Mr. Godfrey wishes to remedy this by replacing the diagonals by rods curved to a radius of from twenty to thirty times their diameter. In common cases this radius will be about equal to the depth of the beam. Let this be assumed to be true. It cannot be assumed that these rods take any appreciable vertical shear until their slope is 30° from the horizontal, for before this the tension in the rod would be more than twice the shear which causes it. Therefore, these curved rods, assuming them to be of sufficient size to take, as a vertical component, the shear on any vertical plane between the point where it slopes 30° and its point of maximum slope, would need to be spaced at, approximately, one-half the depth of the beam. Straight rods of equivalent strength, at 45° with the axis of the beam, at this same spacing (which would be ample), would be 10% less in length.
Mr. Godfrey states:
"Of course 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."
"Of course 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."
He then overlooks the fact that at the end of a beam, such as he has shown, the maximum tension is diagonal, and at the neutral axis, not at the bottom; and the rod is in the best position to resist failure on the plane,AB, if its end is sufficiently well anchored. That this rod should be anchored is, as he states, undoubtedly so, but his implied objection to a bent end, as opposed to a nut, seems to the writer to be unfounded. In some recent tests, on rods bent at right angles, at a point 5 diameters distant from the end, and with a concrete backing, stress was developed equal to the bond stress on a straight rod embedded for a length of about 30 diameters, and approximately equal to the elastic limit of the rod, which, for reinforcing purposes, is its ultimate stress.
Concerning the vertical stirrups to which Mr. Godfrey refers, there is no doubt that they strengthen beams against failure by diagonal tension or, as more commonly known, shear failures. That they are not effective in the beam as built is plain, for, if one considers a vertical plane between the stirrups, the concrete must resist the shear on this plane, unless dependence is placed on that in the longitudinal reinforcement. This, the author states, is often done, but the practice is unknown to the writer, who does not consider it of any value; certainly the stirrups cannot aid.
Suppose, however, that the diagonal tension is above the ultimate stress for the concrete, failure of the concrete will then occur on planes perpendicular to the line of maximum tension, approximately 45° at the end of the beam. If the stirrups are spaced close enough, however, and are of sufficient strength so that these planes of failure all cut enough steel to take as tension the vertical shear on the plane, then these cracks will be very minute and will be distributed, as is the case in the center of the lower part of the beam. These stirrups will then take as tension the vertical shear on any plane, and hold the beam together, so that the friction on these planes will keep up the strength of the concrete in horizontal shear. The concrete at the end of a simple beam is better able to take horizontal shear than vertical, because the compression on a horizontal plane is greater than that on a vertical plane. This idea concerning the action of stirrups falls under the ban of Mr. Godfrey's statement, that any member which "cannot act until failure has started, is not a proper element of design," but this is not necessarily true. For example, Mr. Godfrey says "the steel in the tension side of the beam should be considered as taking all the tension." This is undoubtedly true, but it cannot take place until the concrete has failed in tension at this point. If used, vertical tension members should be considered as taking all the vertical shear, and, as Mr. Godfrey states, they should certainly have their ends anchored so as to develop the strength for which they have been calculated.
The writer considers diagonal reinforcement to be the best for shear, and it should be used, especially in all cases of "unit" reinforcement; but, in some cases, stirrups can and do answer in the manner suggested; and, for reasons of practical construction, are sometimes best with "loose rod" reinforcement.
J.C. Meem, M. Am. Soc. C. E.(by letter).—The writer believes that there are some very interesting points in the author's somewhat iconoclastic paper which are worthy of careful study, and, if it be shown that he is right in most of, or even in any of, his assumptions, a further expression of approval is due to him. Few engineers have the time to show fully, by a process ofreductio ad absurdum, that all the author's points are, or are not, well considered or well founded, but the writer desires to say that he has read this paper carefully, and believes that its fundamental principles are well grounded. Further, he believes that intricate mathematical formulas have no place in practice. This is particularly true where these elaborate mathematical calculationsare founded on assumptions which are never found in practice or experiment, and which, even in theory, are extremely doubtful, and certainly are not possible within those limits of safety wherein the engineer is compelled to work.
The writer disagrees with the author in one essential point, however, and that is in the wholesale indictment of special reinforcement, such as stirrups, shear rods, etc. In the ordinary way in which these rods are used, they have no practical value, and their theoretical value is found only when the structure is stressed beyond its safe limits; nevertheless, occasions may arise when they have a definite practical value, if properly designed and placed, and, therefore, they should not be discriminated against absolutely.
Quoting the author, that "destructive criticism is of no value unless it offers something in its place," and in connection with the author's tenth point, the writer offers the following formula which he has always used in conjunction with the design of reinforced concrete slabs and beams. It is based on the formula for rectangular wooden beams, and assumes that the beam is designed on the principle that concrete in tension is as strong as that in compression, with the understanding that sufficient steel shall be placed on the tension side to make this true, thus fixing the neutral axis, as the author suggests, in the middle of the depth, that is,M= (1/6)b d2S,M, of course, being the bending moment, andbandd, the breadth and depth, in inches.Sis usually taken at from 400 to 600 lb., according to the conditions. In order to obtain the steel necessary to give the proper tensile strength to correspond with the compression side, the compression and tension areas of the beam are equated, that is
where
a= the area of steel per linear foot,xII= the distance from the center of the steel to the outer fiber, andSII= the strength of the steel in tension.
Then for a beam, 12 in. wide,
or
Carrying this to its conclusion, we have, for example, in a beam 12 in. deep and 12 in. wide,
The writer has used this formula very extensively, in calculating new work and also in checking other designs built or to be built, and he believes its results are absolutely safe. There is the further fact to its credit, that its simplicity bars very largely the possibility of error from its use. He sees no reason to introduce further complications into such a formula, when actual tests will show results varying more widely than is shown by a comparison between this simple formula and many more complicated ones.
George H. Myers, Jun. Am. Soc. C. E.(by letter).—This paper brings out a number of interesting points, but that which strikes the writer most forcibly is the tenth, in regard to elaborate theories and complicated formulas for beams and slabs. The author's stand for simplicity in this regard is well taken. A formula for the design of beams and slabs need not be long or complicated in any respect. It can easily be obtained from the well-known fact that the moment at any point divided by the distance between the center of compression and the center of tension at that point gives the tension (or compression) in the beam.
The writer would place the neutral axis from 0.42 to 0.45 of the effective depth of the beam from the compression side rather than at the center, as Mr. Godfrey suggests. This higher position of the neutral axis is the one more generally shown by tests of beams. It gives the formulaM= 0.86dAsf, orM= 0.85dAsf, which the writer believes is more accurate thanM= 5/6dAsf, or 0.83-1/3dAsf, which would result if the neutral axis were taken at the center of the beam.
d= depth of the beam from the compression side to the centerof the steel;As= the area of the steel;andf= the allowable stress per square inch in the steel.
The difference, however, is very slight, the results from the two formulas being proportional to the two factors, 83-1/3 and 85 or 86. This formula gives the area of steel required for the moment. The percentage of steel to be used can easily be obtained from the allowable stresses in the concrete and the steel, and the dimensions of the beam can be obtained in the simplest manner. This formula is used with great success by one of the largest firms manufacturing reinforcing materials and designing concrete structures. It is well-known to the Profession, and the reason for using any other method, involving the Greek alphabet and many assumptions, is unknown to the writer. The only thing to assume—if it can be called assuming when there are so many tests to locate it—is the position of the neutral axis. A slight difference in this assumption affects the resulting design very little, and is inappreciable, from a practical point of view. It can besafely said that the neutral axis is at, or a little above, the center of the beam.
Further, it would seem that the criticism to the effect that the initial stress in the concrete is neglected is devoid of weight. As far as the designer is concerned, the initial stress is allowed for. The values for the stresses used in design are obtained from tests on blocks of concrete which have gone through the process of setting. Whatever initial stress exists in concrete due to this process of setting exists also in these blocks when they are tested. The value of the breaking load on concrete given by any outside measuring device used in these tests, is the value of that stress over and above this initial stress. It is this value with which we work. It would seem that, if the initial stress is neglected in arriving at a safe working load, it would be safe to neglect it in the formula for design.
Edwin Thacher, M. Am. Soc. C. E.(by letter).—The writer will discuss this paper under the several "points" mentioned by the author.
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.
Second Point.—The remarks on the first point are also applicable to the second one. Rod 3 provides for the shear.
Third Point.—In a beam, the shear rods run through the compression parts of the concrete and have sufficient anchorage. In a counterfort, the inclined rods are sufficient to take the overturning stress. The horizontal rods support the front wall and provide for shrinkage. The vertical rods also provide for shrinkage, and assist the diagonal rods against overturning. The anchorage is sufficient in all cases, and the proposed method is no more effective.
Fourth Point.—In bridge pins, bending and bearing usually govern, but, in case a wide bar pulled on a pin between the supports close to the bar, as happens in bolsters and post-caps of combination bridges and in other locations, shear would govern. Shear rods in concrete-steel beams are proportioned to take the vertical and diagonal shearing stresses. If proportioned for less stress per square inch than is used in the bottom bars, this cannot be considered dangerous practice.
Fifth Point.—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.
Sixth Point.—The common method is not "to assume each shear member as taking the horizontal shear occurring in the space frommember to member," but to take all the shear from the center of the beam up to the bar in question.
Cracks do not necessarily endanger the safety of a beam. Any device that will prevent the cracks from opening wide enough to destroy the beam, is logical. By numerous experiments, Mr. Thaddeus Hyatt found that nuts and washers at the ends of reinforcing bars were worse than useless, and added nothing to the strength of the beams.
Seventh Point.—Beams can be designed, supported at the ends, fully continuous, or continuous to a greater or less extent, as desired. The common practice is to design slabs to take a negative moment over the supports equal to one-half the positive moment at the center, or to bend up the alternate rods. This is simple and good practice, for no beam can fail as long as a method is provided by which to take care of all the stresses without overstraining any part.
Eighth Point.—Bars in the bottom of a reinforced concrete beam are often placed too close to one another. The rule of spacing the bars not less than three diameters apart, is believed to be good practice.
Ninth Point.—To disregard the theory of T-beams, and work by rule-of-thumb, can hardly be considered good engineering.
Tenth Point.—The author appears to consider theories for reinforced concrete beams and slabs as useless refinements, but as long as theory and experiment agree so wonderfully well, theories will undoubtedly continue to be used.
Eleventh Point.—Calculations for chimneys are somewhat complex, but are better and safer than rule-of-thumb methods.
Twelfth Point.—Deflection is not very important.
Thirteenth Point.—The conclusion of the Austrian Society of Engineers and Architects, after numerous experiments, was that the elastic theory of the arch is the only true theory. No arch designed by the elastic theory was ever known to fail, unless on account of insecure foundations, therefore engineers can continue to use it with confidence and safety.
Fourteenth Point.—Calculations for temperature stresses, as per theory, are undoubtedly correct for the variations in temperature assumed. Similar calculations can also be made for shrinkage stresses, if desired. This will give a much better idea of the stresses to be provided for, than no calculations at all.
Fifteenth Point.—Experiments show that slender longitudinal rods, poorly supported, and embedded in a concrete column, add little or nothing to its strength; but stiff steel angles, securely latticed together, and embedded in the concrete column, will greatly increase its strength, and this construction is considered the most desirable when the size of the column has to be reduced to a minimum.
Sixteenth Point.—The commonly accepted theory of slabs supported on four sides can be correctly applied to reinforced concrete slabs, as it is only a question of providing for certain moments in the slab. This theory shows that unless the slab is square, or nearly so, nothing is to be gained by such construction.
C.A.P. Turner, M. Am. Soc. C. E.(by letter).—Mr. Godfrey has expressed his opinion on many questions in regard to concrete construction, but he has adduced no clean-cut statement of fact or tests, in support of his views, which will give them any weight whatever with the practical matter-of-fact builder.
The usual rules of criticism place the burden of proof on the critic. Mr. Godfrey states that if his personal opinions are in error, it should be easy to prove them to be so, and seems to expect that the busy practical constructor will take sufficient interest in them to spend the time to write a treatise on the subject in order to place him right in the matter.
The writer will confine his discussion to only a few points of the many on which he disagrees with Mr. Godfrey.
First, regarding stirrups: These may be placed in the beam so as to be of little practical value. They were so placed in the majority of the tests made at the University of Illinois. Such stirrups differ widely in value from those used by Hennebique and other first-class constructors.
Mr. Godfrey's idea is that the entire pull of the main reinforcing rod should be taken up apparently at the end. When one frequently sees slabs tested, in which the steel breaks at the center, with no end anchorage whatever for the rods, the soundness of Mr. Godfrey's position may be questioned.
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.
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.
The writer will state a few facts regarding work which he has executed. Among such work have been columns in a number of buildings, with an 18-in. core, and carrying more than 500 tons; also columns in one building, which carry something like 1100 tons on a 27-in. core. In each case there is about 1-1/2 in. of concrete outside the core for a protective coating. The working stress on the core, if it takes the load, is approximately equal to the ultimate strength of the concrete in cubes, to say nothing of the strength of cylinders fifteen times their diameter in height. These values have been used withentire confidence after testing full-sized columns designed with the proper proportions of vertical steel and hooping, and are regarded by the writer as having at least double the factor of safety used in ordinary designs of structural steel.
An advantage which the designer in concrete has over his fellow-engineer in the structural steel line, lies in the fact that, with a given type of reinforcement, his members are similar in form, and when the work is executed with ordinary care, there is less doubt as to the distribution of stress through a concrete column, than there is with the ordinary structural steel column, since the core is solid and the conditions are similar in all cases.
Tests of five columns are submitted herewith. The columns varied little in size, but somewhat in the amount of hooping, with slight differences in the vertical steel. The difference between Columns 1 and 3 is nearly 50%, due principally to the increase in hooping, and to a small addition in the amount of vertical steel. As to the efficiency of hooping and vertical reinforcement, the question may be asked Mr. Godfrey, and those who share his views, whether a column without reinforcement can be cast, which will equal the strength of those, the tests of which are submitted.
Marks on column—none.
Reinforcement—eight 1-1/8-in. round bars vertically.
Band spacing—- 9 in. vertically.
Hooped with seven 32-in. wire spirals about 2-in. raise.
Outside diameter of hoops—14-1/2 in.
Total load at failure—1,360,000 lb.
Remarks.—Point of failure was about 22 in. from the top. Little indication of failure until ultimate load was reached.
Some slight breaking off of concrete near the top cap, due possibly to the cap not being well seated in the column itself.
Marks on column—Box 4.
Reinforcement—eight 1-1/8-in. round bars vertically.
Band spacing about 13 in. vertically.
Wire spiral about 3-in. pitch.
Point of failure about 18 in. from top.
Top of cast-iron cap cracked at four corners.
Ultimate load—1,260,000 lb.
Remarks.—Both caps apparently well seated, as was the case with all the subsequent tests.
Marks on column—4-B.
Reinforcement—eight 7/8-in. round bars vertically.
Hoops—1-3/4 in. × 3/16 in. × 14 in. outside diameter.
Band spacing—13 in. vertically.
Ultimate load—900,000 lb.
Point of failure about 2 ft. from top.
Remarks.—Concrete, at failure, considerably disintegrated, probably due to continuance of movement of machine after failure.
Marks on column—Box 4.
Reinforcement—eight 1-in. round bars vertically.
Hoops spaced 8 in. vertically.
Wire spirals as on other columns.
Total load at failure—1,260,000 lb.
Remarks.—First indications of failure were nearest the bottom end of the column, but the total failure was, as in all other columns, within 2 ft. of the top. Large cracks in the shell of the column extended from both ends to very near the middle. This was the most satisfactory showing of all the columns, as the failure was extended over nearly the full length of the column.
Marks on column—none.
Reinforcement—eight 7/8-in. bars vertically.
Hoops spaced 10 in. vertically.
Outside diameter of hoops—14-1/2 in.
Wire spiral as before.
Load at failure—1,100,000 lb.
Ultimate load—1,130,000 lb.
Remarks.—The main point of failure in this, as in all other columns, was within 2 ft. of the top, although this column showed some scaling off at the lower end.
In these tests it will be noted that the concrete outside of the hooped area seems to have had very little value in determining the ultimate strength; that, figuring the compression on the core area and deducting the probable value of the vertical steel, these columns exhibited from 5,000 to 7,000 lb. per sq. in. as the ultimate strength of the hooped area, not considering the vertical steel. Some of them run over 8,000 lb.
The concrete mixture was 1 part Alpena Portland cement, 1 part sand, 1-1/2 parts buckwheat gravel and 3-1/2 parts gravel ranging from 1/4 to 3/4 in. in size.
The columns were cast in the early part of December, and tested in April. The conditions under which they hardened were not particularly favorable, owing to the season of the year.
The bands used were 1-3/4 by 1/4 in., except in the light column, where they were 1-3/4 by 3/16 in.
In his remarks regarding the tests at Minneapolis, Minn., Mr. Godfrey has failed to note that these tests, faulty as they undoubtedly were, both in the execution of the work, and in the placing of the reinforcement, as well as in the character of the hooping used, were sufficient to satisfy the Department of Buildings that rational design took into consideration the amount of hooping and the amount of verticalsteel, and on a basis not far from that which the writer considers reasonable practice.
Again, Mr. Godfrey seems to misunderstand the influence of Poisson's ratio in multiple-way reinforcement. If Mr. Godfrey's ideas are correct, it will be found that a slab supported on two sides, and reinforced with rods running directly from support to support, is stronger than a similar slab reinforced with similar rods crossing it diagonally in pairs. Tests of these two kinds of slabs show that those with the diagonal reinforcement develop much greater strength than those reinforced directly from support to support. Records of small test slabs of this kind will be found in the library of the Society.
Mr. Godfrey makes the good point that the accuracy of an elastic theory must be determined by the elastic deportment of the construction under load, and it seems to the writer that if authors of textbooks would pay some attention to this question and show by calculation that the elastic deportment of slabs is in keeping with their method of figuring, the gross errors in the theoretical treatment of slabs in the majority of works on reinforced concrete would be remedied.
Although he makes the excellent point noted, Mr. Godfrey very inconsistently fails to do this in connection with his theory of slabs, otherwise he would have perceived the absurdity of any method of calculating a multiple-way reinforcement by endeavoring to separate the construction into elementary beam strips. This old-fashioned method was discarded by the practical constructor many years ago, because he was forced to guarantee deflections of actual construction under severe tests. Almost every building department contains some regulation limiting the deflection of concrete floors under test, and yet no commissioner of buildings seems to know anything about calculating deflections.
In the course of his practice the writer has been required to give surety bonds of from $50,000 to $100,000 at a time, to guarantee under test both the strength and the deflection of large slabs reinforced in multiple directions, and has been able to do so with accuracy by methods which are equivalent to considering Poisson's ratio, and which are given in his book on concrete steel construction.
Until the engineer pays more attention to checking his complicated theories with facts as determined by tests of actual construction, the view, now quite general among the workers in reinforced concrete regarding him will continue to grow stronger, and their respect for him correspondingly less, until such time as he demonstrates the applicability of his theories to ordinary every-day problems.
Paul Chapman, Assoc. M. Am. Soc. C. E.(by letter).—Mr. Godfrey has pointed out, in a forcible manner, several bad features of text-book design of reinforced concrete beams and retaining walls. The practical engineer, however, has never used such methods of construction. Mr. Godfrey proposes certain rules for the calculation of stresses, but there are no data of experiments, or theoretical demonstrations, to justify their use.
It is also of the utmost importance to consider the elastic behavior of structures, whether of steel or concrete. To illustrate this, the writer will cite a case which recently came to his attention. A roof was supported by a horizontal 18-in. I-beam, 33 ft. long, the flanges of which were coped at both ends, and two 6 by 4-in. angles, 15 ft. long, supporting the same, were securely riveted to the web, thereby forming a frame to resist lateral wind pressure. Although the 18-in. I-beam was not loaded to its full capacity, its deflection caused an outward flexure of 3/4 in. and consequent dangerous stresses in the 6 by 4-in. angle struts. The frame should have been designed as a structure fixed at the base of the struts. The importance of the elastic behavior of a structure is forcibly illustrated by comparing the contract drawings for a great cantilever bridge which spans the East River with the expert reports on the same. Due to the neglect of the elastic behavior of the structure in the contract drawings, and another cause, the average error in the stresses of 290 members was 18-1/2%, with a maximum of 94 per cent.
Mr. Godfrey calls attention to the fact that stringers in railroad bridges are considered as simple beams; this is theoretically proper because the angle knees at their ends can transfer practically no flange stress. It is also to be noted that when stringers are in the plane of a tension chord, they are milled to exact lengths, and when in the plane of a compression chord, they are given a slight clearance in order to prevent arch action.
Fig. 3.Fig. 3.
The action of shearing stresses in concrete beams may be illustrated by reference to the diagrams inFig. 3, where the beams are loaded with a weight,W. The portion ofWtraveling to the left support, moves in diagonal lines, varying from many sets of almost vertical lines to a single diagonal. The maximum intensity of stress probably would be in planes inclined about 45°, since, considered independently, they produce the least deflection. While the load,W, remains relatively small, producing but moderate stresses in the steel in the bottom flange, the concrete will carry a considerable portion of the bottom flange tension; when the loadWis largely increased, the coefficient of elasticity of the concrete in tension becomes small, or zero, if small fissures appear, and the concrete is unable to transfer the tensionin diagonal planes, and failure results. For a beam loaded with a single load,W, the failure would probably be in a diagonal line near the point of application, while in a uniformly loaded beam, it would probably occur in a diagonal line near the support, where the shear is greatest.
It is evident that the introduction of vertical stirrups, as atb, or the more rational inclined stirrups, as atc, influences the action of the shearing forces as indicated, the intensity of stress at the point of connection of the stirrups being high. It is advisable to space the stirrups moderately close, in order to reduce this intensity to reasonable limits. If the assumption is made that the diagonal compression in the concrete acts in a plane inclined at 45°, then the tension in the vertical stirrups will be the vertical shear times the horizontal spacing of the stirrups divided by the distance, center to center, of the top and bottom flanges of the beam. If the stirrups are inclined at 45°, the stress in them would be 0.7 the stress in vertical stirrups with the same spacing. Bending up bottom rods sharply, in order to dispense with suspenders, is bad practice; the writer has observed diagonal cracks in the beams of a well-known building in New York City, which are due to this cause.
Fig. 4.Fig. 4.
In several structures which the writer has recently designed, he has been able to dispense with stirrups, and, at the same time, effect a saving in concrete, by bending some of the bottom reinforcing rods and placing a bar between them and those which remain horizontal. A typical detail is shown inFig. 4. The bend occurs at a point where the vertical component of the stress in the bent bars equals the vertical shear, and sufficient bearing is provided by the short cross-bar. The bars which remain horizontal throughout the beam, are deflected at the center of the beam in order to obtain the maximum effective depth. There being no shear at the center, the bars are spaced as closely as possible, and still provide sufficient room for the concrete to flow to the soffit of the beam. Two or more adjacent beams are readily made continuous by extending the bars bent up from each span, a distance along the top flanges. By this system of construction one avoids stopping a bar where the live load unit stress in adjoining bars is high, as their continual lengthening and shortening under stress would cause severe shearing stresses in the concrete surrounding the end of the short bar.
Fig. 5.Fig. 5.
The beam shown inFig. 5illustrates the principles stated in the foregoing, as applied to a heavier beam. The duty of the short cross-bars in this case is performed by wires wrapped around the longitudinal rods and then continued up in order to support the bars during erection. This beam, which supports a roof and partitions, etc., has supported about 80% of the load for which it was calculated, and no hair cracks or noticeable deflection have appeared. If the method of calculation suggested by Mr. Godfrey were a correct criterion of the actual stresses, this particular beam (and many others) would have shown many cracks and noticeable deflection. The writer maintains that where the concrete is poured continuously, or proper bond is provided, the influence of the slab as a compression flange is an actual condition, and the stresses should be calculated accordingly.
In the calculation of continuous T-beams, it is necessary to consider the fact that the moment of inertia for negative moments is small because of the lack of sufficient compressive area in the stem or web. If Mr. Godfrey will make proper provision for this point, in studying the designs of practical engineers, he will find due provision made for negative moments. It is very easy to obtain the proper amount of steel for the negative moment in a slab by bending up the bars and letting them project into adjoining spans, as shown inFigs. 4and5(taken from actual construction). The practical engineer does not find, as Mr. Godfrey states, that the negative moment is double the positive moment, because he considers the live load either on one span only, or on alternate spans.
Fig. 6.Fig. 6.
InFig. 6a beam is shown which has many rods in the bottom flange, a practice which Mr. Godfrey condemns. As the structure, which has about twenty similar beams, is now being built, the writer would be thankful for his criticism. Mr. Godfrey states that longitudinal steel in columns is worthless, but until definite tests are made,with the same ingredients, proportions, and age, on both plain concrete and reinforced concrete columns properly designed, the writer will accept the data of other experiments, and proportion steel in accordance with recognized formulas.
Fig. 7.Fig. 7.
Mr. Godfrey states that the "elastic theory" is worthless for the design of reinforced concrete arches, basing his objections on the shrinkage of concrete in setting, the unreliability of deflection formulas for beams, and the lack of rigidity of the abutments. The writer, noting that concrete setting in air shrinks, whereas concrete setting in water expands, believes that if the arch be properly wetted until the setting up of the concrete has progressed sufficiently, the effect of shrinkage, on drying out, may be minimized. If the settlement of the forms themselves be guarded against during the construction of an arch, the settlement of the arch ring, on removing the forms, far from being an uncertain element, should be a check on the accuracy of the calculations and the workmanship, since the weight of the arch ring should produce theoretically a certain deflection. The unreliability of deflection formulas for beams is due mainly to the fact that the neutral axis of the beam does not lie in a horizontal plane throughout, and that the shearing stresses are neglected therein. While there is necessarily bending in an arch ring due to temperature, loads, etc., the extreme flanges sometimes being in tension, even in a properly designed arch, the compression exceeds the tension to such an extent that comparison to a beam does not hold true. An arch should not be used where the abutments are unstable, any more than a suspension bridge should be built where a suitable anchorage cannot be obtained.
The proper design of concrete slabs supported on four sides is a complex and interesting study. The writer has recently designed a floor construction, slabs, and beams, supported on four corners, which is simple and economical. InFig. 7is shown a portion of a proposedtwelve-story building, 90 by 100 ft., having floors with a live-load capacity of 250 lb. per sq. ft. For the maximum positive bending in any panel the full load on that panel was considered, there being no live load on adjoining panels. For the maximum negative bending moment all panels were considered as loaded, and in a single line. "Checker-board" loading was considered too improbable for consideration. The flexure curves for beams at right angles to each other were similar (except in length), the tension rods in the longer beams being placed underneath those in the shorter beams. Under full load, therefore, approximately one-half of the load went to the long-span girder and the other half to the short-span girder. The girders were the same depth as the beams. For its depth the writer found this system to be the strongest and most economical of those investigated.
E.P. Goodrich, M. Am. Soc. C. E.—The speaker heartily concurs with the author as to the large number of makeshifts constantly used by a majority of engineers and other practitioners who design and construct work in reinforced concrete. It is exceedingly difficult for the human mind to grasp new ideas without associating them with others in past experience, but this association is apt to clothe the new idea (as the author suggests) in garments which are often worse than "swaddling-bands," and often go far toward strangling proper growth.
While the speaker cannot concur with equal ardor with regard to all the author's points, still in many, he is believed to be well grounded in his criticism. Such is the case with regard to the first point mentioned—that of the use of bends of large radius where the main tension rods are bent so as to assist in the resistance of diagonal tensile stresses.
As to the second point, provided proper anchorage is secured in the top concrete for the rod marked 3 inFig. 1, the speaker cannot see why the concrete beneath such anchorage over the support does not act exactly like the end post of a queen-post truss. Nor can he understand the author's statement that:
"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."
"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."
The latter part of this quotation has reference to the point questioned by the speaker. In fact, the remainder of the paragraph from which this quotation is taken seems to be open to grave question, no reason being evident for not carrying out the analogy of the queen-post truss to the extreme. Along this line, 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 speaker concurs, however, in the author's criticism as to the lack of anchorage usually found in most reinforcing rods, particularly those of the type mentioned in the author's second point.
This matter of end anchorage is also referred to in the third point, and is fully concurred in by the speaker, who also concurs in the criticism of the arrangement of the reinforcing rods in the counterforts found in many retaining walls. The statement that "there is absolutely no analogy between this triangle [the counterfort] and a beam" is very strong language, and it seems risky, even for the best engineer, to make such a statement as does the author when he characterizes his own design (DiagrambofFig. 2) as "the only rational and the only efficient design possible." Several assumptions can be made on which to base the arrangement of reinforcement in the counterfort of a retaining wall, each of which can be worked out with equal logic and with results which will prevent failure, as has been amply demonstrated by actual experience.
The speaker heartily concurs in the author's fourth point, with regard to the impossibility of developing anything like actual shear in the steel reinforcing rods of a concrete beam; but he demurs when the author affirms, as to the possibility of so-called shear bars being stressed in "shear or tension," that "either would be absurd and impossible without greatly overstressing some other part."
As to the fifth point, reference can be given to more than one place in concrete literature where explanations of the action of vertical stirrups may be found, all of which must have been overlooked by the author. However, the speaker heartily concurs with the author's criticism as to the lack of proper connection which almost invariably exists between vertical "web" members and the top and bottom chords of the imaginary Howe truss, which holds the nearest analogy to the conditions existing in a reinforced concrete beam with vertical "web" reinforcement.
The author's reasoning as to the sixth point must be considered as almost wholly facetious. He seems to be unaware of the fact that concrete is relatively very strong in pure shear. Large numbers of tests seem to demonstrate that, where it is possible to arrange the reinforcing members so as to carry largely all tensile stresses developed through shearing action, at points where such tensile stresses cannot be carried by the concrete, reinforced concrete beams can be designed of ample strength and be quite within the logical processes developed by the author, as the speaker interprets them.
The author's characterization of the results secured at the University of Illinois Experiment Station, and described in its Bulletin No. 29, is somewhat misleading. It is true that the wording of the original reference states in two places that "stirrups do not come into action, at least not to any great extent, until a diagonal crack has formed," but, in connection with this statement, the following quotations must be read: