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Transactions of the American Society of Civil Engineers (Volume 81) online

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becomes



1 / 2 \



where M^ is the numerical sum of the positive moment and the nega-
tive moment for the sections parallel to the dimension, l^, and My
is the numerical sum of the positive moment and the negative moment
for the sections parallel to the dimension, l^.

What proportion of the total resistance exists as positive moment
and what as negative moment is not readily determined. The amount
of the positive moment and that of the negative moment may be
expected to vary somewhat with the design of the slab. It seems
proper, however, to make the division of total resisting moment in
the ratio of three-eighths for the positive moment to five-eighths for
the negative moment.

With reference to variations in stress along the sections, it is evi-
dent from conditions of flexure that the resisting moment is not dis-
tributed uniformly along either the section of positive moment or
that of negative moment. As the law of the distribution is not known
definitely, it will be necessary to make an empirical apportionment
along the sections; and it will be considered sufficiently accurate
generally to divide the sections into two parts and to use an average
value over each part of the panel section.

The relatively large breadth of structure in a flat slab makes the
effect of local variations in the concrete less than would be the case for
narrow members like beams. The tensile resistance of the concrete
is less affected by cracks. Measurements of deformations in buildings
under heavy load indicate the presence of considerable tensile resistance
in the concrete, and the presence of this tensile resistance acts to decrease
the intensity of the compressive stresses. It is believed that the use
of moment coefficients somewhat less than those given in a preceding



CONCEETE AND REINFORCED CONCRETE 1139

paragraph as derived by analysis is warranted, the calculations of
resisting moment and stresses in concrete and reinforcement being
made according to the assumptions specified in this report and no
change being made in the values of the working stresses ordinarily
used. Accordingly, the values of the moments which are recommended
for use are somewhat less than those derived by analysis. The values
given may be used when the column capitals are round, oval, square,
or oblong.

(e) Names for Moment Sections. — For convenience, that portion
of the section across a panel along a line midway between coliimns
which lies within the middle two quarters of the width of the panel
(HI, Fig. 2) will be called the inner section, and that portion in the
two outer quarters of the width of the panel (GH and IJ, Fig. 2) will
be called the outer sections. Of the section which follows a panel
edge from column capital to column capital and which includes the
quarter peripheries of the edges of two column capitals, that portion
within the middle two quarters of the panel width {CD, Fig. 2) will
be called the mid-section, and the two remaining portions (ABC and
DEF, Fig. 2), each having a projected width equal to one-fourth of
the panel width, will be called the coliman-head sections. '

(/) Positive Moment. — For a square interior panel, it is recom-
mended that the 'positive moment for a section in the middle of a

1 / 2 \ 2

panel extendiiiir across its width be taken as — wl \ I c) .

25 \ 3 /

Of this moment, at least 25% should be provided for in the inner sec-
tion; in the two outer sections of the panel at least 55% of the specified
moment should be iirovided for in slabs not having dropped panels,
and at least 60% in slabs having dropped panels, except that in cal-
culations to determine necessary thickness of slab away from the
dropped panel at least 70% of the positive moment should be considered
as acting in the two outer sections.

ig) Negative Moment. — For a square interior panel, it is recom-
mended that the negative moment for a section which follows a panel
edge from column capital to column capital and which includes the
quarter peripheries of the edges of the two column capitals (the sec-
tion altogether forming the projected width of the panel) be taken as

1 / 2 \ ^

— wl (l — — c ) . Of this negative moment, at least 20% should be
lo V 8 /

provided for in the mid-section and at least 65% in the two column-
head sections of the panel, except that in slabs having dropped panels at
least 80% of the specified negative moment should be provided for in
the two column-head sections of the panel.

(//) Moments for Ohlong PaneZs.— When the length of a panel does
not exceed the breadth by more than 5%, computation may be made



1140 CONCRETE AND REINFORCED CONCRETE

on the basis of a square panel with sides equal to the mean of the
length and the breadth.

When the long side of an interior oblong panel exceeds the short
side by more than one-twentieth and by not more than one-third of
the short side, it is recommended that the positive moment be taken as

1 / 2 \ '^

— wl.-^ ( Zj • — 77



Online LibraryAmerican Society of Civil EngineersTransactions of the American Society of Civil Engineers (Volume 81) → online text (page 96 of 167)