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This thesis was contributed by
Mr. E. Balbach
under the date indicated by the department

stamp, to replace the original which was
destroyed in the fire of March 5, 1916.

 

THESI 5,

COMPARATIVE STRENGTH OF VARIOUS

CONCRETE TUNNEL SECTIONS,

E. Balbach A.R, Carter

1904

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THESIS
 

The building of tunnels has been practiced for ages:
but although many different shapes and various materials have
been used in their construction, no tests have ever been made to
ascertain which shape is the stronger. With this object in
view our tests were conducted,

No matter of such a nature being available for refere-
ence we were obliged to make our own assumptions and trust that
they were correct. In the first place, we assumed that if we
constructed some small tunnels of various common shapes and pro-
portioned them as near as possible like full sized sections and
loaded them to destruction the same relative result would be ob-
tained as by crushing full sized sections. Four different
shapes were then made, namely: a section with perpendicular
sides and semi-circular arch; one section of horse-shoe shape,
semi-circular arch; another with horse-shoe for inside and
straight on outside, semi-circular arch; and one perpindicular
on inside and slanting on outside, so as to make the base
thicker. (See Blue Print) |

To mould these sections forms were made of galvanized
iron and wood, Ribs of wood were sawed outto the shape de-
sired and the sheet iron nailed on these. A form of the inside
and one for the outside were made and the concrete was rammed

in between these and allowed to set. The inside mould was then

93830
=3=

forced out and the outside mould sprung off. The tunnels were
made two feet long and three of each kind were made, The come
position consisted of three (3) parts of common sand, passed
through a one-fourth (1/4") inch mesh sieve to one part of
Portland cement from Jonesville, Michigan, About 10% of water
was used,

The intention was then to break these at the same age
but owing to the limited time at our disposal this could not be
done, They were, therefore, all broken in one week, with the
age varying from five weeks to nine weeks, They were all
allowed to set dry.

Some concrete beams were also made; cne consisting
of a block 6"x11"x2" with straight sides and one of the same
dimensions with arched sides. Thirteen of these were made,
seven (7) of the former and six (6) of the latter, the composi-
tion being the same as for the tunnels. The molds were made
of wood,

In breaking the tunnels the attempt was made to appe
roach natural conditions as near as possible. <A special machine
was constructed for this purpose, consisting of a compound lever
and acting on the principle of a nut cracker. A photograph
of the machine in operation is included in this report. The
upper lever is a 6"x6"xl4ft. with a lever arm of 12-1/2 ft, The

lower lever is an 8"xl0"xloft. with a lever arm 10 ft., all
whe

of oak, The combined leverage was then 12-1/2 x10 = 125. A
spring balance was attached at the end of the upper lever as
shown and the pressure on the tunnel thus ascertained, The
bearings were made as small as possible with safety so as to
minimize the friction. Cast iron plates were bolted on the
timbers in order to prevent the crushing of the wood. (See
Photograph and Blue Print.)

A wooden box was constructed in which the tunnels
were placed for testing. A layer of sand, about 1-1/2", was
Placed in the bottom of the box and the tunnel placed upright
on this. The box was then compeltely filled with sand, making
about two inches (2") of sand over the top of the tunnel. The
box was completely closed over with the exception of one square
foot in the top through which the pressure was applied. Dry
sand was used. <A pressure applied through this opening would
then distribute through the sand to the sides and practically
the same condition be produced as in actual practice,

The pressure due to the weight of the levers alone
was determined as follows: A Buffalo scale was placed at some
distance from the crushing point and a lever placed so as to
reach under the pressure point and supported a short distance
beyond, The machine lever was then allowed to rest upon this

small lever and the turn-buckle on the machine drawn up until
 

 
 

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the upper lever just balanced. The scales then read 770#. The
lever arm of the saale was 7 ft. 9-3/4 in. and that of the
pressure arm was 4-1/2 in, Therefore 770 x 7* 9-3/4" # 4-1/2" =
16040#, the constant of the machine. This is somewhat smaller
then the theoretical constant for some of the power is consumed
in friction, The load on the tunnel then will be the reading

of the spring balance x 125 + the constant of the machine, In
this way the breaking loads were determined in each case. The
machine was designed for 50000# but this pressure was not reached,
The following table gives a record of the results. (See Table 1)

Description of Fracture,

No, 1 was not full length, one end being broken off
but it was tested, It broke very easily, requiring but 104
pressure on the lever, After uncovering, it was found to be
completely fractured, the arch crushed in and the sides and
bottom broken into small pieces, No. 2 was sound and after une
covering was found to have the entire arch crushed in; the sides
and bottom were but slightly cracked. No. 3 was sound and
after uncovering was found to have the arch crushed entire length
and the sides slightly cracked but standing. The bottom was
cracked but little.
or
 

 

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Table No. l, .
LOG OF RESULTS,

 

 

No.: Date Date Age Shape: Weight Spring Total x
: Made ;Broken 3 3 : Reading 3 Pressure
1 vApril 6 : May 16 5 Wk. 5 DasFig. 1: 50# 10# 17290
2°: March 18: May 16 8 Wk. 3 Da: Fig. l: 49.6 130 ; 32290
3 ‘March 16: May 19 9 Wk. 1 Da: Fig. L: 51 120 31040
Average 31665
4 ; March 18: May 17 8 Wk. 4 Da: Fig. o: 55.4 115 30415
5 April 6 : May 18 6 Wk, Fig. Os 54.6 ; 67 24415
6 : March 16: Fractured: Fig. 2: =< -- --
: $ : : : ¢ Average : 27415
7 April 9 ’ May 18 5 Wk. 4 Da: Fig. 3: 58 8 125 31665
8 : April 12:May 19 5 Wk. 2 Da: Fig. 3: 59 3 85 26665
9 : April 13: May 17 4 Wk. 6 Da: Fig. 3: 60.6 135 32915
Average 30415
10 : April 9 + May 17 5 Wk. 3 Da: Fig. 4: 57 3 117 30665
11 April 12:May 19 5 Wk. 2 Dat Fig. 4: 56.4 132 32540
12 tApril 13 :May 18 5 Wk. ‘ Fig. 4: 58 105 29165
: Average : 30790 |

Constant = 160404

x Total pressure = scale reading x 125 + constant (16040#)
' Made of Wabash Portland Cement
e Only Nos. 2 and 3 were used to get average of Fig. 1

Fig. 1 - Horse-shoe

Fig. 2 = Straight Outside and Inside

Fig. 3 - Straight Inside Slant Outside

Fig. 4 - Straight Outside Horse-shoe Inside
»

se
 

=7=

No. 4 was sound and after uncovering was found in same
condition as No, 3.

No. 5 was also sound but after applying the load the
arch was found crushed in, also one sides the other side re-
mained standing but cracked, the bottom also cracked,

No. 6 was dropped by accident and fractured and so
could not be tested,

No. 7 was sound but after test was found with the arch
crushed in as in the others, The sides were badly broken but
still standing. The bottom was slightly cracked,

No. 8 was in good condition and after test showed the
arch completely crushed in. The sides and bottom were but
slightly broken,

No. 9 was perfectly sound but after load was supplied
showed arch badly crushed in with the sides and bottom in fairly
good condition,

No. 10 was sound and after test showed arch crushed
in with the sides and bottom but slightly cracked,

No. 11 was in good condition before test but afterwards
showed complete crushing in of the arch and extensive fracture
of the sides and bottom,

No. 12 was perfect before the test and afterwards

showed the arch crushed in as far as the springing line, The
-8-

rest of the walis and bottom were very slightly injured,

General Conclusions;-

In every case the tunnel failed by crushing in the
arch a little above the springing line. The sides in some cases
were quite extensively broken and in others showed but few cracks.
In nearly every case the bottom held together well and was
fractured but slightly,

Taking the average load of the three tunnels of the
same shape we find the horse-shoe shape to be the strongest. This
Bhape was the lightest weight indicating that less material
was necessary for construction. This would perhaps be offset
by the greater difficulty of construction, The only advantage
that is obtained by Fig. 3 is the greater base area where heavy
traffic is to take place in the tunnel. Fig. 4 does not give
greater base area and besides has less room on the inside and
uses more material,

If more tunnels of each variety had been made our ree
sults would have been more reliable, The difficulty of getting
all tunnels alike makes the result more or less uncertain where
the average is taken. For instance, in the test of Fig. 3, one
test showed a low result whereas the other two showed high re-
sults, This may have been due to construction. Judging from
the results as a whole, would say that there is no advantage in
thickening the sides for ordinary conditions as most of the
pressure seems to come on the arch above the springing line,

Our conditions perhaps were not ideal for we had but two inches
-G=

(2") of sand above the highest point of the arch and the pressure
was therefore greatest there, If the depth of sand had been

greater better results would have been obtained, without doubt,

Breaking of Beams.

As before stated, beams of concrete were constructed
of the shape of the sides of the tunnels Nos, 1 and 2 for the
purpose of comparing their strength. In a tunnel the pressure
from the load on the arch is sustained by the side walls. Also
the lateral pressure of the earth on the sides must be sustained
by the side walls of the tunnel, To obtain such loading a
machine was designed to operate in conjunction with the Tinius
Olsen testing machine in the M. A. C. laboratory, This con-
sisted of a timber 6"x6"x6', on top of which was placed a casting
supporting the two ends of the concrete beam, One of these
supports was fixed rigidly and the other was mounted on rollers
in order to reduce friction. This movable end was attached to
a dynamometer consisting of a cylinder with a tight fitting
piston, compressing oil. <A screw pressed against the dynamo-
meter and by turning the same the pressure in the dynamometer
could be regulated. This machine was placed in the testing

machine and the load brought directly over the beam,
All of the beams were broken with such double loading
excepting one which was broken with a load only from the top,

(See drawing - for arrangement of machine.)

The diameter of the piston was 5" making an area of
19.635 sq. in. The area of the end of the beam was 2"x6" = 12

8d. in. Therefore the end pressure per sq. in. on the beam was

19.035 _ x gage reading. The beams were of different ages but
one of each kind of the same age was selected to be broken with
the same end pressure. In this way two of each kind were broken
under 50# end pressure per sq. in, by the gage, two under 75#
pressure per sq. in, and two under 100# pressure per sq. in. by
the gage.

The load was applied at tne center of the beam with a
block 3"x5" and the results tabulated below, It will be seen
that the one broken without end pressure sustained but a very
small load compared with the others; also that the breaking load
for all of the arched beams was greater than that for the straight
beam with the exception of No, 12. This one was very weak and
should not be considered in the results,

In every instance, the beam would first crack on the
under side either parallel to the load or at an angle of 45°,
After cracking, the load could be considerably increased before

the beam would yield.
SMITNTON |

 

 

 

 

 

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Table No, ll.

STRAIGHT SIDES,

 

 

 

 

NO. ; Date Date Age Gage : Total Ind: Balance: Average
; Made ; Broken: ; Reading;Pressure:Reading: of Two
1 : April 6 : May 28 7 Wk. 3 Da: 504 981,2.54: 23304 ye
2 April 8 May 28 7 Wk. 1 Da: 50 9812.5 2350 23408
3 vApril 9 : May 28 7 Wk. 0 Da: 75 14720 3350
4 P April 11: May 28 6 Wk. 5 Da: 75 14720 3400 3375
5 April 15: May 28 6 Wk. 1 Da: 100 : 19625 3450
6 S April 16:May 28 6 Wk. 0 Da: 100 19625 3650 3550
7 : April 12:May 28 :6 Wk. 4 Da: 0 0 1200 1200
: ; f @ERGULAR : Pg
8 April 8 : May 28 7 Wk. 1 Da: 50# : 9812.5#: 3200#
9 April 16: May 28 :6 Wk. O Da: 50 9812.5 2750 29 75#
10 April 9 : May 28 7 Wk. 0 Da: 75 14720 3610
11 April 11: May 28 6 Wk. 5 Da: 75 "14720 3540 3575
12 PApril 12:May 28 6 Wk. 4 Da: 100 19625 2990
13 April 15: May 28 :6 Wk. 1 Da; 100 319625 : 3900 . 3900

 

x This reading not used in comparison,

® Balance reading contains dead weight of the machine which was 1204,
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Multibinders
Gaylord Bros., Inc.
Makers

Syracuse, N.Y.

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