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investigations, with aggregates measured dry and carefully rodded or puddled. Allowance must be made when using the tables for .estimating, for the different results obtained when aggregates are measured in the loose condition common to field measurements. There will be but little difference, if any, in the measurement of broken stone or pebbles due to the two methods, but the measurement of sand will show a difference of from 5 to 20 per cent according to the moisture content.

If the proportions to be used in the work are selected from the table without preliminary tests of the materials and control tests are not made during the progress of the work, the mixtures in bold-face type should be used.

The use of these tables as a guide in the selection of concrete mixtures and for comparing different mixtures is based on the following:

(1) Concrete must be plastic;
(2) Aggregates must be clean and structurally sound;
(3) Aggregates must be graded between the sizes indicated;
(4) Cement must meet the requirements of the Standard Specifi-

cations and Tests for Portland Cement of the American

Society for Testing Materials. The plasticity of the concrete shall be determined by the slump test carried out in accordance with the following Tentative Specifications for Workability of Concrete for Concrete Pavements of the American Society for Testing Materials:

“In determining workability, the newly mixed concrete shall be placed in a truncated cone-shaped metal mold 12 in. high, 8 in. in diameter at the base, and 4 in. in diameter at the top, and provided with handles at the sides. The concrete shall be lightly tamped with a rod as it is placed in the mold which, when filled, shall be immediately removed and the slump or settlement of the concrete noted.”

Apply the following rules in determining the size to be assigned to a given aggregate: (1) Sieve analysis shall be made in accordance with the Tenta

tive Method of Test for Sieve Analysis of Aggregates for
Concrete, of the American Society for Testing Materials.
The principal features of this method are: Representative
sample selected by quartering or by use of a sampler; dry
samples separated by use of square mesh wire cloth sieves
having 100, 50, 30, 16, 8, 4 meshes per linear inch and 38, 44.
1% and 3 in. Percentages of sample coarser than each sieve

computed.
(2) Not less than 15 per cent shall be retained between the sieve

which is considered the maximum size and the next smaller
sieve.

(3) Not more than 15 per cent of a coarse aggregate shall be

finer than the sieve considered as the minimum size. (For example: a graded sand with 15 per cent retained on the No. 8 sieve would fall in the O-No. 4 size; if 14 per cent or less were retained, the sand would fall in the O-No. 8 sizé. A coarse aggregate having 16 per cent coarser than

2-in. sieve would be considered as 3 in. aggregate.) (4) 'Only the sieve sizes given in the table shall be considered in

applying rules (1) and (2). Proportions and Quantities of Materials may be interpolated for concrete strengths, aggregate sizes and consistencies not covered by the tables.

October 14, 1921.

QUANTITIES OF MATERIALS FOR CONCRETE OF A GIVEN

COMPRESSIVE STRENGTH

BY DUFF A. ABRAMS*

These tables are based on experimental studies of concrete carried out through the coöperation of the Portland Cement Association and Lewis Institute. The investigations on which these values are based have covered a period of about seven years and included nearly one hundred thousand tests.

Separate tables of Proportions and Quantities of Materials have been prepared for concrete of strengths of 1500, 2000, 2500, 3000, 3500, and 4000 lb. per sq. in. at the age of 28 days, using fine and coarse aggregate of different sizes and a wide range of consistencies as measured by the slump tests.

The proportions are based on the compressive strength of 6 by 12-in. cylinders, made and stored in accordance with the Tentative Methods of Making Compression Tests of Concrete of the American Society for Testing Materials. The principal features of this method are: Aggregates dry and of known sieve analysis, proportion by volume, concrete hand-mixed: puddled in metal cylinder forms, generally 6 by 12 in. in size. Plasticity of concrete controlled by slump test, specimens cured in damp sand and tested in compression at 7 and 28 days.

The quantities of materials per cubic yard of finished concrete given in the tables are net quantities, 110 allowance being made for waste. The conditions peculiar to each job should govern waste allowances which the estimator should base on experience or other data available; for average conditions, the following allowances for waste are suggested :

Cement 2 per cent, fine aggregate 10 per cent, coarse aggregate 5 per cent.

The above percentages do not include any allowance for grouting, patching, washing or replacements.

The purpose of the tables is threefold:

(1) To furnish a guide in the selection of mixtures to be used in preliminary investigations of the strength of concrete from given materials.

(2) To indicate proportions which may be expected to produce concrete of a given strength under average conditions where control tests are not made.

(3) To furnish a correct basis for comparing the relative economies of concrete made from aggregates of different sizes when the plasticity and strength of the resulting concrete are taken into account.

The value of the tables of Quantities of Materials is not in their use for estimating, but in comparative studies of different aggregates and combinations. The quantities are based on laboratory investigations, with aggregates measured dry and carefully rodded or puddled. Allowance must be made when using the tables for estimating, for the different results obtained when aggregates are measured in the loose condition

Professor in Charge of Structural Materials Research Laboratory, Lewis Insti. tute, Chicago.

common to field measurements. There will be but little difference, if any, in the measurement of broken stone or pebbles due to the two methods, but the measurement of sand will show a difference of from 5 to 20 per cent, according to the moisture content.

If the proportions to be used in the work are selected from the table without preliminary tests of the materials, and control tests are not made during the progress of the work, the mixtures in bold-face type should be used.

The use of these tables as a guide in the selection of concrete mixtures and for comparing different mixtures is based on the following:

(1) Concrete must be plastic;
(2) Aggregates must be clean and structurally sound;
(3) Aggregates must be graded between the sizes indicated;
(4) Cement must meet the requirements of the Standard Specifi-

cations and Tests for Portland Cement of the American

Society for Testing Materials. The plasticity of the concrete shall be determined by the slump test carried out in accordance with the following Tentative Specifications for Workability of Concrete for Concrete Pavements of the American Society for Testing Materials:

“In determining workability, the newly mixed concrete shall be placed in a truncated cone-shaped metal mold 12 in. high, 8 in. in diameter at the base, and 4 in. in diameter at the top, and provided with handles at the sides. The concrete shall be lightly tamped with a rod as it is placed in the mold which, when filled, shall be immediately removed and the slump or settlement of the concrete noted."

Apply the following rules in determining the size to be assigned to a given aggregate: (1) Sieve analysis shall be made in accordance with the Tentative

Method of Test for Sieve Analysis of Aggregates for
Concrete, of the American Society for Testing Materials.
The principal features of this method are: Representative
sample selected by quartering or by use of a sampler;
separate dry sample by use of square mesh wire cloth
sieves having 100-50, 30-16, 8 and 4 meshes per linear
inch and 38, 34, 142 and 3 in Compute percentages of

sample coarser than each sieve.
(2) Not less than 15 per cent shall be retained between the sieve

which is considered the maximum size and the next

smaller sieve.
(3) Not more than 15 per cent of a coarse aggregate shall be

finer than the sieve considered as the minimum size.
(For example: a graded sand with 16 per cent retained
on the No. 8 sieve would fall in the 0-No. 4 size; if 14
per cent or less were retained, the sand would fall in the
0-No. 8 size. A coarse aggregate having 16 per cent
coarser than 2-in. sieve would be considered as 3-in. ag-

gregate.)
(4) Only the sieve sizes given in the table shall be considered in

applying rules (1) and (2). Proportions and quantities of materials may be interpolated for concrete strengths, aggregate sizes and consistencies not covered by the tables.

Proportions for 1500 lb. per sq. in. Concrete

Based on 28-day compressive strength of 6x12 in. cylinders.

Proportions are expressed by volume as follows: Portland Cement : Fine Aggregate : Coarse Aggregate.

Thus 1:2.6:4.6 indicates 1 part by volume of portland cement, 2.6 parts by volume of fine aggregate and 4.6 parts by volume of coarse aggregate.

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1:4.6:6.9
1:4.06.2

1:5.2:6 6 1:4.5:59

1% to 1

4

1:3.2:7.1
1:27.63
1:2.1:6.1
1:1.4.38

1:3.6:7.1
1.3 0:6 3
1:2.4:5.2
1 16.3.9

1:4,0:7.0
1:34:6.3
1:2.7:5.2
1:1 8:3.9

* to 3 in.

7 8 ** 10

1:3.1:3.7 1:3.5:4.9

1:21:3.9

1:2.4:3.8

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