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A Comparison of Compressive and Flexural Strength of
Concrete and Design and Construction of Beam

Testing4Machine

A Thesis Submitted to
The Faculty of
HICHIGAN STATE COLLEGE
or
AGRICULTURE AND APPLIED SCIENCE

J
1/
:9.

'~ “ y

1

GZIH. Jennings WIFE; figulon
Candidates for the Degree of

Bachelor of Science

June 1930

THESIS

Acknowledgement

The authors of this thesis are indebted to
Prof. C. L. Allen and Mr. L. J. Rothgery for
their advice and cooperation without which this
thesis would nothave been possible. Also to
the State Highway Department for the use of

beam moulds.

100265

Introduction

In all reinforced concrete design the compressive strength
of the concrete alone is considered. The steel reinforcing
is designed to carry all of the tensile strength. Tests have
proven that concrete structures will carry a greater load
than their calculated load due to the flexural strength of the
concrete. However it is still considered the better practice
to disregard the flexural strength in designing. In concrete
road construction the flexural strength is the controlling
factor in the design. As a definite ratio exists between the
compressive and flexural strength it would be possible to
consider the flexural strength in some designs. This would
give greater economy as the sections would be lighter thus
using less material.

In the experimental work for this report, tests were made
upon different mixes of concrete to determine the compressive

and flexural strength and the ratio existing between them.

 

 

l'1

Test Specimens

The concrete for the test Specimens was made according to
the water-cement ratio theory to give different strengths. The
sand used was clean and graded 0" to %" with a fineness modulus
of about 2.8. Washed gravel having a size of i" to l" and a
fineness modulus of about 7 used for the coarse aggregate. The
mixing was done in a 2% cu. ft. Smith mixer. Curve "A" was
used in the designs of the mixes. Each batch was tested for
slump and a constant consistency of 3" to 4" slump was maintain-
ed.

The moulds were made from 6" and 8" channel sections to
give a 6"x8"x36" beam. This was long enough to give two breaks
on each beam. They were broken with the 8" side vertical. One
' break was made with the tOp as poured and the other with it
down. This method of breaking would tend to eliminate any irreg-
ularity that there might be due to segregation or variation in
the concrete in the beam. The cylinders were the standard cylind-
ers 6" in diameter and 12" high.

All of the beams and cylinders were cured in wet sand for
28 days. Before breaking the test pieces were allowed to dry
for a few hours and then brushed clean. The cylinders were capp-
ed on both ends with plaster of paris to insure an even hear-
ing over the whole surface. A Watson Stillman Hydraulic com-
pression machine of 200,000 lbs. capacity was used. The beams
were fastened in place between the steel plates of the beam

testing machine which was made as a part of this thesis.

Compressive and Flexural Strength

of Test Specimens

Set # 1. Set # 2. Set # 3.
Comp. Hod. of Comp. Kod. of Comp. Hod. of
Str. Rupture Str. Rupture Str. Rupture
4070 481 3180 474 4250 527
2660 470 3720 538 4260 633
3250 510 3450 538 3820 608
1860”’ 570 4070 563 2940 519
3360 479 4000 519 3980 674
2060 489 2600 633 4080 563
2720 512 3600 519 4400 583
4500 583 3980 519 3290*” 521
2300 414 3010 548 4330 597
1660V’ 487 3180 543 3780 570
4040 495 3900 565 4400 591
4140 536 3720 610 4400 508
Av. 3310 547 3534 547 4174 577
Set # 4. Set # 5. Set 4 6.
Comp. mod. of Comp. Mod. of Comp. Hod. of
Str. Rupture Str. Rupture Str. Rupture
4800 643 4960 699 5310 735
5400 557 6480 643 6200 758
5450 643 6020 695 5310 707
5400 625 5520 578 5330 688
4600 625 5660 625 6220 767
5140 570 6020 671 6370 535
5900 614 3210 783 5840 763
5210 587 6370 674 5400 707
5360 591 42500’ 558 5220 688
5150 585 6730 644 5240 631
5860 608 5320 619 5310 707
4810 555 4600‘” 619 4790L4~ 707
Av. 5256 600 5830 667 5577 699

Check Mark thus V/, indicates Specimen
was not used in average of results.

Deviation in Percent of Individual Values for

Flexural Strength From the Kean of Each Set

Set #10

4.18
6.37
1.79
13.50
4.58
2.59
1.98
16.00
17.50
2.98
1.39
6.77

6.64

Deviation in Percent of Individual Values of

Set #2.

13.48
1.65
1.65
2.56
5.12

15.74
5.12
5.12
0.18

0.73
3.30

29.80

7.04

Set #50

8.68
9.72
5.73
9.90

16.83

2.43
1.04
9.72
3.47
1.30
2.43

11.97

6.83

I

“at #40

7.16
7.16
7.16
4.17
4.17
5.00
2.23
2.16
1.50
2.50
1.33
7.50

4.34

Set #5.

4.80
3.60
14.20
13.35
6.30
0.60
17.40
0.75
13.65

Set #6.

5.14
9.74
1.14
l. 57
9.70
23.50
9.15
1.14
1.57

3.45
7.20
7.20

7.71

9.70
1.14
1.14

6.22

Compressive Strength From the Mean of Each Set

Set # 1.

22.90
19.60

1.81
44.20

1.51
37.80
11.80
36.00
30.50
49.50
22.00
41.40

26.58

Set #20

12.85
5.26
3.51

15.20

13.20

26.40
1.86

12.62

12.00

10.00

10.35
5.26

10.71

Set 7515.

1.82
2.06
8.50
29.60
4.65
2.30
6.38
21.20
3.74
9.26
5.42
5.42

8.36

Set #4.

8.70
2.74
3.70
2.74
12.50
2.21
12.20
0.86
1.98
1.98
12.65
8. 50

5.98

[1.
S e t '7)" 5 o

4.80
3.60
14.20
13.35
6.30
0.60
17.40
0.75
13.65
3.45
7.20
7.20

10.82

.’
Set 36.

'5.14
9.74
1.14
1.57
9.70

23.50
9.15
1.14
1.57
9.70
1.14
1.14

7.39

The Machine

The machine used for the flexural tests was built accord-
ing to the enclosed drawing. It is composed of a steel frame
for holding the test beam in place and a wooden lever arm
attached to the test beam in such a manner as to introduce a
bending moment in the beam. The container supported at the
end of the lever arm was gradually filled with sand to increase
the moment. The flow of sand into this container was stopped
as soon as the beam broke. This method of loading gives a
gradual increase in the load and eliminates impact which may
occur when larger weights are placed upon the beam.

Knowing the lever arm, the moment due to the sand load was
easily computed. The moment due to the lever arm and beam
overhang was constant so the total moment was obtained by add-

ing the moment due to the sand load to this constant moment.

 

 

 

 

 

 

 

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Computations

Assume maximum flexural strength as 1500 lb. per sq. in.

LI: fila- 256 X 1500 a 96000 lb. in.
C 4 /2’

V

 

 

 

44'
VV ‘4»
l

 

 

 

 

 

 

0
[L5 7.6' 4??
Diagonal hember

*0
II

96000 = 888 lbs.
108

n, 4.4 x 888—-8.65W w. 450 lbs.
R. 888-+ 450. 1338 x 7.7 = 2570 lbs.

2570 = 1370 lbs. per sq. in.
2 x .94

 

l a 7.7 x 12 . 237
r .37'

 

Allowable stress: 16000 - 50 x 237; 4150 lbs. per sq. in

3/8 in. rivet in shear: 1100 lbs. 2 rivets (0.2)

3/8 in. rivet in bearing: 24000 x 3/8 x 1/8= 1125 lbs. (0.x)
Upright hembers

ggggg - 48000 lbs. in. taken by each 8108

48000 .
10.875

3/8 in. rivets in shear: 1320 3 required

4420 lbs. stress

Bearing with a rivets. 4420 = 16400 lbs. (0.2)
.0703‘0794

Lever Arm

Assume d: 8 in. I: 42.667b

m 1

(mo 4400 400

H: 4000 X 12: 48000 lb. in.
M = I a 42.667ba 48000: 40
s c 4 1200

b 3.75" use 2—-2" x 8" Oak

Clamp Bolts

1.50-+63-+10.5A

r-u
H

t-cl

1.50 + 6(40) +10.5(70)

(l.5-+24-+73.5)Ca 99C

990: 96000
C: 970
70. 6790

6790 = .425 Sq. in. USS 22'" bOltSo
16000

 

.Applying the formula s: %C , in which

s. flexural strength in lbs. per Sq. in.

H:

C:

H
II

0-

total moment in lb. in.
distance to extreme fibre from neutral axis.
moment of inertia about the neutral axis.

0 d: .0 B .0 = o c 3...];—
4 in 8 in b 6 in I 256 in ’1‘“ 64

‘we have s: M/64

But M-
w.
11;:
‘4.-

Manama. w, 1,+w. l,_+‘.-"—I, 13, in which

wt. of beam overhang 50 lbs. (varies slightly)
wt. of lever arm: 95.5 lbs.

wt. of sand load.

distance to center of gravity of beam overhang.

distance to center of gravity of lever arm. 52%

distance to center of gravity of sand load: 121

Therefore a- 17111 + 37.11:. 17,21.

 

64 64
= (50 x 6)+-(95.5 x 52.5) rW'x 121
64 64
: 83+1.89 W

in.

6 in.
in.

in.

The steel frame was fabricated by the Jarvis Engineering Co.

The total cost of the machine was slightly under 45 dollars.

Conclusions

There is a definite relation between the flexural and come
pressive strength of the same concrete. It varies, however,
'with different strengths. The relations we obtained were for
concretes of the higher strengths than ordinarily. They varied
from 11% to 15%. is brought out in tests by the Portland Cement
00., and the Structural materials Laboratory the ratio increases
up to asmuch as 353 as the compressive strength decreases to
about 1500 lb. per sq. in.

The modulus of rupture of the beams in each set increases
over the proceeding one which is as it Should be according to
our design of the mixes. This does not prove to be the case
with the compressive strength of the cylinders. Then, too,
the average deviation of the modulus of rupture of the beams
proved to be less than the average deviation of the compressive
strength of the cylinders from the average compressive strength
of the cylinders. This shows that the results obtained are
more consistant in the case of the modulus of rupture of the
beams than in the compressive strength of cylinders.

Because of the Simplicity of the beam testing machine and
its lightness it is possible to have one in the field and ob-
tain better results with less time and trouble than taking
cylinders to the laboratory.

It means more to field men to see the tests done on the job
and note what each particular concrete can stand than by read-

ing a report from a laboratory.

Bibliography

Report of Director of Research; Portland Cement Association.

Nov. 1928 157-200

Public Roads Vol. 8, Ho. 12, Feb. 1928

The National Sand and Gravel Bulletin mar. 1928 13-31

University of Michigan, Official Publication Vol. 31,
No. 14, Aug. 24, 1929 73-87

Bulletin 11; Structural Materials Research Laboratory.
Proceedings of the American Concrete Institute 701. 22,

1926 388-389

.Proceedings of the American Concrete Institute Vol. 24,

1928 212-237

 

 

 

 

 

 

 

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