Part 7 (1/2)
[Illustration: FIG 10]
When the rod is put in tension, as indicated in Fig 10, ill be the stresses in the surrounding concrete? The greatest stress will come on the rod at the point where it leaves the concrete, where it is a maximum, and it will decrease from that point inward until the total stress in the steel has been distributed to the surrounding concrete At that point the rod will only be stressed back for a distance equal in length to 50 diath the rod may extend
The distribution of the stress from the steel rod to the concrete can be represented by a cone, the base of which is at the outer face of the block, as the stresses will be zero at a point 50 diameters back, and will increase in a certain ratio out toward the face of the block, and will also, at all intermediate points, decrease radially outward from the rod
The intensity of the maximum stress exerted on the concrete is represented by the shaded area in Fig 10, the ordinates,the maximum resistance offered by the concrete at any point
If the concrete had a constantstress, and if the two le would be bounded by straight lines (shown as dotted lines in Fig 10); but as this is not true, the variable le in a manner which will tend to make the boundary lines resele thus constructed will represent by scale the intensity of the stress in the concrete, and if the ordinates indicate stresses greater than that which the concrete will stand, a portion will be destroyed, broken off, and nothing le will adjust itself, and grip the rod farther back This process keeps on until the end of the rod has been reached, when the triangle will assureater ration of the concrete will take place here very rapidly, and the rod will be pulled out
In the author's fourth point he belittles the use of shear rods, and states: ”No hint is given as to whether these bars are in shear or in tension” As a matter of fact, they are neither in shear nor wholly in tension, they are si between the centers of the co 12, and are, besides, stressed slightly in tension between these two points
[Illustration: FIG 11]
In Fig 10 the stress triangle indicates the distribution and the intensity of the resistance in the concrete to a force acting parallel to the rod A si the resistance of the rod and the resultant distribution in the concrete to a force perpendicular to the rod Here the original force would cause plain shear in the rod, were the latter fixed in position Since this cannot be the case, the force will be resolved into two components, one of which will cause a tensile stress in the rod and the other will pass through the centroid of the co 11, which, otherwise, is self-explanatory
[Illustration: FIG 12]
Rods are not very often placed in such a position, but where it is unavoidable, as in construction joints in the ood purpose; but, to obtain the best effect from them, they should be placed near the center of the slab, as in Fig 12, and not near the top, as advocated by some writers
If the concrete be overstressed at the points where the rod tends to bend, that is, if the rods are spaced too far apart, disintegration will follow; and, for this reason, they should be long enough to have ripped by the concrete
This leads up to the author's seventh point, as to the overstressing of the concrete at the junction of the diagonal tension rods, or stirrups, and the bottom reinforceous with the foregoing, it is easy to lay off the stress triangles and to find the intensity of stress at thethe tension rods and the bottoles will start on the rod 50 diah the author has indicated in Fig 1 that only two of the three rods are stressed, there must of necessity also be some stress in the bottom rod to the left of the junction, on account of the defor Therefore, all three rods at the point where they are joined, are under stress, and the triangles can be laid off accordingly
It will be noticed that the concrete will resist the co the various rods, and with the intensities shown by the stress triangles; also, that soles will overlap, and, hence, a certain readjustment, or superimposition, of stresses takes place
The portion which is laid off below the bottom rods will probably not act unless there is sufficient concrete below the reinforcing bars and on the sides, and, as that is not the case in ordinary construction, it is very probable, as Mr Goodrich has pointed out, that the concrete below the rods plays an unile which is non below the rod should be partially o 13 show the intensity of stress in the concrete at any point, or at any section where it is wanted They show conclusively where the components are located in the concrete, their relation to the tensile stresses in the rods, and, furtherles to one another This is in accordance with the theory of beams, that at any point in the web there are tensile and coles to one another, although in a non-hoeneous web the distribution is so found at the point of junction the intensity of stress, it is possible to tell whether or not a bond between the stirrups and the bottom rods is necessary, and it would not seem to be where the stirrups are vertical
It would also seem possible to tell in what direction, if any, the bend in the inclined stirrups should be h not expressly stated, that the bends should curve from the center up toward the end of the bea 13, will show that the intensity of stress is just as great on the opposite side, and it is probable that, if any bends were required to reduce the maximum stress in the concrete, they should as likely be made on the side nearest the abutles it may also be shown that, if the stirrups were vertical instead of inclined, the stress in the concrete on both sides would be practically equal, and that, in consequence, vertical stirrups are preferable
The next issue raised by the author is covered in his seventh point, and relates to bendingled to reduce thener would like to have them This has come to be almost a matter of taste,”
The author see As a itin, that is, froling” is limited in practice by economical considerations
In a series of beae from (_w_ _l{2}_)/8 at the center of each span to zero at the supports, and, in a series of cantilevers, from zero at the center of the span to (_w_ _l{2}_)/8 at the supports Between these two extrele then heof the points of contra-flexure If that were not the case, how could ordinary bridge trusses, which have theirat the center, compare with those which, like arches, are assu at that point?
In his tenth point, the author proposes aaith the complicated formulas which take account of the actual co-operation of the two n can be obtained in the same manner, that is, with the saular beams; but, when he does so, he evidently fails to remember that the neutral axis is not near the center of a reinforced concrete beae of reinforce between three-fourths of 1 to 1-1/2--the neutral axis, when the beam is loaded, is shi+fted from 26 to 10 of the beae of steel reinforce of the neutral axis, so that a design based on the formulas advocated by the author would contain either a waste of materials, an overstress of the concrete, or an understress of the steel; in fact, an error in the design of from 10 to 26 per cent Such errors, indeed, are not to be recoineers
The last point which the speaker will discuss is that of the elastic arch The theory of the elastic arch is noell understood, and it offers such a si solution of the arch design, that it has a great es of other ments of an arch could be ether, cannot be endorsed by the speaker, for, upon such ce of the lines of resistance will take place when the load is applied The speaker does not clai the voussoirs together, but that the lines of pressure will be ed, and the same calculations are not applicable to both the unloaded and the loaded arch
It is quite true, as the author states, that a few cubic yards of concrete placed in the ring will strengthen the arch more than a like amount added to the abutments, provided, however, that this ood can result fro the reinforcing material proe construction, and, in such cases, the material either increased the distance fro the original sectionof the neutral axis followed by a large bendingthe members it had tried to reinforce In other words, the then a structure, unless it is placed in the proper position, and, if so placed, it should be placed all over commensurately with the stresses, that is, the unit stresses should be reduced