A number of promising precast unit types and methods are being actively studied and developed. The fundamental economy of building a house of a few comparatively large prefabricated sections is obvious. Refinement in design and improvement in manufacturing and construction technic and in architectural treatment are included as a part of the current development program.
Plastic Flow of Portland Cement Concrete
Low-Cost Concrete Floors Active research work has been carried on to develop lowcost, fire-safe floors. TTithin the past two years the use of precast concrete floor joists in combination with either castin-place or precast unit floor slabs has become widely adopted. Low-cost homes as mentioned above, built by TVB, FERA, and Subsistence Homestead Division of the Department of Interior have successfully utilized these types of floors. I n areas where termites are a menace t o conventional types of floor construction, the concrete floor has the added advantage of eliminating costly termite-proofing methods. Precast concrete joists are commonly I-shaped, 8 or 10 inches in depth for ordinary spans. They are light weight and can be picked up and carried by two workmen. The joists and job-placed slab are securely bonded together, and tests have shown that the construction performs in the same manner as a monolithic T-beam. Design data are available to architects and others interested in the use of this type of floor. These data are based on accepted design practice and tests in the Portland Cement Association laboratory and a t the University of Michigan. Similar studies have developed valuable information on the manufacture, erection, and structural performance of the type of floor construction consisting of precasl, floor slabs erected on the precast joists. The two components are bonded together with mortar or a combination of mechanical and mortar bond. Some bond joint designs investigated gave strengths greatly exceeding requirements and provided a floor construction of excellent structural properties. There are more than 100 precast joist plants in operation, and this type of light-weight fire-safe floor is available to the prospective owner in almost every community. Several hundred jobs were built last year which seems to be factual evidence of the trend toward fire-safe floors. The use of firesafe concrete floors in hotels, apartments, and large homes has become widespread but cost has deterred their use in small homes. The precast joist type of concrete floor now brings fire-safe, rigid floors within the reach of even the smalleqt home builders or buyer.
“Plastic flow” of concrete is defined, and its application to structural materials is discussed. Sources of test data are cited and the phenomenon is discussed. -4 general curve equation for plastic flow in concretes is offered. Variations in the constants for different concretes under different ages at loading and under different conditions are given. Comparisons with concrete using other cements and other materials are shown. The effects of plastic flow on the distribution of stresses in reinforcement and other structural members are given and illustrated for both sustained stress and sustained strain. J. R. SHAKK Engineering Experiment Station, The Ohio State University,
Columbus, Ohio
T
H E term “plastic flow” as used here is that property of a material which is evidenced by the continuance for an appreciable time of the increase of deformation due to sustained stress or the decrease of stress during sustained strain. Concrete and timber are two of the ordinary structural materials that have this property. Steel, because it is seldom stressed above the elastic limit, and stone masonry may be said to be without it. Steel stressed above the elastic limit does show creep, a form of plastic flow, but this is not common in structures. Where high secondary stresses occur a t joint RECEIIED April 27, 1935. and details, this creep or plastic flow may a t times allow for readjustments which hold the stresses little if any above the elastic limit. If there is an appreciable possible deformation range between the elastic limit and the breaking stress, as for low-carbon or mild steels, a good proportion of the factor ol safety is retained. Timber does show considerable plastic flow and there is littl? known of a quantitative nature about it. The continued increase of sag in house floor joints, often confused with dryingout shrinkage, is evidence of this flow. Large timber trusses have also shown it. However, this paper has to deal with th? plastic flow in concrete only. The originators of the theories of reinforced concrete design were happy when they found that steel and concrete had nearly the same coefficients of temperature expansion. Knowing steel as they did, this discovery was a great reliet. They were not aware of two other properties of concrete which the steel did not have-viz., change of volume due t,i CONCRETE HOUSESTUDIES, PORTLAND CEMENT ASSOCIATION humidity changes and plastic flow. It is now known that t h e
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1012
INDUSTRL4L AND ENGINEERING CHEMISTRY
humidity change may be as great as 100’ F. change of temperature; and plastic flow is the subject of this paper. Both of these properties may conjure up visions of large and varied changes in the distribution of the stresses in the two materials of a reinforced concrete member. One of the early discoverers of this property of plastic flow, after measuring from time to time the continued shortening of a tall reinforced concrete building column, reported that the shortening indicated that the steel in the column was being stressed to as high as 100,000 pounds per square inch according to elastic calculations. Of course this was not correct, for the steel in the column had an elastic limit of probably not over 40,000 pounds per square inch. It did, however, indicate that the steel was stressed a t least to its elastic limit, and no structural designer expects steel t o carry stresses above the elastic limit.
Sources of Data Since 1925 investigations have been and are being carried out a t the University of California, The Bureau of Building Research in England, The Ohio State University, and many other places. At the University of Illinois and a t Lehigh University, and by Faber, of England in 1927-1928 (7), tests were made on reinforced concrete beams, columns, and frames. Others have also contributed to this knowledge, but this paper will deal with the first three investigations mentioned, where efforts were made to find the underlying laws and principles involved. At these three places prisms and cylinders of plain concretes under sustained stress were observed for deformation from time to time. Many sorts of concrete under a variety of conditions were tested, and data are at hand for periods as long as eight years. Because of the complexity of the structure of concrete it is not known just what internal actions produce this phenomenon. Lynam of England (15) and Davis of California (6) believe that there may be three kinds of creep or flow taking place: (1) the movement of particles on or over the other, as in tar, oil, or asphalt, called [‘viscousflow” by these men, (2) slip along planes within the crystal which is similar to creep in metals, and (3) the squeezing of water out of or otherwise compressing the gel formed during hydration. No plastic flow has been found to come from the rocks which make up the aggregate particles. If there is a plastic flow in the rocks, it is so much less than that of the concrete as to be negligible. A short series of tests indicated that what might be called “shear flow” or flow due to shearing action is very small. The same set of tests shows that there is a movement of the bar in the concrete when the steel is acting opposite t o the concrete surrounding it, such as in a beam or bar splice, which is considerably greater than any shear flow. The great majority of tests have been made on direct compression, and they together with the other tests cited, indicate that the large proportion of the plastic flow is due to action on the gel. Whether the other two kinds of creep figure at all is conjectural, though one or the other of them probably accounts for the bond flow of the bar in the concrete. A difference in plastic flow for different aggregates has been observed which indicates that a special type of plastic flow occurs at the surface of steel or aggregate particles. That the greatest part of the plastic flow comes about from the gel is evidenced by the fact that the plastic flow slows down as the concrete ages, when the gels become more solid and more or less crystalline. Concretes loaded at greater ages show less plastic flow than those loaded younger.
Equation for Plastic Flow in Concretes A hundred different tests (thirty made in Ohio, thirty-three in California, and thirty-six in England) were tabulated and studied in order to obtain some algebraic expression to indi-
VOL. 27, NO. 9
cate the plastic flow property of concrete in general and t o tabulate the values to be used for different concretes under different conditions so that the engineer might have some data to draw from when making calculations involving plastic flow. This study brought out that a simple power expression similar to the equation of the parabola would serve quite well in most cases of ordinary concrete. This formula is in the form: y = C G where y = plastic deformation, inches/inch/pound/square inch z = time, days C = coefficient drawn from tests a = a root drawn from tests
Table I gives a r6surn.4 of these findings. Twenty-five tests of concretes made from ordinary aggregates, both ordinary strength and rich and loaded a t 28 days in air, showed an average for C of 0.130 and 2.9 for a. This is very nearly a TABLE I. R ~ S U MOF E POWERCURVEDATA Strength Ordinary Ordinary Ordinary Ordinary Ordinary Ordinary Ordinary Ordinary
Surround- Age a t Equation Values Aggregates ings Loading C a Portland Cement Concrete8 Ordinary Air 7 days 0.207 2.8 Ordinary Air 14 days 0.151 2.8 Ordinary Air 28 days 0.128 2.9 Ordinary Air 2 mo. 0.088 2.5 Ordinary Air 3 ma. 0.072 3.0 Ordjnary Air 4 mo. 0.078 2.3 Ordinary Air 16 mo. 0.005 1.5 Ordinary Water 28 days 0.088 6.0
Averageof 2 2 16 1 1 1 1 1
Rich Rich Ordinary Ordinary Ordinary Ordinary Ordinary
Ordinary Ordinary Granite Granite Granite Granite Granite
Air Water Air Air Water Water Water
28 days 28 days 28 days 3 mo. 7 days 28 days 3 mo.
0.120 0.072 0.287 0.128 0.405 0.145 0.065
3.2 4.2 5.0 3.3 10.0 4.8 4 0
Rich Ordinary Rich Rich Rich Ordinary Rich Rich
Granite Sandstone Sandstone Sandstone Sandstone Silica Silica Basalt
Air Air Air Air Air Air Air Air
28 days 7 days 28 days 2 mo. 7 mo. 28 days 28 days 28 days
0.125 0.105 0.132 0.060 0.050 0.086 0.078 0.170
5.0 3.8 2.6 2.4 3.8 2.8 3.8 3.2
Lean, overloaded Ordinary, overloaded Ordinary oyerloided Ordinary overlodded
Ordinary
Air
28 days
0.370
4.2
Sandstone
Air
7 mo.
0.122
2.8
1
Granite
Air
3 mo.
0.152
3.6
1
Granite Ground glass
Water
3 rno.
0,094
4.7
1
Air
28 days
o’160
2.3
Lean
Ordinary
Air
28 days
0.100
2.6
1
Ordinary Ordinary Ordinary Ordinary Ordinary Rich
Rapid-Hardening Cement Concrete Ordinary Air 7 days 0.096 Air 14 days Ordinary 0.103 Air 28 days Ordinary 0.053 Ordinary Air 3 mo. 0.026 Ordinary Water 28 days 0.055 Air 28 day6 0.057 Ordinary
3.3 3.3 3.2 2.9 4.3 2.5
1 1 1
Ordinary Ordinary Ordinary Ordinary Ordinary
Aluminous Cement Concrete Air 7 days 0.100 Ordinary Air 14 days 0.049 Ordinary .4ir 28 days 0.036 Ordinary Air 3 mo. 0.023 Ordinary 0.094 Water 28 days Ordinary
3.4 2.5 2.6 2.2 4.0
10 3 3 3 2 3 3
1
1 1
5 1 1 2 1 1
cubic parabola. The variations in these twenty-five tests from the averages here shown were rather wide. The value C varied between the extremes of 0.054 and 2.07, and a between 2.1 an 3.9, owing t o variations in mix, aggregates, gradings of aggregates, cement-water ratios, etc. This power expression does not tell the proper story throughout the entire range. It conforms to the observed data quite well up to an average time of one year, but after that, the equation gives values which are too high. The values of C should be progressively scaled down until no more increase in y is obtained
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INDUSTRIAL AND ENGINEERING CHEMISTRY
after five years. In general, no plastic deformation greater than 125 per cent of that a t one year should be considered. The two most clearly established and most important variations from the general values of 0.130 for C and 2.9 for a are due to the age of the concrete when loaded and to the conditions of humidity under which the concrete works, whether in air more or less dry, or in water. The earlier the age a t which concretes are loaded, the greater the plastic flow. Concretes which receive their loads a long time after having been cast or poured show a less amount. From the data examined it appears that the coefficient C for ordinary concretes follows some such law as the following:
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for stresses within the working stress range, and applies t o concrete of ordinary aggregates but does not seem to apply to those of granite aggregate. The plastic flow for the latter, as evidenced by the coefficient, was nearly twice as great for concrete loaded a t 40 per cent of their ultimate strengths as those loaded a t 13 per cent, and the intermediate loadings were proportional. The roots also advanced with the loadings, showing an increasing concentration of the plastic flow in the early ages. For any aggregates a loading in excess of 40 per cent can be expected to produce proportionately higher plastic flows.
Plastic Recovery where -4 = age in days at loading, or the time in days from the date of pouring to the date when the load is applied The data from which this expression was taken are all in the field of ordinary concretes. Insufficient data are a t hand to check it for concretes using special aggregates and concretes of special mix. The indications are that the general variations exist, although the figures given may not fit exactly. It has been definitely established that, the drier the air in which a concrete works, the greater the plastic flow, which means that plastic flow is a more important consideration for concretes in buildings than for water purification plants or similar structures. The data a t hand seem to show that the plastic flow for concretes in water is about half that for concretes in air. However, the movement for the wet concrete is more rapid a t the earlier ages after loading and slower a t the later ages. The coefficient for the wet concrete is lower but the root is higher.
Effect of Different Materials Types of aggregates have a marked effect on the amount of the plastic flow. Unfortunately this field has been too lightly covered to make any safe generalities a t this time. Sandstones show little variation from what has been here called “ordinary” aggregates. Natural sands and gravel and crushed limestone are included in the term ordinary aggregates. Granites, basalts, and broken glass increase both in the coefficient and in the roots, showing greater plastic flows particularly a t the early ages. Silica both in the pebble and crushed form shows considerably less plastic flow, evidenced in the lower coefficient values. One attempt was made to try out the effect of the surface conditions of the aggregates, and broken glass was compared with broken glass having ground surfaces on the coarser particles. The plastic flow for the ground glass surfaces was about three-quarters that of the smooth glass. One apparent observation seems to be that the plastic flow is greater for the smooth, more or less planar aggregate surfaces. A few light-weight porous aggregates mere tried but indefinite results were obtained. Blast furnace slag showed very erratic and undependable results, as did also a special rounded particle consisting of a particularly light, bloated clay aggregate. Haydite showed results about the same as natural gravel and the results were good. Gunite showed very erratic and undependable results ; however, it was evident that a great amount of plastic flow occurred shortly after loading.
A plastic recovery when a load which has been sustained for some time is removed also occurs, and three tests out of five showed that the same power expression fits very nicely for the f i s t few days, although two out of five showed no conformity whatever. The roots for these are quite high, showing rapid recovery a t the early ages. The recovery all takes place in a relatively short time so that periodic stress applications still show a progressive deformation which is some fraction of that for a fully sustained load. This shows that live loadings may be a source of plastic flow as well as dead loadings, although dead loads are usually thought of when considering sustained loads. Special Cements The English tests (9) produced data for Portland cements of high early strength or of rapid hardening properties and for aluminous cements. These data are hardly complete enough to draw any conclusions, but the two important variations, due to age a t loading and humidity conditions, are borne out fairly well for the former. The reduction in plastic flow for the rapid-hardening cement in water appears as an increase of the root rather than as a decrease in the coefficient. The aluminous cement flows faster in water than in air, in so far as these tests indicate.
Cell uloid Some tests were made a t the University of Washington to find out about the plastic flow of celluloid which is being used for models for photoelastic tests. These data showed good conformity to this same power expression for the extent of the time-150 minutes. The roots were close to those for concrete, averaging 2.6 from 2.0 to 3.0, and the coefficients were considerably higher. The coefficients also advanced rapidly as loading increased.
Effect of Plastic Flow on Distribution of Stresses The distribution of stresses in concentrically loaded reinforced concrete columns is ordinarily calculated on the basis of area of cross section and modulus of elasticity ratio. The steel area is usually transformed to an equivalent concrete area by multiplying by the ratio of its modulus of elasticity to that of the concrete, a value which is generally called n. This fits for elastic conditions. As time goes on during the sustaining of the load, the concrete flows and progressively gets out from under the load, leaving a greater and greater proportion of it to the steel. Glanville (9) has expressed the unit stress in the concrete after a time, x, by the expression:
Effect of Stress The power expression given is in terms of unit deformation for unit load, which implies that the plastic flow is directly proportional to the stress. This is generally conceded from the data from the three principal sources and by their authors
If the power expression is introduced, this expression becomes:
INDUSTRIAL AND ENGINEERING CHEMISTRY
1014
where z
time, days unit stress in concrete at loading unit stress in concrete at x days after loading p = proportion of steel cross-sectioned area in the gross column cross section E, = modulus of elasticity of steel = 30,000,000 pounds/ square inch n = modular ratio E,/E, e = Kaperian base =
= fCz = .fc
If we consider a volume of cross-sectional area of 100 square inches having 2 per cent ( p = 0.02) of steel in the cross section and the modular ratio n of 12, under a concentric load of 61,000 pounds, and take the values 0.130 and 2.9 for C and a, respectively, and 365 days for 2, we have by the above formulaf, = 500 pounds per square inch, fc. = 306, f. = 6000, and fsz = 10,160 pounds per square inch. This means that the unit stress in the steel has advanced by 69 per cent. If the steel proportion is changed to 0.5 per cent, the values will change to f c = 578 pounds per square inch, f C z = 510, f v = 6940, and f.. = 20,500 pounds per square inch. Here the increase in the unit stress in the steel is 190 per cent in one year. Another theoretical aspect is that of the release of the stresses and load due to a sustained strain rather than a sustained stress or loading. Whitney (88) gives this expression: jcz
L eEcY
If the value of y from the power expression is introduced, the expression becomes : fcz =
.fc
eEcCI;/;
If the conditions of the two examples shown for sustained load are used, fez at one year after loading will be 415 pounds per square inch for the 2 per cent steel, and the total load will reduce to 16,070 pounds. For the 0.5 per cent column f C z will again be 415 pounds per square inch, and the load will have reduced from 61,000 to 7070 pounds. It will be noticed that f s will remain constant for a sustained strain and will be 6000 pounds per square inch for both cases. From these equations and examples it will be seen that other estimates and calculations can be made for the easement of secondary stresses in frames and arches, and that deflections of beams and other distortions may be more closely estimated than heretofore; these estimations mill aid the engineer in his judgment and may thus save in materials and avoid damage to the working of machinery which cannot allow undue distortion of supports.
Bibliography Bingham, E. C., and Reiner, M., Physics, 4,88-96 (1933). Testma Materials, 23,339 (1923). Clemmer, H . F., Proc. Am. SOC. D a r i s , R. E., Proc. Am. Concrete Inst.. 24,303 (1928). Davis, R. E., and Davis, H . E., Ibid., 27, 837 (1931). ( 5 ) Davis, R. E., and Davis, H. E., Proc. Am. SOC.Testing M u terials, 30, 707 (1930). (6) Davis, R . E., Davis, H. E., and Hamilton, J. S., Ibid., 34, 11, 354 (1934). (7) Faber, Oscar, Proc. Inst. Civil Engrs. (London), 225, P a r t I (1927-28). (8) Fuller, 8.H., and More, C . C., Proc. Am. Concrete Inst., 12, 302 (1916). (9) Glanville, W. H., Dept. Sei. Ind. Research (Brit.), Building Research, Tech. Paper 12 (1930). (10) Goldbeck, A. T., and Smith, E. B., Proc. Am. Concrete Inst.. 12, 324 (1916). (11) H a t t , W. K., PTOC. Am. Soc. Testin0 Materials, 7, 421 (1907). (1) (2) (3) (4)
VOL. 27, NO. 9
(12) Kluge, R. W., and Wilson, W . M., Univ. Ill., Bull. 269 (1935). (13) Kreidler, C. L., and Lyse, Inge, Proc. Am. Concrete Inst., 28, 317 (1932). 114) Lord. A. R.. Ibid.. 13. 45 11917). i15j Lyna‘m, C . ‘G., “Growth and Movement in Portland Cement Concrete,” Oxford University Press, 1934. (16) McMillan, F. R., Trans. Am. Soc. Civil Engrs., 80,1743 (1916). (17) McMillan, F. R., Univ. Minn., Studies in Engineering, Bull. 3 (1915). (18) Richart, F. E., and Stachle, C. C., Proc. Am. Concrete Inst., 28, 279 (1932). (19) Smith, E. B., Ibid., 12 (1916). (20) Smith, E. B.. Ibid.. 13,99 (1917). (21) Straub, Lorens, Trans. Am. SOC.Czvd Engrs., 95,613 (1931) (22) Whitney, C. S., Proc. Am. Concrete Inst., 28,479 (1932).
RECEIVED-4pril 27, 1935.
0 . 0
Portland Cement and Its Possibilities Simple descriptions are given of the changes which take place in limestone and clay as they pass through the kiln and grinding mills to produce Portland cement, and in the cement as it hydrates to produce hardened concrete. The limited demands made upon concrete by the civil engineer indicate that the strength-giving quality of cement can be used only in small measure because of the properties of volume change and brittleness in the concrete. The major factors which influence volume change of concrete are given, and suggestions are made as to possible methods of controlling volume changes. One of these suggestions is to increase the efficiency of the cement so that less can be used per cubic yard of concrete.
R . W. CARLSON Massachusetts Institute of Technology, Cambridge, Mass.
SSEKTIALLY the making of cement consists in combining the oxides of calcium, silicon, iron, and aluminum into crystalline compounds by the application of heat. Limestone and clay are ground together in predetermined proportions until about 90 per cent of the mixture passes the 200-mesh sieve, making the average particle size about 0.001 inch. This ground “raw mix” is fed into the upper end of a rotating kiln to work its way gradually toward the flame a t the lower end. First the moisture is evaporated. As the temperature rises and reaches about 1800” F., the limestone decomposes into calcium oxide and carbon dioxide, the latter escaping as a gas through the flue. -4s soon as the limestone decomposes, the
