John C. (John Cresson) Trautwine.

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Fig. 26.

135. At any cross section, the ordinate, betw the axis, X, of abscissas,
and the curve, (1) m w , (2) m p pos, or (3) m neg, represents, respectively,
by the scale of ordinates on the left, (1) the dead load moment, m w , (2) the
max positive live-load mom, m pos, or (3) the max negative live-load mom,
m p neg, at that section, the dead load (1 per unit of span) being uniformly
distributed over the entire length (two or three spans, as shown) of the beam,
and the live load (1 per unit of span) being uniformly distributed alternately
over two portions of the length of the beam, said portions being, for each
cross section, such that the uniformly distributed live load, placed upon said
portions, will produce, alternately, the max pos and the max neg mom at
that section.

136. In an actual beam, at any point, we have, for bending mom:

M = m w w L? + m p p L*;

m w = the ordinate, at tha point, from X to the curve m w ;

m p = ' " " " " m p pos or m p neg;

w = uniform dead load per unit of span;

p = " live " " " " " , placed as explained in If 135.

L = the actual span.

Thus, at the point, a, Fig 26 (distant 0.7 L from 0), we have, by scale,
m w = 0.035; m p pos = 0.070; m p neg = 0.035. Hence, at point a,

max pos mom = 0.035 w L 2 + 0.070 p L 2 ;
max neg mom = 0.035 w L 2 0.035 p L 2 .

If, therefore, p = w, the max neg mom, at a, is zero, and there is no
resultant neg mom to the left of a; but, if p = 2 w, we have w = p/2 =
(w + p)/3; and, at o, with p = 2 w :
max neg mom = 0.035 w I? 0.035 X 2 w L 2

= 0.035 w L2 0.070 w L 2 = 0.035 w I?

= 0.035 (w + p) L2/3.




For experiments, see p 1135. ,

For specifications, see pp 937, 940, 942, 1184.

For Concrete, see pages 1084, etc.
For abbreviations, symbols and references, see p 947 1.

1. The property of setting and hardening under water is called hydrau-
licity; and cements, which harden under water, are called hydraulic
cements; or, more briefly, cements. For behavior of cement
when mixed with water, with or without sand, see Mortar, p 947 d.


2. The elements, chiefly concerned in the action of lime and
cem mortars, are

Calcium, Ca

Aluminum, Al

Carbon, C ^ Oxygen, O.

Silicon, Si

Hydrogen, H

3. Oxygen combines with each of the others, forming oxides.
Thus : Calcium oxide, CaO, is lime;

Aluminum sesqui-oxide, A1 2 O3,* is alumina;
Carbon dioxide, COj, is carbonic acid;
Silicon dioxide, SiO 2 , is silica, or silicic acid;t
Hydrogen monoxide, H2O, is water.

4. The materials most used in the manufacture of cements are either
(a) calcareous, (b) argillaceous, or (c) both calcareous and argillaceous.

(a) Calcareous (rich in lime carbonates).

Limestone, a lime carbonate, or combination of lime and carbonic acid,
CaO + CO 2 , or CaCO 3 . Marble is limestone.

Dolomite, or magnesian limestone, containing about 45 per cent
of magnesia carbonate, MgO. CO 2 . Where strata of limestone and dolomite
adjoin, the rock varies in composition between the two, containing percent-
ages of magnesia carbonate varying from to 45.

Chalk, a soft limestone, composed of remains of marine shells.

Marl, a soft and impure hydrated J lime carbonate, precipitated from
still water and found in the beds and banks of extinct or existing lakes.

Alkali waste, lime carbonate, precipitated, as a waste product, in the
manufacture of caustic soda.

Coral. See If 5.

(b) Argillaceous (rich in alumina silicates).

Clay (including argillaceous minerals in general), an alumina silicate, or
combination of alumina and silicic acid, Al 2 Oa + SiO 2 .

Shale and slate, clay, solidified by geological processes.

Puzzolana, or pozzuolana, a volcanic slag, found at Puzzuoli, or Poz-
zuoli, near Mount Vesuvius, an impure alumina silicate.

Blast furnace slag, practically an artificial puzzolana.

Brick-dust. See ,';.

(c) Rich in both lime carbonate and alumina silicate.
Cement rock is argillaceous (clayey) limestone. The alumina silicate

usually ranges from 13 to 35 %. There is generally a considerable per-
centage of magnesia carbonate, amounting sometimes to 25 %.

5. A soft coral rock, from the reefs near Colon, Panama, mixt
with clay and silt brought down by the Chagres river, or with "a pumiceous
rhyolite tuff," found on the Isthmus, or with both, and crushed, burned and
tested at the Lehigh Valley Testing Laboratory, at Allentown, Pa., gave a

*The subscripts indicate the combining ratios of the several elements.
Thus, in alumina, A1 2 O 3 means a compound of 2 atoms of alumina with 3
of oxygen.

t Quartz is silica; and most of the sand, used in mortar, is quartz sand.

J Hydrated; containing chemically combined water,


uniform cement, comparing favorably with average standard brands of
Lehigh cement. The coral rock is "a remarkably pure lime carbonate."
The Chagres clay and silt are "rather low in silica, but contain a relatively
large amount of iron as compared with alumina." The tuff "is of approx-
imately the same composition as the argillaceous materials used in the
Lehigh district of Pennsylvania. " (Ernest Howe, U. S. G S, E N, '07/Nov/
21, p 544.) See H1J 29, etc.

6. Mr. Ernest McCullough "mixed fine brick dust and hydrated
lime together and made a fairly satisfactory cem for a small concrete
job in a locality where Portland cem could not be obtained." (E N, '07 /
Nov/21, p 557.)

7. Lime. When limestone (without clay) is "burned," its CO 2 is
driven off, and the remaining ("quick") lime has a strong affinity for
water, absorbing it with such avidity as to develop heat sufficient to pro-
duce steam, the generation of which disintegrates and swells the mass.
Combining thus with the water, the lime forms calcium hydrate, CaO.H 2 O, or
CaH 2 O 2 . This process is called slaking or slacking- ; and lime which
has satisfied its affinity for water is called slaked (or slack) lime. When
slaked lime is used as mortar, it gradually absorbs carbonic acid from the
air, forming lime carbonate, the water being liberated and evaporated.
Hardened lime mortar may thus be regarded as an artificial limestone.


8. Cement. When alumina silicate, such as clay, in sufficient quantities,
is " burned " with calcium carbonate, such as limestone, the burned prod-
uct, called cement, is deficient in, or devoid of, the slacking property; but,
on the other hand, when it is made into mortar, the combinations, formed
between the elements of the lime, the alumina, the silica and the water,
during the burning, and afterward in the mortar, are such that they readily
proceed under water. Chemists differ as to the nature of these combina-
tions, except that these constitute a process of crystallization, resulting
chiefly in the formation of hydrated lime silicate and hydrated lime alumi-
nate, which two compounds constitute the major portion of most cems.

Natural and Portland Cement.

9. In the manufacture of " natural " cement, cement rock, broken
into lumps, is first calcined, at from 1000 to 1400 C (1800 to 2500 F) in
a stationary kiln, in alternate layers with coal of about pea size, as fuel.
It is then ground to a fine powder, and this is sometimes specially mixed,
in order to increase its uniformity.

10. The qualities of nat cems vary widely, owing to diffs in the
compositions of cem rocks found in diff localities.

11. The name Rosendale, originally and properly restricted to nat
cems made in Ulster County, N Y, was at one time applied indiscriminately
to American nat cems in general.

12. In Europe, quick-setting nat cems are called " Roman cements."

13. Portland cement was so called on account of the resemblance of
the hardened mortar to Portland stone, the oolitic limestone of Portland,

14. Portland cem is made from different combinations of the cal-
careous and argillaceous materials named in II 4, and these require different
preliminary treatments. Thus, hard rock is crushed; soft rock and clay are
ground; marl and clay are mixed wet, and the marl is sometimes pumped
to the mill. In any case, the resulting materials are dried and finely ground,
mixed, and then calcined at a temperature of 1450 to 1550 C, or say 2600
to 2800 F, producing incipient vitrifaction, which consists of the chemical
combination of the silica, alumina and lime, into a glassy clinker, essentially
a lime silicate and aluminate. The resulting clinker is again ground to an
impalpable powder, which is the finished product.

15. The proportions of the several materials are carefully adjusted.
There is usually from 74 to 77.5 % lime carbonate, and about 20 % of
alumina silicate and iron oxide. See H 32.

16. Manipulation. The raw material is sometimes molded into bricks
which are burned in a stationary kiln; but it is now more generally fed, as
a fine powder, into the upper end of a nearly bor cyl (rotary kiln) 6 to 8 ft


in diam and from 60 to 100 ft or more in length. Coal dust, as fuel, is in-
jected, by an air blast, into the other end; while most of the air, required
for combustion, is admitted freely from the atmosphere thru other openings.

17. As in the case of lime, the burning' drives off the carbonic acid
and water, and more completely oxidizes any iron present.

18. The higher cost of Portland cement is due to the more
careful selection of the materials and to the more elaborate and expensive
treatment given them, resulting in the ultimate attainment of much greater
strength and uniformity than are usually found in nat cems.

19. The improvements, which have been made in the manufacture
of Portland cement, are driving out other makes. Owing to its
greater sand-carrying capacity, it is often used, by contractors, even where
the specifications permit the use of nat cem.

20. Overbiirning is liable to occur, if the material is deficient in lime
("over-clayed"). Underburning yields a soft brownish clinker, and
weak, quick-setting cem, heating in water. Some cems, slow at first, be-
come quicker after storage.

21. Portland Cement is used for structures subjected to severe or
repeated stresses, for cases where high strgth must be attained in a short
time, for concrete buildings, where water will be in contact with new work,
for thin walls subject to water pres, and for work exposed to abrasion or to
weather; while natural cement may be used in dry sheltered founda-
tions under compressive loads not exceeding 75 Ibs per sq inch and not
imposed until 3 months after placing, for backing and filling in massive
cone or stone masonry where wt and mass are desiderata, and for street and
sewer foundations.


22. Slag- cements (sometimes called pnzzolana cements or puz-
zolana) are intimate mixtures of slaked lime and basic blast-furnace slag,
both finely ground, and not calcined. As the slag leaves the blast-furnace,
it is chilled and disintegrated by running it into water. A little soda is
sometimes added, to hasten setting. Slag cem is not to be confounded with
those Portland cems in which slag is one of the ingredients.

23. In dry air, the sulphides, contained in Puzzolana cement, oxi-
dize, and cause superficial cracking. It sets more slowly than Portland,
unless treated with soda. If so treated, the soda becomes carbonated
under long storage, and the cem again becomes slow-setting. Since puzzo-
lana cem, properly made, contains no free or anhydrous lime, it does not warp
or swell, and requires less water than Portland; but, for permanency after
placing, the finished work should be kept constantly moist. It is recom-
mended for use in sea water, alone or mixed with Portland. Its mortar
is tougher than Portland, but never becomes so hard. It should not be
subjected to attrition or blows. (Report, Board of U S Engr officers,
U. S., Prof'l Papers No 28, '01.)

24. Puzzolana cement is said to work well if used with 2 or 3 parts
sand and not subjected to freezing weather. Its ingredients must be finely
ground and intimately mixed. It is used where extreme strength and
hardness are not required.

Silica Cement.

25. Silica Cement, or sand cement, was originally made by
mixing Portland cem with quartz sand (silica) and grinding the mixture to
extreme fineness It was claimed that the cem thus became much more
finely ground, and that "silica cement," containing one part Portland cem
and three parts silica, could therefore carry, in mortar, nearly as much sand
as could the pure cem alone; also that mortars, made with silica cem, were
less permeable to water than those made with pure cem in the ordinary way.

26. Owing to the high cost of grinding the quartz sand, less refractory
materials, such as lime-stone, are now substituted for it. The product,
so obtained, is still called "silica cement," altho containing a less propor-
tion of silica than Portland cem.

27. Silica cement mortar is said to work more smoothly under
the trowel than that made with ordinary cems.

28. In the construction of a concrete lock at St. Paul, Minn., it was in-
tended to use 1.5 volumes silica cem as equivalent to 1 vol Saylor's Port-



land; but experiments indicated that, at 6 mos, concrete, made with silica
cem, was as strong as that made with Portland.

Otber Cements.

29. White Portland cement, obtained by making certain modifi-
cations in the process of manufacture, is nearly colorless. It is suitable for
making imitation marbles, etc., and capable of taking artificial coloring.
It is higher in price than ordinary Portlands. See If 44.

30. Iron ore cement ("Erz-cement"), Krupp Steel Co. In this
cem, the argillaceous material of Portland cem is mostly replaced by iron
oxide. The material is burned and ground as for Portland cem, HI 13, &c.
Spec grav, 3.31. Slower setting than Portland. Sound. Low early
strgths; but, in time, strgth far exceeds that of Portland. No trace of
expansion or crackg in sea water under 15 atmospheres. (Wm. Michaelis,
Jr., Western Soc of Engrs, Vol xii, No 4, Aug 1907; S. B. Newberry, Cement
Age, Jan 1907.)

31. Hydraulic lime is a name given to cems (much used in Europe)
which, while to some extent hydraulic, do not contain enough of the hydrau-
lic elements to prevent slaking. The slaking, however, is slower, and the
swelling less, than with lime proper.


32. Analyses of cements, in percentages.

Silica. Alumina. Iron Oxide. X,ime.

SIO Z -4/2 8 Fe%0s C<*O

- 10 20 30 10 10 20 10 20 30 40 50 60

Fig 1. Analyses of Cements.

33. The ratio of the wt of alumina silicate to that of the lime, in a cem,
is called its hydraulic index. Other things being equal, it may be used
as an indication of the hydraulicity of the cem.

34. Thus, if a cem contains 30 % alumina silicate and 60 % lime, its hy-
draulic index is 30/60 = 0.50.

35. The hydraulic modulus is approximately the reciprocal of the
hydraulic index; i.e., the modulus is the ratio, by wt, of lime, to silica,

* Richard K. Meade, "Portland Cement," 1906, pp 16-17.

t Edwin C. Eckel, "Cements, Limes and Plasters," 1907, pp 253 etc.,

J 16 analyses of "Steel" (slag) cement, made by Illinois Steel Co., South
Chicago, reported by Board of U. S. Engineer Officers, 1900, gave practi-
cally the same averages, but with generally greater uniformity: silica, 29.9
to 27.8; alumina and iron, 12.1 to 11.1; lime, 52.1 to 50.3; magnesia, 3.0
to 1.6.



alumina and iron oxide. It is sometimes specified that the modulus, in
Portland cement, shall be 1.7.

36. In natural cements, the modulus usually ranges from 0.667 to 1.667.

37. Mr. Spencer B. Newberry uses the ratio :

(lime alumina) -e- silica,

which he terms the lime factor, and which usually varies, in the raw
material, betw 2.7 and 2.8, and, in the best commercial cems, betw 2.5
and 2.6.

38. Mr. Edwin C. Eckel (Cements, Limes and Plasters, p 170) suggests

Cementation index = 2 ' 8 * + ^__^i

I + 1.4m

where 8, a, i, I and m are the percentages, by wt, of silica, alumina, iron
oxide, lime and magnesia, respectively.

39. The most common adulterants of cem are ground limestone, lime,
shale, slag and ashes; and Portland cem is sometimes adulterated with nat
cem. Most of the adulterants commonly used are merely inert, and there-
fore only weaken the cem; but quick lime may do more serious mischief.

See Cement Mortar, Uf 28, etc - P 947 /.


40. Fineness. Even in cem of standard fineness, the inner portions
of the grains seem to remain inert. The finer the cem, the more sand it
will carry and still produce a mortar of a given strength; but, in each case,
there is a point where the cost of additional fineness offsets the additional
advantage which may be gained.

41. Hence, fineness is less important with natural than with Port-
land cem; for the cheapness of nat cem may render it advisable to use
the cem in larger quantities, rather than pay for finer grinding, in order to
secure the desired strgth.

42. Cements, ground to extreme fineness, in order to secure strgths
beyond those of commercial products, set so quickly that they must be used
immediately after adding water. (Wm. Michaelis, Jr., Western Soc of
Engrs, Aug '07.)

43. The fineness of cement and sand is indicated as fol-
lows, where the large numerals represent the sieve numbers; the small
numeral, to the left of each sieve number, represents the percentage retained
upon that sieve; and the final small numeral, to the right of the last sieve
number, represents the percentage passed by the last sieve. The sum of the
small numerals = 100. Thus, 5 20 ^30 35 40 45 means that 5 % were re-
tained on a No. 20 sieve, 15 % on a No. 30, and 35 % on a No. 40, while the
remaining 45 % passed the No. 40 sieve.


44. Color. The lime silicates and aluminates, which constitute the
cem proper, are colorless when pure. (See White Cement, 1 29.) The
color of cems is therefore due to other matter which is unavoidably present,
notably to the iron oxides, and may be affected by either beneficial, harmful
or neutral ingredients. Hence, color, in itself, is of but little value as a
guide to quality; but variations in shade, in a given kind of cem,
may indicate diffs in the character of the rock or in the degree of burning.
Thus, with nat cems, a light color generally indicates an inferior or under-
burned rock. A coarse-ground cem, light in color and wt, would be viewed
with suspicion.

45. "With Portland cem, gray or greenish-gray is generally considered
best; bluish gray indicates a probable excess of lime, and brown an excess
of clay. Natural cems are usually brown, but vary from very light to very
dark. Slag cem has a mauve tint a delicate lilac." (Prof Ira O. Baker,
"A Treatise on Masonry Construction," p 55.)


46. Specific gravity and weight. See spec grav, pp. 940, 942.
The sp gr of the solid particles of cem is not affected by fineness of grinding,


but is diminished by absorption of water and carbonic acid under exposure,
and is therefore increased by drying. The sp gr of Portland cems may
range from 2.9 to 3.25, ordinarily from 3 to 3.2; nat cems, 2.7 to 3.2; Puz-
zolano cem, from 2.7 to 2.9.

47. The weight, per cu ft, of cem powder, is affected by exposure and
by drying, as explained above, and is increased by compression, as in pack-
ing. It is reduced by fine grinding, the finer particles packing less closely.
Faija found a loss, in wt, of about 6 % in a few days after grinding; 17 %
in 6 mos, and 21 % in a year.

48. In a German Portland cem, Eliot C. Clarke found 90 Ibs per cu ft
when 40 % was retained on No. 120 sieve, and 75 Ibs per cu ft when so finely
ground that all passed the same sieve.

49. As a rude approximation, Portland cem is taken as weighing 100 Ibs,
nat cem 75 Ibs, per cu ft.


50. Owing to variations in the specific gravity of cems, there is corre-
sponding variation in sizes ami weights of packages and their contents.
The trade practice is to sell a bbl of Portland cem as 400 Ibs gross (including
wt of bbl); nat, 300 Ibs gross.

51. A Portland Cement barrel is 2 to 2.2 ft high, betw heads,
1.38 to 1.46 ft av diam. It weighs 21 to 29 Ibs, and is lined with paper for
ordinary transportation. Its capacity is 3.1 to 3.5 cu ft, but the cem, com-
pressed into it, in packing, occupies 3.75 to 4.3 cu ft loose, and weighs 370
to 390 Ibs. The bbl is not returnable.

52. A natural eemeiit barrel weighs about 20 Ibs. In the Wes-
tern states it contains 265 Ibs; in the Eastern states, 300 Ibs, of cem.

53. ** Domestic " barrels are used for shipment to all points in the
U. S., with slight reinforcement for Gulf ports; "standard export"
bbls for Mexico and the West Indies; "special export barrels"
where specially severe treatment is expected.

54. The standard export barrel is of better stock than the
"domestic," and is reinforced with cross pieces in the heads and with two
iron hoops. It costs from 5 to 10 cts more than the "domestic" bbl, vary-
ing with cost of cooperage stock.

55. The special export barrel costs 10 to 15 cts more than the
standard export bbl. It is all-hardwood, heavily hooped and reinforced,
with wood cross-pieces in the heads, iron hoops, and clamps to hold the
heads in place. A heavy waterproof lining is used instead of the heavy
Manila paper used with the standard export bbl.

56. Most cem is now packed in "cloth" or paper bags, except for ship-
ment by sea.

57. Cement bag's are made of cloth (canvas or cotton duck) and of
"rope Manila" paper. When empty, they measure about 17 X 28 ins.
(See Digest of specification of the Am Soc for Testing Materials.) A "cloth"
bag is usually charged to the purchaser at about 10 cts, and credited at
about 7.5 cts when returned. Paper bags are charged at 2.5 cts each
and are not returnable.

58. The use of paper bags obviates loss of time in emptying and re-
turning bags, shortage on lost or damaged bags, and loss of cem in transit
or by failure to empty bags completely; but paper bags are more likely to
lose their entire contents by breakage, and pieces of broken bags may get
into the work and weaken it.

59. For large work, cem has frequently been shipped in cars in
bulk, with little loss or damage, provided the cars are carefully selected.
This method is especially advantageous where the cem is tested at the mill,
stored in "accepted bins," and shipped direct to the work, in sealed cars.
The cars may be unloaded by automatic conveyors. Bags and bbls are
often preferred as furnishing a convenient means for keeping account of the
quantities of cem entering the work; but, in large operations, there should
be no difficulty in arranging to keep such accounts with bulk shipments.


60. " Aging " consists in the slaking of the free lime remaining in the
cem after burning. Good Portland cem is improved by a few weeks of


aging in dry air; and, if kept dry, it deteriorates but slowly under even
long storage; but nat cems usually suffer by aeration; and cems in general,
being composed of compounds with a strong affinity for water, deteriorate
if exposed to dampness. Hence, protection from moisture, even that of
the air, is very essential for the preservation of cems, as well as of quick-

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