Some Mooted Questions in Reinforced Concrete Design | Page 8

used, there is the assumption of an initial
unstressed condition of the materials. This is not true of a beam and is
still further from the truth in the case of an arch. Besides shrinkage of
the concrete, which always produces unknown initial stresses, there is a
still more potent cause of initial stress, namely, the settlement of the
arch when the forms are removed. If the initial stresses are unknown,
ideal determinations of stresses can have little meaning.
The elastic theory stands or falls according as one is able or unable to
calculate accurately the deflection of a reinforced concrete beam; and it
is an impossibility to calculate this deflection even approximately. The
tests cited by Professor Lanza show the utter disagreement in the matter
of deflections. Of those tested, two beams which were identical,
showed results almost 100% apart. A theory grounded on such a
shifting foundation does not deserve serious consideration. Professor
Lanza's conclusions, quoted under the twelfth point, have special
meaning and force when applied to a reinforced concrete arch; the
actual distribution of the stresses cannot possibly be determined, and
complex cloaks of arithmetic cannot cover this fact. The elastic theory,
far from being a reliable formula, is false and misleading in the
extreme.
The fourteenth point refers to temperature calculations in a reinforced
concrete arch. These calculations have no meaning whatever. To give
the grounds for this assertion would be to reiterate much of what has
been said under the subject of the elastic arch. If the unstressed shape
of an arch cannot be determined because of the unknown effect of
shrinkage and settlement, it is a waste of time to work out a slightly
different unstressed shape due to temperature variation, and it is a
further waste of time to work out the supposed stresses resulting from
deflecting that arch back to its actual shape.
If no other method of finding the approximate stresses in an arch

existed, the elastic theory might be classed as the best available; but
this is not the case. There is a method which is both simple and reliable.
Accuracy is not claimed for it, and hence it is in accord with the more
or less uncertain materials dealt with. Complete safety, however, is
assured, for it treats the arch as a series of blocks, and the cementing of
these blocks into one mass cannot weaken the arch. Reinforcement can
be proportioned in the same manner as for chimneys, by finding the
tension exerted to pull these blocks apart and then providing steel to
take that tension.
The fifteenth point concerns steel in compression in reinforced concrete
columns or beams. It is common practice--and it is recommended in the
most pretentious works on the subject--to include in the strength of a
concrete column slender longitudinal rods embedded in the concrete.
To quote from one of these works:
"The compressive resistance of a hooped member exceeds the sum of
the following three elements: (1) The compressive resistance of the
concrete without reinforcement. (2) The compressive resistance of the
longitudinal rods stressed to their elastic limit. (3) The compressive
resistance which would have been produced by the imaginary
longitudinals at the elastic limit of the hooping metal, the volume of the
imaginary longitudinals being taken as 2.4 times that of the hooping
metal."
This does not stand the test, either of theory or practice; in fact, it is far
from being true. Its departure from the truth is great enough and of
serious enough moment to explain some of the worst accidents in the
history of reinforced concrete.
It is a nice theoretical conception that the steel and the concrete act
together to take the compression, and that each is accommodating
enough to take just as much of the load as will stress it to just the right
unit. Here again, initial stress plays an important part. The shrinkage of
the concrete tends to put the rods in compression, the load adds more
compression on the slender rods and they buckle, because of the lack of
any adequate stiffening, long before the theorists' ultimate load is
reached.

There is no theoretical or practical consideration which would bring in
the strength of the hoops after the strength of the concrete between
them has been counted. All the compression of a column must, of
necessity, go through the disk of concrete between the two hoops (and
the longitudinal steel). No additional strength in the hoops can affect
the strength of this disk, with a given spacing of the hoops. It is true
that shorter disks will have more strength, but this is a matter of the
spacing of the hoops and not of their sectional area, as the above
quotation would make it appear.
Besides being false theoretically, this method of investing phantom
columns