This section is from the book "Cement And Concrete", by Louis Carlton Sabin. Also available from Amazon: Cement and Concrete.

437. With the increasing use of concrete and steel in combination, the modulus of elasticity of cement mortar and concrete assumes a new importance, since the ratio of the stresses in the two materials depends upon the relative moduli of elasticity. Some of the earlier determinations of the modulus of mortar gave very high values. This may have been due to the use of richer mixtures, and the exercise of greater care in the manipulation, than are employed in actual construction, and also to the fact that the determinations were based upon the deformations resulting from the application of very limited loads.

It is now considered that the ratio of stress to strain is not constant, even for moderate loads, but that the modulus of elasticity decreases with increasing stress, and this fact is brought out in the following tables. The tests cited bring out a wide range of values for concretes and mortars made from a variety of sand and aggregate and of various compositions and ages.

Table 141 gives the modulus of elasticity of mortars as determined by tests of twelve-inch cubes at the Watertown Arsenal.1 These specimens were a portion of those prepared by Mr. Rafter, the compressive strength being given in Table 129. As each value is the result of but one determination, the results are not as regular as might be desired. In general the strength and the modulus decrease together as the amount of water used in mixing is increased. The modulus also decreases with the strength as the proportion of sand increases.

Tests of Twelve-inch Cubes at Watertown Arsenal for State Engineer of New York.

Consistency of Mortar. | Proportions Cement to Sand in Mortar by volume. | ||||||||||||

1-1 | 1-2 | 1-3 | 1-4 | ||||||||||

Modulus of Elasticity in Thousands, | between Loads, in Pounds per Square Inch, of | ||||||||||||

Kind. | Brand. | 100-600 | 100-1000 | 1000-2000 | 100-600 | 100-1000 | 1000-2000 | 100-600 | 100-1000 | 1000-2000 | 100-600 | 100-1000 | |

" " " | Buffalo " " " | Dry Plastic Excess Mean | 1667 2500 2273 2147 | 1452 1875 1800 1709 | 1389 1020 833 1081 | 1471 1250 1250 1324 | 1364 1250 1184 1266 | 1042 ... ... ... | 1042 1087 735 955 | 804 ... ... ... | ... ... ... ... | ... ... ... ... | ... ... ... ... |

" | Empire " | Dry Plastic | ... ... | ... ... | ... ... | 3571 1923 | 2500 1956 | 1923 2083 | 2500 ... | 1956 ... | 1250 ... | 3125 2045 | 1875 1250 |

Notes: —Mortar cubes stored in water three months, then buried in sand about seventeen months. For compressive strength of cubes, see Table 129.

In the compressive tests of twelve-inch concrete cubes made for Mr. George A. Kimball and abstracted in Table 130, many of the specimens were also gaged for compression under load to determine the modulus of elasticity, and a part of the results are presented in Table 142.

Tests Made on Twelve-inch Cubes of Portland Cement Concrete at Watertown Arsenal for Boston Elevated Railroad.

Age of Cubes When Crushed. | Concrete 1-2-4. | Concrete 1-3-6. | Concrete 1-6-12. | |||||

Modulus of Elasticity in Thousands, between Loads, in Pounds per Square Inch, of | ||||||||

100-600 | 100-1000 | 1000-2000 | 100-600 | 100-1000 | 1000-2000 | 100-600 | 100-1000 | |

7 days 1 month 3 months 6 months | 2592c 2662c 3670 3646 | 2053c 2444c 3170 3567 | 1351a 1462c 2157 2581 | 1869c 2438 2976 3608 | 15296 2135 2656 3503 | 1219a 1805 1868 | l376 1642 1820 | 1363 1522 |

Notes: — Results marked "a" are means of five or more tests of one brand.

Results marked "b" are means of five or more tests on each of two brands..

Results marked "c" are means of five or more tests on each of three brands.

Results not marked are means of five or more tests on each of four brands, two American, two German. For compressive strengths of similar cubes, see Table 130.

It is seen that the modulus increases with the age and richness of the specimens, and decreases as the load increases. For one-two-four concrete the modulus at one month, for loads between a hundred and a thousand pounds, is about two and one-half million, and for six months, three and a half million. The corresponding values for the one-three-six concrete are two million and three and one-half million. When the ultimate strength is approached, the modulus of elasticity decreases rapidly, and between loads of one thousand and two thousand pounds per square inch, the richest concrete gives only about one and one-half and two and one-half million at one month and six months, respectively.

1 "Tests of Metals," 1899.

The results in Table 143 are abstracted from the extensive tests made at the Watertown Arsenal for the State Engineer of New York. Although several brands were tested, the results in the table are from one brand only, namely, "Wayland" Portland. These cubes were all stored in the same manner, namely, in water three to four months, and then buried in damp sand until broken at the age of twenty months. The mean ultimate strengths of similar cubes stored according to four methods are given in Table 132.

Since in all of these mixtures the quantity of mortar was a given percentage, either thirty-three or forty, of the volume of aggregate, the effect of the richness of the mortar may be studied. While the proportional strengths of the concretes made with mortars containing from one to five parts sand are 100, 77, 52, 44, and 38, the corresponding proportional moduli of elasticity are 100, 92, 77, 60, and 55, the modulus decreasing less rapidly than the strength, with the addition of sand.

Table 144 gives the results of the determinations of the modulus of elasticity of concrete specimens made and tested at the Watertown Arsenal,1 the strength of which was given in Table 134. As these are all rich concretes, the moduli and the strengths are high. The values of the modulus for the gravel concretes are about 70 per cent, of those for the trap, but the strengths of the gravel concretes are in general about 80 per cent, of those obtained with concretes having trap aggregate. In a general way, however, the modulus and strength vary together.

The modulus of elasticity of cinder concrete prepared for the Eastern Expanded.

1 "Tests of Metals," 1898.

Tests of Twelve-inch Cubes at Watertown Arsenal, for State Engineer of New York.

volume mortar as percent. of volume aggregate. | Proportion Cement to Sand in Mortar. | l-l | 1-2 | 1-3 | 1-4 | 1-5 | Means. | |||||||

Modulus of Elasticity in Thousands, between Loads, in Pounds per Square Inch, of | ||||||||||||||

100-600 | 100-1000 | 1000-2000 | 100-600 | 100-1000 | 1000-2000 | 100-600 | 100-1000 | 100-600 | 100-1000 | 100-600 | 100-1000 | |||

S3 | Moist Earth Mason's . . Quaking . . | 2273 1667 1786 | 2143 1731 1800 | 1136 1087 1087 | 2083 2778 2083 | 1956 2250 1800 | 1136 1429 ... | 2500 2083 1471 | 2045 1667 1452 | 1667 1250 1667 | 1364 ... 1500 | 1471 1562 1250 | 1500 1046 ... | 1773 1686 1590 |

40 | Moist Earth Mason's . . Quaking . . | 2778 4167 2273 | 2250 2500 2045 | 1087 1219 1111 | 2083 2273 2500 | 1875 2143 1956 | 1111 1562 ... | 2083 1786 1667 | 1800 1500 1364 | 1316 1471 1562 | 1184 1184 1286 | 1389 1250 1316 | 1154 ... 1046 | 1676 1914 1648 |

Means. . . | 2491 | 2078 | 1120 | 2300 | 1997 | 1310 | 1932 | 1638 | 1489 | 1304 | 1373 | 1186 | 1714 |

Tests of Twelve-inch Cubes at Watertown Arsenal. 1-1-3, Alpha Cement.

Modulus of Elasticity in Thousands, between Loads of 100 and 1,000 Pounds per Square Inch, at Age, Days, | ||||

7-8 | 19-23 | 29-34 | 61-76 | |

Trap 1/2"....... Trap 3/4"....... Trap 1"....... Trap 1 1/2"....... Trap 2 1/2"....... Trap 1/2"-1, 2 1/2"-2....... Trap 1/2"-1, 1"-1, 2 1/2"-1....... | 1875 3214 4091 4500 3214 5000 3461 | 2500 2368 6429 5625 5625 4500 4500 | 3750 5625 5625 5000 4500 7500 5625 | 3750 ... 5625 4091 7500 5625 7500 |

Mean Results, trap rock alone | 3622 | 4507 | 5375 | 5682 |

Pebbles 3/8"...... Pebbles 1 1/2"...... Pebbles 3/8"-1, 1 1/2"-2...... Pebbles 1/8"-1, 3/8"-1, 1 1/2"-2...... | 1800 3750 2812 1800 | 3750 4091 3461 3214 | 3461 3750 4091 3461 | 3214 3000 4500 3214 |

Mean Results, pebbles alone | 2540 | 3629 | 3691 | 3482 |

Notes: — Tests at Watertown Arsenal, "Tests of Metals," 1898.

For crushing strength of these concretes, see Table 134.

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