank was placed in position 
and a set of readings taken on all instruments. Then 
loads of 91,000, 182,000, and 273,000 pounds of water 
were pumped into the tank, readings being taken at 
the completion of each increment. Thus, the total 
elapsed time between the first and last readings for 
any position of the load was about four hours. 

The temperature changes during this period were 
generally very slight, whereas, if the comparisons had 
been made from zero readings, a period of as much as u 
week would sometimes have elapsed between readings 
in the same set, with the probablity of considerable 
temperature changes. Only results for the maximum 
panel-point loads of 68,250 pounds are shown in the 
cases of stresses and mid-ordinate change because of 
the difficulty of accurately measuring the deformations 
resulting from the smaller increments of load. Defor- 
mations for all three increments of load are shown on 
the rotation and deflection curves. 


STRESSES IN THE CONCRETE AT THE EXTRADOS AND INTRADOS 
OF THE RIB 


The stresses on the intrados and extrados are plotted 
separately and at normal sections of the rib 18 feet 6 
inches apart along the axis of the rib for each position 
of the load and condition of superstructure. 

Figures 4 to 6 are for series 1, in which the super- 
structure was intact. The stress values through 


196 PUBLIC ROADS Vol. 9, No. 16 

















































































































LOAD ON COLUMNS | AND 2 LOAD ON COLUMNS 3 AND 4 
© MODEL ANALYSIS-B Teaceiatiece. 
@ DAY 1ST. NIGHT. & DAN, 
. 4 = N 
62ND NIGHT, EXTRADOS W = 68,250 POUNDS, Be i etal See Wimimaaes POUNDS: 
MEASURED STRESSES :~ = 
Z 400 AVERAGE OF TWO SETS 5 
S OF TELEMETER READINGS. 2 
ul 
i 2 
ke 
S 0 
° 
uv) 
” see 
) S) 
a a + | | 
= w MEASURED STRESSES — 
© ee - AVERAGE OF THREE SETS 
T.C12A. T.C.8A. T.C.6A. T.C.4A. TC.2A. T.C.10. TC.8. TC6. T.C.4. S OF TELEMETER Re AQee: 
MODEL ANALYSIS =B. 
INTRADOS 
400 
TCI2A. TOBA. TC.6A. TC4A. TC2A. TCIO. TC8. TC.6 TC.4 
z INTRADOS 
ie) 
2 MEASURED STRESSES — 
ts AVERAGE OF THREE SETS 
Z 400 
0 O 
Ww) 
A 
Ww 
kK 
z 
° 
a | 0 
3 | t 
w 400 MODEL ANALYSIS-B8. 
oO 
= MEASURED STRESSES:~ z 
3 AVERAGE OF TWO SETS = 
OF TELEMETER READINGS ul 400 
800 $ 
= T.C.OA. TCTAD TC54:. TC.SA, TeolmeTC.®. Tey, TCS marca E 9 
2 LOAD ON COLUMNS 2 AND 3 9 
. EXTRADOS 3 
ed 800 w 800 
eS a TC.9A. T.GTA. TESA TOGA TCOll. 109, Te7. TCS Tow 
= s LOAD ON COLUMNS. AND 5 
o s EXTRADOS 
a) 
[eg 
r 
Ws Ly 
a Q » z= 400 : 
2 wy 400 oe 
ao z zn 
Se 2 Z 
of ore 
o 
l w) 
WY uj 
Ww A 0 
- uJ 
7) 0 ow 
eg S 
= ” 
w" 
5 
a z 400 
A o 
tv 400 MEASURED STRESSES:~ =| o 
: AVERAGE OF THREE SETS ul 
© OF TELEMETER READINGS a 
~ | | z . MEASUREO STRESSES — 
7 UY g00 AVERAGE OF THREE SETS 
MODEE ANAL ae OF TELEMETER READINGS 
800 | a | \ 
T.C.I2ZA. T.C.8A. T.C.6A. T.C.4A. T.C.2A. TCIO. TC8. T.C.6. T.C.4. ODEL ANALYSIS—B. 
INTRADOS 1200 
ae : TC.IZA. T.C.SA. T.C.6A. TC.4A. TGZA. TCIO. TCO Toes Tc 4. 
MEASURED STRESSES = INTRADOS 
AVERAGE OF THREE SETS 800 
— OF TELEMETER READINGS. a 
S | | | OF TELEMETER READINGS 
o 
2 400 z 
F a 400 
Fe) 
| a 
re) 
° 
m4 
2 z 
A , a 
wl 400 “ 
a W400 
2 a. 
© = 
UV re) 
U 
MODEL ANALYSIS—B. 
800 aaG 
Bo a meee Le een aa T.C.9A. T.C7A, T.CSA, TOBA: TOUR TEN TEA TEIN TEM 
LOCATION OF TELEMETER POINTS ALONG RIB AXIS LOCATION OF TELEMETER POINTS ALONG RIB AXIS 
Fig. 8.—C M 'S A f 
a5. OMPARISON OF MEASURED STRESSES IN ARCH Fia. 9.—CoMparRISON OF MEASURED: STRESSES IN 
Rip Unper 1-Tanx Loapine wita Deck Intact Arch Rip Unprer 1-Tanx Loapine wits; Deck 


(sERIEs 1) anp Mopri ANatysis B Intact (sERIES 1) AnD MopEet ANnatysis B4q | seed 





December, 1928 


es — 





PUBLIC ROADS 





LOAD ON COLUMNS’ 5 ANDO 6 


0 MODEL ANALY SIS-B. 
® 1ST. DAY. *1ST. NIGHT. 


+2ND.DAY. S2ND. NIGHT. EXTRADOS 


W= 68.250 POUNDS 





























z 
© 
i) 
Zz 
WwW 
- 
z 
iS] 
i) 
uy 
rT; wW 
oOo £ 
2: MEASURED STRESSES— 
ne AVERAGE OF FOUR sets _~ 
tc OF TEEEMETER BEREINCS. 
= 
9 MODEL anette B. 
tu 
a. T.C.I2A. T.C.8A. T.C.6A. T.C.4A. J 2A. T.C.10. T.C.8. TC.6. TC.4. 
A INTRADOS 
zZ 800 
=> 
co) 
a 
wv) 
D z 
u 2 
x 0 400 
7 a 
Oe 
fe) 
z 
° 
2] 
f @ao 
x 
a, 
= 
S) MEASURED STRESSES :— 





AVERAGE OF FOUR SETS 
OF TELEMETER READINGS. 





800 
T.C9A. TCA. T.C.5A. T.C.3A. T.C.11. T.CQ. WSs, Use [le 


LOCATION OF TELEMETER POINTS ALONG RIB AXIS 


ere 


Fic. 9.—CoMPARISON OF MREASURED STRESSES IN ARCH 
Ris Unpgpr 1-Tanxk Loapine witsa Deck Intact 
(SERIES 1) AND Mopr. ANALYsis B 


which the full lines are drawn are the averages for the 
several sets of readings. Each of the values from which 
the average was derived is shown by a distinctive 
symbol. The computed values through which the 
broken lines are drawn are based on the assumptions 
that the rib is free from restraint by the superstructure 
and that the concrete takes tension, the steel taking 
only its proportionate share. As will be shown later 
in discussing series 2, the compressive stresses calcu- 
lated on the latter assumption are closer to the measured 
stresses than those based on the assumption that the 
concrete takes no tension, even when the tension is 
high enough to produce a visible crack on the tension 
side of the rib. 

The straight lines drawn between the stress values 
are not intended to represent the manner in which the 
stress changes between the plotted points but are 
intended solely to aid in following the points through 
the chart. 

Stresses derived from the model analysis, for the 
two conditions of column fixity, A, and B, are also 
shown on the charts. Figures 7, 8, and 9 show a 
comparison of the average ‘measured stresses ae series 
1 and the stresses derived from model analysis B. 
These charts afford an indication of the effect of the 
superstructure on the stresses produced in the rib, as 
well an an indication of the accuracy with which ‘the 





LOAD ON COLUMNS 2 AND 3 
© MODEL ANALYSIS-C 
@ IST. DAY. x IST. NIGHT. 


+2ND. OAY. S2ND. NIGHT. EXTRADOS W= 68250 POUNDS 


{600 











{200 

















800 











TENSION 








400 



























oO 

































































" 
Y M . 
o “4 
. + é 
AG ‘ 
U O x { 
as fe Ng 
bs gO8 Y/ MEASURED STRESSES: | oS 
= s \ 4 / | AVERAGE OF FOUR SETS 
ro ae) 
: 2 es OF TELEMETER READINGS —— 
aw rr | 
a & 
» 2 800 | aw 
G o THEORETICAL STRESSES:- 
5 ); CONCRETE TAKING TENSION. 
o CONCRETE TAKING NO TENSION. ~~~ 
| ! 
Ww i 
lJ 
7) {200 
a A 18-6" ALONG AXIS 
ce ¥ —-—— 
Ww) 
TEIPAL TO BAD TICGA, TESA. TCeA. Teo. TCG. TOl6, Tc. 
INTRADOS 
800 
z= 
o 
2 400 ; 
wi 
ke , 
= ey io 
, 
x 
7 | 
: | al e 
: | 
z 
° 
» 400 ee oe 
Ww) 
WwW 
a MEASURED STRESSES:- 
2 AVERAGE OF FOUR SETS +_———— 
oO OF TELEMETER READINGS. | 
THEORETICAL STRESSES:- 
CONCRETE TAKING TENSION. 
7 CONCRETE TAKING NO TENSION. 
T.C.9A. T.C.7A. T.C.5A. T.C.3A. TCOMmIC7 TCS TON 
LOCATION OF TELEMETER POINTS ALONG RIB AXIS 
Fic. 10.—StTresses IN Ancu Ris UNpER 1-TAanK LOADING 


WITH Drcxk Cut (SERIES 2) 


stresses may be deduced from an analysis by the use of 
a model. 

These charts indicate that, in general, the rib stresses 
with structure intact are lessin maximum value than the 
computed stresses for the unrestrained rib and that the 
stresses calculated from the model analysis with the two 
assumed conditions of fixity of the tops of the columns 
are less than the measured stresses. ‘There is a closer 
agreement between measured stresses and those obtained 
by the model analysis than between the measured 
stresses and those computed for the unrestrained rib. 





LOAD ON COLUMNS 3 AND 4 
© MODEL ANALYSIS-C 
@ IST. DAY. X IST. NIGHT. 
+2ND. DAY. 42ND. NIGHT, 


EXTRADOS W = 68,250 POUNDS. 


400 





TENSION 





400 


MEASURED STRESSES':- 
AVERAGE OF FOUR SETS 


COMPRESSION 


OF TELEMETER READINGS, 
| | | 

—— THEORETICAL STRESSES:- —; 
CONCRETE TAKING TENSION. 


CONCRETE TAKING NO TENSION. 





800 





TCI2A. T.C.8A. TC.6A. TC:4A. TC.2A, TCIO T.C.8. T.C.6. T.C.4.. 
INTRADOS 


i 18'-6"ALONG AXIS 
| 


400 


TENSION 












STRESSES— POUNDS PER SQUARE INCH. 








400 


“(MEASURED STRESSES:- 
K\-. AVERAGE OF FOUR SETS 


OF TELEMETER READINGS 


| | 
-THEORETICAL STRESSES: 


CONCRETE TAKING TENSION. 


~~ CONCRETE TAKING NO TENSION. 
a ! 


COMPRESSION 


800 








1200 


COA ee A mG OAUm Gr oA Wess  WSate — UKG SE: 


LOCATION OF TELEMETER POINTS ALONG RIB AXIS. 


Fig. 11.—Stressges In Arca Rip Unpgr 1-Tanx LOADING 
wiTtH Deck Cut (sERIBS 2) 


It may be observed that, for model condition B 
(see p. 194), the stresses, in general, check the measured 
stresses closely, while those for model condition A are 
somewhat lower, particularly for maximum stresses. 
It must be said, however, that this check is more or 
less accidental since the size of the connection between 
the floor and columns in model B was arbitrarily se- 
lected. The stresses for conditions A and B differ most 
in the regions of maximum stress. It will be noticed 
that, at some points of low stress, the model results for 
condition A check the measured results more closely 
than for condition B. The rotation curves (to be 
discussed later), will show these relations more 
clearly. 

When the load was placed on columns 5 and 6 in 
series 1, a crack occurred on the intrados of the rib 
between the points of attachment of telemeter No. 11. 
In series 2 and 3 this telemeter was removed from the 
rib and no stresses are shown at this point on the charts. 

Figures 10 to 13 show stress values for series 2 in 
which the continuity of the deck had been destroyed 
by cutting through the floor system and inserting new 
bearing plates. ‘The stresses in this series are plotted 
in the same manner as in series 1, and, in addition, 
where tensile stresses exist, the compressive stresses on 
the opposite side of the rib are calculated on the assump- 


PUBLIC ROADS 


Vol.9 No. 10 





LOAD ON COLUMNS 4 AND 5 
©MODEL ANALYSIS-C 
@1ST. DAY. XIEST. NIGHT. 


+2ND.DAY A2ND. NIGHT, EXTRADOS 


W = 68,250 POUNDS. 


800 


ra A 
Q a a 
ca 
ri [| N 
é 
LA 
. : : \ a 
A R 
N i \ 
400 





\ 
\ 
18'-6"ALONG AXIS Y 
hall « 


OF TELEMETER READINGS. 


| | | 
THEORETICAL STRESSES!- 


CONCRETE TAKING TENSION. 


COMPRESSION 
(e-) 
° 
° 





TC.12A, T.C.8A, T.C.6A. TC.4A. TC.2A, TCIO. T.C.8@ T.C.6. T.C.4, 


INTRADOS 


STRESSES- POUNDS PER SQUARE INCH. 











MEASURED STRESSES: 
AVERAGE OF FOUR SETS 
OF TELEMETER READINGS. 






\I8-6"ALONG AXIS 
}~——>| 





TENSION 
A 
fe) 
oO 









400 









THEORETICAL STRESSES:- i LE 
CONCRETE TAKING TENSION. $ 
CONCRETE TAKING NO TENSION. 


T.C.9A. T.C.7A. T.C.S5A. T.C.3A. -C.950) Cay eine-O merle 


COMPRESSION 


800 





LOCATION OF TELEMETER POINTS ALONG RIB AXiS. 


Pia. 12.—Stresses In Arcu Rip Unper 1-Tank LoapInG 


witH Deck Court (sERIES 2) 


tion that the concrete takes no tension. These latter 
values are indicated by open circles. 

Agreement between the measured and computed 
results is much closer than in series 1, becoming closer 
as the load moves toward the crown and the deflection 
becomes greater. It is also noted that the agreement 
between the measured and computed results is much 
closer when it is assumed that the concrete takes 
tension. ‘The measured stresses were nearly always 
less than the computed stresses. The results from the 


model analysis of the free rib check the computed re- 


‘sults very closely. 


Figure 14 shows the stresses for series 3 in which the 
deck was cut and two tank loads placed so as to produce 
maximum stress at the springing line. The agreement 
between measured and theoretical stresses is again 








December 1928 








LOAD ON COLUMNS 5 AND 6 
© MODEL ANALYSIS-C 
@ IST. DAY. XI ST. NIGHT. 


+2ND. DAY. S2ND. NIGHT. EXTRADOS 


W = 68,250 POUNDS 


zZ 1400 
o 
” 
2 
LJ 
Ie 

re) 

400 —_—_—_ 
5 . 
° ae 
a \ 
7 MEASURED STRESSES:- 
¢ 800 |-AVERAGE OF FOUR SETS _| 
9° OF TELEMETER READINGS: 
THEORETICAL STRESSES:- X 


CONCRETE TAKING TENSION ¢_ [8-6"ALONG AXIS 


CONCRETE TAKING NO ne ol) amis 
1200 


TeIZA. LGA. TC.6A. LEGA. need. TECIO. 6.8. EG.6. T.C.4. 
INTRADOS 





800 


DRESSES —POUNDSRCERS SQUARE SINGH. 


MEASURED STRESSES:- 
400 AVERAGE OF FOUR SETS 


TENSION 





COMPRESSION 
b 
° 
° 


THEORETICAL STRESSES =~ 
CONCRETE ,TAKING TENSION. 
CONCRETE TAKING NO TENSION. 








800 
T.C.9QA. T.C.7A. T.C.5A, T.C.3A. Reo. Ga ero.) 1G.) 


LOCATION OF TELEMETER POINTS ALONG RIB AXIS 


Fig. 13.—Stresses IN Arncu Ris UNpER 1-Tanx LoapDING 
wiTH Drck Cot (SERIES 2) 


close. In this series a visible crack occurred at the 
springing line, extending over four-fifths of the depth 
of the rib. Nevertheless, there is still a much closer 
agreement between the computed and measured com- 
pressive stresses when the former are calculated on the 
assumption that the concrete takes tension. 

Loads of 68,250 pounds at columns 1, 2, 3, and 4 
produced a measured compressive stress of about 
1,600 pounds per square inch in the concrete of the 
intrados at the springing line. When this measured 
stress is combined with the computed stress due to the 
weight of the tank, dead load, shrinkage, and tempera- 
ture, the stress is increased to a value of about 3,000 
pounds per square inch. Such high stresses over a short 
length of the rib apparently do not affect the general 
relation of computed to measured stress, although, as 
will be seen later, the rotations and deflections are 
measurably increased in series 3. 

Figures 15 to 18 present a comparison of measured 
stresses of series 1 and 2, the difference between the 
two showing the effect of the superstructure. It is 
seen that the stresses for series 1 are practically always 
less than series 2 at the maximum values. The difference 


PUBLIC ROADS 199 





LOAD ON COLUMNS | AND 2-3AND 4 




















































































EXTRADOS W = 68,250 POUNDS. 
{ 
LOAD LOAD | 
NS oe hy, | 
2000 www wee ee ee 
é | 
w le | L a a 
z MEASURED STRESSES 
= ONE SET OF TELEMETER | 
— READINGS DAY. —-. —" 
ie | 
‘en p ee ie. 4 7 
fo) | | 
, ™ 
z h \ 
fe) \ , >. 
7) — nee a | = 
ie) \ y t 18-6 ALONG AXIS | 
u aN fe Pe 
000 \ ee | i 
3 " | \ | | Me 
. : /\\ THEORETICAL STRESSES- 
5 a U7“ CONCRETE TAKING TENSION.— +—— 
re y CONCRETE TAKING NO TENSION. 
Ww 
© 2000 
< IGI2ZA. TC.BA. TC.6A IC.4A. TC.2A. TC10. TC8 T.C.6. TC.4. 
o 
7a) 
a INTRADOS 
a. 1000 
2 
a 
A 
5 Z 
a - 
a 0 
WY) 
“” 
iW 
[o4 
lo 
W) 
1000 ciel — a 
; MEASURED STRESSES 
ONE"SET. OF TELEMETER=—-—_ 
| READINGS ae | 
Ze 
S 2000 THEORETICAL STRESSES 
” CONCRETE TAKING TENSION. 
cx im—~—______ CONCRETE TAKING NO TENSION. 
5 = 
fe) 
oO 
3000 4. —_ 
18-6" ALONG AXIS 
a= 
4000 























T.C.9A. T.C.7A. T.C.5A. T.C.3A. iG Oneen, Get -eerleGrO, | Get. 


LOCATION OF TELEMETER POINTS ALONG RIB AXIS 


Fic. 14.—Stresses in Arncu Ris UNpER 2-Tanx LoApING 
witn Drecx Cut (sERIES 8) 


increases as the load moves from the springing line to 
crown and is greatest when the loads are near the crown. 
It was observed in series 2 that the measured stresses 
were nearly always somewhat less than the computed. 

Figures 19 and 20 are intended to show variations in 
stress at the respective telemeter points as the load 
moves from pier to pier. Stresses are shown as ob- 
served and as calculated theoretically. The curves 
for measured values are mean curves, the diagram 
showing each point from which the mean is derived. 
In calculating the averages several obviously erratic 
values were discarded but all values are plotted on the 
diagrams. The points at which the stresses are plotted 
are located at the centers of gravity of the loads or 
midway between the columns on which the loads were 
placed. The curves are plotted on the assumption 
that the rib is symmetrical and: the materials are 
homogeneous and that, therefore, a load placed at any 


200 








STRESSES —-POUNDS PER SQUARE INCH 
TENSION COMPRESSION TENSION 


COMPRESSION 


FIa. 


LOAD ON COLUMNS 2 AND 3 


EXTRAODOS 
——-—MEASURED STRESSES SERIES NO. |! 
MEASURED STRESSES SERIES NO. 2. 





W=68,250 POUNDS. 





1200 





800 





\8'-6"ALONG AXIS 


+» 




















TCI2A. T.C.8A, TC.6A. T.C.4A. TC.2A. T.C.10. T.C.8. T.C.6. 
INTRADOS 


T.C.4 




















TCIA. EGTA. T.C5A> TG.SA. meal: 


WEE Uleate UGS, INSU 


LOCATION OF TELEMETER POINTS ALONG RIB AXIS 


15.—CoMPARISON OF STRESSES IN ArcH Ris UNDER 


1-Tanx Loapine with Deck INTACT, (SERIES 1) AND 
witH Deck Curt (SERIES 2) 


TABLE 2.—Observed and computed stresses in steel in series 2! 


[Load: 68,250 pounds per column. #,=30,000,000 pounds per square inch] 








Computed stresses, 


Telemeter results cangrete faking— 





























| 
| 
Columns | Teleme- | ite, a 
Joaded ters ra a . mall |e 
Irs Irs econ econ oO ten- : 
day | right day night sion Tension 
end 3_.__.| dix. 1A | T10,700 | T 9,220; T 8,180} T 6,280 | T35,850} 4,760 
Doce 1A.|°T 680) (5,700 | aie. Tae) Pr 1270| Mae aire 
He... 52 .| C 1,370 | C 1,650! C 15an, Cio | C2740 | “Cie 
Dos .2 In. 11_| C 2,770; C 5,780 | C 3,350 | C 3,570| C1,940| C 259 
es, 8 .| T 2310) T 1,600) T 1,340) Teo | Tomo | PT ae 
Seam 4____|MaawdiA_| T 2,340 | Tf 3,500 | T1,610| T2i650 | 113,000) 11,7 
....28 TA.| T 600| 1 Gap| C 650| P20 | F geo) T liz 
i — 3.| C 2,430 | C 1,200| C 2,120| C 3,900| C 5,540| C 739 
1 0-....- In. Ji_| C 4,640) C 2,800 C.2,0I0| Camo) © 207| C ae 
Woe. 2.| T 2,000 | T 2,480 | T1,500| T 29200 | 18,770 | TI, 1s 
dyad 5....\0 11A.| C 800! T 1,270| C 220) Twans20| T Sa oT 1B 
‘iy ae IA| C 240! C ” 70! CG 670| GC 860| C1,480| C 197 
io. ._ 20 | C 3,620! C 3,140! C 2,450| C 1,140! C 7,030} C 937 
Do____.- In. 11.| © 3,760| C 670} C1,400/ GC '780/ G '230| GC 30 
Wo... ... _| T 1,280 | T 2,910} T 1,530] T 2,160 | 'T12,900| T1,720 
5and 6 Ex. 11A_| C 2,370; C 750; C1,840| C 490) C 2,150} C 287 
i 1A-| C 2,550) C 4,510 C 3,490 | C 3,380] C 8,510] C1, 135 
0. ees. 3_| © 5,000; C 2,380 | C 2,200! C 1,720| C 4,690; C 626 
(eo... Inedi_| T12,410 | T10,230| T11,930 | T11,380| 114,600; T1,950 
ib eee 2.| T 940] T 1,460| T 1,320! T 1,720] T4,830| T 645 





TT tt mis 





1 Tension and compression are indicated by the letters T and C, respectively. 


PUBLIC ROADS 


Vol 9 No 10 





LOAD ON COLUMNS 3 AND 4 


EXTRADOS 
——-—MEASUREO STRESSES SERIES NO.1. 
MEASURED STRESSES SERIES NO2. 





W=68,250 POUNDS. 


400 





TENSION 





400 





COMPRESSION 


400 





TENSION 








STRESSES~- POUNDS PER SQUARE INCH. 





400 





COMPRESSION 





TG3SA. TGA. T.C.5A: TG.3SAL TEN Ses. Ter eaTes: 
LOCATION OF TELEMETER POINTS ALONG RIB AXIS 
Fic. 16.—CoMPARISON OF STRESSES IN ArncH Ris UNDER 


1-Tank Loapina with Deck Intact (spRIzEs 1) AND 
wita Deck CuT (SERIES 2) 


point, say, at column 8, produces a stress at any point, 
say, telemeter point @’ on the opposite side of the 
crown, equal to the stress at a produced by an equal 
load at 3’, where the position of each of the pairs, 3, 3’, 
and a, a’, are symmetrical with respect to the crown. 


STRESSES IN STEEL DISCUSSED 


Table 2 shows observed and computed stresses in the 
reinforcing steel at the crown and springing lines. It is 
noted that the measured stresses are, in general, less 
than the stresses computed on the assumption that the 
concrete takes no tension and greater than those com- 
puted on the assumption that the concrete takes its 
proportionate part of the tension. In the case of the 
high -tensile stresses, the measured stresses are con- 
siderably less than the computed stresses based on the 
assumption of no tensile strength for the concrete. 


ROTATION OF THE ARCH AXIS DISCUSSED 


In the curves showing rotation, the slope of any 
curve is proportional to the bending moment divided 
by the moment of inertia of the section. Therefore, 
at any section along the rib, the slopes of any series 
of rotation curves are proportional to the bending 
moments. This relation between bending moment 
and slope of the rotation curves should be kept in 
mind in making the following comparisons. The 
smooth curves drawn through the measured rotation 
values are not intended to represent the exact manner 
in which rotations change between sections at which 
measurements were made. 








December, 1928 PUBLIC ROADS aloud 



























































LOAD ON COLUMNS 4 AND 5 LOAD ON COLUMNS 5 AND 6 
EXTRADOS EXTRADOS 
—-——MEASURED STRESSES SERIES NO.}. ——-—MEASURED STRESSES SERIES NO.I. 
MEASURED STRESSES SERIES NO.2. W=#268,250 POUNDS. ——-MEASURED STRESSES SERIES NO.2. W =68,250 POUNDS. 
400 
LOAD <4 
z 400 “ 
5 | | xq Zz 
“ WwW 
Ww ZN & 0 
0 I ‘ r 
- \ \ r 
1) 
\ / IN 3 
: w a 400 
\. ate 
3 NEA = SE 
- 2 400 ges 
zi ia : 
VU. ivy) a 18) 
Za uJ 
a e 800 
« 3 18-6 ALONG AXIS ey 
= v -~-——_> 2 
z 800 9 
a T.C.12A. T.C.8A. TC.6A. TC.4A.TC2A. TC10. TC8 TC6. TC.4. 
“ a INTRADOS 
a 400 
2 Te ISAT TROSA TCEA TC.4A. TC2A. TC10. TC.6, TC.6 TC4. i 
< INTRADOS Eo 
oO ” Ww 
a. z 
is 
® vie = | 
a 8 re) . 
“” 2 Fs 
a _ 2 aN 
pe a 
“a / - \ 
/ a. 
\ A ; 
\ oO 400 
| TEA EGTA, LCSA. 103A, TCIMeTeS. TC7. TC5 TCH. 
| é a LOCATION OF TELEMETER POINTS ALONG RIB AXIS 
2] 
M We Fic. 18.—CoMPpaRIson oF Stresses In ArcH Rip UNbDER 
a 1-Tank Loapine wits Dercxk InrTact (seRIES 1) AND 
5 witH DrscKk Cut (SERIES 2) 


LOAO DIAGRAM 


W=66250 POUNDS 
@ 1ST. DAY. % 1ST NIGHT Piet 
+2NO. DAY. A2ND. NIGHT. AT TELEMETER POINT 2A. 






TC.9A, T.CVA. T.C.5A. T.C.3A. TCA. T.C.9. TC.7% TC.8. T.C.1 
LOCATION OF TELEMETER POINTS ALONG RIB AXIS 


NO TELEMETER ON INTRACOS. 
Ri6 CRAGKED AT CROWN 
T 


















TENSION 


Fic. 17.—CoMPaRIsON OF Stresses In Arco Ris UNDER 
1-Tanx Loapine with Deck Intact (seRiIES 1) AND 
WITH DxcKk CuT (SERIES 2) 























Figures 21, 22, and 23, show rotations in series 1 
for five positions of load. The measured values are 
shown for three increments of load, 22,750 pounds, 
45,500 pounds, and 68,250 pounds per column. The 
computed curve is shown for a column load of 68,250 
pounds only. 

It will be noted that the measured rotations for this 
series are of the same general nature as the computed 
rotations but are much reduced in value at the points 
of maximum values. The influence of the super- 
structure on the moment is clearly seen. The general 
influence of the floor system may be seen in the 
reduction of the maximum values of the rotations and, 
therefore, the reductions in slopes of the curve between 
these high and low points. The local effect of the 
curtain walls between panel points 3 and 3’ may be 
seen by the flattening of some of the curves after ie 
passing panel points 3 and 3’ toward the crown. These 40 
are the points at which the curtain wall ends and has 
its maximum height. The curtain wall tapers off 











THEORETICAL STRESSES. 


cae 


MEAN MEASURED STRESSES. 














COMPRESSION 





































+ + 
MEAN MEASURED 
STRESSES. 


STRESSES - POUNDS PER SQUARE INCH 


TENSION 














+ 


~™ 
P= 
| 

















+> 








ras 
extracos| 

















COMPRESSION 
































to a height of 0.85 foot at the crown where its effect ou al 
is negligible. 

Figures 24 and 25 show the rotations for series 2 fi ) tie | sates 
with loads on each pair of columns from 2 to 6 and for cee 


LOCATION OF COLUMN POINTS ALONG RIB AXIS 


the same increments of loads as in series 1. The 

were Al a ] fan : f Fig. 19.— VARIATION IN STRESS IN THE CONCRETE AT 
computed and measured values of the rotations or TELEMETER PoInts For A 1-TANK Loap Movinc Across 
this series show a remarkable agreement. The maxi- THE Span wita Deck Cut (sERIES 2) 


PUBLIC ROADS 








Vol. 9, No. 10: 








TENSION 


INCH. 
TENSION COMPRESSION 


STRESSES.- POUNDS PER SQUARE 


COMPRESSION 


TENSION 


COMPRESSION 


Fig. 





LOAD DIAGRAM 
W=68,250 POUNDS 
@1ST. DAY. X PStaiGHT. 12+ 
+2ND. DAY. O2ND. NIGHT. AT TELEMETER POINTS SA AND 6A. 


800 








INTRADOS 
400 


EXTRADOS 
= a 
ees — 
— 


400 









800 








400 


EXTRADOS 
400 


800 


MEAN MEASURED 
STRESSES. 


400 





400 - A i 
THEORETICAL 


STRESSES. 


800 


LOCATION OF COLUMN POINTS ALONG RIB AX!5 


20.— VARIATION IN STRESS IN THE CONCRETE AT TELEMETER POINTS FOR A 1-TANK Loap MovING 
ACROSS THE SPAN WITH Deck Cut (SERIES 2) 








December, 1928 PUBLIC ROADS 205 








—————— = = = = ——$—— 


LOAO ON COLUMNS | AND 2 


- 
h-10-+ . 
ALONG AXIS | 














bes ie, < 
(ES Sei 
5 @ "MEASURED ROTATIONS ao 
\ 7] 22,750 POUNDS PER COLUMN. ies 
44 '/ ~— 45,500 POUNDS PER COLUMN. 
See’ 


68250 POUNDS PER COLUMN. 














’ 
{ 





welt | | 
THEORETICAL ROTATIONS 
68,250 POUNDS PER COLUMN. 




















LOAD ON COLUMNS 2 AND 3 









































<f~— 22,750 POUNDS PER COLUMN. 

!/~— 45,500 POUNDS PER COLUMN. 
68,250 POUNDS PER COLUMN. 
! | 
THEORETICAL ROTATIONS 
68,250 POUNDS PER COLUMN. 























LOAD ON COLUMNS 3 AND 4 


bea 2.5 







fe JS? Sine ieee 
10+ 
\ ALONG AXIS 


S) ASS Oe 

| | ESS eee 
| SESE SSA SRA 
| APRESS a ee 
NS ene 
fe) a8) 2 eee See ee 
NEB ARRAS 
a LA MEASURED ROTATIONS \ 













=2.0 


ROTATION- INCHES PER INCH'(THOUSANDTHS OF AN INCH) 











— 0) 











Sa, 







GP ot 

















+1.0 

















a 22,750 POUNDS PER COLUMN. 
Rue 45,500 POUNDS PER COLUMN. \ 
Eas 68,250 POUNDS PER COLUMN. 
THEORETICAL ROTATIONS 
Ce / 68,250 POUNDS PER COLUMN. SS 
_ co SS Riese 
— 
3 4 5 6 7 8 9 10 
LOCATION OF CLINOMETER POINTS ALONG RIB AXIS 


co [late 








Fig. 21.—Rotations oF Arcu Ris UNpDER 1-TAank Loap- 
ING witH Deck INTAcT (SERIES 1) 


mum slopes of the computed and measured curves 
are practically the same over a considerable length 
of the rib. The greatest differences of slopes of the 
two curves occur near the points of maximum rotations 
or zero bending moment. At these points it may be 
expected that the greatest discrepancies between com- 
puted and measured stresses would occur in so far 
as the stress is dependent on the bending moment. 
Figure 26 shows rotations for series 3 with loads over 
columns 1, 2,3, and 4. The maximum measured rota- 





LOAD ON COLUMNS 4 AND 5 

































































co BL : 
ae id 
| re | ALONG AXIS | 
-<25 5 — ——=- —--— 
| ae 2S 
/ \ | 
-2.0 Joa — 
| \ | 
TROTTeV os 
-3.5 1) a = \ + = SSS ae 
\ 







































































MEASURED ROTATIONS | 
22,750 POUNDS PER COLUMN. i + 7 
45,500 POUNDS PER COLUMN. 

68,250 POUNDS PER COLUMN. 


THEORETICAL ROTATIONS 4 
68,250 POUNDS PER COLUMN. 


3 4 5 6 7 8 9 10 Vi 
LOCATION OF CLINOMETER POINTS ALONG RIB AXIS 


Fig. 22.—Rotations or Arco Ris UNDER 1-Tanx Loap- 
ING WITH Deck INTACT (SERIES 1) 





ROTATION- INCHES FER INCH (THOUSANDTHS OF AN INCH) 



























LOAD ON COLUMNS 5 AND 6 


k10—-{ 
ALONG AXIS 
“ 
SSE RE aes 
ee a a aa | 





-25 











-2.0 















































+.5 XJ i 
COCA oY essen, 
aa 22,750 POUNDS PER COLUMN. : 


KY 45:500 POUNDS PER COLUMN. ih 
ar es a il i+ 
THEORETICAL ROTATIONS {I 


68,250 POUNOS PER COLUMN. 


ROTATION~ INCHES PER INCH (THOUSANOTHS OF AN INCH) 





\ 


























3 4 5 6 7 8 2) 10 1! 
LOCATION OF CLINOMETER POINTS ALONG RIB AXIS 


Fic. 23.—Rorations oF ArcH Rip UnNpeErR 1-Tanxk Loap- 
ING wiTH Deck INTACT (SERIES 1) 


tions in this case show greater values than maximum 
computed rotations although the maximum slope and, 
therefore, maximum moments agree very closely. It 
appears that even though the maximum rotations for 
this case are somewhat increased by the cracking at 


204 








| yeee 
| /_ Yoze 








22,750 POUNDS PER COLUMN. 
7— 45500 POUNDS PER COLUMN. 
68250 POUNDS PER COLUMN 


lee 


‘| THEORETICAL ROTATIONS 





ACh 
SESS in 











WE iii 

oe, ANS 

VL ANAL Tt 

Pas SSN ae 

LAIN Ww fe 

if SEEMS? 
fl 











; 


LS OS See 


a 
Q7 
) 
> 








ROTATION- INCHES PER INCH (THOUSANDTHS OF AN INCH) 

















i\\ 22,750 POUNDS PER COLUMN. 


45,500 POUNDS PER COLUMN. \] 
68250 POUNDS PER COLUMN. na 





Li TASS 




















LOCATION OF CLINOMETER POINTS ALONG RIB AXIS 


Fic. 24.—Rotations or ArcH Ris UNpER 1-TANK Loap- 
ING WITH Drck Cut (SERIES 2) 


fie springing line because of high local stresses, the 
arch still continued to deform elastically. 
ROTATIONS FROM MODEL ANALYSIS COMPARED WITH MEASURED 
AND THEORETICAL ROTATIONS 

Moment diagrams for each condition of loading and 
each condition of rib restraint were made from the 
influence lines derived from the model analysis. Rota- 
tions were calculated from these moment diagrams, the 
rotation due to rib shortening caused by thrust being 
neglected. Curves in Figures 27 and 28 show compari- 
sons between measured rotations for series 1 (curve E), 
the computed rotations (curve D) and those calculated 
from the model analysis for the three conditions of rib 
restraint (curves A, B, and C). These curves show 
the relation between the model analysis, for the two 
conditions of the superstructure, and the measured 
rotations. For the free rib, the agreement between 
computed results and the model analysis is very close. 

It is felt that the rotations are the most significant 
of the measurements taken in the field because the 
instrumental work was subject to few inaccuracies and 


PUBLIC ROADS 


Vol. 9, No. 10 


© 


A 


PTE ELLLLLLLLLI_ 
CCAR BSS 
CCEPDre Dr Pp 
CCC EEE 


EPVve2eeae 
Lit | | | | | tt | 


: 
@, 


Wz 





f /| 
Kee 


= 
= 
: 
: 
: 
He 
ane 
wd 
EN 


Ee) 
AN 
aS 


MEASURED ROTATIONS 
22,750 POUNDS PER COLUMN. 
45,500 POUNDS PER COLUMN. 
68,250 POUNDS PER COLUMN. 
ie ot. “aa 
THEORETICAL ROTATIONS 
68,250 POUNDS PER COLUMN. 





LOAD ON COLUMNS 5 AND 6 


|| | PSS CRE eee 
| USPS 
| | Pa See 
|) | Saas | ee 
Pt tT TT NAL [aces | 
FEEEEEE HAN EEE 
2x tEH TEEN ce 





= CAS, 










ROTATION-INCHES PER INCH (THOUSANDTHS OF AN INCH) 





























CCEPASSIR 

CHENEY 

OTA 

Ls 
& 


LOCATION OF CLINOMETER POINTS ALONG RIB AXtsS 


22,750 POUNDS PER COLUMN. 
45,500 POUNDS PER COLUMN. 
68250 POUNDS PER COLUMN. 
| | | | | | 
THEORETICAL ROTATIONS 
68,250 POUNDS PER COLUMN. 












cP es: 






Fic. 25.—Rotations or ArcH Ris UNDER 1-TANK Loap- 
ING WITH DrEcK CuT (SERIES 2) 


because they represent a summation of deformation 
and are not, therefore, as sensitive to sudden local 
changes in moment as in the case of stresses. 


DEFLECTION OF THE RIB 


Figures 29 and 30 show measured deflections for 
series 1 at all columns except those next to the piers and 
also the computed deflections. The stiffening effect 
of the superstructure is shown by the greatly reduced 
deflections. The effect of the curtain wall is indicated 
by the flattening of some of the curves where the curtain 
wall occurs. 

The curves shown in Figures 31 and 32 give compari- 
sons of measured and computed values of deflection for 
series 2. With the curtain wall removed and the effect 
































December, 1928 








4.0 


k10-+4 
ALONG AXIS 


-2.0 





=(|de) 


45500 POUNDS PER COLUMN. 


eceee BOUORS ae Sry 


ROTATION-INCHES PER INCH (THOUSANDTHS UF AN INCH) 





LOCATION OF CLINOMETER POINTS ALONG RIB AXIS 


Fig. 26.—RotTations oF ArcH Ris UNDER 2-TANK LOApD- 
ING witH Deck Cur (SERIES 3) 


of the deck reduced to a minimum, the two curves agree 
very closely. 

Deflections for series 3 are shown in Figure 33. Here, 
as in the rotations for series 3, the maximum measured 
results are somewhat greater than the theoretical, but 
the curves are of almost identically the same form. 


CHANGES IN LENGTH OF MIDORDINATES OF THE ARCH AXIS 


Figures 34 and 35 show measured and computed 
values for the changes in midordinates of successive 
5-foot ares of the axis for series 1 and 2. The ordinates 
of these curves are, of course, proportional to the bend- 
ing moment divided by the moment of inertia of the 
section. 


TEMPERATURE DEFORMATIONS 


Figure 36 shows measured rotations and deflections 
due to a temperature change of 1° C. compared with 
the computed values. <A coefficient of expansion of 
0.00001 per degree centigrade was used in these com- 
putations. Readings were taken with the load con- 
ditions constant at different rib temperatures and these 
readings were divided by the change in average rib 
temperature. All the values for a 1° change were 
averaged to obtain the plotted values. 

The curves for series 1 and 2 check each other very 
closely, indicating that the superstructure in this 
particular case, has little effect on the action of the rib 
due to temperature changes. The curves for series 
1 and 2 check the computed curve very well. 


CONCLUSIONS 


The following conclusions as to the action of a 
reinforced concrete arch appear to be justified by the 
data presented above: 

(1) The action of an arch rib, when free from the 
restraining effect of the superstructure and supported 
by practically immovable piers, conforms closely to the 
action as determined by the generally accepted theory 
of elastic structures, even at high unit stresses over 
short lengths of the rib. 

(2) The observed compressive stress in the concrete 
at any section of the rib checks the computed stress 
more closely when it is assumed that the concrete takes 


PUBLIC ROADS 














S|} 40, 










































pac Z 


\ 








| 

ACK | Se 
\\\A= MODEL ANALYSIS COLUMNS INTERGALWITH FLOOR 
au \B= MODEL ANALYSIS MODIFIED COLUMN CONNECTION 


a | 
\\C=MODEL ANALY SIS FREE RIB | | | 
t \O= THEORETICAL ROTATIONS FREE RIB ' . | 
'E = MEASURED ROTATIONS SERIES | | | | | 

1 ae co 


] | i! 





























LOAD ON COLUMNS 2 AND 3 




























































































ROTATION INCHES PER INCH (THOUSANDTHS OF AN INCH) 



























































ee 
n 7 | D 
+.5 La ve \ : i j 
ae CRIT IRS| \ | i 


! cae ae —_= | 
AC an 



























































) 4 5 6 7 8 9 10 WM 
LOCATION OF CLINOMETER POINTS ALONG RIB AXIS 


Fig. 27.—RotTatTions oR ArcH RIB UNDER 1-TaNK LOAD- 
ING FROM MopEL ANALYSIS COMPARED WITH MEASURED 
ROTATIONS (SERIES 1 AND 2) 


tension than when it is assumed that concrete is not. 
active in resisting tensile stress, even where the high 
tensile stress causes cracks in the concrete. 

(3) The observed tension in the steel was, in general, 
less than that computed by assuming the concrete to 
take no tension. 

(4) The superstructure in an open-spandrel rib arch 
greatly reduces the deformation of the rib; the amount. 


PUBLIC ROADS 

















LOAD ON COLUMNS 4 AND 5 








rio —4 
ALONG AXIS 





























































































































ROTATION- INCHES PER INCH (THOUSANDTHS OF AN INCH) 
+ + + 
































LOCATION OF GLINOMETER POINTS ALONG RIB AXIS 


Fic. 28.—Rortations or Arco Rip UNpzER 1-TANK LOAD- 
ING FROM MopEL ANALYSIS COMPARED WITH MEASURED 
ROTATIONS (SERIES 1 AND 2) 


of reduction depending upon the degree of continuity 
of the floor system, the manner in which the floor 
system is attached to the tops of the spandrel columns, 
and the stiffness of the columns. 

The use of expansion joints of the sliding type in the 
floor system of this bridge apparently did not prevent 
the coaction of the superstructure with the arch ribs 

(5) A quantitative determination of the effect of the 
superstructure on the arch may be made by the use of 
the Beggs deformeter gauges on an elastic model of 
celluloid or some other suitable material, if all members 
are connected in a definite way. While it seems possi- 
ble to get a reliable model analysis when the structure 
has frictional joints such as the floor bearings of the 
Yadkin River Bridge, there is no practical means of 

















LOAD ON COLUMNS | AND 2 


THEORETICAL DEFLECTIONS 
OAD 68250 POUNDS PER COLUMN. 





WW“ 22,750 POUNDS PER COLUMN. 


Can 45,500 POUNDS PER COLUMN. 
68,250 POUNDS PER COLUMN. 











|| ae 
A | ane 
| 
eo TS 


1 - 





MEASURED DEFLECTIONS 
Poy 22780 POUNDS PER COLUMN. 

45,500 POUNDS PER COLUMN. 

68250 POUNDS PER COLUMN. 


aA ce 
THEORETICAL DEFLECTIONS 


68,250 POUNDS PER COLUMN. 





LOAD ON COLUMNS 3 AND 4 


TTT ee 
SERENE 
“CO ae 
CCCP BEERS 
CREE ee TT 

| Jee 






-.4 


























aan POUNDS PER COLUMN. 
Lh eater er! 

THEORETICAL DEFLECTIONS 

68,250 POUNDS PER COLUMN. 






LOCATION OF DEFLECTION POINTS ALONG RIB AXIS 


Fig. 29.—DEFLEcTIONS oF ArcH RIB UNDER 1-Tanxk LOAD- 
ING wiTtH Deck INTacT (SERIES 1) COMPARED WITH 
THEORETICAL DEFLECTIONS 


making a model which represents such joints with cer- 
tainty. 

(6) Temperature deformations of the rib appear to 
be eee of the superstructure for this particular 
arch. 


APPLICATION OF CONCLUSIONS TO ARCH DESIGN DISCUSSED 


These tests were concerned only with deformations 
produced by live loads applied over comparatively 
short periods of time. The conclusions are not, there- 
fore, necessarily true of dead-load deformations due to 
continuous application of the load over long periods of 
time because of the possibility that the elastic proper- 
ties of the concrete may be changed by a continuously 
applied stress. 

It may be inferred from the first conclusion that, 
even though the dead-load stresses are kept down to a 
low value, the combined dead and live load stresses 
may be safely allowed to reach a much higher value, 
depending upon the quality of concrete which may be 
secured in the work. 

Conclusions 4 and 5 indicate that, if full advantage is 
to be taken of the stiffening effect of the superstructure, 
a type of structure must be used which can be accu- 
rately represented by a model. In order to do this, 


Vol. 9, No 10 























‘December, 1928 PUBLIC ROADS | 207 


























LOAD ON COLUMNS 4 AND 5 














| | 
es 
\_| ALONG axis 
a ee ioe 
| 


















































=| are DEFLECTIONS 


a )— 22,750 POUNDS PER COLUMN. 


Pr 45,500 POUNDS PER COLUMN. 









































2 2,750 POUNDS PER COLUMN. 
45,500 POUNDS PER COLUMN. 





—— 68,250 POUNDS PER COLUMN 


ee | 








































































































































Wn g 
w |. THEORETICAL DEFLECTIONS bi CBRE? AER PER COD ed 
D 68,250 POUNDS PER COLUMN. w | 
z x THEORETICAL DEFLECTIONS | 
; z 68,250 POUNDS PER COLUMN. 
ra | 
= Zz 
= 
0 G 
Ww e 
al 1S) 
w Li 
WwW =] 
Oo uw 
W 
a 
ako 
ALONG AXIS 
sot 
| Ye DEFLECTIONS 
27 
Be enes een coun He Meee or 
Be Re cra. colt a 22,750 POUNDS PER COLUMN, 
; J-—— 45,500 POUNDS PER COLUMN. 
68,250 POUNDS PER N. 
THEORETICAL DEFLECTIONS ‘ | " 7 DG 
68,250 POUNDS PER COLUMN. | 
THEORETICAL DEFLECTIONS 
5 = rr z 5 ; - 3 68250 POUNDS PER COLUMN 
LOCATION OF DEFLECTION POINTS ALONG RIB AXIS 
2 3 4 5 6 7 8 9 
Fic. 30.—DeEr.ections or Arc# Ris UNDER 1-Tanxk Loap- ise anicnion be Mec iomieontTe mone aio Axis 


ING wiTH Deck INTACT (SERIES 1) COMPARED WITH 


RE TPOnCr at GciioNs Fig. 32.—DErFr.LectTions or ArcH Rip UNDER 1-TANK LOAD- 


ING WITH Deck CuT (SERIES 2) COMPARED WITH THEO- 


RETICAL DEFLECTIONS 
LOAD ON COLUMNS 2 AND 3 
LOAD ON COLUMNS ! AND 2—3 AND 4 








: S ALONG AXIS 
Se SSee? Zee SS 


MEASURED DEFLECTIONS 

\———_- 22750 POUNDS PER COLUMN 
pte cent cee Dry POUNDS PER COLUMN 
er as Cs) j 
68,250 POUNDS PER COLUMN. 




















THEORETICAL DEFLECTIONS 
68250 POUNDS PER COLUMN. 


AT 
sc ee) 
SOOT 
Nam 4! 


\ a. en MEASURED DEFLECTIONS 
\ AJ “\—22,750 POUNDS PER COLUMN. 


DEFLECTION — INCHES 





\/ 45,500 POUNDS PER COLUMN. 
-68,250 POUNDS PER COLUMN. 
| J | | | | 
THEORETICAL DEFLECTIONS 
68,250 POUNDS PER COLUMN. 








DEFLECTION — INCHES 


























i 2 3 4 5 6 7 8 9 
LOCATION OF DEFLECTION POINTS ALONG RI6B AXIS 
Fig. 33.—DEFLEcTIONS oF ARCH RIB UNDER 2-TANK 
LOADING WITH Deck CuT (SERIES 3) COMPARED WITH 
THEORETICAL DEFLECTIONS 








sliding joints should be eliminated from the structure as 
far as practicable and definite connections made between 
f LOCATION OF DEFLECTION POINTS ALONG RIB AXIS A 

all members. It should be pointed out, however, that, 


| 731.— -Tanxk Loap- . . 
| see Sa onc. Ohm a Be Cones wit Tuo. wu full advantage is taken of the reduction of rib stresses 


RETICAL DEFLECTIONS due to the stiffening effect of the superstructure, a 


i Oe Se. | ee - es a 869 





208 


PUBLIC ROADS 








=—=THEOREMCAL CURME. 


——MEAN MEASURED VALUES. LOAD ON COLUMNS ! AND 2 


W = 68250 POUNDS 


































































































CHANGES IN MID-ORDINATE (60-INCH CHORD LENGTH) - THOUSANDTHS OF AN INCH. 
















| eee 

SPEC ERR EYEE CEES 
|) SiS ee 
RRMA BRAARY eS 


20 22 ‘24 26 
LOCATION OF MID-ORDINATE POINTS ALONG RIB AXIS 











ae 


Fic.34.— MEASURED AND CoMPUTED M1p-ORDINATE CHANGES 
UNDER 1-Tanxk LoapDING witH Deck INTACT (SERIES 1) 


complete investigation should be made of the accom- 
panying increase in the stresses in the spandrel columns. 


DEFORMATION MEASURING INSTRUMENTS DISCUSSED 


Of all the instruments used in this test, the clinometer 
is probably the most dependable because of its simplicity 
of construction and its comparative immunity to tem- 
perature effects. However, it is felt that, when proper 
provisions for temperature corrections are made, the 
electric telemeter gives satisfactory results when rela- 
tively large deformations occur but it is difficult to 
make proper provision for temperature corrections under 
field conditions. 

It seems that the radiusmeter Is subject to some inac- 
curacies in measuring very small quantities such as were 
measured in these tests. 

Deflections measured from a piano wire under high 
tensile stress proved to be very satisfactory. 


O 


-~—THEORETICAL CURVE. 
e | ST. SET MEASURED VALUES. 
x 2ND. SET MEASURED VALUES. 


LOAD ON COLUMNS 2AND 3. W #68250 POUNDS 








» 


CHANGES IN MID-ORDINATE (60-INCH CHORD LENGTH) -THOUSANDTHS OF AN INCH 





2 4 6 22 24 26 
LOCATION OF MIDORDINATE POINTS ALONG RIB AXIS 


Fig. 35.— MEASURED AND COMPUTED Mip-ORDINATE CHANGES 
Unpber 1-Tanxk Loapine with Deck Cut (SERIES 2) 


ROTATION 


THEORETICAL ROTATION PER 


°C. RISE IN TEMPERATURE. 
| | | ! 

MEASURED ROTATION PER [°C. RISE IN 

TEMPERATURE. COMPUTED FROM DIF- 

FERENCES IN READINGS UNDER LOAD. 


ROTATION- INCHES PER INCH 
(THOUSANDTHS OF AN INCH) 





8 ) 
LOCATION OF CLINOMETER POINTS ALONG RIB AXIS 
OEFLECTION 


ASSES 














THEORETICAL DEFLECTION PER 
f° C.OROP IN TEMPE iui! 
| 
MEASURED DEFLECTION PER °C. DROP IN TEMPERATURE. 
COMPUTED FROM DIFFERENCES IN READINGS UNDER LOAD. 
; SERIES NO. !. 
SERIES NO. 2. 

















DEFLECTION- INCHES 






LOCATION OF DEFLECTION POINTS ALONG RIB AXIS 


Fic. 36.—TEMPERATURE CuRVvES—THE MEASURED CURVES 
REPRESENT THE AVERAGES OF ALL DIFFERENCES IN 
READINGS UNDER THE SAME LOADING DIVIDED BY THE 
DIFFERENCE IN AVERAGE TEMPERATURE OF THE ARCH RIB 


Vol. 9, No, 10 





ROAD PUBLICATIONS OF BUREAU OF PUBLIC ROADS 


Applicants are urgently requested to ask only for those publications in 
which they are particularly interested. The Department can not under- 
take to supply complete sets nor to send free more than one copy of any 
publication to any one person. The editions of some of the publications 
are necessarily limited, and when the Department’s free supply is 
exhausted and no funds are available for procuring additional copies, 
applicants are referred to the Superintendent of Documents, Govern- 
ment Printing Office, this city, who has them for sale at a nominal price, 
under the law of January 12, 1895. Those publications in this list, the 
Department supply of which is exhausted, can only be secured by pur- 
chase from the Superintendent of Documents, who is not authorized 
to furnish publications free. 


ANNUAL REPORTS 
Report of the Chief of the Bureau of Public Roads, 1924. 
Report of the Chief of the Bureau of Public Roads, 1925. 


Report of the Chief of the Bureau of Public Roads, 1927. 
Report of the Chief of the Bureau of Public Roads, 1928. 


DEPARTMENT BULLETINS 


No. 105D. Progress Report of Experiments in Dust Prevention 
and Road Preservation, 1913. 
*136D. Highway Bonds. 20c. 
220D. Road Models. 

257D. Progress Report of Experiments in Dust Prevention 
and Road Preservation, 1914. 

*314D. Methods for the Examination of Bituminous Road 
Materials. 10c. 

*347D. Methods for the Determination of the Physical 
Properties of Road-Building Rock. 10c. 

*370D. The Results of Physical Tests of Road-Building 
Rock. 15c. 

386D. Public Road Mileage and Revenues in the Middle 
Atlantic States, 1914. 

387D. Public Road Mileage and Revenues in the Southern 
States, 1914. 

388D. Public Road Mileage and Revenues in the New 
England States, 1914. 

390D. Public Road Mileage and Revenues in the United 
States, 1914. A Summary. 

407D. Progress Reports of Experiments in Dust Prevention 
and Road Preservation, 1915. 

463D. Earth, Sand-clay, and Gravel Roads. 

*532D. The Expansion and Contraction of Concrete and 
Concrete Roads. 10c. 

*537D. The Results of Physical Tests of Road-Building 
Rock in 1916, Including all Compression Tests. 
oc. 

*583D. Reports on Experimental Convict Road Camp, 
Fulton County, Ga. 25c. 

*660D. Highway Cost Keeping. 10c. 

*670D. The Results of Physical Tests of Road-Building 
Rock in 1916 and 1917. 5c. 

*691D. Typical Specifications for Bituminous Road Mate- 
rials. 10c. 

*724D. Drainage Methods and Foundations for County 
Roads. 20c. 

*1077D. Portland Cement Concrete Roads. 15c. 
1216D. Tentative Standard Methods of Sampling and Test- 


ing Highway Materials, adopted by the American 
Association of State Highway Officials and ap- 
proved by the Secretary of Agriculture for use 
in connection with Federal-aid road construction. 


* Department supply exhausted. 


DEPARTMENT BULLETINS—Continued 


No. 1259D. Standard Specifications for Steel Highway Bridges, 

adopted by the American Association of State 
Highway Officials and approved by the Secretary 
of Agriculture for use in connection with Federal- 
aid road work. 

1279D. Rural Highway Mileage, Income, and Expendi- 
tures, 1921 and 1922. 

1486D. Highway Bridge Location. 


DEPARTMENT CIRCULARS 


94C. T. N. T. as a Blasting Explosive. 
331C. Standard Specifications for Corrugated Metal Pipe 
‘Culverts. 


No. 


. TECHNICAL BULLETIN 
No. 55. Highway Bridge Surveys. 


MISCELLANEOUS CIRCULARS 


62M. Standards Governing Plans, Specifications, Con- 
tract Forms, and Estimates for Federal Aid 
Highway Projects. 

93M. Direct Production Costs of Broken Stone. 


FARMERS’ BULLETIN 
No. *388F. Macadam Roads. 5c. 


SEPARATE REPRINTS FROM THE YEARBOOK 


914Y. Highways and Highway Transportation. 
937Y. Miscellaneous Agricultural Statistics. 


TRANSPORTATION SURVEY REPORTS 


Report of a Survey of Transportation on the State Highwav 
System of Connecticut. 

Report of a Survey of Transportation on the State Highway 
System of Ohio. 

Report of a Survey of Transportation on the State Highways of 


Vermont. 
Report of a Survey of Transportation on the State Highways of 
New Hampshire. 


REPRINTS FROM THE JOURNAL OF AGRICULTURAL RESEARCH 
Vol. 5, No. 17, D- 


No. 


No. 


2. Effect of Controllable Variables upon 
the Penetration Test for Asphalts and 
Asphalt Cements. 

3. Relation Between Properties of Hard- 
ness and Toughness of Road-Build- 
ing Rock. 

6. A New Penetration Needle for Use in 
Testing Bituminous Materials. 

8. Tests of Three Large-Sized Reinforced- 
Concrete Slabs Under Concentrated 
Loading. 

Vol. 11, No. 10, D-15. Tests of a Large-Sized Reinforced-Con- 

crete Slab Subjected to Eccentric 

Concentrated Loads. 


Vol. 5, No. 19, D- 


Vol. 
Vol. 


5, No. 24, D- 
6, No. 6, D- 


——— 





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