ON THE QUESTION

OF MIXED SYSTEMS OF HANGING RAFTERS

A. D. Kryachkov.

Many of those who have dealt with the question of designing and constructing wooden and mixed systems of hanging rafters have felt the lack of the necessary information on this subject. This is especially noticeable when resolving practical questions: which system to adopt, how to design it rationally, what the details should be, and so forth—these are questions requiring clear answers, which cannot be found in Russian technical literature. The information set forth in Russian courses on architecture and building art is not extensive and, most importantly, does not provide a thorough critical assessment of systems of hanging rafters and of their individual varieties; in special publications and journal articles this question has likewise not been developed. The working drawings of most railway structures reveal in this field a striking conservatism among Russian engineers and architects. Hanging rafters on all railways are adopted as either only wooden or only iron; mixed structures are not encountered at all. At the same time, one may often find striking examples of the inexpediency and irrationality of the construction of wooden hanging rafters: their use in cases where there is every possibility of arranging simple inclined rafters, or the construction of heavy rafters over small spans. In general, here one observes a fear of wood—all spans greater than 6 sazhens are necessarily covered with iron rafters. A happy exception in this respect is constituted by the Northern Railways, and only on the Petrograd–Vyatka section: on this line the hanging rafters have been designed irreproachably, and systems of mixed rafters are often encountered.

What is especially striking is the predilection of Russian builders for systems of wooden rafters, the so-called “Palladio” type, in its original form. Despite all the irrationality of this system in comparison with others—its static indeterminacy and the weakness of its joints, owing to the obtuse angles of the connections in them—it remains to the present time the most widespread in Russia, beginning with the well-known hanging wooden rafters of the Moscow Manege and ending with modern roofs of railway civil structures and a long series of public buildings in the cities. Other constructions of wooden and mixed rafters are encountered rarely and likewise are not distinguished by rationality; a comparison of them with the wealth of methods in foreign construction brings out especially clearly the backwardness of Russian builders in this field.

As for the causes of this lamentable phenomenon, it will hardly be a mistake to attribute a considerable share of the blame for this backwardness of Russian engineers to the special higher schools. The instructors of the subjects in this specialty are too indifferent to the progress of technology in their field, too inclined to repeat the old, from which life has gone far ahead.

The enumeration and design by students of hanging rafters still begins with the Italian system of timber rafters, “Palladio.” Why precisely with it is incomprehensible. To every thoughtfully working designer, to every engineer, it is clear that this system, while geometrically immutable, does not permit asymmetrical loading, and in rafters one has to deal chiefly with such loads—the pressure on the roof from wind and snow. After the development of the theory of pin-jointed systems (the calculation of rafters), after it had been so clearly and convincingly stated that “the first visible sign of the unsuitability of any truss as a rigid body may be the mobility of some part of it” ¹), it would seem that this geometrically immutable system should be recognized, giving preference to more rational systems developed by contemporary technology.

To almost the same degree, there also applies to this system a second, no less evident sign of the unsuitability of a truss, indicated by Prof. Yasinsky—namely the existence in the truss of “such joints at which only two members lying on one straight line meet” ²).

In trusses of the “Palladio” system the members \(a—b\) and \(b—c\), Fig. 1, with slight roof slopes, meet at a very obtuse angle, i.e., form a line close to a straight line. This connection has an extremely unfavorable effect on the action of the truss. The weakest place from the structural point of view is the complicated joints (notches) of the queen-posts with a dovetail at an obtuse angle. However carefully they may be executed, there will always be small deficiencies which, in the six notches of the truss, will already produce considerable deformation of it. Further, drying and shrinkage in four places perpendicular to the fibers, not to mention accidental warping and cracks, will produce still more considerable changes in the shape of the truss, chiefly in the form of sagging of the tie beam, which, with the common method of rigidly connecting the queen-posts to the tie beam by iron straps, cannot be restored by anything. The arrangement of a purposeful device for tightening the tie beam by means of a strap with two screws is already a rather complicated construction. If, however, a ceiling structure is attached to this rafter truss, then—

Fig. 1.

¹) Prof. F. Yasinsky. Stability of Deformation and Statics of Structures. St. Petersburg, 1902, p. 90.
²) Ibid., p. 90.

…attached to it—this method, the one most often encountered in the practice of civil construction—reveals the weaknesses of the system with particular clarity.

The brilliant architect of Vicenza, Andrea Palladio, having designed the prototype of this truss 480 years ago, undoubtedly made a great step forward in the construction technology of his day for spanning large halls. For the period of the predominance of timber and the complete absence of iron in construction, this was a brilliant solution to an important problem. It may perhaps have been admissible even at the time of the construction (1816) of the well-known hanging rafters of the Moscow Manege, with a span of almost 22 sazhens, with their seven tie-beams, if one takes into account the rational introduction into them of braces that make this system geometrically unchangeable. But for our time, when the study of the strength of materials has shown how great is the settlement (compression) parallel to the fibers in such species of wood as pine,³ on the one hand, and the availability of iron and of the simplest products made from it everywhere, on the other, the repetition of Palladio’s construction and the use of wooden rafters in general are, at the very least, a sign of backwardness in technology.

If one turns to other systems of wooden hanging rafters, it will be seen that all the structural shortcomings of Palladio’s truss apply to them as well.

They reduce to the following:

1. distortion of the trusses when the timber dries out,
2. distortion of the trusses from the settlement of parts working in compression,
3. unreliability of the joints,
4. impossibility of providing simple, unchangeable joints because of the coarseness of the material.

These major shortcomings have compelled Western European and American builders to turn to iron and reinforced-concrete rafters. The latter have come into use recently, but deserve great attention. They are of special interest for the cases of which we are speaking here, i.e., for combining rafters with the ceiling structure of large halls in civil buildings.

Their advantage in this respect over iron ones lies in the expedient and simple connection of the ceiling with the rafters. The lower members of the rafter trusses, joined together by a light reinforced-concrete slab, form a fireproof ceiling over the hall. In view of their impeccable qualities—complete fire resistance, invariability of form, strength, durability—the entire future belongs to them. But at present, because of their price, they are accessible only to the West; for places such as Siberia they are used only as a rare exception.

Alongside iron rafters, Western technology has perfected the design of wooden hanging rafters, taking as its basis the same—

³ According to the latest investigations of the Mechanical Laboratory of the Tomsk Technological Institute, the settlement of pine at the onset of failure reaches up to 26.0% in dry timber (moisture content 8–10%).

V. Mramornov, “Some Data Concerning the Strength of Timber of Siberian Species,” Journal of the Society of Siberian Engineers, 1915, No. 1, p. 19, Table III.

...beginnings as for iron trusses as well. Considering the weakest points of wooden hanging structures to be the joints of the members working in tension, and the impossibility of regulating the settlement of the rafters caused by the loosening of the joints, a whole series of ingenious structures was created in which some wooden parts were replaced by iron or cast-iron ones.

The rational combination of these two materials, based on the principle of using iron for all members of the system subjected to tensile forces or having complex connections, and wood for those subjected to compression, made it possible to build inexpensive, light, and handsome coverings.

Taking into account the ease of constructing strong truss joints of iron or cast iron, the possibility of regulating the deflection and shrinkage of the timber by means of bolted iron connections, and also the insignificant shrinkage of the timber parallel to the fibers, these rafters are just as strong and invariable as iron ones.

These so-called mixed timber-and-iron rafters, representing a rational structure standing at the height of contemporary technology, were the logical development of the obsolete wooden hanging systems. And if in the West, with the easy availability of iron coverings, they are very widespread and successfully compete with iron rafters, then for Russia, and in particular for Siberia, rich in forests and poor in routes of communication, and remote from industrial centers, these structures are of special interest. Iron rafters are a rare luxury for Siberian towns situated along railways and waterways, by which alone their delivery is possible; for places lying to the side they are entirely inaccessible, while meanwhile the need is growing rapidly: the construction of large halls—educational, public, etc.—workshops, and factories increases with every year. This is why engineers working in Siberia must treat mixed systems of coverings with the attention they deserve and which they receive in the West.

In Russian technical literature, as was said above, apart from general and not always satisfactory indications on this question, there is almost nothing.

In V. G. Zalesky’s substantial work, Course of Architecture, several pages are devoted to this question and clear drawings are given. But, unfortunately, the constructions shown in the plates, because of the abundance of complex cast-iron parts at the connections, in the form of boxes, shoes, and the like, may sooner frighten away an engineer wishing to make use of these structures than encourage research in this direction, for complex cast-iron castings are often more difficult to obtain than an entirely iron truss. Moreover, the absence of examples of the most interesting cases of designing these systems, in connection with the construction of ceilings of the upper stories of covered premises, makes the indications given of little value.

French and German literature on this question possess excellent material. In the monumental edition of Breymann, which appeared six times, a chapter of 150 pages is devoted to this section. In special journals one can find a whole series of descriptions of individual cases; handbooks likewise provide abundant material on this question.

In civil structures, the most frequently encountered and complex constructions are the coverings of large halls by hanging rafter structures, combined with ceiling coverings—so to speak, suspended from the rafter trusses. Here what is needed is not only a strong roof covering, but, most importantly, an unchanging structure for the suspended ceiling, i.e. for the tie-beams of the truss; and since sagging of the tie-beams is the most common phenomenon in hanging rafters, it is this that must chiefly be taken into account.

The indications of some authors ^4) regarding the circumstance that ceilings suffer from the variable load of wind and snow on rafters connected with beams have, in my practice of more than ten years ^5), not been confirmed. In all systems of hanging rafters arranged by me and connected with ceiling structures, cracks in the ceiling plaster have not appeared for this reason.

Another type of covering frequently encountered in practice is the so-called warm roof, arranged on open hanging rafters; this construction is used for factory and industrial buildings. The most rational system in these cases is the Polonceau system. In outward appearance it is the lightest and most graceful, does not clutter the premises, and, by virtue of its simplicity, is the easiest to execute.

I should like to cite three examples of constructions of this kind carried out by me.

Here the hanging rafters are made without complicated details—all the cast-iron parts usually recommended are replaced by simple iron connections.

For the first and second coverings—the hall of the city schools in Novo-Nikolaevsk, drawing 8, and the hall of the central city building in Omsk, drawing 14—the American mixed system of rafter trusses was adopted; for the third—the foundry at the workshops of the Omsk Mechanical-Technical School, drawings 15–17—the French mixed Polonceau system.

In choosing one or another system of timber-and-iron rafters, we were guided by the following considerations:

Of the numerous mixed systems of timber-and-iron rafters used abroad, the following four are the most rational and practical:

^4) V. Zalesskii, Prof., Architecture. Moscow, 1904, p. 413.
^5) Hall coverings: Novo-Nikolaevsk Public Assembly—span 6.00 saz.; Novo-Nikolaevsk Real School—span 5.00 saz.; N.-Nikolaevsk City School—span 5.70 saz.; Omsk Mechanical-Technical School—5.60 saz.; Omsk City Building—7.20 saz.; Tomsk Secondary Polytechnic School—8.00 saz.

1, American, Fig. 2;
2, the French tie-beam “Polonceau,” Fig. 3;
3, arched, — a, according to Emy’s system; an example of it is given in Fig. 4;
— b, according to de l’Orme’s system; an example of it is given in Figs. 5 and 6; and
4, German, Fig. 7.

All other systems are a more or less successful variety of the last, German, system.

Fig. 2.

Both these latter systems and the arched systems have hitherto been used chiefly for temporary structures, such as exhibition buildings, or open-type constructions—summer kursaals, railway stations, coverings of hippodrome grandstands, church domed roofs, etc.—structures in which deformations within known limits are not dangerous and are hardly noticeable.

Fig. 3.

Of the drawings presented, Fig. 4 represents the covering of a hall for celebrations and gymnastics in Darmstadt. The use of these constructions for buildings in which great strength and constancy of the dimensions of the construction are required cannot be regarded as rational.

The reason for this is clear: it lies in the fact that these systems of roof trusses, consisting of a multitude of small wooden parts, undergo, over time, considerable changes through drying, warping, and also as a consequence of the considerable pressure experienced by the wood.

in trusses. Consequently, they cannot be considered suitable for permanent heated buildings. In general, as a rule, in the

design of mixed and wooden rafters, systems with the smallest number of separate elements and connections should be preferred—this guarantees smaller subsequent deformations of the trusses.

Of the remaining systems enumerated above, the only one suitable for roofing a hall on the upper story, i.e., for the case of arranging rafters in connection with a horizontal ceiling floor in a residential building—

Drawings 5 and 6.

—is the American system, in which a wooden ceiling beam, either solid or built-up, can successfully serve as the tie.

Drawing 7.

We shall now turn to roof structures executed by the author.

The roofing of the hall of the city schools in the town of Novo-Nikolaevsk is shown in drawing 8.

The construction of the rafters and of the ceiling floor is executed, as shown in the drawing: the distance between trusses is 2 meters; the span being covered—

span of 12 m. The construction of the ceiling—usually arranged over living quarters: beams \(20 \times 25\) cm, hewn on four edges, are placed 2 m from axis to axis; between them are boards 9 cm thick, on edge; on them is a rough ceiling of 6.5 cm boards. On the rough ceiling lies a layer of daubing made of clay and chopped straw, 10 cm thick. Under the beams there is sheathing and plastering of the ceiling over felt.

In designing the trusses, attention was directed chiefly to the simplicity of the iron parts and to the possibility of making them in an ordinary smithy. All shoes and other cast-iron parts are replaced by simple iron straps, bolts, and other forgings.

Thus, in the truss the following are adopted: the tie-beam, rafter legs, and struts are of wood; the rods—instead of wooden king-posts—are of round iron; all connections at the joints, such as straps, plates, etc., are of strip iron.

Drawing 8.

In view of the fact that the trusses support, besides the roof, also the ceiling—plastered and with clay work—it was impossible to allow any deflection of the tie-beam; and since, as the timber dried, such deflection would have to occur, it became necessary, in order to regulate the sag, to provide screw ties on the rods.

Calculation of the rafter parts.

In calculating the rafters it is assumed that the entire thrust is taken up by the tie-beam \(AA_1\), Drawing 9, p. 10, and that therefore the support reaction is vertical.

The calculated span of the rafters \(AA_1 = 12.5\) m,

the calculated length of the rafter leg \(AC = 6.5\) m,

parts \(AB = 3.70\) m, \(BD = 3.30\) m,

the length of the tie-beam \(DC = 3.30\) m;

the angle of inclination of the rafter leg to the horizon:

\[ \alpha = 28^\circ;\quad \cos \alpha = 0.88;\quad \sin \alpha = 0.47. \]

Distance between rafter trusses . . . . . 2 m.

Permanent load.

The load per 1 sq. m of roof is taken as:

roofing of iron . . . . . . . . . . . 49 kg
sheathing . . . . . . . . . . . . . . 41 kg

――――――――――
90 kg,

which will amount, per 1 sq. m of roof projection, to:

\[ \frac{90}{\cos \alpha}=\frac{90}{0.88}=102\ \text{kg}, \]

and together with the self-weight of the rafter truss will give about 150–160 kg per 1 m² of the horizontal projection of the roof.

Drawing 12.

Temporary load.

The load from snow and wind is taken as the greatest of three quantities:

1. the pressure of snow on 1 m² of the horizontal projection of the roof,

\[ Q=100\ \text{kg}; \]

whence the pressure on 1 m² of roof surface is

\[ q_0=100\cos\alpha\ \text{kg}; \]

and the pressure on 1 m², normal to the roof slope, is:

\[ q=100\cos^2\alpha=100\times(0.88)^2=77.44\ \text{kg}; \]

1. the pressure of the wind on 1 m² of a plane perpendicular to its direction, assuming that the direction of the wind makes an angle of \(10^\circ\) with the horizon; take

\[ h=180\ \text{kg}/\text{m}^2; \]

then the wind pressure on 1 m², normal to the roof slope, is:

\[ r=180\sin^2(\alpha+10^\circ)=180\sin^2 38^\circ=180\times(0.63)^2=71.44\ \text{kg}; \]

1. the pressure, normal to the roof slope, on 1 m² of roof surface under the combined action of snow and wind:

\[ P_1=\frac{3}{4}q+\frac{2}{3}r=\frac{3}{4}\cdot77.44+\frac{2}{3}\cdot71.44=105\ \text{kg}. \]

We take the most unfavorable load, normal to the roof slope, which occurs in the third case, i.e. 105 kg per \(1\ \text{m}^2\), which amounts, per \(1\ \text{m}^2\) of horizontal projection of the roof, to

\[ \frac{105}{\cos^2\alpha}=\frac{105}{(0.88)^2}=136.6\ \text{kg}/\text{m}^2. \]

Total load.

Weight of the roof and truss per \(1\ \text{m}^2\) of roof projection . . . 160 kg.
weight of snow and wind . . . . . . . . . . . . . . 137 kg.

\[ \text{total}\quad 297\ \text{kg}. \]

In addition, a ceiling is attached directly to the tie-beams of the rafter trusses, consisting of beams, a rough plank ceiling, clay-and-straw daubing in a layer of 10 cm, felt lining, and felt upholstery; all this gives a load of 70 poods/sq. sazhen \(=177.7\ \text{kg}/\text{m}^2\) ^6).

Since the distance between the axes of the rafter feet is equal to 2 m, the rafter truss along the foot \(AC\) will be loaded with the vertical uniformly distributed load

\[ \frac{12.50\times2\times296}{2}=3700\ \text{kg}. \]

Along the tie-beam the truss is loaded with the load

\[ 177.7\times12\times2=4264.8\ \text{kg}. \]

At point \(B\) the vertical load transmitted is

\[ P_1=\frac{3700}{6.70}\times\frac{(3.50+3.30)}{2}=1932\ \text{kg}. \]

At point \(C\) the vertical load transmitted is

\[ P_2=\frac{3700\times3.30}{6.70}=\infty\ 1823\ \text{kg}. \]

At point \(A\) the vertical load transmitted is

\[ P_3=\frac{3700\times3.50}{6.70\times2}=1022\ \text{kg}. \]

Determination of forces in the parts of the truss.

The force compressing the foot,

\[ S_1=\frac{P_1\sin(90^\circ-\alpha)}{\sin 2\alpha} =\frac{1932\sin62^\circ}{\sin56^\circ} =\frac{1932\times0.88}{0.83}=2050\ \text{kg}. \]

The force compressing the strut,

\[ S_1^{1}=S_1=2050\ \text{kg}. \]

^6) Count N. I. de Rochefort. Illustrated Schedule Regulation, p. 170.

Along the two struts the compressive forces are transmitted to the tie and give the resultant tensile force in the tie

\[ R = 1932 \ \text{kg}. \]

Thus, in all, there is transmitted to point \(C\):

\[ 1823 + \frac{4264}{2} + 1932 = 5887 \ \text{kg}. \]

This force is resolved along the legs, so that on each leg there falls:

\[ T_1=\frac{5887 \sin 62^\circ}{\sin 56^\circ} =\frac{5887 \times 0.88}{0.83}=6241.74 \simeq 6242 \ \text{kg}. \]

The force compressing the lower part of the rafter leg \(AB\),

\[ T_2=T_1+S_1^{1}=6242+2050=8292 \ \text{kg}. \]

The tensile force in the tie with the king-post:

\[ T=\frac{4264}{2}+1932=4064 \ \text{kg}. \]

The tensile force \(T\) in the tie is determined from the condition of equilibrium of forces—the sum of the moments of all the forces \(P_1\), \(P_3\), and \(T\) with respect to point \(C\) is equal to zero:

\[ \Sigma M=P_1 \times 6.25-P_3 \times 3.12-T \times 3.30=0, \]

where \(P_1\) is the bearing reaction, equal to

\[ 3700+\frac{4264}{2}=\simeq 5832 \ \text{kg}, \]

\(P_3\) is the resultant of the vertical load on the leg \(AC\), equal to 3700 kg;

then

\[ T=\frac{5834 \times 6.25-3700 \times 3.12}{3.30}=7549 \ \text{kg}. \]

The value obtained for \(T\) is positive; this indicates that the force in the tie is tensile.

Determination of the dimensions of the parts of the truss:

Part \(AB\) of the rafter leg:

uniformly distributed load:

\[ 2P_3=1022 \times 2=2044 \ \text{kg}; \]

the component normal to the leg,

\[ P=2044 \times \cos \alpha=2044 \times 0.88=1799 \ \text{kg}; \]

compressive force

\[ T_2=8292, \]

\[ M=\frac{Pl}{8}=\frac{1799 \times 370}{8}=83204 \ \text{kg·cm}; \]

the section modulus of the section of the leg, Fig. 11,

\[ W=\frac{23 \times 27^2}{6}=2430 \ \text{cm}^3; \]

whence we obtain the total stress

\[ k=\frac{M}{W}+\frac{T_2}{\omega} =\frac{83204}{2430}+\frac{8292}{396} =55.2 \ \text{kg/cm}^2, \]

which is less than the allowable \(60 \ \text{kg/cm}^2\).

Part \(BC\) of the rafter leg; the section is the same—\(20 \times 27\) cm. It is not necessary to check it, since the forces acting in part \(BC\) are less than in \(AB\).

The uniformly distributed load is \(18.23\) kg.

Compressive force:

\[ T_1 = 6242\ \text{kg}. \]

The strut is subjected to a compressive force:

\[ S_1 = 2050\ \text{kg}. \]

The section of the strut is taken as \(18 \times 20\) cm.

The stress in the material will be

\[ k = \frac{2050}{360} = 5.7\ \text{kg}/\text{cm}^2. \]

The large section has been taken for convenience of arrangement.

The iron tie-rod is subjected to a tensile force equal to \(4064\) kg.

The section of the tie-rod is taken as circular, with a diameter of \(2.5\) cm; the stress in the material will be

\[ k = \frac{4064 \times 4}{314 \times 2.5^2} = 828.12\ \text{kg}/\text{cm}^2, \]

which is less than the allowable \(1000\ \text{kg}/\text{cm}^2\).

The tie beam is subjected to a tensile force \(T = 7549\) kg and, in addition, to a bending moment from the uniform load of \(177.76\ \text{kg}/\text{m}^2\).

Since the tie beam is supported at the middle, the force bending the tie beam will be

\[ P = \frac{12.50 \times 2 \times 177.76}{2} = 2221\ \text{kg}. \]

The bending moment is

\[ M = \frac{2221 \times 600}{8} = 1665.6\ \text{kg}\cdot\text{cm}. \]

The tie beam consists of a timber with section \(20 \times 25 = 500\ \text{cm}^2\).

The section modulus is

\[ W = 2 \frac{20 \times 25^2}{6} = 4166\ \text{cm}^3. \]

The stress in the material of the tie beam will be:

\[ k = \frac{M}{W} + \frac{T}{\omega} = \frac{166560}{4166} + \frac{7549}{500} = 55.10\ \text{kg}/\text{cm}^2, \]

which is less than the allowable \(100\ \text{kg}/\text{cm}^2\).

Further, in Fig. 11 is shown the type of hanging rafters of a mixed “American” system over the large hall of the Omsk Commercial Building, with a span of 15 m. Their construction is close to that described above, Fig. 8; the dimensions of its parts are shown in the drawing.

A special feature of these trusses is that the arrangement of the rafter feet is independent of the trusses. The trusses are placed at a distance of 3.5 meters from one another; between them one intermediate beam is laid, suspended by a bolt from the middle lower purlin; on the trusses are laid two side purlins and a middle upper purlin, serving as supports for the rafter feet. The latter are laid at a distance of 1.75 meters from one another.

Drawing 14.

In conclusion we shall indicate the roofing of the foundry at the workshops of the Omsk Mechanical-Technical School, drawings 15–17.

Drawings 15–17.

The construction of the roof covering is adopted, as was said above, with Polonceau trusses; but a warm roof is arranged on the rafters.

The trusses are placed at a distance of 1.80 m axis to axis. The rafter feet, of pine beams \(20 \times 24\) cm, rest on wooden wall-plates—

rafters. All the remaining parts of the trusses that work in tension are made of strip iron \(5.5 \times 1.5\) cm; the lower ends of the strips, formed into a round bolt shape, are passed through the drilled lower ends of the rafter legs and end in a screw thread; the nut on it, with the aid of a washer of strip iron, of a length corresponding to the thickness of the beam \(5.5 \times 15\) cm, transmits the pressure over a large area of the end of the rafter leg, thereby preventing crushing of the wood. The upper ends of the strips embrace, by means of collars, the slightly notched upper ends of the rafter legs, as shown in the plan. The connection of the strips with one another is made by means of rivets. In this connection one should point out the particular simplicity and lightness of these joints in Polonceau trusses. Since the strips \(a\)-\(b\)-\(c\) and \(c\)-\(d\)-\(e\) are continuous, it remains only to rivet to them the horizontal tie \(b\)—\(d\), i.e., to place 6—8 rivets. Adjustment of deformations due to drying, etc., which in our case, thanks to the small number of joints, is insignificant, is possible with the aid of the screws at the ends of the iron strips. The struts in the trusses, working in compression, are made of old iron \(2^{1/2}\)-inch pipes. The pipes are let 2.5 cm into the rafter leg by means of a square socket, in which, to prevent crushing, a pad of boiler iron \(^{1}/_{4}\) inch = 0.6 cm thick is placed. The other end of the strut bears against the strip of the ties, to which plain rib plates are riveted with the common rivets in order to form a socket. The simplicity, speed of assembly, and cheapness of this roof structure are evident.

In conclusion, we wish Russian builders to pass as soon as possible from the obsolete timber constructions of hanging rafters to modern rafters. May Siberian engineers go ahead in this field and say a new word.

Tomsk. Steam Printing House of P. K. Orlova.