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Beams, continuous over the supports, may have a like value used in design,
if the beams are amply reinfd at top and over the supports.

62. On the score of safety, it is frequently specified that beams,
slabs, etc, shall be regarded as non-continuous over supports, this practice
requiring us to provide, at cen of span, against greater (positive) bendg
moms than if the beam were continuous over supports; but, on the other
hand, few if any beams are wholly non-continuous; i e, even where the
beam is supposed to be non-continuous, there are negative bendg moms
over the supports, due to the width of the support and to the presence of
loading upon the beam over the support. Such moms require reinfmt at
top, over and near supports.

63. Hence, while it is advisable, in the case of non-continuous beams, to
calculate the positive center bendg mom upon the assumption of absolute
non-continuity, the condition of even non-continuous beams, over their
supports, should be carefully investigated, and provision made for any
negative moms there found,



REINFORCED BEAMS.



1127



64. Double Reinforcement. The necessity, under certain condi-
tions, of reinfg against negative, as well as against positive moments (If 62)
gives rise to cases (Fig 6) where reinfmt appears near both top and bottom
of the section. For brevity, that on the side which, under positive mom,
is under compression, will be called "compression reinft."




fs/n
Fig 6. Double Reinforcement.

65. In addition to the symbols of ^ 5, p 1115, let
a g f = cross section area of comp reinft;

p' = a s f fa c = a g ' /b'd = steel ratio for comp reinft;
f s f = unit stress in comp reinft;
C" = total stress " " " ;

d" dist from ' to nearest face of beam;

z = ' " comp resultant, C + C', to nearest face of beam.

66. Then, (neglecting the slight diminution of a c by the presence of a ')



for position of neutral axis :

k = y 2 n (p + p' d"ld~)
for position of compression resultant:

Wd/3 + 2p'n d" (k d"/d) .

k 2 + 2 p' n (k d"/d)
for arm of resisting couple:

jd = d z;

for fiber stresses:

6 M k/b d*



(24)



(25)



.(26)



f s



9k*k* + Qp'n(k d"/d) (1 d"/d)""
= M/pjbd 2 = nf c (l k~)/k

METHODS OF REINFORCEMENT.

1. The commonly accepted theory of reinfd cone



(27)



(28)
(29)



beams re-

quires longitudinal tension reinfmt near the bottom* of the beam, and diag
tension reinfmt at 45, not only betw the hor reinfmt and the neutral axis,
but extending upward into the region of compression, in order to take
advantage of the superior adhesion due to the compression there. It also
requires, usually, tension reinfmt near the top,* at points over or near the
supports.

See ^ 60, etc, p 1126.

*The terms "bottom" and "top" are here used as referring to a beam
supported at the ends, and loaded on top, where the major portion of the
bottom is in tension. In a cantilever, of course, this is reversed.



1128



CONCRETE.



2. Numerous trussed systems (p 1133) have been designed, in order
to meet this requirement, and these are in extensive use where the depths
of the beams are sufficient to admit them and where the loading is such as
to require them.

3. Frequently, vertical stirrups are substituted for the diag members,
or used in conjunction with them; or the trussing is effected by simply
bending some or all of the hor bottom* bars upward, usually at 45 or there-
abouts.

4. Under light loading-, the truss feature is often omitted, and the
reinfmt consists simply of longitudinal bars near the bottom* of the beam.

5. Where the beam is both shallow and broad, as in floor slabs, the
few longitudinal bars, used in the beam, are replaced (1) by numerous and
comparatively slender rods, supplemented by similar or lighter rods, cross-
ing them at right angles and welded or wired to them at their intersections;
or (2) by webbing, such as wire cloth or "expanded metal."

See HU 34, etc.

Bar Reinforcement.

6. For a given wt of metal, small bars give a greater adhesion area,
and therefore a greater total adhesion, than larger bars (f 59, p 1126);
and the stresses are distributed over a larger area of cone. Besides, with
small bars, a larger proportion of the metal can be brought down to the min
allowable dist from the bottom* of the beam. Within certain limits, small
bars are more conveniently handled than larger bars. The bars used are
seldom < M inch or > 2 ins diam, and they usually range betw % and 1 Yi
inch. In deep girders, two or more rows of small bars are usually prefer-
able to one row of larger bars.

7. In vert reinfmt, before completion, the free ends of the rods
project from the already imbedded mass of the work, and accidental blows,
upon these exposed ends of the rods, may be transmitted to the portions
already imbedded in cone, affecting the adhesion there. In this respect
also, light rods are preferable, since they are less capable of transmitting the
effects of such blows.

8. High-carbon steel rods, with their high elastic limits, permit
the use of smaller sections for a given number of rods and given total stress;
but they are more brittle (when of inferior quality) than .softer rods, arid
are not readily bent cold, to desired shapes. The smallness of the sections
commonly used, and the protection afforded by the cone, render brittleness
less objectionable in reinfd cone work than in most other work where steel
is employed.

9. Since the elastic modulus, of rolled steel and iron, is nearly the same
(say 30,000,000 Ibs/sq inch) for all grades, these all stretch about equally,
per unit of length, under equal unit stresses; but steel with high



ou,uuu
70,000
60,000
50,000
40,000
30,000
20,000
10,000




























^~~


1









^






sqtt^SS-


r










^^






4E


<$^''














cAftgjjSi


?












# '*














/
















05


1.S ]


\ z


5 3 3.5



Elongation, inches, In looo.inches.
Fig 1 I. Plain and Twisted Rods.



: See foot-note on previous page.



REINFORCING BARS. 1129

elastic limit, by permitting the use of smaller sections and therefore
higher unit stresses, renders elongation more probable, with the accom-
panying cracking of the cone, and lateral contraction of the steel, which
endangers the adhesion. On this account, it is sometimes specified
that, where the elastic limit exceeds a certain min (say 40,000 Ibs/sq inch)
deformed bars, f 1 15 etc, shall be used. At 30,000 Ibs/sq inch, steel stretches
about 0.10 per cent; at 50,000 Ibs/sq inch, about 0.17 per cent.

Cold working raises the ultimate strength and the elastic limit, but
slightly lowers the elastic modulus; see Fig 1, representing tests at Water-
town Arsenal (Tests of Metals, 1904, p 397) on plain and cold-twisted steel
bars, % inch square. Gaged lengths, 10 inches. The twisted bar had 1
twist in 8 inches. Similar results were shown in tests made at Watertown
Arsenal, July 12, 1902, and published by Ransome Concrete Co, See U 21.

Square bars, of inferior steel, are twisted hot, and are more brittle.

10. Plain round steel bars are very generally used for reinforce-
ment in America, and still more generally in Europe. Square bars also
are used, but are less conveniently handled. Flat bars have been found
deficient in adhesion.

11. In order to increase the resistance of plain bars to
being pulled thru the cone, they are frequently bent up at right angles (or
bent over at 180 so as to form a hook) at their ends.

12. "Anchorage, furnisht by short bends at a right angle, is less effective
than hooks consisting of turns at 180." J. C.

13. For the same purpose, (1 11), the bars may be threaded at their ends,
and provided with steel anchor plates, secured by nuts. Such plates
should be large enough and thick enough to withstand pulls due to the full
tensile strength of the rods. In designing such plates, Prof. L. J. Johnson
assumes a crushing strgth, in the cone, of 900 Ibs/sq inch, and a fiber stress,
in the anchor plate, of 25,000 Ibs/sq inch. Several rods, side by side, pass
thru a common large plate at each end, which serves, also, to hold the rods
in their relative positions while the cone is being placed. Nuts, on the
inside, holding the anchor plate to a firm bearing against the outside nuts,
are an important provision. Room, for such plates, is usually found in a
wall or column, or over a knee-bracket, etc. Otherwise, in order to give
room for the anchor plate, the beam may be deepened locally, or the rods
bent up, near their ends. When bent up, the rod exerts an upwd pres upon
the cone, near the bend. This increases the friction, in the bent portion,
and thus reduces the pull transmitted to the anchor plate.

14. "Adequate bond strgth, thruout the length" of a bar, is preferable to
end anchorage." J. C.

15. Also for the purpose of increasing adhesion (or rather to substitute,
for it, a "mechancial bond") "deformed bars," of various shapes are
used.

16. The principal claim, in favor of deformed bars, is that the
"mechanical bond, which they offer, is the sole reliance of the reinfmt,
after its adhesion proper has been destroyed, as by a stress exceeding the
adhesion, by infiltration of water, by concussion either during or after con-
struction, or by constant and rapid alternations or reversals of loading, in
service. Vert rods especially, during construction, are liable to accidental
blows upon their projecting upper ends; and such blows may affect the ad-
hesion of the portions already imbedded in cone.

17. On the other hand, it is pointed out that innumerable struc-
tures, with plain bars, have satisfactorily withstood, for years, service
involving such vibration; and it is claimed that whatever advantage arises
from deformation is more than offset by the slight increase of cost. Plain
bars are of course free from patent claims, and they are at all times readily
obtainable in the general metal market.

18. The projections, on the surfs of some deformed bars, may injure the
cone covering unless this is of considerable thickness.

19. In studying comparative tests of plain and deformed bars, attention
should be given to the richness of the cone mixture. Unless this is suffi-
ciently rich to insure the complete covering- of each bar with cem
over its entire surf, the adhesion proper will not be fairly developed, and the
pulling test will exhibit chiefly the diff in "mechanical bond," in which, of
course, the deformed bars are superior.



1130



CONCRETE.



20. "Deformed bars offer a suitable means for supplying high bond
resistance." J. C.

The following deformed rods, Figs 2, are in more or less general use:




(6) Cold-
twisted
lug bar



(c) Thacher



Square



rrnTTTrn



Round [ \



Fleet



^




(e) Cup bar



(/) Diamond
(Thacher)



(g}Havemeyer



(h) Priddle







Fig 2. Deformed Rods.



21. Ransome. (a) Square steel rods, twisted cold. Twisted either at
mill, or (conveniently and inexpensively) on the work.



REINFORCING BARS.



1131



22. Cold-twisted lug-bar. (6) Square bar, with angles rounded, to
prevent the starting of cracks in the cone, twisted cold. The lugs are de-
signed to resist any tendency of the bar to untwist under tension. For effect
of cold working, see H 9, p 1129.

23. Thacher. (r) Round rods, deformed by flattening at short intervals.
Cross sec area practically constant. Changes in shape made by means of
gradual curves.

24. Corrugated bars ; (d) ordinarily of steel with yield point 50,000
Ibs/sq inch or over. Square, round and flat.

25. Cup bars, (e).

26. Diamond bar. (/) Rolled round, with two spiral projecting ribs
of equal pitch and in opp directions (dividing the surface into four rows of
diamond -shaped recesses) and two opp longitudinal ribs, at the points
where the upper and lower rolls meet in manufacture. Cross-section area
and weight = those of plain square bars of like denomination. Claims :
uniform cross section area, uniform elongation, uniform distribution of
bond; projecting ribs aid in resisting tension; edges rounded; no tendency
to untwist under tension.

27. Havemeyer bar. (g) Square, with rounded corners and pro-
jections.

28. Priddle Internal-bond Bar. (h) Flat bar, perforated and
twisted,, and the slit flanged, as shown. Small sizes worked cold; larger
sizes, hot, A web may be formed by passing smaller bars, of same or other
pattern, thru the slits.

29. The monolith bar consists of a hor tension member with
separate diag links. In section, the hor member resembles a heavy rail
with two heads instead of head and flange. Each link is a bar of round
steel, bent over at top and thus forming two parallel diag legs, which, at
bottom, are bent hor, and their hor portions, one on each side of the hor
member, are gripped between its heads, which are swedged in, at those
points, for the purpose.

Supports.

SO. It is of course of the first importance that the longitudinal rein-
forcing bars be placed and kept in their proper positions. If,

as finally located, they are too high, their resisting leverage, d' , and the resistg
moment of the beam, are diminished. If they are too low, they have an
insufficient protective depth of cone below them. Various devices are in
use for holding the bars in position.

31. Stirrups, Fig 3, act as hangers for the main rods.



Plan \



FigS.



Fig 4.

Supports for Reinforcing Bars.



Fig 6.



Fig 5.



32. Light rods are sometimes held by wire supports, Fig 4, or by
cone blocks, about 1.2 or 2 ins thick, Fig 5.

33. Heavier rods may be supported by clamps, Fig 6, made of pieces of
r 1" channel iron, held together by round-headed stove bolts, M"

iam, placed in the forms, and 6 or 8 ft apart.

75



1132



CONCRETE.



"Web" Reinforcement.

34. Web reinforcement is used in broad and shallow slabs, in thin walls,
in sewers and conduits, in columns, etc.

35. The simplest form consists of rods, placed at right angles,

and wired or welded together at their intersections. The heavier or main
rods are of course so placed as to take the greater stresses. The transverse
rods hold the main rods in position during construction, and afterward
distribute their tension across the intervening cone. They thus offer a
mechanical bond. The mesh must be large enough to pass the particles of
the agg used in making the cone.

36. Jean Monier, of Paris, used such webbing in the reinforcement of
arches.

37. Expanded metal. Fig 7. Sheet steel, slitted and opened out
into diamond-shaped panels. In sheets, 12 to 72 ins wide, 8 to 12 ft long;
mesh from H" to 6"; metal, Stubs gage, No. 18 to No. 4.




Fig 7. Expanded Metal.

38. When slab reinforcement is furnisht in short sheets, these must
overlap sufficiently to transmit the tension from one sheet to the next.
The lapping uses about 10 % of the area of the metal.

39. Clinton wire lath, in rolls of 100 or 200 ft or more, of drawn
steel wires, crossing at right angles, 23^ inch mesh, electrically welded and
reinfd by longitudinal reinfg warp strands, 6 ins apart, and made up each of
two wires cross-looped and twisted over each crossing strand; and, when
desired, by transverse V-shaped stiffeners of No. 24 gage steel, fastened to
the wires at intervals of about 8 ins. Furnisht plain, japanned or galvd,
in 36 inch width.

40. Clinton welded wire; No 3 to No. 10 drawn steel wire, plain
or galvd; mesh, 3X8, 2 X 12, 3 X 12, 4 X 12 ins.




Fig 8. Rib Metal.

41. Rib metal, Fig 8; expanded from specially rolled steel plates,
ribbed longitudinally. Mesh varying, by single inches, from 2 >o 8 ins.
Sheets up to 16 ft long.



REINFORCING BARS.



1133



42. Rib lath, Fig 9.




Fig 9. Rib-Lath.

Trussed Reinforcement.

43. In general, trussed reinforcement is slightly more expensive than
plain bar reinfmt; and, if shipped in rigid built-up units, it incurs higher
freight charges and is more liable to damage en route; but it has the great
advantage of holding the bars in position while the cone is being placed, and
of obviating the omission or misplacement of stirrups, etc, either by accident
or by design. The trusses may be made up of either plain or deformed bars.
They should be provided with means for connecting them, over the supports.

44. In the liahn trussed bar, Fig 10, the projecting side fins are
slit away, in places, from the central portion, and bent up, as shown. The
same bar, inverted, is used over the supports.





Cross sec at cen. Fig 1O. Kahn Bar.

45. Fig 11 shows the collapsible Economy Unit frame.




Fig 11. "Economy" Collapsible Truss.

Reinforcement with Structural Shapes.

46. The Melan system, invented by Joseph Melan, of Austria-
Hungary, in 1892, and patented in the United States in 1893, comprises a
concrete arch in which iron or steel beams are embedded. For small spans,
the beams are usually rolled I-beams; while, for spans of considerable
length, they usually consist of four angles latticed.

47. Where a structural shape, of considerable size, is imbedded in cone,
to form a beam, so that the steel predominates and furnishes most of
the strgth reqd, the cone acts chiefly as a protecting cover
for the steel; and the case is hardly one of reinfmt properly so called.



1134 CONCRETE.

48. It is difficult to secure perfect filling, with cone, of the
spaces under the flanges of rolled or ouilt-up shapes. In such cases, each
day's work should be stopped either well above or well below the flange.
Otherwise, shrinkage, under the flanges, will aggravate the difficulty.

Column Reinforcement.

49. Columns are reinfd by means of vertical rods, placed near the
circumf and usually wired together at intervals, or by circumferential
(hooped or spiral) wrapping 1 , or both.

See Reinfd cone cols, pp 1112, etc.

50. In tall buildings, the column rods are often faced at the ends
to give good bearing, and connected by loose sleeves, which keep the ends
in proper contact; and an iron or steel plate is placed under the feet of the
rods in the footing, to distribute the load more evenly over the cone of the
foundation.

51. In Mr. C. A. P. Turner's mushroom system of columns and
floors, the cols are splayed, at top, to increase their bearing area, and the



,

and ribs are dispensed with, and the floor is of uniform thickness. See E N,
'09, Feb 18, p 178.



DIRECTORY TO EXPERIMENTS.



1135



EXPERIMENT



PRACTICE.



Directory of Selected Results, pp 114O, etc.

Words in bold-face type, preceding a semicolon, refer to one of two
related matters ; words in plain type, following the semicolon, to the other
one. Numerals and letters refer to the records of experiment, etc.

Example. Under SABJO (below), "Sand. character; density of
mortar, 8c, e, 9d, 86c " refers to Experiments 8c, etc, which give informa-
tion respecting the effect of (1) character of sand upon (2) density of
mortar. Conversely, on p 1136, we find "Mortar, density of ;
character of sand, 8c, e, 9d, 86c."



CEMEXT.



Cement,
character of ;

water reqd, 61 a
Portland V natural ;

water reqd, 4 d

strgth, 14 a, 19 a

abrasion, 4 g

permeability, 65 a

electrolysis, 75 a
silica ; oil, 53 d
typical mix ; 86 /
age of ; soundness, 29 a



Sand,

fineness of ;

density of sand, 2 a, 8 h, 8 /,
8 k

water reqd, 61 a

density of mortar, 8 c, 9 d,
79 e

strgth of mortar, 4 e, 8 a, 52 6,
79 e

permeability of mortar, 8 d, 9 e

lime reqd for waterproofg, 82 b

sea water, 8 g

uniformity coefficient ; 5 a
grading of ;

mortar, 8 e, 86 e
shape of grains;

density of, sand, 8 i, 8 I, 94 a
density of :

fineness, 2 a, 8 j, 8 k

uniformity coeff, 5 a

shape of grains, 8 i, 94 a

compacting, 2 a, 8 h, 8 i, 8 k,
45 a

character, 8 I

mica, 87 a

moisture, 2 a, 8 h, 8 I, 45 a

mortar, 86 c, d
voids ;

spheres of uniform diam, 45 6

ACCIDEJTTAI,

Clay in cement ; 4 a
Clay *V loam ;

strgth of mortar, 4 a, 34 a, 39 g,

50 b, 52 a, 6, 56 a, 80 a
absorption, 56 a
plasticity of paste, 4 a
density of paste, 4 a
permeability, 4 a
mortar for plastering, 4 a
in cone for columns, 92 a



fineness of ;

soundness, 29 b

strgth of mortar, 4 /

water reqd, 4 d

quantity reqd; agg, 79 b, d
quantity used;

strgth of mortar, 8 a

elastic modulus, 70.5
exposure ; 39 a, &
sulfuric acid in ; 49 a
chemical action of ; 26 a,

b, c



compacting :

density of sand, 2 a, 8 h,' 8 i,
8 k, 45 a

fineness of sand, 8 k
moisture in ;

density of sand, 2 a, 8 h, 8 I

water reqd, 61 a
character ;

density of sand, 8 I

density of mortar, 8c,e,9 d, 86 c

strgth, 19c, 39 (j, 50 a, 52 a, 62 a

absorption, 62 a

impurities in ; 19 c, 52 a
clay V loam in ;

strgth, 4 a, 34 a, 39 g, 50 b, 52 a,
6, 56 a, 80 a

permeability, 4 a

absorption, 56 b
mica in : 79 a, 87 a
friction of ; 89 a
percentage of ;

electrolysis, 91 a

abrasion, 4 g
fusing point; 89 b
vs screenings ; 79 a-j

density, 79 c

permeability, 79 h, j

absorption, 55 a
vs crushed limestone ; 50 a

IXGREDIENTS.

Clay V alum ;

permeability, 80 a
Mica ; 79 a, 87 a
Sulfuric acid : 6 a, 49 a
Salt; 4 c, 19 a, 31 a
Gypsum; 51 a
Cwypsum fc lime ; 51 c
Calcium chloride; 51 a, b
Lime ; 80 a, 82 d
Lime fc gypsum ; 51 c



1136



CONCRETE.



Directory to Experiments, pp 1140-1183



MIXING WATER.



Water, mixing ,

salt in; 4 c, 19 a, 31 a
evaporation of ; 9 a
quantity reqd;

nat & Port cem, 4 d



cem, character of , 61 a
size & dry ness of sand grains,

61 a

mica, 87 a
snlfuric acid in ; strgth, 6 a



MORTAR.



Mortar,

neat & sand ; 86 i
consistency of ;

fineness of cem, 4 d

cinder, 83 a

rate of setting, 4 d

volume of cone, 21 a

density, 61 a

strength, 39 e, 61 a, 83 a,

elastic modulus, 61 6, 81 a

permeability, 33 a, 47 c, f, 61 a

laitance, 61 d; fire, 46 e

preferable , 61 e

sea water, 8 g
richness of ;

volume of cone, 21 a

density, 8 c, 9 d

permeability, 8 d, 9 e

sea water, 8 g
density of ;

percentage of voids, t 9 6

character of sand, 8 c, e, 9 d, 86 c

richness, 8 c, 9 d

clay, 4 a

entrained air, evaporation, 9 a
strength of ;

fineness of cem, 4 /

proportion of cem, 8 a

exposure of cem, 39 a, 39 6

character of sand, 4 e, 8 a, 86 d

clay, 4 a, 34 a, 39 g, 50 b, 52 a, 6,
56 a, 80 a

salt, 4 c

sulfuric acid, 6 a

consistency, 39 e

hand and machine mixing, 39 c

treatment of briquet, 39 d
permeability of :

character of sand, 8 d, e,9e

richness, 8 d, 9 e

clay, 4 a

diminution of with time, 8 /



plasticity of ; 4 a
soundness of ;

cement, 29 a, 6
abrasion ; 4 g
expansion of ; 4 h
lime in ; 82 a
sal ammoniac in ; 47 I
briquet, treatment of ;

strength, 39 d
protection of metals by ;

2b
in water ; 46, 8 /

sea , 4 b, 7 a, 8 g
for plastering;

clay in , 4 a
aeration ;

rate of setting, 84 a
proportion of, in cone;

strgth, 79 /

density, 79 / .

permeability, 13 b, 43 a, 79 g

volume of cone, 21 a

PROPORTIONS.

Proportions ;

density of concrete, 9 c

elastic modulus, 81 a

strength, 14 a, 15 a, 18 a, 19 6

shear, 81 b

adhesion, 64 b

strgth of columns, 35 a

permeability, 9 /, g, 13 a, b,

25 a, 43 a, 65 a
thermal conductivity, 46 6
electrolysis, 91 a
Grading :

distribution, 47 d
cement reqd, 79 d
density 79 d
permeability, 93 a
transverse strength, 72 a



AGGREGATE.



Aggregate;

fire, 41 d
proportion to mortar;

volume of cone, 21 a
addition of;

retardation of setting, 84 a
dirt in ;

strgth, 19 c
weight of ; 3 a
density of ; 3 a

gravel <fc broken stone, 8 I, 14 a

compacting, 21 c
voids in ;

spheres of uniform diam 45 b



size of ;

cem reqd, 79 6

permeability, 79 i

density, 81, 79 6; strgth, 79 b

elastic modulus, 70.5
kind of;

density, 8 I

proportions, 17 a

permeability, 79 g, 79 /

strgth, 19 b, 35 a, 83 a
gravel ; 8 I, 79 a

strgth, 39 /, 83 a

fire, 41 c, 70 /

permeability, 9 g



DIRECTORY TO EXPERIMENTS.



1137



Directory to Experiments, pp 1140-1183.



Screening's, atone
grading; 86 b



AGGREGATE. Continued.
stone vs gravel;

permeability, 79 j

density, 79 c

strgth, 14 a, 79 c

fire, 41 c
granite : 83 a
limestone;

water, 69 a

strgth, 83 a

sandstone vs shale; 11 a
quartz; expansion, 70 /



Cinder cone;

strgth, 15 a, 23 a, 83 a
fire, 41 e

thermal conductivity, 46 6
consistency, 23 a, 83 a
proportions ; strength, 15 a



CONCRETE.



MIXING.



Mixing ;

distribution of sizes, 47 d
freezing weather, 44 a
shrinkage, 21 a; fire, 46 e
rate of - , 39 c

hand & machine ; 22 a,
39 c

continuous; 27 a

thoro; strength, 12 a
Re*tempering ; 28 a

FORMS, PLACING,
COMPACTING.

Forms ;

coated with soft soap, 32 a


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