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51. Housing and heating the finished work. Tents or screens
may be used; but wooden sheds are more effective.

52. Covering the cone, as soon as placed, with canvas, cem bags or tar
paper, or with a thick layer of sand, straw, manure, sawdust or other poor
heat-conductors. Straw should be < 1 foot deep. Manure is the best, but
it discolors the work. Canvas etc should be kept an inch or two away from
the cone, leaving an air space. Otherwise use two layers.

53. Heating the materials. Stone is frequently heated by piling it
over a pipe or improvised oven, and building a fire inside; or over a coil of
pipe containing numerous small holes, and then forcing steam thru the pipe.
The cone must be used before the steam is condensed and frozen. Sana is
heated over a long sheet iron stove.

54. Lowering the freezing point of the mixing water,
by the addition of chemicals.

55. Sail is the cheapest and most commonly used material. It lowers
the freezing point about 1.5 F for each 1 % salt added to the water. A
10 % solution (12 Ibs salt per bbl of cem) reduces the freezing point to 17 F
and does not injure the strgth of the cone. For 32 F, dissolve 1 Ib salt in
18 gals water; add 3 oz-salt for each 3 below 32 F. (Ch of Engrs, U. S. A.
Report, 1895.) Larger percentages of salt appear to weaken the cone.

56. Calcium chloride, 15% solution, or 1.25 Ibs per gal of water,
lowers the freezing point to about 20 F, and does not weaken the mortar.
It rapidly absorbs moisture, and it is possible that, if ground dry with the
Portland cem clinker, even to the amount of 0.5 %, it would cause the ma-
terial to gather dampness. The chloride dissolves with extreme rapidity,
and may be added to the mixing water. (Prof. R. C. Carpenter, Cornell
Umv, Sibley Jour of ^ng, Jan 1905.)

57. The major portion of a pile of sand or stone may be in condition for
use altho the surface is frozen.

58. In winter, we may reduce the areas of the exposed layers of
the work, by placing the bulkheads closer together. A day's work will then
run to a greater elevation, and will necessitate the use of stronger forms.


59. Mortars, placed in open air, are more or less injured, by
d ry i fig instead of setting, when the temperature exceeds about 65 to 70 ,
but if mixed only in small quantities at a time, and quickly laid in masonry
of dampened stone, so as to be sheltered from the air, the injury is much
reduced. The sand and stone should both be damp, not wet, in hot weather,
and a little more water may be used in the cem paste; also, if possible, not
only the mortar, while being mixed, but the masonry also, should then be


60. In variable climates, cast iron cylinders, filled with

concrete, are frequently split horizontally by unequal expansion and
contraction. In such structures it is safest to consider the cylinders as mere
molds for the cone; and to depend only upon the cone for sustaining the

For expansion coeffs, see Reinforced Cone, t 9, p 1110.

61. Cracks and joints. In abutments or culverts over 60 ft long,
divide the wall into sections of about 40 ft, and finish one section before be-
ginning the other. Contraction will cause the joint to open, and irregular
cracks thru the body of the wall will thus be avoided. Short sections may
be completed without stopping, and horizontal joints thus avoided. "Very
small cracks, which, in stone masonry, would be difficult to find, show up
very plainly in cone." (W. A. Rogers, R R Gaz, '00 /July 6, p 461.)

62. Effect of high temperatures. During calcination of the ma-
terials for Portland cem, the chemically combined water is driven off. When,
in mixing, this water is returned to the material, hardening takes place; but
the re-application of temperatures, sufficiently high to drive off the water
again, reverses the hardening process and disintegrates the material.

Chemical Effects.

63. " Dehydration of the water of crystallization of cone probably
begins at about 500 F and is completed at about 900 F"; but this cools
surrounding masses, and thus increases the heat resistance of the cone. J. C.*

64. Rehydration. Briquets, kept, for 6 to 8 hours, at 1000 to 1200
F (not in contact with flame) and allowed to cool, showed practically no
strgth; but 28 days immersion in water restored their strgth to that of
unheated briquets.

65. Fire resistance. In quartz sand the expansion coeff is twice that
of feldspar; and the expansion, in one direction, is twice that in the direction
perp to it.

66. At the Baltimore fire the cone, exposed to flames, was seldom dam-
aged to a greater depth than % inch, altho projecting corners were at some
places rounded off by flames to a radius of about 2 inches.

67. Sea water has apparently but little effect uponconcso proportioned
as to secure maximum density, and thoroly mixt. Damage by sea water,
reported as taking place at the water line, has probably been due, in part, to
freezing. J. C.*

68. Destructiy action upon cone by electrolysis appears to be due to
abnormal conditions seldom occurring in practice. J. C.

69. Green cone is injured by acids ; but first class cone, thoroly harden-
ed, is appreciably affected only by strong acids which seriously injure other
materials. J. C.

70. In the reclamation of arid land, where the soil is heavily charged with
alkaline salts, cone, stone, brick, iron and other materials are injured
under certain conditions, at ground water level. Such action can be pre-
vented by the use of an insulating coating. J. C.

71. Cone properly made, and having its surface carefully finished and
hardened, resists the action of petroleum and ordinary engine oils. Oils
containing fat acids appear to injure cone. J. C. a

72. Sulphurous and sulphuric acid gases, combined with moisture, cor-
rode cone, especially if heated

* J. C. Report of Joint Comm, A S C E, A S T M, Am Ry Eng & M W
Assn, and Assn of Am Port Cem Mfrs, '09, Jan.

TESTS. 1109

Tests of Concrete in place.

73. Tests of concrete in place may be made by analysis of a core
of cone, obtained with a core drill,* using chilled steel shot for cutting.
The bore holes are afterward grouted.f

74. The ratio of cement to sand, in the mortar, is found by
means of the amounts remaining undissolved in hydrochloric acid; sand
and cem, of the kinds used, and mortar, taken from the core, being tested
separately in this way. (Prof. R. L. Wales, in E N, '08/Jan 9, p 46.)

75. The ratio of mortar to stone, in the cone, is found (1) by
actual separation and by weighing the stone and the mortar separately, or
(2) by ascertaining separately, and comparing, the specific gravities of the
stone, the mortar, and the cone.

* Made by Cyclone Drill Co., Orrville, O., including small drills, worked
by hand.

t B. G. Cope, in E N, '08/Jan/9, p 41.



1. The tensile and shearing strengths of cone are low as compared with
its comp strgth. Hence metal rods or shapes are embedded in cone struc-
tures in those portions subject to tensile and shearing stresses, and in such
positions as to take those stresses.

2. Uses. Reinfmt is used chiefly in the tension-sustaining portions of
beams and girders, (including floor-slabs), cols, walls, retaining walls, dams,
etc; but it is useful also in many other cases; as for preventing hair cracks
in surfaces, for which purpose a light web of metal (wire mesh, expanded
metal, etc) is placed a few inches back from the face; for preventing fracture
due to unavoidable sudden changes in cross-section; for joining walls meet-
ing at an angle and liable to settle away from each other; and in culverts,
enabling them to withstand hor tension due to the outward pressure of the
embankment. For this purpose old chains may be used, or light rails, with
bolts driven thru the bolt-holes, to increase adhesion.

3. Safety. Modern reinfd cone buildings are practically monolithic, and
therefore more rigid than skeleton steel construction.

4. On the other hand, in the steel building, the details are more accurately
worked out, and the work is usually erected by skilled men, often employed
by the steel mfrs; so that there is but little chance of damage to the material
in erection; whereas, in reinfd cone work, the best material may be injured
in the using, and the work thus rendered unsafe.

5. Good coric protects imbedded steel from corrosion, both above and
below fresh or sea water level; but water may penetrate porous cone and
corrode the metal. Cone laid very dry is apt to be porous.

6. The steel, used in reinfg cone, has its ult strgth usually betw 50,000
and 70,000 Ibs per sq inch, and its elastic limit between 25,000 and 35,000
Ibs per sq inch, but cold working may raise the elastic limit to 40,000 or
50,000 Ibs per sq inch. ' ' Deformed " bars are often rolled of steel with much
higher elastic limit (50,000 to 65,000 Ibs per sq in claimed) for the sake of
economy of steel; but see Bar Reinforcement, pp 1128, etc. As in rolled
iron and steel in general, the elastic modulus may be taken as averaging
approximately 30,000,000 Ibs per sq inch. See H 11.

7. Concrete. In general the necessity of working the cone around the
reinfg bars requires that the agg for the cone in reinfd work shall be smaller
than would be permissible in unreinfd mass work; and the vital importance
of adhesion requires that all the materials for the cone shall be of the best,
and the mortar not too lean or too dry.

Expansion, Contraction, Etc.

8. The shrinkage of cone, while setting in air, produces comp stress
in the reinfmt and tensile stress in the cone itself. Setting under water, the
expansion of the cone produces the opposite effects.

9. The linear expansion coefficient, a, of a material, is that fraction
of its original length which a bar of it gains or loses for each degree of change
in its temp. Approximately: Per degree,

Centigrade Fahrenheit

In steel 10,000 a = 0.117 0.065

In concrete 10,000 a = 0.108 0.060*

10. The large number of reinfd cone structures which have been exposed,
for years, to wide extremes of temp, without injury thru difference in ex-
pansion, confirms the results of experiments, quoted above, as indicating
that the diff, betw the expansion coefficients of the two materials, is negli-

Elastic Modulus.

11. The elastic modulus, E B , of rolled iron and steel, of all

kinds (p 460,) is remarkably uniform and constant, ranging ordinarily betw
27 and 31 (av, say 30) millions of Ibs per sq inch = approx 1.9 to 2.2 (av,
say 2.1 ) millions of kgs per sq cm.

*W D. Pence, 1:2:4 cone, Jour Westn Soc of Engrs, 1901, Vol. 6,

?. 549, 10,000 a = 0.055 Fahr, results nearly uniform. Columbia Univ,
: 3 : 6 cone, 10,000 a = about 0.065 Fahr.


12. On the contrary, the elastic modulus, E^,, of concrete varies
widely, not only as betw diff mixtures differently manipulated, and betw diff
specimens made under like conditions from like materials, but in one and
the same specimen under diff intensities of loading; so that, in stating the
results of expts, it is usual to specify the range of unit stress within which the
observations were made.

13. In stone concrete, E C ranges from 1.5 to 4 (av, say 3) million
Ibs per sq inch, = 0.1 to 0.28 (av, say 0.21) million kgs per sq cm. See
Expt 81 a, p 1172. In cinder cone, E C is ordinarily from 20 to 50 %
less than in stone cone. See f 30, p 1106.

14. The ratio, 11 (sometimes called r and R}, = E a /E c , betw the elas-
tic moduli of steel and of cone respectively, is usually taken betw 10 and
15 for stone cone, with higher values for cinder cone. See Specifications,
If 107, p 1195. Owing to the variability of E C (see H 12), it cannot be a
constant quantity, even during the range of a single experiment carried
from zero load to rupture.

15. The ratio, n, is, however, of constant and important use in all cal-
culations respecting the mutual behavior of cone and steel.

16. Considered experiments (Expt 16 a, p 1146) seemed to show that
cone, when reinfd (being constrained, by its adhesion to the steel, to share in
its movemts), actually underwent, without fracture, far greater elonga-
tions than were possible in unreinfd cone; but later expts (36, 38, 81 e, 81 /),
in which the cone surface was more closely observed, have indicated that
the supposed elongation of the cone was in fact due to the formation of
cracks which had before escaped observation. If the adhesion, betw the
cone and the steel, is uniform, the cracking must be evenly distributed over
the area of contact, and the cracks must therefore be very numerous and very
fine, probably so fine as not to endanger the materials thru the percolation
of water.

Adhesion. See H 58, p 1126.

17. With rich and wet mixtures, such as are used in reinfd con-
struction, the cem adheres very closely to the steel.

18. After the adhesion proper has been overcome, the removal of the
steel from the cone is still opposed by friction betw the two.

19. Upon the ability of this adhesion and friction to resist the forces tend-
ing to overcome them, depends of course the safety of the structure.

20. Both adhesion and friction, and particularly the friction, are greatly
affected by the character of the cone and by its behavior under stress and
under temp changes, by the method of testing, etc.

21. In direct tests for adhesion, whether the steel is pulled or
pushed, the cone is always under comp, which causes some lateral expan-
sion of the cone, and therefore increased pressure upon the reimfmt. Hence,
the adhesion may be found higher than (other things equal) in beams, where
this condition does not obtain.

22. On the other hand, where the hor reinfg bars, in a beam, are bent
upward, near the ends, and pass up into the region of compression and (as is
often the case) to a point over the support, the high pressures upon the bar,
in those portions, may give it greater adhesion, as a whole, than could be the
case with a straight bar under direct test.

23. With great lengths of imbedment, the stretch, in the steel,
under high tensile stresses, may be such as to contract the steel laterally,
sufficiently to reduce adhesion. Hence, tests where the steel is pushed into
the cone, show higher adhesions.

24. IJltimate adhesion. In general, expts (see Expts 64 a, 6)
give, as the ultimate adhesion of good cone to plain round rods, from 200
to 300 Ibs per sq inch of contact surface. With* smooth round rods, in a
beam, Kleinlogel (Beton und Eisen, 1904, pp 227 et seq) obtained 560 Ibs
per sq inch. The conditions of practice generally differ greatly from those
obtaining in the laboratory.

25. Working bond stress. In beams subject to shock, about 50 Ibs
per sq inch; for quiet loading, about double this is sometimes allowed. See
Specifications, tl 113-115.



1. A concrete column usually has longitudinal steel rods embedded,
near the circumference, thruout its length. If there is no deflection, and no
slip between the concrete and the steel, the two materials must shorten
equally under load. Hence (p. 457, Eq (3) ) if L = original length, Z =
change of length, a g and a c cross section areas; s g ands c = unit stresses,
E S and E C elastic moduli, of steel and of cone, respectively; we have

s s = E s l/L; s c = E c l/L; (1)

and, since l/L is necessarily the same for both materials,

s s /s c = E,/E C = n; s s = s c n; (2)


total stress in steel = a g s g = a g s c n (3)

" " " cone = a c s c (4)

" column = P a g s s + a c s c = 8 C (a c + a g n) ...(5)

a c = P/s c a s n (6)

s c = P/(a c + a s n) (7)

2. Example. A square cone col 16 ins X 16 ins, 12 ft long has, em-
bedded in each corner, a round steel rod 1 inch diam; cross section area of
each rod = 0.785 sq inch. Permissible unit comp stress, s c , on concrete,
500 Ibs per sq inch. Required the load which may be carried by the col. Here

Area, a g , of steel = 4 X 0.785 = 3.14 sq ins;
Area, a c , of cone = 16 X 16 3.14 = 253 sq ins;
E s = 30,000,000 Ibs per sq inch;

E c = 2,500,000 Ibs ' ;

n = E t /E c = 12;

Total stress taken by cone = a c s c = 253 X 500 = 126,500 Ibs

" " steel = a c s c n = 3.14 X 500 X 12 = 18,840 Ibs

" column 145,340 Iba

3. Here the steel takes 100 X 18,840 -^- 145,340 = about 13 % of the
entire load, a safe proportion. This proportion should not exceed 20 %, or,
at most 30 %.

4. A convenient rule is to count each sq inch of steel, in cols, as
worth n sq ins of concrete.

5. Conservative designers load cone cols approximately as follows:


Length_ 1:1.5:3 1:2:4 1:2.5:5 1:3:6

"diam p = P/a = Load, in Ibs per sq inch.

< 12 600 500 350 350

12 to 18 550 450 300 300

6. Longitudinal reinfg rods or bars are usually placed symmet-
rically near the outside of the cone, and are covered by from 1% to 2 inches of
cone. The rods should be tied together, by smaller rods or by wires, at in-
tervals not exceeding the diam of the col.

7. Specifications usually require that the aggregrate cross-section area
of compression rods shall not exceed from 2 to 3 % of the cross-
section area of the col.

8. In buildings of say three or four stories, the rods of each sec-
tion are bent in, near their tops, to form a cylinder, 18 or 20 ins
high, of smaller diam than the main cyl below; and the section next above
fits down over this portion, so that the two sections overlap the length of
the reduced portion.

9. Owing to their much greater cross-section areas, and to the lower unit
stresses in their materials, reinfd cone cols are much less liable to failure by
deflection than are steel cols.


10. For ultimate loads on longitudinally reinforced con-
crete columns liable to deflection, we have the Rankine formula:


P = ult total load on col;

a = cross section area of col;

p = P/a = ult unit load on col;

= ult comp unit strgth of cone cubes;

K = L/r = length /least radius of gyration;

Prof. Morsch gives m = 0.0001. Eisenbetonbau, '08, p 73.

Hooped Columns.

11. Columns reinforced with hoops (or spirals) of steel, or with
web reinforcement bent into cylindrical form, show high ult strgths and are
largely used; but they undergo considerable deformation before the strgth
of the hoops is developed; the hoops acting much like a steel cylinder,
filled with sand, such cylinders being unable to act until the sand is com-

12. Expts at Watertown (Tests of Metals, 1905) show that, when the col
is subjected to loads of from 100 to 1000 Ibs per so. inch, the unit lateral de-
formation is less than one-fourth the unit longitudinal deformation. Thus,
if the col shortened 0.0004 of its length, its diam increased less than 0.0001 of
its original dimension.

13. From tests at the Univ of Illinois (Am Soc Testg Matls, Procs, 1907,
p 382) Prof. A. N. Talbot derives the following formulas for the ult strgths of
hooped cylindrical cone cols, 1:2:4, wet mixture, av age, 60 days; cols
12 ins diam, 10 ft long. Covering, over the hoops, generally < % inch.
Hoops, 1 inch wide, gage Nos 8, 12, 16, electrically welded, spaced generally
2 ins c. to c. Let

p = ult strgth of col, Ibs per sq inch;
c = ratio of hooping to cone core;
1600 = comp strgth of cone, Ibs per sq inch.

For mild steel, p = 1600 + 65,000 c ; ................................... (9)

" higher " p = 1600 + 100,000 c .................................. (10)

14. Assuming that the ult unit stress, in longitudinal col reinfmt, is 25
times that in the cone, the hooping gave additional ult strgth from 2 to 4
times that given by longitudinal reinfmt.

15. M. Considered expts (Genie Civil, Nov 1902), with spirally reinforced
cone cols, indicate that the bars, forming the hoops, should have a diam of ap-
proximately 1/40 of the diam of the col; that the pitch of the spirals (dis-
tance between hoops) should be from K to % the diam of the col; and
that the steel, in the hoops or spirals, adds, to the ult resistance of the col,
2.4 times as much as the same weight of metal used as longitudinal reinfg.
He gives the formula

Ultimate total load on col = 1.5 a c c + s e (a + 2.4^4) ............... (11)


a c = cross section area of col inside of spiral;

c = ult comp unit strgth of plain cone in short blocks;

s e = elastic limit of steel;

a = cross section area of existing longitudinal reinfmt;

A = " " " " longitudinal reinfmt of equal wt with the

1.5 a c is taken as representing the area of the entire cone cross sec.



Column Footings.

16. In a column footing, the stresses are analogous to those in a
floor slab resting upon a col; but, owing to the relatively limited spread of
the footing, the moments and shears are heavy, requiring considerable
depth. The heaviest stresses are under the edges of the col. Hor rods, in
the footing, are analogous to rods near the top of a beam, over the support;
i. e., they take negative moms, and some of them should be bent upward,
or provided with stirrups, just beyond the edges of the col.

17. Figs 1 and 2 (T & M, pp 261, 262). Fig 1: Two series of main
reinfg rods, a a', 6 6', crossing at right angles under the col, with diag rods,

Fig 1. Column Footing.

Fig 2. Column Footing.

d d', d d f . Fig 2: Combined beam and slab. Side wings of slab tend to
bend upward, breaking away from the beam at C and C.




1. Cone is ordinarily from eight to ten times as strong in comp as in ten-
sion. Hence, in an unreinforced cone beam of rectangular section, under
bending stresses, failure occurs on the tension side.

2. The ease with which steel can be embedded in cone, the practical
equality of the expansion coeffs of the two substances, the strong adhesion
between cone and steel and the practicability of supplementing this adhesion
by lugs or other lateral projections from the surface of the steel, facilitate
combinations in which the principal service of the cone is to resist comp,
while that of the steel is to resist tension.

3. The method of manufacture of cone is such that its behavior, in a given
case, is less certain than that of steel.

Owing to this and to uncertainty, as to the degree of adhesion betw cone
and steel, on which their united action depends, the theory of such beams
is at once more complicated and less exact than that^of steel beams of eco-
nomical sections. In the design of reinfd cone beams, proper allowance must
be made for this fact, and extreme refinement is out of place.

General Theory.

4. Simple reinfd cone beam, of rectangular section, Fig. 1.



Neutral Axis




* *




4*= Steel Area ->i c a k- j< -f~( >

Fig 1. Reinforced Concrete Beam.' Theory.
Fundamental assumptions.

1. Cross sections, plane before flexure, remain plane under flexure.

2. Initial stresses (from shrinkage, etc) are neglected.

3. No slipping occurs between cone and steel. Hence they deform equally.

4. The tensile resistance of the cone is neglected.

5. The elastic moduli, E S and E , of steel and of cone respectively, and
hence their ratio, n = E 8 /E C , remain constant.

5. Notation. Referring to Fig 1, let:

6 = breadth of cross section of beam, perp to the paper;
d = dist from comp side of beam to cen of grav of steel;
led = " " " " ' ' neutral axis;

z = " " " " " " " resultant of comp forces;
(1-fc) d = " " cen of steel to neutral axis;
d' = jd = " " " " " " resultant of comp forces
= leverage of resisting couple;
= d'/d\


E S elastic modulus of steel;
e s = unit elongation of steel;
fg = unit tensile stress in steel t;

E c = elastic modulus of concrete;
e c = unit shortening of concrete;*
/ = unit comp stress in concrete;*!

* In the outermost fibers on the compression side of the beam,
t/, and f c are the actual unit stresses. See U 13, p 1118.



a g = cross-section area of steel; a c = bd = cross-section area of cone

above cen of steel;

T sum of tensile stresses in steel ; C = sum of comp stresses in concrete;
n = E S /E C = ratio of elastic moduli of steel and cone;
p = o, s /a c = ratio of steel area to that portion of cone area which is

above cen of steel;*
M g = resisting moment, based upon the max allowable value** of f s ;

M actual resisting moment.
Then a s = p a c = p b d.

Stresses, Moments, Design.

6. Figs 1 and 2g and HH 7 to 20 illustrate the relations existing
between the important factors, k, j, f s , f c , p, M s , M c and M; when

1 2 3 4 5 6 7 8 10 12 13 14 15 16 17 18 19 20 21 22 23

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