The last-mentioned argument is as old as Engineering; it is the

"practical man's" mainstay, his "unanswerable argument." The so-called

practical man will construct a building, and test it either with loads

or by practical use. Then he will modify the design somewhere, and the

resulting construction will be tested. If it passes through this

modifying process and still does service, he has something which, in his

mind, is unassailable. Imagine the freaks which would be erected in the

iron bridge line, if the capacity to stand up were all the designer had

to guide him, analysis of stresses being unknown. Tests are essential,

but analysis is just as essential. The fact that a structure carries the

bare load for which it is computed, is in no sense a test of its correct

design; it is not even a test of its safety. In Pittsburg, some years

ago, a plate-girder span collapsed under the weight of a locomotive

which it had carried many times. This bridge was, perhaps, thirty years

old. Some reinforced concrete bridges have failed under loads which they

have carried many times. Others have fallen under no extraneous load,

and after being in service many months. If a large number of the columns

of a structure fall shortly after the forms are removed, what is the

factor of safety of the remainder, which are identical, but have not

quite reached their limit of strength? Or what is the factor of safety

of columns in other buildings in which the concrete was a little better

or the forms have been left in a little longer, both sets of columns

being similarly designed?

There are highway bridges of moderately long spans standing and doing

service, which have 2-in. chord pins; laterals attached to swinging

floor-beams in such a way that they could not possibly receive their

full stress; eye-bars with welded-on heads; and many other equally

absurd and foolish details, some of which were no doubt patented in

their day. Would any engineer with any knowledge whatever of bridge

design accept such details? They often stand the test of actual service

for years; in pins, particularly, the calculated stress is sometimes

very great. These details do not stand the test of analysis and of

common sense, and, therefore, no reputable engineer would accept them.

Mr. Turner, in the first and second paragraphs of his discussion, would

convey the impression that the writer was in doubt as to his "personal

opinions" and wanted some free advice. He intimates that he is too busy

to go fully into a treatise in order to set them right. He further tries

to throw discredit on the paper by saying that the writer has adduced no

clean-cut statement of fact or tests in support of his views. If Mr.

Turner had read the paper carefully, he would not have had the idea that

in it the hooped column is condemned. As to this more will be said

later. The paper is simply and solely a collection of statements of

facts and tests, whereas his discussion teems with his "personal

opinion," and such statements as "These values * * * are regarded by the

writer as having at least double the factor of safety used in ordinary

designs of structural steel"; "On a basis not far from that which the

writer considers reasonable practice." Do these sound like clean-cut

statements of fact, or are they personal opinions? It is a fact, pure

and simple, that a sharp bend in a reinforcing rod in concrete violates

the simplest principles of mechanics; also that the queen-post and Pratt

and Howe truss analogies applied to reinforcing steel in concrete are

fallacies; that a few inches of embedment will not anchor a rod for its

value; that concrete shrinks in setting in air and puts initial stress

in both the concrete and the steel, making assumed unstressed initial

conditions non-existent. It is a fact that longitudinal rods alone

cannot be relied on to reinforce a concrete column. Contrary to Mr.

Turner's statement, tests have been adduced to demonstrate this fact.

Further, it is a fact that the faults and errors in reinforced concrete

design to which attention is called, are very common in current design,

and are held up as models in nearly all books on the subject.

The writer has not asked any one to believe a single thing because he

thinks it is so, or to change a single feature of design because in his

judgment that feature is faulty. The facts given are exemplifications of

elementary mechanical principles overlooked by other writers, just as

early bridge designers and writers on bridge design overlooked the

importance of calculating bridge pins and other details which would

carry the stress of the members.

A careful reading of the paper will show that the writer does not accept

the opinions of others, when they are not backed by sound reason, and

does not urge his own opinion.

Instead of being a statement of personal opinion for which confirmation

is desired, the paper is a simple statement of facts and tests which

demonstrate the error of practices exhibited in a large majority of

reinforced concrete work and held up in the literature on the subject as

examples to follow. Mr. Turner has made no attempt to deny or refute any

one of these facts, but he speaks of the burden of proof resting on the

writer. Further, he makes statements which show that he fails entirely

to understand the facts given or to grasp their meaning. He says that

the writer's idea is "that the entire pull of the main reinforcing rod

should be taken up apparently at the end." He adds that the soundness of

this position may be questioned, because, in slabs, the steel frequently

breaks at the center. Compare this with the writer's statement, as

follows:

"In shallow beams there is little need of provision for taking

shear by any other means than the concrete itself. The writer has

seen a reinforced slab support a very heavy load by simple

friction, for the slab was cracked close to the supports. In slabs,

shear is seldom provided for in the steel reinforcement. It is only

when beams begin to have a depth approximating one-tenth of the

span that the shear in the concrete becomes excessive and provision

is necessary in the steel reinforcement. Years ago, the writer

recommended that, in such beams, some of the rods be curved up

toward the ends of the span and anchored over the support."

It is solely in providing for shear that the steel reinforcement should

be anchored for its full value over the support. The shear must

ultimately reach the support, and that part which the concrete is not

capable of carrying should be taken to it solely by the steel, as far as

tensile and shear stresses are concerned. It should not be thrown back

on the concrete again, as a system of stirrups must necessarily do.

The following is another loose assertion by Mr. Turner:

"Mr. Godfrey appears to consider that the hooping and vertical

reinforcement of columns is of little value. He, however, presents

for consideration nothing but his opinion of the matter, which

appears to be based on an almost total lack of familiarity with

such construction."

There is no excuse for statements like this. If Mr. Turner did not read

the paper, he should not have attempted to criticize it. What the writer

presented for consideration was more than his opinion of the matter. In

fact, no opinion at all was presented. What was presented was tests

which prove absolutely that longitudinal rods without hoops may actually

reduce the strength of a column, and that a column containing

longitudinal rods and "hoops which are not close enough to stiffen the

rods" may be of less strength than a plain concrete column. A properly

hooped column was not mentioned, except by inference, in the quotation

given in the foregoing sentence. The column tests which Mr. Turner

presents have no bearing whatever on the paper, for they relate to

columns with bands and close spirals. Columns are sometimes built like

these, but there is a vast amount of work in which hooping and bands are

omitted or are reduced to a practical nullity by being spaced a foot or

so apart.

A steel column made up of several pieces latticed together derives a

large part of its stiffness and ability to carry compressive stresses

from the latticing, which should be of a strength commensurate with the

size of the column. If it were weak, the column would suffer in

strength. The latticing might be very much stronger than necessary, but

it would not add anything to the strength of the column to resist

compression. A formula for the compressive strength of a column could

not include an element varying with the size of the lattice. If the

lattice is weak, the column is simply deficient; so a formula for a

hooped column is incorrect if it shows that the strength of the column

varies with the section of the hoops, and, on this account, the common

formula is incorrect. The hoops might be ever so strong, beyond a

certain limit, and yet not an iota would be added to the compressive

strength of the column, for the concrete between the hoops might crush

long before their full strength was brought into play. Also, the hoops

might be too far apart to be of much or any benefit, just as the lattice

in a steel column might be too widely spaced. There is no element of

personal opinion in these matters. They are simply incontrovertible

facts. The strength of a hooped column, disregarding for the time the

longitudinal steel, is dependent on the fact that thin discs of concrete

are capable of carrying much more load than shafts or cubes. The hoops

divide the column into thin discs, if they are closely spaced; widely

spaced hoops do not effect this. Thin joints of lime mortar are known to

be many times stronger than the same mortar in cubes. Why, in the many

books on the subject of reinforced concrete, is there no mention of this

simple principle? Why do writers on this subject practically ignore the

importance of toughness or tensile strength in columns? The trouble

seems to be in the tendency to interpret concrete in terms of steel.

Steel at failure in short blocks will begin to spread and flow, and a

short column has nearly the same unit strength as a short block. The

action of concrete under compression is quite different, because of the

weakness of concrete in tension. The concrete spalls off or cracks apart

and does not flow under compression, and the unit strength of a shaft of

concrete under compression has little relation to that of a flat block.

Some years ago the writer pointed out that the weakness of cast-iron

columns in compression is due to the lack of tensile strength or

toughness in cast iron. Compare 7,600 lb. per sq. in. as the base of a

column formula for cast iron with 100,000 lb. per sq. in. as the

compressive strength of short blocks of cast iron. Then compare 750 lb.

per sq. in., sometimes used in concrete columns, with 2,000 lb. per sq.

in., the ultimate strength in blocks. A material one-fiftieth as strong

in compression and one-hundredth as strong in tension with a "safe" unit

one-tenth as great! The greater tensile strength of rich mixtures of

concrete accounts fully for the greater showing in compression in tests

of columns of such mixtures. A few weeks ago, an investigator in this

line remarked, in a discussion at a meeting of engineers, that "the

failure of concrete in compression may in cases be due to lack of

tensile strength." This remark was considered of sufficient novelty and

importance by an engineering periodical to make a special news item of

it. This is a good illustration of the state of knowledge of the

elementary principles in this branch of engineering.

Mr. Turner states, "Again, concrete is a material which shows to the

best advantage as a monolith, and, as such, the simple beam seems to be

decidedly out of date to the experienced constructor." Similar things

could be said of steelwork, and with more force. Riveted trusses are

preferable to articulated ones for rigidity. The stringers of a bridge

could readily be made continuous; in fact, the very riveting of the ends

to a floor-beam gives them a large capacity to carry reverse moments.

This strength is frequently taken advantage of at the end floor-beam,

where a tie is made to rest on a bracket having the same riveted

connection as the stringer. A small splice-plate across the top flanges

of the stringers would greatly increase this strength to resist reverse

moments. A steel truss span is ideally conditioned for continuity in the

stringers, since the various supports are practically relatively

immovable. This is not true in a reinforced concrete building where each

support may settle independently and entirely vitiate calculated

continuous stresses. Bridge engineers ignore continuity absolutely in

calculating the stringers; they do not argue that a simple beam is out

of date. Reinforced concrete engineers would do vastly better work if

they would do likewise, adding top reinforcement over supports to

forestall cracking only. Failure could not occur in a system of beams

properly designed as simple spans, even if the negative moments over the

supports exceeded those for which the steel reinforcement was provided,

for the reason that the deflection or curving over the supports can only

be a small amount, and the simple-beam reinforcement will immediately

come into play.

Mr. Turner speaks of the absurdity of any method of calculating a

multiple-way reinforcement in slabs by endeavoring to separate the

construction into elementary beam strips, referring, of course, to the

writer's method. This is misleading. The writer does not endeavor to

"separate the construction into elementary beam strips" in the sense of

disregarding the effect of cross-strips. The "separation" is analogous

to that of considering the tension and compression portions of a beam

separately in proportioning their size or reinforcement, but unitedly in

calculating their moment. As stated in the paper, "strips are taken

across the slab and the moment in them is found, considering the

limitations of the several strips in deflection imposed by those running

at right angles therewith." It is a sound and rational assumption that

each strip, 1 ft. wide through the middle of the slab, carries its half

of the middle square foot of the slab load. It is a necessary limitation

that the other strips which intersect one of these critical strips

across the middle of the slab, cannot carry half of the intercepted

square foot, because the deflection of these other strips must diminish

to zero as they approach the side of the rectangle. Thus, the nearer the

support a strip parallel to that support is located, the less load it

can take, for the reason that it cannot deflect as much as the middle

strip. In the oblong slab the condition imposed is equal deflection of

two strips of unequal span intersecting at the middle of the slab, as

well as diminished deflection of the parallel strips.

In this method of treating the rectangular slab, the concrete in tension

is not considered to be of any value, as is the case in all accepted

methods.

Some years ago the writer tested a number of slabs in a building, with a

load of 250 lb. per sq. ft. These slabs were 3 in. thick and had a clear

span of 44 in. between beams. They were totally without reinforcement.

Some had cracked from shrinkage, the cracks running through them and

practically the full length of the beams. They all carried this load

without any apparent distress. If these slabs had been reinforced with

some special reinforcement of very small cross-section, the strength

which was manifestly in the concrete itself, might have been made to

appear to be in the reinforcement. Magic properties could be thus

conjured up for some special brand of reinforcement. An energetic

proprietor could capitalize tension in concrete in this way and "prove"

by tests his claims to the magic properties of his reinforcement.

To say that Poisson's ratio has anything to do with the reinforcement of

a slab is to consider the tensile strength of concrete as having a

positive value in the bottom of that slab. It means to reinforce for the

stretch in the concrete and not for the tensile stress. If the tensile

strength of concrete is not accepted as an element in the strength of a

slab having one-way reinforcement, why should it be accepted in one

having reinforcement in two or more directions? The tensile strength of

concrete in a slab of any kind is of course real, when the slab is

without cracks; it has a large influence in the deflection; but what

about a slab that is cracked from shrinkage or otherwise?

Mr. Turner dodges the issue in the matter of stirrups by stating that

they were not correctly placed in the tests made at the University of

Illinois. He cites the Hennebique system as a correct sample. This

system, as the writer finds it, has some rods bent up toward the support

and anchored over it to some extent, or run into the next span. Then

stirrups are added. There could be no objection to stirrups if, apart

from them, the construction were made adequate, except that expense is

added thereby. Mr. Turner cannot deny that stirrups are very commonly

used just as they were placed in the tests made at the University of

Illinois. It is the common practice and the prevailing logic in the

literature of the subject which the writer condemns.

Mr. Thacher says of the first point:

"At the point where the first rod is bent up, the stress in this

rod runs out. The other rods are sufficient to take the horizontal

stress, and the bent-up portion provides only for the vertical and

diagonal shearing stresses in the concrete."

If the stress runs out, by what does that rod, in the bent portion, take

shear? Could it be severed at the bend, and still perform its office?

The writer can conceive of an inclined rod taking the shear of a beam if

it were anchored at each end, or long enough somehow to have a grip in

the concrete from the centroid of compression up and from the center of

the steel down. This latter is a practical impossibility. A rod curved

up from the bottom reinforcement and curved to a horizontal position and

run to the support with anchorage, would take the shear of a beam. As to

the stress running out of a rod at the point where it is bent up, this

will hardly stand the test of analysis in the majority of cases. On

account of the parabolic variation of stress in a beam, there should be

double the length necessary for the full grip of a rod in the space from

the center to the end of a beam. If 50 diameters are needed for this

grip, the whole span should then be not less than four times 50, or 200

diameters of the rod. For the same reason the rod between these bends

should be at least 200 diameters in length. Often the reinforcing rods

are equal to or more than one-two-hundredth of the span in diameter, and

therefore need the full length of the span for grip.

Mr. Thacher states that Rod 3 provides for the shear. He fails to answer

the argument that this rod is not anchored over the support to take the

shear. Would he, in a queen-post truss, attach the hog-rod to the beam

some distance out from the support and thus throw the bending and shear

back into the very beam which this rod is intended to relieve of bending

and shear? Yet this is just what Rod 3 would do, if it were long enough

to be anchored for the shear, which it seldom is; hence it cannot even

perform this function. If Rod 3 takes the shear, it must give it back to

the concrete beam from the point of its full usefulness to the support.

Mr. Thacher would not say of a steel truss that the diagonal bars would

take the shear, if these bars, in a deck truss, were attached to the top

chord several feet away from the support, or if the end connection were

good for only a fraction of the stress in the bars. Why does he not

apply the same logic to reinforced concrete design?

Answering the third point, Mr. Thacher makes more statements that are

characteristic of current logic in reinforced concrete literature, which

does not bother with premises. He says, "In a beam, the shear rods run

through the compression parts of the concrete and have sufficient

anchorage." If the rods have sufficient anchorage, what is the nature of

that anchorage? It ought to be possible to analyze it, and it is due to

the seeker after truth to produce some sort of analysis. What mysterious

thing is there to anchor these rods? The writer has shown by analysis

that they are not anchored sufficiently. In many cases they are not long

enough to receive full anchorage. Mr. Thacher merely makes the dogmatic

statement that they are anchored. There is a faint hint of a reason in

his statement that they run into the compression part of the concrete.

Does he mean that the compression part of the concrete will grip the rod

like a vise? How does this comport with his contention farther on that

the beams are continuous? This would mean tension in the upper part of

the beam. In any beam the compression near the support, where the shear

is greatest, is small; so even this hint of an argument has no force or

meaning.

In this same paragraph Mr. Thacher states, concerning the third point

and the case of the retaining wall that is given as an example, "In a

counterfort, the inclined rods are sufficient to take the overturning

stress." Mr. Thacher does not make clear what he means by "overturning

stress." He seems to mean the force tending to pull the counterfort

loose from the horizontal slab. The weight of the earth fill over this

slab is the force against which the vertical and inclined rods of Fig.

2, at _a_, must act. Does Mr. Thacher mean to state seriously that it is

sufficient to hang this slab, with its heavy load of earth fill, on the

short projecting ends of a few rods? Would he hang a floor slab on a few

rods which project from the bottom of a girder? He says, "The proposed

method is no more effective." The proposed method is Fig. 2, at _b_,

where an angle is provided as a shelf on which this slab rests. The

angle is supported, with thread and nut, on rods which reach up to the

front slab, from which a horizontal force, acting about the toe of the

wall as a fulcrum, results in the lifting force on the slab. There is

positively no way in which this wall could fail (as far as the

counterfort is concerned) but by the pulling apart of the rods or the

tearing out of this anchoring angle. Compare this method of failure with

the mere pulling out of a few ends of rods, in the design which Mr.

Thacher says is just as effective. This is another example of the kind

of logic that is brought into requisition in order to justify absurd

systems of design.

Mr. Thacher states that shear would govern in a bridge pin where there

is a wide bar or bolster or a similar condition. The writer takes issue

with him in this. While in such a case the center of bearing need not be

taken to find the bending moment, shear would not be the correct

governing element. There is no reason why a wide bar or a wide bolster

should take a smaller pin than a narrow one, simply because the rule

that uses the center of bearing would give too large a pin. Bending can

be taken in this, as in other cases, with a reasonable assumption for a

proper bearing depth in the wide bar or bolster. The rest of Mr.

Thacher's comment on the fourth point avoids the issue. What does he

mean by "stress" in a shear rod? Is it shear or tension? Mr. Thacher's

statement, that the "stress" in the shear rods is less than that in the

bottom bars, comes close to saying that it is shear, as the shearing

unit in steel is less than the tensile unit. This vague way of referring

to the "stress" in a shear member, without specifically stating whether

this "stress" is shear or tension, as was done in the Joint Committee

Report, is, in itself, a confession of the impossibility of analyzing

the "stress" in these members. It gives the designer the option of using

tension or shear, both of which are absurd in the ordinary method of

design. Writers of books are not bold enough, as a rule, to state that

these rods are in shear, and yet their writings are so indefinite as to

allow this very interpretation.

Mr. Thacher criticises the fifth point as follows:

"Vertical stirrups are designed to act like the vertical rods in a

Howe truss. Special literature is not required on the subject; it

is known that the method used gives good results, and that is

sufficient."

This is another example of the logic applied to reinforced concrete

design--another dogmatic statement. If these stirrups act like the

verticals in a Howe truss, why is it not possible by analysis to show

that they do? Of course there is no need of special literature on the

subject, if it is the intention to perpetuate this senseless method of

design. No amount of literature can prove that these stirrups act as the

verticals of a Howe truss, for the simple reason that it can be easily

proven that they do not.

Mr. Thacher's criticism of the sixth point is not clear. "All the shear

from the center of the beam up to the bar in question," is what he says

each shear member is designed to take in the common method. The shear of

a beam usually means the sum of the vertical forces in a vertical

section. If he means that the amount of this shear is the load from the

center of the beam to the bar in question, and that shear members are

designed to take this amount of shear, it would be interesting to know

by what interpretation the common method can be made to mean this. The

method referred to is that given in several standard works and in the

Joint Committee Report. The formula in that report for vertical

reinforcement is:

_V_ _s_

_P_ = --------- ,

_j_ _d_

in which _P_ = the stress in a single reinforcing member, _V_ = the

proportion of total shear assumed as carried by the reinforcement, _s_ =

the horizontal spacing of the reinforcing members, and _j d_ = the

effective depth.

Suppose the spacing of shear members is one-half or one-third of the

effective depth, the stress in each member is one-half or one-third of

the "shear assumed to be carried by the reinforcement." Can Mr. Thacher

make anything else out of it? If, as he says, vertical stirrups are

designed to act like the vertical rods in a Howe truss, why are they not

given the stress of the verticals of a Howe truss instead of one-half or

one-third or a less proportion of that stress?

Without meaning to criticize the tests made by Mr. Thaddeus Hyatt on

curved-up rods with nuts and washers, it is true that the results of

many early tests on reinforced concrete are uncertain, because of the

mealy character of the concrete made in the days when "a minimum amount

of water" was the rule. Reinforcement slips in such concrete when it

would be firmly gripped in wet concrete. The writer has been unable to

find any record of the tests to which Mr. Thacher refers. The tests

made at the University of Illinois, far from showing reinforcement of

this type to be "worse than useless," showed most excellent results by

its use.

That which is condemned in the seventh point is not so much the

calculating of reinforced concrete beams as continuous, and reinforcing

them properly for these moments, but the common practice of lopping off

arbitrarily a large fraction of the simple beam moment on reinforced

concrete beams of all kinds. This is commonly justified by some virtue

which lies in the term monolith. If a beam rests in a wall, it is "fixed

ended"; if it comes into the side of a girder, it is "fixed ended"; and

if it comes into the side of a column, it is the same. This is used to

reduce the moment at mid-span, but reinforcement which will make the

beam fixed ended or continuous is rare.

There is not much room for objection to Mr. Thacher's rule of spacing

rods three diameters apart. The rule to which the writer referred as

being 66% in error on the very premise on which it was derived, namely,

shear equal to adhesion, was worked out by F.P. McKibben, M. Am. Soc. C.

E. It was used, with due credit, by Messrs. Taylor and Thompson in their

book, and, without credit, by Professors Maurer and Turneaure in their

book. Thus five authorities perpetrate an error in the solution of one

of the simplest problems imaginable. If one author of an arithmetic had

said two twos are five, and four others had repeated the same thing,

would it not show that both revision and care were badly needed?

Ernest McCullough, M. Am. Soc. C. E., in a paper read at the Armour

Institute, in November, 1908, says, "If the slab is not less than

one-fifth of the total depth of the beam assumed, we can make a

T-section of it by having the narrow stem just wide enough to contain

the steel." This partly answers Mr. Thacher's criticism of the ninth

point. In the next paragraph, Mr. McCullough mentions some very nice

formulas for T-beams by a certain authority. Of course it would be

better to use these nice formulas than to pay attention to such

"rule-of-thumb" methods as would require more width in the stem of the T

than enough to squeeze the steel in.

If these complex formulas for T-beams (which disregard utterly the

simple and essential requirement that there must be concrete enough in

the stem of the T to grip the steel) are the only proper

exemplifications of the "theory of T-beams," it is time for engineers to

ignore theory and resort to rule-of-thumb. It is not theory, however,

which is condemned in the paper, it is complex theory; theory totally

out of harmony with the materials dealt with; theory based on false

assumptions; theory which ignores essentials and magnifies trifles;

theory which, applied to structures which have failed from their own

weight, shows them to be perfectly safe and correct in design;

half-baked theories which arrogate to themselves a monopoly on

rationality.

To return to the spacing of rods in the bottom of a T-beam; the report

of the Joint Committee advocates a horizontal spacing of two and

one-half diameters and a side spacing of two diameters to the surface.

The same report advocates a "clear spacing between two layers of bars of

not less than 1/2 in." Take a T-beam, 11-1/2 in. wide, with two layers

of rods 1 in. square, 4 in each layer. The upper surface of the upper

layer would be 3-1/2 in. above the bottom of the beam. Below this

surface there would be 32 sq. in. of concrete to grip 8 sq. in. of

steel. Does any one seriously contend that this trifling amount of

concrete will grip this large steel area? This is not an extreme case;

it is all too common; and it satisfies the requirements of the Joint

Committee, which includes in its make-up a large number of the

best-known authorities in the United States.

Mr. Thacher says that the writer appears to consider theories for

reinforced concrete beams and slabs as useless refinements. This is not

what the writer intended to show. He meant rather that facts and tests

demonstrate that refinement in reinforced concrete theories is utterly

meaningless. Of course a wonderful agreement between the double-refined

theory and test can generally be effected by "hunching" the modulus of

elasticity to suit. It works both ways, the modulus of elasticity of

concrete being elastic enough to be shifted again to suit the designer's

notion in selecting his reinforcement. All of which is very beautiful,

but it renders standard design impossible.

Mr. Thacher characterizes the writer's method of calculating reinforced

concrete chimneys as rule-of-thumb. This is surprising after what he

says of the methods of designing stirrups. The writer's method would

provide rods to take all the tensile stresses shown to exist by any

analysis; it would give these rods unassailable end anchorages; every

detail would be amply cared for. If loose methods are good enough for

proportioning loose stirrups, and no literature is needed to show why or

how they can be, why analyze a chimney so accurately and apply

assumptions which cannot possibly be realized anywhere but on paper and

in books?

It is not rule-of-thumb to find the tension in plain concrete and then

embed steel in that concrete to take that tension. Moreover, it is safer

than the so-called rational formula, which allows compression on slender

rods in concrete.

Mr. Thacher says, "No arch designed by the elastic theory was ever known

to fail, unless on account of insecure foundations." Is this the correct

way to reach correct methods of design? Should engineers use a certain

method until failures show that something is wrong? It is doubtful if

any one on earth has statistics sufficient to state with any authority

what is quoted in the opening sentence of this paragraph. Many arches

are failures by reason of cracks, and these cracks are not always due to

insecure foundations. If Mr. Thacher means by insecure foundations,

those which settle, his assertion, assuming it to be true, has but

little weight. It is not always possible to found an arch on rock. Some

settlement may be anticipated in almost every foundation. As commonly

applied, the elastic theory is based on the absolute fixity of the

abutments, and the arch ring is made more slender because of this

fixity. The ordinary "row-of-blocks" method gives a stiffer arch ring

and, consequently, greater security against settlement of foundations.

In 1904, two arches failed in Germany. They were three-hinged masonry

arches with metal hinges. They appear to have gone down under the weight

of theory. If they had been made of stone blocks in the old-fashioned

way, and had been calculated in the old-fashioned row-of-blocks method,

a large amount of money would have been saved. There is no good reason

why an arch cannot be calculated as hinged ended and built with the arch

ring anchored into the abutments. The method of the equilibrium polygon

is a safe, sane, and sound way to calculate an arch. The monolithic

method is a safe, sane, and sound way to build one. People who spend

money for arches do not care whether or not the fancy and fancied

stresses of the mathematician are realized; they want a safe and lasting

structure.

Of course, calculations can be made for shrinkage stresses and for

temperature stresses. They have about as much real meaning as

calculations for earth pressures behind a retaining wall. The danger

does not lie in making the calculations, but in the confidence which the

very making of them begets in their correctness. Based on such

confidence, factors of safety are sometimes worked out to the hundredth

of a unit.

Mr. Thacher is quite right in his assertion that stiff steel angles,

securely latticed together, and embedded in the concrete column, will

greatly increase its strength.

The theory of slabs supported on four sides is commonly accepted for

about the same reason as some other things. One author gives it, then

another copies it; then when several books have it, it becomes

authoritative. The theory found in most books and reports has no correct

basis. That worked out by Professor W.C. Unwin, to which the writer

referred, was shown by him to be wrong.[T] An important English report

gave publicity and much space to this erroneous solution. Messrs. Marsh

and Dunn, in their book on reinforced concrete, give several pages to

it.

In referring to the effect of initial stress, Mr. Myers cites the case

of blocks and says, "Whatever initial stress exists in the concrete due

to this process of setting exists also in these blocks when they are

tested." However, the presence of steel in beams and columns puts

internal stresses in reinforced concrete, which do not exist in an

isolated block of plain concrete.

Mr. Meem, while he states that he disagrees with the writer in one

essential point, says of that point, "In the ordinary way in which these

rods are used, they have no practical value." The paper is meant to be a

criticism of the ordinary way in which reinforced concrete is used.

While Mr. Meem's formula for a reinforced concrete beam is simple and

much like that which the writer would use, he errs in making the moment

of the stress in the steel about the neutral axis equal to the moment of

that in the concrete about the same axis. The actual amount of the

tension in the steel should equal the compression in the concrete, but

there is no principle of mechanics that requires equality of the moments

about the neutral axis. The moment in the beam is, therefore, the

product of the stress in steel or concrete and the effective depth of

the beam, the latter being the depth from the steel up to a point

one-sixth of the depth of the concrete beam from the top. This is the

method given by the writer. It would standardize design as methods using

the coefficient of elasticity cannot do.

Professor Clifford, in commenting on the first point, says, "The

concrete at the point of juncture must give, to some extent, and this

would distribute the bearing over a considerable length of rod." It is

just this local "giving" in reinforced concrete which results in cracks

that endanger its safety and spoil its appearance; they also discredit

it as a permanent form of construction.

Professor Clifford has informed the writer that the tests on bent rods

to which he refers were made on 3/4-in. rounds, embedded for 12 in. in

concrete and bent sharply, the bent portion being 4 in. long. The 12-in.

portion was greased. The average maximum load necessary to pull the rods

out was 16,000 lb. It seems quite probable that there would be some

slipping or crushing of the concrete before a very large part of this

load was applied. The load at slipping would be a more useful

determination than the ultimate, for the reason that repeated

application of such loads will wear out a structure. In this connection

three sets of tests described in Bulletin No. 29 of the University of

Illinois, are instructive. They were made on beams of the same size, and

reinforced with the same percentage of steel. The results were as

follows:

Beams 511.1, 511.2, 512.1, 512.2: The bars were bent up at third points.

Average breaking load, 18,600 lb. All failed by slipping of the bars.

Beams 513.1, 513.2: The bars were bent up at third points and given a

sharp right-angle turn over the supports. Average breaking load, 16,500

lb. The beams failed by cracking alongside the bar toward the end.

Beams 514.2, 514.3: The bars were bent up at third points and had

anchoring nuts and washers at the ends over the supports. Average

breaking load, 22,800 lb. These failed by tension in the steel.

By these tests it is seen that, in a beam, bars without hooks were

stronger in their hold on the concrete by an average of 13% than those

with hooks. Each test of the group of straight bars showed that they

were stronger than either of those with hooked bars. Bars anchored over

the support in the manner recommended in the paper were nearly 40%

stronger than hooked bars and 20% stronger than straight bars. These

percentages, furthermore, do not represent all the advantages of

anchored bars. The method of failure is of greatest significance. A

failure by tension in the steel is an ideal failure, because it is

easiest to provide against. Failures by slipping of bars, and by

cracking and disintegrating of the concrete beam near the support, as

exhibited by the other tests, indicate danger, and demand much larger

factors of safety.

Professor Clifford, in criticizing the statement that a member which

cannot act until failure has started is not a proper element of design,

refers to another statement by the writer, namely, "The steel in the

tension side of the beam should be considered as taking all the

tension." He states that this cannot take place until the concrete has

failed in tension at this point. The tension side of a beam will stretch

out a measurable amount under load. The stretching out of the beam

vertically, alongside of a stirrup, would be exceedingly minute, if no

cracks occurred in the beam.

Mr. Mensch says that "the stresses involved are mostly secondary." He

compares them to web stresses in a plate girder, which can scarcely be

called secondary. Furthermore, those stresses are carefully worked out

and abundantly provided for in any good design. To give an example of

how a plate girder might be designed: Many plate girders have rivets in

the flanges, spaced 6 in. apart near the supports, that is, girders

designed with no regard to good practice. These girders, perhaps, need

twice as many rivets near the ends, according to good and acceptable

practice, which is also rational practice. The girders stand up and

perform their office. It is doubtful whether they would fail in these

rivet lines in a test to destruction; but a reasonable analysis shows

that these rivets are needed, and no good engineer would ignore this

rule of design or claim that it should be discarded because the girders

do their work anyway. There are many things about structures, as every

engineer who has examined many of those erected without engineering

supervision can testify, which are bad, but not quite bad enough to be

cause for condemnation. Not many years ago the writer ordered

reinforcement in a structure designed by one of the best structural

engineers in the United States, because the floor-beams had sharp bends

in the flange angles. This is not a secondary matter, and sharp bends in

reinforcing rods are not a secondary matter. No amount of analysis can

show that these rods or flange angles will perform their full duty.

Something else must be overstressed, and herein is a violation of the

principles of sound engineering.

Mr. Mensch mentions the failure of the Quebec Bridge as an example of

the unknown strength of steel compression members, and states that, if

the designer of that bridge had known of certain tests made 40 years

ago, that accident probably would not have happened. It has never been

proven that the designer of that bridge was responsible for the accident

or for anything more than a bridge which would have been weak in

service. The testimony of the Royal Commission, concerning the chords,

is, "We have no evidence to show that they would have actually failed

under working conditions had they been axially loaded and not subject to

transverse stresses arising from weak end details and loose

connections." Diagonal bracing in the big erection gantry would have

saved the bridge, for every feature of the wreck shows that the lateral

collapse of that gantry caused the failure. Here are some more simple

principles of sound engineering which were ignored.

It is when practice runs "ahead of theory" that it needs to be brought

up with a sharp turn. It is the general practice to design dams for the

horizontal pressure of the water only, ignoring that which works into

horizontal seams and below the foundation, and exerts a heavy uplift.

Dams also fail occasionally, because of this uplifting force which is

proven to exist by theory.

Mr. Mensch says:

"The author is manifestly wrong in stating that the reinforcing

rods can only receive their increments of stress when the concrete

is in tension. Generally, the contrary happens. In the ordinary

adhesion test, the block of concrete is held by the jaws of the

machine and the rod is pulled out; the concrete is clearly in

compression."

This is not a case of increments at all, as the rod has the full stress

given to it by the grips of the testing machine. Furthermore, it is not

a beam. Also, Mr. Mensch is not accurate in conveying the writer's

meaning. To quote from the paper:

"A reinforcing rod in a concrete beam receives its stress by

increments imparted by the grip of the concrete, but these

increments can only be imparted where the tendency of the concrete

is to stretch."

This has no reference to an adhesion test.

Mr. Mensch's next paragraph does not show a careful perusal of the

paper. The writer does not "doubt the advisability of using bent-up bars

in reinforced concrete beams." What he does condemn is bending up the

bars with a sharp bend and ending them nowhere. When they are curved up,

run to the support, and are anchored over the support or run into the

next span, they are excellent. In the tests mentioned by Mr. Mensch, the

beams which had the rods bent up and "continued over the supports" gave

the highest "ultimate values." This is exactly the construction which

is pointed out as being the most rational, if the rods do not have the

sharp bends which Mr. Mensch himself condemns.

Regarding the tests mentioned by him, in which the rods were fastened to

anchor-plates at the end and had "slight increase of strength over

straight rods, and certainly made a poorer showing than bent-up bars,"

the writer asked Mr. Mensch by letter whether these bars were curved up

toward the supports. He has not answered the communication, so the

writer cannot comment on the tests. It is not necessary to use threaded

bars, except in the end beams, as the curved-up bars can be run into the

next beam and act as top reinforcement while at the same time receiving

full anchorage.

Mr. Mensch's statement regarding the retaining wall reinforced as shown

at _a_, Fig. 2, is astounding. He "confesses that he never saw or heard

of such poor practices." If he will examine almost any volume of an

engineering periodical of recent years, he will have no trouble at all

in finding several examples of these identical practices. In the books

by Messrs. Reid, Maurer and Turneaure, and Taylor and Thompson, he will

find retaining walls illustrated, which are almost identical with Fig. 2

at _a_. Mr. Mensch says that the proposed design of a retaining wall

would be difficult and expensive to install. The harp-like reinforcement

could be put together on the ground, and raised to place and held with a

couple of braces. Compare this with the difficulty, expense and

uncertainty of placing and holding in place 20 or 30 separate rods. The

Fink truss analogy given by Mr. Mensch is a weak one. If he were making

a cantilever bracket to support a slab by tension from the top, the

bracket to be tied into a wall, would he use an indiscriminate lot of

little vertical and horizontal rods, or would he tie the slab directly

into the wall by diagonal ties? This is exactly the case of this

retaining wall, the horizontal slab has a load of earth, and the

counterfort is a bracket in tension; the vertical wall resists that

tension and derives its ability to resist from the horizontal pressure

of the earth.

Mr. Mensch states that "it would take up too much time to prove that the

counterfort acts really as a beam." The writer proposes to show in a

very short time that it is not a beam. A beam is a part of a structure

subject to bending strains caused by transverse loading. This will do as

a working definition. The concrete of the counterfort shown at _b_, Fig.

2, could be entirely eliminated if the rods were simply made to run

straight into the anchoring angle and were connected with little cast

skewbacks through slotted holes. There would be absolutely no bending in

the rods and no transverse load. Add the concrete to protect the rods;

the function of the rods is not changed in the least. M.S. Ketchum, M.

Am. Soc. C. E.,[U] calculates the counterfort as a beam, and the six

1-in. square bars which he uses diagonally do not even run into the

front slab. He states that the vertical and horizontal rods are to "take

the horizontal and vertical shear."

Mr. Mensch says of rectangular water tanks that they are not held

(presumably at the corners) by any such devices, and that there is no

doubt that they must carry the stress when filled with water. A water

tank,[V] designed by the writer in 1905, was held by just such devices.

In a tank[W] not held by any such devices, the corner broke, and it is

now held by reinforcing devices not shown in the original plans.

Mr. Mensch states that he "does not quite understand the author's

reference to shear rods. Possibly he means the longitudinal

reinforcement, which it seems is sometimes calculated to carry 10,000

lb. per sq. in. in shear;" and that he "never heard of such a practice."

His next paragraph gives the most pointed out-and-out statement

regarding shear in shear rods which this voluminous discussion contains.

He says that stirrups "are best compared with the dowel pins and bolts

of a compound wooden beam." This is the kernel of the whole matter in

the design of stirrups, and is just how the ordinary designer considers

stirrups, though the books and reports dodge the matter by saying

"stress" and attempting no analysis. Put this stirrup in shear at 10,000

lb. per sq. in., and we have a shearing unit only equalled in the

cheapest structural work on tight-fitting rivets through steel. In the

light of this confession, the force of the writer's comparison, between

a U-stirrup, 3/4-in. in diameter, and two 3/4-in. rivets tightly driven

into holes in a steel angle, is made more evident, Bolts in a wooden

beam built up of horizontal boards would be tightly drawn up, and the

friction would play an important part in taking up the horizontal shear.

Dowels without head or nut would be much less efficient; they would be

more like the stirrups in a reinforced concrete beam. Furthermore, wood

is much stronger in bearing than concrete, and it is tough, so that it

would admit of shifting to a firm bearing against the bolt. Separate

slabs of concrete with bolts or dowels through them would not make a

reliable beam. The bolts or dowels would be good for only a part of the

safe shearing strength of the steel, because the bearing on the concrete

would be too great for its compressive strength.

Mr. Mensch states that at least 99% of all reinforced structures are

calculated with a reduction of 25% of the bending moment in the center.

He also says "there may be some engineers who calculate a reduction of

33 per cent." These are broad statements in view of the fact that the

report of the Joint Committee recommends a reduction of 33% both in

slabs and beams.

Mr. Mensch's remarks regarding the width of beams omit from

consideration the element of span and the length needed to develop the

grip of a rod. There is no need of making a rod any less in diameter

than one-two-hundredth of the span. If this rule is observed, the beam

with three 7/8-in. round rods will be of longer span than the one with

the six 5/8-in. rods. The horizontal shear of the two beams will be

equal to the total amount of that shear, but the shorter beam will have

to develop that shear in a shorter distance, hence the need of a wider

beam where the smaller rods are used.

It is not that the writer advocates a wide stem in the T-beam, in order

to dispense with the aid of the slab. What he desires to point out is

that a full analysis of a T-beam shows that such a width is needed in

the stem.

Regarding the elastic theory, Mr. Mensch, in his discussion, shows that

he does not understand the writer's meaning in pointing out the

objections to the elastic theory applied to arches. The moment of

inertia of the abutment will, of course, be many times that of the arch

ring; but of what use is this large moment of inertia when the abutment

suddenly stops at its foundation? The abutment cannot be anchored for

bending into the rock; it is simply a block of concrete resting on a

support. The great bending moment at the end of the arch, which is found

by the elastic theory (on paper), has merely to overturn this block of

concrete, and it is aided very materially in this by the thrust of the

arch. The deformation of the abutment, due to deficiency in its moment

of inertia, is a theoretical trifle which might very aptly be minutely

considered by the elastic arch theorist. He appears to have settled all

fears on that score among his votaries. The settlement of the abutment

both vertically and horizontally, a thing of tremendously more magnitude

and importance, he has totally ignored.

Most soils are more or less compressible. The resultant thrust on an

arch abutment is usually in a direction cutting about the edge of the

middle third. The effect of this force is to tend to cause more

settlement of the abutment at the outer, than at the inner, edge, or, in

other words, it would cause the abutment to rotate. In addition to this

the same force tends to spread the abutments apart. Both these efforts

put an initial bending moment in the arch ring at the springing; a

moment not calculated, and impossible to calculate.

Messrs. Taylor and Thompson, in their book, give much space to the

elastic theory of the reinforced concrete arch. Little of that space,

however, is taken up with the abutment, and the case they give has

abutments in solid rock with a slope about normal to the thrust of the

arch ring. They recommend that the thrust be made to strike as near the

middle of the base of the abutment as possible.

Malverd A. Howe, M. Am. Soc. C. E., in a recent issue of _Engineering

News_, shows how to find the stresses and moments in an elastic arch;

but he does not say anything about how to take care of the large bending

moments which he finds at the springing.

Specialists in arch construction state that when the centering is

struck, every arch increases in span by settlement. Is this one fact not

enough to make the elastic theory a nullity, for that theory assumes

immovable abutments?

Professor Howe made some recent tests on checking up the elastic

behavior of arches. He reports[X] that "a very slight change at the

support does seriously affect the values of _H_ and _M_." The arch

tested was of 20-ft. span, and built between two heavy stone walls out

of all proportion to the magnitude of the arch, as measured by

comparison with an ordinary arch and its abutment. To make the arch

fixed ended, a large heavily reinforced head was firmly bolted to the

stone wall. Practical fixed endedness could be attained, of course, by

means such as these, but the value of such tests is only theoretical.

Mr. Mensch says:

"The elastic theory was fully proved for arches by the remarkable

tests, made in 1897 by the Austrian Society of Engineers and

Architects, on full-sized arches of 70-ft. span, and the observed

deflections and lateral deformations agreed exactly with the

figured deformation."

The writer does not know of the tests made in 1897, but reference is

often made to some tests reported in 1896. These tests are everywhere

quoted as the unanswerable argument for the elastic theory. Let us

examine a few features of those tests, and see something of the strength

of the claim. In the first place, as to the exact agreement between the

calculated and the observed deformations, this exact agreement was

retroactive. The average modulus of elasticity, as found by specimen

tests of the concrete, did not agree at all with the value which it was

necessary to use in the arch calculations in order to make the

deflections come out right.

As found by tests on blocks, the average modulus was about 2,700,000;

the "practical" value, as determined from analysis of a plain concrete

arch, was 1,430,000, a little matter of nearly 100 per cent. Mansfield

Merriman, M. Am. Soc. C. E., gives a digest of these famous Austrian

tests.[Y] There were no fixed ended arches among them. There was a long

plain concrete arch and a long Monier arch. Professor Merriman says,

"The beton Monier arch is not discussed theoretically, and, indeed, this

would be a difficult task on account of the different materials

combined." And these are the tests which the Engineering Profession

points to whenever the elastic theory is questioned as to its

applicability to reinforced concrete arches. These are the tests that

"fully prove" the elastic theory for arches. These are the tests on the

basis of which fixed ended reinforced concrete arches are confidently

designed. Because a plain concrete bow between solid abutments deflected

in an elastic curve, reinforced concrete arches between settling

abutments are designed with fixed ends. The theorist has departed about

as far as possible from his premise in this case. On an exceedingly

slender thread he has hung an elaborate and important theory of design,

with assumptions which can never be realized outside of the schoolroom

or the designer's office. The most serious feature of such theories is

not merely the approximate and erroneous results which they give, but

the extreme confidence and faith in their certainty which they beget in

their users, enabling them to cut down factors of safety with no regard

whatever for the enormous factor of ignorance which is an essential

accompaniment to the theory itself.

Mr. Mensch says, "The elastic theory enables one to calculate arches

much more quickly than any graphical or guess method yet proposed." The

method given by the writer[Z] enables one to calculate an arch in about

the time it would take to work out a few of the many coefficients

necessary in the involved method of the elastic theory. It is not a

graphic method, but it is safe and sound, and it does not assume

conditions which have absolutely no existence.

Mr. Mensch says that the writer brings up some erratic column tests and

seems to have no confidence in reinforced concrete columns. In relation

to this matter Sanford E. Thompson, M. Am. Soc. C. E., in a paper

recently read before the National Association of Cement Users, takes the

same sets of tests referred to in the paper, and attempts to show that

longitudinal reinforcement adds much strength to a concrete column. Mr.

Thompson goes about it by means of averages. It is not safe to average

tests where the differences in individual tests are so great that those

of one class overlap those of the other. He includes the writer's

"erratic" tests and some others which are "erratic" the other way. It is

manifestly impossible for him to prove that longitudinal rods add any

strength to a concrete column if, on one pair of columns, identically

made as far as practicable, the plain concrete column is stronger than

that with longitudinal rods in it, unless the weak column is defective.

It is just as manifest that it is shown by this and other tests that the

supposedly reinforced concrete column may be weaker.

The averaging of results to show that longitudinal rods add strength, in

the case of the tests reported by Mr. Withey, includes a square plain

concrete column which naturally would show less compressive strength in

concrete than a round column, because of the spalling off at the

corners. This weak test on a square column is one of the slender props

on which is based the conclusion that longitudinal rods add to the

strength of a concrete column; but the weakness of the square concrete

column is due to the inherent weakness of brittle material in

compression when there are sharp corners which may spall off.

Mr. Worcester says that several of the writer's indictments hit at

practices which were discarded long ago, but from the attitude of their

defenders this does not seem to be true. There are benders to make sharp

bends in rods, and there are builders who say that they must be bent

sharply in order to simplify the work of fitting and measuring them.

There are examples in engineering periodicals and books, too numerous to

mention, where no anchorage of any kind is provided for bent-up rods,

except what grip they get in the concrete. If they reached beyond their

point of usefulness for this grip, it would be all right, but very often

they do not.

Mr. Worcester says: "It is not necessary that a stirrup at one point

should carry all the vertical tension, as this vertical tension is

distributed by the concrete." The writer will concede that the stirrups

need not carry all the vertical shear, for, in a properly reinforced

beam, the concrete can take part of it. The shear reinforcement,

however, should carry all the shear apportioned to it after deducting

that part which the concrete is capable of carrying, and it should carry

it without putting the concrete in shear again. The stirrups at one

point should carry all the vertical tension from the portion of shear

assumed to be taken by the stirrups; otherwise the concrete will be

compelled to carry more than its share of the shear.

Mr. Worcester states that cracks are just as likely to occur from stress

in curved-up and anchored rods as in vertical reinforcement. The fact

that the vertical stretching out of a beam from the top to the bottom,

under its load, is exceedingly minute, has been mentioned. A curved-up

bar, anchored over the support and lying near the bottom of the beam at

mid-span, partakes of the elongation of the tension side of the beam and

crosses the section of greatest diagonal tension in the most

advantageous manner. There is, therefore, a great deal of difference in

the way in which these two elements of construction act.

Mr. Worcester prefers the "customary method" of determining the width of

beams--so that the maximum horizontal shearing stress will not be

excessive--to that suggested by the writer. He gives as a reason for

this the fact that rods are bent up out of the bottom of a beam, and

that not all of them run to the end. The "customary method" must be

described in literature for private circulation. Mention has been made

of a method which makes the width of beam sufficient to insert the

steel. Considerations of the horizontal shear in a T-beam, and of the

capacity of the concrete to grip the steel, are conspicuous by their

absence in the analyses of beams. If a reinforcing rod is curved up and

anchored over the support, the concrete is relieved of the shear, both

horizontal and vertical, incident to the stress in that rod. If a

reinforcing rod is bent up anywhere, and not carried to the support, and

not anchored over it, as is customary, the shear is all taken by the

concrete; and there is just the same shear in the concrete as though the

rods were straight.

For proper grip a straight rod should have a diameter of not more than

one two-hundredth of the span. For economy of material, it should not be

much smaller in diameter than this. With this balance in a beam,

assuming shear equal to bond, the rods should be spaced a distance

apart, equal to their perimeters. This is a rational and simple rule,

and its use would go a long way toward the adoption of standards.

Mr. Worcester is not logical in his criticism of the writer's method of

reinforcing a chimney. It is not necessary to assume that the concrete

is not stressed, in the imaginary plain concrete chimney, beyond that

which plain concrete could take in tension. The assumption of an

imaginary plain concrete chimney and determinations of tensile stresses

in the concrete are merely simplified methods of finding the tensile

stress. The steel can take just as much tensile stress if its amount is

determined in this way as it can if any other method is used. The

shifting of the neutral axis, to which Mr. Worcester refers, is another

of the fancy assumptions which cannot be realized because of initial and

unknown stresses in the concrete and steel.

Mr. Russell states that the writer scarcely touched on top reinforcement

in beams. This would come in the class of longitudinal rods in columns,

unless the reinforcement were stiff members. Mr. Russell's remarks, to

the effect that columns and short deep beams, doubly reinforced, should

be designed as framed structures, point to the conclusion that

structural beams and columns, protected with concrete, should be used in

such cases. If the ruling motive of designers were uniformly to use what

is most appropriate in each particular location and not to carry out

some system, this is just what would be done in many cases; but some

minds are so constructed that they take pleasure in such boasts as this:

"There is not a pound of structural steel in that building." A

broad-minded engineer will use reinforced concrete where it is most

appropriate, and structural steel or cast iron where these are most

appropriate, instead of using his clients' funds to carry out some

cherished ideas.

Mr. Wright appreciates the writer's idea, for the paper was not intended

to criticize something which is "good enough" or which "answers the

purpose," but to systematize or standardize reinforced concrete and put

it on a basis of rational analysis and common sense, such a basis as

structural designing has been or is being placed on, by a careful

weeding out of all that is irrational, senseless, and weak.

Mr. Chapman says that the practical engineer has never used such methods

of construction as those which the writer condemns. The methods are

common enough; whether or not those who use them are practical engineers

is beside the question.

As to the ability of the end connection of a stringer carrying flange

stress or bending moments, it is not uncommon to see brackets carrying

considerable overhanging loads with no better connection. Even wide

sidewalks of bridges sometimes have tension connections on rivet heads.

While this is not to be commended, it is a demonstration of the ability

to take bending which might be relied on, if structural design were on

as loose a basis as reinforced concrete.

Mr. Chapman assumes that stirrups are anchored at each end, and Fig. 3

shows a small hook to effect this anchorage. He does not show how

vertical stirrups can relieve a beam of the shear between two of these

stirrups.

The criticism the writer would make of Figs. 5 and 6, is that there is

not enough concrete in the stem of the T to grip the amount of steel

used, and the steel must be gripped in that stem, because it does not

run to the support or beyond it for anchorage. Steel members in a bridge

may be designed in violation of many of the requirements of

specifications, such as the maximum spacing of rivets, size of lattice

bars, etc.; the bridge will not necessarily fail or show weakness as

soon as it is put into service, but it is faulty and weak just the same.

Mr. Chapman says: "The practical engineer does not find * * * that the

negative moment is double the positive moment, because he considers the

live load either on one span only, or on alternate spans." It is just in

such methods that the "practical engineer" is inconsistent. If he is

going to consider the beams as continuous, he should find the full

continuous beam moment and provide for it. It is just this disposition

to take an advantage wherever one can be taken, without giving proper

consideration to the disadvantage entailed, which is condemned in the

paper. The "practical engineer" will reduce his bending moment in the

beam by a large fraction, because of continuity, but he will not

reinforce over the supports for full continuity. Reinforcement for full

continuity was not recommended, but it was intimated that this is the

only consistent method, if advantage is taken of continuity in reducing

the principal bending moment.

Mr. Chapman says that an arch should not be used where the abutments are

unstable. Unstable is a relative and indefinite word. If he means that

abutments for arches should never be on anything but rock, even such a

foundation is only quite stable when the abutment has a vertical rock

face to take horizontal thrusts. If arches could be built only under

such conditions, few of them would be built. Some settlement is to be

expected in almost any soil, and because of horizontal thrusts there is

also a tendency for arch abutments to rotate. It is this tendency which

opens up cracks in spandrels of arches, and makes the assumption of a

fixed tangent at the springing line, commonly made by the elastic

theorist, absolute foolishness.

Mr. Beyer has developed a novel explanation of the way stirrups act, but

it is one which is scarcely likely to meet with more serious

consideration than the steel girder to which he refers, which has

neither web plate nor diagonals, but only verticals connecting the top

and bottom flanges. This style of girder has been considered by American

engineers rather as a curiosity, if not a monstrosity. If vertical

stirrups acted to reinforce little vertical cantilevers, there would

have to be a large number of them, so that each little segment of the

beam would be insured reinforcement.

The writer is utterly at a loss to know what Professor Ostrup means by

his first few paragraphs. He says that in the first point two designs

are mentioned and a third condemned. The second design, whatever it is,

he lays at the writer's door in these words: "The author's second design

is an invention of his own, which the Profession at large is invited to

adopt." In the first point sharp bends in reinforcing rods are condemned

and curves recommended. Absolutely nothing is said of "a reinforced

concrete beam arranged in the shape of a rod, with separate concrete

blocks placed on top of it without being connected."

In reply to Professor Ostrup, it should be stated that the purpose of

the paper is not to belittle the importance of the adhesion or grip of

concrete on steel, but to point out that the wonderful things this grip

is supposed to do, as exhibited by current design, will not stand the

test of analysis.

Professor Ostrup has shown a new phase of the stress in shear rods. He

says they are in bending between the centers of compressive resultants.

We have been told in books and reports that these rods are in stress of

some kind, which is measured by the sectional area of the rod. No hint

has been given of designing stirrups for bending. If these rods are not

in shear, as stated by Professor Ostrup, how can they be in bending in

any such fashion as that indicated in Fig. 12?

Professor Ostrup's analysis, by which he attempts to justify stirrups

and to show that vertical stirrups are preferable, merely treats of

local distribution of stress from short rods into concrete. Apparently,

it would work the same if the stirrups merely touched the tension rod.

His analysis ignores the vital question of what possible aid the stirrup

can be in relieving the concrete between stirrups of the shear of the

beam.

The juggling of bending moments in beams is not compensating. The

following is a concrete example. Some beams of a span of about 20 ft.,

were framed into double girders at the columns. The beams were

calculated as partly continuous, though they were separated at their

ends by about 1-1/2 or 2 ft., the space between the girders. The beams

had 1-1/8-in. tension rods in the bottom. At the supports a short

1/4-in. rod was used near the top of the beam for continuity. Does this

need any comment? It was not the work of a novice or of an inexperienced

builder.

Professor Ostrup's remarks about the shifting of the neutral axis of a

beam and of the pressure line of an arch are based on theory which is

grounded in impossible assumptions. The materials dealt with do not

justify these assumptions or the hair-splitting theory based thereon.

His platitudes about the danger of misplacing reinforcement in an arch

are hardly warranted. If the depth and reinforcement of an arch ring are

added to, as the inelastic, hinge-end theory would dictate, as against

the elastic theory, it will strengthen the arch just as surely as it

would strengthen a plate girder to thicken the web and flange angles.

The writer's complaint is not that the theories of reinforced concrete

are not fully developed. They are developed too highly, developed out of

all comparison with the materials dealt with. It is just because

reinforced concrete structures are being built in increasing numbers

that it behooves engineers to inject some rationality (not high-strung

theory) into their designs, and drop the idea that "whatever is is

right."

Mr. Porter has much to say about U-bars. He states that they are useful

in holding the tension bars in place and in tying the slab to the stem

of a T-beam. These are legitimate functions for little loose rods; but

why call them shear rods and make believe that they take the shear of a

beam? As to stirrups acting as dowel pins, the writer has already

referred to this subject. Answering a query by Mr. Porter, it may be

stated that what would counteract the horizontal cleaving force in a

beam is one or more rods curved up to the upper part of the beam and

anchored at the support or run into the next span. Strangely enough, Mr.

Porter commends this very thing, as advocated in the paper. The

excellent results shown by the test referred to by him can well be

contrasted with some of the writer's tests. This floor was designed for

250 lb. per sq. ft. When that load was placed on it, the deflection was

more than 1 in. in a span of 20 ft. No rods were curved up and run over

the supports. It was a stirrup job.

Mr. Porter intimates that the correct reinforced concrete column may be

on lines of concrete mixed with nails or wires. There is no doubt but

that such concrete would be strong in compression for the reason that it

is strong in tension, but a column needs some unifying element which is

continuous. A reinforced column needs longitudinal rods, but their

office is to take tension; they should not be considered as taking

compression.

Mr. Goodrich makes this startling remark: "It is a well-known fact that

the bottom chords in queen-post trusses are useless, as far as

resistance to tension is concerned." The writer cannot think that he

means by this that, for example, a purlin made up of a 3 by 2-in. angle

and a 5/8-in. hog-rod would be just as good with the rod omitted. If

queen-post trusses are useless, some hundreds of thousands of hog-rods

in freight cars could be dispensed with.

Mr. Goodrich misunderstands the reference to the "only rational and only

efficient design possible." The statement is that a design which would

be adopted, if slabs were suspended on rods, is the only rational and

the only efficient design possible. If the counterfort of a retaining

wall were a bracket on the upper side of a horizontal slab projecting

out from a vertical wall, and all were above ground, the horizontal slab

being heavily loaded, it is doubtful whether any engineer would think of

using any other scheme than diagonal rods running from slab to wall and

anchored into each. This is exactly the condition in this shape of

retaining wall, except that it is underground.

Mr. Goodrich says that the writer's reasoning as to the sixth point is

almost wholly facetious and that concrete is very strong in pure shear.

The joke, however, is on the experimenters who have reported concrete

very strong in shear. They have failed to point out that, in every case

where great strength in shear is manifested, the concrete is confined

laterally or under heavy compression normal to the sheared plane.

Stirrups do not confine concrete in a direction normal to the sheared

plane, and they do not increase the compression. A large number of

stirrups laid in herring-bone fashion would confine the concrete across

diagonal planes, but such a design would be wasteful, and the common

method of spacing the stirrups would not suggest their office in this

capacity.

As to the writer's statements regarding the tests in Bulletin No. 29 of

the University of Illinois being misleading, he quotes from that

bulletin as follows:

"Until the concrete web has failed in diagonal tension and diagonal

cracks have formed there must be little vertical deformation at the

plane of the stirrups, so little that not much stress can have

developed in the stirrups." * * * "It is evident, then, that until

the concrete web fails in diagonal tension little stress is taken

by the stirrups." * * * "It seems evident from the tests that the

stirrups did not take much stress until after the formation of

diagonal cracks." * * * "It seems evident that there is very little

elongation in stirrups until the first diagonal crack forms, and

hence that up to this point the concrete takes practically all the

diagonal tension." * * * "Stirrups do not come into action, at

least not to any great extent, until the diagonal crack has

formed."

In view of these quotations, the misleading part of the reference to the

tests and their conclusion is not so evident.

The practical tests on beams with suspension rods in them, referred to

by Mr. Porter, show entirely different results from those mentioned by

Mr. Goodrich as being made by Mörsch. Tests on beams of this sort, which

are available in America, seem to show excellent results.

Mr. Goodrich is somewhat unjust in attributing failures to designs which

are practically in accordance with the suggestions under Point Seven. In

Point Seven the juggling of bending moments is condemned--it is

condemnation of methods of calculating. Point Seven recommends

reinforcing a beam for its simple beam moment. This is the greatest

bending it could possibly receive, and it is inconceivable that failure

could be due to this suggestion. Point Seven recommends a reasonable

reinforcement over the support. This is a matter for the judgment of the

designer or a rule in specifications. Failure could scarcely be

attributed to this. It is the writer's practice to use reinforcement

equal to one-half of the main reinforcement of the beam across the

support; it is also his practice to curve up a part of the beam

reinforcement and run it into the next span in all beams needing

reinforcement for shear; but the paper was not intended to be a treatise

on, nor yet a general discussion of, reinforced concrete design.

Mr. Goodrich characterizes the writer's method of calculating reinforced

concrete chimneys as crude. It is not any more crude than concrete. The

ultra-theoretic methods are just about as appropriate as calculations of

the area of a circle to hundredths of a square inch from a paced-off

diameter. The same may be said of deflection calculations.

Mr. Goodrich has also appreciated the writer's spirit in presenting this

paper. Attention to details of construction has placed structural steel

designing on the high plane on which it stands. Reinforced concrete

needs the same careful working out of details before it can claim the

same recognition. It also needs some simplification of formulas. Witness

the intricate column formulas for steelwork which have been buried, and

even now some of the complex beam formulas for reinforced concrete have

passed away.

Major Sewell, in his discussion of the first point, seems to object

solely to the angle of the bent-up portion of the rod. This angle could

have been much less, without affecting the essence of the writer's

remarks. Of course, the resultant, _b_, would have been less, but this

would not create a queen-post at the sharp bend of the bar. Major Sewell

says that he "does not remember ever to have seen just the type of

construction shown in Fig. 1, either used or recommended." This type of

beam might be called a standard. It is almost the insignia of a

reinforced concrete expert. A little farther on Major Sewell says that

four beams tested at the University of Illinois were about as nearly

like Fig. 1 as anything he has ever seen in actual practice. He is the

only one who has yet accused the writer of inventing this beam.

If Major Sewell's statement that he has never seen the second point

exemplified simply means that he has never seen an example of the bar

bent up at the identical angle given in the paper, his criticism has not

much weight.

Major Sewell's comment on the retaining wall begs the question. Specific

references to examples have been given in which the rods of a

counterfort are not anchored into the slabs that they hold by tension,

save by a few inches of embedment; an analysis has also been cited in

which the counterfort is considered as a beam, and ties in the great

weight of the slab with a few "shear rods," ignoring the anchorage of

either horizontal, vertical, or diagonal rods. It is not enough that

books state that rods in tension need anchorage. They should not show

examples of rods that are in pure tension and state that they are merely

thrown in for shear. Transverse rods from the stem to the flange of a

T-beam, tie the whole together; they prevent cracking, and thereby allow

the shearing strength of the concrete to act. It is not necessary to

count the rods in shear.

Major Sewell's comparison of a stirrup system and a riveted truss is not

logical. The verticals and diagonals of a riveted truss have gusset

plates which connect symmetrically with the top chord. One line of

rivets or a pin in the center line of the top chord could be used as a

connection, and this connection would be complete. To distribute rivets

above and below the center line of the top chord does not alter the

essential fact that the connection of the web members is complete at the

center of the top chord. The case of stirrups is quite different. Above

the centroid of compression there is nothing but a trifling amount of

embedment of the stirrup. If 1/2-in. stirrups were used in an 18-in.

beam, assuming that 30 diameters were enough for anchorage, the centroid

of compression would be, say, 3 in. below the top of the beam, the

middle point of the stirrup's anchorage would be about 8 in., and the

point of full anchorage would be about 16 in. The neutral axis would

come somewhere between. These are not unusual proportions. Analogy with

a riveted truss fails; even the anchorage above the neutral axis is far

from realization.

Major Sewell refers to shallow bridge stringers and the possibility of

failure at connections by continuity or deflection. Structural engineers

take care of this, not by reinforcement for continuity but by ample

provision for the full bending moment in the stringer and by ample

depth. Provision for both the full bending moment and the ample depth

reduces the possibilities of deflection at the floor-beams.

Major Sewell seems also to have assumed that the paper was a general

discussion on reinforced concrete design. The idea in pointing out that

a column having longitudinal rods in it may be weaker than a plain

concrete column was not to exalt the plain concrete column but to

degrade the other. A plain concrete column of any slenderness would

manifestly be a gross error. If it can be shown that one having only

longitudinal rods may be as bad, or worse, instead of being greatly

strengthened by these rods, a large amount of life and property may be

saved.

A partial reply to Mr. Thompson's discussion will be found in the

writer's response to Mr. Mensch. The fault with Mr. Thompson's

conclusions lies in the error of basing them on averages. Average

results of one class are of little meaning or value when there is a wide

variation between the extremes. In the tests of both the concrete-steel

and the plain concrete which Mr. Thompson averages there are wide

variations. In the tests made at the University of Illinois there is a

difference of almost 100% between the minimum and maximum results in

both concrete-steel and plain concrete columns.

Average results, for a comparison between two classes, can mean little

when there is a large overlap in the individual results, unless there is

a large number of tests. In the seventeen tests made at the University

of Illinois, which Mr. Thompson averages, the overlap is so great that

the maximum of the plain columns is nearly 50% greater than the minimum

of the concrete-steel columns.

If the two lowest tests in plain concrete and the two highest in

concrete-steel had not been made, the average would be in favor of the

plain concrete by nearly as much as Mr. Thompson's average now favors

the concrete-steel columns. Further, if these four tests be eliminated,

only three of the concrete-steel columns are higher than the plain

concrete. So much for the value of averages and the conclusions drawn

therefrom.

It is idle to draw any conclusions from such juggling of figures, except

that the addition of longitudinal steel rods is altogether

problematical. It may lessen the compressive strength of a concrete

column. Slender rods in such a column cannot be said to reinforce it,

for the reason that careful tests have been recorded in which columns of

concrete-steel were weaker than those of plain concrete.

In the averages of the Minneapolis tests Mr. Thompson has compared the

results on two plain concrete columns with the average of tests on an

indiscriminate lot of hooped and banded columns. This method of boosting

the average shows anything but "critical examination" on his part.

Mr. Thompson, on the subject of Mr. Withey's tests, compares plain

concrete of square cross-section with concrete-steel of octagonal

section. As stated before, this is not a proper comparison. In a fragile

material like concrete the corners spall off under a compressive load,

and the square section will not show up as well as an octagonal or round

one.

Mr. Thompson's contention, regarding the Minneapolis tests, that the

concrete outside of the hoops should not be considered, is ridiculous.

If longitudinal rods reinforce a concrete column, why is it necessary to

imagine that a large part of the concrete must be assumed to be

non-existent in order to make this reinforcement manifest? An imaginary

core could be assumed in a plain concrete column and any desired results

could be obtained. Furthermore, a properly hooped column does not enter

into this discussion, as the proposition is that slender longitudinal

rods do not reinforce a concrete column; if hoops are recognized, the

column does not come under this proposition.

Further, the proposition in the writer's fifteenth point does not say

that the steel takes no part of the compression of a column. Mr.

Thompson's laborious explanation of the fact that the steel receives a

share of the load is needless. There is no doubt that the steel receives

a share of the load--in fact, too great a share. This is the secret of

the weakness of a concrete column containing slender rods. The concrete

shrinks, the steel is put under initial compression, the load comes more

heavily on the steel rods than on the concrete, and thus produces a most

absurd element of construction--a column of slender steel rods held

laterally by a weak material--concrete. This is the secret of nearly all

the great wrecks in reinforced concrete: A building in Philadelphia, a

reservoir in Madrid, a factory in Rochester, a hotel in California. All

these had columns with longitudinal rods; all were extensive

failures--probably the worst on record; not one of them could possibly

have failed as it did if the columns had been strong and tough. Why use

a microscope and search through carefully arranged averages of tests on

nursery columns, with exact central loading, to find some advantage in

columns of this class, when actual experience is publishing in bold type

the tremendously important fact that these columns are utterly

untrustworthy?

It is refreshing to note that not one of the writer's critics attempts

to defend the quoted ultimate strength of a reinforced concrete column.

Even Mr. Thompson acknowledges that it is not right. All of which, in

view of the high authority with whom it originated, and the wide use it

has been put to by the use of the scissors, would indicate that at last

there is some sign of movement toward sound engineering in reinforced

concrete.

In conclusion it might be pointed out that this discussion has brought

out strong commendation for each of the sixteen indictments. It has also

brought out vigorous defense of each of them. This fact alone would seem

to justify its title. A paper in a similar strain, made up of

indictments against common practices in structural steel design,

published in _Engineering News_ some years ago, did not bring out a

single response. While practice in structural steel may often be faulty,

methods of analysis are well understood, and are accepted with little

question.