TESTS OF CAST-IRON AND REINFORCED CONCRETE
CULVERT PIPE
I. INTRODUCTION
1. Scope of the Bulletin.-The use in recent months of concrete
and reinforced concrete pipe for culverts in railway embankments has
brought to the minds of engineers anew the question of the action of a
pipe when subjected to the external pressure or load of an embankment
and of its resistance to this external pressure. The subject is somewhat
related to the action of sewers under earth pressure in a trench. The
question of distribution of loads and pressures in a trench or embank-
ment is varied and complicated, depending as it does upon the variety
and conditions of the earth and the manner of the filling. The laws of
the pressure of earth of themselves would require an extensive investi-
gation and treatment, and this phase is not taken up here. The main
tests described were made with a specially prepared testing apparatus
which included a box of strong and stiff construction, and the pipes
were embedded in sand and the load applied through a saddle which
rested on a sand cushion. The results throw light upon the resistance
of pipe to embankment pressures and also upon the action of sewers
under similar conditions. Cast-iron pipes, concrete pipes, and reinforced
concrete pipes were tested. Auxiliary tests were made to connect the
results of the investigation with the strength of the materials. Thus,
rings which were cut from the spigot end of the cast-iron pipe were
tested under concentrated load, and small test specimens cut from the
pipe were tested in cross bending. Short rings of concrete and rein-
forced concrete were tested, both under concentrated load and under
distributed load. In different ways these auxiliary tests served to check
up the phenomena of the tests of the pipes and to assist in interpreting
the action of the testing apparatus, the distribution of the load, and the
resisting strength of the structures themselves. In planning the tests
the relation of the various phenomena was kept in mind,, and the results
are compared and discussed.
2. Acknowledgment.-The investigation was made possible through
the co-operation of five railroad companies: Atchison, Topeka & Santa
Fe Ry. System; Chicago, Burlington & Quincy R. R. Co.; Chicago, Mil-
waukee & St. Paul Ry. Co.; Chicago, Rock Island & Pacific Ry. Co., and
Illinois Central R. R. Co. These companies furnished the cast-iron pipe
and the reinforced concrete pipe for the tests. Acknowledgment is due
to C. H. Cartlidge, Bridge Engineer C., B. & Q. R. R.; A. F. Robinson,
Bridge Engineer A., T. & S. F. Ry.; C. F. Loweth, Engineer and Su-
3
ILLINOIS ENGINEERING EXPERIMENT STATION
perintendent, Bridges and Buildings, C., M. & St. P. Ry.; J. B.
Berry, Chief Engineer C., R. I. & P. Ry., and R. E. Gaut, Bridge
Engineer I. C. R. R., for the assistance they gave in arranging for
furnishing the pipes. The tests were made between November, 1906,
and January, 1908. The work was an outgrowth of the thesis investi-
gation of W. A. Slater ('06, municipal and sanitary engineering) upon
the strength of concrete rings. Part of the experimental results of Mr.
Slater are included, and a reference is made to the thorough analytical
treatment made by Mr. Slater along the lines of Bach's method for
curved beams. The 1907 tests of concrete and reinforced concrete rings
were part of the thesis work of Messrs. H. B. Bushnell, J. Cermak
and A. P. Poorman, senior students in civil engineering, Class of '07.
The rings used in these tests were made by employees of the Engineer-
ing Experiment Station. Supervision of the tests and assistance were
also given. The main tests were made by the Engineering Experiment
Station. Special acknowledgment is made to D. A. Abrams, Associate,
and W. R. Robinson, First Assistant in the Engineering Experiment
Station for assistance in these tests and in the preparation of this
bulletin.
II. MECHANICS OF PIPES AND RINGS SUBJECT TO
EXTERNAL PRESSURE
3. Bending Moment and Conditions of -Loading.-The stresses de-
veloped in rings subject to external earth pressure, as in sewers and
railroad culvert pipes, are of course dependent upon the bending mo-
ments developed, and, as the exact load coming upon the ring and its
distribution over the surface are difficult to determine, the bending
moment is in general quite uncertain. The amount of the load and its
distribution, and therefore the bending moments on different parts of
the ring, depend upon a number of conditions, among them the nature
of the earth used in the filling, the method of bedding the pipe, the way
of tamping the, earth at the sides, the amount of the lateral restraint or
pressure of the earth horizontally, the method of filling and packing the
earth above, the condition of moisture in the earth, etc. Evidently in
such earth as saturated quick-sand, the conditions may approach those
of external hydrostatic pressure, and on the other hand, in deep sewer
trenches, the earth filling may act in such a way that much of its weight
is carried against the sides of the trench. In discussing the stresses in
rings, it may be well first to find the bending moment for certain as-
sumed conditions of loading, then to make tests under various conditions
of loading, and finally to compare these results with a view of determin-
TESTS OF CAST-IRON AND REINFORCED CONCRETE CULVERT PIPE
ing the probable range of bending moments under the actual conditions
of construction. The assumed loadings may include (1) a concentrated
load at the crown of the ring, (2) a vertical load distributed uniformly
over the horizontal section, (3) a distributed vertical load together
with a horizontal load distributed vertically over the sides of the ring,
and (4) an oblique loading. In these calculations, since much uncer-
tainty is involved, the difference in the intensity of the load at the crown
and at the extremities of the horizontal diameter, due to the different
depths of earth, need not be considered. In general the pressures and
distribution on the lower half of the ring will be considered to be the
same as on the upper half. It is apparent that in a ring of considerable
thickness in comparison with its diameter there is a different distribu-
tion of stresses from that found in thin rings, but for the rings under
consideration the simplicity of analysis for thin rings will outweigh the
small loss in accuracy. The possible modifications and complications
in the analysis of thick rings may also be considered. As refinements
are not essential and approximations are permissible, the analysis will
assume a thin ring of homogeneous material having a constant modulus
of elasticity and it will also be assumed that the changes from a circular
form will have little effect upon the dimensions of the ring.
/
___jA
0
6'
y^
FIG. 1. RING UNDER CONCENTRATED LOAD.
4. Concentrated Vertical Load on Thin Elastic Ring.-Consider
that a concentrated load Q is applied along the top element of a cylin-
drical ring and that the ring is supported along an element at the bot-
tom, as indicated .in Fig. 1 (a). Since the ring is a continuous curved
beam, the analysis will require a slight modification of the convention
commonly used for simple straight beams. However, in any segment
of the ring, the external forces acting on the ring will be held in equili-
brium by the internal or resisting forces acting upon this segment at its
ILLINOIS ENGINEERING EXPERIMENT STATION
two ends. The moment of the internal forces acting at right angles to
a section of the ring at an end of the segment is the resisting moment
developed, and the bending moment may be considered to be an equal
moment having the opposite sign. If we take a quadrant of the ring,
as shown in Fig. 1 (b), it is evident from a consideration of the external
and internal forces acting upon this ring that this quadrant will be in
equilibrium under the action of 1Q at B, a reaction or thrust of ½Q at
A, a resisting moment in the section of the ring at A which we will call
MA, and a resisting moment in the section of the ring at B which we
will call MB. The amounts of the two resisting moments so developed
and thus of the two bending moments it is important to determine.
Similarly, if we consider a portion of the ring shown in Fig. 1 (c), the
forces which hold it in equilibrium may be shown to be ½Q at A, ½Q
at C, the moment MA at the section A, and a variable moment M at C,
the value of which will change with a change in the angle 0. Taking
moments about A, the following equation for the value of the bending
moment at any point on the ring results:
M = ½Qr (1 - cos ) - MA (1)
When MA is known, the value of M may be determined for any point
in the ring. The bending moment at A, as is shown by making 0 = 0
in equation (1), is -MA.
When a straight beam deflects under load its axis becomes a curve
of varying curvature. Each normal section of the beam will change
direction through an angle which we will call 0, and at each point there
will be a definite radius of curvature. By the common theory of flexure
the following equation is true for straight beams:
M 1
El~ R
where R is the radius of curvature of the elastic curve, E is the modulus
of elasticity of the material, I is the moment of inertia of the cross sec-
tion of the beam, and M is the bending moment at the point considered.
By calculus we know that the reciprocal of the radius of curvature is
dO
equal to d , this derivative here expressing the rate of change of the
direction- of the normal to the elastic curve from its original position
with respect to the length of curve in which the change is made. Sub-
stituting this,
711r 7in
L'T ~.L.
1Z~.L U,,~
TESTS OF CAST-IRON AND REINFORCED CONCRETE CULVERT PIPE
This equation is ordinarily applied to the straight beam, but it is
general and is therefore applicable to the elastic ring, if we consider
that dO refers to the angular change of the normal relatively to its orig-
inal position. Substituting for ds its equal rd4 (Fig. 1 (d) ), where r is
the mean radius of the ring, the equation takes the form
M dO
7 7= ¾ (3)
EI rd4
Mrdo
This may be conveniently used in form dO = EI . It may help
dO
to a comprehension of the significance of the expression de to study the
representation of the elements in Fig. 1 (d). The line OM shows the
change in position of a section at the end of this element due to the
thrust or pure compression and the line NP that due to the bending
moment. The angle dO is the resulting change in the direction of the
normal due to the bending moment in the length ds, and the ratio at
dO dO
the limit becomes d". Then d- represents the rate of change of the
rd 0 do
deflected normal with respect to the angle 4 passed over. For our pur-
poses we may consider that r remains constant in equation (3).
It is plain that for the part of the ring between A and B in Fig.
1 (b), whatqver may be the local changes in directions at the various
points along the quadrant, the tangent at A remains constantly vertical
and the tangent at B remains constantly horizontal, and therefore the
total change in 0 between A and B is zero and hence that
i7r MB
aO Mr
d ~ ~ El
o MA
The general value of M, applicable to any point on the quadrant, must
of course be used in this expression. Substituting the value of M from
equation (1), using the modified form of equation (3) and integrating
with respect to 0, we have
Qr 1
. MA = - (1 - -) = .091 Qd (4)
where d is the mean diameter of the ring.
ILLINOIS ENGINEERING EXPERIMENT STATION
Substituting this value of MA in equation (1) and making 4 = 90°,
we have
M_ -Qd
MB 4 - .091 Qd = .159 Qd
It will be seen that the bending moment at B is about sixteen-ninths
times that at A.
FIG. 2. VARIATION IN BENDING MOMENT FOR CONCENTRATED LOAD.
To determine the point of zero bending moment place equation (1)
equal to zero. cos 0 = .636 and 0 = 500 30'. At this point the alge-
braic sign of the-bending moment changes from negative to positive.
Fig. 2 gives the variation of the bending moment from A to B.
It may be shown that if the load be applied equally at two points
on either side of the crown (and similarly supported below) the bending
moment at the crown will be decreased and that if these points are im-
mediately above the quarter points of the diameter the value of the
bending moment at the crown becomes 0.054 Qd and that at the ex-
tremities of the horizontal diameter 0.071 Qd. This has a bearing upon
the effect of the methods of bedding a pipe.
5. Distributed Vertical Load on Thin Elastic Ring.-Consider
that the vertical load is distributed uniformly over the horizontal pro-
jection of the ring, as shown in Fig. 3 (a), and call w the load per lineal
unit of horizontal width for a ring ofie unit long and r the mean radius
TESTS OF CAST-IRON AND REINFORCED CONCRETE CULVERT PIPE
of the ring. The conditions for a quadrant segment AB are indicated
in Fig. 3(b). It is easily shown that this segment is in equilibrium
under the resultant of the load wr applied at D, an equal thrust or re-
action wr applied at A, a moment in the section of the ring at A which
FIG. 3. RING UNDER DISTRIBUTED VERTICAL LOAD.
we will call MA and a moment in the section of the ring at B which we
will call MB. It is seen that there is no thrust and no shear at B.
Similarly the segment AC is in equilibrium under the forces and mo-
ments shown in Fig. 3(c). The vertical force at C is the resultant of
the tangential thrust and normal shear at that point, and is equal to
the load applied between C and the crown of the ring. The expression
for the bending moment M at any point C on the ring is found by taking
moments about C.
M = wr2 (1 - cos ') - wr2 (1 - cos 0)2 - MA
= ½ wr2 (1 - cos ) - MA (6)
Mr dO
The general relation El do (equation (3), p. 7) used in the
discussion of moments for concentrated vertical load is applicable to
dO
this loading. Here again d- measures the rate of angular change of
the normal to the elastic curve, and since the total angular change in
curvature between A and B is zero, the tangents at A and B do not
change from their original position. We may then substitute the value
of M from equation (6) in equation (3). Putting it in the modified
form, equating it to zero and integrating with respect to 0, with the
assumption that E, I, and r are constants, we have the following:
ILLINOIS ENGINEERING EXPERIMENT STATION
wr2 (1 - cos ) d4 - wr2 (1 - cos )2 d4 - MA de = 0
- MA = MB = B wd2 = 1'6 Wd (7)
where d is the mean diameter of the ring and W is the total load on a
ring of unit length.
A very neat determination of the value of MA and MB has been
given as follows: If a system of horizontal forces equal to the vertical
forces here considered be applied to a ring, the bending moment pro-
duced at A by the horizontal forces will be the same as that produced
at B with the vertical load, and the bending moment produced at B
will be the same as that found at A with a vertical load, but with op-
posite signs in each case. Similarly, at any point between A and B it
seems evident that an equal numerical bending moment will be pro-
duced with the new loading as at corresponding points with the old
loading, but with opposite signs. The effect of a combination of this
vertical and horizontal loading (Fig. 3 (d)) will be the same as that of
a load normal to every part of the ring, thus producing pure compres-
sion in every part of the ring and making the bending moment at every
section zero. It follows then that
- MA = MB = 6 Wd.
To find the point of zero bending moment make equation (6)
zero. This gives 4 = 45°. Above this point the bending moment is
positive and below it negative.
Fig. 4 shows the variation of the bending moments between A
and B.
FIG. 4. VARIATION IN BENDING MOMENT FOR DISTRIBUTED LOAD.
TESTS OF CAST-IRON AND REINFORCED CONCRETE CULVERT PIPE
6. Distributed Vertical and Horizontal Loads on Thin Elastic Ring.-
Let us consider that the vertical load is distributed over the horizontal
section of the pipe as before (w per lineal unit of width of pipe) and
that there is a horizontal pressure uniformly distributed vertically
against the pipe, the amount of this horizontal pressure per lineal unit
of vertical distance being qw, where q is the ratio of the horizontal to the
vertical intensity of pressure. The conditions are indicated in Fig. 5 (a).
We may consider that the effect of these loads is the combined effect
of the two loads. Call M', MA, and MBs the bending moments produced
by the vertical load and M", M and M ", the bending moments pro-
duced by the horizontal load. The bending moment at any section
C (Fig. 5 (b) ) produced by the vertical load is
M' = wr2 (1 - cos ) - 1wr2 (1 - cos 0)2 - MA.
(17) (hi (c)
FIG. 5. RING UNDER DISTRIBUTED VERTICAL AND HORIZONTAL LOAD.
It may be shown that the bending moment produced at any section C
by the horizontal load is
M" = - l qwr2 sin2 + MA
and that the value of MA is , qwr2. The resulting moment therefore is
M = M' + M" = 1 wr2 [1 + q - 2cos2 - 2q sin2 (8)
The moment at B and A will therefore be
MB = - MA = 4 (1 - q) wr2 = 1,6 (1 - q) Wd (9)
where W is the total vertical load on the ring. The bending moment
becomes zero at 0 = 450 as in the other case.
If the intensity of the horizontal pressure is the same as that of the
vertical pressure, q = 1 and M becomes zero at all points. This cor-
ILLINOIS ENGINEERING EXPERIMENT STATION
responds to uniform external pressure as shown in Fig. 5(c) and pro-
duces equal compression in all parts of the ring.
7. Oblique Load on Thin Elastic Ring.-In the case of both the
concentrated load and the distributed load it is seen that the bending
moments at A and B are large and that the moment decreases to zero
amount at some point between A and B. If we were sure that this
loading obtained, no provision against bending need be made at the
points of zero moment and but little for points close on either side.
However, it must be borne in mind that if there is a change from the
specified loading, the conditions of the bending moment are likewise
changed. If, for example, the method of filling over the pipe should
be such as to make the pressure come obliquely as shown in Fig. 6 (a),
(b,}
FIG. 6. VARIETIES OF LOADING.
the maximum bending moment would be at the 450 points and the
minimum moments at the ends of horizontal and vertical diameters.
Similarly, if in a sewer trench, a slip of earth from the side caused the
pressure to come against the sewer as shown in Fig. 6 (b), the dis-
tribution and amount of the bending moment would be materially dif-
ferent from that of the vertical loading usually assumed. In the case
of a large sewer in a shallow trench, during the time of filling, especially
with the concrete still green, the direction of pressures indicated in Fig.
6 (c) would give bending moments quite unlike those before described.
It will be necessary to provide separate analyses for such cases. While
an accurate measure of the bending moments in such cases is impos-
sible, yet in any case it is feasible to judge of the amount and location
of the bending moments within reasonable limits and to provide strength
in the section of the sewer to take the consequent stresses.
8. Resisting Moment and Calculation of Stresses.-For a ring whose
thickness is small in comparison with the diameter the difference in the
I %l1
1P
TESTS OF CAST-IRON AND REINFORCED CONCRETE CULVERT PIPE
length of the inner fiber and outer fiber is small and the expression for
the resisting moment given for ordinary straight beams may be applied
with a close degree of approximation. In the following formulas the
length of the ring (width of beam) will be considered unity. Call t
the thickness of the ring.
For the rectangular section of the ring the resisting moment will
then be i ft2 where f is the unit-stress at the remotest fiber. In those
sections where there is no thrust, the maximum stress (stress at the re-
motest fiber) may be found by equating the expression for the resisting
moment and the expression for bending moment given by equations
(1), (5), (6), (7), etc., and substituting the numerical values at the
section considered. If a thrust exists at the given section, this thrust
may be considered to be uniformly distributed over the section and the
stress will be equal to the sum or difference of the resisting moment
stress and the thrust stress.
For a concentrated load at the crown (Fig. 1) the stress at B,
since there is here no thrust, may be determined from the formula
ft2 = MB = 0.159 Qd (10)
where Q is the concentrated load applied at the crown and d is the
mean diameter of the ring. The maximum tensile stress and the maxi-
mum compressive stress at this section will be equal. As this is the
section of greatest bending moment and as the tensile strength usually
governs the strength of the rings under consideration, this equation is
the one to be used in tests with a concentrated load.
At A the same form of expression may be used for the resisting
moment, but this must be combined with the stress due to the vertical
thrust, ½Q. Considering this thrust to be uniformly distributed, the
stress in the remotest fibers will be
S9Q MA 1 Q 0.091 Qd
f 2 t2 t t2
The - sign will be used for the outer fiber and the + sign for the inner
fiber.
At any point C (Fig. 1 (c) ) the stress at the remotest fiber may be
shown to be
Qcos < M (12)
2 t ± (2t2
For a uniformly distributed horizontal load the stress at the crown
B will be, calling W the total distributed load on a ring of unit length
and d the mean diameter of the ring,
14 ILLINOIS ENGINEERING EXPERIMENT STATION
MB = 1/16 Wd (13)
and at A
_W_ MA 1_ W 3 Wd
2 t22 8 t2 (14)
and at any point C
wr cos2 M (15)
S= - (15)
For rings in which tensile stresses control, the weakest section is at
the crown, and equation (13) may be used.
For a distributed vertical and horizontal load (Fig. 5) there will be
a thrust at both A and B. The stresses at the crown B will then be
given by the following equation, calling q the ratio of the horizontal
intensity of the load to the vertical intensity,
qwr -Wd (16)
f= t (16)±
and at A the extremity of the horizontal diameter
wr Wd (17)
= - t2(17)
At any point C (Fig. 7) the expression for 'the stresses may be written
f wr cos2 4 qwr sin2 M18)
f - -- - t (18)
These formulas are directly applicable to homogeneous elastic rings
in which the modulus of elasticity of the material remains constant.
These conditions are not strictly true for rings made of cast iron or of
concrete or reinforced concrete. However, they may be applied with-
out any great error to cast-iron rings and plain concrete rings at the
breaking loads, if the modulus of rupture of the materials obtained
.under the same condition of thickness and loading be substituted for
the maximum tensile stress f.
For a ring made of reinforced concrete the conditions differ some-
what from the foregoing. For ordinary cases it will be not far from the
truth to equate the bending moment determined as above and the re-
sisting moment of the reinforced concrete section. As the amount of
reinforcement is usually lower than that in which the circular beam
TESTS OF CAST-IRON AND REINFORCED CONCRETE CULVERT PIPE . 15
would fail by compression in the concrete, we may, without material
error, take for the resisting moment of the reinforced concrete section
the value .87 Aft, where t is the distance from the compression face to
the center of the steel reinforcement, A is the area of the cross-section
of the reinforcement for a unit of length of ring, and f is the tensile unit-
stress in the steel due to the bending moment. To equate the bending
moment determined as before to this resisting moment is not exactly
correct, since among other reasons the neutral axis does not come at
the center of the thickness of the ring (which is the point about which
the bending moments were taken), and since the elastic curve is not
the same as in a ring of homogeneous material, and hence the distribu-
tion and amounts of the bending moments will not be exactly the same.
However, the use of the bending moments determined for homogeneous
rings is the nearest approximation we have, and is not seriously in
error. At sections where thrust occurs, as at A (Fig. 3), the tension
in the steel determined as above will be reduced by the resisting com-
pressive stresses there set up. The amount of the tension in the steel
at the point A may be calculated by the formula
SnT
fn = f - - (19)
S t(1 + np) (19)
which is applicable for both concentrated and distributed loads. In
this formula f is the tensile stress in the steel due to the bending moment
(as calculated by equating .87 Aft to the bending moment at the section
considered), p is the ratio of the area of reinforcement for a unit length
of beam or ring to the distance between the center of the steel and the
compression face of the concrete, T is the thrust or pressure against the
face of the section, and n is the ratio of the moduli of elasticity of steel
and concrete, which, for purposes of this calculation, may be taken as
15. At the extremity of the horizontal diameter the thrust is 1 W.
At the crown it is zero for vertical loading, and for both concentrated
and distributed load the greatest tensile stress is found at this section.
9. Horizontal and Vertical Deflections of Thin Elastic Ring.-
When a thin elastic ring is loaded with a symmetrical vertical load, the
vertical deflection or change in vertical diameter may be determined
from the expression f x dO, where x is the abscissa with respect to the
vertical diameter of the ring and 0 is the angle which the normal section
at any point has moved through due to the flexural distortion. This 0
is the same as the angle used in the analysis on p. 6 for determining
the bending moment for a concentrated load. Similarly, Jy d is the
ILLINOIS ENGINEERING EXPERIMENT STATION
expression for the horizontal movement, y being the ordinate with
respect to the vertical diameter. It should be stated that these expres-
sions neglect the change in shape due to the tangential thrust, but the
amount of this change is slight. In this analysis the effect of the direct
compression caused by the load is neglected, but this also is slight and
for the dimensions discussed will have a very slight effect.
Space will not be taken here to derive these formulas by rigid
analysis. The following may be helpful to the reader, however, in
seeing the reasonableness of the expressions. In Fig. 7, the element
of arc ds is subtended by the element of angle do, only the center line
of the ring being shown. 0 (not indicated on this diagram) represents
the change in direction of any normal section of the ring from its origi-
nal direction, and any element of arc ds, as the one at C, will change di-
rection by this angle 0. However, independently of this, each element
will, by its own flexibility, change direction with respect to the ad-
B
FIG. 7. DEFLECTION OF RINGS.
jacent element by an angle dO. By Fig. 7 it is seen that the effect of
this change in direction is to throw the point at the end of the line CD
to E, a distance x do. The effect is the same as to cause a movement
of the origin a distance x dO upward, or what is the same thing, the
point C must, by this action, be moved downward x do, and this is the
measure of the part of the movement of the element due to its own flex-
ure. Of course by the methods of limits the seeming approximations
of the diagram vanish and J x dO gives the total movement of the
quadrant of the ring due to flexure.
Having the expressions fx dO and fy do, the next step is to sub-
stitute for dO its value found from equations (2) and (3). The value
of the variable bending moment M from equations (1) and (6) may
then be substituted. Integration will be facilitated by expressing x and
TESTS OF CAST-IRON AND REINFORCED CONCRETE CULVERT PIPE
y in terms of r and 0. Integration may then be taken between 4 = 0
and k = -ir. To get the change in diameter (two sides of the axis)
the factor 2 must be introduced. The notation used will be that used
in the analysis of bending moments.
For a concentrated load Q, we shall then have for the change in
the vertical diameter
A 2 fxd j Mxds 2 Mr cos o do
Ay 2 xdO = 2J --- = 2ft
2Qr3 f7r
E- I / (0.318 cos 0 do - i cos2 do)
= -0.15 Qr3 (20)
El
and for the change in the horizontal diameter
Ax 2fMyds = 2f Mr2 sin , do
Ax = 2 yd6 = 2 -EI- = EI
- 2Qr (0.318 sin dr - - cos 0 sin 4 do)
EI Jo
= 0.136 QrV (21)
ElI
For a vertical load W distributed uniformly over the horizontal
section we shall have for the change in the vertical diameter
, Mxds Mr' cos 2 dt
Ay = 2 xdO = 2 Mxs = 2f r COS - d
= E __ I (cos do - 2cos3 do)
wr4 __ Wd3
E - - - 96 (22)
and for the change in the horizontal diameter
A 2 Myds 2 Mr2 sin dk
Ax = 2 yd6 = 2 -E- = 2 EIls-
ILLINOIS ENGINEERING EXPERIMENT STATION
I
= - (sin 0 de - 2 cos'2 sin 0 de)
EI o
wr4 1 Wd3(
E-6- E = 6 E (23)
For a combined distributed horizontal and vertical load, a similar
treatment gives for the change in the vertical diameter
1 Wd
Ay = - 9a (1 - q) El (24)
and for the change in the horizontal diameter
1 Wd3
Ax = 96 (1 - q) El (25)
where q is the ratio of the intensities of the vertical and horizontal loads.
These equations apply to rings of constant section and of constant
modulus of elasticity. Although the modulus of elasticity of cast iron
is not a constant, the formulas may be used with cast-iron rings, some-
FIG. 8. THICK RING.
what empirically. Reinforced concrete rings have a varied moment
of inertia, due to the varying position of the reinforcement and to the
effect of the tensile strength of the concrete, and the equations here
given are not applicable.
10. Modification for Thick Rings.-In case the thickness of the
ring is large in comparison with the diameter, (Fig. 8), the assump-
tions of the ordinary theory of flexure do not hold. The length of the
inner fiber is less than that of the outer fiber, a condition which mod-
ifies the analysis considerably. As a result, it is found that the neu-
TESTS OF CAST-IRON AND REINFORCED CONCRETE CULVERT PIPE
tral axis is not at the center of the rectangular section, and a new set
of formulas must be derived. The analysis of this condition will not
be made here, since it is quite complicated and since, fortunately, for
the thickness used in ordinary construction the errors involved in using
the common assumptions will be relatively small.
In the thesis of W. A. Slater on "Stresses in Concrete Rings Due
to External Pressure," heretofore referred to, a thorough analysis is
made of the stresses in thick rings. The treatment follows the method
of Bach for curved beams. The analysis and the resulting equations
are so long and complicated that the space available will not permit
their publication in this bulletin. Table 1 gives the ratio of the stresses
in a ring by formulas for curved beams to the results obtained by the
formulas here given for several thicknesses of wall. The thickness of
wall is given in terms of the mean diameter of the ring. The stresses
obtained by the use of equations (10), (11), (13), and (14) multiplied
by the ratios given in the table will be the amounts of stresses found
by the formulas for curved beams. It is seen that the difference by the
two methods is not large for the thinner rings. The moments in all
cases were calculated on the assumption that the load was distributed
over the mean diameter of pipe instead of over the exterior diameter.
This approximation of itself will give a considerable error for thick
TABLE 1
RATIO OF STRESSES
The stresses by the formulas for curved beams may be found by multiplying
the results obtained with equations (10), (11), (13), and (14) by the ratios given in
the table.
Ratio of Thickness of Wall to
Mean Diameter.
Concentrated load
Top and bottom points
Tension
Compression
Side points
Tension
Compression
Uniformly distributed load
Top and bottom points
Tension
.05 .10
1.03
0.97
0.97
1.02
1.03
Compression 0A. 97
Side points
Tension 0.98
Compression 1.03
1.08
0.94
0.93
1.07
1.08
0.94
.15
1.12
0.92
0.91
1.12
1.12
0.92
0.93 0.89
1.07 1.10
.20 .25
1.16
0.89
0.89
1.15
1.16
0.89
0.85
1.13
1.22
0.87.
0.86
1.21
1.22
0.87
0.81
1.16
ILLINOIS ENGINEERING EXPERIMENT STATION
rings. Of course, for thicker rings the effect of the difference in length
of inner and outer fiber increases rapidly, and the value of the stresses
obtained by the method here employed is soon in material error. How-
ever, it must be borne in mind that, as the reinforced concrete pipe has
varying stiffness around the circumference depending upon whether
the concrete has failed in tension and upon the position of the steel in
the section, the values of the bending moments given by equations
(5) and (7) are only approximate and refinements in the calculation
of the resisting moment are not warranted.
11. Conditions of Bedding and Loading Found in Practice.-The
foregoing discussion assumes certain definite conditions of loading.
These are useful in establishing definite formulas which may be used as
a basis for calculations. It is not to be expected that these conditions
represent accurately the condition of bedding and loading to be found
in practice. It is then desirable that the nature and extent of possible
or probable variations from these assumed conditions be discussed
and the effects of such a divergence considered. The following are
suggestions of variations; the engineer will easily extend the discussion
by numerous examples taken from his own experience.
If the layer of earth immediately under the pipe is hard or uneven,
or if the bedding of the pipe at either side is soft material or not well
tamped as indicated in Fig. 9 (a), the main bearing of the pipe may
be along an element at the bottom and the result is in effect concen-
trated loading. The result is to greatly increase the bending moment
developed and hence the tendency of the pipe to fail. This condition
may be aggravated in the case of a pipe with a stiff hub or bell where
settlement may bring an unusual proportion of the bearing at the bell
and the distribution of the pressure be far from the assumed condition.
In bedding the pipe in hard ground it is much better to form the trench
so that the pipe will surely be free along the bottom element, even
after settlement occurs, and so that the bearing pressures may tend
to concentrate at points say under the one-third points of the hori-
zontal diameter (or even the outer quarter points). This will reduce
the bending moments developed in the ring, as has been suggested on
page 8.
In case the pipe is bedded in loose material, the effect of the settle-
ment will be to compress the earth immediately under the bottom of
the pipe more completely than will be the effect at one side, as indi-
cated in Fig. 9 (b), with the result that the pressure will not be uniformly
distributed horizontally. Similarly, in a sewer trench, if loose material
is left at the sides and the material at the extremity of the horizontal
diameter is loose and offers little restraint, as indicated in Fig. 9(c),
TESTS OF CAST-IRON AND REINFORCED CONCRETE CULVERT PIPE
the pressure on the earth will not be distributed horizontally and the
amount of bending moment will be materially different from that
where careful bedding and tamping give an even distribution of bearing
pressure over the bottom of the sewer.
(c) (d}
FIG. 9. CONDITIONS OF LOADING.
In case of a small sewer in a deep trench, the load upon the sewer
may be materially less than the weight of the earth above, as in the
jA^ &
(b)y-^^yl'^
(C)
FIG. 10. CONDITIONS OF LOADING.
case shown in Fig. 9(d), where the earth forms a hard compact mass
and is held by pressure and friction against the sides of the trench.
In case a culvert pipe is laid in an ordinary embankment by cut-
ting down the sides slopingly as shown in Fig. 10(a), it is evident that
the load which comes upon the pipe will be materially less than the
weight of the earth immediately above it. If a culvert pipe replaces a
trestle and the filling is allowed to run down the slope as shown in Fig.
10(b), the direction and amount of the pressure against the pipe will
i;
ILLINOIS ENGINEERING EXPERIMENT STATION
differ considerably from that which obtains in a trench or in the case of
a level filling shown in Fig. 10(c). It is possible in the latter case that
the smaller amount of settlement of the earth directly over the culvert
pipe, due to the greater depth of earth on the adjacent sections, may
allow a greater proportion of the load to rest upon the culvert pipe than
would ordinarily be assumed.
Attention should be called to the fact that the distribution of the
pressure by means of earth under and over a ring assumes that the
earth is compressed in somewhat the same way as when other material
of construction is given compression. Unless the earth has elasticity,
the distribution of pressure cannot occur. To secure the uniform distri-
bution assumed the ring itself must give enough to allow for the move-
ment of the earth which takes place under pressure. This is especially
true with reference to the presence and utilization of lateral restraint,
and a ring which does not give laterally, as for example a plain concrete
ring, will not develop lateral pressure in the adjoining earth under ordi-
nary conditions of moisture and filling to any great extent. As the
conditions of earth and moisture produce mobility and approach hydro-
static conditions, the necessity for this elasticity and movement do not
exist, but here the lateral pressure approaches the vertical pressure in
amount and the bending moments become relatively smaller.
The discussion is sufficiently extended to indicate the importance
of care in bedding culvert pipe and sewers and in filling over them, and
to indicate the great difference in the amount of bending moment de-
veloped with different conditions of bedding and filling. Where there
is any question of needed strength, it will be money well expended to use
care and precaution in bedding the pipe and in filling around and over
it. I am convinced that a little extra expense will add considerable
stability, life, strength, and safety to such structures, far out of propor-
tion to the added cost. It is possible that under careful conditions of
laying, lighter structures may be used with a saving in the cost of con-
struction.
III. MATERIALS, TEST PIECES, AND METHODS OF TESTING
12. Cast-Iron Pipe and Rings.-Nine cast-iron culvert pipes were
tested, four being of 36-in. inside diameter and five of 48-in. inside diame-
ter. Four pipes were furnished by the Atchison, Topeka & Santa Fe
Ry., two each by the Chicago, Milwaukee & St. Paul Ry., and the Chi-
cago, Rock Island & Pacific Ry., and one by the Illinois Central R. R.
Both light-weight pipe and medium-weight pipe were tested. With the
exception of No. 990 there was little variation in the thickness in differ-
TESTS OF CAST-IRON AND REINFORCED CONCRETE CULVERT PIPE
TABLE 2
TESTS OF CROSS-BREAKING SPECIMENS FROM CAST-IRON PIPES
From
Pipe No.
991
991
991
991
992
992
992
992
993
993
993
993
993
993
994
994
994
994
995
995
995
995
995
995
996
996
996
996
996
996
997
997
997
997
997
997
998
998
998
998
998
998
998
998
Span
inches
24
24
24
24
24
24
22
22
24
24
24
24
22
22
24
24
24
24
24
24
24
24
22
22
24
24
22
22
24
24
24
24
22
22
24
24
24
24
24
24
24
24
22
22
Cross-section
in. x in.
1.995 x 1.355
1.984 x 1.358
1.990 x 1.350
1.995 x 1.385
1.980 x 1.298
1.985 x 1.293
1.990 x 1.340
1.995 x 1.236
1.980 x 1.500
2.000 x 1.460
1.960 x 1.440
2.000 x 1.440
1.970 x 1.472
1.985 x 1.481
1.987 x 1.575
1.987 x 1.552
2.019 x 1.450
1.976 x 1.442
2.015 x 0.845
1.980 x 0.851
1.990 x 1.000
1.979 x 1.000
1.991 x 1.100
1.980 x 1.096
1.996 x 1.180
1.986 x 1.205
1.980 x 1.248
1.988 x 1.248
1.984 x 1.229
1.988 x 1.223
1.979 x 0.962
1.993 x 0.948
1.980 x 0.787
1.993 x 0.830
1.996 x 0.695
1.976 x 0.687
1.978 x 1.170
1.975 x 1.175
2.005 x 1.300
2.000 x 1.280
1.987 x 1.361
1.997 x 1.318
1.981 x 1.426
1.997 x 1.458
Modulus of
Rupture
lb. per sq. in.
41 000
37 500
38 700
32 300
42 000
43 100
39 500
41 600
39 500
43 500
42 800
43 300
38 600
36 300
35 600
33 400
31 300
33 200
30 500
34 900
30 400
33 500
35 400
36 100
33 400
32 800
31 800
31 500
31 300
30 100
35 800
37 600
30 900
28 600
34 800
35 900
38 500
39 500
40 300
39 200
33 100
33 800
38 200
38 900
Modulus of
Elasticity
lb. per sq. in.
10 700 000
11 500 000
12 800 000
11 200 000
12 600 000
12 600 000
10 900 000
12 200 000
11 000 000
12 000 000
12 850 000
13 200 000
11 000 000
10 600 000
9 900 000
10 400 000
10 900 000
11 100 000
10 500 000
10 400 000
9 940 000
10 000 000
13 200 000
13 400 000
11 200 000
11 300 000
12 600 000
11 800 000
12 300 000
12 500 000
14 200 000
14 500 000
13 800 000
13 000 000
13 100 000
13 800 000
12 100 000
12 100 000
11 800 000
12 700 000
11 900 000
14 000 000
12 800 000
11 500 000
ILLINOIS ENGINEERING EXPERIMENT STATION
ent points of the pipes, the uniformity being greater than is found in
the usual run of pipe. In Pipe No. 990 the thickness varied from 0.75
to 1.75 in. One pipe was 6 ft. 8 in. long, and the other ranged from 8
ft. 0 in. to 8 ft. 5 in. over all after the rings for use in the auxiliary tests
TABLE 3
CAST-IRON CULVERT PIPE AND RINGS
Thickness
Internal Length
No. Diameter Over All Furnished by
inches Range Average inches
inches inches
Cast-Iron Pipes
990 48 1.25 80 I. C. R. R.
991 48 1.25 99 C. M. & St. P. Ry.
992 48 1.25 99 C. M. & St. P. Ry.
993 48 1.50 101 C. R. I. & P. Ry.
994 48 1.50 96 C. R. I. & P. Ry.
995 36 1.00 96 A. T. & S. F. Ry.
996 36 1.25 96 A. T. & S. F. Ry.
997 36 1.00 96 A. T. & S. F. Ry.
998 36 1.25 96 A. T. & S. F. Ry.
Cast-Iron Rings
1.4
1.25
1.31-1.25
1.47-1.35
1.50-1.34
1.63-1.53
1.13-0.90
1.50-1.27
0.98-0.92
1.31-1.05
1.28
1.43
1.42
1.58
1.6
1.02
1.1
1.44
1.42
1.00
0.91
1.25
1.19
24
24
24
23
24
24
24
24
24
24
24
24
24
24
24
24
C. M. & St. P. Ry.
C. M. & St. P. Ry.
C. M. & St. P. Ry.
C. M. & St. P. Rv.
C. R. I. & P. Ry.
C. R. I. & P. Ry.
C. R. I. & P. Ry
C R. I. & P. Ry.
A. T. & S. F. Ry.
A. T. & S. F. Ry.
A. T. & S. F. Rv.
A. T. & S. F. Ry.
A. T. & S. F. Ry.
A. T. & S. F. Ry.
A. T. & S. F. Ry.
A. T. & S. F. Ry.
had been cut from them. Test pieces, 2 inches wide and about 24 inches
long, were afterward cut from the rings and pipes and tested in cross
breaking. The results are given in Table 2. The quality of the cast
iron in the pipes was very good. Data on the pipes and rings are given
in Table 3.
13. Reinforced Concrete Culvert Pipe.-Five reinforced concrete
culvert pipes were furnished by the Chicago, Burlington & Quincy R. R.
991A
991B
992A
992B
993A
993B
994B
994C
995A
995B
996A
996B
997A
997B
998A
998B
48
48
48
48
48
48
48
48
36
36
36
36
36
36
36
36
TESTS OF CAST-IRON AND REINFORCED CONCRETE CULVERT PIPE
These pipes were designed by Mr. C. H. Cartlidge, Bridge Engineer.
They were made at Montgomery, Ill. Owl portland cement was used.
The gravel came from a pit at Montgomery. A mechanical analysis
of the gravel is given in Table 4. In two pipes, the reinforcement
was i-in. corrugated bars, placed as shown in Fig. 11, and ½-in.
corrugated bars were used in one pipe, No. 982. One pipe, No. 988,
TABLE 4
MECHANICAL ANALYSIS OF GRAVEL USED IN REINFORCED
CONCRETE CULVERT PIPE
Sieve
No.
%3
3
5
10
12
16
18
30
40
50
74
150
Per cent passing
Test Test
No. 1 No. 2
90.5
77.1
63.0
50.7
35.4
33.4
33.1
32.0
31.7
29.6
23.4
9.0
5.1
1.3
93.8
81.5
68.4
58.0
43.7
41.5
41.1
40.4
39.4
36.1
28.4
10.5
6.4
1.9
Test
No. 3
91.0
78.1
65.8
55.0
40.2
38.3
37.8
37.2
36.1
32.9
26.0
10.1
6.0
1.7
Average
91.8
78.9
65.7
54.9
39.8
37.7
37.3
36.5
35.7
32.9
25.9
9.9
5.8
1.6
was reinforced with "Clinton Wire Mesh," No. 3 wire being used, and
the fifth pipe was reinforced with fence wire laid in the center of gravity
of the concrete. The steel which was placed lengthwise of the pipe is
not considered in figuring the reinforcement. To allow the circumfer-
ential reinforcement to be made circular in shape, the pipes were made
with the vertical diameter four inches longer than the horizontal diame-
ter. This brought the reinforcement at the points where tension would
be present in the loaded pipe. Four of these pipes had a nominal inside
horizontal diameter of 48 in. and the other, a nominal inside horizontal
diameter of 36 in. This horizontal diameter will be used in referring
to the pipe, the vertical diameter being 4 in. longer. The barrel of the
pipe was 4 in. thick. The bell extended 4 in. beyond the barrel and
had the same thickness, its inside diameter being 1 in. greater than the
outside diameter of the barrel.
The forms were of wood lined with galvanized iron and were placed
vertically with the bell up. These forms were removed when the con-
ILLINOIS ENGINEERING EXPERIMENT STATION
crete was from two to four days old and the pipes were stored in the
open air until after shipment to the University, where they were stored
in the testing laboratory. Pipe No. 982 was made in cold weather and
was heated by steam coils to aid the curing of the concrete. Examin-
ation indicated that the quality of the concrete was somewhat injured
thereby. All the pipes had very good surface and, when broken up,
appearances indicated a very good quality of concrete.
Lorrugred gata
3"c. to c. -
/8 Lo;ngit//dira'/ Corrvactea' Bars'
Lefono/icen C2/c-eSece oon
~e/'nForcead Concrete P/pf
Cross Sec/ion
ReiDnforced Con cre/e A'?'7s
FIG. 11. DISPOSITION OF REINFORCEMENT IN THE REINFORCED CONCRETE PIPE
AND RINGS.
Two pipes furnished were of the type known as Jackson pipe,
which one of the railroad companies had in stock. They were made
by the Reinforced Concrete Pipe Co., Jackson, Mich. The pipe was 48
in. in internal diameter with walls 5 in. thick. The length was 3 ft. and
two sections were placed together in the test. This pipe has steel bands
at the middle of the thickness. It is not expected that the reinforcement
is placed most advantageously, but the steel serves to strengthen the
pipe in handling and obviates sudden failure. It is here treated with
the plain concrete rings.
7.
, ,,
8-8
* N
P..
(-' £/,
TESTS OF CAST-IRON AND REINFORCED CONCRETE CULVERT PIPE 27
14. Concrete and Reinforced Concrete Rings.-The concrete and
reinforced concrete rings were made in the laboratory at the University.
The sand came from near the Wabash River at Attica, Indiana. It
was of good quality and contained from 28% to 30% voids, as deter-
mined by standard methods. A mechanical analysis of this sand
TABLE 5
MECHANICAL ANALYSIS OF SAND
Sieve Separation Per cent passing
Sieve Separation
No. Size
No. inches Test Test
No. 1 No. 2
5 .174 99.8 99.5
10 80.8 80.0
12 .067 73.8 71.2
16 67.4 63.4
18 .043 52.9 48.2
30 .027 26.2 25.9
40 .019 15.0 16.1
50 .013 5.4 7.6
74 .009 1.9 3.6
is given in Table 5. The stone was Kankakee limestone which
showed about 50% voids. In Table 6 is given a mechanical anal-
ysis of this stone. Universal portland cement, furnished by the
manufacturers, was used. Table 7, p. 28, gives the results of tensile
TABLE 6
MECHANICAL ANALYSIS OF STONE
Size of
Mesh
inches
1.25
1.00
.50
.25
.125
Per cent passing
Test Test
No. 1 No. 2
100.0 100.0
95.0 95.0
40.0 29.0
7.5 2.0
2.5 1.0
tests of briquettes made from this cement according to standard meth-
ods. The concrete, which was made rather wet, was thoroughly mixed
by hand in the usual manner, the mixture being 1-2-4 in all cases.
ILLINOIS ENGINEERING EXPERIMENT STATION
The steel used in the reinforced rings was '-in. mild steel corrugated
bars. Table 8 shows the results of tension tests of this steel, each
result being the average of two to four tests.
TABLE 7
TENSILE STRENGTH OF CEMENT
Ultimate Strength, lb. per sq. in.
Age 7 days
Neat 1-3
410 187
470 200
360 120
405 145
320 195
310 180
379 171
Age 28 days
Neat 1-3
680 370
670 330
560 360
570 290
600 295
620 310
617 324
The rings were all circular in section, 4 ft. inside diameter, and 2
ft. long, the reinforcement being placed as shown in Fig. 11. The rein-
forced rings, of which there were 16, were 4 in. thick, while the 8 plain
concrete rings were made 6 in. thick. -
TABLE 8
TENSION TESTS OF STEEL USED IN REINFORCED CONCRETE RINGS
Specimen
takenfrom
Ring No.
921
922
923
926
927
928
931
932
933
934
951
952
953
971
972
977
Nominal
Size
inches
%in. corr.
it
(I
It
14
it
it
cc
it
"
it
a
a "
"t
"
"
Area
sq. in.
0.06
0.06
0.06
0.06
0.06
0.06
0.06
0.06
0.06
0.06
0.06
0.06
0.06
0.06
0.06
0.06
Per cent
Elongation in
8 inches
21
22
22
23
22
23
23
23
23.5
24
22
24
22
22
22
24
Yield Point
lb. per sq. in.
45 550
47 000
47 700
46 600
47 400
47 150
44 900
46 900
46 400
45 300
44 300
47 400
45 650
44 550
47 900
45 100
Ultimate
Strength
11b). per sq. in.
62 700
64 550
68 450
66 000
69 000
68 400
63 700
65 900
66 200
63 250
66 200
66 800
65 700
64 950
67 000
64 550
Ref.
No.
1
2
3
4
5
6
Av.
TESTS OF CAST-IRON AND REINFORCED CONCRETE CULVERT PIPE
In most of the rings the steel was shaped somewhat like an ellipse
in order to bring the reinforcement near the tension side at the quarter
points. In No. 934, 971, and 972 the bars were flattened for a distance
of 18 inches at both top and bottom of the ring, and in No. 976 and
977 three crimped pieces of steel were placed at top and bottom across
the ring. These were spaced 9 in. apart and served the same purpose
as stirrups in a beam.
The rings were made on the floor of the laboratory, the forms being
removed 7 days after making, after which the rings were wet twice daily
with a hose until tested. Fig. 12 shows a group of these rings. From
FIG. 12. VIEW SHOWING CONCRETE AND REINFORCED CONCRETE RINGS.
each batch of concrete from which a ring was made there was taken
enough concrete to make an unreinforced beam 6 in. x 8 in. x 40 in.
These were tested in flexure when about 30 days old as a check on the
modulus of rupture of the concrete which went into the ring. They
were tested with 3 ft. span with load at the one-third points. The
average modulus of rupture, as obtained from the tests of 22 of these
beams, was 195 lb. per sq. in.
15. Testing Machine for Distributed Load.-The machine used
for testing the culvert pipe is shown in Fig. 13. The photograph given
in Fig. 14 will aid in giving an idea of the apparatus used. The floor
of the machine rested on two I-beams. A layer of sand was spread over
this floor. On this layer of sand was placed the pipe to be tested. The
sides of the box were built up with bridge timbers and held firmly lat-
erally by heavy rods. Sand was put around and over the pipe. The
ILLINOIS ENGINEERING EXPERIMENT STATION
sand was leveled off at the top and the saddle built. Two I-beams,
similar to those below the pipe, were placed on the saddle and at the
four corners were placed hydraulic jacks with a capacity of 100 tons
each. The plungers bore against heavy cast-iron blocks which were
connected to blocks under the lower I-beams by means of 16 heavy
FIG. 13. HYDRAULIC JACK TESTING MACHINE.
wrought-iron rods. The jacks were operated by pumps placed on top
of the saddle. In this way a very even loading of the pipe was obtained.
The loads were read from a gauge attached to each pump. The cali-
bration of these gauges shows an initial error, but the per cent of error
is small on high loads.
16. Methods of Testing.-Every effort was made to have the pipe
level in the sand. As the sides of the box were built up, the sand was
frequently soaked down with water from a hose to insure firm bearing
around and over the pipe. The operation of bedding the pipe and
building up the box for each test was carefully done, and the time and
labor involved in this and in making the tests were considerable.
Points were marked on the inside of the pipe to indicate the extrem-
ities of vertical and horizontal diameters at sections 1 ft. inside each end
of the pipe. Initial readings of the diameters were taken. Then the
load was put on in increments of 16 000 lb. and held while readings of
the diameters were taken. As each crack appeared, its size and loca-
tion were carefully noted. This was continued until the pipe had reached
complete failure.
TESTS OF CAST-IRON AND REINFORCED CONCRETE CULVERT PIPE
The rings which were tested with distributed load were set up in a
similar way except that the box and saddle were only long enough to
accommodate a 2-ft. length of pipe. The box was set up on the bed of
the 600 000-lb. Riehle testing machine and the load was applied by
running the head down on the saddle. Readings of the horizontal and
vertical diameters were taken at the center of the ring, the load being
applied in increments of 1000 lb.
FIG. 14. VIEW OF HYDRAULIC JACK TESTING MACHINE.
All the testing under concentrated load was done in the 600 000-lb.
machine. A layer of plaster of paris about i-in. thick was spread on
a strip of building paper lying on the bed of the machine. The ring
was put in place so that the bottom element rested in the plaster of
paris. A similar layer of plaster was put on the top of the ring and a
ILLINOIS ENGINEERING EXPERIMENT STATION
cast-iron bar 3 in. wide by 2 in. thick by 2 ft. long was carefully cen-
tered in the plaster over the top element. A second bar of the same
dimensions was afterward placed on top of this to give greater stiffness.
The head of the machine was then run down and the load applied
through a spherical bearing block. In the tests of cast-iron rings cush-
ions of wood replaced the plaster of paris.
IV. EXPERIMENTAL DATA WITH CAST-IRON PIPE AND RINGS
17. Data of Tests.-Table 3 (p. 24) gives dimensions of the cast-
iron culvert pipe and rings and the name of the railroad company which
furnished the pipe. The suffix A denotes the ring cut from the spigot
end and the suffix B the ring next to it. In all cases the remainder of
TABLE 9
CAST-IRON RINGS. CONCENTRATED LOAD
Breaking Load
lb. per lin. ft.
16 250
10 300
11 720
12 850
17 400
16 500
9 650
13 500
17 500
18 500
6 950
6 650
17 500
13 100
Modulus of
Rupture
lb. per sq. in.
32 600
26 000
27 300
25 200
27 600
25 500
27 500
24 000
33 300
26 800
20 600
21 800
33 300
23 800
Modulus of
Elasticity
lb. per sq. in.
11 000 000
12 700 000
9 700 000
7 780 000
8 300 000
8 600 000
10 200 000
14 300 000
11 840 000
8 800 000
6 500 000
10 900 000
12 400 000
9 700 000
Remarks
Failed at top.
Failed at bottom.
Failed at top.
Failed at bottom.
do.
Failed at top.
Failed at bottom.
Failed at top.
Failed at bottom.
do.
Failed at top.
Failed at bottom.
Failed at top.
Failed at bottom.
the pipe as tested contained the bell of the original pipe (given in
Table 3, under the heading of Cast-Iron Pipes). Table 9 gives the re-
sults of the concentrated-load tests and Table 10 (p. 42) the results of
the distributed-load tests.
In Fig. 16 to 21 (p. 34 to 41) are given diagrams showing the
amount of the vertical and horizontal deflections of the pipe, at both
the spigot end and the bell end, which were produced under the load
per lineal foot of pipe or ring indicated by the vertical scale. These
diagrams will be discussed for the two methods of loading.
No.
991A
991 B
992B
993B
994B
994C
995A
995B
996A
996B
997A
997B
998A
998B
TESTS OF CAST-IRON AND REINFORCED CONCRETE CULVERT PIPE
18. Concentrated-Load Tests.-The cast-iron rings which were
tested under a concentrated load gave phenomena similar to what
would be expected from the analysis of the bending moments and re-
sisting moments. As is shown on the diagram in Fig. 16, the amount
0oo-00 -+-
W0 4- 1 M/ 11116 + Z - i T -
/0 00 7^^=a/:?^ =
2 - --f. ay _ - _ _ - V- _
0s , __0 I
+*a I- I--- -,, - " " " - - HfS9 M j
0oo - T _ . j ",
/OOCT^-^t 4& U ^
T// "? T T?'! L T ~ /
-o00 MaX -2 0 as ft.-6C0
jJj~J0XO~44444]4
QAtar
- 00 iL d 2122
/0001-4--
+*~oer
-70
77
F
liii
I III
0.0 O0 0.0 0 .0 00/ 00 0C1 00 0
00 0/ O. 2 00 O.f O.o 0.0 .0 0 0.0 0a 0O 03 00 O./ oz 03
IjEr-ECT701Rons WV INCHES
FIG. 15. LOAD-DEFLECTION DIAGRAMS FOR CAST-IRON TEST SPECIMENS.
/
I
IIII
IIII
_.
B 6 . . . . . . . . .
ILLINOIS ENGINEERING EXPERIMENT STATION
of deflect'on is nearly proportional to the applied load. The value of
the modulus of elasticity given in Table 9, calculated from equation
(20) for loads and deflections near the breaking load, 10 200 000 lb.
per sq. in., is somewhat smaller than the average value of the modulus
of elasticity determined from the tests of rectangular specimens cut
from the pipe given in Table 2. The latter are determined from the
straight portion of the load-deflection diagrams given in Fig. 15. This
is not unexpected for a material as variable in its elastic properties as
cast iron and with such a difference in form as the ring and the straight
rectangular beam. It seems that the value of the modulus of elasticity
determined from the deflections of the rings may best be used in the
investigation of the rings and pipes.
15000 1 1 o I " l II I ! [ I I E" I I I I I I I
14
.W0
L -
lom H
14 4"I -i i I ' I ~ I I II - ... I I I 1 1 1 .
.rH'~q1Y6o //Y 'Aq~t rfp /11/tI HtJ14ý
FIG. 16. LOAD-DEFLECTION DIAGRAMS FOR CAST-IRON RINGS.
CONCENTRATED LOAD.
At the maximum load sustained the rings failed at either the top
or the bottom, and the rupture extended over the entire length of the
pipe in every case. This accords with the theoretical determination
already made, it having been found that the bending moment at the
top or bottom is about 1,6 that at the extrem:ties of the horizontal
I
I
I
TESTS OF CAST-IRON AND REINFORCED CONCRETE CULVERT PIPE
diameter. After rupture occurred the machine was in some cases run
on down to give greater deflections, but the load then sustained was
much less than the breaking load and the rings finally broke again,
this time at the ends of the horizontal diameter.
10000
56OO0
50000
/5000
15000
k
/SO00
10000
S9000
4
-m
-4
iI~
7fi
''. - - ... I. ....IIII .1I. :I 1
Io000
/0000
.-1000
CH,/6m/ O/t mNeTrf /YI /IchfJ
FIG. 17. LOAD-DEFLECTION DIAGRAMS FOR 48-IN. CAST-IRON PIPES.
DISTRIBUTED LOAD.
El -
z
-i-
-H
36 ILLINOIS ENGINEERING EXPERIMENT STATION
It will be seen that the average value of the modulus of rupture
calculated by equation (10) and given in Table 9, is 27 000 lb. per sq.
in. This is 25% less than the value of the modulus of rupture given
s.500
i000<
.500e
40000
4500,
co000
5004
10000
eooo
FIG. 18. LOAD-DEFLECTION DIAGRAMS FOR 48-IN. CAST-IRON PIPES.
DISTRIBUTED LOAD.
Cmv cMG£ /.r 9m17,-rcP li ,,'meH£i
TESTS OF CAST-IRON AND REINFORCED CONCRETE CULVERT PIPE
in Table 2 as determined by loading at the center the rectangular test
specimens taken from the rings. The difference which exists in the
distribution of the stresses by these two methods of testing and the dif-
FIG. 19. LOAD-DEFLECTION DIAGRAMS FOR 36-IN. CAST-IRON PIPES.
DISTRIBUTED LOAD.
CH1fMCe /&f p0IYMr"R /M 11C£,Y5
ILLINOIS ENGINEERING EXPERIMENT STATION
ferences in strength of the materials in the two directions will partly
account for this difference. It seems probable that the results given
in Table 9 are more nearly representative of the condition in the rings
and pipes, and in the calculations for the pipes and rings under distrib-
uted load the value obtained in the concentrated tests of the corres-
ponding ring has been used.
19. Phenomena of the Distributed-Load Tests.-In the distrib-
uted-load tests the pipe or ring was bedded in sand, the load was ap-
plied through a saddle resting on sand, and the sides of the test box
Z'
N HIY/5f6E 11 I/RIfT[eP /X /Z7eH,5
FIG. 20. LOAD-DEFLECTION DIAGRAMS FOR 48-IN. CAST-IRON RINGS.
were restrained, as described on p. 29. It is not probable that such
a method of loading will give a uniform distribution of the load either
longitudinally or transversely. It is evident from a study of results
that the distribution of the load is uncertain and that the amount of the
lateral restraint is also uncertain. While for the purposes of calcula-
tion and discussion the distribution of the pressure may be assumed to
be uniform over a horizontal section, yet it is plain that this does not
express at all accurately the manner in which the load was distributed.
However, a uniform distribution of the load may be used as a basis of
comparison of the discussion of the results. A study of the load-de-
flection diagrams given in Fig. 17 to 21, will show that the deflection at
the spigot end generally began at once and increased nearly proportion-
ally to the amount of the applied load, as is indicated by the approx-
imation to a straight line. This is in accord with the analysis and with
the form of equation (22). At the bell end the deflections lagged be-
TESTS OF CAST-IRON AND REINFORCED CONCRETE CULVERT PIPE
hind and generally formed a curved diagram. It is evident that the
great stiffness of the bell is the cause of this and that after the barrel
of the pipe becomes distorted the effect is transmitted to the bell in
varying proportions. At a load varying from 75% to 100% of the maxi-
mum a crack appeared in the top or bottom of the pipe except in No.
996 where it appeared at one side. Usually with an increase of load
this crack extended toward the other end, and finally the pipe broke
throughout the full length at or near the maximum load. This break
generally occurred at the top or bottom of the pipe, and gave a loud
report. The further operation of the testing apparatus gave increased
deflections, sometimes without a material reduction in the load and
sometimes at a much lower load, until the pipe broke at some other
point in the section.
The general phenomena of the tests of the cast-iron pipes are given
in the following notes.
No. 990. Diameter 48 in. Length 6 ft. 8 in. over all. Variable thickness, ranging
from Y4 in. to 13% in. Heavy bell. Center of loading apparatus placed 12 in. from
middle of pipe toward bell end. Crack appeared in barrel next to bell at a load of
26 700 lb. per lin. ft. At 27 900 lb. the crack extended from the bell 7 in. At 30 300
lb. the crack extended 1Y2 in. into the bell and at 31 500 it extended entirely through
the bell and 14 in. along the barrel. At 36 300 lb. a crack appeared on the north
side next to the bell. At 37 500 lb. per lin. ft. complete failure occurred, the crack
on north side extended from end to end, a crack in the south side appeared and
extended from the spigot end to within 2 ft. of the bell and then through the bell, and
a crack formed at the bottom. Test discontinued.
No. 991. Diameter 48 in. Length 8 ft. 3 in. over all. Light-weight pipe, 7000
lb. for a 12-ft. net length. Average thickness 1Y4 in. Loaded 2 in. off center. At a
load of 22 600 lb. per lin. ft a crack appeared at the top and extended 3 ft. from the
spigot end. At 24 500 lb. a crack appeared at the bottom and extended through the
bell and 3 ft. into the barrel. At 26 500 lb. per lin. ft. complete failure occurred,
the crack at the bottom extended the full length of the pipe and the crack at the top
extended past the center. The load dropped to 26 000 lb. and cracks appeared at
both north and south sides. Test discontinued.
No. 992. Diameter 48 in. Length 8 ft. 3 in. over all. Light-weight pipe, 6900
lb. for 12-ft. net length. Small bell. Average thickness 1.3 in. Loaded 2 in. off center.
At a load of 16 300 lb. per lin. ft cracks formed at the top and bottom and extended
through the bell 8 in. into the barrel. At 17 700 lb. the bottom crack extended from
end to end, and at 18 700 lb. the top crack extended likewise. At 21 600 lb. both
sides cracked from end to end. The load dropped off, and finally rose again, reaching
22 600 lb. per lin. ft. Test discontinued.
No. 993. Diameter 48 in. Length 8 ft. 5 in. over all. Heavy-weight pipe, 8900
lb. for 12-ft. net length. Average thickness 1.42 in. Loaded 22 in. off center.
No crack appeared until the maximum load of 54 600 lb. per lin. ft., when the pipe
cracked from end to end at the top. The load dropped off to about 44 000 lb per lin.
ft., and the pipe almost immediately cracked from end to end at bottom and two
sides without further application of the testing apparatus. Test discontinued.
No. 994. Diameter 48 in. Length 8 ft. net. Heavy-weight pipe, 8900 lb. for
12-ft. net length. Average thickness 1.58 in. This pipe was cut into two pieces and
the end of one was loosely inserted in the bell of the other at the middle of the testing
box. The piece containing the bell is denoted as the bell section, and the other the
ILLINOIS ENGINEERING EXPERIMENT STATION
spigot section. The center of the loading apparatus was over the bell. The first crack
appeared in the bell at the top and extended 2 ft. into the barrel at a load of 47 200
lb. per lin. ft. At the maximum load of 49 300 lb. per lin. ft. this crack extended the
full length of the bell section. No crack appeared in the spigot section. Test dis-
continued.
No. 995. Diameter 36 in. Length 8 ft. 0 in. over all. Light-weight pipe, 4575
lb. for 12-ft. net length. Average thickness 1.02 in. Loaded 2Y/ in. off center. At
a load of 19 300 lb. per lin. ft. a crack appeared and extended along the top 6 ft.
from the spigot end. This crack lengthened at succeeding loads and extended from
end to end at the maximum load of 22 300 lb. per lin. ft. At this load a crack appeared
at the bottom and extended from end to end. Cracks also appeared at the sides at the
spigot end and instead of extending along an element of the cylinder they turned
upward and joined the first crack at the top just inside the bell. Test discontinued.
No. 996. Diameter 36 in. Length 8 ft. 0 in. over all. Medium-weight pipe,
5600 lb. for a 12-ft. net length. Average thickness 114 in. Loaded 21 in. off cen-
ter. The first crack appeared at one side at the spigot end at a load of 37 300 lb.
per lin. ft., and extended 6 ft. The load dropped off and a crack at once appeared
on the other side extending almost the entire length of the pipe. Upon increasing the
deflections, at a load of 30 300 lb. a crack appeared at the top and extended from end
to end, and with further deflection the one side crack extended through the bell and
the other turned upward and joined the top crack just inside the bell. The crack at
the bottom extended from end to end. Test discontinued.
No. 997. Diameter 36 in. Length 8 ft. 0 in. net. Light-weight pipe, 4300 lb.
for a 12-ft. net length. Nominal thickness 1 in. This pipe was cut into two pieces
and the end of one was loosely inserted in the bell at the middle of the testing box.
The center of the loading apparatus was over the bell. The first crack appeared in
the bell at the top at a load of 25 200 lb. per lin. ft. and was 4 in. long. At the maxi-
mum load, 27 300 lb. per lin. ft. this crack had lengthened to 20 inches. The load
dropped to 25 500 lb., and with increased deflection, a crack formed in the bottom of
the bell section passing through the bell 24 in. into the barrel. This was at once fol-
lowed by the formation of a crack at the bottom in the spigot section extending
from end to end. With further application of the testing apparatus the cracks at the
top and bottom of the bell section extended from end to end at a load but little below
the maximum. Finally both sections had cracked from end to end at all four quarter
points. Test discontinued.
No. 998. Diameter 36 in. Length 8 ft. 0 in. net, cut in two sections, with the
bell placed in the center as in No. 997. Medium-weight pipe, 5700 lb. for a 12-ft.
net length. Nominal thickness of barrel 114 in. Center of load over bell. First
crack appeared at both top and bottom of the bell section at a load of 29 200 lb. per
lin. ft. and was 6 in. long, soon extending to 18 in. The bell section cracked end to
end at the top and half of the length at the bottom at the maximum load, 37 200 lb.
per lin. ft. On increasing the deflection at about the same load, the spigot section
cracked from end to end at both top and bottom, and the bell section cracked from
end to end along the south side. Test discontinued.
In the tests of cast-iron rings No. 992A and 993A under a distrib-
uted load, the first crack appeared at the bottom at the maximum load
and extended from end to end. The diagram is given in Fig. 20.
The effect of the lateral restraint is illustrated in the results of a
preliminary test on Pipe No. 990. In this test, the hydraulic jack ma-
chine was not used, but I-beams were used to transfer the load from th e
600 000-lb. testing machine to the saddle, since the box was too large
to be placed on the bed of the machine. The distance of the saddle
from the testing machine was such that only one-fifth of the load on the
TESTS OF CAST-IRON AND REINFOCRED CONCRETE CULVERT PIPE 41
machine was applied to the saddle. The load was run up to 16 200 lb.
per lin. ft. on the pipe. At this load the change in the vertical di-
ameter was 0.37 in. The load having been taken off, the rods holding
the sides of the box were loosened and kept loose and pressure again
applied. This time, at a load of 15 500 lb. per lin. ft., the average
change in the vertical diameter was 1.05 in. with no sign of failure.
When the load was removed there was a set of 0.65 in. at the spigot
i-.
/j l 1 lt
-^ I'-- ^7 ^-7 +-
-__5,01ýp- --
. - --pI9fo [nd -
Cq Iz- ii, //Y-lf ý" //Y 1/ C10'[J
FIG. 21. LOAD-DEFLECTION DIAGRAMS FOR PIPE No. 990 TESTED WITH AND
WITHOUT LATERAL RESTRAINT.
end. Four hours-later this set was reduced to 0.30 in. The deflections
in the two, tests are shown in Fig. 21. This pipe was finally tested to
destruction in the hydraulic jack machine, the first crack appearing at
a load of 26 400 lb. per lin. ft. and the pipe finally carrying 37 500 lb.
per lin. ft. as has already been described.
20. Comparison and Discussion.-Table 10 gives data of the dis-
tributed load tests of the cast-iron pipe and rings. The loads are
given in pounds per foot of length of ring or pipe. The first crack for
which the load is given appeared at the bell end in four pipes and at
the spigot end in three. In No. 993 the crack ran from end to end and
in No. 994, in which the pipe was cut and the spigot end placed in the bell
at the middle of the test box the first crack was at the bell. The break-
ing load was the maximum load and generally the indicated load of the
testing apparatus fell off at once though in some cases the maximum
load held until the deflections had been increased somewhat. M' is
the bending moment based on a uniform distribution of the breaking
load over the horizontal section of the pipe and without any allowance
for lateral pressure or restraint, as calculated by equation (7). Mo is
the resisting moment of a rectangular section of the pipe, calculated
with the value of the modulus of rupture f determined from the con-
S20000
K
K1O000
S10000
5000
0
ILLINOIS ENGINEERING EXPERIMENT STATION
centrated-load tests of the rings cut from the pipe, except that for No.
990, from which no ring was cut, the average modulus of rupture de-
termined from other pipe was used. In the expression for the resisting
moment b is the length of pipe or ring and t is the average thickness.
The last column gives the ratio of the resisting moment to the bending
moment thus calculated. If Mo properly measures the resisting mo-
TABLE 10
CAST-IRON PIPE AND RINGS. DISTRIBUTED LOAD
W' W M' Mo Ratio
Load at Breaking
No. First Crack Load Wd fbt Mo
lb. per lb. per - -
lin. ft. lin. ft. 16 6 M'
Pipes
Rings
992A 22 150 22 150 68 000 92 500 1.36
993A 29 250 29 250 90 000 104 000 1.16
ment and if the load is uniformly distributed over the horizontal section
in both the longitudinal and transverse direction this ratio should be
unity. If there is lateral pressure of the sand similarly distributed over
the vertical section, the value of the ratio should be less than unity and
would represent the 1 - q of equation (9). That is to say, if the ratio
is 0.75 the lateral pressure would, by this method of reasoning, be 25%
of the vertical load. This treatment does not consider the effect of the
greater strength and stiffness of the bell nor the effect of the stiffness of
the bell upon the stresses in the barrel next to the bell. It is seen that
there is a considerable variation in the value of this ratio. The higher
values may be due to an uneven distribution of the load either longi-
tudinally or transversely. In cases where the break occurred at one end
or the other the lack of distribution seems evident. It is possible that
TESTS OF CAST-IRON AND REINFORCED CONCRETE CULVERT PIPE
in these cases the pipes were not so well bedded or that the sand was
not so well packed about them. The lower values of the ratio indicate
considerable lateral pressure. Evidently there is a great variation in
condition of loading and the distribution of the pressures and it is pos-
sible that uneven resisting stresses of the pipe may account partly for
this variation. This question will be discussed further on.
V. EXPERIMENTAL DATA WITH CONCRETE AND REINFORCED
CONCRETE PIPE AND RINGS
21.. Data of Tests.-Table 11 gives dimensions and other data of
concrete and reinforced concrete rings and Table 12 of reinforced con-
crete culvert pipes.. Table 13 gives manner of loading of the plain and
reinforced concrete rings and pipes and the. loads carried. Tables 14
and 15 give the results of the concentrated load tests and Tables 16 and
17 the results of the distributed load tests. These will be discussed for
the two methods of loading under different heads.
In Fig. 22 to 27 (p. 47 to 55) are given diagrams of the amount of
the vertical and horizontal deflections of the pipe and rings which were
produced by the load per lin. ft. of length of pipe indicated by the ver-
tical scale. These diagrams will be discussed for the two methods of
loading.
22. Concentrated-Load Tests.-The method used in testing the
cast-iron rings and pipes was used for the tests on concrete and rein-
forced concrete rings. As the plain concrete rings broke before there
was an appreciable deflection no measurement of deflections was made.
The modulus of rupture calculated from equation (10) is given in Table
14. The average modulus of rupture obtained from the 1907 tests of
the small concrete beams was 195 lb. per sq. in. It is seen that the
modulus of rupture from the ring tests is 20% higher than the modulus
of rupture found in the beam tests. This variation is in the opposite di-
rection from that found in the computation of the modulus of rupture
of the cast-iron rings and the test beams. The variation in the values
for the concrete is probably explainable by difference in the conditions
attending setting in the two kinds of test pieces and by differences in
the development of the stresses. As before, the value of the modulus
of rupture obtained in the rings will be considered the better as a basis
of comparison.
All failures occurred in either the top or bottom section of the cyl-
inder as is to be expected from the relative value of the bending mo-
ment at these points and that at the extremities of the horizontal di-
ameter. The breaks were sudden and the load which could be carried
ILLINOIS ENGINEERING EXPERIMENT STATION
TABLE 11
CONCRETE AND REINFORCED CONCRETE RINGS
Internal
No. Diameter
901
902
907
908
911
912
903
906
921
922
927
951
926
928
931
932
933
*934
952
953
*971
*972
+976
t977
inches
48
44
44
it
it
Thick-
ness
inches
6
it
it
it
it
4
'4
cc
Iti
it
it
1i
It
41
41
it
iti
aI
11
"
a
"
Reinforcement
Length
inches
24
it
11
it
it
I,
ii
It
It
it
I,
14
It
41
a
"
"
"a
"
it
ti
Per cent
Kind
None
It
"
it
41
8 11/4-in.
corr. bar.
9 1
it
"
(I
I(
it
it
it
It
I(
I,
it
"
"
"
"
Age at
Test
days
37
36
40
35
42
41
36
34
36
41
38
36
38
32
44
31
37
34
98
36
45
93
87
92
90
*In these rings the reinforcing steel was flattened at top and bottom.
fin these rings stirrups were used, three at top and bottom.
TABLE 12
REINFORCED CONCRETE CULVERT PIPE
Reinforcement
Internal thAge at
No. Diameter Thickness ength Test
inches inches inches Kind Per days
cent
981 48 4 102 Y4-in. corrugated bars 0.66
982 48 4 104 }s-in. corrugated bars 1.39 149
983 48 4 102 /4-in. corrugated bars 0.66 118
988 48 4 104 Clinton mesh, No. 3 0.88 183
wire
987 36 4 102 Fence wire 0.28 92
0
it
It
it
it
it
0.80
it
it
ti
0.73
0.80
0.73
0.66
1.00
0.80
1.00
0.89
0.73
0.66
"
901
902
907
908
911
912
903
906
n),)
TESTS OF CAST-IRON AND REINFORCED CONCRETE CULVERT PIPE
TABLE 13
CONCRETE AND REINFORCED CONCRETE RINGS AND PIPE
DATA OF TESTS
Age at Maximum
No. Test Manner of Critical Load Load
days Loading lb. lb.
Rings
901 37 Concentrated
36
40
35 "
42
41
36
34
32
44
31
37
34
98
36
45
93
36
41
38
36
38
88
92
90
14
"
Distributed
it
Concentrated
"t
D i
Distributed
"
a
"t
ti
n
t
Ditibtd
"
14 000
20 000
20 000
16 000
18 000
16 000
18 000
20 000
902
907
908
911
912
903
906
926
928
931
932
933
934
952
953
971
923
921
922
927
951
972
976
977
5 000
3 900
5 600
5 200
3 000
4 200
61 000
88 000
5 700
7 100
5 000
6 000
6 350
6 300
4 700
7 200
8 250
21 000
47 000
37 000
52 000
50 000
35 000
38 000
32 000
Pipe
985 & 6
981
982 149
983 118
988 183
987 92
Distributed
"
"
"
"
"
200 000
166 000 268 000
129 000 215 000
106 000 202 000
76 500 262 000
76 500 202 000
after this break was very much less than the load at the time of the
formation of the cracks.
The reinforced rings deflected considerably before final failure, as
shown in Fig. 22. At a load of 1000 to 2150 lb. per lin. ft., fine cracks
appeared in the tension face, generally at the top or bottom much as
they appear in tests of reinforced concrete beams. With the applica-
tion of higher loads, numerous fine cracks appeared on the tension faces
20 000
ILLINOIS ENGINEERING EXPERIMENT STATION
TABLE 14
CONCRETE RINGS. CONCENTRATED LOAD
W. A. Slater's 1906 Tests.
1265
3720
2110
6040
1907 Tests.
at the top, bottom, and sides. Two forms of critical failure were appa-
rent; one a tension failure of the reinforcing bars at the top or bottom
of the ring (stretching beyond the yield point of the metal), and the
other a failure of the concrete by the stripping and shearing of the con-
crete from the tension face. The latter form of failure may correspond
to the diagonal tension failure in beams. Sometimes the concrete was
split off along the reinforcing bars and these bars were straightened
from their original circular form. The following are notes of the tests:
No. 932. Fine cracks at top, bottom, and sides at 1500 lb. per lin. ft. At the
maximum load of 3000 lb. per lin. ft. the deflection was 0.85 in. Later the concrete
began to strip off.
No. 933. A fine crack appeared at the top at 1150 lb. per lin. ft., and at bottom
at 1350 lb. per lin. ft., cracks at sides at 2100 lb. per lin. ft. At the maximum load,
3170 lb. per lin. ft., the deflection was 0.8 in.
No. 934. A fine crack appeared at the top at 1300 lb. per lin. ft., at the bottom
at 1550 lb. per lin. ft., and at the sides at 2050 lb. per lin. ft. At 3050 lb. per lin. ft.
the deflection was 0.73 in. and at the maximum load, 3150 lb. per lin. ft., it was 1.05
in., and the cracks at the top and bottom soon opened up Y in., showing tension
failure.
No. 928. A fine crack appeared at the bottom at 1400 lb. per lin. ft. and one at
the top at 1600 lb. per lin. ft. These were soon followed by various fine cracks at
TESTS OF CAST-IRON AND REINFORCED CONCRETE CULVERT PIPE
the sides, bottom, and top. Deflection at 3450 lb. per lin. ft. was 0.88 in., and at the
maximum load of 3550 lb. per lin. ft., 1Y4 in.
No. 931. Fine cracks appeared at bottom and top at a load of 2200 lb., per lin.
ft. At the maximum load, 2500 lb. per lin. ft. the deflection was 0.49 in. On further
deflection the concrete inside the reinforcing bars at the top and bottom stripped off.
No. 952. A fine crack appeared at the bottom at 1000 lb. per lin. ft., at the
sides at 1250 lb. per lin. ft., and at the top at 1450 lb. per lin. ft. At a load of 2250
lb. per lin. ft., the deflection was 0.97 in. at the maximum load, 2350 lb. per lin.ft.,
the concrete split off and the rods broke through at the top.
No. 953. A fine crack appeared at the bottom at a load of 1200 lb. per lin. ft.,
one at the top at 1350 lb. per lin. ft., and at the sides at 2200 lb. per lin. ft. Many
fine cracks then appeared at bottom, sides, and top. At a load of 3300 lb. per lin.
ft. the deflection was 0.77 in., and at the maximum load, 3600 lb. per lin. ft., 1.57 in.
No. 971. Fine cracks appeared at the top and bottom at 1500 lb. per lin. ft. and
at the sides at 1750 lb. per lin. ft. At the maximum load, 4120 lb. per lin. ft., the
deflection was 0.6 in. Failed by tension in the steel at both top and bottom.
No. 926. Fine cracks appeared on the inner face at the top and bottom at a
load of 1500 lb. per lin. ft. More fine cracks appeared near these at 2000 lb. per lin.
ft., and the number of such cracks increased as the load was increased. Two cracks
at the bottom increased in size, and one of these became quite large before the
maximum load was reached, indicating a failure of the ring by tension in the steel.
The maximum load was 2850 lb. per lin. ft. with a deflection of 0.53 in. The load
then fell off, and as the deflections were increased by running the head of the testing
machine down, part of the bottom sheared off on either side of the support and the
concrete split off between the reinforcing rods and the inside surface of the ring.
I,.
14
k
kfO
6"H'O£A'1 //i Dn/lip Tr //n ICH[.5
FIG. 22. LOAD-DEFLECTION DIAGRAMS OF REINFORCED CONCRETE RINGS.
CONCENTRATED LOAD,
Table 15 gives the calculated moments at the maximum loads.
In part of them failure came by splitting of the concrete along the re-
inforcing bars. In some cases this was caused by imperfect fabrication,
the bars being left too close to the interior face of the ring. The de-
flection curves have much the same characteristics. The maximum
load gave a deflection of 0.5 to 0.8 in.
ILLINOIS ENGINEERING EXPERIMENT STATION
23. Distributed-Load Tests. of Concrete Rings.-The plain con-
crete rings which were tested under a distributed load, bedded and
covered with sand and restrained at the sides as already described,
cracked at the bottom, top, and sides at an early load. With the con-
tinued application of the testing apparatus the load dropped off at first
until at a somewhat greater deflection sufficient side restraint had been
developed when the load again increased and continued to rise until
TABLE 15
REINFORCED CONCRETE RINGS. CONCENTRATED LOAD
Load at First
Crack Maximum Load
lb. per lin. ft. lb. per lin. ft.
1500 2850
1400 3550
2150 2500
1500 3000
1170 3170
1300 3150
1000 2350
t
inches
2.75
2.5
2.75
3.0
2.0
2.5
2.0
0 o2
IZu U 60.uU
1500 4120 2.75
0.16 Wd
23 700
29 500
20 800
25 000
26 400
28 400
19 600
29 900
34 500
0.87 Aft
26 600
24 200
26 600
29 100
19 400
Ratio
1.12
0.82
1.28
1.16
0.73
19 400 0.99
21 800 0.73
26 600 0.77
a considerable change had been made in the vertical and horizontal
diameters when the test wag discontinued. The load-deflection dia-
grams are given in Fig. 25 for No. 903 and No. 906. The following
are notes of the tests of the two plain concrete rings.
No. 903. At a load of 3550 lb. per lin. ft. and a deflection of 0.09 in., a crack
appeared at the bottom and the load dropped off to 2150 lb. per lin. ft. The indi-
cations were that the pressure of the sand of the bed was not well distributed. As
the loading head was run down, cracks appeared at the east side of the ring at a load
of 2150 lb. per lin. ft., the crack at the bottom opened to 1-16 in., and a crack formed
at the top of the ring. At 2500 lb. per lin. ft. the crack at the bottom had opened
to Y in. As the deflections were increased, the indicated load increased, and the
cracks at the top, bottom, and sides increased in width, though the amount of the
opening of the cracks at the sides could not well be measured. At a load of 8000 lb.
per lin. ft. and a deflection of 1.45 in., the crack at the bottom was Y in. wide and that
at the top Y in. At 13 000 lb. per lin. ft. another crack appeared at the west side
6 in. above the horizontal diameter, and crushing of the concrete at the extremities
of the horizontal diameter became apparent. The crack at the bottom was Y in.
wide and that at the top 2 in. At 23 000 lb. per lin. ft. a crack appeared on the west
side somewhat above the horizontal diameter. At 30 500 lb. per lin. ft. the vertical
diameter was 3 ft. 7Y in. and the horizontal 4 ft. 412 in. The test was discontinued,
although the ring was still taking an increasing load.
No. 906. At a load of 4800 lb. per lin. ft. and a deflection of 0.03 in. a crack
appeared at the bottom. At 4950 lb. per lin. ft. one appeared at the top. The load
fell off to 4250 lb. per lin. ft. At a deflection of 0.3 in. and a load of 5050 lb. per lin.
ft. cracks formed at the sides. These cracks gradually widened as the deflections and
No.
926
928
931
932
933
934
952
953
971
I
TESTS OF CAST-IRON AND REINFORCED CONCRETE CULVERT PIPE
loads were increased. A new crack appeared at one side 8 in. above the extremity
of the horizontal diameter at 15 500 lb. per lin. ft. and one in a similar place on the
other side at 20 500 lb. per lin. ft. The crack at the bottom was 14 in. wide at a
load of 10 500 lb. per lin. ft., 2 in. at 30 500 lb. per lin. ft., and 4 in. at 40 500 lb.
per lin. ft., and that at the top was 3-16, 5-8, and 1 in., at the same loads. At the
maximum load of 44 000 lb. per lin. ft., there was crushing at the sides, and a cir-
cumferential crack formed. The vertical diameter was 3 ft. 812 in. and the horizontal
4 ft. 3Y2 in.
It is evident that in these tests after the cracks appeared the rings
did not act as a single structure but instead formed four pieces under
equilibrium somewhat as shown in Fig. 23. Without adequate lateral
restraint, equilibrium would not be maintained, and if the elasticity of
FIG. 23. ACTION OF UNREINFORCED PIPE UNDER DISTRIBUTED LOAD.
an embankment failed, stability would be lost. With the lateral pres-
sure maintained, failure occurs by crushing of the concrete.
Fig. 24 gives the load-deflection diagram for the Jackson pipe. It
will be seen that the curves are similar to those for the plain concrete
rings.
24. Distributed-Load Tests of Reinforced Concrete Rings.-The
tests on the reinforced concrete rings and pipe followed the method
used in the tests of the cast-iron rings and pipe. The reinforced con-
crete rings were tested in the small box, using the 600 000-lb. testing
machine, and the reinforced concrete pipes were tested in the hydraulic
jack machine.
In the reinforced concrete rings cracks appeared early in the test
on the tension side at the top and bottom, but the load continued to
increase, and from this point to a load of 12 000 lb. per lin. ft. the re-
ILLINOIS ENGINEERING EXPERIMENT STATION
inforced concrete rings were much stiffer than the plain concrete rings
and were evidently acting as reinforced concrete structures. During
this stage numerous cracks appeared at the top, bottom, and sides sim-
ilar to the tension cracks found in the test of reinforced concrete beams,
K
30000
1,000
30000
~.10 000
SO000
. O1 O
2 H/Lf/6E /LE 9/ DAfreAlP //y / ACSOej
FIG. 24. LOAD-DEFLECTION DIAGRAMS FOR "JACKSON" PIPE.
and these increased in size. In part of the rings the cracks at the top
and bottom increased in width to such an extent as to show failure by
the steel becoming stressed past its yield point. In a number of the
rings this did not occur, but instead the concrete was stripped or split
off over the bars by the bars straightening out and pulling away
from the interior concrete. In a few cases this was due to poor fabri-
cation, the bars being placed too close to the inner surface, but evi-
dently this feature is a source of weakness in such construction. In
No. 972, in which the bars at the top and bottom are made with a
much flatter arc, and in No. 976 and 977, in which stirrups were used,
stripping of the concrete did not develop and the steel was stressed be-
yond its yield point. This was done also in No. 923. In all cases
after the yielding of the steel or the stripping of the concrete the action
of the ring in the test was much the same as in the tests of the plain
concrete rings, and there seems to be no characteristic difference either
in the loads or the amount of deflection except that the cracks did not
open up wide at the sides and the angular displacement was distributed
I
TESTS OF CAST-IRON AND REINFORCED CONCRETE CULVERT PIPE 51
e000,
Z0,90,
A0oo
1000
Soo00
Qs
If-
IVc
.f,9
*-'4
. 00
I 0
loo
^f0
Cltlrle /11 d9/1ncrfe // IMCHe.5
FIG. 25. LOAD-DEFLECTION DIAGRAMS FOR CONCRETE AND REINFORCED CONCRETE
RINGS. DISTRIBUTED LOAD.
ILLINOIS ENGINEERING EXPERIMENT STATION
over a larger number of cracks. This view is borne out by the fact that
for this stage of the test the deflections for all the reinforced concrete
rings (see Fig. 25), fall between the lines for No. 903 and 906, the two
plain concrete rings. It is evident that the action of the ring in the
later part of the test is much the same as that of the plain concrete
TABLE 16
CONCRETE RINGS AND PIPE. DISTRIBUTED LOAD
Load at
First Crack
lb. per
lin. ft.
3 550
4 800
2 000
Resisting
Moment
*ifbtl
17 640
17 640
12 250
16 Wd Ratio
12 000 0.68
16 200 0.92
6 630 0.54
Maximum
Load
lb. per Remarks
lin. ft.
30 500 Load still going
up. Test discon-
44 000 tinued.
40 000 Pipes from Jack-
son, Michigan.
*Assume f = 245.
rings in that equilibrium is maintained by the lateral restraint of the
sand and that the integrity of the structure is based upon the develop-
ment and the maintenance of this lateral pressure. The following are
notes of the tests:
No. 921. A fine crack appeared at the bottom at 3500 lb. per lin. ft. at a deflec-
tion of 0.14 in., two more at 4500, and one at top at 5000 lb. per lin. ft. The concrete
began breaking off at the bottom at 5500 lb. and at the top at 7000 lb. per lin. ft.
The rods broke through and the concrete stripped off at 9000 lb. per lin. ft. Cir-
cumferential cracks appeared at a load of 13 000 lb. per lin. ft. and others appeared
at higher loads. Crushing at sides noticed at 16 500 lb. per lin. ft. and was crushing
freely at a load of 23 500 lb. per lin. ft., when the deflection was 5.5 in.
No. 922. Fine crack appeared at bottom at 3500 lb. per lin. ft. and one at top
at the same load. Other cracks appeared at top and bottom from 4500 to 6500 lb.
per lin. ft. and at sides 7500 lb. per lin. ft. Rods broke through concrete at 12 500 lb.
Load continued constant at 18 500 lb. per lin. ft.
No. 923. In this test the rods holding the sides of the box were loosened at times,
leaving little side restraint. The load then would not increase until there was sufficient
increase in the diameter to bring added pressure against the ring. A fine crack ap-
peared at the bottom at 2250 lb. per lin. ft. and one at the top at 3000 lb. per lin. ft.
Crushing at sides at 8000 lb. per lin. ft., and circumferential cracks formed. At 10 500
lb. per lin. ft. one rod broke out at bottom. Test discontinued. The large deflection
due to this method of testing is shown in Fig. 23.
No. 927. Fine crack at top and bottom at 3500 lb. per lin. ft. Other fine cracks
formed at higher loads. Concrete stripped at bottom at 8500 lb. per lin. ft. Crushing
at sides at 13 000 lb. per lin. ft. Freely crushing at sides at 16 500 lb. per lin. ft.
Circumferential cracks formed at 23 000 lb. per lin. ft. Test discontinued at 26 000
lb. per lin. ft. and deflection of 4.4 in.
No.
903
906
985
&
986
TESTS OF CAST-IRON AND REINFORCED CONCRETE CULVERT PIPE
No. 951. Crack at bottom at 2950 and one at top at 4000 lb. per lin. ft. Other
cracks soon formed. Stripping at bottom at 12 000 lb. per lin. ft. Crushing at sides
at 14 000 lb. per lin. ft. Circumferential crack at top at 18 000 lb. per lin. ft. Test
discontinued at 20 000 lb. per lin. ft. and deflection of 4.1 in.
No. 972. Fine crack at top at 4500 and three at bottom at 5500 lb. per lin. ft.
Cracks opening up at 7500 lb. per lin. ft. Crushing began at 15 500 lb. per lin. ft.
Test discontinued at 17 500 lb. per lin. ft.
No. 976. Fine crack appeared at top and bottom at 4000 and 6000 and 7000
lb. per lin. ft. Three tension cracks finally opened up wide at the bottom and two at
the top. No evidence of bars pulling away from the ring. Crushing began at 19 000
lb. per lin. ft.
No. 977. Fine cracks appeared at top at 4000 and 6000 and at the bottom at
7000 lb. per lin. ft. More at 8000 lb. Bottom cracks were gradually opening at 9000
lb. per lin. ft. Failure by tension in steel at top and bottom was apparent at 16 000
lb. per lin. ft. No signs of bars pulling away. Crushing of concrete at 20 000 lb. per
lin. ft. Test discontinued at 21 000 lb. per lin. ft.
25. Distributed-Load Tests of Reinforced Concrete Pipe.-The
results of the distributed load tests of reinforced concrete pipe are quite
similar to those of the tests of rings. Fine cracks became visible on
the inner surface at the top and bottom at loads from 5000 to 11 000
lb. per lin. ft., the amount of the load depending upon the percentage
of reinforcement, and numerous fine cracks soon formed. Circumferen-
tial cracks appeared at loads somewhat greater, generally next to the
bell. At higher loads the cracks became somewhat larger though they
did not open up until much later and in several cases in place of ten-
sion cracks opening diagonal shear cracks appeared, similar to those
found in tests of reinforced concrete beams. As may be seen from Fig.
26 and 27 there was evidently a change in the character of the load-
deflection diagram at this time, and the critical load given in Table 17
is somewhat above the changes here noted. The amount of the deflec-
tion of the pipe at the time of the critical load averaged about 0.4 in.
In several cases stripping of the concrete from the reinforcing bars at
the top and bottom of the pipe occurred as in the tests of rings, but it
generally appeared later and was not so serious as in the case of the
rings. The action of the pipe at loads beyond the critical load above
referred to was quite different from that at previous loads, but the re-
inforcement evidently acted to hold the concrete together in the four
quarters and the pressure was concentrated near the edge at the four
quarter points, the pipe being held from total failure by the lateral
restraint formed by the pressure of the sand at the sides of the pipe
in much the same way as has already been described for the reinforced
concrete rings. Crushing of the concrete began to take place at the
sides and top at loads near the maximum load, and after the vertical
deflections had increased to three or four inches this crushing became
marked, the load dropped off, and the test was discontinued. Fig. 28
ILLINOIS ENGINEERING EXPERIMENT STATION
4o 000
40000
31000
30000
25000
2O 00
4I 000
_1000
J 000
2O00a
12000
1/,000
6000
FIG. 26. LOAD-DEFLECTION DIAGRAMS FOR REINFORCED CONCRETE PIPES.
DISTRIBUTED LOAD.
t
t _4'' tlýl
[F
_7
Tý4
4HIT
dl 1__ý t
ýýell '17a' -,:;0/?0/ IdT_ I
FTTTT
# #
__T
_4 4-,
_T_ a T_
T:
t
E
Ed
TESTS OF CAST-IRON AND REINFORCED CONCRETE CULVERT PIPE 55
45000
20000
J1000
a
e00
Zsoooo
/5000
K
20000
I
"N /6000
K
/O000
J6000
"N 20000
/ ooo
fooo000
_wooo
/000
e9
FIG. 27. LOAD-DEFLECTION DIAGRAMS FOR REINFORCED CONCRETE PIPES.
DISTRIBUTED LOAD.
ILLINOIS ENGINEERING EXPERIMENT STATION
and 29 give views of the condition of the reinforced concrete pipe at
the end of the test. The following are notes of the tests:
Pipe No. 981. This pipe, which was reinforced with n-in. corrugated bars,
was given a preliminary loading in the testing box, the load being applied through
I-beams used as levers. The center of the load was placed so that it was 11 in. closer
to the bell than was the center of the pipe. In this test cracks first became visible
at top and bottom at a load of 8100 lb. per lin. ft. These cracks extended from end
to end of the pipe. Others appeared at top and bottom as the deflection increased,
and circumferential cracks appeared in the bell at 11 100 lb. per lin. ft. The loading
was increased to 11 600 lb. per lin. ft. at which point the I-beams commenced to
buckle and the test was discontinued.
This pipe was afterward tested to destruction in the hydraulic jack testing
machine. This time the load center was 8 in. off the pipe center toward the bell.
The cracks above noted reopened and large radial and circumferential cracks appeared
in the bell at a load of 18 800 lb. per lin. ft. At 21 500 lb. per lin. ft. one crack in the
bottom was quite large from end to end and at 27 000 lb. per lin. ft. crushing of the
concrete commenced on the inside. Large pieces fell off the bell, exposing the steel
when 29 700 per lin. ft. was reached, and at 30 600 lb. per lin. ft. the maximum was
reached and the test discontinued.
Pipe No. 982. This pipe was reinforced with Y-in. corrugated bars and was
149 days old at the time it was tested. This pipe was heated by steam coils to
accelerate its hardening and an examination showed that the concrete was somewhat
injured thereby. It was loaded 8 in. off center. At a load of 11 000 lb. per lin. ft.
circumferential cracks appeared at top and bottom in the bell, and hair cracks ap-
peared at top and bottom in the spigot end. The cracks opened up wider as the
deflection increased and at 18 500 lb. per lin. ft. crushing commenced inside the bell
end, soon extending from end to end of the pipe. At 22 200 lb. per lin. ft. diagonal
FiG. 28. VIEW OF REINFORCED CONCRETE PIPE AFTER TEST.
TESTS OF CAST-IRON AND REINFORCED CONCRETE CULVERT PIPE
cracks appeared at top and sides somewhat like shear cracks and soon crushing
commenced on both sides about 20 degrees above the horizontal diameter. At a
load of 25 000 lb. per lin. ft. the test was discontinued.
Pipe No. 983. This pipe was reinforced with 4-in. corrugated bars. The load
center was 5 in. off the pipe center toward the bell. Tension cracks developed at the
top in both ends at a load of 4900 lb. per lin. ft. and a crack appeared at the bottom
at 6700 lb. per lin. ft. These cracks opened up wider and cracks appeared in the bell
at a load of 10 400 lb. per lin. ft. Crushing commenced on both sides at 21 600 lb.
per lin. ft. and at 23 400 lb. per lin. ft., the maximum, and the average change in the
vertical diameter of 3.03 in. was noted, which increased rapidly as the load was held
on the pipe.
Pipe No.987. This test was made with the load 2Y in. off center. This pipe, which
was reinforced with fence wire, cracked end to end at both top and bottom at a load
of 4950 lb. per lin. ft. At 6800 lb. per lin. ft. radial and circumferential cracks appeared
all through the bell. As the deflection increased the cracks opened wider and when a
load of 10 500 lb. per lin. ft. was reached, crushing commenced on both sides near
the bell and immediately extended end to end of the pipe. The bell commenced
breaking away from the barrel at 20 000 lb. per lin. ft. and a maximum was reached
at a load of 23 800 lb. per lin. ft. The appearance of this pipe in the later stages of
the test indicated that the load was applied over a small portion of the surface, thus
approaching a concentrated load. This may be the explanation of the large deflection
found in this. test.
Pipe No. 988. This pipe, which was loaded 1Y2 in. off center toward the bell,
was reinforced with Clinton wire mesh, the wire being No. 3. The first fine cracks
appeared in both top and bottom and extended from end to end at a load of 6 700
lb. per lin. ft. At a load of 12 300 lb. per lin. ft. the first cracks had opened wider
and shear cracks were appearing in the bottom of the spigot end. At 16 000 lb. per
FIG. 29. VIEW OF REINFORCED CONCRETE PIPE AFTER TEST.
ILLINOIS ENGINEERING EXPERIMENT STATION
lin. ft. shear cracks opened in the top of the bell and tension cracks opened at both
ends in the sides of the pipe. Crushing then started on the inside and a maximum
was reached at a load of 30 900 lb. per lin. ft.
26. Comparison and Discussion.-Table 17 gives the loads at the
appearance of the first crack, the maximum load carried, a so-called
critical load, and a comparison of the critical load with the resisting
moment of the pipe or ring acting as a reinforced concrete structure.
By the first crack is meant the first crack which was observed, a very
fine crack similar to the fine cracks which appear in reinforced concrete
beams and which did not interfere with the strength or durability of the
structure. The critical load is taken at the point where there is a
marked change in the direction of the load-deflection diagram and
where it becomes more nearly a straight line. There was at or about
this load a noticeable change in the pipe, shown by the tension cracks
enlarging or by the shear cracks forming. It seems evident that up to
this point the resistance of the pipe is that of a reinforced concrete
beam and that beyond this critical load the action of the reinforcement
is principally to hold the parts of the ring together and the main resist-
ance is the compressive strength of the concrete at the top, bottom,
and side points against pressure induced by the arch action made pos-
sible by the lateral pressure and restraint of the sand at the sides.
This view is corroborated by the amount of deflection and by the sim-
ilarity of action and of deflection in the tests of the Jackson pipe and of
the plain concrete rings. The column headed t gives the average dis-
tance from the center of the reinforcing bars to the compression face of
the concrete at the top and bottom. No allowance has been made in
the calculations for the greater size and stiffness of the bell. The col-
umn headed M' gives the bending moment calculated from the critical
load on the basis that the load is evenly distributed over the horizontal
section and that there is no side restraint. The column headed Mo
gives the resisting moment as a reinforced concrete beam by the form-
ula 0.87 Aft and is based upon the strength of the steel at its yield
point as the controlling element. A is the area of reinforcement in a
length of pipe of 1 foot, t is the distance from the center of the rein-
forcement to the compression face of the concrete and f is the strength
of the steel at the yield point which is here taken to be 46 400 lb. per
sq. in. for the rings, and 55 000 lb. per sq. in. for the pipe. For the
condition that the reinforced concrete fails by the tension of the steel
at its yield point, that the load is uniformly distributed over a horizon-
tal section and that there is no lateral restraint, the ratio of the two
moments should be unity. If the resisting moment due to the steel is
not developed, as in the case of No. 982 where a large amount of re-
TESTS OF CAST-IRON AND REINFORCED CONCRETE CULVERT PIPE
inforcement is used, this ratio will be greater than unity. In case
there is side restraint the effect will be to reduce the ratio to an amount
less than unity, provided both the horizontal pressure and the vertical
pressure are uniformly distributed. For these conditions the amount of
the ratio should be 1 - q given in equation (9). That is to say, if the
TABLE 17
REINFORCED CONCRETE RINGS AND PIPE. DISTRIBUTED LOAD
No. Load at First .Cr . L MI M Ratio Maximum
Crack ritical Load M . Mo Load
lb. per n. ft. lb. per lin. ft. inches 6 Wd .87 Aft Mo lb. per ad. ft.
-. lb. per l1n. ft.
Reinforced Concrete Rings
*Q9-l 0 5^n 7 000 20 27 24 20 . i
921 3 500
922 3 250
927 3 250
951 3 200
972 4 500
976 4 000
977 4 000
10 000 2.50 32 500 24 200
10 000 2.50 32 500 24 200
8 000 2.50 26 000 24 200
9 000 2.50 29 200 24 200
8 000 2.75 26 000 26 700
9 000 3.00 29 200 29 000
10 000 3.00 32 500 29 000
1.06 10 500
0.74 23 500
0.74 18 500
0.93 26 000
0.83 25 000
1.03 17 500
0.99 19 000
0.89 21 000
Reinforced Concrete Pipe
981 8 360 19 500 3.00 63 500 34 700 0.55 31 500
982 10 960 15 000 3.00 48 800 72 600 1.49 24 800
983 4 950 12 500 3.00 40 600 34 700 0.86 23 800
988 6 700 9 000 3.00 29 200 31 400
987 4 950 9 000 3.00 29 200 23 800
*No lateral restraint.
ratio is 0.75 the lateral pressure would be 25% of the vertical pressure.
In case the load is not uniformly distributed over the horizontal section
this relation would not hold and the tendency of any concentration of
the load near the center of the top of the pipe would be to give a smaller
ratio than would otherwise be found. This is complicated by the
probability of uneven distribution of the loads along the length of the
pipe.
It is noticeable that No. 982 has a high ratio. This is the pipe
with the large percentage of reinforcement and made of concrete which
seems to have been injured in the curing. With this exception the
ratios are generally less than unity and their average, 0.92, is not far
*09q ý7 nfin 0
ILLINOIS ENGINEERING EXPERIMENT STATION
from the average found in the distributed load tests of the cast-iron
pipe and rings. Ring No. 923 in which the rods were kept loosened so
that there was no lateral restraint has a somewhat higher ratio and
agrees fairly well with the calculated value.
After the critical load has been passed the reinforced concrete ring
will, under the conditions of the test, bear a considerably higher load
than the critical load, though it must be understood that this load
comes after the reinforcement ceases to act as in a reinforced concrete
beam, that the cracks formed are such that the reinforcement may be
exposed and the durability of the structure threatened, and that the
strength of the pipe is dependent upon the maintenance of the lateral
restraint of the sand at the sides.
VI. GENERAL COMPARISON OF RESULTS
27. Comparison of Methods of Loading.-The tests under con-
centrated load for both the cast-iron rings and the reinforced concrete
rings gave results which are consistent with analysis, both as to strength
of the rings and as to the nature of the deflection curves and the amount
of the deflection. The cast-iron rings broke suddenly, but the rein-
forced concrete rings (as shown in Fig. 22) maintained the maximum
load until the deflections had increased materially. It is evident that
the reinforced concrete structure may be deflected much beyond the
amount which is produced by the critical load before final failure
results.
In the discussion of the tests under distributed load for both the
cast-iron pipe and the reinforced concrete pipe, it was noted that the
determination of the resistance of the pipe to distributed load is much
complicated by the uncertainty in the distribution of the load and in
the amount of lateral pressure which may be developed. It is worth
while, however, to make a discussion of the observations and calcula-
tions to see what conclusions may be drawn. In Table 10 already re-
ferred to are given values of the bending moment and resisting moment
developed in the cast-iron pipe, and in Table 16 values of these mo-
ments for the reinforced concrete pipe. As has already been noted,
the expression used for the bending moment, Y16 Wd, is based upon the
assumption that the load is uniformly distributed over the horizontal
section both longitudinally and transversely, and also that there is no
lateral restraining pressure. The value of the resisting moment in
Table 10 is based upon the modulus of rupture determined from the
tests of the cast-iron rings under concentrated load. The value of
the resisting moment of the reinforced concrete pipe in Table 16 is
TESTS OF CAST-IRON AND REINFORCED CONCRETE CULVERT PIPE
based upon the ordinary formula for strength of a reinforced concrete
beam at the yield point of the reinforcement and does not consider that
failure by diagonal shear or other cause may occur earlier.
Under the above assumptions the ratio of the resisting moment
to the bending moment developed, as given in the above table, should
be unity. If a lateral pressure acts, the ratio should be less than unity
and its value would correspond to the 1 - q of equation (9). If the
lateral pressure is 25% of the vertical pressure, both being assumed
to be uniformly distributed, the ratio would be 0.75. If, however, the
load is not uniformly distributed over the horizontal section the effect
would be to give a larger ratio in the calculations made than would be
found if the actual distribution of the load were known and used. The
effect of the bell itself may possibly make the resisting moment of the
pipe smaller than is assumed in the tables.
The average value of the ratio in the table for the cast-iron pipe is
somewhat less than unity. It has been suggested that the higher val-
ues of this ratio may be due to uneven bedding and distribution of
the load and this is borne out by some of the observations of the test.
The lower values of the ratio indicate the presence of considerable lat-
eral pressure, and the effect of no lateral pressure upon deflections is
quite apparent in the test of cast-iron pipe No. 990, and in the rein-
forced concrete ring No. 923, where the horizontal restraining rods were
kept loosened.
Evidently there is more or less variation in the conditions of the
test and probably also in the resisting strength of the pipe. In the re-
inforced concrete rings and pipe the selection of the critical load given
in Table 16 is dependent somewhat upon judgment, but the values
have been compared with the conditions in the concentrated load tests,
and changes which may be made by different individuals would not
affect the results materially. The value of the ratio of the two mo-
ments is seen to be quite similar to those given in the table for the
cast-iron pipe, and its average is under unity. Evidently the conditions
relating to the distribution of load and the effect of the lateral pressure
are similar to those found in the test of cast-iron pipe. For high per-
centages of reinforcement or with steel of a high elastic limit, like
drawn wire, the pipe is likely to fail by other forms of failure than
through the steel being stressed beyond its yield point.
In the reinforced concrete pipe beyond the so-called critical load
the action of the structure, as has already been stated, is quite different
and the final failure is through crushing of the concrete. It would
seem that this strength is available in an emergency, though the con-
ILLINOIS ENGINEERING EXPERIMENT STATION
dition of the concrete in reference to cracks and defects may be such
as to affect the durability of the structure.
28. Measure of Strength of Pipe.-From these tests it seems
evident that the lateral restraint is considerable and that the pressure
exerted at the sides aids considerably in holding the pipe from large
deflections and thus strengthens it materially, but at the same time
the apparent effect of this is largely counteracted by the lack of uni-
formity in the distribution of the load and the lateral pressure, which
results in making the bending moment of the vertical load larger than
the assumed moment. Any reduction in the ratio 1 - q below unity
which may be found in the tests may be considered to be merely an
added safeguard. It will probably be best then to use /16 Wd for the
bending moment coming upon such a pipe when the bedding and later
filling are well done, considering any reduction in the ratio of moments
here discussed only as a margin of safety. In case of careless or in-
different bedding or filling the lack of uniformity of distribution of
pressure transversely and longitudinally will require that a higher
bending moment than /1f6 Wd be used.
The strength of cast-iron pipe may be calculated by using, in the
expression for resisting moment, a value of the modulus of rupture,
say, 25% less than the modulus of rupture obtained by breaking small
beam test specimens of the same metal. The effect of the presence of
the bell is somewhat uncertain but it is quite probable that greater
strength could be obtained by distributing the metal of the bell
throughout the barrel of the pipe. It seems probable, too, that as
ordinarily laid in the embankment the stiffness of the bell will inter-
fere with the distribution of pressure over the bed and thus reduce the
strength of the culvert. It should be noted, too, that it is probable
that the quality of the cast-iron pipe tested was better than the ordin-
ary run of cast-iron culvert pipe used by railroads. In the tests the
cast-iron pipe failed at the maximum load and the load sustained
dropped off suddenly, indicating that there would be a complete col-
lapse under a dead load.
The critical strength of reinforced concrete culvert pipe where the
reinforcement does not exceed, say 0.75 of 1%, and is of medium steel
may be measured by the resisting moment calculated by the ordinary
beam formula. This, of course, is with good concrete. The resistance
against diagonal tension and stripping of the concrete over the bars
may be improved by flattening the arc around the top and bottom and
possibly by the use of stirrups at these points. The actual load which
the reinforced concrete pipe will take above this critical load is a
great safeguard. The property which a reinforced concrete beam has
TESTS OF CAST-IRON AND REINFORCED CONCRETE CULVERT PIPE
of holding a load near its maximum load through a considerable deflec-
tion may be of great value in case the earth at the sides yields and the
pipe must follow it to get the benefit of side restraint.
29. Loads and Failures.-The distributed load tests herein de-
scribed were made with the filling of sand carefully placed and packed.
It is evident that the condition of the bedding and filling and also the
nature of the materials used in filling over the pipe will have a great
influence upon the amount of the load and upon its distribution. The
experience in the breaking of vitrified pipe sewers is analogous. Many
cases of breakage of lines of pipe sewer have been reported in diameters
from 18 in. upward. These instances have occurred in rock and clay
more generally, through such failures are found in sand and quick-sand.
The load which will come upon such sewer pipe from the trenches will
vary with the manner of filling and the nature of the soil, as has already
been suggested. Failures of cast-iron pipe under high embankments
have been reported. In some of these cases the loose rock which was
used for filling produced high loads. The effect of the manner of fill-
ing and of the nature of the material and the cause and prevention of
such breakages would make a long paper by themselves. It is hoped,
however, that the publication of this paper will bring to light instances
of the failure of culvert pipe and sufficient data to throw light upon the
loads which were produced by the embankment. If engineers will
report the circumstances attending such failures, the height of the em-
bankment, the conditions of the bedding, the nature of filling, the
nature of the materials placed in the filling, and the time which had
elapsed after construction, the information will be very helpful in plan-
ning new structures, particularly where new types of construction like
concrete and reinforced concrete are to be used. Such data will add
much to the information given in this paper.
30. Summary.-From the tests and the discussions it would seem
evident that among the facts-brought out are the following:
1. The cast-iron rings broke under a concentrated load at a calcu-
lated modulus of rupture 25% less than the modulus obtained from
rectangular test pieces cut from the rings. The average value of the
modulus of rupture for the ring tests was 27 000 lb. per sq. in., and it
should be noted that this value was obtained with an excellent quality
of iron.
2. The cast-iron pipe loaded in sand broke suddenly at one end or
the other, finally breaking through the entire length of the pipe. Upon
failure the load dropped materially and there was little further strength
to the structure. The stiffness of the bell affected the deflections and
acted to prevent a uniform distribution of stress throughout the length
ILLINOIS ENGINEERING EXPERIMENT STATION
of the barrel. The presence of the bell adds to the difficulties of secur-
ing a uniform distribution of the load, and detracts from the strength
of the pipe.
3. The plain concrete rings broke under slight deflections at loads
which agreed well with the calculated strength, both under concentrated
load and distributed load. In the testing box under the restraining
lateral pressure these rings held high loads after the segments had been
deflected considerably from their original position, finally breaking by
crushing of the concrete under conditions shown in Fig. 23.
4. The reinforced concrete rings in the concentrated load tests
held their maximum loads or about their maximum loads through a
considerable deflection, thus showing a quality which is of value when
changes in earth conditions permit a gradual yielding of the surround-
ing earth. The calculated restraining moment agrees fairly well with
the calculated bending moment.
5. The reinforced concrete rings and pipes tested under distributed
load made a satisfactory showing. The so-called critical failure may
occur by either tension failure in the steel or a diagonal tension failure
(ordinarily called shearing failures) in the concrete. A flattened arc
for the reinforcement where it approaches the inner face is of assistance
and stirrups may be of some value. Beyond the critical load the re-
inforcement is of service in distributing the cracks and in holding the
concrete together. Final failure is by crushing of the concrete in much
the same way as was obtained with the plain concrete rings. The ad-
ditional strength beyond the critical load may be taken into considera-
tion in selecting the factor of safety or working strength.
6. The restraint of the sand in the tests is very important, and
the effect is to reduce the bending moment developed by a given
vertical load, or, as it would be commonly stated, to add strength to
the pipe. The degree of permanency of this side restraint is uncertain.
It seems evident in these tests that the distribution of the pressure,
both horizontal and vertical, was not uniform, and that with the usual
method of placing a pipe in an embankment, and especially when
other materials than sand are used, the distribution would be even less
uniform than here found. In view of this it will be well in making
calculations and designs to use the formula Y1 6 Wd for the bending mo-
ment, thus considering that the side restraint is offset by the uneven
distribution of the load, any surplus from this being considered merely
an additional margin of safety. For pipes poorly bedded and filled a
larger bending moment than 16 Wd should be used.
7. The method of bedding and laying pipes and the nature of the
bed and the surrounding earth have a great effect upon the bending
TESTS OF CAST-IRON AND REINFORCED CONCRETE CULVERT PIPE 65
moment developed and upon the resistance of the pipe to failure. If
the method of laying, or the hardness of the soil below, or the condition
of the settlement of the pipe is such that the pipe is supported only or
mainly along an element of the cylinder at the bottom the bending
moment developed will be greatly increased over that of a uniformly
distributed support. If the greatest supported pressure comes at points
well to the side of this bottom element, as may be obtained by careful
bedding, the bending moment is reduced. It is also plain that the
bell should be left free from pressure at the bottom. It is possible that
the presence of the bell detracts from the strength of the pipe. Any
action in filling which increases the lateral restraint against the pipe
will add to the security of the structure.