I L L I N 0 I
S
UNIVERSITY OF ILLINOIS AT URBANACHAMPAIGN
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University of Illinois at
UrbanaChampaign Library
Largescale Digitization Project, 2007.
UNIVERSITY OF ILLINOIS
ENGINEERING EXPERIMENT STATION
BULLETIN No. 4 APRIL 1906
TESTS OF REINFOR(ED CONCRETE BEAMS
SERIES OF 1905.
BY ARTHUR N. TALBOT, PROFESSOR OF MUNICIPAL AND SANITARY ENGINEERING, IN
CHARGE OF THEORETICAL AND APPLIED MECHANICS.
In Bulletin No. 1 of the University of Illinois Engineering
Experiment Station, Tests of Reinforced Concrete Beams, the re
sults of the investigations made in the Laboratory of Applied Me
chanics of the University of Illinois in 1904 were recorded and
discussed. Further tests were made in 1905. It is the purpose of
this bulletin to describe and discussthe results of the series of 1905.
As was stated in Bulletin No. 1, the principles governing the
strength and action of reinforced concrete construction have not
been fully established, and the opinions and theories presented
by engineers are somewhat conflicting. However, many of these
points are being cleared up, and experimental work on reinforced
concrete is gradually establishing the principles. The results giv
en in Bulletin No. 1 have a bearing upon the action of reinforced
concrete in simple flexure and upon the calculation of the strength
of beams. The following topics and conclusions, among others,
are there considered: the general action of the beam during the
progress of the loading and the division of the phenomena includ
ed in the tests into four stages representing different conditions
in the steel and concrete; the determination of deformations in
the steel and concrete by careful instrumental work; the deter
mination of the position of the neutral axis by experimental meth
ods and the checking up of the tension developed in the steel by
the use of the observed deformations and the position of the neu
tral axis thus obtained; an experim.ntal determination of the
amount of steel which will develop the full compressive strength
of the concrete; for beams not having a sufficient amount of steel
to develop the full compressive strength and not failing by sec
ondary or web stresses, the conclusion that the maximum strength
of the beam occurs at slightly above the yield point of the steel
instead of the ultimate strength of the steel, and hence that the
ILLINOIS ENGINEERING EXPERIMENT STATION
yield point of the steel used has an important bearing on the de
sign of the beam; the conclusion that the form of the loaddefor
mation curve goes to show that during the second stage the con
crete fails in tension in such a way as to make this tension neg
ligible in the calculation of the bending moment, instead of that
the stretch is kept up in such a way as to continue to furnish
strength to the beam, as has been contended. In general the re
sults were such as to give confidence in the value of experimental
methods in establishing principles for use in the design of rein
forced concrete construction if only the tests are made in a sys
tematic and scientific manner.
The Series of 1905 was undertaken with a view of further de
veloping the fundamental principles governing reinforced concrete
construction as well as uncovering the field for future experimen
tation. It was considered best to restrict the tests of the year to
matters bearing on the principles involved in beam action rather
than to take up features involving details of construction. Among
the topics taken up for consideration were the following: effect
of amount of reinforcement; use of steel with high elastic limit
but having a very smooth surface; failure by tension in steel,
compression in concrete, bond, and diagonal tension; abnormal
concretes, including lean mixtures, poorly mixed concrete, and
socalled plane of set; effect of method of loading, of repetition
of load, of rest, of retention of load, and of position of the rein
forcing bars; position of neutral axis; plain concrete in com
pression; shearing strength of concrete; encased steel in tension;
thermal conductivity of concrete. The tests were made in the
Laboratory of Applied Mechanics of the University of Illinois.
In common with a number of engineering schools, the work was
done in cooperation with the Joint Committee on Concrete and
Reinforced Concrete which was composed of representatives of
several of the leading engineering societies of the country. The
writer was chairman of the Committee on Tests for the Joint Com
mittee and this series was the part of the work assigned to the
University of Illinois. The Joint Committee furnished the ce
ment, sand, stone and steel. The work of testing the beams was
done principally as thesis work. The data have now been worked
over and the calculations checked, new drawings made, and re
sults more fully studied and discussed. The following list gives
the names of the members of the class of 1905 in civil engineering
TALBOTTESTS OF REINFORCED CONCRETE BEAMS
who presented theses in the line of reinforced concrete. They are
entitled to credit for the care, skill, and interest and for the
thorough and competent way in which they conducted their work.
D. A. Abrams, Distribution of stresses.
Ralph Agnew and C. E. ims, Plain concrete in compression and encased
steel in tension.
F. I. Blair, Effect of repetition of load.
M. B. Case, Effect of retention of load.
V. R. Fleming, Comparison of methods of loading.
J. C. Gilmour, Varying percentages of reinforcement.
S. C. Hadden, Effect of removal of load.
E. T. Renner, Effect of release of load.
W. I. Roney, Effect of position of reinforcing bars.
J. E. Shoemaker and C. S. O'Connell, Shearing strength of concrete.
W. H. Warner, Abnormalconcretes.
The investigation of plain concrete in compression and en
cased steel in tension and of shearing strength of concrete, as
well as the investigation by L. A. Waterbury on thermal con
ductivity of concrete, is reserved for separate bulletins.
It will be noted that the problems are made as simple as pos
sible with a view of getting data bearing on the establishment of
principles, and for this reason the number of variables was made
as small as possible. The experience gained in the tests of
the Series of 1904 was taken advantage of. Supervision of this
work was given by R. V. Engstrom, Instructor in Theoretical and
Applied Mechanics, whose aid in this and in planning the tests
and in interpreting the results has added much to the value of
the work. Acknowledgment is also made to D. A. Abrams,
Assistant in Laboratory of Applied Mechanics, for aid in the
preparation of this bulletin.
As in the discussion of the results of the tests reference will
be made to the formulas and methods of making computations, it
seems well first to make a summary of the principles involved
and the nomenclature used in the analytical treatment of flexure,
as well as of the methods of failure of beams, and this is given
under the head of Resistance of Beams to Flexure. The following
division of the subject matter of the bulletin will be made: I.
Resistance of Beams to Flexure. II. Materials, Test Pieces and
Testing. III. Experimental Data and Discussion. Diagrams
showing loaddeformation curves and deflections of representative
beams and positions of the neutral axis follow the text. The
outline on the following page gives the order of presentation:
I. RESISTANCE OF BEAMS TO FLEXURE
1. Prelim inary ........................................ ......... .... Page 5
2. Notation .......................................... .............. " 6
3. Relation between Stress and Deformation for Concrete in Compression " 7
4. Distribution of Stresses in Beams................................... " 9
5. Relations in the Stress Diagram ....................... ............ " 11
6. N eutral A xis ...................................................... " 13
7. Resisting Moment..................... .......................... " 15
8. Compressive Stress at Upper Fiber................................. " 17
9. Bond or Resistance to Slipping of Reinforcing Bars.................. " 18
10. Vertical and Horizontal Shearing Stresses .......................... " 20
11. Diagonal Tension in Concrete............................. ....... " 21
12. M ethod of Failure................................................. " 22
13. Primary and Ultimate Failure...................................... 22
14. Failure by Tension in Steel....................................... ' 23
15. Failure by Compression of Concrete................................ " 24
16. Failure of Bond between Steel and Concrete ......................... " 24
17. Failure by Shearing of Concrete............................ ....... " 25
18. Failure by Diagonal Tension in Concrete........................... " 26
19. Failure by Splitting of Bars away from Upper Portion of Beam ...... " 27
II. MATERIALS, TEST PIECES AND TESTING.
20. Stone .............. ........................................... " 28
21. Sand ........................................................ .... " 28
22. Cem ent ........................................................... " 29
23. Steel............................ ................... ............ " 29
24. C oncrete .......................................................... " 31
25. Test Beam s ........................... ........................... " 31
26. Making of Beams .................................................. " 33
27. Storage ........................... . ........................... " 33
28. D etails of T ests.................. ................................ " 34
III. EXPERIMENTAL DATA AND DISCUSSION.
29. O utline.................................... ....................... " 37
30. Calculation of Deformation and of Position of Neutral Axis........... " 37
31. D iagram s ..... ................................................... " 37
32. Explanation of Tables 11 to 16.................................... " 39
33. 1% Mild Steel Reinforcement, Loading at OneThird Points........... " 41
34. 1% Mild Steel Reinforcement, Miscellaneous Loading................ " 41
35. 1% Mild Steel Reinforcement, with Abnormal Concrete............... " 41
36. 2.2% Mild Steel Reinforcement....................... . ........... " 41
37. Miscellaneous Reinforcement with Mild Steel ...................... " 44
38. Beams with Rods Bent out of Horizontal ........................... " 44
39. Tool Steel Reinforcement ......................................... " 44
40. Failure by Tension in Steel............................. ......... " 45
41. Failure by Compression of Concrete ............................... " 46
42. Failure by Diagonal Tension in Concrete ............................ " 47
43. Failure of Bond............. ..................................... " 49
44. Effect of Artificial Vertical Cracks and Spaces....................... 53
45. Effectof Method of Loading....................................... " 54
46. Effect of Repetition of Load........................................ " 56
47. Progressively Applied and Released Loads .......................... " 59
48. Effect of Rest after Release of Load ................................. " 60
49. Effect of Retention of Load........................................ " 61
50. Effect of Position of Reinforcing Bars ............................... " 64
51. Effect of Lean and Abnormal Concretes ............................. " 65
52. Effect of Exposing Reinforcing Bars...... .......................... " 67
53. Position of Neutral Axis and Value of Modulus of Elasticity......... " 68
54. Summary.................... ................................ " 70
55. Diagrams........................ . ............................. " 74
TALBOTTESTS OF REINFORCED CONCRETE BEAMS
I. RESISTANCE OF BEAMS TO FLEXURE
1. Preliminary.Flexure of reinforced concrete beams
seems more complicated than is the case with steel and timber
beams. In steel and timber beams it is usual to consider only
horizontal tensile and compressive stresses with perhaps a check
on horizontal or vertical shearing stresses. Other stresses exist
which are ordinarily negligible. In reinforced concrete beams
these secondary stresses may form the element of weakness.
Unless it is known from the general dimensions and makeup of
the beam that the secondary stresses do not control the strength
of the beam, it will be necessary to calculate the stresses devel
oped in the various ways. In general it may be said that a
reinforced concrete beam may fail by one or more of the following
methods: 1. Tension of steel; 2. Compression of concrete;
3. Shearing of concrete; 4. Bond or slip of bars; 5. Diagonal
tension of concrete; 6. Miscellaneous methods, like the splitting
of bars away from the concrete, the effect of the bearings, etc.
What one of these methods of failure will govern the strength of
a beam is dependent upon percentage of reinforcement, kind of
steel, quality of concrete, relation of depth of beam to length of
span, disposition of reinforcement, and other conditions. Gener
ally, for a given beam, we may narrow down the number of
probable methods of failure without much calculation.
Before discussing these methods of failure further, it will be
well to go over the analytical treatment of the resistance of
beams to flexure. This treatment will be made as brief as pos
sible, a summary only of part of the work being given and no
effort being made to cover the field thoroughly. The analysis
governing the tension in the steel and the compression in the
concrete follows the lines of the article of the writer in the Jour
nal of the Western Society of Engineers, Vol. 9, August, 1904,
page 394. The usual assumptions 'that the loads are applied at
right angles to the length of the beam, that the supports will
permit free longitudinal movement, that a plane section before
bending remains a plane section after bending, and that the
metal and surrounding concrete stretch together, are made. It is
further assumed that the tensile strength of the concrete is neg
ligible in the part of the beam where the bending moment is
greatest, at least in the calculation of the resisting moment of the
beam at the time of maximum load. The analysis is restricted
ILLINOIS ENGINEERING EXPERIMENT STATION
to rectangular beams with reinforcement on the tension side only,
and refers generally to simple beams free from end restraints.
2. Notation. The following notation will be used:
b = breadth of rectangular beam.
d = distance from the compression face to the center of the
metal reinforcement.
A = area of cross section of metal reinforcement.
A
p = = ratio of area of metal reinforcement to area of
concrete above center of reinforcement.
o = circumference or periphery of one reinforcing bar.
m = number of reinforcing bars.
 = modulus of elasticity of steel.
E, = initial modulus of elasticity of concrete in compression, a
term which will be defined.
n = E = ratio of two moduli.
f = tensile stress per unit of area in metal reinforcement.
c = compressive stress per unit of area in most remote fiber of
concrete.
c' = compressive stress per unit of area which causes failure by
crushing.
Es = deformation per unit of length in the metal reinforcement.
c = deformation per unit of length in most remote fiber of the
concrete.
e'e = deformation per unit of length when crushing failure occurs;
i. e., ultimate or crushing deformation.
q =  ratio of deformation existing in most remote fiber to
ultimate or'crushing deformation.
k = ratio of distance between compression face and neutral axis
to distance d.
z = distance from compression face to center of gravity of com
pressive stresses.
d' = distan e from the center of the reinforcement to center of
gravity of compressive stresses.
2X = summation of horizontal compressive stresses.
M resisting moment at the given section.
8 = horizontal tensile stress per unit of area in the concrete.
t = diagonal tensile stress per unit of area in the concrete.
TALBOTTESTS OF REINFORCED CONCRETE BEAMS
u = bond stress per unit of area on the surface of the reinforcing
bars.
v = vertical shearing stress and horizontal shearing stress per
unit of area in the concrete.
3. Relation between Stress and Deformation for Concrete in
Compression.Concrete does not possess the property of propor
tionality of stress and deformation for wide ranges of stress as
does steel; in other words, the deformation produced by a load is
not proportional to the compressive stress. The relation between
stress and deformation is not entirely uniform; there are even
considerable differences in deformations for the same mixtures.
Various curves have been proposed to represent the stressdefor
mation relation but the parabola is the most satisfactory general
representation. Frequently the parabola expresses the relation
almost exactly, and in nearly every case the parabolic relation
will fit the stressdeformation diagram very closely throughout
the part which is ordinarily developed in beams, the lack of agree
ment near the crushing point not being of importance. The
analytical work with the parabola is not complicated, and this
curve offers easy comparison with the straightline relation and
easy translation to this relation. Even if the straightline rela
tion be accepted as sufficient for use with ordinary working
stresses, the parabolic or other variable relation must be used in
discussing experimental data when any considerable deformation
is developed in the concrete. The parabola will be adopted as the
basis of the analytical work used in this bulletin.
Fig. 1 shows such a stressdeformation curve. For purposes
of illustration, the crushing strength of the concrete is repre
sented as 2000 lb. per sq. in. and the ultimate unit deformation as
.002. The relation between proportionate stress or ratio of stress de
veloped to ultimate compressive strength of the concrete 
and proportionate deformation or ratio of deformation developed
at the given stress to ultimate or crushing deformation c_ ,
which forms the basis of this analysis, is also shown by the figure.
Modulus of elasticity is a term which has been used very
loosely in connection with reinforced concrete. In the general
theory of flexure it is defined to be the ratio of the unit stress to
the unit deformation within the elastic limit of the material. As
8 ILLINOIS ENGINEERING EXPERIMENT STATION
applied in this way to materials having the property of propor
tionality of stress and deformation the modulus of elasticity is a
constant. For materials with a variable stressdeformation rela
tion like concrete it may not be considered proper to call the
variable ratio the modulus of elasticity and such a use in connec
tion with formulas for flexure of concrete may lead to misunder
standings. However, it is important that a definite expression
for this ratio be found. The writer obtains this relation from the
initial modulus of elasticity and uses the term " initial modulus
Proport'/ona1te stress = c
N N. O '^ 4 'On 'OON 0
1z Z CS o i' o i s '^
11 t~  iiH 11 *i i i '' i ' i r '" 1 ' i j
 / i
*^C I
.^ _ _ _  / _ _ _  _ _ _ __ _
.0010 I
0'
/.o I
4D
09 ^
0.8
0.7 ':
0.6
0
0..5
0.4
0.3 3
1.
a2
a/'
.5ress 47 pounds per square nch=c
FIG. 1. STRESSDEFORMATION CURVE FOR CONCRETE IN COMPRESSION.
of elasticity" to express the relation which would exist between
stress and deformation if the concrete compressed uniformly at
the rate it compresses for the lower stresses. The tangent of the
angle which the line AC in Fig. 1 makes with the vertical gives
this initial modulus of elasticity Ec. The line is tangent to the
parabola at A, and its equation is x=Ecy. By means of this ini
tial modulus of elasticity the parabolic stressdeformation relation
may, from the properties of the parabola, be expressed as
C=c! cI Ee e= (1q) Ee .E....... (1)
ni which q is the ratio of the deformation developed to the ulti
TALBOTTESTS OF REINFORCED CONCRETE BEAMS
mate or crushing deformation of the concrete. From this the fol
lowing equation is also true:
= (1q)2q............... .........(2)
These relations are fundamental. The values of E,, c, and ee
must be obtained experimentally. The line for E, should be
taken as the line which will give a relation which will best fit
throughout the range used in the test of beams and E', should be
taken as the abscissa of the vertex of the parabola which
fits best and not necessarily as the actual crushing de
formation of the 'concrete. It is the general relation
which is important and not the values at the point of
failure. Many stressdeformation diagrams have been gone over
in this way, and this representation has been found quite satisfac
tory. It may be noted from Fig. 1 that while 2000 lb. per sq.
in. will give a deformation of .002, it will take 1500 lb. per sq. in.
to produce onehalf of that deformation. For small stresses the
stressdeformation curve does not differ much from the line of
initial modulus of elasticity.
4. Distribution of Stresses in Beams.Let Fig. 2 show the
section of the beam. kd is the distance of the neutral axis below
I
I
A/6atra/ ox/a
*. uau"
FIG. 2. SECTION OF BEAM.
the top of the beam, k being a ratio. In Fig. 3, the left diagram rep
resents the deformations above and below the neutral axis. Con
sider that the upper fiber is stressed to the point of failure; the
upper deformation will then be the ultimate or crushing deforma
tion. Since the deformations are proportional to the distances
from the neutral axis, the curve of compressive stresses shown on
the right will be a parabola with its vertex at 0. The horizontal
distances to the "line for initial modulus of elasticity" represent
the stresses which would exist for the same deformation with a
constant modulus of elasticity equal to E,. The stress in the steel
ILLINOIS ENGINEERING EXPERIMENT STATION
is represented by a length proportional to the ratio of the modulus of
elasticity of the steel to the initial modulus of elasticity of the
concrete n  = . In like manner Fig. 4 gives the stress and de
Ee
formation distribution for a deformation of the upper fiber equal
to threefourths of the ultimate deformation of the concrete and
1/nr,,,afinn Compressive ftress.
De/ormation Tensi/e stress
o/f tee/
FIG. 3. STRESS AND DEFORMATION DISTRIBUTION AT ULTIMATE
DEFORMATION OF CONCRETE.
a stress of fifteensixteenths of the crushing stress. Fig. 5 shows
a similar distribution for onehalf ultimate deformation and three
De/or/nation Compressive .4ress
DeforM1llol /en/7ile 51ress
0/ s/eel
FI. 4. STRESS AND DEFORMATION. DISTRIBUTION AT THREEFOURTHS
ULTIMATE DEFORMATION OF CONCRETE.
P
TALBOTTESTS OF REINFORCED CONCRETE BEAMS
fourths the crushing stress. It will be noted that the parabolic
arc appears somewhat different from that in Fig. 3, and that it
differs much less from the "line for initial modulus of elasticity".
5. Relations in the Stress Diagram.In deriving formulas
for resisting moment, position of neutral axis, and compressive
stress at upper fiber, three relations in the stress diagram are
needed: (1) the relation of the 'stress c and the deformation Ce at
the upper fiber; (2) the total compressive stress, here called TX;
and (3) the position of the center of gravity of the compressive
stresses given by the distance z. These relations vary for different
Delro/l9n1ti Cod7resive 5tres
Delormloliof Tensile stwess
ofsteel
FIG. 5. STRESS AND DEFORMATION DISTRIBUTION AT ONEHALF
ULTIMATE DEFORMATION OF CONCRETE.
values of the deformation in upper fiber. Basing the variation on
the parabolic stressdeformation law previously stated, and using
EC
q= as the ratio of the deformation developed in the upper
fiber to the ultimate deformation of the concrete, the following
relations are readily deduced, though their derivation will not be
given here.
. . = 1. .q............ .......................(3)
SX Parabolic area .
 1 ............ (4)
J Ecekbd Triangular area
z  __  q ...... (5)
kd 124q 3 3qJ
ILLINOIS ENGINEERING EXPERIMENT STATION
Equation (3) gives the ratio of the compressive stress in the
upper fiber to the stress which would exist for the same upper fiber
deformation with a straightline stressdeformation relation.
Equation (4) gives the ratio of the summation of compressive
stresses to the stress which would exist for the same upper fiber
deformation with a straightline stressdeformation relation.
Equation (5) gives the ratio of the distance between the com
pression surface and the center of gravity of compressive stresses
to the distance between that surface and the neutral axis.
Values for several ratios of the deformation developed in the
upper fiber to the ultimate or crushing deformation of the con
crete are given in the following table :
TABLE 1.
PROPERTIES OF THE STRESS DIAGRAM.
Property
c
IX
2ypf
k
At ultimate
deformation
q=1
i Eeed
Skd
3
T
At ý ultimate
deformation
q=3
1 E.ldd
Skd
If
At 9 ultimate
deformation
q=
,EcEkbd
ykd
Tf
At 4 ultimate
deformation
J Esed
4 1Eckbd
rr
By straight
line relation
q=0
Eeekbd
SEcsekbd
½kd
1
Fig. 6 shows graphically the relations given by equations (3),
(4) and (5). It will be seen that the center of gravity of the com
pressive stresses ranges from j distance down to neutral axis
(the value for a deformation equal to the ultimate deformation)
to j distance down to neutral axis at the lower limit, ratio, N .
The position for q=3 is 1, equal to .36. This is not far from the
value 4 which was used in the discussion of the experimental work
in Bulletin No. 1, and which was obtained by another method of
analysis. The position for .q=j is .341 and for q=0 it becomes
j as in the straightline relation. The other ratios are less nearly
constant. The ratio for compressive stress at most remote fiber
TALBOTTESTS OF REINFORCED CONCRETE BEAMS
to that for direct proportionality with same deformation
( C ranges from I when ultimate deformation of concrete is
developed to 1 for no deformation. The range for summation
of compressive stress is from I to 1. It should be remembered
FIG. 6. VARIATION OF FUNCTIONS WITH q.
that these formulas are not applicable when tensile stresses of
concrete need consideration.
6. Neutral Axis.The foregoing relations and the analytical
condition that the total horizontal compressive stresses and the
total horizontal tensile stress are equal will, if tensile stresses in
the concrete be neglected, readily enable the position of the
neutral axis to be determined for rectangular beams. From the
proportionality of deformation (Fig. 3, 4, and 5),
1k ........ .. .... ...................(6)
Equating horizontal stresses,
Af=½(lkq)Eoekbd...................... ... (7)
Dividing (7) by (6) and substituting f=EEss,
AE(1 k) = (1iq)Ek'bd
Calling n _ and =_P,
pn (1k)=i(1q)k"
ILLINOIS ENGINEERING EXPERIMENT STATION
Solving,
I_ 2pn p n'1 pn
k  (l q)2 ] q.................. (8)
This gives the position of the neutral axis after tensile stresses
in'the concrete have become negligible and before the concrete
reaches its ultimate strength. The value of k will vary some
what for the range of q considered.
For q =1 equation (8) becomes
k= 3 pn + p   pn....................(9)
which is the expression when the concrete is at the limit of its
compressive strength.
For q = 0, equation (8) becomes
k= 2pn+p'' pn ......................(10)
which is the same as the value of k derived with a straight line
stressdeformation relation.
1.1
S.'
R,
Proportionate stress = amd proporionate deformatiotn= ,=7
FIG. 7. VARIATION IN POSITION OF NEUTRAL Axis FOR DIFFERENT
VALUES OF q.
Fig. 7 shows the variation in k for n = 15 and a 1 % rein
forcement (p=.01) given both in terms of q and in terms of c
c
In this diagram the position of the neutral axis changes from
.418 when q = 0 to .484 when the full or crushing deformation is
TALBOTTESTS OF REINFORCED CONCRETE BEAMS
developed. It shows a slow change for increasing values of the
compressive stress until twothirds of the full compressive
strength of the concrete is developed. Beyond this the neutral
axis lowers rapidly. Ordinarily a 1 % reinforcement will not
develop the full compressive strength of concrete, but the diagram
serves to illustrate the change in the position of the neutral axis
both in this and with other amounts of reinforcement. It is seen
that the position remains nearly constant during what will be
termed the third stage of beam action.
Of course for low values of q, the tensile strength of the con
crete would modify the position somewhat.
For the calculations in this bulletin and for the reinforce
ments used, k for q= ý gives results which are representative for
the range considered and will be used in the discussion. For q  ¼,
equation (8) becomes
k= pn + 'p.  pn ............ (11)
This equation gives the position of the neutral axis for defor
mations which correspond closely with those developed under
working stresses.
Fig. 8, page 16, gives the position of the neutral axis based
upon equation (11) (q =1) for n=10, 12, 15, and 20. Calling
the modulus of elasticity of steel, 30000000 lb. per sq. in., these
ratios correspond to initial moduli of elasticity of concrete of
3 000 000, 2 500 000, 2 000 000 and 1 500 000 lb. per sq. in., respec
tively.
Attention is called to the change in position of the curves from
that given in Bulletin No. 1, which was based upon q = and is
applicable when the compressive stress is well developed, while
that here used is more generally applicable for ordinary working
stresses.
7. Resisting Moment.When the tensile stresses in the con
crete are neglected and the center of gravity of the compressive
stresses is known, the value of the resisting moment of the beam
(which it is readily seen is the moment of the couple formed by
the tensile stress in the steel and the resultant of the compressive
stresses in the concrete) is easily expressed as the product of the
tensile stress in the steel and the distance from the center of the
ILLINOIS ENGINEERING EXPERIMENT STATION
steel to the center of gravity of the compressive stresses. Hence
the formula for the resisting moment for a rectangular beam is
M= Af(d z) . ... ... .. ......... . ......... (12)
It was shown that z varies slightly for different compressive
stresses. The value of z when the concrete at the remote fiber is
stressed threefourths of its ultimate deformation (q = 3) is
FIG. 8. POSITION OF NEUTRAL Axis.
TALBOTTESTS OF REINFORCED CONCRETE BEAMS
approximately .36kd; for q = j, .35kd, and for q = j, .34kd. For
q  0, z = l kd. This is the position when the straightline stress
deformation is used; i. e., when the modulus of elasticity is con
stant and equal to the initial modulus of elasticity.
When the E. of the concrete is known and the amount of re
inforcement is fixed, equation (12) will take the form
= A fd' ........... .... ....... ... (13)
where d' is the moment arm of the couple and may be expressed
as a proportionate part of d. Thus for q = , with Eo = 2 000 000
lb. per sq. in. (n = 15) and 1 % reinforcement (p =.01),
d'= .853d. For 1.5 % reinforcement (p .015), d'=.831d. The
values of the resisting moment for these reinforcements become
.853 A f d and .831 A f d, respectively.
This method offers the most convenient way of calculating
the resisting moment so far as it is controlled by the tension of
the steel within its elastic limit. The position of the neutral axis
may well be taken from a diagram like Fig. 8, and the value of d'
is then easily obtained.
Generally it will be best to use the resisting moment in terms
of the tension in the steel, but if it is desired to express it in
terms of the compression in the concrete the following equation
may be used.
M= 1 q c k b d (dz)..... .......(14)
At least an approximate value of q will be known which may
be used in equation (14). The fractional coefficient is the recipro
c
cal of the function 2pf given in Fig. 6.
k
8. Compressive Stress at Upper Fiber.The formulas for the
position of the neutral axis and moment of resistance are based
upon the assumption that the compressive stress in the upper
fiber is within the crushing strength. To determine the value of
the upper compressive stress substitute equation (3) in equation
(7). This reduces to
2A/ 1 q 2pf 1jq (
kbd 1 q  k 1q .q(' '
For a deformation of upper fiber equal to threefourths of de
ILLINOIS ENGINEERING EXPERIMENT STATION
formation at crushing or c = 1 c, this becomes c= k " For
an upper deformation equal to onehalf of ultimate deformation
this becomes c = k . For the crushing point of the concrete it
becomesc 3 3 p As the upper deformation decreases, the
=4 Ak
2pf
value of c approaches k , which is the amount of the stress for a
constant modulus of elasticity equal to the initial modulus of
elasticity. By multiplying  , the stress found on the basis of a
constant modulus of elasticity and a known position of the neutral
1 i
axis, by this ratio 1  , the value of the compressive stress is
found. The variation in this ratio may be seen in the upper curve
in Fig. 6 and also in the last line of Table 1. It will be seen that
for high compressive stresses the stress developed is much less
than that given by the straightline relation using the value of
the initial modulus of elasticity, being only threefourths as much
if the full compressive stress is developed. For low compressive
stresses the discrepancy is much less.
It should be noted that when the compressive deformation
developed is well up to the ultimate, the compressive stress cal
culated from equation (15) is much less than that found by using
2pf
the formula , (or any formula based on a straightline stress
deformation relation), but when the load develops a deformation
which is a small proportion of the ultimate, as may be the case
for working loads, the coefficient found in equation (15) will not
differ much from unity and the straightline formula will be but
little in error.
9. Bond or Resistance to Slipping of Reinforcing Bars.In
order to have beam action there must be a proper web connection
between the tension and the compression portions of the beam.
When there is no metallic web reinforcement the concrete of the
beam acts as this web. Of course the amount of stress in the
reinforcing bars and also in the compression area of the concrete
TALBOTTESTS OF REINFORCED CONCRETE BEAMS
varies at different cross sections along the length of the beam.
The increment between consecutive sections or increase in the
tensile stresses of the reinforcing bars is transferred to or con
nected with the increments of the compressive stresses of the con
crete by means of this web. In transmitting the increment of
tension from the reinforcing rods to the surrounding concrete,
there is developed a tendency of the rods to slip in the concrete,
and the amount of resistance to slip thus developed is called bond
and will be measured in terms of the area of the surface in con
tact with the concrete. It will be seen that the total bond de
veloped on the surface of the bars in one inch of length is equal
to the total change in total tensile stress in the bar for the same
inch of length. Bond may be compared to the action of the
rivets joining flange to web in a riveted steel girder, except that
in the reinforced concrete beam the contact is continuous.
For horizontal reinforcement the formula for bond may be
derived as follows: For any vertical section of the beam equation
(13) (MI= Afd') gives the resisting moment. Differentiating this
d = A d'. By the principles of mechanics of beams  = V,
dx dx dx
where Vis the total vertical shear at the given section (reaction
at support minus loads between the support and the section con
sidered). Substituting and transposing,
Adf _ V
d  . ................................ .(16)
dx d
Now the derivative A df expresses the rate of change of the
dx
total tensile stress in the reinforcing bars at the section under
consideration; it is given in terms of a unit of length of beam
(lb. per sq. in. of length) and measures what is transmitted to the
concrete by the bond. Using m as the number of bars, o as the
efficient circumference or periphery of one bar, the total surface
of bar for one inch of length of beam is m o and the bond stress
developed is m o u, where u represents the bond developed per
unit of area of surface of bar. Equating this to the value of the
derivative in equation (16) and solving,
od . . 0.. . ............. ...... ............ (17)
ILLINOIS ENGINEERING EXPERIMENT STATION
Equation (17) is not applicable in just this form when the bars
are bent up or inclined from the horizontal, since in this case d'
is a variable and this fact will modify the differentiation.
10. Vertical and Horizontal Shearing Stresses.It is shown
in the mechanics of beams that there exist throughout a beam
vertical and horizontal shearing stresses which vary in intensity,
and that at any point in a beam the vertical shearing unit stress
is equal to the horizontal shearing unitstress there developed.
As noted under bond the total tension in the reinforcing bars
varies along the length of the beam, as does also the total com
pressive stress. The horizontal shearing stress may be consid
ered to transmit the increments or increase of the total tensile
stresses in the reinforcing bars (which is transmitted to the sur
rounding concrete by the bond stresses) to the corresponding
increments of compression in the compression area of the con
crete, the concrete thus forming the stiffening web of the beam.
The amount of this horizontal tensile stress so transmitted from
the reinforcing bars per unit of length of beam is by equation (17)
V
m o u7. Consider this distributed over a horizontal section
just above the plane of the bars for a unit of length of beam,
and call the horizontal unit shearing stress v. The shearing re
sistance per unit of length of beam thus developed is then b v,
and equating this to mo u,
V
S= bd ..............................(18)
This equation gives the horizontal shearing unitstress, and
therefore also the vertical shearing unitstress, at a point just
above the level of the reinforcing bars. As no tension is here
considered as acting in the concrete, there will be no change in
the intensity of the horizontal and vertical shearing stresses be
tween this level and the neutral axis. For the part of the beam
where tensile stresses extend well down to the reinforcement
some modification of this treatment may be made. Above the
neutral axis the intensity of the shearing stresses will decrease
by the law of change of horizontal shearing stresses for homo
geneous rectangular beams modified to suit the parabolic stress
deformation relation. The distribution of the intensity of the
TALBOTTESTS OF REINFORCED CONCRETE BEAMS
horizontal shearing stress over a vertical section is represented in
Fig. 9.
A
Compression /oHnzon/al 5sheari/g ye5,5
FIG. 9. DISTRIBUTION OF HORIZONTAL AND VERTICAL SHEAR.
As d' generally will not vary far from .85d, the shearing
stress by equation (18) will be say 18% more than if considered to
be uniformly distributed over a vertical section extending down
to the center of the reinforcing rods. Even if tension is consid
ered to exist in the concrete for a short distance below the neutral
axis, the shearing stress will not be greatly modified thereby. If
the bars are inclined or bent up from the horizontal, equation
(18) must be changed to allow for a variable d'.
11. Diagonal Tension in Concrete.In the flexure of a beam
stresses are set up in the web which are sometimes called web
stresses and sometimes secondary stresses. Besides the horizontal
and vertical shearing stresses already discussed, tensile or com
pressive and shearing stresses exist in every diagonal direction.
In determining the bending moment only the horizontal compo
nents of these are taken. When there is no metallic web rein
forcement all the diagonal stresses are taken by the concrete. By
the analysis of combined shear and tension the value of the maxi
mum diagonal tensile unitstress (see Merriman's Mechanics of
Materials, p. 265, 1905 edition) is found to be
t = s + I/ s'+v .......................(19)
where t is the diagonal tensile unitstress, s is the horizontal ten
sile unitstress existing in the concrete, and v is the horizontal or
vertical shearing unitstress. The direction of this maximum
ILLINOIS ENGINEERING EXPERIMENT STATION
diagonal tension makes an angle with the horizontal equal to one
half the angle whose cotangent is 1
2 v'
If there is no tension in the concrete this reduces to
t= v ............................... ... . (20)
and the maximum diagonal tension makes an angle of 450 with
the horizontal and is equal in intensity to the vertical shearing
stress.
12. Mfethod of Failure.The several stresses developed in a
reinforced concrete beam will vary according to the dimensions,
reinforcement, and method of loading. The stress which reaches
the limit of the resisting property of the material is the one which
will control the strength of the beam. It is not likely that two
or more of these stresses will reach their point of failure at the
same time. It is not even generally feasible so to proportion a
beam that its strength shall be the same in tension, compression,
bond and diagonal tension. For other reasons the amount of re
inforcement or depth of beam may be made the same in spans of
different length or carrying different loads, and such a variation
will change the relative value of tension, compression, bond, etc.
While it may be well to calculate the various stresses, in many
cases the relative dimensions and amount of reinforcement are
such that the method of failure may be told without much cal
culation. In such cases only the formulas which determine the
stress for the most probable methods of failure need be used.
13. Primary and Ultimate Failure.In judging of the re
sults of tests a distinction must be'made between primary failure
and ultimate failure. Some change or failure may take place in
the beam during the test which will greatly modify the conditions,
and we may not properly judge of the conditions existing at this
time by what happens later. This early or critical failure maybe
named the primary failure and its cause should be called the
cause of the failure of the beam. Thus, in a beam having a
moderate or small amount of reinforcement, after the load is
reached which stresses the steel beyond its yield point, the steel
stretches rapidly, the neutral axis rises, and the compressive
stresses are thereby materially increased until ultimate failure
by compression may result. The real cause of failure, however,
is the passing of the yield point of the steel, and the maximum
TALBOTTESTS OF REINFORCED CONCRETE BEAMS
load is generally but little more than that carried at the yield
point of the reinforcement. Again, slipping of bars may come
after diagonal tension failure has occurred. Confusion has arisen
from ultimate failures being reported instead of primary failures.
It is not always possible to know positively the cause of failure,
but generally a careful study of the test will give a trustworthy
conclusion. Too frequently only an exterior appearance is re
ported which does not represent the true cause of failure and the
report is likely to be misleading.
14. Failure by Tension in Steel.Beams having shallow
depth as compared with their length and having a moderate
amount of reinforcement may, when tested with usual way of
loading, be expected not to fail before the steel has been stretched
to its yield point; and the maximum load carried will generally
be but little higher than that carried when the yield point is
reached. Fig. 10 (a) illustrates the typical form of failure by
(6)
^
FIG. 10. TYPICAL FORMS OF FAILURE.
a) Tension in Steel. (b) Compression of Concrete. (c) Diagonal Tension Failure.
tension in steel. When deformations have been measured, the
plotted stressdeformation curve for tension will show a sudden
ILLINOIS ENGINEERING EXPERIMENT STATION
and marked change at the yield point and there will be a corres
pondingly sudden change in the compression curve. As stated in
Bulletin No. 1, for the 136 concrete used, failure by tension in
steel occurred in beams having a reinforcement of not more than
1.5% for steel of 33 000 lb. per sq. in. elastic limit and not
more than 1.0% for steel of 55000 lb. per sq. in. elastic
limit. The calculated stress in the steel may be found by equa
tions (12) or (13). Whether other forms of failure, as by diagonal
tension, will cause failure before the yield point is reached is a
matter for further consideration. It should be noted that tension
cracks as shown in Fig. 10 (a) will appear considerably before the
steel reaches its yield point. With other forms of failure, these
cracks may appear but they do not grow to the extent they do in
tension failures.
15. Failure by Compression of Concrete.Beams having a
large amount of reinforcement may fail by the crushing of the
concrete at the top of the beam before the steel has been stressed
to its elastic limit. The amount of reinforcement necessary so to
develop the full compressive strength of the concrete will of course
depend upon the quality of the concrete and upon the elastic
limit of the steel. The 1 and 1.5% noted in the preceding para
graph may be taken as tentative limits for the concrete here used.
Fig. 10 (b) illustrates this form of failure. If stressdeformation
diagrams are made, the line showing the shortenings of the upper
fiber of the concrete will curve away rapidly from the usual
straightline position, but the steel deformation line will not be
modified materially until near the point of failure. This condi
tion of the stressdeformation curves is the best evidence that the
crushing strength of the concrete has been reached without devel
oping the strength of the steel to its yield point. The calculated
value of the compressive stress may be found by equation (15).
Whether the strength of beams having a reinforcement large
enough to develop the full compressive strength of the concrete
should be based upon the ultimate strength may require some
discussion. The effect of repetition of load and even of retention
of load upon concrete under considerable stress seems to lead to
the choice of a lower stress than the ultimate strength of concrete
for a limit to correspond to the yield point of steel.
16. Failure of Bond Between Steel and Concrete.Primary
failure by the breaking of the bond between steel and concrete is
TALBOTTESTS OF REINFORCED CONCRETE BEAMS
unusual for beams having the proportions of ordinary test beams.
The bond stress developed in such beams at their ultimate load as
calculated by equation (17) u= mod , ranges from 70 to 193
lb. per sq. in., and the bond testson plain mild steel rods give
values from 200 to 500 lb. per sq. in. and on some forms of de
formed bars from 300 to 1000 lb. per sq. in. It is true that condi
tions under which the bond tests are made differ from those in
the beam and also that bond stresses may not be distributed in
the beam exactly as assumed and considerable allowance should
be made for these. Besides, the effect of time and of repetition
of stress upon bond resistance is not known. For bars bent up
out of the horizontal a much higher stress is brought into action
near the end of the bar than with the bars laid horizontally
throughout the length of the beam. The value of the bond resist
ance will depend upon the smoothness of the surface of the bar,
the uniformity of its diameter, the adhesive strength of the con
crete, and the shrinkage grip developed in setting. In most of
the failures reported to be caused by slipping of the bars, it seems
certain that this slipping occurred subsequent to diagonal tension
failures or other changes which were the primary causes of fail
ure. For mild steel reinforcement placed horizontally in beams
of ordinary dimensions, the diagonal tensile strength of the beam
will be a much weaker element than the bond stress between steel
and concrete. An interesting illustration of the reverse of this
condition is found in the tests of beams reinforced with tool steel
described herein.
17. Failure by Shearing of Concrete.The horizontal and
vertical shearing unitstresses obtained by the use of equation (18)
v=  are low, the highest value developed for the beams
herein tested being 151 lb. per sq. in. Even if we consider a
point in a beam at which the concrete is carrying stress in ten
sion up to its ultimate strength, the value of the diagonal shearing
stress will scarcely reach twice the vertical shearing stress. The
shearing strength of concrete is much higher than this,probably
from 50 to 75% of the compressive strength. Tests made at the
University of Illinois and elsewhere show as great strength as this.
ILLINOIS ENGINEERING EXPERIMENT STATION
The low values frequently quoted, which range from 15 to 35% of
the compressive strength, are from tests made in such a way that
bending action controls and the failures are more nearly tension
failures. It can hardly be said, then, that reinforced concrete
beams fail by shear. What have been called shearing failures
are really diagonal tension failures.
18. Failure by Diagonal Tension in Concrete.When the
diagonal tensile stresses developed become as great as the tensile
strength of the concrete, the beam will fail by diagonal tension,
provided there is no metallic web reinforcement. Fig. 10 (c)
gives the typical form which this failure takes. As the value of
the maximum diagonal tensile stress developed in a beam is by
equation (19) dependent upon the horizontal tensile stress devel
oped at the same point it is difficult to compute its actual amount.
The best method seems to be to compute the horizontal and verti
cal shearing unitstress and make all comparisons on the basis of
this value. Beams which fail by diagonal tension and which are
without metallic web reinforcement give a value of 100 to 150 lb.
per sq. in. for the vertical shearing unitstress when calculated
by equation (18) (and lower values for poorer concrete), the limit
depending upon the strength of the concrete. When these values
are combined in equation (19) with the probable horizontal ten
sile stress developed in the concrete below the neutral axis, the
resulting diagonal tensile stress is evidently the full tensile
strength of the concrete. Diagonal tension failures are frequently
characterized by sudden breaks, without much warning, as is the
case in the failure of plain concrete beams. A variation from
this gives a slower failure, part of the shear being carried through
the reinforcing bars, and the ultimate failure involving the split
ting and stripping of the bars from the beam above as described
under the next heading.
It is evident, since the vertical or external shear is independ
ent of the resisting moment, that the relation between the depth
and length of a beam will determine whether the beam will fail
by diagonal tension or by tension of steel or compression of con
crete. In relatively short and deep beams the diagonal tensile
strength will fix the strength of the beam, while in long shallow
beams this element may be disregarded.
Since the diagonal tension may be resolved into horizontal
and vertical or other components, the concrete may be relieved
TALBOTTESTS OF REINFORCED CONCRETE BEAMS
of a part of the diagonal tensile stress by one or both of two
means: (1) by bending the reinforcing rods or strips sheared from
them into a diagonal position, and (2) by making use of stirrups
to take the vertical component of the diagonal tension. The
necessity and efficacy of these metallic web reinforcements can
not be discussed here but will be taken up in a later bulletin.
19. Failure by Splitting of Bars away from Upper Portion
of Beam.Failures sometimes occur, either after a diagonal crack
has appeared or at the same time that such a crack is observed,
in which the reinforcing bars and the concrete below the level of
the bars are split away from the remainder of the beam, the crack
running horizontally for some distance. This stripping is caused
by vertical tension in the concrete transmitted to it by the stiff
ness of the reinforcing bars after the concrete fails to carry its
assignment of diagonal tension. In Fig. 11 consider that a diag
onal crack CD has been formed. Take a vertical section through
AD. On account of the diagonal crack normal beam action does
not exist and part of the vertical shear from the main portion of
FIG. 11. FAILURE WHEN BARS SPLLT AWAY FROM UPPER PORTION OF
BEAM.
the beam is transmitted by the projecting portion of the beam
DCB acting as a cantilever and the flexural stiffness of the bars to
the point C and there applied to the left portion of the beam as a
downward force. (a) shows the part at the left of AD acting
as a free body. The part of the vertical shear applied at C tends
to split the bars from the beam, starting at C and running toward
ILLINOIS ENGINEERING EXPERIMENT STATION
E. This action is resisted by the tensile strength of the concrete
in a vertical direction, and when this is exceeded the bars will
split from the concrete above. This may happen without any
horizontal movement or slip of the bars. Splitting of the bars
from the beam presupposes a failure in diagonal tension, for
as long as true beam action exists vertical tension is not
developed. After the diagonal crack is formed this part of the
beam takes on the nature of a truss. This form of failure is then
a secondary failure, though under some conditions the load carried
before splitting occurs may be considerably more than that at
which the diagonal crack appeared. This explanation shows why
the concrete at the bottom of the bars continues to adhere to the
bars. There is no evidence of shearing failure in these cases.
Attention should also be called to the danger from spacing
bars too closely or with not sufficient concrete below the bars.
II. MATERIALS, TEST PIECES AND TESTING.
The materials, method of making test pieces, and manner of
testing the beams were much the same as in the tests described
in Bulletin No. I of the University of Illinois Engineering Exper
iment Station, Tests of Reinforced Concrete Beams.
20. Stone.The stone used was Kankakee limestone, ordered
screened over a ¼in. screen and through a 1in. screen. It weighed
87 lb. per cu. ft. loose and contained 45% voids. Table 2 shows the
proportion of sizes as determined from two samples of 15 lb. each.
TABLE 2.
ANALYSIS OF STONE.
Diameter of Mesh
inches
2
1
1/2
1/4
No. 10 sieve
Dust
Amount Retained
pounds
0
.53
9.03
4.06
1.12
.25
In the determination of voids in both stone and sand, the material
was poured slowly into the water so that the voids became filled
with water, and no air was entangled.
21. Sand.The sand was furnished by the Garden City Sand
Co., of Chicago, and was of the quality known locally as torpedo
Per cent
passing
100.0
96.5
37.2
9.2
1.7
TALBOTTESTS OF REINFORCED CONCRETE BEAMS
sand. It was clean and sharp, and was screened through a sieve of
iin. mesh before using, except for Beams No. 1 to 11 in which it
was used unscreened. The sand weighed 103 lb. per cu. ft. loose
and contained 28 to 30% voids. Table 3 gives the result of the me
TABLE 3.
ANALYSIS OF SAND.
Sieve No.
4
10
20
50
74
100
Diameter of Mesh
inches
.208
.073
.034
.011
.0078
.0045
Per cent
passing
99.0
73.0
46.0
8.0
2.3
1.0
chanical analysis of the sand. The gradation of particles is not as
desirable as that found in the sand used in the Series of 1904.
22. Cement.The cement was furnished by the Joint Com
mittee and was formed of a mixture of five standard brands of
American portland cement mixed in equal proportions at one of
the mills in Pennsylvania. Table 4 gives the tensile strength of
TABLE 4.
TENSILE STRENGTH OF CEMENT.
Ultimate Strength, lb. per sq. in.
Ref. Age 7 Days Age 75 Days
No. Neat 13 Mortar Neat 13 Mortar
1 685 397 760 500
2 710 345 720 610
3 630 325 580 560
4 880 330 640 540
5 700 340 760 490
6 735 385 .... 500
Aver. 723±23 354 8 692±24 533±13
neat cement and 13 mortar. The briquettes were stored in damp
air for one day and under water for the remainder of the time.
23. Steel.In accordance with the recommendation of the
Committee on Tests of the Joint Committee on Concrete and Re
inforced Concrete, that the operations of the year be restricted to
beams reinforced with plain bars, no deformed bars were used.
The bars used were round rods, j and 1 inches in diameter. Both
ILLINOIS ENGINEERING EXPERIMENT STATION
mild steel and tool steel were used. Although it was thought
that care had been exercised in getting the mild steel of the same
grade, it was found that the ½in. rods could be divided into two
classes, one in which the yield point was about 33 000 lb. per sq. in.
TABLE 5.
TENSION TESTS OF MILD STEEL.
G.S.*
G. S.
G. S.
G. S.
Average
G. S.
G. S.
G. S.
Average
Beam No. 36
1/2
Beam No. 36 1/2
Beam No. 36 1/2
Beam No. 37 1/2
Beam No. 37 1/2
Beam No. 37 1/2
Beam No. 37 1/2
Beam No. 37 1/2
Beam No. 47 1/2
Beam No. 47 1/2
.a
2840(
29000
28800
28300
28600
33100
34100
34000
33700
33400
32400
31100
31700
32700
34700
32900
33500
4670(
4640(
4600(
4590(
4625(
5160(
5290(
5290(
5240(
5320C
5020C
50200
50300
52200
53000
52000
50800
34100 52000
32600 51200
eam No. 47 1/2 34100 51000
Beam No. 47 1/2 33400 51100
Beam No. 48 1/2 36700 55100
Beam No. 48 1/2 33900 51800
Beam No. 48 1/2 33800 51500
Beam No. 48 1/2 32700 51000
Beam No. 54 1/2 34200 54400
Beam No. 54 1,2 33300 50900
3
0
3
3
3
3
3
3
3
3
3
3
3
3
3
31
3
3
3
2
3
3
3
3
3
3
3
3
3:
3:
3'
3;
3;
3(
3.
3:
3:
3]
3(
0
7.
5.0
6.s
CýO
8.
6.5
3.
0.
1.
1.2
1.5
3.
2.
4.
1.5
4.
2.
2.5
2.
1.5
2.5
3.
1.
8.
3.5
3.5
1.
0.5
3.5
3.
1.
3 .
.5
.54
'i.
!.
.5
..4
Beam INo. 54 1/2 335000 50800 3
Beam No. 54 1/2 33700 50900 32
Beam No. 58 1/2 32300 51600( 2
Beam No. 58 1/2 33800 547CO 28
Beam No. 58 1/2 32400 51100 33
Beam No. 58 1/2 33800 54500 28
Beam No. 59 1/2 32400 51400 31
Beam No. 59 1/2 32800 51900 30
Beam No. 59 1/2 32700 52100 28
Beam No. 59 1/2 31600 51600 31
Average 33200 51900 31
* G. S. refers to general stock.
" _
0 Beam No. 20(
Beam No. 2(
Beam No. 20
Beam No. 2(
Beam No. 2]
Beam No. 2]
Beam No. 2]
Beam No. 21
Beam No. 21
Beam No. 2'
Beam No. 2i
Beam No. 21
Average
Beam No. 11
Beam No. 11
Beam No. 11
Beam No. 11
Beam No. 18
Beam No. 18
Beam No. 18
Beam No. 18
Beam No. 19
Beam No. 19
Beam No. 19
Beam No. 19
Beam No. 27
Beam No. 27
Beam No. 27
Beam No. 30
Beam No. 30
Beam No. 30
Beam No. 30
Beam No. 31
Beam No. 31
Beam No. 31
Beam No. 31
1/2 4530(
1/2 45501
1/ 2 4490
V12 4120(
1/2 4240(
1/ 2 4260(
1/2 4380(
1/2 4290(
1/2 4310(
1/2 4420(
1/2 4460(
1/2 4290(
4360(
1/2 4220(
1/2 3530(
1/2 3970(
1/2 4140(
1/2 3450C
1/2 3590C
1/2 42200
1/2 4170C
1/2 3590C
1/2 34500
1/2 45300
1/2 45000
1/2 33900
1/2 41500
1/2 39800
1/2 34600
1/2 41500
1/2 42500
1/2 42000
1 /2 35400
1/2 34600
1/2 41900
1/2 42500
6280(
6290(
6290(
6130(
6170(
6170(
6240(
6240(
6120(
6240(
6220(
6230(
6235(
59200
5000C
58000
58200
49900
50000
61600
61500
50000
49600
62900
62900
49300
59700
58200
49700
58700
59200
59300
49200
50200
58700
59200
28.5
27.
30.
29.
27.5
29.
27.
27.
29.
29.5
27.5
28.
28.3
27.5
30.5
28.
29.
34.5
34.
27.
26.5
33.
33.5
27.
27.5
34.5
30.
33.
27.5
27.5
32.
32.5
30.
29.5
TALBOTTESTS OF REINFORCED CONCRETE BEAMS
and another averaging 43 600 lb. per sq. in. Unfortunately some of
the beams contained a mixture of these two classes. Table 5 gives
the results of tests made on rods taken from near the ends of some
of the tested beams, as well as on bars taken from the general
stock. Some of the beams were destroyed before the variation in
the steel was discovered, and the strength of this steel is not fully
known. The 3in. mild steel was quite soft, the yield point aver
aging 28 600 lb. per sq. in. The tests of the tool steel are given in
Table 6. Its elastic limit averaged 52 900 lb. per sq. in.
TABLE 6.
TENSION TESTS OF TOOL STEEL.
Specimen Nominal Yield Point Ultimate Elongation
Taken From Diameter lb. per sq. in. Strength in 8 inches
inches lb. per sq. in. per cent
Gen'l Stock. 3/4 52500 83900 25.4
Gen'l Stock. 3/4 53200 85400 25.5
Gen'l Stock. 3/4 53000 85400 23.2
Gen'l Stock. 3/4 53000 84000 25.4
Average .... 52900 84700 24.9
24. Concrete. Table 7 gives the results of compression tests
of 6in. concrete cubes. The concrete used in making cubes was
taken from the mix used in making a test beam. The number of
the test beam corresponding to the cubes is given in the first col
umn. The cubes were left exposed in a room, and were not moist
ened in any way. It seems evident that they became very dry
and that their strength suffered from this cause even more than
did the concrete beams. It is felt that the compressive strength
of the concrete in the test beams was considerably greater than
that developed in the cubes.
Table 8 gives the flexural strength of three plain concrete
beams. The effect of the weight of the beam and of the loading
apparatus is included in determining the modulus of rupture. The
results are about the same as those for the concrete beams tested
in 1904.
25. Test Beams.The size of the test beam used was that
adopted by the committee on Plan and Scope of the Joint Com
mittee, i. e., 8 inches wide, 11 inches deep and 13 feet long, with
test span of 12 feet. The center of the steel reinforcement was
placed 10 inches below the top surface, except that in special cases
ILLINOIS ENGINEERING EXPERIMENT STATION
TABLE 7.
COMPRESSION TESTS OF 6INCH CONCRETE CUBES.
Concrete
as in
Beam No. 35
Beam No. 44
Beam No. 65
Average
Beam No. 59
Beam No. 60
Beam No. 66
Average
Beam No. 48
Kind of
Concrete
136
136
136
124
124
124
136
Age
days
66
67
59
58
58
57
69
Crushing
LQad
pounds
48000
47980
57400
38400
39800
29400
47200
41600
48850
45400
37800
64500
73200
64200
54560
55000
41240
28200
28300
28000
Compressive
Strength
lb. per sq. in.
1330
1330
1590
1065
1105
816
1310
1156
1355
1230
1290
1050
1790
2070
1780
1510
1530
1140
1520
783
786
777
TABLE 8.
TESTS OF PLAIN CONCRETE BEAMS.
Dimensions, 8 in. x 11 in. x 13 ft. Span, 12 ft.
Beam Kind of Age at Test Maximum Modulus of
No. Concrete days AppliedLoad Rupture
pounds lb. per sq. in.
64 136 58 1200 357
65 136 59 1260 366
66 124 59 1320 375
it was bent up at the ends. These beams were much more easily
made and handled than the larger size of test beams (12 in. x 13J
in. x 15 ft. 4 in.) used in 1904. The amount of reinforcement
given is in terms of the area of the concrete above the center of
TALBOTTESTS OF REINFORCED CONCRETE BEAMS
the metal, no deduction being made for the area taken by the
metal.
26. Making of Beams.Beams were made directly on the
concrete floor of the testing laboratory, a strip of building paper
being first spread on the floor. The forms used for the sides and
ends were in general similar to those used in 1904 which are
shown in Fig. 5, of Bulletin No. 1. They were of dressed pine
with braces and bolts as before. They proved entirely satisfac
tory, except for some warping of the timber which was overcome
by soaking the boards in water between applications. The con
crete was mixed by hand with shovels, a man experienced in
mixing concrete assisting in the work. All materials were meas
ured by loose volume. Cement and sand were thoroughly mixed
on a large sheetsteel mixing board before stone was added. The
stone, cement, and sand were then mixed, water was added, and
the mixture was turned until it had a uniform consistency. A
moderately wet concrete was used. Table 9 shows the probable
* TABLE 9.
AMOUNT OF WATER USED IN MIXING CONCRETE.
Beam Weight of Dry Material, pounds Weight of Per cent
 Water of Water
No. Stone Sand Cement Total pounds
24 657 369 105 1131 85.5 7.6
45 667 394 96.5 1157.5 101.5 8.8
range of the amount of water used. For beam No. 24 the sand
was already moist and in No. 45 it was dry. With few exceptions
batches of concrete were mixed just large enough for one beam,
and for three 6inch cubes. Concrete was deposited in layers of
about 3 inches, each layer being thoroughly tamped. The side
faces of the beams were spaded as the work progressed. Forms
were allowed to remain in place about 48 hours. The proportions
for most of the beams were 1 cement, 3 sand, 6 stone by loose vol
ume. A few beams were made of concrete with the proportions
124. The beams were numbered in the order of making. The
average weight of the beams was about 1200 lb., making the con
crete weigh about 150 lb. per cu. ft.
27. Storage.The temperature of the room during the curing
of the beams ranged from 60 to 70 degrees, F. and no protection
ILLINOIS ENGINEERING EXPERIMENT STATION
from drying out was used, except that the beams were sprinkled
with water for a few days after being made. It seems probable
that the beams dried out too much to secure the best quality of
concrete. The general age of the beams at testing was 60 days;
the exact age is given in the table. The storage space of the room
being limited it was necessary to pile the beams in tiers five beams
high. The beams were moved from their place of construction,
generally after more than two weeks had elapsed, and were piled
in tiers with thin strips between. An unfortunate accident hap
pened to the first fifty beams. Not being securely braced, the last
tier fell over sideways and struck the next tier and thus caused
all to tumble like a pile of bricks. The age at time of fall ranged
from two to six weeks. Fifteen beams were broken by the fall,
the blow producing tension in the upper side. The older beams
being in the rear had the severest fall. Several of the broken
beams were tested, interesting results being obtained. These re
sults are of value in showing the abuse which such beams may stand.
Beam No. 18 which was broken in the fall at a point 2A ft. from the
middle carried a load of 18000 lbs., the highest load carried. In
this test the loads were applied at two points 7j ft. apart, and it
should be borne in mind that between these two points no shear
existed and hence no diagonal tension was developed. The loads
held by the broken beam and their action during the tests are to
the credit of reinforced concrete construction. Broken beams
which were not tested or which showed untrustworthiness in the
tests are omitted from the tables.
28. Details of Tests.The method of testing followed in gen
eral the plan used in 1904 tests as described in Bulletin No. ;, page
9, under Details of Tests. The tests were made on the 200 000lb.
Olsen testing machine. The span length was 12 feet. The sup
ports at the end of the span rested on the table of the machine,
their bases being cylindrical surfaces of 12inch radius and their
tops being curves of small radius, thus allowing a rocking action
with changes in the length of the lower surface of the beam. For
a beam loaded at two points, the load was transferred from the
machine by a 19inch Ibeam and two turned rollers. Iron bear
ing plates I x 3 x 8 inches were placed above and below the beam
for the bearing of the rollers and pedestals. A layer of plaster
of paris was placed between these bearing plates and the beam
to overcome unevenness of surface and was allowed to set un
TALBOTTESTS OF REINFORCED CONCRETE BEAMS
der such load as came from the weight of beam and the appa
ratus used in loading. It is thought that this method of loading
brings very little longitudinal stress before an adjustment results.
The loads were applied at a slow speed of the machine, the
increase of deflection averaging about .03 in. per minute. Re
peated loads were applied at, say, .3 in. per minute and the release
was made at, perhaps, .6 in. per minute. The time of the ordi
nary test was a half hour to one hour. Load was increased by in
crements of 1000 lb., except when the loads were being released
or reapplied when readings were taken at intervals of 2000 or
3000 lb:
Deflections at the middle of the span were observed. The de
flections were obtained by means of a fine thread stretched at
constant tension between points over the supports and at the
middle of the depth of the beam, and passing in front of a paper
scale attached to the side of the beam at the middle of the span.
The scale was pasted on the face of a mirror and readings were
obtained by lining up the thread and its reflection. These read
ings were accurate to .01 in. The ordinary deflectometer could
not be used satisfactorily on account of the deflection of the table
of the machine under the load and the yielding of the plaster of
paris over the lower bearing plates. On part of the tests a cathe
tometer was used.
* To obtain the longitudinal elongation and. shortening at the
top and bottom of the beam (fiber deformation), the extensome
ter device shown in Fig. 12 was used. This device was the out
growth of the experience with the apparatus used in the tests of
1904 and which was described in Bulletin No. 1. The two yokes
were placed symmetrically with respect to the center of the span
and generally 42 inches apart. The upper pair of contact points
of a yoke was applied to the side of the beam at points onehalf
inch below the top of the beam, and the lower pair at the level of
the center of the steel reinforcement, i. e., ten inches below the
top of the beam. The rollers and dials, similar to those of the
Johnson extensometer, were attached to the yoke in such a way
that the middles of the rollers were in direct vertical line with the
contact points, and the axes of the rollers were at right angles to
the plane of the side of the beam. The rollers were 204 inches
apart vertically, the upper one being 54 inches above the upper
contact points. The rollers were .5 in. in circumference, the dials
ILLINOIS ENGINEERING EXPERIMENT STATION
Side View.
End View
FIG. 12. EXTENSOMETER DEVICE
four inches in diameter, and the graduations such that readings
were obtained to .0001 in. The second yoke was provided with a
fixed pin in a position corresponding to the four rollers. Connec
tion was made between this pin and the corresponding roller by a
horizontal rod which consisted of a }in. brass pipe and a steel strip'
about 9 inches long A Vshaped notch at one end of the brass
pipe engaged the pin of the fixed end. The steel strip at the other
end had a rounding surface which rested and rolled on the roller
of the measuring device. The calibration of the appliance by
means of a standard screw micrometer showed a possible error of
1% in the extensometer measurements. The extensometer device
was generally removed before ultimate failure of the beam was
reached. This apparatus gave satisfactory results except that in
the time tests the changes in the length of the brass rods due to
variations in temperatur& affected the results.
TALBOTTESTS OF REINFORCED CONCRETE BEAMS
III. EXPERIMENTAL DATA AND DISCUSSION.
29. Outline.Fiftyfour reinforced concrete beams were
tested. Table 10 gives general data of the beams. Further in
formation is given in the tables referred to in the column headed
Classification. The methods of calculation of deformations and
of position of neutral axis will be first described, followed with
an explanation of the loaddeformation curves, deflection curves,
etc. A description is then given of Tables 11 to 16 including an ex
planation of the classification and contents 6f these tables. The
following topics are then taken up; failure by tension in steel;
failure by compression of concrete; failure by diagonal tension;
failure of bond; effect of artificial cracks and spaces; effect of
method of loading; effect of repetition of load; progressively ap
plied and released loads; effect of rest after release of load; ef
fect of retention of load; effect of position of reinforcing bars;
effect of lean and abnormal concrete; effect of exposing reinforc
ing bars; position of neutral axis and value of modulus of elas
ticity.
30. Calculation of Deformation and of Position of Neutral
Axis.The calculation of the position of the neutral axis and of
the deformations at the extreme fibers was based upon the assump
tion that a plane section before bending remains a plane section
after bending. This work was done graphically from the observed
readings of the extensometers and the position of the rollers with
respect to the beam. The deformation per unit of length was cal
culated by dividing the total deformation by the gauged length or
distance between corresponding contact points, and this average
unitdeformation is used in the diagrams and tables. In general,
also, the values of the deformations used refer to the zero or ini
tial position of the beam under its own weight and that of the
Ibeam at the time the load was first applied. In other words, any
set which the beam may have taken has not been considered in
this calculation, nor has the effect of the breaking of the concrete
in tension.
31. Diagrams.Loaddeformation curves, deflection curves
and position of the neutral axis are shown in Fig. 20 to 58 at the
end of the text. The data are presented in the same way as in
the diagrams given in Bulletin No. 1. The curve marked "Upper
Fiber" represents the shortening per unit of length at the com
ILLINOIS ENGINEERING EXPERIMENT STATION
TABLE 10.
DATA ON BEAMS.
Beam Kind of
No. Concrete
5 136
11 "
13 "
14 "
15
16
17
18 "
19 "
20
21 "
22 "
23 "
24
26
27
28 "
29
30
31 "
33 "
34
35
36
37
38
39 Abnormal
40
41
42
43
44 "
45 136
46
47
48
49 "
50
51
52
53 "
54
55
56 "
57 "C
59 "
60 136
61
62
63 "
67 "
Amount of
Reinforcement
4 2in. Round
4 ½in. Round
3 2in. Round
4 ,in. Round
4 Iin. Round
3 ,in. Round
{ 3 in. Round
2 ain. Round
3 Sin. Round
5 2in. Round
{2 iin. Round
2 iin. Round
4 in. Round
{3 [in. Round
2 ain. Round
5 Jin. Round
4 [in. Round
2 4ain. Round
4 ½in. Round
3 4a:in. Round
2 34in. Round
4 in. Round
3 2in. Round
2 iin. Round
4 ½in. Round
2 iin. Round
3 in. Round
2 iin. Round
CCt n
Per cent of
Reinforcement
.98
.98
.98
.98
.98
.98
.98
.98
.98
.98
.98
.98
.98
2.21
.98
.74
2.21
2.21
.98
.98
1.66
1.66
1.84
.74
1.24
1.60
.98
.98
.98
.98
.98
.98
1.84
2.76
.98
.98
1.10
.98
1.66
1.66
1.10
.98
1.66
1.10
1.10
.98
.98
1.10
1.66
1.10
1.10
1.10
Age at
Test
days
69
65
62
63
63
63
65
72
63
64
62
63
62
63
64
68
60
62
62
62
60
60
60
62
59
57
61
61
61
62
61
61
61
61
60
64
60
387
63
60
61
63
59
59
59
59
59
59
59
59
58
57
Classifica
tion
Table 11
" 11
" 11
" 12
" 12
" 11
" 11
" 12
" 11
" 11
" 11
" 11
" 14
" 11
" 15
" 14
" 14
" 12
" 11
" 15
" 15
" 15
" 15
" 15
" 15
" 13
" 13
" 15
" 13
" 13
" 13
" 15
" 15
" 12
" 16
" 17
" 11
" 17
" 17
" 17
" 16
" 17
" 17
" 17
" 16
" 16
" 17
" 17
" 17
" 16
" 17
58s 24A
TALBOTTESTS OF REINFORCED CONCRETE BEAMS
pression face of the beam. The curve marked "Steel " indicates
the elongation per unit of length in the plane of the reinforce
ment and considers that the steel elongates the same as the con
crete at the same depth. The curve of deflection has a separate
scale of abscissas. The applied load is here used, and no account
is taken of the weight of the beam, which has already stressed
the fibers at the time the extensometers are read at zero load, nor
of the Ibeam, etc., used in transmitting the load. In the figures
following, (Fig. 56 to 58), positions of the neutral axis are given as
ordinates and correspond to the load given on the scale of abscissas.
The position of the neutral axis is given in per cent of the distance
from the compression face of the beam to the center of the metal
reinforcement. The detailed record of the observed readings of
extensometers and deflection measurements is so voluminous and
is covered so well by these diagrams that it does not seem neces
sary to reproduce it here.
32. Explanation of Tables 11 to 16.The beams are classified
in Tables 11 to 16 according to the nature of the reinforcement, the
loading and the kind of concrete. The neutral axis is given as a
proportionate part of the distance from the upper fiber to the cen
ter of the reinforcement for the first part of the third stage as
hereafter discussed. The columns headed Maximum Applied Load
and Load Considered do not include the weight of the beam and
the loading apparatus. The beams weighed about 1200 lb. each and
the loading apparatus for loads applied at two points about 300 lb.
The bending moment due to this, about 25 000 in.lb. if the over
hang is considered, is not included in the moments used in cal
culating the stress in the steel, since one use of these stresses is
the comparison of observed and computed values. The inclusion
of these weights will for 1% beams add about 3600 lb. per sq. in.
to the tension in the steel calculated from the resisting moment.
The values given in column headed From Resisting Moment are
calculated by equation (18) from the resisting moment due to
the applied load, using the position of the neutral axis given in
the table. The values given under From Deformations are ob
tained by multiplying the observed unit deformations by the mod
ulus of elasticity of steel, 30000000 lb. per sq. in. The two col
umns of calculated stresses in steel are not exactly comparable,
since there is included in the deformations an amount due to the
part of the weight of the beam which was originally taken by
ILLINOIS ENGINEERING EXPERIMENT STATION
TABLE 11.
1 PER CENT MILD STEEL REINFORCEMENT.
LOADING AT ONETHIRD POINTS.
.~ ~
~
 C)
D I
4500
11
13
16
17
19
20
22
23
Calculated Stress in
75 Steel
a ) lb. per sq. in.
"n Z From
0 0 g r Resisting
4 a . Moment
11000 11000
11000 11000
11800
11600
11100
011
Continuous
Continuous
Progressively
applied and
released
8000 lb. re
tained 28
hours
9000 lb. re
peated 10
times
6000 lb. re
peated 8
times, 10 000
lb. 6 times
Progressively
applied and
released
9000 lb. re
tained 20
hours
13 hours' rest
after 6000 lb.
9000 lb. re
peated twice
,5000 lb. re
tained 25
hours
15 hours' rest
after 8000 lb.
Continuous
11800
11600
11100
10000
10000
12500
12000
11000
11000
10250
40000
40600
43600
41600
41200
36400
36200
44500
43700
40000
39600
37100
From
Deforma
tions
39600
46000
41400
48000
36900
36900
49500
44000
44100
41700
40800

<0
z
6000
7000
5000
9000
4800
6000
26
31*
50t
10800
10200
12700
12800
11450
11400
10250
Tension
in steel
Tension
in steel
Tension
in steel
Tension
in steel
Tension
in steel
followed
by diag
onal ten
sion
Tension
in steel
Diagonal
tension
Tension
in steel
Tension
in steel
Tension
in steel
Tension
in steel
tension
in steel
in steel
.450
.470
.430
.440
* Beam No. 31 was cracked before test.
? Beam No. 50 was loaded up to 2000 lb. at age of 60 days and observations
made on the effect of rest; at the age of 387 days load was applied continuously to
failure.
I ......
t /I'
TALBOTTESTS OF REINFORCED CONCRETE BEAMS
tensile stresses and deformations in the concrete. The amount of
stress thus added for a beam with 1% reinforcement would per
haps be in the neighborhood of 2000 lb. per sq. in. The manner
of failure assigned in the tables is based on considerations of the
appearance of fracture, the behavior of the stressdeformation
diagram, and other evidence.
33. 1% MJildSteelReinforcement. Loading at Onethird Points.
Beams having .98% reinforcement are here for convenience called
1% beams. Table 11 gives the results of the twelve beams which
were thus reinforced with mild steel. This amount of reinforcement
was taken as representing an ordinary amount and one for which
under usual methods of loading, failure would come through steel
being stressed beyond the yield point,a form of failure which is
here called a steeltension failure. The beams included under
this heading had the bars in a horizontal position throughout the
length of the span. Those in which the bars were bent up or inclined
toward the ends of the beam are given under a separate heading.
These 1% beams were tested in different ways and with different
objects in view,continuous application, progressively applied
and released loads, repetition of the same load, retention of load
for a period of time, and time effect after release of load. These
phases of the subject are treated under separate headings further
along. In general these beams failed by tension in steel as might
be expected from the relation of depth, span, and amount of rein
forcement. The variation in the stress at which the steel began
to stretch considerably is explained by the variation found in the
yield point of the bars.
34. 1% Mild Steel Reinforcement. Miscellaneous Loading.
Table 12 includes the beams with 1% reinforcement which were
tested with loads applied at other than the onethird points. The
load was applied continuously to failure. The differences in man
ner of failure and in deformations developed will be discussed
under Effect of Method of Loading.
35. 1% Mild Steel Reinforcement with Abnormal Concrete.
Table 13 gives the results of six beams made of concrete mixed
or proportioned, or built by other than the methods employed gen
erally in making the test beams. These are discussed under Ab
normal Concrete and Diagonal Tension.
36. 2.2% Mild Steel Reinforcement.Table 14 gives the re
sults of beams having 2.2% reinforcement loaded at onethird
ILLINOIS ENGINEERING EXPERIMENT STATION
TABLE 12.
1 PER CENT MILD STEEL REINFORCEMENT.
MISCELLANEOUS LOADING.
be
0
At two points
7½ ft. apart
At two points
7½ ft. apart
At two points
72 ft. apart
At middle
At middle
At eight points
..5 7( a
.En '
..... 15400 15000
14000 17600 17600
...... 18800 18000
5000 9800 9500
5000 8000 7000
8000 13000 13000
Calculated Stress
in Steel
lb. per sq. in.
From From
Resisting Deforma
Moment tions
32700 27500
35400 32700
36800 39000
51200 47000
37900 31800
47100 37200
* Beams No. 14 and 18 were cracked before test.
TABLE 13.
1 PER CENT MILD STEEL REINFORCEMENT.
ABNORMAL CONCRETE.
LOADS APPLIED CONTINUOUSLY AT ONETHIRD POINTS.
Kind of
Concrete
Poorly mixed
Poorly mixed
Lean concrete
at bottom
Lean concrete
at bottom
Plane of set
1 in. from
bottom
Plane of set
51 in. from
bottom
.423
.490
.390
.520
.390
.404
0 1 0
7000 7000 6000
8800 8800 8000
8800 8800 8800
6000 6000 6000
9100 9300 9000
8000 9400 9000
Calculated Stress
in Steel
lb. per sq. in.
From From
Resisting Deforma o
Moment tions
21500 20700 Diagonal
tension
29500 30900 Diagonal
tension
31200 27900 Diagonal
tension
22400 19200 Diagonal
tension
31900 37800 Tension
in steel
32000 41400 Diagonal
tension
Diagonal
tension
Diagonal
tension
Diagonal
tension
Tension
in steel
Tension
in steel
Tension
in steel
TALBOTTESTS OF REINFORCED CONCRETE BEAMS
points. The amounts of the loads at time of release are given in
the text of the discussion farther on and are also shown in the
loaddeformation diagrams of these beams.
TABLE 14.
2.21 PER CENT MILD STEEL REINFORCEMENT.
LOADING AT ONETHIRD POINTS.
8000 15600
7000 14300
10000
15900
15600
14000
15000
Calculated Stress
in Steel
lb. per sq. in.
From From Z.
Resisting Deforma
Moment tions ;
25800 25500 Diagonal
tension
24200 29400 Diagonal
tension
25900 30000 Diagonal
crack fol
lowed by
compres
sion
TABLE 15.
MISCELLANEOUS MILD STEEL REINFORCEMENT.
LOAD APPLIED CONTINUOUSLY AT ONETHIRD POINTS
Calculated Stress
in Steel
lb. per sq. in.
From
Deforma
tions
44100
36000
d6000
35400
30000
37200
27200
30000
26400
Tension in steel
Tension in steel
Tension in steel
Diagonal tension
Diagonal tension
Diagonal tension
Diagonal tension
Tension in steel
Compression in
concrete
Method of
Applying
Load
Progressively
applied and
released
Progressively
applied and
released
12 000 lb. re
peated 15
times
.516
.610
.605
'U
a4 ý_
.380
.410
.470
.501
.505
.374
.606
.552
.680
 M'
5000
6000
8000
7000
10000
12800
10000
10000
From
Resisting
Moment
37400
33100
35000
29500
30600
24900
25600
28300
21400
8000
7400
13000
13950
14400
12800
12400
15000
15200
8000
7000
12000
13000
14000
12000
12400
14000
15000
* Beam No. 27 was tested for effect of rest after a load of 6000 lb. had been
applied.
t A load of 6000 lb. was retained 22 hours.
I Beam No. 45 was cracked before the test.
ILLINOIS ENGINEERING EXPERIMENT STATION
37. Miscellaneous Reinforcement with Xild Steel.Table 15
includes beams made .with a variety of percentages of reinforce
ment. These are discussed under Failure by Tension in Steel,
Failure by Compression of Concrete, Failure by Diagonal Tension,
Effect of Repetition of Load, and Progressively Applied and Re
leased Loading.
38. Beams with Rods Bent out of IHorizontal.Table 16 gives
five beams in which the reinforcing rods were bent into a para
bolic or trapezoidal form, as shown in Fig. 15. It is evident from
TABLE 16.
BEAMS WITH RODS BENT OUT OF HORIZONTAL.
1 PER CENT REINFORCEMENT.
LOADS APPLIED CONTINUOUSLY.
*
Z Loading
p £3 ~'*r 3r
48 At onethird
points
54 At middle
58 At onethird
points
59 At onethird
points
63* At onethird
points
.440 6000
.445 6000
.374 4000
.360 4000
.410 4000
7 
9300 9000
6600 6000
8900 8000
7900 7900
7400 7000
Calculated Stress in Steel
lb. per sq. in.
From
Resisting
Moment
32500
32600
28200
27600
25000
From
Deforma
tions
37800
30600
36000
80000
Tension
in steel
Tension
in steel
Tension
in steel
Tension
in steel
Tension
in steel
* Beam No. 63 had 1.10% reinforcement.
the results of the tests that the bending of these rods should com 
mence at points nearer the ends of the beam and that some of the
rods should remain horizontal. This is discussed under Effect of
Position of Reinforcing Bars.
39. Tool Steel Reinforcement.Table 17 gives eleven beams
which were reinforced with round rods of tool steel iinch in dia
meter having an elastic limit of 52 000 lb. per sq. in. These were
used to find the effect of high elastic limit metal. Owing to the
extremely smooth surface and uniform cross section of this steel,
these beams did not develop as much strength as those reinforced
with mild steel, the tensile stress developed being well below the
elastic limit of the material. The beams failed by slipping of the
TALBOTTESTS OF REINFORCED CONCRETE BEAMS
rods, followed by vertical and longitudinal cracks. The form of
failure is so marked, and the conditions are so unusual, however,
that the results may prove of more value than if the beams had
broken in the manner which might otherwise be expected. The
discussion of these tests will be taken up under Failure of Bond.
40. Failure by Tension in Steel.As shown in Table 11, all the
1% beams which were loaded at the onethird points except Beam
No. 20 failed by tension in steel, i. e., by a primary failure (soon
followed by the ultimate failure of the beam) which came when
the steel was stretched beyond its yield point and without any
other sign of failure appearing until the greatly increased stretch
of the steel beyond the yield point brought entirely new condi
tions into action. Unfortunately, the steel used was quite variable
in elastic limit, tests made afterward showing that iin. bars in
the same beam gave yield points at about 33 000 and 45 000 lb. per
sq. in., and hence the breaking values of the beam are not as uni
form as would otherwise be the case. Evidently, two lots of bars
must have become mixed in shipping. The yield point of the 3in.
bars was 28000 lb. per sq. in. However, it is evident from the
results that beams made of 136 concrete of the quality here used,
reinforced with 1% of mild steel may be expected to fail by ten
sion, unless, of course, the relation of depth to length of span is
such that failure by diagonal tension occurs. For beams failing
by tension in steel, the resisting moment of the beam may well
be calculated by multiplying the total stress permitted in the
steel by the distance from the center of the steel to the center of
gravity of the compression area of the concrete. Of the beams in
Table 15 having more than 1% reinforcement, Beam. No. 37 (1.24%
reinforcement) and No. 35 (1.84%) failed by tension in steel, and
No. 46 (2.76%) failed by compression of the concrete. No. 38
(1.60%), No. 33 (1.66%), No. 34 (1.66%) and No. 45 (1.84%)
failed by diagonal tension in concrete before the elastic limit of
the steel was reached and before the full compressive strength of
the concrete had a chance to develop. The same is true of the
beams in Table 14. The beams in Table 16 failed by tension in
steel. It seems evident, therefore, as noted in the next paragraph,
that the conclusion given in Bulletin No. 1, that beams made of
136 concrete of good quality reinforced with 1.5% of steel of
say 33000 lb. per sq. in. elastic limit will fail by steeltension, is
ILLINOIS ENGINEERING EXPERIMENT STATION
correct provided the dimensions of the beam are such that the
failure is not by diagonal tension.
41. Failure by Compression of Concrete.None of the beams
failed primarily through the development of the ultimate com
pressive strength of the concrete except No. 46, which had 2.76%
reinforcement. Some of them, of course, crushed at the top with
the rapid rise in the neutral axis after the steel had passed the
yield point, but this must not be considered a compression failure.
The beams having a large enough reinforcement of mild steel to
counterbalance the compressive strength of the concrete gave
diagonal tension failures before the full compressive strength of
the concrete was reached. However, the loaddeformation dia
grams and computations of the compressive stresses throw some
light on the effect of the larger reinforcement. The loaddefor
TABLE 17.
TOOL STEEL REINFORCEMENT.
LOADS APPLIED AT ONETHIRD POINTS.
1.10
1.10
1.10
1 10
.430 9000 11300
.510 6000 8000
.... .... 860
72 2 0n0n 7'A0
1.10 .380 6000 13200
1.10 .480 2000 8100
1.10 .381 6000 8600
1.66 .500 5000 11800
1.66 .520 6000 15000
1.66 .590 8000 9950
1.66 .481 5000 6600
11000
8000
0 00
11000
8000
'7000
Calculated Stress in Steel
lb. per sq. in.
From
Resisting
Moment
35400
26600
22900
13000 23500
8000 26300
8000 25200
11000 24100
15000 33100
9950 22600
From
Deforma
tions
37800
29700
28500
27000
22500
27500
32A0o
o 2
Bond
Bond
Bond
Bond
Bond
Bond
Bond
Bond
Bo~nd
40800 Bond
21000 Bond
0 066 14300 16200 Bond
* Beam was cracked before test. In Beam No. 56 reinforcing bars were
wrapped in oiled tissue paper.
t Beam No. 60 was loaded at two points 7? ft apart.
mation curve for the upper fiber shows no change of direction up
to a unit shortening of .0010 and .0012 in beams where the defor
mation reached this amount. In Beams No. 28 and 29 (Table 14)
in which the unit shortening curves went to the highest values, the
concrete did not show sign of failure when the unitdeformation
reached .0020 and .0026. In Beam No. 26, the deformation at upper
Beam
No.
49
53
56*
57
60t
62
67
51*
52
55
61
TALBOTTESTS OF REINFORCED CONCRETE BEAMS
fiber at maximum load was .0026. A study of these curves in con
nection with the amount of reinforcement used shows that these
tests confirm the conclusions reached in Bulletin No. 1, that with
136 concrete of the quality here used, a reinforcement of 1.5%
of steel of an elastic limit of, say, 33 000 lb. per sq. in., will not de
velop the full compressive strength of the concrete. This conclu
sion of course is independent of whether the diagonal tensile
strength of the beam is large enough to resist that method of fail
ure. A calculation of the compressive stress developed with 1.5%
reinforcement of 33 000 lb. per sq. in. metal, based upon equation
(15) using 2 000 000 lb. per sq. in. for the modulus of elasticity
and q  .6, gives 1600 lb. per sq. in. A comparison of the deforma
tions with the ultimate deformations of the concrete cylinders
tested indicates that this value is about 80% of the ultimate com
pre ssive strength of this concrete.
42. Failure by Diagonal Tension in Concrete.As noted in the
statement made on page 25, it is believed that the shearing
strength of concrete is great enough to resist any shearing stresses
which come on beams of ordinary dimensions. What are frequently
called diagonal shearing failures are really diagonal tension fail
ures. Since the actual amount of the diagonal tensile stress can
not be calculated without knowing the horizontal tensile stress
developed in the concrete at the same place, it may be best to
make comparisons through the medium of the horizontal and ver
tical shearing stresses, as given by equation (18). The amount
of the diagonal tensile unitstress may under some circumstances
be two or more times as much as the vertical shearing unit
stress, as may be seen by a study of equation (19). Perhaps in
the beams under consideration the maximum diagonal tensile
stress may be considered to be in the neighborhood of two and a half
times the vertical shearing stress. Bearing this in mind, we may
use the value of the vertical shearing unitstress as calculated by
V
the formula v =  (where d' is the distance from the center of
the steel to the center of gravity of the compressive stresses in
the concrete) for making comparisons of the diagonal tensile
stresses developed. Table 18 gives the calculated values of the
vertical shearing unitstresses developed in beams which gave
diagonal tension failures, as calculated by the above formula.
The highest value is 151 lb. per sq. in. for Beam 18 which failed
ILLINOIS ENGINEERING EXPERIMENT STATION
under an applied load of 18 800 lb. Evidently the diagonal tensile
stress developed in this beam was between 300 and 400 lb. per sq.
in. The lowest values for normal concrete were Beam No. 34 which
failed with v =104 lb. per sq. in. and No. 20 with 86 lb. per sq. in.
The average value for failures of this type was v  123 lb. per
sq. in. Beam No. 20 gave especially low results. Of the beams
not failing by diagonal tension, twb developed a vertical shearing
stress of 123 lb. per sq. in., and four reached 100 lb. per sq. in.
None of these beams, then, developed a stress higher than the
average given above.
It should be borne in mind that these results are with 136
concrete, that the bars were laid horizontally throughout the
length of the beam and that there was no vertical or diagonal
steel reinforcement used.
TABLE 18.
VALUES OF VERTICAL SHEARING STRESS AND BOND DEVELOPED IN BEAMS FAILING
BY DIAGONAL TENSION.
Vertical Shearing
Stress
lb. per sq. in.
V
bd'
133
143
151
86
130
124
137
120,
104i
117
109
123
62
78
75
57
80
70
Bond
lb. per sq. in. of
surface of bars
V
mod'
170
182
193
109
110
106
117
135
116
143
112
136
80
100
95
73
101
90
Remarks *
Loaded at two points 7} ft. apart
Loaded at two points 7z ft. apart
Loaded at two points 7½ ft. apart
2.21% mild steel reinforcement
2.21% mild steel reinforcement
2.21% mild steel reinforcement
1.66% mild steel reinforcement
1.66% mild steel reinforcement
1.60% mild steel reinforcement
1.84% mild steel reinforcement
Abnormal concrete
Abnormal concrete
Abnormal concrete
Abnormal concrete
Abnormal concrete
Beam
No.
14
15
18
20
24
28
29
33
34
38
45
Av.
39
40
41
42
44
Av.
* Unless otherwise stated, all beams in this table were of 1% mild steel rein
forcement, loaded at onethird points.
The socalled abnormal concrete gave lower results. Beams No.
39 and 40, made of concrete which was unevenly and insufficiently
TALBOTTESTS OF REINFORCED CONCRETE BEAMS
mixed, broke at v ý 66 and 78 lb. per sq. in. Beams No. 41 and
42, made with the lean mixture (1612) at the bottom, broke at
v = 75 and 57 lb. per sq. in., respectively. Beam No. 43, made
with a "plane of set" above the bars, did not fail by diagonal ten
sion, but Beam No. 44 broke at 80 lb. per sq. in.
It seems apparent from these tests that the richness and the ten
sile strength of the concrete enter into the diagonal tensile strength
of a beam in a way not usually recognized and that for beams hav
ing a short length in comparison with the depth it may be the con
trolling element of strength, unless, of course, some metallic form
of web reinforcement is used.
43. Failure of Bond.Failure of the bond between the re
inforcing rods and the concrete is difficult to detect. The fact
that a rod has been found after failure of the beam to have slipped
is not evidence that slipping occurred before failure began
and hence was the primary cause of failure. In so.ne instances
reported as failure by slipping, the slipping evidently occurred
as a consequence of the new conditions brought into play by what
ever was the primary cause of failure, and slipping may not be
considered the primary failure.
The smooth and almost polished surface and uniform cross
section of the tool steel used in eleven beams gave an opportunity
to study failure of bond or slip of bars. These bars were jin.
round tool steel of about 52000 lb. per sq. in. elastic limit, bought
of the Crescent Steel Co. The surface of these bars was dense and
smooth, the finishing work leaving the surface almost like a
glaze. The cross section of the rods was very nearly uniform;
for example, measurements of the diameter of a rod taken at inter
vals of j inch were as follows: .7590, .7590, .7590, .7588, .7589,
.7589 in. Measurements of mild steel rods taken at two points j
inch apart will vary as much as .0015 in.
All these beams failed by bond of steel and concrete or slip
ping of the bars. Fig. 13 shows their appearance after failure.
In this figure, the numbers for Beams No. 52 and 53 should be
transposed. Table 19 gives the bond developed in lb. per sq. in.
V
at the time of failure, as calculated by equation (17) u = ,
mod'
and also the vertical shearing stress developed with the same load.
The weight of the beam and loading apparatus is included in these
calculations. Beam No. 49 failed suddenly. The failure shows a
ILLINOIS ENGINEERING EXPERIMENT STATION
nearly vertical crack with a horizontal crack extending along the
plane of the reinforcement toward the support. Fig. 14 is from
photographs. It seems likely that slipping occurred from the end
of the rods to the vertical crack and also that the horizontal crack
developed at the time of slipping and in connection with the ver
tical tension coming on the rod. The bond stress developed, 161
lb. per sq. in. of surface Qf bar, is the largest except one devel
TABLE 19.
VALUES OF VERTICAL SHEARING STRESS AND BOND DEVELOPED IN
BEAMS REINFORCED WITH TOOL STEEL.
Vertical
Shearing Stress
lb. per sq. in.
V
95
72
66
107
73
73
101
126
107
91
61
Bond
lb. per sq. in.
of surface of bar
V
=mod'
161
123
112
181
124
124
114
143
120
133
69
Remarks *
1.10% reinforcement
1.10% reinforcement
1.10% reinforcement
1.10% reinforcement
1.10% reinforcement
1.10% reinforcement
1.66% reinforcement
1.66% reinforcement
1.66% reinforcement
1.66% reinforcement
1.10% reinforcement
* See Table 17 for additional notes.
t Beam No. 61 had artificial cracks outside of the load points.
oped in this series. The vertical crack was closer to the support
than was the case with the other beams. The record of Beam No.
60 is not definite enough to give the exact conditions of failure. It
developed the highest bond stress of the tool steel series, 181 lb.
per sq. in. Probably the slipping and consequent failure were
sudden. The fact that the loads were closer to the supports than
in the other beams may have a bearing on the high value devel
oped. It seems probable also that the additional anchorage of 3
inches of rod which in all the beams projected beyond the point
of support would act to raise the calculated bond stress for beams
in which slipping occurred from the ends.
Eight beams may be described as slipping and failing gradu
Beam
No.
49
53
57
60
62
61
51
52
55
Av.
61t
56
TALBOTTESTS OF REINFORCED CONCRETE BEAMS
ally. At a load of 75% to 95% of the maximum, a crack, vertical
or nearly vertical in position, appeared between the load point
and the support and not very far from the former, and gradually
increased in height until the maximum load was reached. The
load then fell off, and this crack grew until suddenly failure oc
curred at a load from 1000 to 4000 lb., less than the maximum. In
Beam No. 52 the critical crack appeared at 13000 lb., 87% of the
maximum load. The direction and position of the critical crack
are indications that slipping of the rods was the primary cause
of failure. The cracks shown in Fig. 13 and Fig. 14 are as they
Deaem No. 6Z
FIG. 13. SKETCH SHOWING FAILURE OF BEAMS REINFORCED WITH TOOL
STEEL BARS.
appeared near the time of final failure. At first appearance
only the vertical portion showed. It seems likely that this slip
ping occurred from the crack to a point under the load, there be

ILLINOIS ENGINEERING EXPERIMENT STATION
ing no shear andhence no bond stress on the portion of the beam
between the two loads. The calculated bond stress at maximum
loads for these beams ranged from 114 to 143 lb. per sq. in. Bond
tests made with this tool steel by Mr. Kirk, the rods being em
bedded 6 inches in the concrete, gave values of 153, 147, 154, and
141 lb. per sq. in. of surface, averaging 149 lb. per sq. in. It may
be noted that at the first appearance of the critical crack in these
eight beams, the bond stress developed ranged from 90 to 125 lb.
per sq. in. The position of the critical crack and the manner of
failure in this group of beams are materially different from the
conditions accompanying diagonal tension failures, it must not
be overlooked, however, that the presence of this initial crack
does weaken the resistance of the beam to diagonal tension, and
thus increases the web stresses above the crack and also the ver
tical tension transmitted from the rod just beyond the crack,
which together cause the final failure to be of the form shown.
Beam No. 61, (Fig. 14), is interesting as showing the effect of
artificial cracks in a part of the beam where vertical shear exists.
In making the beam, strips of tin covered with paper were placed
in the beam forming vertical cracks running from the reinforcing
rods four inches in height. In this beam there were thirteen of these
cracks 8 inches apart, six of them being outside of the load points.
Failure occurred in a crack 16 inches outside of a load point in a
manner quite similar to that described in the preceding paragraph.
The crack showed at the bottom of the beam at a load of 5000 lb.
and extended to within 3 inches of top of beam at the maximum
applied load of 6600 lb. The load fell off, the crack extended,
and final failure occurred at a lower load. The value of the
bond stress developed was 69 lb. per sq. in. Mortar below the
rods was not broken except at these artificial cracks. This is low
er than found in the other beams, but it must be remembered
that the presence of the vertical artificial crack gave a different
distribution of web stresses from the beginning.
The failures here discussed indicate that there are two types
of failure of bond. 1. Slip from the direction of the middle of the
span, with a slowly developing crack slightly inclined from the ver
tical which extends upward as the load is increased to the maxi
mum load, growing still more as the test is continued at a dropping
load, and finally breaking by splitting below and cracking di
agonally above. 2. Slip from the end of the beam and a sudden
FIG. 14. VIEWS SHOWING FAILURE OF BEAMS REINFORCED WITH
TOOL STEEL BARS.
TALBOTTESTS OF REINFORCED CONCRETE BEAMS
failure at maximum load by the formation of a crack slightly in
clined from the vertical and near to the support together with ac
companying splitting and diagonal cracking to the top of the beam.
The characteristic of the first is slow failure along a crack which
is nearly vertical and which gradually grows with increasing
load, and of the latter a sudden failure through a crack in a nearly
vertical position not visible until time of failure is reached. It is
likely that both are variations of a single form of failure, the former
appearing when the vertical tensile strength of the concrete is
exceeded. In failures by diagonal tension the cracks formed are
inclined more from the vertical than are these cracks. Again,
attention should be called to the fact that the rods were laid hor
izontally and that there was no vertical or diagonal steel rein
forcement used. It may be added that in none of the beams made
with mild steel bars placed horizontally was there any evidence
of slip of bar, and Beam No. 18 developed 193 lb. per sq. in. bond
stress. (Table 18.)
An effort was made to discover whether bond is affected by
grip of the concrete as distinguished from adhesion. In Beam
No. 56 the rods were wrapped in thin oiled paper. Unfortunately,
in the accident before described this beam was broken in two, and
it seems likely that any bond which existed was greatly disturbed.
Bond tests made with the same steel wrapped in paper in the
same way gave 60 and 56 lb. per sq. in. of surface, so that it may
be expected that if the beam had not been injured the load car
ried would have been higher.
44. Effect of Artificial Vertical Cracks and Spaces.In Beams
No. 51 and 52 artificial vertical cracks were formed as in No. 61
except that there were only five cracks and these were placed be
tween the load points where the shear is zero. Outside the load
points the beam then acted as a normal beam. Another point of
difference was that these cracks extended to the bottom of the
beam. A comparison of the deformations with those of normal
beams shows little difference, a result which was to be expected
if the tensile strength of the concrete in a horizontal direction is
not to be relied on.
Another variation consisted in cutting out a space 24 inches
long and 5 inches high across the full width of the beam,thus
leaving the rods exposed, as was done in Beams No. 49 and 52, Fig.
16, Art. 52. Beam No. 62 was similar, the portion cut away being
ILLINOIS ENGINEERING EXPERIMENT STATION
16 inches long and 3 inches high. Although cracks appeared at the
corners of these spaces, failure occurred outside of the load points,
and the cutting out of these spaces apparently was not a source of
weakness. A discussion of the deformations observed on the ex
posed bars will be given under Effect of Exposing Reinforcing Bars.
45. Effect of Mlethod of Loading.Considerable interest has
been manifested by engineers in the effect of method of loading
test beams. The opinion has been advanced that a uniformly
distributed load will allow a higher moment of resistance to be
developed, and cases of tests with loads formed of sacks of
sand or bars of iron have been cited in support of this. On the
other hand the moment of resistance developed in beams loaded
at the middle has been found to be higher than was to be expected
if the distribution of stress is as assumed in the ordinary theo
ry of flexure. A few beams were tested with the view of finding
out something concerning the effect of changing the point of
application of loads.
These beams had 1l% reinforcement (Tables 11 and 12). No. 5
and No. 11 were loaded at the onethird points. No. 21 and No.
30 were loaded at the middle of the span (concentrated load).
No. 47 was loaded at eight points, 11 feet apart, the load being
divided equally among these eight points. In No. 14, 15, and 18,
the load was applied equally at two points 7i feet apart. The
behavior of the beams which were loaded at the onethird points
was of course similar to what has already been described. In the
beams loaded at the middle, cracks appeared under the load on the
tension side early in the test and extended vertically higher until
within 3 or 4 inches of the top of the beam at the maximum load.
As was to be expected these beams gave steeltension failures.
No. 47, loaded at eight points, failed at the middle by steelten
sion, the crack at the middle of the span finally extending ver
tically to within two inches of ihe top of the beam. Fig. 32 gives
its loaddeformation diagram. The beams which were loaded at
two points 71 feet apart failed by diagonal tension in the concrete
at the highest loads carried by any of the standard size of beams
tested and hence developed the highest vertical and horizontal
shearing unitstress. In general, then, it may be said that all of
these beams failed in the manner which would have been pre
dicted.
The moment of resistance developed in the beams which were
TALBOTTESTS OF REINFORCED CONCRETE BEAMS
loaded at the middle, as calculated from the maximum loads by
the usual formulas, was higher than that developed by the other
methods of loading, the excess in No. 21 being particularly
marked. The fact that in the tests made afterward on steel taken
from the beams, one rod of No. 30 was found to have a yield point
of 34 600 lb. per sq. in., while those from No. 21 were above 42 000
lb. per sq. in. may be sufficient explanation for No. 30 not devel
oping so high a moment of resistance as No. 21. An attempt was
made to find the distribution of the stresses through the length of
the beams by placing an extensometer on an 8inch gauged length
at the middle of the span in addition to the regular extensometer
which was used with a gauged length of 42 inches, but the exten
someter device which was rigged up proved not to be serviceable
for the purpose, although it did give information of value in other
ways. However, it is evident from the deformations measured,
as well as from the resisting moments developed, that the distri
bution of the stresses in a centerloaded reinforced concrete beam
is not as assumed in the ordinary theory of flexure. The stress in
the steel at the middle of the span evidently is less than the amount
given by calculations, and at points somewhat away from the
middle the stress in the steel is greater than the calculated amount.
The fact that the load is applied at the top of the beam affects the
distribution. The results of tests made with center loading by
various experimenters agree in showing that the moment of resist
ance developed in tests by center loading is considerably in ex
cess of that obtained from calculations by the theory of flexure
and that such results may not be relied on for ordinary loading.
Tests of beams loaded at or near the onethird points agree in
general very closely with the calculations based on the theory of
flexure. The one tested with load applied at eight points compares
well with the other loading in a general way, although the mo
ment of resistance developed was somewhat lower than for the
beams loaded at onethird points. This was due in part at least
to the fact that all four of the reinforcing bars in Beam No. 47 were
of steel with yield point of only 33000 lb. per sq. in. It seems
proper to say, then, that the results of tests made with center
loading are not comparable with other loading and that. as center
loading is not ordinarily assumed in designing, this method of load
ing test beams should not be used. It seems proper to add also,
that a loading at the onethird points or thereabout is an allow
ILLINOIS ENGINEERING EXPERIMENT STATION
able method of testing and gives results fairly comparable with
uniform loading so far as the development of tensile and com
pressive stresses is concerned. It does not give as high shearing
stresses and hence as high diagonal tensile stresses as uniform
loading, but this is counteracted by the fact that with uniform
loading these stresses remain high only a short distance from the
supports and that in this distance the resistance to such stresses
is greater than beyond, and also that at a point oneeighth the span
length from the supports these stresses decrease to less than those
of the beam loaded at the onethird points. The convenience of
the latter method of loading makes it, all things considered, the
best general form of loading test beams.
46. Effect of Repetition of Load.Most tests of reinforced
concrete beams have been made by applying the load increasingly
until rupture takes place. It is known that when the load is taken
off, or released, it will not return to its original position. Part
of the effect is due to the fact that a portion of the weight of the
beam which had produced tension in the concrete in the lower
part of the beam must after the failure of the tension of the con
crete have the effect of giving additional tension to the steel. A
part may be due to the overcoming of initial or shrinkage stresses
in the concrete and steel. It would seem that a considerable part
must be due to the failure of the concrete on the tension side
properly to interlock or mesh so as to occupy its original position,
thus leaving tension in the steel during the release of the load,
and on the compression side to the inability of the concrete to
spring back to its original place. How much of this effect may
properly be called "set" can not be discussed here.
It is not so generally known that when a load is reapplied the
second application produces a different effect, both on the com
pression side and on the tension side of the beam. It seemed im
portant to learn the effect of a number of applications or repeti
tions of the same load on a beam, and repetitions of different
loads were made on Beams No. 17, 19, and 29. In the diagrams, to
secure clearness only a part of the repetitions have been platted.
The number of the application is indicated by a figure.
Beam No. 17 (1% reinforcement) was loaded with 9000 lb.
eleven times. This load and the weight of beam and loading ap
paratus gave a stress of, say, 37 000 lb. per sq. in. in the steel, 1400
lb. per sq. in. compression in the extreme fiber of the concrete, and
TALBOTTESTS OF REINFORCED CONCRETE BEAMS
77 lb. per sq. in. horizontal and vertical shear. The loaddeforma
tion diagram (Fig. 85) shows little increase or change in the steel
deformation after the second application, going and returning on
the same line, but the compressive deformation of the concrete
increased with successive applications and releases of the load.
It should be noted that the compressive stress reached with this
load was fairly high for the quality of concrete used. Upon the
eleventh application, the load was run up to a maximum of 11100
lb., failing immediately after at a load of 10 500 lb. Although a
diagonal crack outside of the onethird point was the outward
cause of failure it seems likely from the high stress in the steel
(over 40000 lb. per sq. in.), the shape of the loaddeformatioi.
curve, and the position of the cracks, that these cracks were not
the primary cause of failure, but that failure should be attributed
to the stretch of the steel beyond the yield point. The cracks
appeared at 6000 lb. at the first application of the load, and the
one under consideration became somewhat more prominent with
the repetition of the loading.
Beam No. 19 (1% reinforcement) (Fig. 33) was loaded with
6000 lb. eight times and then with 10 000 lb. six times. The sixth
time the load was run past 10 000 to a maximum load of 10800, fall
ing off to 10 000 and failing by tension in the steel in the middle
third. The stresses at the load of 6000 lb. together with the
weight of beam and loading apparatus may be estimated to be
25 000 lb. per sq. in. tension in the steel and 1000 lb. per sq. in.
compression in the concrete; and at the applied load of 10 000 lb.,
38 000 lb. per sq. in. tension in the steel and 1500 lb. per sq. in.
in the concrete. These are high stresses at which to test repeti
tion of loading. The stressdeformation curves indicate that the
concrete was compressed well up toward its crushing point at the
time of maximum load. Two diagonal cracks appeared just out
side the middle third at the first application of the 6000 lb. load,
and upon the third application, another became visible. The
crack in the middle which finally became the seat of failure ap
peared at the first application of 8000 lb.
Beam No. 29 (2.2% reinforcement) (Fig. 34) was loaded with
12 000 lb. fifteen times, and upon the sixteenth application the
load was increased to the maximum of 15 900 lb., failing soon after
at 15 900 lb. The stresses at the load of 12 000 lb. together with
the weight of beam and loading apparatus were, say, 23000 lb. per
ILLINOIS ENGINEERING EXPERIMENT STATION
sq. in. tension in the steel, 1500 lb. per sq. in. compression in the
concrete, and 110 lb. per sq. in. vertical and horizontal shear. Rep
etition of the loading gave greatly increased shortenings in the
upper fiber of the concrete. In considering this, the high per
centage of reinforcement and the large values of the compressive
stresses developed in the concrete by virtue of this reinforcement
should be borne in mind. The final failure of the beam was by
compression at, say, 1700 lb. per sq. in. and at a time when failure
by diagonal tension seemed imminent.
The tests of these beams throw considerable light on the ef
fect of repeated application of loads under high stresses and point
to important conclusions. The deflections under the last repeti
tion of load were 12%, 15% and 30% in excess of those obtained with
the first application. The source of this increase is mainly on the
compression side, for the deformation observed in the remote fiber
of the concrete increased from 30% to 50% beyond that of the first
load, while the deformation at the level of the steel increased
only 7% to 9% and in one beam the steel deformation ran backward
and forward along the same lines after the second application.
The increments of these changes in general decreased somewhat
with the repetitions. It would be interesting to know, with such
high stresses in the concrete, what would be the final effect of
continued application of the load. It seems plain that the defor
mation at the level of the steel does not change much, and would
not change except as it is modified by the changed distribution
of the compressive stresses. It would also be interesting to know
the effect of repetition of loads at lower stresses in the concrete.
Since in the phenomena of failure of such materials as concrete
the amount of the deformation is correlative in effect with amount
of stress, it would likewise be of interest to know the effect of
repetition of load upon both denser and more porous mixtures.
The results here given indicate that the compressive stress to be
taken as the basis of ultimate load in designing beams should be
somewhat less than the ultimate strength of the concrete. It may
be added that there was no general marked growth in the cracks
with the repetition of load, and a comparison of the determina
tions at the maximum load with those of other beams of the same
makeup does not show any special difference in results due to
the repetition of the application of the load.
The deflection retained on the first release of load seems to
TALBOTTESTS OF REINFORCED CONCRETE BEAMS
be nearly the same proportion of the deflection due to that load
as the deflection retained after the last application bears to that
under the last load. This retained deflection is from 20% to 35%
of the deflection under load. The larger part of this is due to
failure of the concrete to return to the original condition, the re
tained deformation of the upper fiber being 30% to 50% of the
deformation under load.
47. Progressively Applied and Released Loads.The usual
method of testing beams is to apply the load by increments until
failure occurs. To determine the effect of removing the load as
the testing progresses, in the tests of four beams the load was
released after each application, the load being increased each time,
generally in increments of 1000 lb. Beam No. 13 (Fig. 36) had
1% reinforcement and failed by tension in steel. Beam No. 20
(1%) failed by diagonal tension, the diagonal crack appearing at
a load of 9000 lb., starting from a point at the bottom one foot from
a support. The beam failed suddenly at a load of 10 200 lb., giv
ing the lowest shearing stress (86 lb. per sq. in.) of all the
beams made of normal concrete which failed by diagonal tension.
No explanation is offered for this unusually low value. Beams
No. 24 (Fig. 38) and No. 28 (Fig. 39) had 2.2% reinforcement and
failed by diagonal tension of concrete with an average vertical
shearing stress of 116 lb. per sq. in. in the concrete and at a high
compressive stress. The phenomena accompanying the tests of
these beams did not differ from those of beams of similar makeup
tested in other ways; appearance of cracks, position of neutral
axis, manner of failure, amount of deflection, etc., were not no
ticeably different. The effect on the loaddeformation curves and
deflection curves is interesting. These curves conform to the gen
eral outline of the curves given on page 48 of Bulletin No. 1. Upon
release of load the beam does not return to its original shape, but
retains a part of the deformations and deflection. The amount
of this retained deformation increases with the amount of the
load, though the amount of increase for the deformation at the
level of the steel is less than that at the upper fiber of the con
crete. In general it may be said that the retained deflection after
a given load ranged from 20% to 35% of the total deflection for
that load. The retained deformation for the upper fiber ranged
from 25% to 40% of the deformation under load, this percentage
increasing somewhat with the increase of the load. The retained
ILLINOIS ENGINEERING EXPERIMENT STATION
deformation of the steel ranged from 8% to 30%, this percentage
being smaller for the larger loads.
An important feature shown in the loaddeformation curves
and one which has a bearing on the calculation of stresses in beams
is the effect of the release of load upon the general form of the
curve. Although upon the reapplication of a load the deforma
tion is greater than that at the first application of this amount,
yet upon the application of larger load the deformations return
to the general form of the curve. In fact, the outlines of the curves
conform very closely both in shape and amount to those formed
without release of load, all differences being explainable by vari
ations in properties of the concrete. This is further evidence
that in the calculation of stresses, in the determination of the
position of the neutral axis, and in the determination of the
modulus of elasticity, gross deformations and not net or elastic
deformations give results most nearly representative of conditions
in the beam and should be used in the design of beams. The
effect found in repetition of loading adds weight to this con
clusion.
No difference in method of failure or in appearance of cracks
from that of similar beams was found by the use of this method
of applying loads. The position of neutral axis, calculated from
gross deformations, agrees with other methods of applying loads.
The set on the tension side is probably mostly due to the failure
of the particles of concrete to interlock, and tension is thus left
in the steel. Some part of this failure to return to original posi
tion is due to the added stress in the steel due to its taking a
further part of the weight of the beam after the concrete has
failed in tension, and a part may be due to the removal of initial
stresses existing in the concrete. On the compression side most
of the set is due to the plastic nature of concrete, though part
seems to be of the nature of a final stress in the material. What
ever it is, the application of a greater stress carries the material
to the same point it would have gone to with a continuously applied
load. This phenomenon is worthy of further study.
48. Effect of Rest after Release of Load. An effort was
made to determine to what extent the deflections and deforma
tions remaining in the beam after the load had been released were
permanent, or in other words to find whether the beam returned
toward the original position within a given interval of time.
TALBOTTESTS OF REINFORCED CONCRETE BEAMS
Beam No. 23 (1% reinforcement) was loaded with 6000 lb.; the
load was then released and the deflections and deformations meas
ured at intervals extending over a number of hours. The calcu
lated stress in the steel at this load including weight of beams
was 25 000 lb. per sq. in. and that in the concrete, say, 1000 lb.
per sq. in. Beam No. 27 (.74% reinforcement, 6000 lb. load, cal
culated stress in steel 33 000 lb. per sq. in. and in concrete 1150
lb. per sq. in.), No. 31 (a broken beam, load of 8000 lb.) and No.
50 (1% reinforcement, 2000 lb. load, calculated stress in steel
11 000 lb. per sq. in., and in concrete 450 lb. per sq. in.) were
tested in the same way. The results of these tests are in some
respects not satisfactory. It was not appreciated in advance that
changes in temperature would have so great an effect upon the
brass rods used in the extensometer device. The cathetometer
observations of deflections gave constant readings except for one
or two sudden changes which it seems must have been due to a
change at the instrument rather than in the beam. Greater reli
ance may be placed on the results by the thread method of deter
mining deflections of the beam. From observations made with
the thread the indications are that the beams made no apprecia
ble recovery of the set formed in the beam even after periods
of 15 to 40 hours of rest. This is not what might be expected, and
it should not be accepted as a conclusion without confirmation by
other tests.
49. Effect of Retention of Load. To determine the effect of
retaining a load for a time longer than that of the ordinary
test, four beams were kept in the machine for periods ranging
from 20 to 38 hours and the deflections and deformations observed.
It was found as was to be expected that the load indicated on the
scale beam of the machine usually dropped down somewhat, de
creasing during the first three hours as much as 1200 lb. for an
original load of 8000 lb. Part of this was due to a decrease in
the deflection of the beam, although no motion of the gears of the
machine could be detected. Each time that observations were
made the load remaining on the beam was first noted, and then
the extensometers and the deflection were read. A careful
search was then made for cracks which might have developed, and
then the original load was applied, after which the extensometers
and deflection were read again. The load was retained as nearly
ILLINOIS ENGINEERING EXPERIMENT STATION
as possible in this manner for various lengths of time, after which
the load was increased until the beam failed.
Perhaps the following condensed log of the tests will best
state the conditions found.
Beam No. 16 (1% reinforcement) (Fig. 49). The first crack
was discovered at a load of 4500 lb. one foot north of the middle
of the span length. It was visible only on one side of the beam
and extended vertically to within 7 inches of the top. At 7000
lb. there were three fine cracks a few inches apart just outside
both load points and inclined slightly toward them. These were
all on the west side of the beam and extended to within'6½ inches
of the top. A load of 8000 lb. was then retained for 38 hours
with no perceptible change in the cracks. With increased load,
none of them increased much until the load reached 11000, the
maximum load being 11 600 lb.
Beam No. 22 (1% reinforcement) (Fig 40). The first crack
was discovered under the north load on the west side at 5000 lb.
At 8000 lb. two cracks appeared near the middle on the west side
and one just outside the south load. None of these cracks ex
tended to within 6 inches of the top. The cracks had not risen
materially at 9000 lb. After 9000 had been retained three hours
the cracks near the middle had become visible on the east side
and a new one 6 inches south of the middle on both sides was
found, but no change was found in the remainder of the 20 hours'
retention of load. At the maximum load of 12 700 lb. the crack
6 inches south of the middle had risen to within 4 inches of the
top and had opened nearly 1/32 inch at the bottom. The cracks
in the middle were approximately vertical. Those outside the
load points inclined slightly towards them. The load was ap
plied until the deflection was more than two inches.
Beam No. 26 (1% reinforcement) (Fig. 41). A load of 5000
lb. was retained 25 hours. No cracks were observed in the appli
cation of this load and none was observed until the load of 5000
lb. had remained on the beam 25 hours, when three cracks were
found along the middle third extending to within 7 inches of the
top. The load was then increased to 10 000 lb. when several more
cracks appeared under both load points. The maximum was
reached at 11 450 lb. when a crack 6 inches south of the middle be
gan to open up, the deflection being then . 72 inch. The final break
ing load was 10 000 lb. which occurred with a deflection of 2.14 in.
TALBOTTESTS OF REINFORCED CONCRETE BEAMS
Beam No. 36 (.74% reinforcement) (Fig. 42). The first crack
appeared at a load of 6000 lb. just outside the north load and ex
tended within 6 inches of top on both sides. This load of 6000 lb.
was retained for 18 hours, and there was no apparent change in
cracks during this time. After the maximum load of 7400 lb.
had been passed a crack was discovered 14 inches north of the cen
ter, which extended almost vertically to within 5 inches of the top,
and failure occurred at this crack.
It will be seen that while the stress in the steel at the re
tained loads was say 29 000, 32 000, 18 000, and 28 000 lb. per sq.
in., respectively, (not including weight of beam), there was little
effect shown in the stretched concrete by changes in appearance
or growth of cracks. In Beam No. 26 the first crack became visi
ble after the load of 5000 lb. had been retained 25 hours, but the
stretch in the steel at this load is about the average stretch at
which cracks became visible in these beams. In Beam No. 22 a
crack which had been noted on one side of the beam became visible
on the other side and a new crack was found during the reten
tion of the load, but this was at a load which indicates a stress of
32 000 lb. per sq. in. in the steel. In general, little effect in the
appearance and growth of cracks was noted.
Fig. 43 shows the change in load indicated on the scale beam
for a constant deflection during the first fourteen minutes for
Beams No. 26 and 36. As the deflections are approximately pro
portional to the loads, it may be judged from the diagram how
rapidly the beam would deflect if a constant load were applied.
The changes in deformations and deflections during the reten
tion of load are not reproduced, as the changes in temperature of
the measuring apparatus rendered the observations irregular and
somewhat untrustworthy. The increase in the deflection during
the retention of the load was for Beam No. 16 18%, for Beam No.
22 12%, for Beam No. 26 35%, and for Beam No. 36 28% of the
amount of the deflection when the load was first applied. The
observations show that the deformation in the steel and that in
the upper fiber of the concrete are both increased, the increase
being greater for the compression side. The average of the in
crease in the steel deformation for BeamsNo. 16, 26 and 36 is 15%,
and that for the upper fiber of the concrete is 41% of the amount
of the deformations when the load is first applied. It appears
that at the beginning of the test the deformation in the steel in
ILLINOIS ENGINEERING EXPERIMENT STATION
creases more rapidly than that in the compression side of the beam
and the neutral axis rises somewhat. Later the deformation
in the steel decreases and that on the compression side increases
considerably, and the neutral axis reaches a position lower than
its first position. While the values observed may not be quanti
tatively correct, it is felt that the general results are worthy of
consideration. It may be added that no effect of the retention of
the load was apparent in either the form of failure or the amount
of the maximum load. It is worthy of note that except in Beam
No. 36, in which the retained load was well up toward the maxi
mum, the loaddeformation curves and deflection curves rise up
ward upon the application of larger loads after a load has been
retained and finally take the general shape of such curves for pro
gressively applied loads, much as was found to be the case with
the curves for released loads.
50. Effect of Position of Reinforcing Bars.A few test
beams were made to learn something of the effect of bending the
reinforcing bars into parabolic and trapezoidal form. Fig. 15
FIG. 15. SKETCH SHOWING FORM IN WHICH BARS WERE BENT.
shows the two positions used. These beams were not designed
with an amount of reinforcement or a relation of depth to span
which would develop the full diagonal tensile strength of the con
crete, and hence these tests have no bearing upon the efficacy of
bending up bars to aid in taking the diagonal component of the
stresses. Moreover, all of the bars were bent up. The bars, par
ticularly in the parabolic form, were bent up from points too near
the middle of the span to get high loads. The tests are chiefly of
value in the peculiarity of the place and form of failure. Although
failure took place at vertical cracks with an outward appearance
of steeltension failures, these cracks appeared generally outside
the load points. In Beam No. 48 a vertical crack appeared at a
point about half way between one load point and the support at
a load of 6000 lb. and extended upward to the steel. At 7000 lb.
this crack had risen further and a small crack branched out from
it and ran alopg the line of steel for about 10 inches. At the
TALBOTTESTS OF REINFORCED CONCRETE BEAMS
same time a second vertical crack appeared at a point about half
way between the other support and load point. At the maximum
load, 9300 lb., these vertical cracks had reached nearly to the top
of the beam. The load then rapidly decreased. The cracks along
the steel were fine cracks and did not open up. The calculated
stress in the steel within the middle third was 33000 lb. per sq. in.,
which is about the elastic limit of the steelused in these five beams.
It would seem that the stress at the vertical crack must have been
less than this. Beam No. 63 failed in the same way except that
the maximum load was 7400 lb. and the stress must have been
less than in No. 48. Beam No. 58 having bars bent in parabolic
form failed in a similar manner with a maximum load of 8900 lb.
Beam No. 59, also with bars bent in parabolic form, failed at
cracks near the load points at a maximum of 8900 lb. Beam No.
54, also with bars bent up in parabolic form, was, unlike the fore
going, tested with center loading and failed at a vertical crack at
a load of 6600 lb. The information concerning these beams is
not explicit enough to tell whether any of them failed by other
cause than failure of the steel in tension. It would be interesting
to know whether slipping of the bars occurred in any of these
beams.
51. Effect of Lean and Abnormal Concretes.These tests are
of interest in showing the direction of the effect of poor workman
ship and lean mortar. Beams No. 39 and 40 were made of concrete
which was mixed about onethird as much as that for the ordi
nary beams and was not so well rammed. On account of the
poor mixing, patches of unmixed material could be detected and
the sand grains and stone were not well coated. They failed
suddenly by diagonal tension at maximum applied loads of 7000
lb. and 8800 lb. (vertical shearing stress of 62 and 78 lb. per sq.
in. including weight of beam, etc.). As normal beams with the same
reinforcement broke by failure of steel at loads from 9500 to 11 000
lb., and as diagonal tension corresponding to a vertical shear of 125
lb. per sq. in. was developed in the normal beams before failure
by diagonal tension occurred, it will be seen that the effect of
poor mixing on the resistance to diagonal tension is quite marked.
Beams No. 41 and 42 were made to see the effect of using lean
concrete in the lower half of the beam, the part whose chief func
tion is to transmit stresses from the tension of the steel to the
compression area of the concrete; in other words, to act as a web.
ILLINOIS ENGINEERING EXPERIMENT STATION
In these two beams the lower 5j inches of the beam was made of
concrete with 1 part cement 6 parts sand and 12 parts stone by
loose volume and the upper 5j inches was made of the usual 136
mixture. The top layer was placed over the leaner concrete in the
usual manner. Beam No. 41 broke by diagonal tension of the con
crete (sudden) at a maximum load of 8800 lb. Beam No. 42
broke in the same way at a maximum load of 6000 lb. The calcu
lated vertical shearing stresses (including weight of beam, etc.)
are 75 and 57 lb. per sq. in. respectively, as compared with, say,
125 lb. per sq. in. in normal beams. Considering that the diagonal
tensile resistance developed is proportional to these vertical shear
ing stresses, it is evident that the richness and the strength of the
concrete have much to do with its ability to resist diagonal or web
stresses. The importance of quality of concrete for the purpose
of resisting diagonal stresses is not usually recognized, and this
element should be considered even when metallic web reinforce
ment is used.
Beams No. 43 and 44 (136 concrete) were made with "planes
of set"; that is, the bottom of the beam was made and allowed to
set before finishing the construction of the beam. In Beam No.
43 a 1inch layer of concrete was placed in the bottom of the form,
the rods were embedded half their thickness, the layer left un
tamped and this layer left to set for 24 hours. The remainder of
the depth of the beam was then built as usual. It will be seen
that this is a severe condition. In Beam No. 44 the bottom 5j inches
of the beam was built as usual, except that the top surface was
roughened with the point of a trowel and was left to set for 24
hours, when it was completed in the usual way. Beam No. 43
failed at a vertical crack at 1 foot from the center at a maximum
applied load of 9300 lb. in a manner and with a calculated stress
which indicates a steeltension failure. The load is no lower than
that in some normal beams made with the same low steel bars.
How much more stress the "plane of set" would have stood is not
known. The bond developed is calculated as 101 lb. per sq. in.
of steel surface. Beam No. 44 failed by diagonal tension of the
concrete at a maximum applied load of 9400 lb. A vertical crack
extending to the level of the steel appeared 3 ft. from one sup.
port at 8000 lb., and the diagonal crack causing failure originated
at this point. The calculated vertical shearing stress at a load
of 9400 lb. is 80 lb. per sq. in. Nothing is known which would
TALBOTTESTS OF REINFORCED CONCRETE BEAMS 67
connect the diagonal tensile stress corresponding to this low value
of vertical shear with the manner of making the beam, and no
explanation is offered of the cause of the failure of this beam by
diagonal tension of the concrete at so low a stress.
52. Effect of Exposing Reinforcing Bars. In the construc
tion of three beams no concrete was put in a space at the bottom
on either side of the middle, thus making an archlike opening
and leaving the reinforcing rods exposed for a length of 16 to 24
inches. Fig. 16 shows the form of the opening. Deformations
FIG. 16. SKETCH SHOWING EXPOSED RODS.
were taken both on the exposed portion of the reinforcing rods
and on the usual gauged length of 42 inches. The gauged length
used for the extensometer on the exposed rods was 8 inches. Table
20 gives the stresses calculated from the observed deforma
TABLE 20.
STRESSES IN STEEL IN BEAMS HAVING TOOL STEEL REINFORCEMENT
WITH BARS EXPOSED.
Stress in Steel
lb. per sq. in.
Beam Load
Consid From From Elongations in
No. ered Resisting Exposed Exposed and
Moment Steel Encased Steel
49 8000 25900 23000 27000
53 8000 26100 25200 29400
62 8000 26100 25800 23100
Average 26000 24700 26600
tions for the usual gauged length and for 8 inches on the exposed
rods, as well as the stresses calculated from the bending moments
by the formulas heretofore given. The three stresses compare
very favorably. If allowance were made for the portion of the
weight of the beam which after the concrete has broken in ten
sion has the effect of adding to the deformation of the part of the
steel bar which is embedded in the concrete, the stress in the
last column would be smaller, and the agreement would be closer.
ILLINOIS ENGINEERING EXPERIMENT STATION
It should be noted that this effect of the breaking of the concrete
in tension does not affect the exposed steel observation, and hence
the stress in the steel should compare with that calculated from
the moment of the applied load only. This agreement is what is
to be expected from the usual assumption that the deformation
in the concrete at the level of the steel is the same as thab in the
steel.
It is of interest to compare the effect upon the exposed steel
and upon the encased steel when the load is released. In Beam
No. 49, after a load of 9000 lb. had been applied, the load was re
leased and readings taken. As usual the observations indicated
retained deformations in the 42inch gauged length, but the in
strument on the exposed rods returned almost to the original read
ing. The retained deformation indicated by the extensometer on
the exposed rod amounted to .000023, corresponding to a stress of,
say, 600 lb. per sq. in.
53. Position of Neutral Axis and Value of Modulus of Elas
ticity. The successive positions of the neutral axis within the
middle third of the span length, as determined experimentally by
the method already explained, are shown for the various beams
on the diagrams given in Fig. 56, 57 and 58 at the end of the bul
letin. In general, the change in the position of the neutral axis
as the applied load is increased follows the law outlined on page
29 of Bulletin No. 1. The neutral axis rises during the second
stage and remains nearly stationary during the third stage. (For
the use of the terms second stage and third stage see page 21 and
Fig. 15 of Bulletin No.1.) For beams in which, by reason of a
large amount of reinforcement high compressive stresses in the
concrete are developed, the neutral axis falls considerably during
the stage of rapid deformation of the upper fiber. An example
of this is shown in Beam No. 46. (Fig. 56.) Beams with low or
medium amounts of reinforcement, as for example the 1% beams,
do not of course develop large deformations in the upper fiber.
That a slight lowering of this position of the neutral axis during
the third stage is not always markedly noticeable, as would be
indicated by theory, is probably due to the decrease in the total
amount of tension in the concrete in a given section as the load
is increased, the moiety of tension remaining in the concrete
affecting the position of the neutral axis much more than it does
the resisting moment of the beam.
TALBOTTESTS OF REINFORCED CONCRETE BEAMS
The position of the neutral axis given in Tables 11 to 17 is for
the first part of the third stage of flexure. Generally the value
there recorded represents an average of the positions above and
below a load which produces a deformation in the upper fiber of
.0004 or .0005 per unit of length. These deformations correspond
to something like . 2 to . 25 of the ultimate deformation of the con
crete. It will be recalled that the value q=. 25 was selected
for the formula for position of neutral axis for the calculations of
this bulletin. (Page 15.)
In Fig. 8, page 16, the proportionate depth of the neutral axis
for the beams made with normal 136 concrete and reinforced
with mild steel are platted. The values for the 1904 beams, which
are also platted, do not differ much from these.
The agreement of the points platted is as close as may be ex
pected when variations in quality of concrete, lack of knowledge
of exact position of reinforcing bar, effect of a contact point rest
ing against one edge of a large stone, and other variations are
taken into account. It will be seen that the positions range some
what below the line drawn for position of neutral axis with an ini
tial modulus of elasticity of 2 000 000 lb. per sq. in. (n=15) and
q .25, as calculated from equation (11) given on page 15 As the
concrete grows older, the modulus of elasticity will increase
somewhat and the neutral axis will rise accordingly, although the
change may not be great after an age of 60 days. However, it
would seem proper with 136 limestone concrete of the kind here
used to use the line for n=15 shown in Fig. 8 for getting the
position of neutral axis and for use in calculating stresses, and to
call the initial modulus of elasticity 2 000 000 lb. per sq. in. Of
course for high reinforcements, a larger value than q=. 25 will be
developed, but this change will not seriously affect the position
of the neutral axis. If it is desired to use the straightline de
formation relation, a lower value than 2 000 000 for the constant
modulus of elasticity should be selected.
The straight line given on Fig. 16 of Bulletin No. 1 gives fair
results up to a reinforcement of 1.5%, but it seems better to use
the analytical determination, especially as the proportionate
depth may be easily found by means of a diagram. It may be
added that the value of the initial modulus of elasticity of 2 000 090
lb. per sq. in., n=15, corresponds closely with results found
ILLINOIS ENGINEERING EXPERIMENT STATION
in compression tests on concrete of the character used in these
tests.
54. Summary.It is difficult to summarize the results of the
investigation, since it covers considerable ground and the results
are intimately connected with a variety of conditions and many
sided phenomena. A careful perusal of the data and discussion
will give a clearer insight and perhaps a fairer grasp of the results
than can be gained from a summarized statement. The following
statements are not intended to stand forth as conclusions, but
rather as partial interpretations of some of the general phenom
ena of the tests:
1. The general phenomena of the tests, like stages of flexure,
the failure of tension in the concrete, moment of resistance of
the beam, effect of elastic limit of the steel, etc., agree well with
those described in Bulletin No. 1.
2. The tests confirm the conclusion given in Bulletin No. 1
that for normal 136 concrete of the quality used a reinforcement
of 1.5% of steel of 33 000 lb. per sq. in. elastic limit will not de
velop the full compressive strength of the concrete. In beams
having a smaller amount of reinforcement, failure will be due
to the stretching of the steel beyond its yield point. This
assumes that the beam is so proportioned or so reinforced that
bond or diagonal tension will not be the cause of failure.
3. Beams which failed by diagonal tension developed an
average vertical shear of 123 lb. per sq. in., as calculated by
equation (18). The diagonal tensile stress corresponding to
the shearing stress may be considered to be the tensile strength of
the concrete. The results have a bearing upon the importance of
web reinforcement.
4. Beams reinforced with tool steel failed by slipping of the
bars with 133 lb. per sq. in. as the average bond stress developed.
These beams showed a characteristic type of failure. The special
tests to determine the bond resistance of these tool steel rods
averaged 149 lb. per sq. in. In the beams reinforced with mild
steel placed horizontally, there was no evidence of slip, although
in onebeam a bond stress of 193 lb. per sq. in. was developed.
5. Center loading may be expected to give results which are
higher than those found by the ordinary beam formula. Moments
of resistance derived from results of center loading tests may not
properly be used as a basis of calculation for other forms of load
TALBOTTESTS OF REINFORCED CONCRETE BEAMS
ing. The results with loading at the onethird points compare
favorably with multiplepoint loading and are comparable with
uniform and other distributed loading.
6. Repeated applications of a load which sets up high com
pressive stresses in the concrete give increasing deformations.
The deflections after ten to fifteen applications were found to be
12% to 30% in excess of the deflection at the first application.
7. Beams which were loaded to give a stress of 15 000 lb. per
sq. in'. in the steel and 800 lb. per sq. in. in the concrete, or
more, failed to return to their original position upon the removal
of the load, the amount of the retained deflection being 20% to
35% of the deflection. No appreciable recovery of the set was
apparent after periods of 15 to 40 hours.
8. Beams loaded so as to develop stresses of 18 000 to 32 000
lb. per sq. in. in the steel and compressive stresses of 800 to
1400 lb. per sq. in. in the concrete gave little perceptible
change in appearance or growth of cracks after the load had been
retained 20 to 38 hours, and upon the application of greater loads
the loaddeformation curves and deflection curves rose upward
and took the general shape for such curves for progressively ap
plied loads. During the retention of load, the deflection increased
12% to 35%, the principal cause of this increase evidently being
the increased compression of the concrete.
9. The general form of the stressdeformation curves for
continually increasing loads, progressively applied and released
loads, and repeated loads is the same, until the compressive
deformations of the concrete become large.
10. Poorlymixed concrete and lean concrete when used in
the lower half of beams gave failures by diagonal tension at shear
ing stresses not much more than onehalf the stresses developed
in beams made with normal concrete which failed in the same
manner. Tensile strength of mortar is therefore of importance,
at least when metallic web reinforcement is not provided. No
noticeable effect from the socalled " plane of set" was found.
11. The tests of beams having artificial cracks and exposed
rods give results which tend to confirm the analytical basis used
for determining stress in steel and for explaining slipping of bars
and splitting of bars away from upper portion of beam.
12. The position of the neutral axis found for the various
beams indicates that for a limestone concrete of the proportions
ILLINOIS ENGINEERING EXPERIMENT STATION
used the value of the initial modulus of elasticity is 2 000000 lb.
per sq. in. or less. It may not be much higher than this for older
concrete or richer concrete. If a straightline stressdeformation
relation, (constant modulus of elasticity), is assumed, the value
may well be less than that of the initial modulus of elasticity
here used.
It may not be out of place to add a few comments on the ana
lytical treatment of the resistance of beams to flexure and on the
discussion of methods of failure.
13. The parabolic stressdeformation relation for concrete in
compression offers a satisfactory solution for use with beams in
which any considerable deformation is developed in the concrete.
The algebraic work based upon the proportion of the ultimate de
formation developed, (q), is not particularly complicated, and the
final formulas are not more difficult of use than are those based up
on the straightline stressdeformation relation (constant modulus
of elasticity) and are easily transformed into the straightline
relation for use or comparison.
14. The resisting moment of a beam which does not have an
excess of reinforcement may well be expressed in terms of the to
tal tensile stress in the steel and the distance from the steel to
the center of the compressive stresses as given by equation (13).
Its calculated value will not differ greatly whether the parabolic
or the straightline stressdeformation relation be used, or for any
ordinarily assumed position of the neutral axis. The moment
arm will, however, decrease somewhat as the amount of reinforce
ment increases. Whether the position of the neutral axis is ob
tained from a formula or taken from a diagram, the calculation by
equation (8) is not more difficult with the parabolic than with the
straightline relation.
15. For any considerable compression in the concrete, the
formula based on the straightline stressdeformation relation
gives too high a value for the compressive stress. If the straight
line relation is to be used, even for calculations at working loads,
the modulus of elasticity selected should be lower than the value
of the initial modulus of elasticity for the same concrete, or a
higher limiting compressive stress may be chosen than is actually
veloped in the beam.
TALBOTTESTS OF REINFORCED CONCRETE BEAMS 73
16. Equation (17) for bond and equation (18) for shear are
applicable to the method of reinforcement here discussed. A di
rect calculation of diagonal tensile stress may not be made, since
the intensity is dependent upon an unknown horizontal tension;
but comparison of diagonal tensile stresses may well be made
upon the basis of the vertical shearing stresses developed.
17. Failure by splitting of the bars away from the upper
portion of beam must be a secondary form of failure, following
failure by diagonal tension or other form of primary failure.
18. In all tests involving a determination of the cause of
failure, care should be taken to distinguish primary failure from
secondary or ultimate failure. While such distinction can not
always be made, the value of the conclusions must depend upon
the accuracy of the information on this point.
ILLINOIS ENGINEERING EXPERIMENT STATION
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BEAM NO. 40 SEE FIG. 46 BEAM NO. 41 SEE FIG. 47
BEAM NO. 4A SEE FIG. 50 BEAM NO. I SEE FIG. 4I
Position of Neitl Axis, iepth is to Center of Steel Postio of Neutral Axis. Depth i to Center of Steel
BEAM NO, 52 SEE FIG. 52 BEAM NO. 61 SEE FIG. 53
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Positions o Neutral Axis, Depth is to Center o Steel.
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