Eng. K. N. KARTASHEV

TESTING

NAIL JOINTS

Tomsk

1929

Eng. K. N. Kartashov.

Testing of Dowel Joints.

I. Varieties of rod-type joints.

In the erection of timber structures, both of a temporary and of a permanent character, nails often have to be used as the connecting means; this is especially often encountered where rapid construction of a structure is required in the absence of a sufficiently highly qualified labor force and where it is impossible to obtain, in finished form, or to manufacture on the job site, the various more complicated joints, such as wedges, various inserts, keys, and so forth.

Considering, as a whole, the group of metal joints for timber structures, in whose operation bending at the place where it is inserted is of predominant importance, we see that it falls into three principal types: nail, bolt, and dowel pin (Fig. 1: a, b, c).

A bolt is a round rod from 12 to 35–40 mm thick, provided with a head at one end and a thread with a nut at the other end, which hold it in the socket. Usually the bolt hole, predrilled in the elements to be joined, is made 1–2 mm larger than the diameter of the bolt placed in it, in order to ensure assembly of the structure. Therefore, in the case of external forces, before the bolt begins to work in crushing and bending, after overcoming insignificant frictional forces caused by the initial tightening of the joint, a slight displacement of the elements relative to one another will occur (Fig. 2). Under forces of alternating sign this phenomenon manifests itself to an even greater degree with each change in the direction of action of the force. A considerable number of investigations has been devoted to joints of this type, and therefore we shall not dwell on it in greater detail¹.

A dowel pin is usually made in the form of a cylindrical rod without a head and without a point, from the best grades of steel, with a temporary resistance reaching 10,000 kg/sq. cm.

When it is set in place, a hole is first drilled 1–1½ mm smaller than the diameter of the dowel pin, which is then driven into place by blows; for this purpose pneumatic hammers are quite often used. Thanks to this method of carrying out the work, as experience has shown, the dowel pin fits tightly in its socket and at the same time does not produce splitting of the wood or transverse crushing of its fibers, and is held in place by the frictional forces developing on its surface. How great these frictional forces may be can be seen even from the following example: during inspection, after 8 years of service, of the timber structures of a locomotive—

of a building in Kornwestheim, Germany, constructed by the method of the firm Meltzer and covering a useful area of 1100 sq. m., with a free span of the middle bay equal to 24 meters, it turned out that, owing to the drying of the timber, gaps appeared between the individual boards of the built-up sections of the trusses; in order to eliminate them, the structural bolts, placed at a small distance from one another, were tightened, but, under the influence of the drying and the tight fit during assembly, the pins proved to be so strongly clamped in their sockets that this measure did not lead to the desired results.

One of the principal merits of joints of this type is the extremely small magnitude of the deformations of the joints during their operation, which is caused by the tight fit of the pins and by the great stiffness of the material used for their manufacture. At the same time, they cause only a slight weakening of the cross-section of the connected members by holes of small diameter, which entails the overall lightness of the structure and good utilization of the timber material (Fig. 3).

The normal diameter of the pins is taken (by the firms Meltzer—Darmstadt and Theodor Birkmann—Nürnberg) as from 8 to 15 mm. At the same time it must be said that the erection of structures of this kind, accompanied by the installation of a colossal number of individual pins, requires great accuracy and attentiveness on the part of the worker, and at the same time the necessary high quality of the structure can be obtained only with mechanization of the drilling of holes, and partly also of the driving-in of the pins. In view of all this, it is difficult to count on the rapid spread of this method of executing timber structures under our conditions.

Passing next to the consideration of the nailed joint, we see that it differs from those described above chiefly in that, in this case, a hole is not drilled in advance for the metal rod; rather, it is driven into the wood by blows upon the end provided with a head.

To facilitate the driving process, the nail has a point at its front end, which partly reduces the disturbance of the structure of the wood fibers. A nail set in place and seated in the wood with considerable friction nevertheless causes, when driven in, a number of undesirable phenomena: rupture of fibers, splitting in the longitudinal direction, and crushing in the transverse direction. In addition, nails are usually made of soft iron, which naturally reduces their load-carrying capacity in comparison with steel pins.

Despite all these qualities, which diminish the merits of the nailed joint, it also has certain quite significant advantages which in some cases place it above the others—namely, the speed, simplicity, and general availability of its manufacture, as well as its relatively low cost.

II. The nailed joint and examples of its application.

Nails may be smith-made—forged—and wire or machine-made (Fig. 4). The former have a pyramidal shape with sharp edges, which promote the development on their surface of greater frictional forces than with wire nails; but at the same time, in view of their hand manufacture, they are insufficiently uniform both in their dimensions and in their material, and are relatively more expensive than the latter.

Machine-made nails have a shank with a round or square cross-section that is constant along its entire length, and are provided with a head at one end and a point at the other. In view of their regular geometric form and more constant mechanical properties, their use is more convenient both from the structural and from the computational standpoint, owing to which they have become considerably more widespread than the former type.

In erecting various structures with the aid of nails, both structures with a solid cross-section and lattice structures may be executed. Among the former we shall point to wooden I-beams (Fig. 5), formed from a board set on edge with four square bars nailed along its edges, or with squares obtained by longitudinally sawing round timber¹. The height of such beams, when bars are used, ranges from 18 to 24 cm, and when squares are used from 20 to 34 cm (about 8 vershoks). In the present case the greatest possible height of the beam is determined by the availability of boards of the corresponding width. The attachment of the bars is effected by means of nails or dowels. In testing a model of such a beam, it worked as a single solid section, and failure occurred from longitudinal stresses which reached 577 kg/sq. cm. The crushing stress of the nail, computed on the assumption of its uniform distribution over the whole length of the shank, reached 234 kg/sq. cm, which, as we shall see below, agrees with our own experiments (Tables I and II). Measurement of deflections during the test showed that, within the limits of proportionality, they fully corresponded to the calculated values.

By using beams of this type in the intermediate floors and attic floors of residential buildings, spans of up to 12 m can be covered.

The next example of an I-beam may be the Leichtholz system (Wilhelm Rallenbach—Gotha), formed from three beams joined together with nails and glue (Fig. 6). The use of glue in this case is explained by the fact that, with this type of formation of the flange of an I-section, in the plane of the joint the shearing stresses develop to values considerably higher than in the preceding case, owing to which nails alone are no longer capable of taking upon themselves the whole shearing force. At the place of contact of the boards being joined, along part of their length, slots are made by means of a circular saw, indicated on the drawing by the letters $C_1$ and $C_{11}$. When gluing, these slots are filled with glue, forming a kind of comb firmly bonded with the wood. Before the glue finally hardens, the beam is nailed together with nails not less than 15 cm long and not thinner than 0.5 cm. To reduce the possibility of the board splitting, the nails in the transverse direction are alternately given an inclination in different directions. To increase still further the strength of the connection, the nails are also given a certain inclination in the longitudinal direction.

When passing to beams of greater depth, for which it is no longer possible to select an integral board for making the vertical web of the I-section, it is necessary to proceed to the type shown in Fig. 7. Here the vertical web is formed by two intersecting plates inclined to the middle axis of the structure at an angle of 40–45°.

In the transfer of the normal bending stresses in this structure, only the chord beams take part, since under the influence of

the drying of the tree, especially strongly manifesting itself across the fibers; between the individual planks of the wall boards gaps appear. Thus, in this case the wall serves only to take up transverse forces. Exactly the same method is often used for curved arched and frame structures, an example of which is the construction of the hangar at Warnemünde, erected by the firm Karl Tuchscherer and representing an arched system with a clear span of 55 m (Fig. 8).

We note that in the design of such structures, for the perception of shearing stresses appearing in the planes of contact of the wall and the flanges, it is assumed abroad that, when placed on every 50 sq. cm of contacting surfaces, one nail can take up a stress equal to 2 kg/cm². By means of nails, wooden arches are also made according to the well-known systems of de l’Orme and Emy (Figs. 9 and 9a).

The arches of de l’Orme are made of several rows of vertical planks placed side by side, described along a curve on one or both sides and connected to one another by nails and dowels. Most often nails are used for making Emy arches, the rectangular or I-shaped section of which is made from separate thin boards bent in the direction of their smallest height in order to reduce initial stresses. In order to obtain a solid section from the separate boards, as they are laid one upon another they are nailed to the preceding ones. Abroad, special clamps are often used instead of nails.

Among lattice structures we shall point to the Tuchscherer system (Figs. 10, 11, 12 and 12a) and Noack (Figs. 13 and 14).

In both cases the outline of the upper chord approaches a parabolic one. In trusses made by the firm Tuchscherer, the compressed chord is formed either of two layers of straight boards joined through the joint in staggered order (Fig. 10), or of bent boards, part of which are bent flatwise and part of which, having a small width, are bent in the vertical position (Figs. 11 and 12). The second method, although it creates a number of inconveniences and difficulties from the point of view of the production of the work, nevertheless reduces to the limit the number of joints. The lattice is fastened to the chords by means of sawn shaped gusset plates, made of glued (in 12 layers) plywood under high pressure and nailed to the chord boards with nails. The lattice members are fastened to the gusset plate by means of a thick metal rod. The disadvantage of this type of joint is that here the proper intersection of the geometric axes of all the members at one point is not achieved; moreover, the lattice is asymmetrical with respect to the longitudinal axis of the truss. Owing to this, additional stresses arise in the chord, both from bending and from torsion. These harmful influences are almost completely eliminated by choosing a parabolic outline for the upper chord, owing to which, under the action of a permanent and total temporary load, the lattice is completely unstressed and in it there appear, only under one-sided loading, insignificant forces.

The firm Noack makes the upper parabolic chord according to a combined system of Emy and de l’Orme, namely composing it of two rows of vertical planks, between which are placed boards bent flatwise. This makes it possible, with a comparatively simple pro—

...the work, to obtain a compressed chord of sufficiently rigid cross-section and at the same time with a small number of joints. In these trusses, both the chords themselves and the attachment of the lattice to them are carried out with the aid of nails.

The use of nails is also encountered in the construction of compressed elements of lattice structure, if they are formed from thin boards spaced so far apart that it is impossible to place ordinary spacers between them. In such cases the boards are joined together into one whole of tubular section by means of a wooden lattice of boards fastened to them with nails (Fig. 15).

We think that the examples given are quite sufficient to show the vitality and importance of nailed joints in the construction of both temporary and permanent load-bearing timber structures.

III. General description of the investigation.

In the experiments undertaken by the author the aim was to study the properties of nailed joints. At first it was proposed to test a series of specimens with nails of various length and diameter, with different thicknesses of the boards used for making the specimens; but then, after preliminary experiments, it turned out that the proposed program was excessively broad, would require a very great deal of time for its execution, and, moreover, in its separate particular cases there appeared some parallelism. On the basis of all this it was decided to dwell in greater detail on the study of the properties of one particular size of joint, determining the influence on its strength of various factors, such as, for example: bending the ends of the nails across and along the direction of the acting force, preliminary reaming of the holes, planing of the contacting surfaces, etc., which made it possible, if necessary, when using a structure with other sections, to carry out only a small number of experiments, reconstructing the further picture by analogy with that found for the main group of specimens.

Regardless of the purely theoretical interest of the work being carried out, the dimensions of the specimens were chosen so that the results obtained could be used directly in practice; namely, pine boards about 25 mm thick were taken as a basis, and round wire machine nails 125 mm long (5 inches) with a diameter of 4.06 mm, and 100 mm long with a diameter of 4.03 mm.

Thus a structure was adopted which can most often be encountered in timber construction, both in the formation of arches, trusses, etc. according to Lorma’s norms, and in the construction of the wall chord of a two-flange section with a wall of intersecting boards, etc.

First, 34 longitudinal and 14 transverse specimens were tested; but later, when doubt arose as to the correctness of some of the results obtained, a second group of specimens was made, consisting of 15 longitudinal and 15 transverse ones. In addition, about 250 experiments were carried out to determine the strength of wood in compression, and the necessary number of experiments to determine the moisture content of the material used.

The first type of specimens, the so-called “longitudinal” ones (Fig. 16), consisted of three separate boards measuring \(28 \times 10\) cm, joined by means of five nails, the ends of which remained unbent, bent upward, or bent downward; in addition, in some of the specimens the nails were placed in pre-drilled holes, while in others the adjoining surfaces were also planed. In testing such a specimen, the middle board advanced between the outer ones, and in all the boards the material was subjected to stress acting along the fibers.

In the “transverse” specimens, between two boards \(30 \times 10\) cm in size, placed in the same way as in the preceding specimens, there was inserted a board with a direction of fibers perpendicular to them (Fig. 17), measuring \(24 \times 20\) cm. For these specimens it was at first assumed, on the basis of a calculation of the presumed breaking force from the condition of the crushing of the fibers of the middle board, to transmit pressure to the middle board through two side pads 7 cm long each; but the very first specimen showed the erroneousness of this calculation: the force exceeded the value that is destructive for an analogous longitudinal specimen, after which failure followed, not from the limit of strength of the nailed joint, but from severe crushing (up to 1.5 cm) of the middle board over the area of pressure and its bulging sideways under the influence of the longitudinal bending phenomenon (Fig. 18). Both kinds of deformations reached so large a magnitude and continued to increase so rapidly that the test had to be stopped and the specimen discarded as completely spoiled.

In testing the following specimens, made before the unsuccessful testing of the first of them, it was necessary artificially to increase the pressure area by means of a device along the entire length of the middle board in the form of a square iron rod of section \(22 \times 22\) mm. In making the second group of specimens the length of the middle board was increased to 35 cm, which, in connection with the preservation of the metal pad, completely excluded the possibility of the occurrence of the undesirable phenomena described above.

The testing of the specimens was carried out on a large lever-type five-ton Olsen machine\(^1\) with automatic regulation of the load and a self-recording apparatus for recording diagrams. On this machine it is possible, within the range from zero to five tons, to determine the load with an accuracy of up to 0.1 kg, which in the present case was more than sufficient.

In addition to recording diagrams, within limits of approximately up to 1.0—1.3 mm, the displacement of the middle board relative to the outer ones was measured at four points by means of Kennedy instruments, with an accuracy of up to \(1/250\) mm; the method of mounting them on the specimen is clear from Figs. 19, 20, 21, which also show the arrangement of the points at which measurements were made. After the displacements had reached the indicated magnitude, the instruments were removed, since the pointer went beyond the sector, and subsequently, up to the moment of complete destruction of the specimen, only the recording of the diagram was made on the scale of the force acting—

\(^1\) For a description of the Olsen machine and Kennedy instruments, see Prof. N. N. Mitinskii’s book Strength of Materials, pp. 227 and 251.

convenient for reading it (Figs. 22–23)¹, namely with a deformation scale of 1 mm of deformation = 4 mm, and a force scale of 1000 kg = 25 mm.

In testing the first five specimens, the load was increased from zero to the maximum at intervals of 100 kg (in the tables given below, to save space, their rows are omitted almost everywhere after 200 kg); in the subsequent specimens, after each measurement of deformation the specimen was unloaded and the residual deformation was measured, which in some cases yielded rather characteristic phenomena, as will be reported below.

It should be noted that, when measuring deformations in longitudinal specimens, it may be considered that the place of their measurement does not affect the result, in view of the insignificance of the compressive stresses acting in the transverse section of the elements (not more than 90–100 kg/sq. cm for pine boards) and the large modulus of elasticity of the first kind for wood along the fibers. An entirely different picture is obtained in specimens with a transverse middle board, to which the force is transmitted along the line aa. With such a method of transmitting pressure, the displacement at point c will be considerably greater than at point c’, since in the first of them it will be determined not only by the work of the joint itself, as is the case at point c’, but also by deformations caused by the compressive stress across the fibers, which not infrequently exceeded the allowable values (in some specimens the stress reached 55 kg/sq. cm).

On this basis, since in practice normal deformations in such structures are caused mainly only by the work of the joint itself, measurement of these deformations was carried out at points c’, which is clearly seen from the drawings showing the installation of the instruments.

In preparing the specimens, the main straight-grained boards used had a moisture content of 12 to 15% and cube strengths in compression from 424 to 570 kg/sq. cm, and in only one case as low as 312 kg/sq. cm. Initially, tests were made on compression of wood for each of the boards used to prepare the specimens; but it was then found that some of them possessed a greatly differing strength in their upper and lower parts. Therefore, for all tested specimens, cubes were additionally cut from the undestroyed part and subjected to compression tests, while in the further preparation of the specimens the boards were cut according to a definite system so that, from every 100–120 cm required for preparing two specimens, a compression test could be made. All this made it possible, for each group of specimens, to establish precisely the corresponding strength of the wood. The cubes were tested on an Amsler press.

After destruction of the specimens, small pieces were cut out to determine the moisture content; before testing these had been placed in jars with ground-glass stoppers, and were then ground to a grain size of 1–1½ mm and dried in a special oven (in the flour-milling laboratory of the S.T.I.), in which, with the aid of electric heating devices, the temperature was maintained at 110°C. Each test consisted of 4–5 separate experiments, lasting until the point when periodic weighings showed that the weight of the sample had ceased to decrease.

¹ In these figures only a part of the most characteristic diagrams from the second series of experiments is given.

1. Table of data obtained from testing the first series of specimens (45 pcs.)

II. Table of data obtained from testing the first series of specimens (30 pcs.)

Failure by ball load \(P\), kg

IV. Results of observations and conclusions.

All the necessary data and results obtained from the experiments performed, both for the first and for the second group, have been entered in the appended tables, where, for the individual types of specimens, in order to economize space, the mean values from an entire series of tests have been taken; in this, for each specimen, the deformation was determined as the mean value from the readings of four Kennedy instruments.

In order to obtain comparable results from all the varied experiments with specimens having different timber strengths, different board thicknesses, different nail diameters, and, in addition, different bending lengths, the calculation method of Dr. P. Nittmann¹) was chosen, applied to the case of considering dowel joints in wooden structures. In this case, for determining the greatest acting crushing stresses for the middle board, we have the formula:

\[ \sigma = \frac{576N + 2.35}{576N + 1.1}\cdot \frac{2P}{ld} = n\frac{2P}{ld} \]

and for the outer board:

\[ \sigma = 4\cdot \frac{576N + 2.35}{576N + 1.1}\cdot \frac{P}{ld} = m\frac{P}{ld}, \]

where

\[ N=\frac{E_cJ}{Cl^4d} \quad \text{and} \quad m=n+3. \]

Here we denote:

\(P\) — the force acting on one outer board;
\(l\) — the thickness of the board;
\(d\) — the diameter of the nail;
\(E_c\) — the modulus of elasticity of the metal, taken in the present case as \(2100000\ \mathrm{kg/sq.\ cm}\);
\(J\) — the moment of inertia of the transverse section of the nail;
\(C\) — the coefficient of the bed of the wood, adopted by us in calculating the longitudinal specimens, according to the experiments of Jansson and Graf, as equal to \(2500\ \mathrm{kg/cu.\ cm}\), and for the middle board of the transverse specimens \(1100\ \mathrm{kg/cu.\ cm^2}\).

On the basis of the formulas given, the following two tables were calculated for the coefficients \(n\) and \(n_1\), for the three nail diameters adopted in the experiments, board widths from 2 to 3 cm, and for both possible values of the bed coefficient, which fully covered all the cases encountered in the experiments.

III. Table of values of \(n\) for \(C = 2500\ \mathrm{kg/cu.\ cm}\).

¹) 1) A. Jansson, “Wooden Structures.”
2) K. N. Kartashov, “Graphs for the Design of Bolted Joints in Wooden Structures.”
3) Ihnatz, “Wooden Structures of Civil Buildings.”
4) H. Seitz, “Grundlagen des Ingenieurholzbaues.”
A. Jansson, “Wooden Structures.”

IV. Table of values of \(n_1\) for \(C = 1100\) kg/cu. cm.

With the aid of these tables a graph was constructed (Fig. 24), the curves of which give the dependence between the quantities \(n\) and \(l\), which made it possible without difficulty to find the values of \(n\) and \(m\) with a sufficient degree of accuracy for any thickness of boards and, from them, to calculate both the stresses acting in the specimens under various magnitudes of the external force \(P\), and also the greatest stress at the failure of the specimen. Then, reducing the stress values at failure to a timber strength equal, for example, to 500 kg/sq. cm, we obtain comparable results, expressed as percentages of the stress for unplaned specimens with unbent nails.

In determining the failure stresses, we first determined them from the condition of operation of the middle board along the fibers (including, for comparison, also for transverse specimens); then only for transverse specimens from the condition of operation of the middle board across the fibers and, finally, of the outer boards along the fibers. The last condition was adopted only for transverse specimens on the grounds that they all, with rare exceptions, failed from splitting of the outer boards (Fig. No. 27), and only rarely from complete rupture and pulling-out of the nails.

For greater clarity, we give a selection of the percentage ratios of the strength of different types and construct, for the principal groups of specimens, diagrams (Figs. 28—31) of the dependence between the acting greatest edge stress and the corresponding total (upper curve) and residual (lower curve) deformations.

Considering in aggregate the results of the individual observations and comparing them, we arrive at a number of conclusions, set forth below.

V. Comparative table of failure stresses.

1) In specimens with unbent nails no more rapid displacement was observed relative to the middle board of that one of the outer boards which was on the side of the unbent ends of the nails. This indicates that, despite the observed slight indentation of the heads into the wood, they nevertheless had no appreciable influence.

2) Under loads close to failure, when the deformation of the specimen reached 2—2½ cm and the ends of the nails bent strongly upward (see the second specimen from the right in Figures No. 25 and 26), in some specimens slipping of the boards occurred along the bent-back free ends of the nails, accompanied by a sharp creak.

3) Considering the deformation diagrams of the longitudinal specimens given in Figure 22, irrespective of the method of bending the nail ends, we note that in all cases without exception failure proceeded in exactly the same way, with the following characteristic phenomena clearly marked: as the load increased, the deformations at first increased almost according to the law of a straight line up to a value of 1—1.5 mm, where the proportionality was disturbed and the diagram became considerably flatter; nevertheless the load still continued to increase to a certain maximum value, after which, at a constant or barely noticeably changing load, the deformations increased strongly right up to the moment of failure.

This phenomenon is explained by the fact that, with thin rods such as the nails are in our case, the crushing stress is exceeded sooner than the shearing stress, all the more so since inter-

two separate nails and the end by a sufficiently large distance so that there is no pulling-out or splitting of the board. Under the influence of large stresses in an oblique section, the nail not only crushes the wood along the fibers, but the nail as it were pushes apart the fibers lying in its path and advances through the thickness of the wood, cutting it on its way (see Fig. 25), which is clearly visible on sections of longitudinal specimens after their failure, especially in the middle board of the specimen with nails bent upward, where the path traversed by the nail is the greatest of all.

Since throughout its movement the nail encounters equal and constant resistance of the surrounding medium (in the present case, wood along the fibers), the diagram under this load is represented by a horizontal or only slightly inclined line.

4) In the manufacture of transverse specimens it turned out that, despite the fact that fairly well dried wood was used and the specimens were tested 2–3 days after their manufacture, in some of them, under the influence of drying and the reduction in width of the clamped transverse board, cracks appeared along it, caused by the nails preventing it from deforming freely. Such specimens, when determining deformations up to 1–1.5 mm, were not taken into account, since in them, under small loads, the entire force was transmitted to the lower nails until the shrinkage crack closed, after which only the upper nails began to enter into action.

This shows that, wherever the displacements were measured, they still could not be attributed to the action of all five existing nails, in view of their unequal participation in taking up the external load. On this basis, more transverse specimens were made, with the expectation that some of them would be spoiled before testing; nevertheless such specimens were also brought to failure in order to determine the greatest force \(P\) and to obtain a complete diagram of deformations when the middle board was displaced by 2.5–3.0 cm, upon which the insignificant crack had no influence.

This shows once again that, in the manufacture of such structures, well dried wood must be used.

5) The failure of transverse specimens is of a somewhat different character than that of longitudinal specimens. Under the influence of the ever-increasing stress and deflection of the nail, the fibers of the middle board begin to be strongly compacted, as generally occurs in the compression of wood across the fibers; but the compaction is considerably greater at the edges of the board than in the middle. In this case it is evident from the diagram that, after the proportional limit, the load continues to increase steadily, although slowly. The compacting fibers, owing to the smallness of the absolute magnitude of the acting forces, are not cut through by the nail, which is explained by the high shearing strength in the perpendicular direction, but only bend strongly, which causes rupture along the line \(aa'\) (Fig. 32), the beginning of which was already laid down when the nail was driven in, during which a slight tearing of the wood always appears (Fig. 1). The bent fibers are stretched and finally tear along the lines \(ab\) and \(a'b'\); moreover, the resulting rupture has the greatest opening at the top, at the outer surface of the board, and decreases both downward and inward, i.e., as the deflection diminishes and, consequently, as the stretching of the corresponding fiber diminishes.

The onset of destruction of the specimen and the abrupt decrease in the external load usually occurred in transverse specimens under the influence of splitting of the outer boards. As the calculation of stresses shows, despite the fact that the stresses in the outer boards theoretically exceed the stress in the middle boards by approximately a factor of two, nevertheless, in longitudinal specimens destruction usually occurred because of splitting of the middle board; and therefore, naturally, specimens with a transverse middle board, failing for the same reason for which longitudinal specimens cannot fail, showed in all cases, without exception, greater strength.

6) Turning to consideration of the individual properties of the separate groups from Tables I, II, and V, we see that bending the nail is reflected in the strength of the specimen; namely, bending the nail upward gives in all cases an increase in strength from 9.5 to 41%, while bending it downward gives a decrease in strength of up to 13%.

This phenomenon may be explained as follows: with the nail end unbent, the force, bending it under the influence of the stresses acting on its surface, unhindered draws it, as it bends, into the interior of the specimen, producing double curvature with two points of inflection (Fig. 33); when the sharp end is bent upward (Fig. 34), in addition to the same vertical stresses, horizontal ones also appear at the nail shank and at the bent end, under the influence of which the nail receives tensile forces that create reverse bending moments tending to straighten it, thanks to which in these specimens the nail bends considerably less, the stress distribution becomes more uniform, and, in addition, the force stretching the nail compresses the specimen in the direction perpendicular to the deformations and produces additional friction forces on the contact surfaces of the boards; not to mention that during the very splitting of these specimens the boards are pressed together much more tightly than in specimens with unbent nails. Under the influence of the tendency of the nail ends, under bending, to deflect upward, as the load increases the end bent upward is pressed more and more tightly against its seat. In view of the fact that, under the influence of strong tension of the nail, there occurs a certain crushing of its shank and hook at the point of its upward inflection, for the purpose of increasing the strength of the joint in shear and bending, small metal washers are sometimes placed.

When the nail is bent downward, the opposite picture appears, i.e., a decrease in the strength of the joint. This phenomenon is explained by the fact that the end bent downward freely moves away from its seat (Fig. 35) and, in view of the fact that here an inflection of the end downward has already been preliminarily created, the force needed to bend the nail is reduced.

After the specimen has deformed strongly—1.5–2.0 cm—and the end with the bend has begun to draw into the thickness of the specimen, there again begins an increase in the external force, in view of the necessity of bending the deflected end, which causes both the appearance of new crushing areas and a certain tension of the nail and additional friction forces. In general, we note that even in the last stage of operation these specimens give magnitudes of the destructive force approaching only that which we had with unbent ends¹.

7) With the ends of the nails joining the boards left unbent, planing has almost no effect on the magnitude of the destructive force. The greatest decrease in strength observed in one case, by 6.8%, may be attributed to other factors, since by simple compression of the boards it is impossible to obtain any significant transverse forces capable of producing friction on the joined surfaces. When specimens with nails bent upward were used, a considerable decrease in strength was observed in longitudinal specimens, which could be explained by the fact that on planed surfaces the coefficient of friction is reduced; but at the same time, in transverse specimens this reduction was not observed. All this indicates that, in general, with planed boards one should expect a decrease in the strength of the joint, which may also be extended to joints made by other means in which there is a transverse compressive force caused by the initial tension of the bolt; however, for establishing more exact data the experiments carried out are insufficient, and further additional investigations are required.

8) Preliminary drilling of holes for nails reduces the possibility of the wood splitting by the nail, which is also evident from the first series of specimens, where with unbent ends an increase in strength of 9.5% was obtained, and with the ends bent upward and planed boards, an increase of 10.6%. In the latter case this increase in strength may be regarded as follows: as is seen from the second series of specimens, planing of the boards in longitudinal specimens reduces the benefit of bending almost exactly by a factor of two; consequently, here, of the existing 10.6%, 5.6% may be attributed to the bending and the remaining 5% to the drilling of holes. As a characteristic beneficial effect of drilling, one should also point to the increase in deformations, both elastic and residual, in specimens with unbent ends throughout the entire increase of load; whereas in specimens with the ends bent upward, at low loads, and at higher loads as well, the deformations become equal to those for undrilled specimens.

This phenomenon is easily explained by the fact that in drilled holes there is not such tight contact of the nail shank with the wood as is observed when nails are driven in the ordinary way.

9) From Tables I and II and the diagrams of deformations (Figs. 28–34) we see that at the beginning of the work of the joint the residual deformations amount, in almost all specimens, to about 30% of the total deformation and increase more rapidly than the total deformation, reaching, at a deformation of 1 mm, 60–75% for longitudinal specimens and 45–60% for transverse specimens.

In correspondence with strength, specimens with an upward bend give a decrease in deformations, those with a downward bend give an increase, and planed specimens with unbent nails likewise, as do unplaned specimens with unbent nails. Planing, like drilling of holes, greatly increases the deformations of specimens with nails bent upward.

10) Turning attention to the results obtained from the testing of thick nails, we note that thinner nails in longitudinal specimens offer less resistance, since they cut through the wood more freely and more easily produce its splitting.

In transverse specimens the opposite picture appears, i.e., a relative increase in strength, which is due to the greater strength of wood in compression in the transverse direction. It follows from this that with thick nails there is a greater effect on the strength of the spec—

…of the specimen the ultimate strength of the wood in compression, and for full-length ones, in shear.

11) Comparing the first and second series of specimens as a whole, we note that in the first case the influence of the various features of manufacture of the specimens is expressed much more weakly than in the second case; this can be explained by the fact that in the second case the wood used was of lower strength, i.e., the influences considered manifest themselves more strongly with strong wood than with weak wood.

V. Conclusion.

Summarizing the results of the present article and comparing, on the basis of Tables I, II, and V, the breaking stresses for different types of specimens, taking into account the strength of the wood, we may conclude that, when thin dowel-type fastenings such as nails are used, the magnitude of the breaking bearing stress does not depend on the angle between the direction of the force and the fibers; moreover, when calculating by the formulas given, it may be assumed that for middle boards it is equal to \(0.7R\), and for outer boards to \(1.3R\), where \(R\) is the ultimate compressive strength; i.e., for example, assuming that the wood has a strength of 500 kg/sq. cm, we obtain the corresponding crushing breaking stress:

\[ \sigma = 0.7 \cdot 500 = 350 \ \text{kg/sq. cm} \]

and

\[ \sigma = 1.3 \cdot 500 = 650 \ \text{kg/sq. cm}, \]

below which the stress obtained from the tests proved to be only insignificantly lower, and only in isolated cases.

In determining the allowable stress, we may proceed from two principal assumptions: first, to allow a certain factor of safety, and second, to allow some maximum deformation of the joint. Taking a threefold factor of safety, we obtain an allowable design stress equal to:

\[ \frac{1}{3} \cdot 350 = 116 \ \text{kg/sq. cm}, \quad \text{and} \]

\[ \frac{1}{3} \cdot 650 = 216 \ \text{kg/sq. cm}. \]

The first of the figures obtained agrees almost exactly with the standards in force among us, which give the maximum allowable bearing stress as 110 kg/sq. cm.

Taking the second path and setting the allowable displacement at 1 mm (Drawings 28–31), we obtain, for the middle board, 140–160 kg/sq. cm for longitudinal specimens and 130–140 kg/sq. cm for transverse specimens, and, correspondingly, for the outer boards from 220 to 330 kg/sq. cm.

In the case of using nails with bent ends, through tenons, through dowels, etc., the values obtained above may be modified in accordance with Tables I, II, and V and Drawings 28–31; that is, from the tables we shall take the initial coefficient, and from the graphs we shall check whether the expected deformations exceed the allowable values.

When high-quality wood is used, it is better to make use of the data obtained from the first series of specimens, for which in all cases the strength of the wood was above 500 kg/sq. cm, but at the same time did not differ greatly from it; with weak wood, however, the data of the second series should be used.

Considering now a particular case—the joining of elements no thicker than 3 cm by nails no thinner than 4.03 mm, and with \(\sigma = 500\) kg/sq. cm—on the basis of Tables III and IV we could, with an assured margin of strength, take into the calculation for the middle board a stress, uniformly distributed over the entire area of pressure of the nail, equal to:

\[ \sigma_{\mathrm{av}}=\frac{116}{1.251}=92.7\ \text{kg/sq. cm.}\approx 90\ \text{kg/sq. cm.} \]

and for the outer boards:

\[ \sigma_{\mathrm{av}}=\frac{216}{4.251}=50.8\ \text{kg/sq. cm.}\approx 50\ \text{kg/sq. cm.} \]

or, for the indicated dimensions, one nail placed in an outer board can sustain a force
\(P=50\cdot 3\cdot 0.403=60.5\) kg, and with a nail 4.53 mm in diameter,
\(P=50\cdot 3\cdot 0.453=68\) kg.

For the middle board the force, respectively, is obtained as:

\[ P=90\cdot 3\cdot 0.403=109\ \text{kg.} \]

\[ P=90\cdot 3\cdot 0.453=122\ \text{kg.} \]

Professor P. Ya. Kamentsev gives in this case, for a 3″ nail, a force of 40 kg; for a 5″ nail—a force of 70 kg; and for a 7″ nail—100 kg, irrespective of its thickness¹.

Assuming that for every 50 sq. cm of contacting surfaces there is 1 nail, we obtain the shearing stress taken up by the joint as respectively 1.21; 1.32; 2.18 and 2.44 kg/sq. cm, whereas German firms under such conditions take 2 kg/sq. cm.

In conclusion, it is necessary once again to emphasize that nails, being one of the simplest and cheapest joints, should in time become widely used in the erection of large, responsible structures; but for this it is still necessary to carry out a series of laboratory investigations and to obtain practical material from observations of existing structures, in order to give the designer sufficiently reliable material for proper design.

1928.

Sheet 1

to the article by Eng. K. N. KARTASHOV

Fig. 1.

Fig. 4.

Fig. 3.

Fig. 5

Fig. 2.

Fig. 6

Sheet 2

To the article by engineer K. N. Kartyshov.

Fig. 7.

Visible dimensions: 6000; 8, 19, 8; 5, 13, 3, 5; 35; 6, 23, 6.

Fig. 9.

Fig. 9a.

Sheet 3.

To the article by Eng. K. N. Kartashov.

Fig. 10.

Fig. 11.

Fig. 12.

Annotations in Fig. 12a:

• 20×3 cm
• 4×15 cm
• thickness 4 cm
• 4×20 cm

Fig. 12a.

Sheet 4

for the article by engineer K. N. Kartashov.

Fig. 14.

Visible annotations in the drawing: \(40\ \mathrm{cm}\); scale marks \(0, 10, 20, 30\); \(3\frac12\); \(3\frac12\); cross-section dimensions \(3.5\), \(6\), \(3.5\), \(20\), \(3.5\), \(3.5\), \(3.5\).

Fig. 13.

Visible annotations in the drawing: \(20.0\ \mathrm{m}\); \(2.20\ \mathrm{m}\); \(4 \times 0.25\); \(3 \times 6.35\); \(3\frac12\); \(2.60\).

Fig. 15.

Sheet 5

To the article by engineer K. N. Kartashov

Fig. 16.

Visible inscriptions and dimensions: 3, 7, 6, 6, 7, 3; 3, 4, 3; 10; 7, 10, 7; 20; 24; 35; 29.

Labels:

• Straight end
• Bend upward
• Bend downward

Fig. 17.

Visible inscriptions and dimensions: P, P, 2P; 30; 3, 4, 6, 6, 4, 7.

Fig. 18.

Sheet 6

to the article by Eng. K. N. Kartashov

Note: In all projections, the right-hand instruments have been omitted for clarity.

Fig. 19.

Fig. 20.

Plate 7.

To the article by Eng. K. N. Kartashov.

Fig. 8.

Fig. 21.

Plate 8

to the article by Eng. K. N. Kartashov

\(P\)
kg

\(\Delta = \mathrm{mm}\)

Longitudinal specimens:
① unplaned, unbent.
② unplaned, bent upward.
③ planed, bent upward.

Longitudinal specimens:
④ planed, unbent.
⑤ unplaned, bent downward.

Transverse specimens:
① unplaned, unbent.
② same — bent upward.

Transverse specimens:
③ planed, unbent.
④ same — bent upward.

Fig. 22 and 23.

Plate 9
to the article by Eng. K. N. Kartashov

Graph for determining the coefficients \(n\), \(n_{1}\), and \(m\) for the nail diameters used in the experiments.

Vertical axis: \(n\) and \(n_{1}\)

Horizontal axis: \(L = 2.0,\ 2.2,\ 2.4,\ 2.6,\ 2.8,\ 3.0\ \mathrm{cm}\)

Curve labels:
\(d = 4.03\)
\(d = 4.06\)
\(d = 4.53\)

Right-side braces: \(n\), \(n_{1}\)

Fig. 24.

Plate 10.

For the article by Eng. K. N. Kartashov.

Fig. 25

Fig. 26.

Plate 11.

For the article by Eng. K. N. Kartashov.

Fig. 27.

I group of specimens

\[ \frac{P_{\max}\,\cdot\,1?\,?}{a}\ \text{mm} \times 100 \]
[[unclear: formula at upper left of Figure 28]]

Longitudinal specimens

\[ \delta \]

Fig. 28.

Transverse specimens

The designations are the same as for the longitudinal specimens.

In both cases, data are given only for nails with \(\varphi 4.53\ \mathrm{mm}\).

To the article by Engineer N. N. Kartyshov.

\[ \frac{\mathrm{kg}}{\mathrm{cm}^{2}} \]

Fig. 29.

II group of specimens

Sheet 13½
\(\Delta\)—mm × 100.

Fig. 30

Longitudinal specimens.

Legend:

• — planed, not bent
• -- not planed, not bent
• -·- not planed, bend upward
• -··- not planed, bend downward
• -···- planed, bend upward

Horizontal axis: \(0, 20, 40, 60, 80, 100, 120, 140, 160, 180, 200\), kg/cm².

For the article by Eng. K. N. Kartashov

Fig. 31

Transverse specimens.

The designations are the same as for the longitudinal specimens.

(Here only the data concerning nails with \(d = 4.06\) mm are given.)

Horizontal axis: \(0, 20, 40, 60, 80, 100, 120, 140, 160, 180, 200\), kg/cm².

Plate 14 to the article by Eng. N. N. Kartashov.

Fig. 32.

Facade

Section

Rupture

Nail before loading

Nail after loading

Fig. 33.

Fig. 34.

Fig. 35.

1. Handbook for Engineers of the Building Specialty, Vol. I, p. 427. ↩↩↩↩