DEPARTMENT OF THE INTERIOR 

UNITED STATES GEOLOGICAL SURVEY

 GEOKGE OTIS SMITH, DIRECTOR

BULLETIN 344

THE

STRENGTH OF CONCRETE BEAMS

(FIRST SERIES)

MADE AT THE STRUCTURAL-MATERIALS 

TESTING LABORATORIES

Br RICHARD L. HUMPHREY

WASHINGTON

GOVERNMENT PRINTING OFFICE

1908

CONTENTS.

Page.

Introduction.............................................................. 5

Scope of investigations.................................................. 5

' Methods of testing............. '............................. 1.......... . 6

Results of tests.....................'................:.........."........... 6

Acknowledgments. .................................................... 8

Tests of constituent materials................... r ........................... !)

Cement. ........................................................,...:. 9

Preparation of typical cement.......;.................. ........ /.:.. 9

Results of tests............................:........................ 9

Sand...................................... : ............... '....... 16

Aggregate. .....................-.......:......:....................... 18

Preparation of test pieces................::.:............................... '18

Methods of proportioning.... ..................:... ^.................... 18

Method of mixing and consistency:.. ...'........'..;............. ......... 19

Mixing............................................................ 19

Consistency........................................................ 20

Method of molding................... ^................................. 21

Beams............................................................ 21

Cylinders and tubes.........-...-:..-;..: -.-........................... 21

Moving and storage. .................................................... 22

Methods of testing.........................................:..........:..... 22'

Beams.........'....................................................... 22

Long beams...... ................................................ 22

Apparatus..................................................... 22

Method of zero deformation............................:....... 23

Method of testing........................................'....... 27

Short beams. ...................................................... 27

Cylinders and cubes................................................... 28

Results of tests............................................................. 28

Beams of constant span................................................. 28

Beams of variable span................................... '.............. 55

Cylinders and cubes................................................... 55

Illustrative diagrams.................................................. 57

Survey publications on tests of structural materials........................... 59

3
ILLUSTRATIONS.

Page.

PLATE I. Concrete beam in machine ready for testing........................ 22

FIG. 1. Diagrams illustrating method for computation of concrete beams.,.... 25

2. Effect of age and consistency on the strength of cinder concrete....... 28

3. Effect of age and consistency on the strength of granite concrete...... 29

4. Effect of age and consistency on the strength of gravel concrete....... 29

5. Effect of age and consistency on the strength of limestone concrete.... 30

6. Compression-stress deformation diagrams of cinder concrete........... 30

7. Compression-stress deformation diagrams of granite concrete.......... 31

8. Compression-stress deformation diagrams of gravel concrete........... 32

9. Compression-stress deformation diagrams of limestone concrete........ 33

10. Deformation curves of cinder concrete in flexure..................... 35

11. Deformation curves of granite concrete in flexure..................... 54

12. Deformation curves of gravel concrete in flexure...................... 56

13. Deformation curves of limestone concrete in flexure................... 58

TABLES.

TABLE 1. Chemical analyses of the individual brands used in the preparation

of typical Portland cement..................................... 10

2. Physical tests of individual brands of cement....................... 10

3. Strength tests of individual brands of cement....................... 11

4. Physical properties of cements used in concrete beams.............. 14

5. Mortar tests of Meramec River sand used in concrete beams......... 17

6. Physical properties of sand and other materials forming aggregates.. 17

7. Strength tests of cement (Ct. 140) used in testing Meramec River

sand.........j................................................ 18

8. Tests of 13-foot concrete beams of constant (12-foot) span; ages 4,

13, and 26 weeks.............................................. 36

9. Tests of concrete beams of variable span; ages 4, 13, and 26 weeks.. 42

10. Compression tests of concrete cylinders and cubes accompanying

beams; ages 4, 13, and 26 weeks................................ 48

4
THE STRENGTH OF CONCRETE BEAMS.

By RICHARD L. HUMPHREY.

INTRODUCTION.

SCOPE OF INVESTIGATIONS.

The tests of concrete beams described in this bulletin form a part 

of a comprehensive series of investigations undertaken by the United 

States Geological-Survey for the purpose of determining the strength 

of concrete and reinforced concrete.

The work involved in these investigations consists of a study 

(1) of the constituent materials of concrete, (2) of its strength when 

molded into various structural shapes, and (3) of the methods by 

which its maximum strength may be developed through various 

forms of metallic reinforcement.

Although it is true that concrete possesses but little strength in 

tension and must be reinforced with metal to resist tensile stresses, 

it is believed that no study of concrete would be complete without 

a series of tests establishing its strength without reinforcement.

The tests herein reported indicate.that concrete is unsuitable for 

use under conditions where it must resist tensile stresses, because 

of the small loads it will sustain and particularly because' of the 

suddenness with which it fails, in striking contrast to the behavior 

of reinforced concrete, which usually shows a gradual development 

of cracks preceding failure.

This first series of beam tests covers 144 beams without rein1 

forcement 8 by 11 inches in section and 13 feet long, together with 

the corresponding compression test pieces, consisting of cylinders 8 

inches in diameter by 16 inches in length and of 6-inch cubes. Of 

these tests those on 108 beams of 12-foot span, with their cylinders 

and cubes, and those on 108 beams of variable spans, 6 to 9 feet, which 

were made of the larger part of the 13-foot beams after rupture, are 

herein reported and comprise all of this series except the 52-week tests.

An attempt has been made to bring out, if possible, the comparative value of gravel, granite, limestone, and cinders for use in concrete; the effect of age and consistency on the strength, as shown by 

the modulus of rupture of the long and short beams and by the ultimate strength of the cylinders and cubes; and the influence of age 

and consistency on the stiffness, which is indicated by the unit

5
6 STRENGTH OF CONOEETE BEAMS.

elongation of the long and short beams and by the initial modulus of 

elasticity, as determined by tests of the cylinders.

Three consistencies wet, medium, and damp were somewhat 

arbitrarily chosen, and are described on pages 20-21 in greater detail. 

Tests were made at the ages of 4, 13, 26, arid 52-weeks. There are, 

then, as indicated in the following table, but two variables aggregate and consistency for each age.

Outline of tests of concrete benms.

Aggregate.

Granite............

Gravel:;. ,w. >,....'

Consistency.

4 weeks. . . -.

Wet. 

;..do.. 

..do.

..do.

Med.

...do . 

..do.

. .do .

Damp.

...do ..... 

..do...

..do..:

. - ..13 weeks. ....

Wet.

..do. 

..do.

.:do .

Med.

..do.. 

..do.

do

Damp.

-. .do . . . 

..do...

i/do...

26 weeks.

Wet.

J.do . 

..do.

do

Med. 

;.do. 

do "do

Damp. 

..do... 

..do...

.:do....

52 weeks.

Wet. 

..do. 

..do.

..do.

Med. 

..do. 

..do.

..do.

Damp. 

..do... 

..do...

..do'...

NOTE. Three beams, three cylinders, and three cubes were made for each variation shown in the 

table. ' . ' 

% METHODS OF TESTING.

The methods of testing beams of 12-foot and variable spans, 

together with cylinders and cubes, have been described in considerable detail in Bulletin No. 329. It is thought best, however, to repeat 

and in some cases amplify matter which appears there, as the intelligent interpretation of much of the test data is greatly aided by ready 

access to an account of the methods of testing that were used. .

RESULTS OF TESTS.

No attempt has been made in this bulletin to generalize the results 

of the tests herein presented, or to draw any conclusions, however 

warranted they may appear from an examination of the test data. 

It is hoped that the matter herein contained will provoke discussion, 

and in order to promote this end extended expressions of opinion or 

attempted applications of theory to results have been avoided. A 

running commentary on the results of the tests, however, emphasizing 

matters of particular interest and indicating a few. points that might 

lead to interesting, analyses, is included in this report. When the 

results of the 52-week tests become available it is the intention to 

publish a thorough analysis of the entire series in another bulletin.

The purpose of this series of tests was to determine 

(1) The effect of age on the strength of concrete;

(2) The effect of variation in the consistency on the strength of 

concrete; and

(3) The effect of different types of aggregates on the strength of 

concrete.

The first question is perhaps the most important, since an early 

attainment of considerable strength and no subsequent decrease in
INTEODUCTION. . 7

strength are two essential qualities in concrete, in order that a structure may be put to the use for which it is intended as soon as possible 

and that there shall be no subsequent deterioration in strength.

The least age at which any tests were made was four weeks,,and at 

that period in no case except that of the cinder concrete, wet consistency, did the compressive strength fall below 2,000 pounds per 

square inch, while the cinder concrete had in every case a compressive 

strength of at least 1,000 pounds per square inch.

In every instance the compressive strength shows a substantial 

increase from four to thirteen weeks, with the single exception of 

limestone concrete mixed to a wet consistency, for which a decreased 

strength is indicated by the tests, a decrease which continues to the 

age of twenty-six weeks. This decrease in the strength of the limestone concrete is unexplainable, and the results of the 52-week tests 

on this material will be of value as indicating whether or not this 

decrease continues to the latter period. The other aggregates show 

either the same or a slightly greater strength at twenty-six weeks 

than at thirteen weeks.

The transverse tests on both the long and the short beams bear out 

very closely the fact indicated by the compression tests on the cylinders and cubes, and lead to the belief that the tensile and compressive 

strength are affected alike by both age and consistency. The effect 

on the strength of the variation in the consistency is clearly shown. 

In almost every case the concrete of the damp consistency is the 

strongest and that of the wet consistency the weakest. This is true 

for the three ages at which the concrete was tested, and is' confirmed 

by the tests of the beams as well as of the cylinders and the cubes. 

Attention is called to the fact that the damp consistency used is 

much wetter than the damp consistency used in making mortar 

building blocks, for which the same conclusions may not apply.

The difference in strength of the stone and gravel concretes of the 

three consistencies is more pronounced than in the case of the cinder 

concrete. The effect of the consistency on the strength seems to 

depend .to a great extent on the behavior of the concrete while being 

tamped and to the method used in tamping. Great care was taken 

to tamp all the concretes in the same manner. The thorough mixing 

of the concrete is absolutely essential and has a marked influence on 

the consistency.

The relatively slight influence exerted by the consistency on the 

strength of cinder concrete may be partly due to the structural weakness of the cinders themselves, which in the drier mixtures were to a 

great extent broken up by the tamper, while in the wet mixtures, the 

cinders would move from beneath the tamper.

While it is true that in almost every instance the drier mixtures 

give the greater strength, it does not follow that dry (or damp)
8 STEENGTH OF CONCEETE BEAMS.

mixtures should be used in construction. Practical considerations 

warrant the use of a wet mixture. The difficulty in securing efficient 

tamping and a smooth finish in a damp concrete, the loss of strength 

due to the unavoidable drying out of the concrete used above water, 

the difficulty of securing in reinforced concrete an intimate union 

with the steel, and the far greater ease of placing wet concrete all 

seem to warrant the sacrifice of what in many cases is but a slight 

difference in strength for a greater ease of manipulation and a 

thorough bedding of the steel, which is of the utmost importance in 

reinforced concrete work.

It is dangerous to draw any general conclusions as to the relative 

value of concrete made of the four aggregates used unless the character of the aggregates used in this particular series of tests is carefully kept in mind. The gravel, granite, limestone, and cinders were 

used as available representative type*s of aggregates, and while the 

results indicate that the granite makes the strongest concrete, it 

should not be assumed, therefore, that a granite concrete is stronger 

than a gravel, limestone, or cinder concrete. Every material should 

be accepted or rejected on the results of the tests of its qualities, 

regardless of the tests of other materials of the same type. Apparently insignificant differences in two materials which appear to be 

similar often cause considerable difference in the strength of concrete 

 made from them. For instance, two limestones from the same 

quarry crushed and screened under similar conditions except that 

one was screened while wet, which caused the dust to adhere to the 

surface of the. stone would make concretes of considerable difference 

in strength.

Because the hard, flinty gravel used in these tests gave excellent 

results, it does not necessarily follow that a similar well-graded gravel,

but composed of soft limestone or shale, would give like results. No 

series of investigations, however elaborate, will do away with the 

necessity of careful inspection of the materials to be used. The relative value of materials reported in this bulletin should be recognized, 

therefore, as applicable only to the particular materials from which 

the reported physical properties were obtained.

ACKNOWLEDGMENTS.

All the material used in the tests herein reported was donated by 

the following companies, who deserve credit for their interest and 

hearty cooperation in advancing the work:

Cement. lola Portland Cement Company, Tola, Kans.

Atlas Portland Cement Company, Hannibal, Mo. 

Whitehall Portland Cement Company, Cementon, Pa. 

Universal Portland Cement Company, Chicago, 111. .. 

Edison Portland Cement Company, New Village, N. J. 

Omega Portland Cement Company, Mosherville, Mich.
TESTS OF CEMENT. 9

Old Dominion Portland Cement Company, Fordwick, Va. 

Lehigh Portland Cement Company', Mitchell, Ind. 

St. Louis Portland Cement Company, St. Louis, Mo.

Sand. Union Sand and Material Company, St. Louis, Mo. A recent river sand 

dredged from Meramec River at Drake, Mo.

Gravel. Union Sand and Material Company, St. Louis, Mo. A recent river gravel 

dredged from Meramec River at Drake, Mo'.

Granite. Schneider Granite Company, St. Louis, Mo. A hard, red granite quarried near Graniteville, Mor

Cinders. United Railways Company, St. Louis, Mo. These cinders were obtained 

from the Dehodiamont power house, St. Louis, and gave better results than those 

selected from other sources.

Limestone. Fruin-Bambrick Construction Company, St. Louis, Mo. Obtained 

from a quarry in St. Louis.

The tests were supervised by Louis H. Losse, and the results were 

computed and collated by Harry Kaplan.

TESTS OF CONSTITUENT MATERIALS.

CEMENT. 

.PREPARATION OF TYPICAL CEMENT.

The cement used in all the tests in these laboratories is known as 

typical Portland cement. It is prepared by thoroughly mixing together a number of Portland cements. The method of preparing the 

typical Portland cement that was used in the tests herein reported and 

in the tests on the second'and third series, reinforced beams, including 

in all 576 beams, cylinders, and cubes, was as follows:

One thousand eight hundred sacks of cement, 200 from each of 

nine companies, were used. Two hundred sacks of one brand were 

spread over a concrete floor 25 by 40 feet in area and thoroughly 

mixed by hoeing from side to side. Two samples were then taken, a 

50-pound sample for tests to be made by the constituent-materials 

section, and a smaller one for chemical tests. The cement was then, 

resacked. When all the brands had been separately mixed in this 

way, two sacks of each brand were spread on the floor in a layer about 

3 inches thick. One brand was spread upon another in blanket form, 

making nine separate layers of cement for the nine brands used. The 

mass was mixed very carefully with shovels until a uniform mixture 

was obtained. A 10-pound sample was taken for physical tests and 

the cement was sealed in air-tight cans, two cans of 800 pounds 

capacity each being required to hold one mix.

RESULTS OF TESTS.

Table 1 contains the results of the chemical tests of the individual 

brands, made on samples taken as indicated above. The average of 

the columns may be taken as the analysis of the typical Portland 

cement.
10 STRENGTH. OF CONCRETE BEAMS.

TABLE 1. Chemical analyses of individual brands, used in the ..preparation of typical

Portland cement. ....

Cement No.

200.................

201... ...............

202.................

203.................

204. ................

205.................

206. .................

207.................

208.................

Silica 

(Si08).

20.34

' 22. 12

20.96

20.52

20. 04

22.04

'22.80

22.96

23.48

21.70

Alumina 

(A120,).

9.36

6.50

8.08

8.54

7.70

9.50

9 ^i\

9.34

8.22

"' 8.53-

Ferric 

oxide 

(Fe208).

3.04

3.22

2.80

2.68'

2.74

1.42

1.06

1.32

1.80

2.23

Lime 

(CaO).

63.40

61. 39

62.68

62.47

63.26

61.46

61.04

61.20

61.10

62.00

Magnesia 

(MgO).-

1.35

" 2.58

1.45

1.92

 2.24

1.68

1 Q7

1.47

1.62

- ' 1. 74'

. Sulphuric 

anhydride 

(SO,)..

1.47

 " 1 89

1.54

1.50

1.56

1.58

1 89

1.81

1.68

1.67

Water 

(H,0)-.

' 0.94

.18

.29

.08

.55

.64

.28

.44

.43

Ignition 

 loss.

0.55

1.61

1.43

.96

.84

.77

.86 ' - .81

.98

Undetermined.

1.04

.97

.70

.65

1.60

.93

.94

.76

.85

.94

- Table 2.contains the results of the physical tests-, except those for 

strength of the individual brands.- 'All these tests were made according to. the methods, recommended by the' special committee on uniform tests of cement of the American Society of Civil Engineers.

TABLE 2. Physical tests of individual brands used in typical Portland cement. a

 . Cement $Tp;

... -.. _.-^

200................

201.:.. .'..:.

202:.............

203.;..........

204. ...........

205. ...........

206............

207'::.........-

208............

Average....

Residue on 

sieve (per 

. cent)^-

100.

,, 59 5.5- 

- 7.8. 

4. 4-

2.0 

6.0

' 5. 3- 

6.0 

3.1

5.1

200.

20.9 

22.1 

24.6 

20.6

12.0 

22.2

21.5 

23:2 

21.6

21.0

Specific 

gravity.

 3.136 

'3.058 

 3.121 

3.099

'"3.087 

- 3. 165

3.127 

 3. 129 

3.141

3.108

Water 

(per . 

cent).

21.0 

' 20.5 

20.5 

21.5

24. 0 

.21.0

. 21.0 

- 20/5

: 22. 5

21.4

Time of set (minutes) .

Vicat.

Initial.

. 184 

93 

138 

117

124 127

113 

146 

 170

135

Final.

340 

378 

329 

315

416 

370

338 

391 

332

357

Gilmore.

Initial.

155- 

110 

 152 

150

229 

178

-195 

182 

217

174

Final.

325 

486 

393 

352

458 

394

441 

372 

400

402

Normal pat tests.

Air (70° F.).

.....do........ 

.....do........ 

Crack 1" long 

i" from edge.

Warped 3y 

from edge.

.....do........ 

.....do........

Water 

(70° F.).

Normal. 

Do. 

Do. 

Do.

'Do. 

Do.

Do. 

Do. 

Do.

 a In the accelerated pat tests, in water at 212° F. for 3 hours and in steam maintained at normal 

pressure for 5 hours, the results were normal in each case for each brand of cement.

Table 3 contains the results of the strength tests of the individual brands. Tests were made for both neat cement and 1:3 mortar 

with. Ottawa .sand, in, tension, compression on -2-inch cubes, and 

modulus of rupture on a 1 by 1 inch prism tested by a center load on 

a 12-inch span.. .All tests were made according to the methods rec- 

.ommended by the'special committee on uniform tests of cement of 

the American Society of Civil Engineers.
TABLE 3. Strength tests of individual brands used in the preparation 

Cement No.

1

200................. .

201.....................

202................. . .

203.;...................

204.....................

205.....................

206.....................

. Average. ............

Temperature (°F.).

Air.

2

64.4

68.8

64.4

66.4

68.0

72.0

70.0

Water.

3

68.0

. 68.0

68.0

68.0

68.0

68.0

 68.0

Closet

4

64.4

61.4

64.4

 68.9

66.2

71.6

 71-. 6

Tanks.

5

53.6

70.0

68.9,

73.4

71.6

74.3

. 69.8

Water 

(per 

cent) .

6

21.0

20.5

20.5

21.5

24.0

21.0

21. oi

Strength of neat t

Tensile.

1 

day.

.7

332 

324 

332

329

144 

172 

171

162

401 

475 

487

454

299 

312 

292

301

276 

285 

275

279

305 

308 

326

313

452 

434 

438 

441

7 

days.

8

655 

698 

. 672

675

616 

601

608

754 

725 

760

746

562 

585 

548

565

622 

640 

623

628

638 

616 

620

625

576 

548 

57S

567

28 

days.

9

864 

870 

852

862

772 

729 

728

743

792 

776 

780

783

781 

814 

809

801

715 

712 

732

720

790 

762 

806

786

758 

735 '742

745

90 

days.

10

859 

842 

846

849

835 

886. 

842

854

842 

803 

832

826

827 

886 

881

865

790 

815 

821

809

820 

811 

809

813

809' 

827 

851

829

180 

days.

11

886 

878 

859

874

880 

861 

848

863

832 

881 

870

861

840 

835 

854

843

835 

837 

826

833

855 

862 

888

868

770 

810 

775

785

i 

day.

12

2,375 

2,500 

2,400

2,425

1,425 

1,;400

1, 413 '

3,900 

3,750 

4,025

3,892

2,400 

1,625 

2,125

2,050

2,325 

2,200 

2,225

2,250

2,075 

1,975 

2,000

: 2,017

3,500 

3,225 

3,400

 3.375

7 

days

13

10,09

9,22

10,92

10,08

5,89

5,63

5,08

5,54

7,50

8,12

7,81

6,77

7,30

6,99

7,02

6.67

e;os

6,19

6,30

6,55

7,05

7,17

6,92

6,62

6,97

7,30

6.96
TABLE 3. Strength tests of individual brands used in the preparation of ty

Cement No.

1

207. ....................

208. ....................

Average ..... . . .

Temperature (F°.).

Air.

2

73.0

66.2

Water.

3

64.4

68.0

Closet.

4

69.8

69.8

Tanks.

5

66.2

65.3

Water 

(per 

cent).

6

20.5

22'. 5

21.4

Strength of neat 

Tensile.

1

day.

7

375 

375 

358

369

326 

355 

342

341 

336

7 

days.

8

685 

720 

692

699

820 

792 

784

799 

659

28 

days.

9

827 

825 

788

813

748 

762 

750

753

778

90 

days.

10

798 

810 

793

800

810 

807 

814

810

828

180 

days.

11

820 

800. 

804

808

825 

828 

835

829 

840

1 

 day.

12

3,550 

3,800 

3,700

3,683

3,675 

3,350 

3,575

3,533 

2,789

7 

day

13

8,4

8,0

8,3

8,2

7,3

7,9

7,6

7,6

7,3

Cement No.

1

200................................

201................................

202................................

A veraere ........................

Temperature (°F.).

Air.

2

64.4

68.8

64.4

Water.

3

68.0

68.0.

68.0

Closet.

4

64.4

61.4

64.4

Tanks.

5

53.6

70.0

68.9

Water 

(per 

cent) .

22

8.9

8.9

8.9

Strength of 1 : 3 stand

Tensile.

7 days.

23

364 

375 

395

378

171 

156 

194

174

335 

320 

328

328

28 

days.

24

425 

419 

413

419

290 

330 

320

313

425 

457 

435

439

90 

days.

25

426 

461 

445

444

412 

410 

428

417

408 

439 

445

431

180 

days.

26

515 

510 

486

504

421 

454 

430

435-

430 

478 

464

457
203................................

204................................

205................................

206. . . .

207................................

308................................

66.4

68.0

72.0

70.0

73.0

66.2

68.0

68.0

68.0

68.0

64.4

68.0

68.9

66.2

71.6

71.6

69.8

69.8

73.4

71.6

74.3

69.8

66.2

65.3

9.1

,

9.5

9.0

9.0

8.9

9.3

9.1

265

272

271

363

322-

OOA

338

247

219

229

284

281 

272

279

324

330 

358

337

327

330 

291

316

294

355

411

376

420

406 

394

407

401

424 

387

404

406

445

426

455

418 

464

446

427

472 

462

454

409

431

446

440

495

472 

466

478

446

430 

449

442

450

436 

493

460

488

476 

452

472

535

509 

530

525

457

452

445 

456

451

475

450 

460

462

482

465 

460

469

465

493 

468

475

445

438 

450

444

496

521

526

514

468
TABLE 4. Physical properties of cements used in co

Register 

No.

209. ..........

210. .:........

214...........

218. ..........

220............

223...........

224...........

226. ..........

227. .......:..

229. ..........

230...........

231...........

232...........

233. ..........

335. ..........

336. ..........

237...........

271...........

272...........

274...........

275. ..........

283. ..........

289...........

9Q1

292...........

293...........

301...........

302...........

303...........

304. ;.........

309. ..........

312. ..........

Specific 

gravity.

3.112 

3.116 

3.111 

3.111 

3.116 

3.108 

3.113 

3.112 

3.113 

3.114 

3.118 

3.113 

3. 113 

3.111 

3.113 

3.115 

3.109 

3.112 

3.114 

3.113 

3.115 

3.115 

3.118

3.111 

3.116

3.111 

3.114 

3.113 

3.114 

3.112 

3.112 

3.110 

3.110 

3.113 

3.111 

3.110

Temperature 

(°F.).

Water.

75.2 

75.2 

75.2 

74.0 

74.0 

75.0 

75.0 

77.0 

73.0 

73.0 

73.0 

73.0 

70.0 

70.0 

67.1 

67.1 

67.1 

68.0 

68.0 

64.4 

64.4 

68.0 

68.0

68.0 

68.0

68.0 

68.0 

68.0 

68.0 

68.0 

68.0 

68.0 

68.0 

68.0 

68.0 

68.0

Air.

71.6 

71.6 

71.6 

70.6 

70.6 

71.6 

71.6 

65.0 

68.0 

68.0 

68.0 

68.0 

68.5 

68.5 

72.5 

7^.5 

7^.5 

55.4 

55.4 

48.2 

48.2 

50.0 

59.0

59.0 

68.0

70.0 

70.0 

75.0 

75.2 

75.2 

74.5 

74.5 

59.9 

59.9 

70.7 

62.6

Water 

. (per 

cent).

21.0 

21.0 

21.0 

21.0 

21.0 

21.0 

21.0 

21.0 

21.0 

21.0 

21.0 

21.0 

21.0 

21.0 

21.0 

21.0 

21.0 

21.0 

21.0 

21.0 

21.0 

21.0 

21.0

21.0 

21.0

21.0 

 21.0 

21.0 

21.0 

21.0 

21.0 

21.0 

21.0 

21.0 

21.0 

21.0

Time of set (minutes).

Vicat.

Initial.

138 

137 

132 

180 

195 

200 

195 

222 

174 

192 

182 

171 

203 

180 

195 

206 

194 

200 

233 

262 

263 

300 

238

219 

170

147 

138 

153 

139 

152 

134 

190 

208 

225 

156 

176

Final.

370 

372 

386 

389 

379 

 443 

432 

446 

435 

415 

419 

411 

438 

424 

443 

443 

458 

498 

470 

472 454* 

500 

. 381

432 

416

419 

240 

377 

369 

364 

450 

466 

447 

464 

388 

425

 Gilmore.

Initial.

180 

239 

226 

275 

262 

192 

275 

279 

245 

250 

242 

231 

271 

244 

223 

243 

235 

265 

282 

268 

250 

357 

255

353 

143

175 

239 

184 

189 

259 

297 

318 

290- 

320 

227 

215

Final.

403 

429 

401 

 430 

410 

475 

470 

512 

472 

474 

466 

457 

478 

468 

485 

472 

460 

505 

484 

487 

357 

532 

465

451 

403

404 

444 

405 

405 

, 456 

486 

517 

508 

524 

461 

468

Residue on 

sieve (per 

cent) 

100.

4.8 

4.6 

5.0 

5.2 

5.0 

4.9 

4.8 

5.0 

4.6 

4.7 

5.4 

5.1 

4.8 

5.0 

4.0 

4.9 

5.0 

5.2 

4.6 

4.5 

4.5 

. '4.7 

4.8

4.8 

4.8

4.9 

5.0 

4.9 

4.9 

4.7 

4.9 

4.8 

5.0 

4.7 

4.8 

4.8

200

19.8 

20.8 

22.4 

20.8' 

21.8 

21.3 

20.7 

20.8 

21.2 

21.1 

21.0 

20.8 

20.7 

21.2 

21.4 

21.4 

21.6 

21.5 

20.7 

20.5 

20.5 

21.1 

21.4

21.2 

2M

21,1 

21.1 

21.0 

21.1 

20.7 

21.5 

21.3 

21.6 

21.4 

21.5 

21.6

Tensile s

(poun

1 

day.

422 

468 

496 

451 

470 

373 

371 

382 

368 

425 

451 

424 

372 

409 

427 

389 

441 

290 

316 

220 

221 

309 

433

420

387

404 

421 

431 

436 

425 

'427 

 433 

428 

* 422 

403 

386

7 

day

6

6

6

6

7

7

7

7

7

7

7

. 7

' 7

8

7

7

7

6

 6

6

6

7

7

7

7

7

7

7

7

7

7

7

7

7

7

7
313...........

314...........

316...........

317...........

318...........

Average . . .

3.112

3.112

3.116

3.114

3.118

3.113

68.0-

68.0

68.0

68.0

68.0

69.7

62.6

62.6

66.0

66.0

66.0

66.5

21.0

21.0

21.0

21.0

21.0

182

1 ^4

135

IT?

184

437

AAQ

425

Af\A

421

206

252

174

188

244

474

482

440

AA'Z

459

5.1

4.8

4 9

5.2

4.9

21.7

21.5

21.2

21.2

376

356

408

420

398
16 STRENGTH OF CONCRETE BEAMS.

Table 4 contains the results of all the physical tests made of the 

typical Portland cement that was used in the present series of concrete beams. In the column "Register No." is given the register 

number of the cement used. Each number corresponds to two cans 

of 800 pounds each of typical Portland cement. . The sample for 

each test was taken as already indicated.

As these tests were made with the sole idea of checking the uniformity with which the typical Portland cement was prepared, a full 

series of neat and sand tests was thought unnecessary and undesirable, for it would entail too much routine work on the part of the 

constituent-materials laboratory. Accordingly, only tension tests 

on neat cement were made.

SAND.

The same sand was used with all the aggregates tested. It is 

known as Meramec River sand, and is composed of flint grains having 

comparatively smooth surfaces. The yellowish-brown color of the 

flint imparts a tint of the same color to the sand as a whole.

Tables 5 and 6 (p. 17) give the results of the physical tests on this 

material. The granulometric. analysis in Table 6 shows the sand to 

be rather finer than desirable. The percentage of voids was computed from the weight per cubic foot and the specific gravity.

Table 7 (p. 18), which contains the results of the tests made on the 

cement used in the preparation of the test pieces reported in Table 5, 

will aid in the interpretation of the values given in the latter table.
TABLE 5. Tests of mortar made with Meramec River sand (Sd. 43) and typical 

Fineness of sand.

Passed J-inch 

screen.

Size, 30-40. .........

Proportion of 

mortar.

fl:3. ...... .........

1:4................

A-V6r8,2G

1:3................

Water 

(per 

cent) .

11.5

11.0

11.5

Temperature 

(-°F.).

Air.

71.0

71.0

65.0

Water.

68.0

68.0

68.0

Tensile strength (pounds per 

square inch) .

7 

days.

274 

263 

260

266

180 

186 

190

185

215 

224 

207

215

28 

days.

438 

422 

416

425

302 

294 

306

301

293 

294 

299

295

90 

days.

418 

415 

446

426

352 

352 

361

355

343 

350 

344

346

180 

days.

443 

467 

487

466

391 

355 

373

373

359 

353 

335

349

360 

days.

480 

473 

486

480

401 

408 

416

408

360 

372 

368

367

Compressi

7 

days.

2,375 

2,250 

2,325

2,317

1,375 

1,375 

1,325

1,358

1,425 

1,400 

1,425

1,417

28 

day

4,0

4,1

4,0

4,1

2,4

2,3

2,37

2,3

2,7

2,7

2,6

2,7

H*-

I

TABLE 6. Physical properties of sand and other materials forming a

Kind of material.

Specific 

gravity.

1.530 

2.585 

2.450 

2.489 

2.597

Percentage of 

voids 

(computed) .

50.7 

40.9 

33.0 

37.1 

37.9

Weight 

(pounds 

per cubic 

foot).

47.0 

' 95.3 

102.4 

97.7 

100.6

Percen

200.

2.84 

1.59 

0 

2.96 

.20

100.

4.17 

2.29 

0 

3.48 

1.30

80.

4.91 

2.62 

0 

3.70 

3.60

50.

6.45 

3.22 

0 

4.18 

13.90

40.

8.26 

3.74 

0 

4.68 

37.00
18 STEENGTH OF CONCRETE BEAMS.

AGGREGATE.

The results of the physical tests on the granite, gravel, cinders, and 

limestone used in the plain beams are reported in Table 6. The 

crushing strength of the 1:2:4 concrete made of these aggregates is 

given in connection with the results of tests on the plain beams, in 

Table 10 (pp. 48-53).

TABLE 7. Tests of cement 140, used in testing Meramec River sand (strength in pounds

per square inch).

Kind of test.

Compression.....

Neat.

Iday.

362 

* 375 

372

370

3,425 

3,275 

3,300

3,333

756 

792 

774

774

7 days.

710 

700 

718

709

9,300 

9,325 

9,175

9,266

1,440 

1,440 

1,470

1,452

28 

days.

696 

705 

709

703

10, 512 

11, 125 

10, 497

10,711

1,.872 

1,908 

1,944

1,908

90 

days.

775 

792 

781. 

783

12,288 

12,612 

12, 862

12,590

1,998 

2,016 

1,962

1,992

ISO 

days.

827 

811 

813 

817

13, 980 

13, 725 

13, 803

13, 836

1,944 

2,088 

2,034

2,022

360 

days.

846 

853 

831 

843 

14, 274 

14, 410 

14, 320

13, 335

2,142 

2,232 

2,124

2,166

1 : 3 mortar.

7 

days.

342 

375 

364

360

1,570 

1,555 

1, 735

1,620

28 

days.

527 

540 

531 

533

3,200 

3,300 

3,025

3,175

90 

days.

445 

445 

413 

434

3,098 

3,400 

3,549

180 

days.

405 

388 

394

396

5,025 

5,025 

4,800

4,950

360 

days.

414 

408 

405

408

5,500 

5,425 

5,239

5,388

Remarks. Fineness: Residue on No. 100 sieve, 6.8 per cent; on No. 200 sieve, 22.8 

per cent. Specific gravity, 3.12. Time of set: Initial, 142. minutes; final, 428 minutes. Soundness: Pat test in air at 70° F., normal; in water at 70° F., normal; in 

water at 212° F., 3 hours, normal; in steam at normal pressure, 5 hours, normal. Water 

used in mixing: Neat, 20.5 per cent; mortar, 8.9 per cent. Temperatures: Of air, 

71.0° F.; of water, 68.0° F.

PREPARATION OF TEST PIECES.

METHODS OF PROPORTIONING.

A 1:2:4 volume proportion was adopted for all the concrete used 

in the following tests. Since, however, the volume of a given weight 

of dry sand is greatly affected by the percentage of moisture present, 

it was thought best to do the actual proportioning by weight. The 

weight of 1 cubic foot of cement was assumed to be 100 pounds. The 

weight per cubic foot of the dry, loose sand and the dry, loose aggregate as determined by tests in the constituent-materials laboratory, 

was used in reducing the proportions by volume to the proportions 

by weight.

With this as a basis, the necessary weight of dry material for the 

desired batch was determined. Since the sand and stone, as stored 

in the bins, contained an appreciable amount of moisture, the dry 

weight of the material had to be increased by the weight of the moisture present before the batch could be weighed out. The percentage 

of moisture was determined on a 500-gram sample of the sand and 

stone each day on which beams were molded.
PKEPAKATION OF TEST PIECES. 19

The above method of correcting for moisture was followed in the 

series of concrete beams and in the greater part of the first reinforced 

beam series. It was noticed from time to time, however, that the 

concrete when dumped from the mixer was not always of the same 

consistency, in spite of the fact that the total weight of water present 

(weight of water added plus the weight of the moisture in the sand and 

the stone) was a constant. A moisture determination was then made 

on a sample representing as nearly an average of the material in the 

bin as it was possible to obtain, and this was then maintained constant 

and gave much better results. The effect on the consistency of a given 

change in the weight of the moisture in the sand or stone does not 

appear to be the same as that of an identical change in the weight of 

the water added to the batch, the difference probably being due to the 

fact that the moisture test is only local and does not represent the 

true average of the material in the bin.

It should be noted here that the proportions by volume of the cinder concrete are nearer 1:2:5 than 1:2:4. This is due to an error in 

making the moisture determination at the time the weight per cubic 

foot was determined. The weight per cubic foot of the cinders, including apparently 11.1 percent moisture, was reported as 68.1 pounds. 

Using these figures gives 61.3 pounds per cubic foot for the weight of 

the dry, loose cinders. These determinations were accepted as correct until a sample, which had been forgotten in the oven, showed 23 

per cent moisture present. This error in the weight per cubic foot, 

due to insufficient drying of the test sample, was not discovered until 

the series of cinder beams was almost completed. While a new determination of the weight per cubic foot was made and the proportions 

by weight and volume modified accordingly, it was thought best to 

use these proportions and the correct weight per-cubic foot on the remaining cinder beams rather than the 1:2:4 volume proportions, in 

order to make the cinder beams comparable among themselves even 

if not strictly comparable with the beams of other aggregates.

The weight per cubic foot, as redetermined, was found to be 47.0 

pounds.

METHOD OF MIXING AND CONSISTENCY. 

MIXING.

All concrete was mixed in a motor-driven cubic-yard cube mixer, 

which is equipped with a charging hopper. All water used in mixing 

concrete was weighed and was supplied to the mixer through a hose 

attached to a water barrel, which is mounted on a platform scale on a 

support above the mixer. To insure uniform conditions the interior 

of the mixer was wetted down each morning before the first mix of 

the day. All concrete was mixed two minutes dry and three minutes
20 . STRENGTH OF CONCRETE BEAMS.

wet, after which it was dumped on the cement floor, shoveled into 

wheelbarrows and wheeled to the molding floor. Sufficient material 

was charged into the mixer to make two beams, two cylinders, and 

two cubes from the same batch of concrete.

CONSISTENCY.

Definition. The three consistencies, wet, medium, and damp, as 

here used, represent each a certain characteristic behavior and appearance of the concrete in the mixer, on the floor, and in the mold when 

subjected to tamping. In order to eliminate the personal equation as 

far as possible, the amount of water required to bring the batch to a 

desired consistency for a particular aggregate was carefully determined by trial before the test pieces were molded. Thereafter the 

weight of water to be used with each aggregate for that consistency 

could be obtained by making a simple correction each day, depending 

upon the percentage of water contained in the aggregate as it came 

from the bins. The total amount of water, including moisture, was 

expressed as a percentage of the total weight of the dry material and 

was maintained constant.

A brief description of the consistencies is given. It should be recognized that the consistencies as defined are purely arbitrary, but each, 

it is thought, represents a characteristic appearance and behavior, 

and, with a little practice, is readily distinguished from the others.

Wet consistency. Concrete of wet consistency has a smooth and 

somewhat viscous appearance in the mixer, or immediately before 

dumping. It flows back from the ascending side of the mixer without 

any tendency toward "breaking" over at the top. The upper surface of the concrete in the bottom of the mixer rolls underneath the 

mass smoothly and is carried upward by adhesion, to the metal. 

When dumped, it stands on the floor in a low pile, having a smooth 

surface, and showing neither voids nor individual stones. It can not 

be compacted by tamping in the molds, but splashes under the action 

of the tamper. When finished, water stands from one-fourth to onehalf inch deep over the surface of the mold.

Medium consistency. Concrete of medium consistency has a smooth 

appearance in the mixer, but shows a tendency to lump. As compared to that of wet consistency it flows less smoothly and is carried 

higher by the ascending side of the mixer, part flowing back smoothly 

and part breaking over at the top in lumps. When dumped, it stands 

in a higher pile with steeper side slopes, exhibiting a somewhat lumpy 

appearance, and showing individual stones, but no voids. The stones 

show an even coating of sand mortar. No water collects on the surface of the beam in the mold. The surface is easily finished with a 

trowel.
PREPARATION OF TEST PIECES. 21

Damp consistency. Concrete of damp consistency is decidedly 

granular in the mixer with "little tendency to lump. The material is 

carried to the top of the mixer and falls in individual stones, and fragments of mortar. When dumped, it stands at the same angle as 

medium concrete, showing both individual stones and voids. The 

surface of the pile is irregular. In the mold it offers considerable resistance to tamping, but compacts fairly well under hand tamping. 

No water flushes to the surface and it can not be finished smooth by 

troweling.

METHOD OF MOLDING. 

BEAMS.

The beam molds consisted of three long steel channels with flanges 

turned outward, forming the sides and bottom of the mold. The ends 

were closed b}r short pieces of channels. The side and end pieces 

were removable. The molds were oiled before the concrete was 

placed, to prevent adhesion to the surface of the steel. In molding 

the plain beams the concrete was deposited in three layers of about 

equal thickness. The tamping was done by hand with a 13f-pound 

tamper having a rectangular head 1J by 3£ inches. The tamping was 

started at one side of one end of the mold and the tamper moved 

toward the opposite side, the width of the tamper at each stroke. 

The tamper was then set forward and the process repeated. In this 

way each part of the layer was tamped once. The mold was gone 

over twice in this way, after which the concrete was spaded back from 

the sides of the mold and the layer tamped a third time. The same 

operation was followed for each of the three layers. The surface of 

each beam was finished as smooth as possible by troweling.

The side and end pieces of the mold were removed at the end of 

twenty-four hours, and the beam was covered with burlap and allowed 

to remain on the bottom channel until moved into the moist room.

CYLINDERS AND CUBES.

In order to make the compression test representative of the true 

crushing strength of the concrete in the beam, the cylinders and 

cubes were molded from the same batch as the beam of the same 

number. They were molded in cast-iron separable molds, which were 

oiled previous to placing the concrete. The concrete was deposited 

in layers approximately 3 inches thick, and each layer was tamped 

twice, a circular hand tamper 3£ inches in diameter and weighing 7 

pounds being used for the cylinders and a rectangular tamper 3£ by 1J 

inches, weighing 13f pounds, for the cubes.

In molding the cubes an effort was made to "spade" back the concrete from the sides of the mold, as was done in molding the beams.
22 STRENGTH OF CONCRETE BEAMS.

The top surfaces of the cubes and cylinders were finished smooth with 

a trowel. All molds were removed at the end of twenty-four hours, 

and the test pieces were marked and transferred to the moist room.

MOVING AND STORAGE.

The large number of beams to be molded and the small space available made it imperative that the beams be moved as soon as possible. 

In no.case could they remain where molded for more than 12 or 16 

days. Since a concrete beam without reinforcement, and weighing 

about 1,200 pounds, has very little tensile resistance at this age, it 

was very important that they be handled at points that would prevent 

any chance of injury when being moved to the moist room. The 

following plan was followed, and was entirely satisfactory:

The channel forming the bottom of the mold was placed with the 

flanges turned down. At the points where the beams were supported 

in moving them, the webs of the bottom channels were cut away for 

a width of 1^ inches. Prior to molding this slot was closed by a filler 

resting on the uncut flanges. When the beam was to be moved, this 

filler was driven put and a slightly narrower piece, which projected 1£ 

inches beyond each side of the beam, was substituted.

A stirrup hanging from the chain blocks suspended from trolleys 

running on overhead I beams, was hooked under these projecting ends 

and lifted a 13-foot beam at two points 8 feet apart, which give equal 

positive and negative bending moment, and consequently minimum 

stresses in a beam of that length.

The beams in the moist room were stored six high, being supported 

at the same points as when brought to the damp closet.

All test pieces were sprinkled from a hose three times each day 

at midnight, at 8 a. m., and at 4 p. m. both before and after being 

placed in the moist room.

The temperature on the molding floor and in the moist room was 

recorded on a self-recording thermometer, and was maintained as 

near 70° as possible.

METHODS OF TESTING.

BEAMS. 

LOttG BEAMS.

APPARATUS.

PI. I shows a photograph of a beam in place. The supports "P" 

for the beams have cylindrical top surfaces, and are so designed as 

to give a slight yielding motion outward, the object being to prevent 

any restraint of the beam which might follow from the lengthening 

of the lower fiber.
U. 8. GEOLOGICAL SURVEY 

CONCRETE BEAM IN MACHINE READY FOR TEST
METHODS OF TESTING. 23

The deformeter yokes (E, E') are fastened to the beam by tightening the nuts A, which force the contact points (b) and those directly 

opposite on the far side of- the beam, against the surface of the concrete. The yokes are equidistant from the center of the beam, the 

contact points being 29.25 inches apart for the outer yokes and 24 

inches apart for the inner set. The contact points of the outer set 

were 10 inches apart vertically and those of the inner yokes 5.75 

inches apart. Both yokes were centered on the horizontal axis of 

the beam, thus bringing the contact points of .the- outer yokes 0.5 

inch.below the top and 0.5 inch above the bottom. The inner yokes 

were used only on some of the earlier beams in order to test the conservation of plane section. Four pins directly in line with the contact points onE engage cylindrical holes in the ends of the four rods? 

the other ends of which rest lightly on hard rubber rollers fastened 

to the arms C, which are rigidly connected to the yoke E.

Four micrometer screws reading directly to 0.0001 inch work in 

bushings fastened to the yoke E'. When any micrometer screw is 

brought in contact with the end of the corresponding rod, an electric 

contact is made, which causes a click in the telephone receiver F. 

Both yokes are divided into two vertical halves by rubber insulation, 

thus making it possible to read micrometers on both sides of the 

beam simultaneously.

METHOD OF ZEKO DEFOKMATIONS.

The deformation of concrete in compression in a beam is obtained 

from a reading of the upper micrometers'while the lower ones give 

the elongation of concrete. The readings of both upper and lower 

micrometers, making the usual assumption of conservation of plane 

section, fix the position of the neutral axis. The beams were all 

tested on a 12-foot span by two equal loads, applied at the third 

points of the span.

The load apparatus consists of a box girder (H) built of two 6-inch 

channels with a ^-inch cover plate on the top and the bottom. The 

load is transmitted from the testing machine to the box girder through 

a spherical bearing block (I), and from the box girder to the beam 

by two 2-inch steel rollers (J) bearing on two steel blocks (not shown) 

set in plaster of Paris. The upper surface of these blocks is a cylinder of very large radius whose axis is parallel to the length of the 

beam. With the exception of these bearing blocks the entire load 

apparatus is suspended from the top head (L) of the testing machine 

by a bolt passing through the spherical bearing block and engaging 

a plate on the inner surface of the box girder. The. steel rollers (J) 

are kept in place by the casting which extends a trifle below their 

axis.
24 STRENGTH OF CONCRETE BEAMS.

On commencing a test the bearing blocks are removed and yokes 

(K) are passed under the test beam and over the box girder directly 

above the 2-inch rollers. The head (L)'is then run up until the 

reaction at the ends of the test beam has been so reduced that the 

total positive bending moment area is equal to the total negative 

bending moment area within the gage length, considering the beam 

as a continuous girder over four supports, viz, the two end supports 

and the two intermediate yokes.

This method is used for the following reason: In tests of beams as 

usually made, the upper and lower fibers of the beam are already 

deformed and are under stress due to the weight of the beam when 

the first, or zero, reading of the deformeters is taken; the deformations computed from these readings are too small by an amount 

which becomes relatively more and more important as the breaking 

loads decrease and which in the case of plain beams (many of which 

fail by a load but little in excess of the weight of the beam) becomes 

a very large part of the ultimate deformation.

When a beam rests freely on supports, the upper and lower fibers 

are deformed on account of the bending moment due to the weight of 

the beam. When the supports are at the ends of the beam the upper 

fibers are shortened and the lower are lengthened. For equal moduli 

of elasticity in tension and compression, which are constant for concrete under small loads, the deformation at any point of the beam is 

proportional to the area of the bending-moment diagram over that 

length. Therefore, when the total positive bending moment area in 

the gage length of the deformeters equals the total negative bending 

moment area in the gage length, the net total deformation in that 

length is zero, and both the upper and lower fibers of the beam have 

the same length as when unstressed. For a particular reaction at the. 

ends of the beam the positive bending moment area in the gage 

length is equal to the negative .bending moment area. In order to 

get this reaction the beams are supported at the third points by the 

head of the machine as previously described. As the stirrups under 

the third points of the span take more and more of the weight of the 

beam the end reactions become smaller and smaller and the character 

of the bending-moment diagram within the gage length changes 

until the desired condition is reached.
METHODS OF TESTING. 25

The method of finding the required reactions for total zero deformations within the gage length, in terms of the weight of the beam 

and other known quantities, may be understood by reference to fig. 1, 

as follows:

I"

i

...

\

3

i TA

j

3--, -J

A

 2

r -y

\ 

Hr

.J

FIG. 1. Diagrams illustrating method for computation of concrete beams. Upper diagram: Notation used. Lower diagram: Curve of bending moment within gage length (beam supported at third 

points).

Let L = distance between the supports, 

g = gage length of deformeters. 

Z = overhang of beam at each end.

o- = distance from each support to force exerted by each stirrup.

o

W = total weight of beam. 

 R = force exerted by each stirrup at a distance of -5- from the

2i . o

supports.

R = each reaction at end. 

SS. = any vertical section within the gage length at a distance,

x, from one of the gage points. 

Mx = bending moment at section SS. 

M0 = bending moment at deformeters, where x = 0.

Mc = bending moment at center of beam, where x = |.

in = constant bending moment over the gage length due to the 

weight of all attachments, such as bearing blocks under 

the load points and the deformeters. This weight is 

applied outside of the gage length and equally on each 

side of the center of the beam.

The bending moment at section SS, considering forces to the left 

only, is as follows:

M -=R( ~
26 ' STRENGTH OF CONCRETE BEAMS.

Reducing to a simpler form gives:

W 

, , RL W/

The bending moment at the end of the gage length (x =0) is as 

follows :

,, RL W/L

The bending moment at the center of the gage length ( x = | ) is as

V zy

follows :

RL W/L

The moment diagram between the third points, when there is 

both positive and negative bending moment in the gage length, is 

shown in fig. 1, in which xx' is the horizontal axis of the moment 

diagram. The curve bee'b' is a parabola and crosses the axis at 

two points (viz, e and e') between the ends of the deformeters. Then 

in the gage length cc' there is negative bending moment from c to e 

and from e' to c', and positive bending moment from e to e'. The 

dotted lines cb, c'b', and bb' are drawn for the purpose of demonstration. Then the distance Mc represents the bending moment 

at the center of the gage length, and M0 represents the bending 

moment at the end of the gage length. The negative bendingmoment areas within the gage length are cbe and c'b'e', each being 

represented by -B. The positive bending moment area within the 

gage length is eFe' and is represented by A.

The condition that the positive bending moment area is equal to 

the negative bending moment areas is represented by the equation 

A = 2B. Adding the quantity C to both sides of the equation gives A + ( C) = 2B C. The first part of this equation 

 is the area included between the horizontal line bb' and the parabola bFb'; thatis,A + (-C)=?g[Mc + (-Mo)].

o

The second part of the equation is equal to the area of the rectangle bcc'b'; that is, -2B-C = -gM0 .

Therefore |g [Mc + ( -MJ] = -gM0 ! Whence 2MC - -M0 .
METHODS OF TESTING. 27 

Substituting the values of M0 and Mc as found* above gives:

2RL W/L 7\ _ RL W/L 7\ Wg2 3 " 2^6 +/V +2m ~~ 3 + 4V6 +/V + ~~^ ~~m'

Whence KL = - +Z + ^ -3m

, T, 3W/L , ^\ , Wg2 3m and R =-rr(. TT +Z + ^v- =r rIn almost all the beams tested at the laboratories.L, Z, g, and m 

are constant. It only remains to find W and to compute. R. A 

table computed by the above formula has been compiled for all the 

usual values of W, from which the corresponding value of R in any 

case can be directly read.

METHOD OF TESTING.

When the test is commenced, the top head is run up until the reactions causing equal positive and negative bending moments over the 

gage length are developed at the ends of the beam. The sum of these 

reactions will appear on the weighing beam, the testing machine 

having been balanced before the weight of the beam and all test 

apparatus comes on it. A full set of deformeter readings is then 

taken.

After the readings at zero total deformations in the gage length 

and when the beam rests under its own weight are taken, the load is 

applied in increments of 200 to 1,000 pounds, depending on the stiffness of the beam, the top and bottom set of micrometer readings being 

recorded on the log sheets. Wood blocks are placed underneath the 

beam during the test, so that the distance it falls at rupture is not 

more than one-fourth inch.

SHORT BEAMS.

The longer portion of each beam after first failure is again tested 

on as great a span as its length permits, thus making a secondary 

series of short beams.

The load is applied by the same apparatus as that used for the 

long beams, but instead of being applied at the third points it is 

applied at points 2 feet from the center of the span. The short 

beams are not suspended for zero deformation readings, since for such 

small spans the deformation of the beam under its own weight is very 

small. On all short beams the outer yokes having a gage length of 

29.25 inches are alone used.
28 STRENGTH OF CONCRETE BEAMS. 

CYLINDERS AND CUBES.

The cylinders and cubes are tested on a four-screV, 200,000-pound 

Olsen machine. To insure an even distribution of load over the 

entire cross section the ends of the cylinders are bedded in plaster of 

Paris to a thickness of about one-half inch on a piece of plate glass 

(previously oiled to prevent adhesion of the plaster). The bearing 

surfaces are made normal to the axis of the cylinder by means of a 

spirit level applied to its sides. The cubes are not capped with plaster of Paris, but a thin piece of asbestos is placed on a spherical bearing plate when under test, in order to take up all nonparallelism of 

the ends.

The load is in each case carried to failure, being applied continuously tq rupture in the case of the cubes and in increments of 5,000 

pounds, or approximately 100 pounds per square inch for the cylinders. For each increment gross deformations are read on two opposite sides of the cylinder over a gage length of 12 inches.

RESULTS OF TESTS. 

BEAMS OF CONSTANT SPAN.

The detailed results of the tests of concrete beams 8 by 11 inches 

in section, 13 feet long, tested on a 12-foot span by two equal loads 

applied at the third points are given in Table 8 (p. 36), comprising the

/oo

v

A6£ S/V Mr££ftS

FIG. 2. Diagrams showing the eflect of age and consistency on the strength of cinder concrete.
EESULTS OF TESTS. 29

three ages of 4, 13, and 26 weeks, and some*of the results are graphically shown in figs. 2-5 and 10-13.

300 f (V

' tvfffts 

FIG. 3. Diagrams showing the effect of age and consistency on the strength'of granite concrete.

tV£ftf3 AGf M

FiG. 4. Diagrams showing the effect of age and consistency on the strength of gravel concrete.

The percentage of water is expressed in the table in terms of the 

total weight of the dry material. This percentage includes the 

weight of the moisture in the sand and aggregate, which varies from
30 STRENGTH OF CONCRETE BEAMS.

1.5 to 2.0 per cent of the weight of the stone,from 3 to 4 per cent of the 

weight of the sand, and may include as much as 21 per cent of the 

weight of the cinders. A simple computation, using the proportions

3OO

T

AS? //v wfr/rs 

FIG. 5. Diagrams showing the effect of age and consistency on the strength of limestone concrete

2600

2400

2200

^ 2000

1 I80° 

I 1600

| 1400

§.

.!= 1200

is

 a 1000

800

600

400

200

E

26 weeks

4 weeks

8 8 § I i

Deformation per unit of length

FIG. 6. Characteristic compression-stress defonnation diagrams, cinder concrete of medium consistency; ages 4,13, and 26 weeks.

by weight, will show that this 21 per cent moisture forms as much as 

43 per cent of the total amount of water, including moisture, that is 

necessary to bring the concrete to the desired consistency. Deduct-
RESULTS OF TESTS. 31

ing this 43 per cent moisture from the total percentage of water 

leaves about 12 per cent of the total weight of the dry material as the 

weight of the water added plus- the weight of the moisture in the 

sand. This does not differ so very much from the percentage of 

water used for the other aggregates. As already indicated, it would 

seem that the influence of the water, present in the stone or cinders and 

even for usual values of 3 to 4 per cent in the sand does not influence 

the consistency as greatly 

as does the same weight 

of water when added to 

the batch.

Column 6 of the table 

gives the consistency of 

the concrete and must be 

compared with the definitions of wet, medium, and 

damp concrete already 

given (p. 20).

Columns 7, 8, and 9 

give the dimensions of the 

beam, thespan being kept 

constant at 12 feet.

Column 10 gives the 

total weight of the beam, 

which is obtained by 

weighing the beam on the 

testing machine. The error in weighing is in no 

case greater than 5 pounds 

in either direction. Column 11 gives the weight 

per cubic foot of thebeam.

Column 12 gives the unit 

elongation of the lower 

fiber when the beam rests 

freely on a 12-foot span 

subjected only to its own weight and the weight of the deformeters. 

This value is obtained by first taking a reading for zero total deformation as already described (p. 23) and a second reading when the beam 

rests as above. This value is included for the reason that in all tests 

made up to the present time deformations due to applied load only 

were read. If it is desired to compare the present tests with others 

already made the unit elongation, as given in column 14, which was 

measured at a load just previous to rupture, when decreased by the

4UUU

3600

.3400

.3200 

3000

2800

.2600

| ^4UU

1 2000

i

 E 1800

a

£

« 1600 

3 1400

1200

VUU

400

200

n

5

!/

f

A

ffv.

/

F

c

tt\

f

- f

m

f

it

w7

fw

7AT

V

f

/

/

/'

/

a . 

\SX*

/"

P

««'

/*

&

1

^

^

~~~

(.»

8 3

Deformation per unit of length

FIG. 7. Characteristic compression-stress deformation diagrams, granite concrete of medium consistency; ages 4, 13, 

and 26 weeks.
32 STRENGTH OF CONCBETE BEAMS.

A

value in column 12 will give the unit elongation at a point near rupture for the applied load alone.

M Column 13 sliowsr-r-j (pounds per square inch) for the last load

previous to failure. The relation of this value to the breaking value 

in column 19 is readily seen by comparison. In computing all the

M values of j-r2 given in these tables the nominal values 8 inches and 11

inches were used for the 

breadth (b) and the depth 

(d) of the beam.

Column 14 shows the 

unit elongation of the 

lower outer fiber for the 

load previous to rupture. 

An unsuccessful attempt 

was made to obtain an 

exact value for the unit 

elongation of the lower 

fiber at rupture; but it 

was found impossible to 

take a reading of the micrometers at the exact 

instant of the breaking of 

the beam. Just previous 

to the break the concrete 

in the lower fiber elongates so rapidly that it is 

impossible to revolve the 

micrometer fast enough 

to maintain contact with 

the rod. While the lower 

micrometers on both sides 

of the beam may be read 

as the beam breaks the 

values obtained are so 

erratic that they have 

not been included in the tables of this bulletin.

The unit elongations reported under "Final deformeters" (columns 

13, 14, and 15) in Table 8 are the values obtained at the last full set of 

readings preceding the breaking of the beam, and it must therefore 

be recognized that while they approximate the elongations at maximum load they are not absolute. Attention is called to the apparent

4000

3800

3600

3*00

3200

2800

2600

£ 2400

 g 2000 

I

 ^ 1800

j? 1600 

1400 

1200 

1000

800

600

400

200

I § 1.

Deformation per unit of length

FIG. 8. Characteristic compression-stress deformation diagrams, grave.l concrete of medium consistency; ages 4, 13, 

and 26 weeks..
EESULTS OF TESTS. 33

relation between the values in columns 13 and 14. Separating the 

aggregates into cinders on one hand.and the'three stone concretes on

M the other, the elongation'seems to bear a direct relation to fr^ 2 or the

load carried. This comparison, however, can not be made for the 

cinders, owing perhaps to the nonuniformity in the strength of the 

clinker itself.

Column 15 shows the position of the neutral axis for the load preceding failure. This is 

obtained from the usual 

assumption of proportionality between deformation and position of 

the neutral axis.

The maximum load applied at the third points 

of the span (column 16) 

excludes the weight of 

the deformeters. The

corresponding: , n is 

5 bd2

shown in column 17. 

Column 18 shows the

,-^r,, for the weight of the bd

beam, taking into consideration the effect of 

the 6-inch overhang on 

each end and also the 

constant weight of the 

deformeters.

Column 19 shows the 

M R2 '

which is equal to the 

sum of the values in columns 17 and 18.

Column 20 shows the modulus of rupture in pounds per square inch. 

These values were obtained by multiplying those in column 19 by 6. 

The method of computing the modulus of rupture should be emphasized. It is based on the assumption that the coefficients of elasticity in tension and compression are equal and constant and that

37206 Bull. 344 08 3

41W 

3800

Ifidfl

*>

3400

3200

3000 

2800

26*00

.g

S 2400 

5 2200

| 2000

o

.= 1800

S 1400

1200

iboo

600 

400

9nn

0

/

T

I

r

/

r

 i

a

7

A

i

, /

/

ip

/

/

/'/

/

/9

r

/

/

/

/<

5

?

^

/

^

j 

P\

^-

s

^

6** 

i*

»^v

>* * 

>»

\

, . , maximum total

Deformation per unit of length

FIG. 9. Characteristic compression-stress deformation diagrams, limestone concrete of medium consistency; ages 4,13, 

and 26 weeks.
34 STRENGTH OF CONCRETE BEAMS.

consequently the neutral axis remains in the center of the beam. An 

examination of the table shows, however, that the neutral axis 

actually varies from 30.4 to 63.0 per cent of the depth of the beam' 

below the top.

Column 21 gives the distance of the break from the center of the 

beam, which in few cases is more than 1 foot.
CO

80 

CO 

40 

20 

100

> » o- 0--

o o -0.

-o- o 

-O- Q ' ^

o -0- 

Values oi M-^-bd'

 CMtCmco^^-Ku^SlSrValues ol M ^ bd 

Oeformation per unit of length Oelonnation per unit ol length 

FIG. 10. Characteristic deformation curves for flexure, cinder concrete of med
TABLE 8. Tests of 13-foot concrete beams of constant 1

TESTED AT FOUR WEEKS.

Register 

No.

1

18.........

19.........

21......'...

Average 

24.........

28......... 

29.........

Average 

37. ........

38.........

Average 

53. ........

54. ........

55.........

Average 

51.........

64. ........

65......... 

Average 

72......... 

73.........

78......... 

Average

Aggregate.

.. 2

.....do....

.....do....

.....do....

.....do.... 

.....do....

.....do....

.....do....

.....do....

Granite... 

.....do....

.....do....

.....do....

.....do....

.....do....

.....do.... 

.....do....

.....do....

Proportion.

Volume.

3

1:2:5. 06 

1:2:5. 06 

1:2:5. 06

1:2:5.06 

1:2.06:5.40 

1:2.06:5.40

1:2:5. 19 

1:2:5. 19

1:2:4 

1:2:4 

1:2:4

1:2:4 

1:2:4 

1:2:4

1:2:4 

1:2:4 

1:2:4

Weight.

4

1:2. 02:2. 38 

1:2.02:2.38 

1:2. 02:2. 38

1:2.02:2.38 

1:2. 07:2. 54 

1:2.07:2.54

1:2. 01:2. 44 

1:2.01:2.44 

1:2. 01:2. 44

I:2.01:a82 

1:2.01:3.82 

1:2.01:3.82

1:2.01:3.80 

1:2.01:3.82 

1:2.01:3.82

1:2.01:3.82 

1:2.01:3.82 

1:2.01:3.82

Water 

(per 

cent) .

5

21.6 

21.8 

21.6

19.4 

20.4 

20.4

19.0 

19.0 

19.0

9.2 

9.0 

9.0

7.3

8.4 

8.4

6.9 

6.9 

6.9

Consistency.

6

Wet. . . 

...do. . 

...do..

Med... 

...do.. 

...do..

Damp. 

...do.. 

...do..

Wet. . . 

...do., 

...do..

Med... 

...do.. 

...do..

Damp. 

...do. . 

...do..

Dimensions of beam 

(inches).

Length 

in excess of 

13 feet.

7

0

1 

1

1

i

5

I

Section.

Wide.

8

I*

8

8 

8 

8

8

P

8

8

Deep.

9

11 

11 

11

11 

11 

11

11 

H|

HI

IH 

HA 

ill

101

"1 

"A

Weight 

(pounds) .

Total.

10

940 

960 

950

950

910 

900 

920

910

920 

940 

940

933

1,220 

1,170 

1,170

1,187

' 1, 190 

1,190 

1,240

1,207

1,100 

1,220 

1,220

 1,200

Per 

cubic 

foot.

11

117.4 

120.5 

119.3

119.1

114.3 

112.9 

115.6

1143

111.9 

115.5 

115.1

1142

150.2 

144.8 

146.7

147.2

147.5 

147.3 

153.8

149.5

148. 3 

149.8 

150.8

149.6

Unit 

elongation, 

lower 

outer fiber (own 

weight 

+ deformeters) .

12

0.000092 

.000096 

.000108

.000099

.000096 

.000100 

. 000089

.000095

.000110 

. 000125 

.000097

. 000111

.000024 

. 000034 

000022

. 000027

.000028 

. 000031 

.000028

. 000029

. 000018 

. 000029 

.000024

. 000024

(t
88.........

on n

90.........

100........ 

101........

102........

112........

113........

115........

128........

129........

130........

141........

142........ 

143........

150........

151........ 

152........

Gravel....

.....do....

.....do....

.....do.... 

.....do....

.....do....

.....do....

.....do....

.....do....

.....do....

.....do....

.....do....

.....do.... 

.....do....

.....do....

.....do.... 

.....do....

1:2:4

1:2:4

1:2:4

' 1:2:4 

1:2:4

1:2:4

1:2:4

1:2:4

1:2:4

1:2:4

1:2:4

1:2:4

1:2:4

1:2:4 

1:2:4

1:2:4

1:2:4 

1:2:4

1:2.01:4.10

1:2. 01:4. 10

1:2.01:4.10 

1:2.01:4.10

1:2.01:4.10

1:2. 01:4. 10

1:2.01:410

1:2.01:4.10

1:2.01:3.91

I:2.01:a91

1:2. 01:3. 91

I:2.01:a91

1:2.01:3.91 

1:2.01:3.91

1:2.01:3.91

1:2.01:3.91 

I:2.01:a91

9.5

9.5

9.7

8.6 

8.6

9.0

7.6

7.6

7.6

10.8

10.8

11.0

10.0

10.0 

10.0

8.4

8.4

a4

Wet. . .

...do..

...do..

Med. . . 

...do..

...do..

Damp.

...do..

Wet. . .

...do..

...do..

Med. . .

...do.. 

...do..

. . . do . . 

...do..

111

1 iiJ*1t

. J

i t51

8

8A

7M 

8&

8&888TV

Q I

ST"B s 

Q 1

|T^ 

7}| 8

8 8

11

HIIB

111 

Hi

 10}!

11

lli

10H

HTIB

1 1 S

iir

11^ S*

g*

Hi's

1,110

1,150 

1,130

1,140 

1,130

1,160 

1,143

1,110

1, 15C

1,110 

1,123

1,170

1,150

1,170 

1,163

1, 170

1,170 

1,170

1,170

1,170

1,140 

1,150

1,153

139.5

142.6 

141.1

142.4 

137.8

145.5 

141.2

139.3

142.9

140.6 

140.9

145.0

139. 1

142.0 

142.0

143.2

146.1 

147.8

145.7

144.2

143.2 

143.5

143.6

.000025

.000028 

.000027

.000025 

.000026

.000023 

.000025

'. 000023

.000021

.000035 

.000026

.000032

.000023

. 000026 

.000027

.000028

.000028 

.000032

. 000029

.000026

.000027 

.000038

.000030

Accidentally broken before test.
TABLE 8. Tests of 13-foot concrete beams of constant 12-f

TESTED AT THIRTEEN WEEKS.

Register 

No.

1

2..........

8...:..-...

9

Average 

3..........

33.........

34......... 

Average 

40.........

41.........

42.........

Average 

56. ........

57.........

58.........

Average 

68.........

69. ........

70. ........

Average 

79. ........

80. .........

81.........

Averaee

Aggregate.

2

.....do....

.....do....

Cinders . . . 

.....do....

.....do.:..

Cinders . . . 

.....do....

.....do....

Granite... 

.....do....

.....do....

Granite... 

.....do....

.....do....

Granite... 

.....do....

.....do....

Proportion.

Volume.

3

1:2:4.86 

1:2:4.79 

1:2:4.79

1:2:5.13 

1:2:5.21 

1:2:5.21

1:2:5.19 

1:2:5.19 

1:2:5.19*

1:2:4 

1:2:4 

1:2:4

1:2:4 

1:2:4 

1:2:3.97

1:2:4 

1:2:4 

1:2:4

Weight.

4

1:2.02:2.29 

1:2.02:2.25 

1:2.02:2.25

1:2.02:2.41 

1:2.01:2.45 

1:2.01:2.45

1:2.01:2.44 

1:2.01:2.44 

1:2.01:2.44

1:2.01:3.82 

1:2.01:3.82 

1:2.01:3.82

1:2.01:3.82 

1:2.01:3.82 

1:2.01:3.78

1:2,01:3.82 

1:2.01:3.82 

1:2.01:3.82

Water 

(per 

cent) .

5

22.15 

22.3 

22. 0

21.4 

21.0 

20.0

19.0 

19.0 

18.9

8.7 

8.7 

9.0

8.2 

8.2 

8.6

6.9 

7.0 

7.0

Consistency.

6

Wet... 

...do.. 

...do..

Med... 

...do.. 

...do..

Damp. 

...do.. 

...do..

Wet . . 

...do.. 

...do..

Med . . 

...do.. 

...do..

Damp. 

...do.. 

...do..

Dimensions of beam 

(inches) .

Length 

in excess of 

13 feet.

7

^

i

s

I 

1

i

I

*

Section.

Wide.

8

8 

8 

8

8 

8 

8A

I" 

8

8 

8 

8^

8A 

I*

ST*B 

I*

Deep.

9

Sf

HJ

Hi

J*

11} 

lit 

"A

"t 

"A

HA

Hi 

"A 

ill

11

H?

Weight 

(pounds) .

Total.

10

960 

940 

930

943

920 

920 

930

923

940 

940 

930

937

1,200 

1,200 

1,200

1,200

1,240 

1,240 

1,220

1,233

1,160 

1,200 

1,160

1,173

Per 

cubic 

foot.

11

118.4 

116.6 

115.3

116.8

114.2 

 114. 8 

114.4

114.5

114.3 

116.8 

115.9

115.7

149.1 

149.7 

148.7

149.2

149.2 

151.9 

145.0

148.7

144.5 

146.9 

143.9

145.1

Unit 

elongation, 

lower 

outer fiber (own 

weight 

+ deformeters) 

12

0.000042 

.000053 

.000066

.000054

.000051 

. 000073 

.000058

.000061 

.000062 

.000073 

. 000091

.000075

.000023 

.000026 

.000028

.000026

.000023 

.000026 

.000021

.000023

.000032 

. 000024 

.000024

.000027
91

92......... 

93.........

103 .......

104. .......

105........

116........

117........ 

118........

131........

132........

133. .......

126. .......

127........

140........

153........

154........

155........

.....do.... 

.....do....

.....do....

.....do....

.....do.... 

.....do....

.....do....

.....do....

.....do....

.....do....

.....do....

.....do....

1:2:4

1:2:4 

1:2:4

1:2:4

1:2:4

1:2:4

1:2:4

1:2:4 

1:2:4

1:2:4

1:2:4

1:2:4

1:2:4

1:2:4

1:2:4

1:2:4

1:2:4

1:2:4

1:2.01:4.10

1:2.01:4.10 

1:2.01:4.10

1:2.01:4.10

1:2.01:4.10

1:2.01:4.10

1:2.01:4.10

1:2.01:4.10 

1:2.01:4.10

1:2.01:3.91

1:2.01:3.91

1:2.01:3.91

1:2.01:3.91

1:2.01:3.91

1:2.01:3.91

1:2.01:3.91

9.7

9.9 

9.9

9.0

9.0

9.0

7.6

8.0 

8.1

11.0

11.0

11.0

10.4

10.4

10.0

8.4

8.4

8.4

Wet ..

...do.. 

...do..

Med..

...do..

...do..

...do.. 

...do..

Wet..

...do..

...do..

Med..

...do..

...do..

^i4I}ii,31,r11I

74-° 8

ai a

gl 7

15

88

T

888

716

I'"

HI

11

ion

HTB

"X

lOif

ioi!

Hi

11

HTB

«S

Hi

10J

104-5

1,160

1,160 

1,170

1,163

1,170

1,150

1,140 

1,153

1,140

1,150 

1,120

1,137

1,190

1,170

1,180 

1,180

1,150

1,200

1,170 

1,173

1,150

1,150

1,160 

1,153

141.9

145.2 

143.7

143.6

146.5

143.6

143.3 

1445

142.7

145.0 

144.1

143.9

147.6

147.7

146.6 

147.3

143.5

146.4

146.1 

145.3

144.0

146.1

146.3

.000017

.000023 

.000026

.000022

.000021

.000024

,000021 

.000022

.000026

.000025 

.000029

.000027

.000028

.000026

.000024 

.000026

.000025

.000026

.000018 

.000023

.000026

.000032

.000034 

.000031
TABLE 8. Tests of IS-foot concrete beams of constant 12-f

TESTED AT TWENTY-SIX WEEKS

Register 

No.

1

19

15.........

16.........

Average 

5..........

6..........

35......... 

Average 

43.........

44.........

45.........

Average

60.........

61.........

Average 

71. ........

74.........

75.........

Average 

82.........

83.........

84;........ 

Average

Aggregate.

2

.....do....

.....do....

.....do....

.....do....

Cinder.... 

.....do....

.....do....

Granite... 

.....do'....

.....do....

Granite.-.. 

.....do....

.....do....

Granite... 

.....do....

.....do....

Proportion.

Volume.

3

1:2:4.79

1:2:4. 79 

1:2:5.06

1:2:4.79

1:2:4.79 

1:2:5.21

1:2:5.19 

1:2:5. 19 

1:2:5.19

1:2:4 

1:2:4 

1:2:4

1:2:3.97 

1:2:4 

1:2:4

1:2:4 

1:2:4 

1:2:4

Weight.

4

1:2.02:2.25

1:2.02:2.25 

1:2.02:2.38

1:2.02:2.25 

1:2.02:2.25 

1:2.01:2.45

1:2.01:2.44 

1:2.01:2.44 

1:2.01:2.44

1:2.01:3.82 

1:2.01:3.82 

1:2.01:3.82

1:2.01:3.78 

1:2.01:3.82 

1:2.01:3.82

1:2.01:3.82 

1:2.01:3.82 

1:2.01:3.82

Water 

(per 

cent) .

5

22.4

22.4 

21.3

21.7 

21.7 

20.0

19.0 

19.0 

18.5

' 9.0 

8.8 

9.0

8.6 

8.4 

8.4

7.0 

7.0 

7.1

Consistency.

6

Wet. . .

...do... 

...do...

Med. . . 

...do... 

...do...

Damp. 

...do.. . 

...do...

Wet. . . 

...do... 

...do...

Med. . . 

...do.. . 

...do...

Damp. 

...do.. . 

...do...

Dimensions of beam 

(inches) .

Length 

in excess of 

13 feet.

' 7

- i

1

1 

I 

*

1

!

t 

§

Section. '

Wide.

8

8 

8 

STO

8 

8 

8

t* 

8A

SA

|A

8

8 

8J 

8J

Deep.

9

HA

HA

HAHA

HA

HJ

HA

HA*

Hi

HA 

lit

Weight 

(pounds) .

Total.

10

930 

900 

910

913

940 

930 

930

933

910 

920 

910

913

1,220 

1, 230 

1,230

1,227

1,250 

1,220 

1,200

1,223

1,190 

1,190 

1,230

1,203

Per 

cubic 

foot.

11

115.9 

114.2 

112.8

114.3

117.2 

116.0 

116.1

116.4

111.3 

114.0 

111.8

112.4

145.2 

151.9 

150. 3 

149.1

149.4 

150.5 

147.0

149.0

147.5 

146.1 

146.9

146.8

Unit 

elonga

tion, 

lower 

outer f

ber (ow

weigh

+ defo

meters

12

0. 0000

.0000

. 0000

. 0000

. 0000

. 0000

. 0000

. 000

. 000

. 000

.0000

. 000

. 000

. 000

. 000

. 000

. 000

. 000

. 000

. 000

.000

' .000

. 000

. 000
94.........

95.........

96.........

106........

107........

108........

119........

120........

121........

134........

135........

136........

144........

145........

258........

158. .......

259........ 

260........

.....do....

.....do....

.....do....

.....do....

.....do....

.....do....

.....do....

.....do....

.....do....

.....do....

.....do.... 

.....do....

1:2:4

1:2:4

1:2:4

1:2:4

1:2:4

1:2:4

1:2:4

1:2:4

1:2:4

1:2:4

1:2:4

1:2:4

1:2:4

1:2:4

1:2:4

1:2:4

1:2:4 

1:2:4

1:2.01:4.10

1:2.01:4.10

1:2.01:4.10

1:2.01:4.10

i -o m .0 on

1:2.01:3.91

i '9 m -^ QI

1:2.01:3.91 

1:2.01:3.91

9.9

9 9

9.9

9.1

9.1

9.0

8.1

8.1

8.1

n.o

11.0

11.0

10.0

10.0

8.6

8.6 

8.6

Wet. . .

...do...

...do...

Med. . .

...do...

...do...

...do...

Wet. . .

...do...

...do...

Med. . .

...do...

...do...

...do... 

...do...

§ff|f5f15JJ5f§5|

848

848

01

8*

84

of

8*

o i

CT5

Ql

8*8

Hi's

11^B

HT'B

Hi

%»

11

HI

lli

Hi

11*

11*

11 

iii

1,150

1,140

1,153

1,140

1,160 

1,150

1,140 

1,140

1,190

1,190

1,190

1,180

1, 190

1,190 

1,187

1,210

1,200

136.4

139.0

140.5

138.6

138.0

142.7 

140.9

141.8 

141.3

146.4

145.6

144.0

145.1 

145.3

'1 4Q 9

149.4

148.6

.000021

.000021

.000022

. 000019 

. 000023

 .000023

.000021 

. 000022

fifl(W>l

nnnn9^

000024

. 000021

. 000026

.000021 

. 000023

.000026

.000023

. 000023

o Not included in average.
TABLE 9. Tests of concrete beams of variable 

TESTED AT FOUR WEEKS.

Register

No.

1

1ft

19

21..........

Ofi

OQ

37..........

38..........

53..........

54..........

55..........

51..........

f\A

65..........

72..........

73..........

78..........

Averaee..

Aggregate.

2

Cinder.... 

.....do....

.....do....

do

Proportion.

Volume.

3

1:2:5.06 

1:2:5.06

1:2:5.06

1:2:5.06 

i -I OR-* 40

do 1 '5 Ofir/i. 40

Cinder.... 

.....do....

.....do....

.....do....

.....do....

Granite. . . 

.....do....

.....do....

Granite... 

.....do....

.....do....

1:2:5.19 

1:2:5.19

1:2:5.19

1:2:4 

1:2:4

1:2:4

1:2:4 

1:2:4 

1:2:4

1:2:4 

1:2:4 

1:2:4

Weight.

4

1:2.02:2.38 

1:2.02:2.38

1:2.02:2.38

1:2.02:2.38

 1:2.07:2.54

1:2.01:2.44 

1:2.01:2.44

1:2.01:2.44

1:2.01:3.82 

1:2.01:3.82

1:2.01:3.82

1:2.01:3.80 

1:2.01:3.82 

1:2.01:3.82

1:2.01:3.82 

1:2.01:3.82 

1:2.01:3.82

Water 

(per 

cent).

5

21.6 

21.8'

21.6

19.4

20.4

19.0 

19.0

19.0

9.2 

9.0

9.0

7.3 

8.4 

8.4

6.9 

6.9 

6.9

Consistency.

6

Wet . . 

...do..

...do..

Med.. 

...do..

...do..

Damp

...do..

Wet . . 

..do...

...do..

Med . . 

...do.. 

...do..

Damp 

...do .. 

...do..

Dimensions of beam.

Length.

Ft.

7

9 

6

7

6 

6 

6

6

8

7

7 

7 

6

8

7 

8

7 

6

7

In.

8

7 

10 

5

8 

6 

9

6 

0 

0

7 

0 

6

0 

2 

1

2 

8 

2

Section 

(inches).

Wide.

9

8

oooooo

»-H

°°° CM2

P

8

8 

8 

8

Deep.

10

11 

11 

11

11 

11 

11

11 

111

HI 

11* 

11

11*'

101 

11

"A

Span 

(ft.).

11

9 

6

7

6 

6 

6

6

ei

6

7 

7

6

Weight 

(pounds) .

Total. 

i

12

693 

508 

542.

467 

450 

478

460 

578 

506

712 

630

585

732 

656 

771

639 

626 

673

:

Pet 

cubic 

foot.

13

117.4 

120.5 

119.3

119.1

114.3 

112.9 

115. 6

114.3

111.9 

115.5 

115.1

114.2

150.2 

144.8 

144.9

146.6

145.7 

147.3 

153.8

148.9

147.2 

149. 8 

150.8

149.3

(t

2

2

2

3

2

2
88..........

89..........

90..........

100.........

101.........

102..........

112.........

113.........

115.........

128.........

129.........

130.........

141.........

142.........

143. ........

150. ........

151.........

152. ........

.....do....

.....do....

.....do....

.....do....

.....do....

.....do....

.....do....

.....do....

.....do....

.....do....

.....do....

.....do....

1:2:4

1:2:4

1:2:4

1:2:4

1:2:4

1:2:4

1:2:4

1:2:4

1:2:4

1:2:4

1:2:4

1:2:4

1:2:4

1:2:4

1:2:4

1:2:4

1:2:4

1:2:4

1:2.01:4.10

1:2.01:4.10

1:2.01:4.10

1:2.01:4.10

1:2.01:4.10

1:2.01:4.10

1:2.01:4.10

1:2.01:4.10

1:2.01:4.10

1:2.01:3.91

1:2.01:3.91

1:2.01:3.91

1:2.01:3.91

1:2.01:3.91

1:2.01:3.91

1:2.01:3.91

1:2.01:3.91

1:2.01:3.91

9.5

9.5

9.7

8.6

8.6

9.0

7.6

7.6

7.6

10.8

10.8

11.0

10.0

10.0

10.0

8.4

8.4

8.4

Wet . .

...do..

...do..

Med..

...do..

...do..

...do ..

...do..

Wet..

...do..

...do..

Med..

...do..

...do..

...do..

777

. 767776766776667

692

10791062

11

11099

11

119

8

8J

RJ*.

Ql

8J

8J_

Ql

8*

8^

01s8

O 1

«?8 1 *

O 1

88

11

11*

11*

HI

11T3*

11*

11

11

11

11*

Hi

Hi

11*

"A

11*

11*

10M1fU-£

77

6J767

6i

Al f

6*66

6*76667

640

700

634

687

572

692

605

619

555

645

612

623

630

698

608

623

607

686

139.5

142.3

142.6

141.5

142.4

137.8

145.5

141.9

139.3

142.9

140.6

140.9

145.0

139.1

142.0 

142.0

143.2

146.1

147.8

145.7

144.2

143.2

143.5

143.6
TABLE 9. Tests of concrete beams of variable span 

TESTED AT THIRTEEN WEEKS.

Register

No.

1

2...........

8., ..... ;...

9...........

3...........

33.......... 

34..........

Average. .

40. .........

41 .......... 

42..........

Average. . 

56..........

57..........

58..........

68..........

69

70..........

79..........

80...........

81 ..........

' Average..

Aggregate.

2

.....do....

.....do....

Cinder .... 

.....do.... 

.....do....

Cinder .... 

.....do.... 

.....do....

Granite... 

.....do....

.....do....

Granite... 

.....do....

.....do....

Granite... 

.....do....

.....do....

Proportion.

Volume.

3

1:2:4.86 

1:2:4.79

1:2:4.79

1:2:5.13 

1:2:5.21 

1:2:5.21

1:2:5.19 

1:2:5.19 

1:2:5.19

1:2:4 

1:2:4 

1:2:4

1:2:4 

1:2:4 

1:2:3.97

1:2:4 

1:2:4 

1:2:4

Weight.

4

. 1:2.02:2.29 

1:2.02:2.25

1:2.02:2.25

1:2.02:2.41 

1:2.01:2.45 

1:2.01:2.45

1:2.01:2.44" 

1:2.01:2.44 

1:2.01:2.44

1:2.01:3.82 

1:2.01:3.82 

1:2.01:3.82

1:2.01:3.82 

1:2.01:3.82 

1:2.01:3.78

1:2.01:3.82 

1:2.01:3.82 

1:2.01:3.82

Water 

(per 

cent) .

5

22.15 

22.3

22.0

21.4 

21.0 

20.0

19.0 

19.0 

18.9

8.7 

8.7 

9.0

8.2 

8.2 

8.6

6.9 

7.0 

7.0

Consistency.

6

Wet.. 

...do..

...do..

Med .. 

...do.. 

...do..

Damp 

...do.. 

...do..

Wet.. 

...do.. 

...do..

Med.. 

...do.. 

...do..

Damp 

...do.. 

. . . do . .

Dimensions of beam.

Length.

Ft.

7

7 

7 

8

7 

7 

6

8 

7 

6

7 

6 

7.

8 

6 

6

7 

7 

6

In.

8

9 

8 

3

4 

3

8

1

9 

9

10 

9 

0

0 

11 

10

10 

3 

6

Section 

(inches).

Wide.

9

8J 

8 

8

8J 

?

8 

8 

8

I* 

»A

8T'B 

8

8A

8

Deep.

10

n* 

nj

11

UA 

lit

iiA

11 

11

11* 

11HA

nf

114

nf

11 nT5B

lOIf

Span 

(ft.).

11

7 

7 

71

61 

6* 

6

n

6

7 

6 

61

71 

6 

6

7 

61 

6

Weight 

(pounds).

Total.

12

572 

554 

590

519 

513 

477

584 

560 

483

723 

623 

646

763 

660 

563

699 

669 

580

Per 

cuhic 

foot.

13

118.4 

116.6 

115.3

116.8

114.2 

114.8 

114.4

114.5

114.3 

116.8 

115.9

115.7

149.1 

149.7 

148.7

149.2

149.2 

151.9 

% 145. 0

148.7

144.5 

146.9 

143.9

145.1
91 ..........

92..........

93..........

103.........

104.........

105... ......

Average. .

116.........

117.........

118.........

131 .........

132.........

133.........

126..... ...

127.........

140.........

153.........

154.........

155.........

.....do....

.....do....

.....do....

.....do....

.....do....

.....do....

..'...do....

.....do....

.....do....

.....do....

.....do....

.....do....

1:2:4

1:2:4

1:2:4

1:2:4

1:2:4

1:2:4

1:2:4

1:2:4

1:2:4

1:2:4

1:2:4

1:2:4

1:2:4

1:2:4

1:2:4

1:2:4

1:2:4

1:2:4

1:2.01:4.10

1:2.01:4.10

1:2.01:4.10

1:2.01:4.10

1:2.01:4.10

1:2.01:3.91

1:2.01:3.91

1:2.01:3.91

1:2.01:3.91

9 7

9.9

9.9

9 0

9.0

9 0

7.6 8 n

11.6

11.0

10.4

10.0

8.4

8.4

8.4

Wof

...do..

...do..

Med..

...do..

...do..

...do..

Wet . .

...do..

...do..

Med..

...do..

. . . do . .

...do..

...do..

7876

fi86

8- 66S7

0

fi58

?, 8

10

fi

116g449

7^§ 88888

74.5 8 1(i

01

7i6 8 16 s8

715

7«

716 8 1

H|

HJ

113

11

Hr3*

11

11

HA

101

nj

llT3B

HT%

11}

io»

11

fil 8

(U7

6fc 686

6J

7*66

/M

6J

7i 7

625

668

634

585

599

en 7

633

660

734

575

660

(\AQ

737

699

141 9

143.7

143.6

143.6

143.3

144.5

144.1

143.9

146.6

143.5

146.4

146.1

144.0

146.1

-l^e K

C1 

59

67

74

74

73

83

62

Of) 

74

76

73
TABLE 9. Tests of concrete beams of variable span 

TESTED AT TWENTY-SIX WEEKS.

Register

1

12..........

15..........

16..........

5...........

6...........

35..........

43..........

44..........

45..........

59..........

60.......... 

61..........

71..........

74. .........

75..........

82..........

83..........

84..........

 Average. .

Aggregate.

2

Cinder. ... 

.....do....

.....do....

Cinder. . . . 

.....do....

.....do....

Cinder.... 

.....do....

.....do....

Granite. . . 

.....do.... 

.....do....

Granite.. . 

.....do....

.....do....

Granite... 

.....do....

.....do....

Proportion.

Volume.

3

1:2:4.79 

1:2:4.79 

1:2:5.06

1:2:4.79 

1:2:4.79 

1:2:5.21

1:2:5.19 

1:2:5.19 

1:2:5.19

1:2:4 

1:2:4 

1:2:4

1:2:3.97 

1:2:4 

1:2:4

1:2:4 

1:2:4 

1:2:4

Weight.

4

1:2.02:2.25 

1:2.02:2.25 

1:2.02:2.38

1:2.02:2.25 

1:2.02:2.25 

1:2.01:2.45

1:2.01:2.44 

1:2.01:2.44 

1:2.01:2.44

1:2.01:3.82 

1:2.01:3.82 

1:2.01:3.82

1:2.01:3.78 

1:2.01:3.82 

1:2.01:3.82

1:2.01:3.82 

1:2.01:3.82 

1:2.01:3.82

Water 

(per 

cent).

5

22.4 

22.4 

21.3

21.7 

21.7 

20.0

19.0 

19.0 

18.5

9.0 

8.8 

9.0

8.6 

8.4 

8.4

7.0 

7.0 

7.1

Consistency.

6

Wet... 

...do.. 

...do..

Med... 

...do.. 

...do..

Damp 

...do .. 

...do..

Wet... 

...do.. 

...do..

Med... 

...do.. 

...do..

Damp. 

...do.. 

...do..

Dimensions of beam.

Length.

Ft.

7

6

7 

6

7 

7 

6

7 

7 

6

8 

6 

6

7 

7 

6

8 

7 

6

In.

8

11 

5

8

0 

4 

10

0 

0 

10

4 

9

7

2 

9 

8

1 

9 

10

Section 

(inches).

Wide.

9

> 

7«

8A

!*

I!

8£

If

8

8A

!*

tr

8&

Deep.

10

11* 

io| 

11

n* 

11

11*

Hi Hi's

11*

llT7B 

11*

11* 

"ft 

"A

11* 

HI 

HA

Span 

(ft.).

11

6 

?

6

?

II

6

?

6

6^ 

6

?* 

6

Weight 

(pounds).

Total.

12

495 

513 

467

506 

525 

489

490 

495 

478

782 

639 

623

689 

727 

615

740 

709 

647

Per 

cubic 

foot.

13

115.9 

114.2 

112.8

114.3

117.2 

116.0 

116.1

116.4

111.3 

114.0 

111.8

119 4

145.2 

151.9 

150.3

149.1

149.4 

150.5 

147.0

149.0

147.5 

146.1 

146.9

146.8

(t

3

3

4

4

3

3

4

3

3

8

8

7

8

8

8

8

8

8
94..........

95..........

96..........

106.........

107.........

108. ........

119.........

120.........

121 .........

134.........

135.........

136......:..

144.........

14=;

258.........

158.........

259.........

260.........

.....do....

.....do....

.....do....

.....do....

.....do....

.....do....

.....do....

.....do....

.....do....

.....do....

.....do....

.....do....

1:2:4

1:2:4

1:2:4

1:2:4

1:2:4

1:2:4

1:2:4

1:2:4

1:2:4

1:2:4

1:2:4

1:2:4

1:2:4

1:2:4

1:2:4

1:2:4

1:2:4

1:2:4

1:2.01:4.10

1:2.01:4.10

1:2.01:4.10

1:2.01:4.10

1:2.01:4.10

1:2.01:4.10

1:2.01:4.10

1:2.01:3.91

1:2.01:3.91

1:2.01:3.91

1:2.01:3.91

1:2.01:3.91

1:2.01:3.91

9.9 Wet...

9.9 ...do..

9.9 ...do..

9.1 Med...

8.1 ...do..

11. 0 Wet.. .

10.0 Med...

10.0 ...do..

8.6 ...do..

8.6 ...do..

77

 6

fi667

fi978866

888

1078

10970

**0587

R I- 8 1U

84

. 88

Q 1

IT,B &

Q 1

SIB

Q 1

8 ia

8i's

O 1

Q 1

HI

116

116

Hi's

n£

in i R

HA

11*

11*

"I

113

Hy8*

H&

Hi

"1

77766766687

74

 6

716

678

672

690

CQQ

582

684

CQQ

592

636

603

JXM

702

ficO

732

770

613

136.4

139.0

140.5

138.6

140.9

141 5

141 ft

146 4

145-6

144.0

145.1

1 AZ Q

14Q 9

149 4

1/47 o

148.6
TABLE 10. Compression tests of concrete cylinders and cube

TESTED AT FOUR WEEKS.

Register 

No.

1

18.........

19.........

21.........

Average . 

24.........

28. ........

29.........

Average . 

37.........

38......... 

39.. .......

Average . 

53.........

54.........

55. ........

Average . 

51.........

64. ........

65.........

Average . 

72.........

73. ........

78......... 

Average . 

88.........

89.........

90. ........

Averaee .

Aggregate.

2

.....do......

.....do......

.....do......

.....do......

Cinder. ..... 

.....do...... 

.....do......

Granite. .... 

.....do......

.....do......

Granite..... 

.....do......

.....do......

Granite..... 

.....do......

.....do......

.....do......

.....do......

Proportion.

Volume.

3

1:2:5.06 

1:2:5.06 

1:2:5.06

1:2:5.06 

1:2.06:5.40 

1:2.06:5.40

1:2:5.19 

1:2:5.19 

1:2:5.19

1:2:4 

1:2:4 

1:2:4

1:2:4 

1:2:4 

1:2:4

1:2:4 

1:2:4 

1:2:4

1:2:4 

1:2:4 

1:2:4

Weight.

4

1:2.02:2.38 

1:2.02:2.38 

1:2.02:2.38

1:2.02:2.38 

1:2.07:2.54 

1:2.07:2.54

1:2.01:2.44 

1:2.01:2.44 

1:2.01:2,44

1:2.01:3.82 

1:2.01:3.82 

1:2.01:3.82

1:2.01:3.82 

1:2.01:3.82 

1:2.01:3.82

1:2.01:3.82 

1:2.01:3.82 

1:2.01:3.82

1:2.01:4.10 

1:2.01:4.10 

1:2.01:4.10

Water 

(per 

cent).

5

21.6 

21.8 

21.6

19.4 

20.4 

20.4

19.0 

19.0 

19.0

9.2 

9.0 

9.0

7.3

8.4 

8.4

6.9 

6.9 

6.9

9.5 

9.5 

9.7

Consistency.

6

Wet .... 

....do...

....do...

Med..... 

....do...

....do...

Damp . . 

....do...

....do...

Wet.... 

....do...

...-.do...

Med. .... 

....do...

....do...

Damp . .

....do...

Wet .... 

....do...

....do...

Cylinders.

Dimensions 

(inches) .

Diameter.

7

8.00 

8.00 

8.00

8.00 

8.00 

8.00

8.00 

8.00 

8.00

8.00 

8.00 

8.00

8.00 

7.99 

8.07

8.03 

8.04 

8.02

8.02 

7.99 

7.99

Length.

8

16.00 

16.00 

16.00

16.00 

16.00 

16.00

16.00 

16.00 

16.00

16.00 

16.00 

16.00

16.00 

16.05 

16.19

15.95 

16.14 

15.97

16. 24 

16.11 

16.22

Weight 

(pounds 

per 

cubic 

foot).

9

149.3 

146.6 

150.4

148.8

150.9 

148.8 

146.6

148. 8.

149.8 

148.7 

148. 9

149.1

141.1 

138.2 

141.6

140.3

Maximum 

unit 

stress.

10

1,243 

1,000 

1,000

1,081

1,114 

1,250 

1,240

1,201

1,055 

1,210 

1,090

1,118

3,093 

2,350 

2,607

2,683

3,990 

3,250 

3,199

.3,480

4, 000 

4,000 

4,000

4,000

2,336 

2,087 

1,758

2.060

I

m

ela

1

1

1

1

2

1

1

1

1

1

1

1

3, 

3, 

4, 

3, 

4, 

4, 

3

4

4, 

4

4

4

3

4

3, 

3
101.........

102.........

Jo 112.........

<=> 113........

| 115.........

£ 128.........

~ 129.........

CO 130.........

4, 141.........

I 

142.........

143.........

Average .

151..:......

152. ........

153.........

.....do......

.....do......

.....do......

.....do......

.....do......

.....do......

.....do......

.....do......

.....do......

.....do......

.1:2:4

1:2:4

1:2:4

1:2:4

1:2:4

1:2:4

1:2:4

1:2:4

1:2:4

1:2:4

1:2:4

1:2:4

1:2:4

1:2:4

1:2.01:4.10

1:2.01:4.10

1:2.01:4.10

1:2.01:4.10

1:2.01:4.10

1:2.01:3.91

1:2.01:3.91

1:2.01:3.91

1:2.01:3.91

1:2.01:3.91

1:2.01:3.91

1:2.01:3.91

1:2.01:3.91

1-9 m ^ Qt

8.6

9.0

7.6

7.6

7.6

10.8

10.8

11.0

10.0

10.0

10.0

8.4

8.4

8.4

....do...

....do...

....do...

Wet ....

....do...

....do...

Med.....

....do...

....do...

....do...

7.99

7 QQ

Q AA

8.07 7 QO

8.02

8.07

7 99

7 97

8.01

8.03

7 98

8 04

16.18

16.18

Ifi f\A

16.08

16.02

16.07

16.04

16.11

16.08

16.04

16.22

16.07

16.12

142.7

142.7

142.7

141.7

14ft Q

142.9

141.8

143.2

145.4

 f AK. C

145.9

146.6

146.0

146. 2

149 0

148.7

2; 486

3,022

2,961

3,437

o2,392

3,377

3,407

2,591

3,884

3,072

^ aso

2,458

2,382

2,910

3,171

2,749

2,761

2,894

3,900

3,875

4 640 

3,840

3,730

4,070

3 dfif\ 

3 RQA 

3,415

3,588

3,400

3,700

3,195

3,432

4,025

4,720

4,025

4,257

<* Not included in average.
TABLE 10. Compression tests of concrete cylinders and cubes accomp

TESTED AT THIRTEEN WEEKS.

Register 

No.

1

2.. .........

9...........

Average . 

3...........

33..........

34..........

Average . 

40-... -..:..

41...........

42..........

Average . 

56". .......

57..........

58..........

Average . 

68..........

69. .........

70. .........

Average . 

79. .........

80. .........

81. -.--....-

Average .

Aggregate.

2

Cinder......

.....do......

.....do......

Cinder. ..... 

.....do......

.....do......

Cinder...... 

.....do......

.....do......

Granite..... 

.....do......

.....do......

Granite.. . . . 

...: .do......

.....do......

Granite..... 

.....do......

.....do......

Proportion.

Volume.

. 3

1:2:4.86 

1:2:4.79 

1:2:4.79

1:2:5.13 

1:2:5.21 

1:2:5.21

1:2:5.19 

1:2:5.19 

1:2:5.19

1:2:4 

1:2:4 

1:2:4

1:2:4 

1:2:4 

1:2:3.97

1:2:4 

1:2:4 

1:2:4

Weight.

4

1:2.02:2.29 

1:2.02:2.25 

1:2.02:2.25

1:2.02:2.41 

1:2.01:2.45 

1:2.01:2.45

1:2.01:2.44 

1:2.01:2.44 

' 1:2.01:2.44

1:2.01:3.82 

1:2.01:3.82. 

1:2.01:3.82

1:2.01:3.82 

1:2.01:3.82 

1:2.01:3.78

1:2.01:3.82 

1:2.01:3.82 

1:2.01:3.82

Water 

(per 

cent) .

5

22.15 

22.3 

22.0

21.4 

21.0 

20.0

19.0 

19.0 

38.9

8.7 

8.7 

9.0

8.2 

8.2 

8.6

6.9 

7.0 

7.0

Consistency.

6

Wet.... 

....do...

....do...

Med .... 

....do...

....do...

Damp . . 

. ...do. ..

....do...

Wet.... 

....do... 

....do...

Med .... 

....do...

....do...

Damp . .

....do...

Cylinders.

Dimensions 

(inches) .

Diameter.

7

8.02 

8.02 

8.01

8.01 

8.00 

8.01

8.00 

8.06 

8.07

8.00 

8.07 

7.99

8.00 

8.03. 

8.01

8.05 

8.03 

8.08

Length.

8

16.00 

15.88 

16.13

15.75 

15.99 

,16.02

16.15 

16.15 

16.03

16.10 

16.15 

16.00

16.13 

16.24 

16.01

16.09 

16.11 

16.10

Weight 

(pounds 

per 

cubic 

foot) .

9

120.3 

117.2 

111.9

116. 5

118.7 

114.5 

113.7

115.6

113.6 

112.5 

111.4

112.5

146.6 

144.9 

146.7

146.1

147.9 

145.8 

147.5

147.1

148.2 

148.3 

147. 6

148.0

Maximum 

unit 

stress.

10

1,651 

1,963 

1,678

1,764

1,830 

1,643 

1,984

1,819

1,725 

1,790 

1,662

1,726

3,528 

3,197 

3,805

3, 510

(« )

( c) 

3,777

(d) 

( c) 

(/)

Ini

mod

o

elast

1

3,50

1,74

2,73

2,65

3,12

2,03

' 1,67

2,27

1,94

1,46

1, 50

1,63

4,84

3, 69

4,32

4, 28

4,80

4, 78

4,66

4, 74

4,34

5, 28

4, 47

4, 69
91..........

92..........

93..........

103.........

104.........

105.........

116.........

117.........

118.........

131.........

132.........

133.........

126 I .......

127 I.......

140 1 .......

153. ........

154.........

155.........

.....do......

.....do......

Gravel

.....do......

.....do......

.....do......

.....do......

.....do......

.....do......

.....do......

.....do......

.....do......

.....do......

1:2:4

1:2:4

1:2:4

1:2:4

1:2:4

1:2:4

1:2:4 .

1:2:4

1:2:4

1:2:4

1:2:4

. 1:2:4

1:2:4

1:2:4

1:2:4

1:2:4

1:2:4

1:2.01:4.10

1:2.01:4.10

1:2.01:4.10

1:2.01:4.10

1:2.01:4.10

1:2.01:4.10

1:2.01:4.10

1:2.01:4.10

1:2.01:3.91

1:2.01:3.91

1:2.01:3.91

1:2.01:3.91

1:2.01:3.91

1:2.01:3.91

1:2.01:3.91

9.7

9.9

9.9

9.0

9.0

9.0

7.6

8.0

8.1

11.0

11.0

11.0

10.4

10.4

10.0

8.4

8.4

8.4

Wet ....

....do...

....do...

Med....

....do...

....do...

....do...

Wet ....

....do...

....do...

Med ....

....do...

....do...

....do...

8.01

. 8.01

8.03

8.09

8.05

8.03

8.02

8.01

8.03

8.05

8.00

7.99

8.03

8.05

8.02

8.02

8.00

8.02

16.37

16.16

16.37

16.10

16.13

16.17

16.15

16.16

16.18

16.23

16.12

16.10

16.16

16.11

16.27

16.41

16.22

139.6

140.9

139.7

140.1

140.7

142. 3

141.1

141.4

145.1

146.4

143.4

145.0

142.0

145.5

144.2

147.0

146.2

 143. 5

145.6

146.7

148.3

149.0

148.0

2,699

2,967

3,195

2,954

«

i3,930

2,765

(>)

(*)

( c)

3,397

3,318

3,385

3,508

3,458

3,445

3,470

(?)

W(>) '

a Cylinder spalled before test. 

6 Cylinder did not fail at 3,979 unit stress. 

c Cylinder did not fail at 3,950 unit stress. 

d Cylinder did not fail at 3,929 unit stress. 

e Cube did not fail at 5,528 unit stress

5,36

5,00

4,31

4,89

5,92

5,30

4,38

5,20

5,14

5,14

5,20

5,16

3, 70

4,24

4,01

3,98

3,80

3,96

4,1

3,96

4,68

4,5

4,8

4,6

/Cylinder did not fail at 3,900 unit stress.

g Cube did not fail at 5,483 unit stress.

& Cylinder did not fail at 3,891 unit stress.

f Cylinder broke after several minutes under loa
TABLE 10. Compression tests of concrete cylinders and cubes accompa

TESTED AT TWENTY-SIX WEEKS.

Register 

No.

1

12..........

15. .........

16..........

Average . 

5...........

6. ..........

35..........

Average . 

43. .........

44. .........

45..........

Average . 

59..........

60..........

61..........

Average . 

71..........

74. .........

75. .........

Average . 

82. .........

83. .........

84. .........

Average . 

94. .........

95. .........

96. .........

Average .

Aggregate.

2

Cinder...... 

.....do......

.....do......

.....do......

.....do......

Cinder. ..... 

.....do......

.....do......

Granite..... 

.....do......

.....do......

Granite..... 

.....do......

.....do......

Granite. . . . j 

.....do......

.....do......

.....do......

.....do......

Proportion.

Volume.

3

1:2:4.79 

1:2:4.79 

1:2:5.06

1:2:4.79 

1:2:4.79 

1:2:5.21

1:2:5.19 

1:2:5.19 

1:2:5.19

1:2:4 

1:2:4 

1:2:4

1:2:3.97 

1:2:4. 

1:2:4

1:2:4 

1:2:4 

1:2:4

1:2:4 

1:2:4 

1:2:4

Weight;

4

 1:2.02:2.25 

1:2.02:2.25 

1:2.02:2.38

1:2.02:2.25 

1:2.02:2.25 

1:2.01:2.45

1:2.01:2.44 

1:2.01:2.44 

1:2.01:2.44

1:2.01:3.82 

1:2.01:3.82 

1:2.01:3.82

1:2.01:3.78 

1:2.01:3.82 

1:2.01:3.82

1:2.01:3.82 

1:2.01:3.82 

1:2.01:3.82

1:2.01:4.10 

1:2.01:4.10 

1:2.01:4.10

Water 

(per 

cent).

5

22.4 

22.4 

21.3

21.7 

21.7 

20.0

19.0 

19.0 

18.5

9.0 

8.8 

9.0

8.6 

8.4 

8.4

7.0 

7.0 

7.1

9.9 

9.9 

9.9

Consistency.

6

Wet.... 

....do...

....do...

Med .... 

....do...

.... do ...

Damp. . 

.... do ... 

....do...

Wet .... 

....do...

....do...

Med .... 

.... do ...

....do...

Damp . . 

....do...

....do...

Wet.... 

....do...

....do...

Cylinders.

Dimensions 

(inches) .

Diameter.

7

7.99 

8.00 

7.98

8.01 

7.98 

8.00

8.02 

8.01 

7.98

8.03 

7.99 

8.02

8.02 

8.00 

8.00

8.02 

8.01 

8.00

8.00 

8.01 

8.01

Length.

8

15. 95 

16.11 

16.02

15.85 

15.91 

16.10

16.16 

16.02 

16.10

15.81 

15.90 

16.02

16.08 

16.11 

16.10

16.11 

16.11 

16.02

16.09 

16.15 

16.15

Weight 

(pounds 

per 

cubic 

foot) .

9

113.2 

113.9 

114.6

113.9

113.4 

116.2 

 113. 4

114.3

112.2 

114.2 

114.8

113. 7

147.6 

147.1 

149.2

148.0

146.8 

147.5 

147.1

147.1

149. 9 

150.3 

149.1

149.8

138.4 

139. .1 

138.3

138.6

Maximum 

unit 

stress.

10

1.872 

2,090 

2,100

2,021

2,481 

2,132 

1,995

2,203

1,940 

1,895 

2,001

1,945 

(a)

i'j

8(d)

(«)' 

 («>

(?)

ft3,461 

3,431 

3,565

3,486

Init

modu

of 

elasti

11

1, 720

1,580

1,530

1, 610

1, 680

1,535

1,640

1,618

1,300

1, 245

1,600

1, 382

4,000

4,040

4, 130

4,057

4, 020

3,800

3, 920

3,913

4,700

4,310

4, 220

4,430

4,090

3, 660

4,400

4,050
106.........

107.........

108. ........

119.........

120. ........

121.........

Average .

134. ........

135.........

136. ........

Average .

144.........

145. ........

258. ........

Average .

158.........

259.........

260.........

.....do......

.....do......

.....do......

.....do......

.....do......

.....do......

.....do......

.....do......

.....do......

.....do......

1:2:4

1:2:4

1:2:4

1:2:4

1:2:4

1:2:4

 1:2:4

1:2:4

1:2:4

1:2:4

1:2:4

1:2:4

1:2:4

1:2:4

1:2.01:4.10

1:2.01:4.10

1:2.01:4.10

. 1:2.01:3.91

1:2.01:3.91

1:2.01:3.91

1:2.01:3.91

1:2.01:3.91

1:2.01:3.91

1:2.01:3.91

9.1

9 1

9.0

8.1

8.1

8.1

11.0

11.0

11.0

10.0

10.0

8.6

8.6

8.6

Med ....

....do...

....do...

....do...

Wet ....

....do...

....do...

Med ....

....do...

....do...

....do...

S.'Ol

S ftft

8.00

8.03

8.00

8.02

8.00

8.03

.8.00

8.02

8.00

8.13

7 99

8.00

16.17

16.14

16.02

16.02

16.00

16.03

16.05

16. 13

16.06

16.13

16.19

16.19

142.7

143 9

143.0

1 4A Q

147.0

146.8

144.3

145.8

143 4

144.5

146.8.

146.2

145.7

149 0

148.4

147.7

(«)

(<0

(<)

(d)

(a)

(O

3

1 10

3,473

3,216

3 

en 7

3 Qft9

3,605

(0

(b)

(d)

4 74

4 4

5, 4

4 4

4,87

3,98

3 n

3 9

3,42

4,03

3, 6

4, 1

3, 9

3,69

4, 2

4,3

e Cylinder did not break at 3,950 unit stress. 

6 Cylinder did not break at 3,989 unit stress. 

c Cylinder did not break at 3,959 unit stress. 

<* Cylinder did not break at 3,979 unit stress

e Cylinder did not break at 3,969 unit stress. 

/Cube did not break at 5,556 unit stress. 

a Cylinder did not break at 3,978 unit --tress.
20

"5 40

1 

 u 60

190

JOO 

95

;90

85

I

eo

i75 

 (70 

'65 

. 0

? 55

r*>

§ 45 

-* 40

35 

30 

.25 

20 

15

to

S

 o

*!> o J ' c

,

c

.

 < O o-

 

"i s sc s S 8 8. ? * .8 S?. 8. S3. S ° " 2 -..,..8 S S S! _.?,.«.' 8 S. S. S3 S. ° 

Values of M -=- bd ' Values of M -5- bd' 

.

$ 

*

/

?

rn

)

-f

<?

ft y*

»/

¥'* 

 4

/

Y

If

wee

/

r

3ks

/

/°

/

f

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/ 

/

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<S^

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»£

(/

-13

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we

y

ekj

^

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/

CSartBation per'uriil of lejgh OeTbrmalipn per unit"ol length 

FIG. 11. Characteristic deformation curves for flexure, granite concrete of mediu
RESULTS OF TESTS. 55 

BEAMS OF VARIABLE SPAN.

The detailed results of tests of the beams of variable span are given 

in Table 9 (pp. 42-47), and some of the results are graphically shown 

in figs. 2-5. The information given in columns 1-14, 17, 18, 21, and 

22 of the table is identical in character with that given in the 

corresponding columns of Table 8.

Column 15 contains the unit elongation of the lower outer fiber 

for tliQ, applied load only, since the short beams were not suspended 

for zero total deformations as were the long beams. The values 

of the unit elongation,, including that due to the weight of the beam 

and the deformeters, may be approximated by increasing the values 

in column 15 by. an amount obtained from the averages in column 

12, Table 8, on the assumption that the elongation is directly proportional to the values for -, which is approximately true for values

below those for the weight of the beam plus the weight of the deformeters. The values for j ^ for own weight and deformeters are given

in column 19 and, as may be seen by comparing with the maximum 

total values in column 20, are in the rnajority of cases but a small 

percentage of the total.

Column 16 gives the position of the neutral axis in percentage of 

the depth below the top of the beam. These values are not strictly 

comparable with those in column 15, Table 8, since they are based 

on deformations due to the applied load alone.

CYLINDERS AND CUBES.

The detailed results of the compression tests of cylinders 8 inches 

in diameter by 16 inches in length and of 6-inch cubes are given in 

Table .10. Some of the results are also graphically shown in figs. 2-9.

Columns 1-6 contain the same kind of- information as is given for 

the beams in the corresponding columns of Tables 8 and 9.

Columns 7 and 8 and columns 13 and 14 show the dimensions of the 

cylinders and cubes, respectively, in inches.

Columns 9 and 15 show the weight in pounds per cubic foot, as 

figured from the dimensions and the actual weight of each cylinder 

and cube when, tested.

Columns 10 and 16 show the ultimate strength of each cylinder and 

cube in pounds per square inch.

The initial modulus of elasticity (given in column 11) was obtained 

from a curve showing the relation between the unit gross deformation 

and the compressive stress in pounds per square inch, by drawing a 

line tangent to the curve at the origin or where, possible coincident 

with the straight line or initial .part of the curve. The range in pounds
Values olM-r-bd*

2 S ' 8' 33 88 § $ 8 tS S 

Values of M-:-bd*

4 weeks

?

//

13 weeks

Ddonratino pe» unS d length ' Detonation pet urtl ol length 

FIG. 12. Characteristic deformation,curves for flexure, gravel concrete of mediu
RESULTS OF TESTS. 57

per square inch within which the line drawn coincides with the curve 

is also shown (column 12).

Column 17 gives the ratio of the ultimate strength of the cylinders 

to that for the cubes.

It is to be regretted that the capacity of the machines composing 

the equipment was exceeded by the strength of many of the cylinders 

and cubes at the time these tests were made, preventing the accurate 

determination of the actual growth of strength with age. There is, 

however, in almost every case a substantial increase in strength 

with age.

The effect of consistency on the strength is much more noticeable, 

and leads to much more uniform results for the cubes and cylinders 

than for the beams. This would lead one to believe that the effect 

of consistency is much more noticeable and much more uniform on

the compressive strength of concrete than on the tensile strength.

Owing to a breakdown of the engine it became necessary to apply 

the load by hand for a number of tests. The beams and cylinders, 

being deemed the most important, were tested in this way, but because 

of the difficulty of turning the gears of the testing machine by hand 

the testing of the cubes was omitted.

ILLUSTRATIVE DIAGRAMS.

Figs. 2, 3, 4, and 5 show graphically the effect of age and consistency 

on the ultimate compressive strength of cinder, granite, gravel, and 

limestone concretes, as obtained from the tests on the cylinders and 

cubes and in the modulus of rupture as given by the tests in the 

beams of constant and variable span.

Figs. 6, 7, 8, and 9 show graphically several characteristic compression-stress deformation curves obtained frqm tests on the cylinders, while figs. 10, 11, 12, and 13 show the deformation curves for a 

few of the beams of 12-foot span.
58 STRENGTH OF CONCRETE BEAMS.

(

' (

o

(

I,

-1

(

<

1

J

1

1

L

 

8 8

^&

ozotxv

 5

'c 

01000' ' &

^^

SOOOO1

\0

»N-i-W|OSon|eA .

\^

-

SQOQOJ.
SURVEY PUBLICATIONS ON TESTS OF STRUCTURAL

MATERIALS.

The following reports, published by the Geological Survey, relate 

to structural materials, etc.:

BULLETIN 238. Economic geology of the lola quadrangle, Kansas, by G. I. Adams,

Erasmus Haworth, and W. R. Crane. 1904. 8°. 83 pp., 11 pis. 

BULLETIN 243.* Cement materials and industry of the United States, by E. C. Eckel.

1905. 8°. 395 pp., 15 pis. 65c.

BULLETIN 260.* The American cement industry, pp. 496-505. 1905. 40c. 

BULLETIN 324. The San Francisco earthquake and fire of April 18, 1906, and their

effects on structures and structural materials, by G. K. Gilbert, R. L. Humphrey,

J. S. Sewell, and Frank Soule". 1907. 170 pp. 

BULLETIN 329. Organization, equipment, and operation of the structural-materials

testing laboratories at St. Louis, Mo., by R. L. Humphrey. 1908. 85 pp. 

BULLETIN 331. Portland cement mortars and their constituent materials; results of

tests made at the structural-materials testing laboratories, St. Louis, Mo., by R. L.

Humphrey and William Jordan, jr. 1908. 130 pp. 

WATER-SUPPLY PAPER 143. Experiments on steel-concrete pipes on a working scale,

by J. H. Quintan. 1905. 8°. 61 pp., 4 pis. 

MINERAL RESOURCES U. S. FOR 1901,* 1902, 1903,* 1904, AND 1905.* Cement. A

series of annual articles on the cement industry and the production of cement

in the United States, by L. L. Kimball. 50c. for each volume. 

MINERAL RESOURCES U. S. FOR 1906, pp. 897-905. Advances in cement technology,

1906. by E. C. Eckel.

Reports marked with an asterisk (*) are out of stock, but may 

be had from the Superintendent of Documents, Washington, D. C., 

at the prices named. The others will be sent free to anyone interested on application to The Director, United States Geological 

Survey, Washington, D. C.

59 

0