Prof. M. I. Evdokimov-Rokotovsky

THE CURIOUS CASE

OF THE DESTRUCTION OF A BRIDGE TRUSS

with a span of 123.75 meters.

Tomsk

1929

Prof. M. I. Evdokimov-Rokotovsky.

The Curious Case of the Destruction of a Bridge Truss

with a span of 123.75 m

On one of the railway lines of the U.S.S.R., at the crossing over a river flowing into Big Lake, there is a bridge with a span of 123.75 m. (58 sazhens). In recent years the bridge truss has produced a number of mysterious cracks. Hairline cracks, in small number, were first noticed as early as 1918. At that time, however, no particular significance was attached to them. During an inspection of the bridge trusses in the spring of 1925, 13 cracks were already counted. Some of them reached a width of 0.3 mm. In the autumn of 1926, during the most careful inspection of the bridge truss, as many as 52 cracks were counted.

The cracks noticed and, so to speak, registered in the spring of 1925, numbering 13, are schematically marked on the appended drawing (Fig. No. 1).

Lower truss

West                                                                                                                                                                        East

Upper truss

Fig. No. 1. Diagram of the bridge showing the locations of the 52 cracks. The numbered thirteen cracks were discovered in the spring of 1925.

Crack No. 1 in the post \(S_{8-9}\), on the western side of the right truss, is barely noticeable; it passes only through part of the angle, starting from the edge.

Crack No. 2 in the angle of the upper chord \(O_{9-11}\) of the right truss. The width of the crack is about 0.1 mm. The crack passes through the entire angle.

Fig. No. 2. Crack No. 3 in the angle of the upper chord \(O_{13-15}\). Crack width 0.3 mm. The crack passes through the entire angle.

Crack No. 3 is likewise in the angle of the upper chord \(O_{13-15}\) of the same right-hand truss, but its width is somewhat greater and reaches 0.3 mm (Drawing No. 2). The crack passes through the entire angle.

Cracks No. 4 and No. 5 are in post \(S_{24-25}\) of the right-hand truss (Drawing No. 3). The cracks pass through one leg of the angle.

Crack No. 6 is in post \(S_{28-29}\) of the right-hand truss (Drawing No. 4).

Crack No. 7 is in post \(S_{8-9}\) of the left-hand truss (Drawing No. 5).

Cracks No. 8 and 9 are in post \(S_{16-17}\) of the left-hand truss (Drawing No. 6).

Drawing No. 3. Cracks No. 4 and No. 5 in post \(S_{24-25}\). Width of the cracks: 0.2 mm. The cracks pass through one leg of the angle.

Drawing No. 4. Crack No. 6 in post \(S_{28-29}\) of the right-hand truss. Width of the crack: 0.25 mm.

Crack No. 10 is in post \(S_{20-21}\) of the left-hand truss.

Cracks No. 11 and 12 (Drawing No. 7) are located in post \(S_{21-23}\) of the left-hand truss. Crack No. 11, 203 millimeters long and up to 0.3 mm wide, begins at the corner of the angle, runs for 57 mm perpendicular to the edge, and then turns parallel to the edge, runs for another 146 mm, and there dies out.

Crack No. 12 is hairline, barely noticeable; it runs from the edge of the angle along one leg, cuts the angle completely, and on the other leg does not reach the end by 8 mm.

Crack No. 13 is in the same post as the preceding two cracks, but somewhat below them. The size of crack No. 13 is considerably smaller.

In view of such destruction of the bridge truss, already in the spring of 1925 there arose concern for the integrity and preservation of the structure. The first measur—

the enterprise was that all 13 cracks noticed then were covered with riveted cover plates, just as joints are usually covered.

In the autumn of 1926, upon a very careful inspection of the bridge, as many as 52 cracks were counted.

Drawing No. 5. Crack No. 7 in post \(S_{16-17}\) of the left truss. Width of the crack 0.3 mm; it runs from the leg of the angle, through one flange.

Here is the final list of the known and, so to speak, registered cracks of the bridge (September 1926).

Top (southern) truss:

Lower chord: in the chord angles—\(U_{4-6}\), \(U_{6-8}\), \(U_{8-10}\), \(U_{10-12}\), \(U_{12-14}\), \(U_{18-20}\) (two cracks), \(U_{20-22}\) (two cracks), \(U_{22-24}\).

Upper chord: in the chord angles—\(O_{9-11}\), \(O_{13-15}\), \(O_{15-17}\), \(O_{31-32}\).

Posts: in the main angles—\(S_{4-5}\), \(S_{8-9}\) (three cracks), \(S_{12-13}\), \(S_{16-17}\), \(S_{24-25}\) (two cracks), \(S_{28-29}\) (three cracks).

In all, in the top (southern) truss, 25 cracks.

Bottom (northern) truss:

Lower chord: in the chord angles—\(U_{0-2}\) (two cracks), \(U_{2-4}\) (two cracks), \(U_{6-8}\) (three cracks), \(U_{10-12}\) (three cracks), \(U_{12-14}\) (two cracks), \(U_{20-22}\), \(U_{30-32}\) (two cracks).

Drawing No. 6. Cracks No. 8 and No. 9 in post \(S_{16-17}\) of the left truss. The cracks are located in the braces running from the post. View from the side of the eastern abutment of the bridge.

Posts: in the main angles—$S_{8-9}$ (two cracks), $S_{12-13}$ (two cracks), $S_{16-17}$ (two cracks), $S_{20-21}$ (two cracks), $S_{24-25}$ (four cracks).

In all, in the bottom (northern) truss there were 27 cracks.
And in total, 52 cracks.

By their nature, the cracks may be divided into three types. The majority of cracks occur only on one leg of an angle and run from the edge perpendicular to the edge of the angle.

Much less frequent are cracks that pass through both legs of the angle.

Finally, the third type of crack (there are only three such cracks in all) is when the cracks run parallel to the edge of the angle.

In three cracks paint was found, indicating that these cracks had formed before the bridge was painted the last time, i.e., apparently, before July 1915.

In addition to cracks, buckling and local distortion were found in many members of the truss. Bending and cracks were also found in the diagonals of the sway bracing.

The riveting was everywhere found to be quite satisfactory.

In view of all the above, it is entirely natural that it was necessary to examine the circumstances under which the cracks arose and to investigate the question of the origin of the cracks as fully and comprehensively as possible.

In view of the above-described damage to the bridge truss, in September 1926 a thorough inspection was carried out, followed by static and dynamic testing of the truss.

1. Inspection of the bridge truss.

The truss was designed by Prof. L. D. Proskuryakov according to the Schwedler system and calculated by the standards for moving railway loading of 1896. The design of the bridge truss, as a type, was at the time adopted for the Vitebsk–Zhlobin Railway, for which it was approved by the Committee of the Administration for the Construction of Railways on March 9, 1900, under No. 214.

The principal dimensions of the truss are as follows:

Item	Value
Calculated span of the truss	126.796 m = 416′
Length of the large panel	15.850 m = 52′
Length of the small panel	7.925 m = 26′
Calculated height of the truss at midspan	18.897 m = 62′
Number of panels	16
Ratio of the greatest calculated height of the truss to the span	1 : 6.71
Distance between truss axes	7.010 m = 23′
Actual height of the truss at midspan	19.297 m = 63′ 3.75″

Camber: 0.4 m, which amounts to $\dfrac{1}{3170}$ of the span.

Item	Value
Weight of the trusses with bracing	504.667 t = 30807.86 poods
Weight of the metal of the roadway	108.981 t = 6652.85 poods
Weight of the railings	3.409 t = 208.05 poods
Weight of the bearing parts	17.768 t = 1084.67 poods
Thus the total weight of metal in the bridge	634.825 t = 38753.43 poods

According to the design and the longitudinal profile of the track, the bridge was to be located on a straight line and on a horizontal grade.

The inspection and measurement of the bridge trusses gave the following data:

The full length of the bridge superstructure along the roadway, according to measurements in situ, is 128.60 m.

![Engineering drawing showing truss-column details with riveted plates, cross-bracing, dimensions, and section labels. Visible annotations include: “410,” “700,” “810,” “720,” “110×110×12,” “wall of the top chord,” “axis of the truss,” and “wall of the bottom chord.”]

Drawing No. 7. Cracks Nos. 11, 12, and 13 in post \(S_{24-25}\) of the left truss.

The chords of the trusses are of box section, the diagonals of I-section, and the posts of tubular section.

Longitudinal bracing is provided in the planes of both chords, and transverse bracing at the supports and in the planes of the main posts. The longitudinal bracing consists of struts and crossing diagonals; the transverse bracing is in the form of inclined support frames at the supports and in the form of struts and St. Andrew’s crosses in the span.

The roadway consists of continuous solid longitudinal beams, openwork transverse beams, and the bridge deck. The longitudinal beams of the roadway are connected rigidly to the transverse beams by means of vertical angles, and the transverse beams are connected rigidly to the trusses by means of gusset plates.

The movable bearing parts of the bridge are located on the western abutment and consist of upper and lower rockers, a hinge between them, cylindrical rollers, and a lower bedplate.—The fixed bearing parts consist of two rockers, a hinge between them, and a lower bedplate.

The absolute elevations of the tops of the bearing stones according to the leveling are given in Table I.

Table I.

Bearing stones	Abutment	Abutment
Bearing stones	Western	Eastern
Bearing stones	Movable bearing	Fixed bearing
Southern (right) . . . .	617,862	617,830
Northern (left) . . . .	617,860	617,841

Fig. No. 8. Results of leveling along the upper plate of the lower chord.

Thus the sub-truss bearing platforms proved not to be at the same elevation, as a result of which the bridge is not located on a horizontal plane, and in addition there is a skew of the trusses in situ.

Next, leveling was carried out at the nodes of the main trusses along the upper flange of the first horizontal plates of the lower chord. During the leveling, the air temperature was \(+8^\circ\) C. The weather was rainy; the sky was completely (100%) covered with clouds. The rods used in leveling were simple, non-folding, without levels.

The results of the leveling are collected in Table II and presented graphically (drawing No. 8).

Table II.

Nos. of truss nodes	Leveling results along the upper plate of the lower chord (absolute elevations): Upper (southern) truss	Leveling results along the upper plate of the lower chord (absolute elevations): Lower (northern) truss	Excess of the lower chord of the lower truss over the upper truss in mm	Absolute elevations of the ideally straight line of the upper plate of the lower chord: Upper (southern) truss	Absolute elevations of the ideally straight line of the upper plate of the lower chord: Lower (northern) truss	Ordinates (by leveling) of the upper plate of the lower chord from the ideally straight line: Upper, southern truss, mm	Ordinates (by leveling) of the upper plate of the lower chord from the ideally straight line: Lower, northern truss, mm
0	618,760	618,759	−1	618,760	618,759	0	0
1	618,791	618,783	−8	618,758	618,758	33	25
2	618,819	618,809	−10	618,757	618,757	62	52
3	618,846	618,834	−12	618,755	618,756	91	78
4	618,863	618,861	−2	618,754	618,755	109	106
5	618,871	618,877	+6	618,752	618,754	129	123
6	618,881	618,878	−3	618,751	618,753	130	125
7	618,885	618,883	−2	618,750	618,752	135	131
8	618,891	618,887	−4	618,748	618,750	143	137
9	618,886	618,886	0	618,746	618,749	140	137
10	618,882	618,882	0	618,745	618,748	137	134
11	618,878	618,873	−5	618,744	618,747	134	126
12	618,858	618,856	−2	618,742	618,746	116	110
13	618,831	618,833	+2	618,741	618,745	90	88
14	618,803	618,802	−1	618,739	618,743	64	59
15	618,761	618,780	+19	618,738	618,742	23	38
16	618,736	618,741	+5	618,736	618,747	0	0

Thus, on the basis of the leveling, it turned out that, contrary to the design and the longitudinal profile, the bridge is not located on a horizontal plane, but with a slope from west to east.

The greatest difference in the elevations of the bearing points in the transverse direction is 5 mm; namely, the eastern end of the upper truss is lower than the corresponding end of the lower truss.

For determining the longitudinal profile of the rail track, the latter was leveled along the rail heads. The results of the leveling are summarized in Table III and presented graphically (Fig. No. 9).

Fig. No. 9. Results of leveling along the rail head.

Table III.

No.	Leveling results along the rail head, in absolute elevations: upper (southern) chord	Leveling results along the rail head, in absolute elevations: lower (northern) chord	Excess of the lower chord over the upper chord, in mm	Theoretical position of the rail head, in absolute elevations: upper (southern) chord	Theoretical position of the rail head, in absolute elevations: lower (northern) chord	Ordinates (by leveling) of the rail head relative to the theoretical position: upper (southern) chord, mm	Ordinates (by leveling) of the rail head relative to the theoretical position: lower (northern) chord, mm
0	620,660	620,660	0	620,660	620,660	0	0
1	620,668	620,664	−4	620,656	620,654	12	10
2	620,681	620,681	0	620,652	620,652	29	29
3	620,686	620,683	−3	620,647	620,647	39	36
4	620,708	620,707	−1	620,643	620,643	65	64
5	620,722	620,720	−2	620,639	620,638	83	82
6	620,730	620,725	−5	620,635	620,634	95	91
7	620,727	620,725	−2	620,631	620,630	96	95
8	620,727	620,727	0	620,626	620,626	101	101
9	620,730	620,728	−2	620,622	620,621	108	107
10	620,726	620,725	−1	620,617	620,616	109	109
11	620,723	620,721	−2	620,613	620,612	110	109
12	620,700	620,699	−1	620,609	620,608	91	91
13	620,674	620,673	−1	620,605	620,604	69	69
14	620,647	620,647	0	620,601	620,599	46	48
15	620,618	620,618	0	620,596	620,594	22	24
16	620,592	620,590	−2	620,592	620,590	0	0

The construction height of the span structure, as measured with a steel tape, proved to be:

On the movable support . . . . . . 2800 2800 mm.
On the fixed support . . . . . . 2750 2760 mm.

The question was clarified as to how far the construction camber of the truss had been preserved. From Fig. No. 8 it is seen that the curves of the construction camber of the truss have a satisfactory outline; specifically, the magnitudes of the camber at midspan are equal to:

For the lower (northern) truss, 137 mm, or

\[ \frac{1}{925}\,l. \]

For the upper (southern) truss, 143 mm, or

\[ \frac{1}{886}\,l. \]

This must be regarded as normal; in other words, the construction camber has been preserved.

Next, the magnitudes of the rises of the trusses and of the rail track were determined at midspan and at the maximum. The results obtained were as follows (Fig. No. 9).

For the lower (northern) rail thread, for the middle of the bridge span, 101 mm, or

\[ \frac{1}{1252}\,l. \]

For the upper (southern) rail thread, for the middle of the bridge span, 102 mm, or

\[ \frac{1}{1242}\,l. \]

Fig. No. 10. Arrangement of the trusses and of the rail track with respect to the geometric axis of the bridge.

The maximum elevation of the rails, however, was not in the middle and was equal to:

For the lower (northern) rail line, 109 mm, or \(\dfrac{1}{1160}\,l\).

For the upper (southern) rail line, 110 mm, or \(\dfrac{1}{1150}\,l\).

Finally, measurements were made of the positions of the trusses and of the rail track relative to the geometric axis of the bridge. The theoretical axis was laid out by the bearing frames of the bridge trusses; then measurements were made with respect to each truss joint, both of the northern (lower) and of the southern (upper) truss. The setting-out of the axes was performed for the lower chord with a Zeiss level, and for the upper chord with a Gerlach theodolite. The results of these measurements are given in the table and shown graphically in the drawing (Drawing No. 10).

Table IV.

		Lower (northern) truss	Lower (northern) truss	Axis of the upper chord	Axis of the rail track	Upper (southern) truss	Upper (southern) truss
		Lower chord	Upper chord			Lower chord, m	Upper chord, m
1	1	+3,411	+3,411	0	−0,015	−3,411	−3,411
2	3	+3,403	+3,410	−0,03	−0,003	−3,416	−3,419
4	5	+3,395	+3,407	−0,020	−0,008	−3,403	−3,414
6	7	+3,399	+3,411	−0,008	+0,009	−3,408	−3,412
8	9	+3,392	+3,418	−0,011	+0,008	−3,409	−3,418
10	11	+3,399	+3,413	−0,008	+0,010	−3,407	−3,418
12	13	+3,399	+3,408	−0,006	+0,023	−3,415	−3,418
14	15	+3,405	+3,415	+0,002	+0,009	−3,421	−3,417
16	17	+3,408	+3,402	−0,001	+0,001	−3,412	−3,403
18	19	+3,398	+3,400	−0,004	−0,001	−3,414	−3,405
20	21	+3,410	+3,409	+0,015	−0,001	−3,429	−3,409
22	23	+3,419	+3,417	+0,023	−0,002	−3,444	−3,418
24	25	+3,417	+3,417	+0,020	−0,008	−3,438	−3,423
26	27	+3,425	+3,425	+0,014	−0,019	−3,432	−3,438
28	29	+3,421	+3,434	+0,020	−0,004	−3,445	−3,445
30	31	+3,409	+3,422	+0,009	−0,016	−3,433	−3,437
32	32	+3,411	+3,411	0	−0,022	−3,411	−3,411

Thus we see that the positions of the axes of the upper and lower chords of the right and left trusses are incorrect: the whole truss is bent in the longitudinal direction in an S-shape. The greatest deviation of the lower chord from its theoretical axis reaches 33 m. toward the northern side (at joint 23 of the upper southern truss) and 19 mm toward the southern side (at joint 8 of the lower northern truss). The greatest deviation of the upper chord is 34 mm (at joint 29 of the upper truss).

The greatest magnitude of displacement of the upper chord in plan relative to the lower chord reaches 26 mm for joints 8–9 of the lower truss.

On the basis of the data from measuring the geometric positions of the truss elements, it is possible to take into account the influence of the deviation in the distribution of loads between the trusses from the theoretical one.

If we denote by \(\Delta\) the discrepancy between the axis of the span structure (the geometric locus of the midpoints of the distances between the trusses) and the axis of the track, and by \(b\) the width of the bridge, the distance between the trusses, then the truss located closer to the track must take upon itself the greater share of the load.

Maximum discrepancy according to the measurement

\[ \Delta_{\max}=33\ \text{mm}, \qquad b=7{,}010\ \text{mm}. \]

\[ \frac{\dfrac{\frac{b}{2}+\Delta}{b}-\frac{1}{2}}{\frac{1}{2}}\cdot 100 =0{,}954\%. \]

Thus the magnitude of the overload turns out to be quite insignificant.

Determination of the geometrical regularity of the individual members of the truss gave the following results.

Table V.

Upper truss: name of truss member	Upper truss: absolute amount of deformation, m	Upper truss: ratio to length	Upper truss: direction of deflection	Lower truss: name of truss member	Lower truss: absolute amount of deformation, m	Lower truss: ratio to length	Lower truss: direction of deflection
\(O_{1-3}\)	—	—		\(O_{1-3}\)	—	—
\(O_{3-5}\)	—	—		\(O_{3-5}\)	—	—
\(O_{5-7}\)	0,018	\(\frac{1}{467}\)	inward	\(O_{5-7}\)	0,007	\(\frac{1}{1203}\)	inward
\(O_{7-9}\)	0,008	\(\frac{1}{1055}\)	outward	\(O_{7-9}\)	0,010	\(\frac{1}{842}\)	inward
\(O_{9-11}\)	0,003	—	S-shaped	\(O_{9-11}\)	0,006	—	S-shaped
\(O_{11-13}\)	0,008	\(\frac{1}{1000}\)	outward	\(O_{11-13}\)	0,008	\(\frac{1}{1000}\)	S-shaped
\(O_{13-15}\)	0,011	\(\frac{1}{720}\)	outward	\(O_{13-15}\)	0,005	\(\frac{1}{1587}\)	S-shaped
\(O_{15-17}\)	0,012	\(\frac{1}{660}\)	outward	\(O_{15-17}\)	0,012	\(\frac{1}{660}\)	outward
\(O_{17-19}\)	0,017	\(\frac{1}{466}\)	outward	\(O_{17-19}\)	0,005	\(\frac{1}{1587}\)	outward
\(O_{19-21}\)	0,006	\(\frac{1}{1132}\)	S-shaped	\(O_{19-21}\)	0,008	\(\frac{1}{992}\)	outward
\(O_{21-23}\)	0,006	\(\frac{1}{1333}\)	shaped	\(O_{21-23}\)	0,014	\(\frac{1}{571}\)	outward
\(O_{23-25}\)	0,004	\(\frac{1}{2000}\)	inward	\(O_{23-25}\)	0,012	\(\frac{1}{665}\)	outward
\(O_{25-27}\)	0,010	\(\frac{1}{842}\)	S-shaped	\(O_{25-27}\)	0,010	\(\frac{1}{842}\)	S-shaped
\(O_{27-29}\)	0,006	\(\frac{1}{1403}\)	outward	\(O_{27-29}\)	0,003	\(\frac{1}{1910}\)	outward
\(O_{29-31}\)	—	—	—	\(O_{29-31}\)
\(O_{31-32}\)	—	—	—	\(O_{31-32}\)

Table VI.

Top (southern) truss	Top (southern) truss	Top (southern) truss	Top (southern) truss	Bottom (northern) truss	Bottom (northern) truss	Bottom (northern) truss	Bottom (northern) truss
Name of truss element	Absolute magnitude of deformation, m	Ratio to length	Direction of deflection	Name of truss element	Absolute magnitude of deformation, m	Ratio to length	Direction of deflection
\(V_{4-5}\)	0.014 0.008	\(\dfrac{1}{783}\) —	To the east inward	\(V_{4-5}\)	0.007 0.018	— \(\dfrac{1}{609}\)	To the west Inward
\(V_{8-9}\)	0.005	\(\dfrac{1}{2200}\)	To the west	\(V_{8-9}\)	0.008	\(\dfrac{1}{1372}\)
\(V_{12-13}\)	0.009	\(\dfrac{1}{1220}\)	—	\(V_{12-13}\)	0.011	\(\dfrac{1}{1100}\)	—
\(V_{16-17}\)	—	—	—	\(V_{16-17}\)	—	—
\(V_{20-21}\)	0.003 0.007 0.007 0.005	\(\dfrac{1}{1118}\)	To the west	\(V_{20-21}\)	0.003 0.008 0.005	—	—
\(V_{24-25}\)	0.005 0.007	\(\dfrac{1}{1565}\)	To the east	\(V_{24-25}\)	0.008 0.005	\(\dfrac{1}{1370}\)	To the west 〃 〃

Table VII.

Top (southern) truss	Top (southern) truss	Top (southern) truss	Top (southern) truss	Bottom (northern) truss	Bottom (northern) truss	Bottom (northern) truss	Bottom (northern) truss
Name of truss element	Absolute magnitude of deformation, m	Ratio to length	Direction of deflection	Name of truss element	Absolute magnitude of deformation, m	Ratio to length	Direction of deflection
\(D_{13-15}\)	0.008 0.007	\(\dfrac{1}{1578}\)	Outward. Outward.	\(D_{13-15}\)	0.003 0.005	\(\dfrac{1}{2528}\)	Inward Inward
\(D_{16-21}\)	0.015 0.015	\(\dfrac{1}{841}\)	Outward. Outward.	\(D_{16-21}\)	0.012 0.0 5	\(\dfrac{1}{1052}\) \(\dfrac{1}{841}\)	Inward Inward

II. Static Test of the Bridge.

The static test of the bridge trusses was carried out on September 5–6, 1926, by a train according to the scheme:

Drawing No. 11.

The test consisted of the following measurements:
1. The vertical deflection of both trusses.
2. The longitudinal displacements of the movable end of both trusses.
3. The stresses in individual members of the trusses.

The test was carried out in sunny weather. Temperature \(+20^\circ C\). Wind speed NNE—about 0.7 m/sec.

The vertical deflections of both trusses were measured with deflectometers of the Frenkel and Klebs system.

The elastic deflection under the static test was:

For the upstream (southern) truss, 39.2 mm, or \(\dfrac{1}{3230}l\)

For the downstream (northern) truss, 38.5 mm, or \(\dfrac{1}{3230}l\)

The theoretical elastic deflection is calculated by the well-known Faerman formula,

\[ f=\alpha \frac{Pl^2}{h^2} \]

where \(P\) is the equivalent load for the bending moment at midspan, in tons per running meter, for one truss.

\(l\) is the design span, in meters.

\(h\) is the design height of the truss at midspan, in meters.

\(\alpha\) is a numerical coefficient, equal to

0.0036 for bridges with triangular and Schwedler lattice, designed according to the standards of 1896 and 1907.

0.0025 for bridges with multiple-web and multiple-strut systems.

0.0030 for bridges with multiple-web and multiple-strut systems, designed according to the standards of 1896 but built after 1901, i.e., taking into account the increased allowable stress of the metal.

With \(\alpha=0.0030\),

\[ P=\frac{6.74}{2}\text{ tons per running meter.} \]

\[ l=126.796\text{ m.} \qquad h=18.897\text{ m.} \]

We have:

\[ f=57.4\text{ mm, or }\frac{1}{2210}l \]

Thus the structural correction (i.e., the ratio of the actual deflection to the theoretical one) will be equal to:

For the upstream (southern) truss, 0.68

For the downstream (northern) truss, 0.67

The same measurements, when reduced to the 1925 N design train, give the absolute deflection:

For the upstream truss, 67.1 mm, or relative deflection \(\dfrac{1}{1881}l\)

For the downstream truss, 65.9 mm, or \(\dfrac{1}{1925}l\)

The absolute deflection permitted by the NKPS standards is

84.3 mm; relative deflection \(\dfrac{1}{1500}l\).

Table

Statement of the results of stress measurements

Group	Name of elements	\(O_{9-11}\) Wheel 15 over joint 10 Top	\(O_{9-11}\) Wheel 15 over joint 10 Bottom	\(O_{15-17}\) Wheel 19 at joint 14 Top	\(O_{15-17}\) Wheel 19 at joint 14 Bottom	\(U_{4-5}\) Wheel 6 over joint 4 Top	\(U_{4-5}\) Wheel 6 over joint 4 Bottom	\(U_{14-16}\) Wheel 18 over joint 12 Top	\(U_{14-16}\) Wheel 18 over joint 12 Bottom
Measured	Truss — at separate fibers, a	−271	−254	−329	−274	+326	+260	+209	+201
Measured	Truss — at separate fibers, b	−227	−264	−301	−274	+299	+250	+226	+210
Measured	Truss — at separate fibers, c	−257	−84	−284	−325	+215	+228	+336	+329
Measured	Truss — at separate fibers, d	−358	−428	−150	−139	+226	+245	+314	+323
Measured	Axial	−281	−258	−294	−265	+290	+251	+243	+233
Measured	Greatest	−358	−428	−329	−325	+326	+260	+336	+329
Measured	Fiber	−227	−84	−150	−139	+215	+228	+209	+201
Measured	Additional in fibers	+27	+66	+12	+23	+12	+4	+38	+41
Measured	In % of axial	−19	−67	−49	−48	−26	−9	−14	−14
Calculated from	Permanent load	−376	−376	−367	−367	+386	+386	+383	+383
Calculated from	Test train	−310	−310	−290	−290	+330	+330	+311	+311
Calculated from	Structural correction	0,91	0,83	1,01	0,91	0,88	0,76	0,78	0,75
Calculated from	Measured stress, reduced to design 1925 train “H”	−479	−437	−504	−454	+498	+430	+409	+393
Total from	Test train and permanent load	−657	−634	−661	−632	+676	+637	+626	+616
Total from	Design train and permanent load	−855	−813	−871	−821	+884	+816	+792	+776
	Allowable by gross section	−899	−899	−901	−901	+933	+933	+792	+792
	Maximum allowable in % of the 1925 train according to scheme H	109	109	106	106	109	109	100	100

Table VIII.

…stresses during the static test (in kg/cm²).

\(D_{5-8}\) Wheel 3 over joint 8 Upper	\(D_{5-8}\) Wheel 3 over joint 8 Lower	\(D_{13-16}\) Wheel 4 over joint 16 Upper	\(D_{13-16}\) Wheel 4 over joint 16 Lower	\(D_{13-16}\) Wheel 18 *) over joint 12 Upper	\(D_{13-16}\) Wheel 18 *) over joint 12 Lower
+377	+380	+370	-365	-210	-230
+438	+447	+450	+460	-240	-250
+516	+511	+296	+386	-112	-219
+466	+525	+466	+442	-218	-217
+449	+466	+396	+413	-195	-229
+516 +377	+525 +380	+466 +296	+460 +365	-240 -112	-250 -217
+15 -16	+13 -19	+18 -25	+11 -12	+23 -43	+9 -5
+270	+270	+188	+188	+188	+188
+418	+418	+404	+404	-247	-247
1,07	1,12	0,98	1,02	0,79	0,93
+784	+814	+706	+736	-344	-403
+719	+736	+584	+601	-7	-41
+1054	+1084	+894	+924	-156	-215
+864	+864	+788	+788	-185	-185
73	73	81	81	221	221

NOTE

Layout of instruments:

1. In the chords.

Outer side.

a . ───── ───── . q
c .   │     │   . d
      c     d
      .     .
a     │     │     b′
  ─────────────
              .

1. In the diagonals.

Outer side.

c        d
.        .
│        │
│        │
│ ──  ── │
│        │
.        .
a        b

*) The cars were uncoupled.

Table

Statement of the results of stress measurements

Name of elements	V 8—9	V 8—9	V.16—17	V.16—17
Train set according to drawing No. 11.	Wheel 1 over joint 10	Wheel 1 over joint 10	Wheel 7 over joint 14	Wheel 7 over joint 14
TRUSS	Upper	Lower	Upper	Lower
Measurements: in individual fibers: a	−82	−79	−265	−163
Measurements: in individual fibers: b	−54	−63	−4	−16
Measurements: in individual fibers: c	−164	−132	−200	−259
Measurements: in individual fibers: d	−159	−203	−50	0
Axial	−115	−119	−130	−110
Greatest	−164	−203	−265	−259
Fiber	−154	−63	−4	0
Additional in fibers	+43	+70	+104	+136
In % of axial stress	−53	−47	−97	−100
Calculated from: permanent loads	+30	+30	−302	−302
Calculated from: test train	−225	−225	−317	−317
Structural correction	0.51	0.53	0.41	0.35
Measured stress reduced to the design 1925 “H”	−204	−212	−244	−208
Full from: test train and permanent load	−85	−89	−432	−412
Full from: design train and permanent load	−174	−182	−546	−510
Allowable by gross section	−602	−602	−719	−719
Greatest allowable in % of the 1925 train according to scheme H	298	298	171	171

Table IX.

… strains during the static test, in g/cm²

\(V_{24—25}\)*) Wheel 20 above joint 22	\(V_{24—25}\)*) Wheel 20 above joint 22	Longitudinal beam, spans 4–6 in section 4.37 m from joint 4 Wheel 7 above section	Longitudinal beam, spans 4–6 in section 4.37 m from joint 4 Wheel 7 above section	Lower chord of cross beam of joint 6 Wheel 7 above joint 6	Lower chord of cross beam of joint 6 Wheel 7 above joint 6	NOTE
Upper	Lower	Upper	Lower	Upper	Lower
−159	−143	+295	+306	+624	—
−150	−120	+404	+406	+454	—	Arrangement diagram for the instruments. 1. In the posts. West side c . ┌──── . d │ │ │ │ a . └──── . b East side
−80	−37	—	—	+202	—	West side
−71	−59	—	—	+69	—
−115	−90	+350	+356	+337	—
−159 −71	−143 −37	+404 +295	+406 +306	+624 +69	—
+38 −38	+59 −58	±15	±14	+85 −80	—	2. In the diagonals. c .────────── . d │ │ a .────────── . b
+30		+42		+74		West side
−176		+440		+483
0.65	0.51	0.80	0.81	0.70	—	3. In the lower chord of the cross beam. c ┌──── . d │ │ a . └──── . b West side  East side
−260	−204	+523	+530	+571	—
−85	−60	+392	+398	+411	—
−230	−174	+565	+572	+645	—	*) The cars were uncoupled.
−602		+694		+728
243		123		114

In view of the fact that trains were running over the bridge the entire time, no residual deflection of the trusses was found.

The longitudinal displacements of the movable end of the trusses, when measured, proved to be equal to:

For the upper (southern) truss . . . 13.8 mm.
For the lower (northern) truss . . . 13.7 mm.

The calculated value, however, is obtained from the formula

\[ \Delta = \frac{P l^3}{21 I h} F . \]

This gives \(\Delta = 19.0\) mm.

Thus, the structural coefficient is equal to:

For the upper truss . . . . . 0.73
For the lower truss . . . . . 0.72

In addition to determining the deflections of the bridge truss, during the static test the stresses in individual members of the bridge were determined. Having four deflectometers available, the stresses in individual fibers of the members were determined.

III. Dynamic Test.

The dynamic test of any bridge, in its essence, is, generally speaking, the most important part of the investigation, since it corresponds most closely to the actual operation of the bridge and makes it possible to penetrate more deeply into the nature of the processes developing during the action of a live load. Passing trains bring the bridge into an oscillatory state: vertical and lateral oscillations are observed.

In testing our bridge, the vertical oscillations were measured with deflectometers of the Frenkel system. It is known that vertical oscillations occur not only while a train is on the bridge (forced oscillation), but also after the train has left the bridge (free oscillation). The Frenkel deflectometer is a rather coarse instrument. By means of it, in most cases it is possible to observe only the forced oscillation. As for the free oscillations of bridges, they are usually so small that they can be measured only by instruments more sensitive than the Frenkel instrument.

The lateral oscillations in the planes of both chords of the bridge were measured with a pendulum of the Leiner system.

The truss test was carried out on September 6 and 7, 1926.

The dynamic test was carried out with a train consisting of one El-series locomotive, with its smokestack directed westward; then, eastward from the locomotive, there were: the tender, 4 American gondola cars, 2 American boxcars, 2 covered standard freight cars, 1 flatcar, 3 covered freight cars, 1 flatcar, and 1 four-axle passenger coach.

The test was carried out in sunny weather. The air temperature was \(+20^\circ\text{C}\), and the wind speed was about 0.1 m/sec and less.

The arrangement of the test train for the dynamic test was as follows:

Fig. No. 12. Diagram of the train during the dynamic test.

A total of 7 runs were made. The speed of the train was from 7 to 40 km/hour, namely: 7; 11.5; 18.3; 19; 23; 26, and 40 km/hour.

In the slow runs, perfectly smooth diagrams were obtained. The general character of the diagrams at considerable speeds is somewhat distorted.—However, despite the fact that the speeds reached 40 km/hour, no impact effect was nevertheless detected.

The maximum elastic deflection under dynamic load proved to be equal to 36.0 mm, or

\[ \frac{1}{3526}\,l \]

The greatest dynamic coefficient was obtained at the speed \(v = 18.3\) km/hour for the top truss, where it proved equal to 1.03.

The dynamic coefficient is determined by the empirical formula of the NKPS

\[ D = 1 + \frac{1500}{5000 + l^{2}} = 1.07 \]

First run at a speed of 19 kilometers per hour. The diagrams of the deflections of the top (southern) and bottom (northern) trusses are shown in Figs. 13 and 14. The deflection obtained was 35.5 mm for the top truss and 34.7 mm for the bottom truss.

Fig. No. 13. Diagram of deflections of the top southern truss.
Speed \(v = 19\) km/hour. Deflection \(f = 35.5\) mm, \(\delta = 1.01\), \(a = 2.0\) mm.

Fig. No. 14. Diagram of deflections of the bottom northern truss.
Speed \(v = 19\) km/hour. Deflection \(f = 34.7\) mm, \(\delta = 1.00\), \(a = 1.2\) mm.

The longitudinal displacements of the movable end of the upper truss are presented for the first run, at a speed of 19 km per hour, in Fig. 15. The total magnitude of the deflection reached a maximum of 12.9 mm; the amplitude of oscillation is 0.5 mm.

Dynamic coefficient equals 1.03.

Fifth run at a speed of 26 kilometers per hour. The diagrams of truss deflections are presented: for the upper (southern) truss in Fig. 16 and for the lower (northern) truss in Fig. 17. The deflection obtained was 35.8 mm for the upper truss and 35.0 mm for the lower truss.

The diagram of longitudinal displacements of the movable end of the upper truss for the fifth run is presented in Fig. 18. The maximum magnitude of deflection was 12.9 mm; the amplitude of oscillation was 0.6 mm. The dynamic coefficient is 1.03.

Seventh run at a speed of 40 kilometers per hour. The truss-deflection diagrams are presented: for the upper (southern) truss in Fig. No. 19 and for the lower (northern) truss in Fig. No. 20. The deflection obtained was 35.3 mm for the upper truss and 35.0 mm for the lower truss. The amplitudes of oscillation were, respectively, 2.1 mm and 1.2 mm. The dynamic coefficient in both cases is 1.01.

The diagram of longitudinal displacements of the movable end of the upper truss for the seventh run is presented in Fig. No. 21. The maximum magnitude of deflection was obtained as \(\Delta = 12.6\) mm. The amplitude of oscillation is 0.8 mm. The dynamic coefficient is 1.01.

Fig. No. 15. Diagram of the longitudinal displacement of the movable end of the upper (right-hand) truss. Speed \(v = 19\) km/hour; \(\Delta = 12.9\) mm; \(\delta = 1.03\); \(\alpha = 0.5\) mm.

Frequency of vertical oscillations. As has already been said, vertical oscillations are forced and free.

The frequency of oscillations can be determined with a sufficient degree of accuracy on the basis of the deflection diagram of a bridge truss under dynamic loading. The task is reduced to counting the number of waves recorded per unit time. In the case where marks have been made on the diagrams by a special instrument—for example, a chronograph—at certain definite intervals of time, for example every 5 sec., the determination of the frequency of vertical oscillations is reduced to a simple count of the oscillations contained between two chronograph marks and division by the number of seconds in the period of the chronograph mark. In our case, when recording the vertical oscillations of the trusses of the bridge under investigation, there was no chronograph. Therefore the frequency of oscillations has to be determined by a cruder method. Knowing the speed of motion of the train and the length of the train, we can determine with a sufficient degree of accuracy...

time, beginning from the moment when the first wheel of the locomotive entered the bridge, and ending with the moment when the last wheel in the train left the bridge. This period of time will correspond to the time of motion of the paper tape of the deflectometer.

Forward  \(v = 26\ \mathrm{km/h}\)

Deflection of the truss
\(f = 35.8\ \mathrm{mm}\)  \(\alpha = 1.8\ \mathrm{mm}\)

Drawing No. 16. Diagram of deflections of the upper right truss.
Speed 26 km/hour. Deflection equals 35.8 mm.

Forward  \(v = 26\ \mathrm{km/h}\)

Deflection of the truss
\(f = 35.0\ \mathrm{mm}\)  \(\alpha = 2.6\ \mathrm{mm}\)

Drawing No. 17. Diagram of deflections of the lower northern truss.
Speed 26 km/hour. Deflection equals 35.0 mm.

Forward  \(v = 26\ \mathrm{km/h}\)

\(\Delta = 12.9\ \mathrm{mm}\)

Drawing No. 18. Diagram of the longitudinal displacement of the movable end of the upper southern truss. Speed 26 km/hour.

Let us calculate, for the upper truss according to Drawing No. 16, the number of oscillations during the fifth run at a train speed of 26 km per hour. The stated speed corresponds to 7.4 m/sec.

The length of the bridge is approximately 127 m; the length of the train is 160 m. Thus the run over the whole bridge, counting the time from the entrance onto the bridge of the first wheel of the locomotive to the departure of the last wheel of the train, is 287 m, for which 41.5 sec are required.

A count of the oscillations directly from the diagram gives 88 oscillations over this entire period of time. Thus we obtain that in 1 sec. there occur 2.1 oscillations per second. This is the frequency of the forced oscillations.

It is known that the frequency of forced oscillations varies with the span and the weight of the train in so regular a manner that it has proved possible to draw curves characterizing the change in frequency as a function of the bridge span. The practice of bridge engineering shows that the frequency of forced oscillations falls quite regularly with an increase in the span of bridges.

Forward  \(v = 40\ \mathrm{km/h}\)

Deflection of the truss
\(f = 35.3\ \mathrm{mm}\)

\(a = 2.1\ \mathrm{mm}\)

Draw. No. 19. Diagram of deflections of the upper southern truss.
Speed \(v = 40\) km/hour. Deflection \(f = 35.3\) mm, \(\delta = 1.01\), \(a = 2.1\) mm.

Forward  \(v = 40\ \mathrm{km/h}\)

Deflection of the truss
\(f = 35.0\ \mathrm{mm}\)

\(a = 1.2\ \mathrm{mm}\)

Draw. No. 20. Diagram of deflection of the lower northern truss.
Speed \(v = 40\) km/hour. Deflection \(f = 35.0\) mm, \(\delta = 1.01\), \(a = 1.2\) mm.

\(a = 0.6\ \mathrm{mm}\)

Forward  \(v = 40\ \mathrm{km/h}\)

\(\Delta = 12.6\ \mathrm{mm}\)

\(a = 0.8\ \mathrm{mm}\)

Draw. No. 21. Diagram of longitudinal displacement of the movable end of the upper southern truss. Speed \(v = 40\) km/hour.

For the article by Prof. M. I. Evdokimov-Rokotovsky, “The Curious Case of the Destruction of a Bridge Truss with a Span of 123.75 m.”

\(v = 7\ \mathrm{km/h};\quad a = 3.0\ \mathrm{mm}\)

\(v = 18\ \mathrm{km/h};\quad a = 3.5\ \mathrm{mm}\)

\(v = 26\ \mathrm{km/h};\quad a = 6.3\ \mathrm{mm}\)

Drawing No. 22. Diagrams of the horizontal oscillations of the truss during dynamic testing at various speeds.

To the article by Prof. M. I. Evdokimov-Rokotovsky
“The Curious Case of the Destruction of a Bridge Truss
with a span of 123.75 m.”

Photograph No. 1. Macrostructure of the material of the truss angle after deep etching with a weak solution of hydrochloric acid. The section was taken from the end of the angle. Natural size.

To Prof. M. I. Evdokimov-Rokotovsky’s article
“The Curious Case of the Destruction of a Bridge Truss
with a Span of 123.75 m.”

Photograph No. 2. Microstructure of the material of the truss angle. Etching with Prof. Izhevsky’s reagent. Magnification 100×.

Photograph No. 3. Microstructure of the material of the truss angle. Etching with Prof. Izhevsky’s reagent. Magnification 150×.

Frequency of free vibrations. It is known that, when free vibrations are present, their maximum amplitude is always observed at the moment when the train leaves the span. However, free vibration is very difficult to record by means of instruments. This requires very sensitive instruments, which in our case, during the testing of the bridge truss, were not available. Examination of the diagrams shows that these free vibrations were not reflected in the diagrams drawn by the instrument.

Bridge-engineering practice does not so often have occasion to operate with data from observations of free vibrations. In those cases, however, where such observations have been available, it appears that the frequency of free vertical vibrations, just like that of forced vibrations, depends on the span of the bridge. As the span increases, the frequency decreases, and for spans of about 127 m it is approximately equal to 2.5 vibrations per second.

The frequency of free vibrations, i.e., vibrations continuing after the train has left, can theoretically be calculated by Bleich’s formula:

\[ \nu = \frac{\pi}{2l^2}\sqrt{g\cdot\frac{EJ}{p}}. \]

where \(\nu\) is the frequency of free vibrations (number of vibrations in 1 second),

\(l\) is the span of the truss \(= 126.796\) m,

\(p\) is the dead load per 1 linear m of one truss,

\(E\) is the modulus of elasticity of the metal of the truss,

\(J\) is the moment of inertia of the bridge, determined from the formula

\[ J = \frac{\max(M_p + M_k)h}{2\sigma} \]

where \(M_p\) and \(M_k\) are the maximum moments from the design dead load and from the vertical load due to rolling stock, \(h\) is the height of the truss, \(\sigma\) is the allowable stress, and \(g\) is the acceleration of gravity.

Table X.

Statement of stresses in the truss members during the dynamic test.

Train speed	V 8–9: outer fiber, east side	V 8–9: inner fiber, east side	V 8–9: dynamic coefficient	D 15–16: upper outer fiber	D 15–16: dynamic coefficient	D 15–16: upper inner fiber	D 15–16: dynamic coefficient
7 km/hr	—	+215 +52	1.00	+341 −73	1.00	+412 −62	1.00
11.5 km/hr	—	+200 −58	0.93	+342 −71	1.00	+406 −77	0.98
18.3 km/hr	—	+210 −75	0.96	+366 −73	1.04	+434 −56	1.05
19 km/hr	−97 +28	+207 −74	0.96	+356 −73	1.04	+434 −56	1.05
23 km/hr	—	+222 −71	1.03	+351 −70	1.03	+434 −64	1.05
26 km/hr	—	+217 +83	1.01	+356 −73	1.04	+452 −65	1.10
40 km/hr	—	+230 −71	1.07	+356 −73	1.04	+422 −74	1.02

The diagrams have a normal form.
The vibrations reach, at a speed of 26 km/hr, 65 kg/cm², or 14% of the greatest measured fiber stress.

Horizontal oscillations of the trusses. The large period of the horizontal oscillations of the span structure and their slow damping characterize the low rigidity of the trusses in the horizontal direction. The magnitude of the amplitude is usually referred to the design span, and it is assumed that the ratio

\[ \frac{1}{11000}\,l \ \text{to}\ \frac{1}{13000}\,l \]

indicates sufficient rigidity of the span structures in the horizontal plane.

In our case, for the bridge trusses, the amplitude of the horizontal lateral oscillations in the plane of the lower chord, as measured with Frenkel’s deflectometer (Fig. No. 22), is equal to:

\[ \text{at speed } v = 7 \ \frac{\mathrm{km}}{\mathrm{hr}} \qquad a = 3.0 \ \mathrm{mm}. \]

\[ v = 18 \ \frac{\mathrm{km}}{\mathrm{hr}} \qquad a = 3.5 \ \mathrm{mm}. \]

\[ v = 26 \ \frac{\mathrm{km}}{\mathrm{hr}} \qquad a = 6.3 \ \mathrm{mm}. \]

\[ v = 40 \ \frac{\mathrm{km}}{\mathrm{hr}} \qquad a = 9.4 \ \mathrm{mm}. \]

The amplitude calculated according to the indicated formula would be within the limits from

\[ \frac{1}{11000}\,126.796 \ \mathrm{m} \quad \text{to} \quad \frac{1}{13000}\,126.796 \ \mathrm{m}. \]

\[ 11.53 \ \mathrm{mm} \quad \text{to} \quad 9.75 \ \mathrm{mm}. \]

Their period, as is seen from the diagrams, is small.
Their damping, as is seen from the same diagrams, is rather rapid.

All this, taken together, testifies to the sufficient rigidity of the trusses in the horizontal (lateral) direction.

IV. Mechanical testing and metallographic investigation of the truss metal.

Mechanical testing. Specimens taken from the angle and the flat bar were subjected to mechanical and metallographic testing.

Eight specimens were tested in tension. Of these, the first six specimens gave: ultimate strength from 4111 kg/cm² to 4530 kg/cm². Relative elongation from 25.3% to 30.0%. The last two specimens from the flat bar gave ultimate strengths of 3250 kg/cm² and 3480 kg/cm², and relative elongation in both cases of 30.0%.

Testing the iron of the angles on a Charpy pendulum machine gives values of the specific work of fracture per unit area from 990 kg/cm².

up to 4250 kg/cm², on average 1970 kg/cm², which indicates a low resistance of cast iron to impacts and a high degree of its brittleness, explained, according to metallographic tests, on the one hand by the presence of harmful impurities and, on the other hand, by improper treatment in the manufacture of this iron.

The Technical Conditions of the N.K.P.S., ed. 1924, require, in addition to tensile testing, also tests for bending in the hot state and bending in the annealed state, for welding and riveting, for rivet iron. In carrying out the technological test, the specimen from the angle, when bent until the sides became parallel, produced a crack. The specimen from the plate did not produce cracks.

Metallographic investigation. In investigating the macro- and microstructure, three photographic images were made and polished sections in many other places were examined.

Image No. 1, relating to the macrostructure, was made from a polished section of the cross-section of an angle subjected to deep etching with a weak solution of hydrochloric acid. The macrostructure indicates sharply expressed segregation with a considerable content in the iron of sulfurous and phosphorous compounds. These compounds disrupt the bond between the grains of the metal and make the iron brittle. It is important that sulfurous compounds produce brittleness when heated, while phosphorous compounds produce brittleness when cold. The latter circumstance is more dangerous for the bridge.

Image No. 2, relating to the microstructure, indicates low-carbon cast iron, consisting in its main mass of white ferrite grains with dark interlayers along the boundaries of these grains, consisting of pearlite. Ferrite is the principal component, and the iron is thus low in carbon. Planimetric measurement of the areas of pearlite grains indicates a carbon content in the iron of approximately about 0.07%. The predominant arrangement of pearlite grains along the diagonals of the image, as well as the presence of banding, passing in some places of the polished section into a columnar structure of ferrite, indicates reduced resistance to forces perpendicular to the pearlite interlayers, and also indicates a capacity for easy formation of cracks. Such a structure is a consequence of rolling at low temperatures.

Image No. 3, relating to the microstructure, indicates the presence of manganese sulfide. Manganese sulfide, enclosed within the boundaries of ferrite grains, is a harmless inclusion. However, this same manganese sulfide has very harmful slag inclusions of ash-gray color and elongated spindle-shaped form. The presence of slags disrupts the uniformity of the metal structure, reduces the toughness of the metal, and makes the metal brittle.

V. Preliminary Conclusions.

The formation of cracks in the bridge truss is a very serious indication of the deteriorated condition of the bridge metal. The question of cracks is all the more important because the appearance of cracks often speaks of changes taking place in the structure of the metal, of fatigue of the metal, of its aging. Unfortunately, observation of cracks, and detection of cracks, is a difficult matter, since one usually has to deal with a painted span structure of a bridge. The large number of cracks found in the trusses of the bridge under investigation, reach—

numbering up to 52, cannot but call for the most serious and attentive attitude. It is not impossible that not all existing cracks are known to us, and that many more are hidden beneath the layer of paint.

It is extremely interesting to have information as to where, in what places, and in what number cracks have had to be observed in the trusses of other bridges. Experience in bridge engineering shows that cracks are observed, generally speaking, rather rarely. In terms of the number of observed cases, the first place must be given to cases in which cracks in the metal were found in the beams of the roadway, since it is precisely this part of the span structures that works under the severest conditions. Usually cracks are observed in the vertical angles by means of which the longitudinal beams are fastened to the crossbeams.

However, in the span structure of our bridge no cracks at all were found in the roadway beams. On this basis one may consider that if the parts of the bridge which are stressed by the temporary vertical load under especially severe conditions do not undergo deformation in the form of cracks, then, it would seem, deformation in the form of cracks of those parts which work under easier conditions cannot be attributed to the stressed action of the temporary load. To base oneself only on such a consideration would perhaps be incomplete and insufficiently demonstrative, but in any case the consideration stated must, among a number of other arguments, take its place and receive its proper assessment.

Considering further the various cases in which cracks have to be observed in the trusses of other bridges, the second place in the number of cases must be assigned to the case in which cracks were found in the web angles of the span beams at the middle of their span. All such cracks either pass through rivet holes or are located at bends of the angles. The probable cause of such cracks, noted on many foreign and on some of our bridges, is the working of the metal above the elastic limit as a result of the angles of the longitudinal beams being crushed or bent, which is also indicated by direct observation of their condition. In other words, fatigue of the metal apparently manifests itself here. In some cases metal fatigue was recorded metallographically in these places, as for example for the bridge over the Volkhov River.

Finally, considerably more rarely during the external inspection of a bridge are cracks encountered in the members of the main trusses. In the overwhelming majority of cases they are found only in bridges that have served for a long time. It must be supposed that fatigue of the metal is the cause of such destruction of the bridge. However, as a rare exception, cracks have to be observed in bridges built quite recently. Such are the cases of the appearance of cracks on the bridges over the Dnieper River of the Moscow–Belorussian–Baltic Railway, and over the Ustye River of the Northern Railway, where cracks were found at the bends of angles. Here the poor quality of the factory work made itself felt. On the bridge over the Shosha River of the October Railway and on the bridge over the Nerl River, a transverse crack was found in the angle and channel of a diagonal. On these bridges the careless use, for the span structure, of material having deformation made itself felt.

On the basis of the foregoing, it should be considered that the permissible stresses for the metal of the bridge must not exceed the permissible stresses for weld iron; and in view of the brittleness of the metal in the fracture test, a reduction in the speed of train movement over the bridge is necessary.

Assuming the permissible stress for the bridge metal, as for wrought iron under Order 9/VII—1928, No. 1427, we obtain the following table for the tested bridge members:

Name of members	$O_{9—11}$	$O_{15—17}$	$U_{4—6}$	$U_{14—16}$	$D_{5—8}$	$U_{13—16}$	$U_{8—\text{[[unclear]]}}$
Total stress . . . . .	$-855$	$-871$	$+844$	$+792$	$+1084$	$+924$	$-215$
Permissible:	$-775$	$-776$	$+804$	$+682$	$+745$	$+679$	$-160$
Maximum permissible, in % of the 1925 train according to scheme H	83	81	84	75	58	67	86

From this table it is evident that the measured axial stresses, reduced to the design train 1925 H and added to the calculated stresses from the permanent load, reached their greatest value, $+1084$ kg/cm², for $D_{5—8}$ of the lower chord, i.e., proved to be greater than the permissible $+745$ kg/cm².

The greatest permissible load, as a percentage of the design train 1925 H, determined from the measured stresses reduced to this train and added to the stress from the permanent load, proved to be equal to 81% for the upper chord, 73% for the lower chord, 78% for the diagonals, and 130% for the posts.

Since the metallographic examination of the iron specimens confirmed the brittleness of the metal, it is necessary to establish continuous observation of the condition of the bridge.

The movement of trains over the bridge must be carried out with single traction by locomotives no heavier than series “E,” with the speed of movement limited to 10 km per hour.

Thus, judging from the data of the external inspection of the bridge truss, the static and dynamic testing of the bridge, and the metallographic examination of the metal, the appearance of cracks in the truss of the bridge under investigation is mysterious and incomprehensible.

First of all, there is as yet no possibility of establishing with absolute certainty when these cracks appeared. It may be that the formation of cracks is taking place even now!..

During the most careful inspection in the autumn of 1926, three small cracks were discovered, as though puttied over, and thus apparently belonging, by their origin, to a time earlier than July 1915. (The last painting of the bridge was precisely in July 1915.) But then again it remains mysterious when exactly all the other 49 cracks, out of the total number of 52 cracks now, so to speak, registered, appeared. If one assumes that they belong to the time before 1915, then much is incomprehensible: first, that they were not noticed during the inspection of the bridge in May 1915; second, that they were not noticed when the bridge was painted in July 1915; third, that all these 49 cracks remained without puttying—without traces of painting—and have the appearance of cracks of more recent origin. It must also be pointed out that among these 49 cracks we see cracks which, in their size, reach 0.1 mm and even 0.3 mm, and they are now unputtied and unpainted, whereas the three cracks which proved to be puttied over are, by their size, already considerably smaller, barely visible, hairline cracks.

Under such circumstances, before drawing a final conclusion on the question of the causes of the appearance of the cracks and of the reliability of the bridge trusses for operation, it is necessary to investigate the matter as deeply as possible. Quite by chance it was possible to ascertain the history of the bridge truss. It turns out that the history of the truss is of interest and, possibly, has some bearing on the appearance of the cracks.

VI. History of the Bridge Truss.

The truss on the bay (1904–1914)

At the 90th km of the railway line under discussion, the shoreline of a large lake forms a bay. The width of the bay is about 100 m, and its greatest depth in the direction of the railway line is about 28 m. The shore at this point, as indeed along its entire western side, consists of rocky cliffs descending steeply into the water and sometimes reaching an enormous height (drawing No. 23).

In designing the railway line in 1904, great difficulties were encountered here. It did not appear possible to go around the two capes forming the shore bay, even with limiting radii of 320.04 m (150 sazhens). As a result, it was necessary to approach the bay from the western side by means of a gallery 47 m long.

The considerable depth of the bay did not allow the construction of intermediate supports; consequently it was decided to cross the bay with a single-span bridge having an opening of 123.75 m (58 sazhens). The abutments of this bridge were founded on rock, leveled with a layer of concrete 0.85 m thick, without foundations.

The truss, manufactured in 1902 at the Kolomna Works, was delivered from the works in dismantled form and erected here in 1904 at the 90th km of the railway.

Unfortunately, I do not have the report of the bridge test in 1904. However, on the basis of oral reports from engineers who took part in the construction of the railway, there is reason to suppose that no defects in the assembly of the truss were discovered at that time. During the ten years that the truss remained on the bay, no peculiarities in the condition of the truss were observed either.

During this period the load on the truss was produced by trains hauled by locomotives of classes Shch, O, E and El.

The maximum speed of movement was up to 40 km/hour.

Transportation of the Truss.

In designing the second track of the railway in 1911, still greater difficulties were encountered in locating the line than had been encountered in 1904 when designing the first track. Particularly serious difficulties arose in crossing the bay with the second track and in laying out the line here. After prolonged and detailed investigations of all the circumstances of the matter, in the presence of a whole series of alternatives, it was decided to build a double-track tunnel around the bay (drawing No. 23). With this solution, along the length of the tunnel alternative all the structures of the first track located on this section were abandoned, and it became possible to use the 58-sazhen truss from the bay for construction of the second track.

In accordance with the order of the Administration for Railway Structures of August 14, 1914, No. 1255, it was decided to move this truss and install it on the abutments of the bridge over the river at the 248th km of the railway. The reasons for placing the 58-sazhen truss on the river were exclusively economic considerations: to use the truss, to avoid the construction of intermediate supports

and of costly deep foundations. For the first track on the river,* two 25-sazhen trusses were installed.

In view of the fact that all bridge trusses for the second railway track were designed according to the 1907 standards for railway rolling load, this 58-sazhen truss from the bay therefore had to be recalculated and strengthened for the new load, as will be discussed in detail.

In view of the extreme difficulty of transporting the truss as an entire span, and in view of the possible deformations of the truss during such transport, it was initially decided (in July 1914) to dismantle the truss and, in dismantled form, transport it by train, strengthen it, then assemble it and install it on the river at kilometer 248.

When it was finally decided that the truss was to be transported by river,* the question arose as to the method of transport. Both for the transport and for the forthcoming strengthening of the truss it had to be dismantled. The dismantling could be carried out in various ways. In the course of discussion the following methods were proposed.

To dismantle the truss on the span, simultaneously removing the truss from the span in parts. For this it would have been necessary to use temporary falsework. There could be two variants: falsework on pontoons or falsework on ice. As for the use of pontoons, owing to the waves on the lake the work would have been associated with the risk of having displacements—

No. 23. Plan of the location of the bridge across the bay at 20 km, railway line (1904–1914).

stresses in the parts of the truss being dismantled. As for the method of erecting falsework on the ice, this method, too, proved far from rational. The point is that, of the 123.75 m span, only about 80 m lay above the surface of the lake. If the weight of the falsework is taken into account, the lifting force of the ice proved insufficient.

In view of the foregoing, it was necessary to abandon the dismantling of the truss on falsework between the supports, as a method that did not ensure the safety of the work and, moreover, was associated with considerable overstressing of the metal of the truss.

The second method submitted for discussion was the erection of falsework in the form of a concrete arch. Although the falsework for concreting could possibly have been suspended from the truss itself, this method nevertheless proved excessively expensive and was therefore rejected.

A third method was proposed: dismantling the truss within the limits of the span without lower falsework. In conception this method appeared very attractive, since it placed all the work of dismantling the truss in a position wholly independent of the characteristics of the lake and of the contingencies connected with it. There could be two variants: to use the upper chord of the truss as an arch, or else to suspend the truss from shore towers. To make use of the upper curved chord of the truss as an arch, bracing it between the abutments, did not appear possible, in view of the unusually high overstresses of the metal that, according to calculation, would result. The second variant was satisfactory (Fig. No. 24).

I stage

II stage

III stage

IV stage

Fig. No. 24. Variant for dismantling the truss by suspending the truss from shore towers.

However, when a tender was announced, no one could be found who wished to undertake such work. Therefore, the bidding set for February 7, 1914, did not take place, and the Head of Works did not consider it acceptable to carry out the work by this method under the direct authority of the Works Administration.

Thus, all the methods set forth above had to be rejected, and at the same time it was necessary to abandon the transport of the truss by trains in disassembled form.

It was necessary to turn to the method of transporting the truss by water by means of pontoons or barges. The method of moving trusses on pontoons, in comparison with the preceding alternatives, proved to be well known to the local technical personnel, and therefore this method was chosen as the most suitable and was in fact carried out.

The work of moving the truss was entrusted to contractor Kopylevich. He carried out some preparatory work, proved unreliable, and was removed.—The preparatory work was completed and the actual shifting of the truss was carried out by direct order of the Works Administration. The Head of the Technical Department, Engineer V. O. Freiberg, and the District Chief, N. V. Antonov, were continuously present at the work and directed it.

There was one very important circumstance that substantially influenced the choice of the method for removing the truss from the span: this was the configuration of the bottom of the bay, on which depended the closest possible approach of the barges to the shore during the shifting. In this respect the removal work was in much worse conditions than when the truss had been launched onto the span. At that time, in 1904, special pontoons measuring 10 × 21 m were constructed, allowing them to approach the shore more closely than the available barges, which were up to 34 m long.

In order to counteract the unfavorable effect of the length of the barges, it seemed more advisable to make as large a transverse shift of the trusses as possible toward the lake. However, even this method of carrying out the work proved difficult to implement, since its execution was hindered by the considerable depth of the lake, which caused great difficulties in founding the shore falsework on the rock under water.

As a result of all these considerations, the method finally adopted for execution consisted of a combination of using the three barges that happened to be available, with strengthening of the trusses by constructing a reinforced-concrete core in four posts of the truss \(S_{8-9}\) and \(S_{24-25}\), placing four additional struts in the second large panels from the ends of the truss, and arranging a series of diaphragms in the lower chord of the truss.

The principal requirements that had to be satisfied by the work of removing the truss from the span were as follows:

first, that there be complete safety in carrying out the work,

second, that there be no overstressing in the parts of the truss during the work,

and, third, that the work be as inexpensive as possible.

In order to carry out the adopted method of performing the work over the deep bay, the following work plan was outlined and actually executed:

1) Timber falsework was constructed on both shores of the bay at the existing stone abutments.

2) Three barges were braced, with additional sleepers laid on the bottom and on the deck, with the construction of three longitudinal and five transverse watertight plank bulkheads, and with falsework erected above the deck to a height of 9.5 m.

3) Four posts \(S_{5-0}\) and \(S_{24-25}\) and the diaphragms in the lower chord were concreted in.

4) Additional diagonals were installed in the second panels from the ends of the truss (Fig. No. 25).

Fig. No. 25. Additional diagonals for strengthening the truss for transport.

5) Part of the roadway flooring was removed, and the truss was first raised above the abutments by approximately 1.7 m.

The lifting of the truss to a height of 1.7 m was carried out with the aid of four hydraulic jacks. For this purpose, cribs made of rails were laid on the lifting platform, and the jacks were set on them. After the truss had been lifted, the rockers were taken out from under the truss and rail cribs were put in their place.

Thereafter further lifting and building up of the rail cribs was carried out.

Both ends of the trusses were lifted simultaneously by 4 jacks. During the work, strict care was taken to ensure that the trusses did not skew. The lifting capacity of each jack was 200 tn. The travel of the piston rod was 15 cm. Above the rods of the jacks, platforms made of short rail pieces were arranged to prevent bending of the lower plates of the truss.

6) Then the truss was shifted toward the lake: the eastern end by 2.1 m, and the western end by 1 m.

The shifting was carried out on solid rail cribs.

A transverse carriage was attached to the lower chord of the truss, and with the aid of rollers the truss was moved transversely to the longitudinal axis. The shifting was carried out by ordinary locomotive jacks, which bore against the stone abutments. Both ends were moved either simultaneously or in turn. During the transverse shifting, strict care was taken that the rollers remained at all times under the chords of the main trusses at the smallest possible distance from one another. The track for the transverse shifting at each end of the truss consisted of four lines, with 3 rails in each. The track was laid perpendicular to the original position of the longitudinal axis of the truss and had a certain slope in the direction of shifting; moreover, to avoid any spontaneous movement of the truss, a series of timber stops was installed, bearing against the abutment and chiefly against the rock. As the shifting proceeded, these stops were removed. After the proper transverse shifting, before proceeding

For the longitudinal movement, the truss was raised on jacks and placed with its end trolleys on rollers.

Drawing No. 26. Details of the trolleys for rolling the truss.

7) On the scaffolding, on the falsework, and behind the falsework on the eastern side, a track of sufficient length was laid on cross-ties and sleepers.

Drawing No. 26. Details of the trolleys for rolling the truss.

Rails were fastened to the lower chord of the truss along the timbers (Drawing No. 26).

Drawing No. 26. Details of the trolleys for rolling the truss.

8) The truss was set at its ends on rollers with the aid of jacks (Drawing No. 27).

9) Then, with the aid of ropes and winches, the truss was moved approximately 7–6½ meters, after which the eastern end of the truss was

Drawing labels: “Side view”; “View from its place”; “truss.”

Drawing No. 27. Arrangement of the end of the truss on rollers.

raised on jacks, the rollers were removed from under the end carriage and brought under the carriage of the concreted post at the eastern end. The truss was lowered onto these rollers.

10) Barges No. 1 and No. 2 were brought under the nodes at \(3/8\) and \(1/4\) of the span from the lake side; after this, about 100 cubic meters of sand were unloaded from the first and about 180 cubic meters from the second, until the western end of the truss hung freely above the rollers. Then the truss was moved approximately 20 meters to the east (Drawing No. 28).

I stage

water level 6/IV 47

II stage

water level 6/IV 47

Drawing No. 28.

11) A barge No. 3 was brought under the northern, lake-side end of the truss; from it sand was transferred into barge No. 2, at the same time loading barge No. 1 with sand as well. When, in this way,

by this route about 180 cubic meters of sand had been transferred, it became possible to remove barge No. 1 from under the truss.

When the truss had been shifted in the transverse direction toward the lake, the following operations were carried out:

The necessary area of the lake surface was cut out and cleared of ice.

By this time the loading of three barges with a sufficient quantity of sand had been completed. On the eastern shore a reserve of sand had been prepared for topping up barges No. 1 and No. 2.

In order to bring the barges in by an icebreaker, with the participation in the work of a steamer in the bay, an area measuring about 100×200 meters was cut out and cleared of ice. The cut-out ice, up to 1.5 meters thick, was pulled out in separate pieces onto the surface of the frozen lake and dragged aside.

III stage

IV stage

Fig. No. 28.

12) Then the truss was moved farther east until the gap between barge No. 2 and the timber trestles was reduced to approximately 20 meters.

13) Into barge No. 2, a further 10 cubic meters of sand were transferred from barge No. 3, after which it became possible to remove barge No. 3 from under the truss.

14) Then the truss was moved approximately another 30 meters to the east.

15) Rollers were brought under the joint at one-quarter of the span on the lake side, so that at this joint the truss could bear upon the trestles and upon the track.

16) After this, barge No. 3 was loaded with sand until it became possible to remove this barge from under the truss.

17) All further movement of the truss was carried out exclusively on rollers (Fig. No. 27).

18) Finally, dismantling of the truss was begun.

Calculation of stresses in the truss during transportation.

As has already been said, one of the principal requirements which the method of shifting had to satisfy was the requirement that overstresses be avoided in any part of the truss, at any moment of the shifting. For this purpose all the greatest stresses that the members of the truss could experience during the shifting were determined.

To determine the greatest tensile and compressive forces from the support reactions and from the barges in the truss members at the various stages, the forces for each of these stages were computed separately, on the basis of which the greatest and least tensile and compressive stresses in the truss members were determined. Stages III and IV, as regards the distribution of forces, differ little from those in stages II and V. Therefore, for these stages no separate determinations of forces were made. The forces were determined from influence lines taken from the principal calculation of the truss.

Drawing No. 28.

Upper and lower chords. The calculation shows that the stresses in the upper and lower chords of the truss during transportation theoretically should not have exceeded 282 kg per sq. cm, and in most cases should have been considerably lower.

As for the additional stresses in the lower chords resulting from the distribution of reactions from the rollers and barges, these are given in Table XI (see p. 39).

Posts. The greatest stresses in all posts, except the main posts, are very small; as for posts $S_{3-9}$, $S_{12-13}$, $S_{20-21}$ and $S_{24-25}$, their stresses during transportation of the truss were large.

As has already been said, posts $S_{8-9}$ and $S_{24-25}$ were strengthened with a reinforced-concrete core, and thus the question of installing measuring instruments here fell away of itself.

The question remains concerning the posts \(S_{12-13}\) and \(S_{20-21}\). With respect to these posts the Technical Department of the Works Administration made the following calculation.

Gross sectional area \(\omega = 93.495\ \text{cm}^2\).

Net sectional area \(\omega = 89.411\ \text{cm}^2\).

Length \(l = 18.897\ \text{m}\).

Moment of inertia \(J = 76108.13\ \text{cm}^2\).

Hence \(\varphi\) is the coefficient of reduction of the allowable stresses as a function of longitudinal buckling:

For \(l = 18.897\ \text{m}\),

\[ \varphi = \frac{1}{1 + 0.00008\,\frac{89.411 \cdot 18.897^2}{76108.13}} = 0.7401. \]

For \(l = 9.4485\ \text{m}\),

\[ \varphi = 0.92 \]

When the post is braced at mid-height by being connected with the neighboring joints of the intermediate posts, we may take the coefficient \(\varphi = 0.92\), the post being assumed, as a reserve of strength, to have freely rotating ends, whereas in fact these ends are to some degree fixed. Thus, with an allowable stress of \(500\ \text{poods}/\text{dm}^2 = 1269.56\ \text{kg}/\text{cm}^2\), the principal stress will correspond to

\[ \frac{500}{0.92} = 544\ \text{poods}/\text{dm}^2 = 1381\ \text{kg}/\text{cm}^2. \]

In reality the actual stress will not exceed the allowable one, owing to participation in the transfer of the forces of the roadway and to the bending resistance of the upper and lower chords of the truss, which are stressed very slightly as members of the principal statically determinate system of the truss.

Concreting of the truss for transportation

As has already been said, for transportation of the truss the posts \(S_{8-9}\) and \(S_{24-25}\) were reinforced with a reinforced-concrete core of section \(0.502 \times 0.635\ \text{m}\) (drawing No. 29). The longitudinal reinforcement consisted of 4 bars 36 mm in diameter, tied along their length in horizontal planes, spaced 0.5 m apart, by stirrups of round iron 12 mm in diameter and about 0.15 m long. Concrete of the mix \(1 : 1\frac{1}{2} : 2\frac{1}{2}\) was used. As regards the execution of the concreting work, throughout the entire height of the posts, inside the section, sheets of roofing iron were gradually inserted as the concreting proceeded to retain the concrete; these served only as temporary forms during concreting. The upper box was filled with neat cement mortar through the upper rivet holes, into which long iron rods were then driven for compacting the concrete. For a better bond of the chords with the concrete core, the rivets in the vertical plates opposite the concrete core were cut out and replaced by through iron bolts.

In the compressed panels of the lower chord, reinforced-concrete and iron diaphragms were installed, in a quantity of from 5 to 6 pieces per small panel 7.925 m long.

Four additional reinforced-concrete diaphragms were arranged at a distance of 0.4 m toward the middle of the span from the outer face of the encased truss posts in the lower chord. For this purpose two bolts were passed crosswise, one of which had a thread and the other a hook. Both were placed as close as possible to one another. As close as possible to them, a gas pipe, through which the bolt passed, was clamped tightly between the vertical plates of the lower chord. The rivets where the crosswise bolts had to be placed were cut off and removed.

Drawing No. 29. Reinforcement with a reinforced-concrete core of posts \(S_{8-9}\) and \(S_{24-25}\) for transporting the truss.

When all the above-mentioned works had been completed, a verification calculation and summary were made once again, which showed that during the pe–

during the movement of the truss, in all cases of its placement on supports, rollers, and barges, the following stresses may be expected in the separate parts of the truss.

Table XI.

Member	Greatest tensile stresses kg/cm²	Greatest compressive stresses kg/cm²	Member	Greatest tensile stresses kg/cm²	Greatest compressive stresses kg/cm²
\(U_{1-4}\)	183,59	39,47	\(D_{20-23'}\)	1386,08	—
\(U_{4-8}\)	254,15	76,94	\(D_{23'-25}\)	1529,56	48,59
\(U_{8-12}\)	248,95	172,80	\(D_{27'-29}\)	301,70	484,30
\(U_{12-16}\)	208,81	111,58	\(D_{24-27'}\)	253,97	726,00
\(U_{16-20}\)	205,26	59,36	\(D_{28-31}\)	522,02	304,27
\(U_{20-24}\)	245,87	173,23	\(S_{2-3}\)	228,96	78,89
\(U_{24-28}\)	246,23	80,54	\(S_{4-5}\)	198,60	74,75
\(U_{28-32}\)	176,38	39,62	\(S_{6-7'}\)	228,96	—
\(O_{1-3}\)	31,32	143,61	\(S_{7'-7}\)	—	161,57
\(O_{3-5}\)	78,56	250,24	\(S_{8-9}\)	11,46	1624,10
\(O_{5-9}\)	157,81	281,61	\(S_{10-11'}\)	228,96	—
\(O_{9-13}\)	103,58	244,78	\(S_{11'-11}\)	—	161,57
\(O_{13-17}\)	36,27	179,81	\(S_{12-13}\)	216,66	1328,62
\(O_{17-21}\)	36,27	179,81	\(S_{14-15'}\)	228,96	—
\(O_{21-25}\)	46,58	241,02	\(S_{15'-15}\)	—	161,57
\(O_{25-29}\)	158,06	278,46	\(S_{16-17}\)	—	161,57
\(O_{29-31}\)	78,84	247,88	\(S_{18-19'}\)	—	161,57
\(O_{31-32}\)	31,50	142,24	\(S_{19'-19}\)	228,96	—
\(D_{3-4}\)	527,41	304,27	\(S_{20-21}\)	224,41	1311,55
\(D_{7'-8}\)	260,65	725,53	\(S_{22-23'}\)	—	161,57
\(D_{5-7'}\)	306,73	425,43	\(S_{23'-23}\)	228,96	—
\(D_{11'-12}\)	903,86	38.07	\(S_{24-25}\)	15,98	2311,35
\(D_{9-11'}\)	862,99	—	\(S_{26-27'}\)	—	161,57
\(D_{15'-16}\)	954,61	394,00	\(S_{27'-27}\)	228,96	—
\(D_{13-15'}\)	913,31	214,07	\(S_{28-29}\)	317,40	72,21
\(D_{16-19'}\)	904,44	223,55	\(S_{30-31}\)	228,96	78,23
\(D_{19'-21}\)	944,02	405,51

Observations with instruments.

In order to verify whether, during the movement of the truss, the stresses would indeed not exceed those calculated theoretically, measurements of the stresses were made by means of measuring—

of the instruments of the Rabio–Manet–Mantel system. At the disposal of the Construction Administration in February–March 1915 there were only two instruments. The question arose where to place them. If one examines the table of stresses expected in the members of the truss during its movement, it is seen that the upper chords would have insignificant stresses.

The lower chords would likewise have very insignificant stresses.

Four posts would have very high stresses, namely:
$S_{8-9} = 1624.10\ \mathrm{kg/cm^2}$, $S_{12-13} = 1328.62\ \mathrm{kg/cm}$, $S_{20-21} = 1311.55\ \mathrm{kg/cm}$.
$S_{24-25} = 2311.35\ \mathrm{kg/cm^2}$.

During the shifting, a stress meter of the Rabio–Manet–Mantel system was installed on the additional diagonal $D_{24-29}$. During the removal of the end support of the eastern end of the truss and the lowering of the truss onto the rollers under the post in the quarter of the span on the same eastern side, the instrument did not show any deflection of the pointer. Therefore it must be assumed that the additional diagonal remained unstressed during the shifting.

The same measuring instrument, placed on the diagonal $D_{5-8}$ on the western side, after the onset of stage II and then after the onset of stage V, gave a pointer deflection corresponding to a tensile stress of $760\ \mathrm{kg/cm^2}$. Since, according to the table of stresses, the stress here should have been within the limits from compression of $725.53\ \mathrm{kg/sq.\ cm}$ to tension of $260.65\ \mathrm{kg/sq.\ cm}$, i.e. a change in length corresponding to a tensile stress of $986.18\ \mathrm{kg/sq.\ cm}$, the reading obtained from the stress meter, $760\ \mathrm{kg/sq.\ cm}$, is confirmation that the additional diagonals worked to a very small degree or did not work at all, since the discrepancy between the readings of the meter and the calculated values can be explained by the influence of the rigidity of the joint connections.

Thus, on the basis of all the foregoing, the Construction Administration came to the conclusion that during the shifting of the truss no overstresses arose in its members.

At the same time it is necessary to note that during the shifting itself no deformations were observed in the members of the truss, with the exception of one half-diagonal $d_{2'-21}$ in the third large panel on the eastern side, which in stage V of the shifting gave a deflection equal to $0.17\ \mathrm{m}$, just as, during the advancing of the truss, the half-diagonal of the second large panel on the western side gave a deflection of up to $0.21\ \mathrm{m}$; this, however, apparently had no harmful consequences for the operation of the truss.

During the movement of the truss there was one circumstance to which, apparently, sufficient attention was not paid. It consists in the following. During movement, the lower chord of the truss must be in a strictly normal position: there must be neither bulging of it, nor skewing, nor other distortions. That is how matters stand theoretically. Considering the question practically, we see that the formation of bulges and skews of the lower chord, and in general the disturbance of its normal outline, could have been influenced by the following factors:

1) The swell on the lake and the resulting dynamic load from the barges supporting the truss.

2) The agitation of the lake could also have caused a simple overloading of the barges, etc., i.e. a phenomenon of a purely static nature.

3) During transverse displacement, distortion of the outline of the lower chord could also have resulted from irregularities and unevenness of the track, its skewing, skewing in the motion of the trolleys and rollers, and so on.

There are no data by which to judge whether all this actually occurred. Only one thing is known: leveling along the lower chord of the truss was not carried out during the displacement itself.

Drawing No. 30. Strengthening of the truss after transport from the bay over 248 km.

Strengthening of the bridge truss.

As has already been said, before being installed on the river the truss from the bay was recalculated according to the 1907 standards for temporary moving load and strengthened.

The strengthening of the section of the upper chord consisted in riveting on three plates, each 0.9 m wide and 13 mm thick (Drawing No. 30).

The lower chord was strengthened with two plates of the same dimensions, and only in half-panels No. 1 and No. 2; in addition to these two plates, two more narrow plates were added, each 22.5 cm wide and 13 mm thick.

The strengthening of posts No. 1, No. 3, No. 5, and No. 7 was carried out according to Drawing No. 30,

Testing of the bridge truss in 1915.

By a fortunate chance I managed to obtain some data from the static and dynamic testing of the bridge truss after it had been transported from the bay and installed at km 248 in 1915.

Static test in 1915.

The total deflection of the truss under static testing was \(f_c = 36.0\) mm.

The elastic deflection of the truss was \(f = 32.5\) mm, or

\[ \frac{1}{3902}\,l \]

The residual deflection after removal of the train was \(f = 3.5\) mm, or

\[ \frac{1}{36228}\,l \]

The permissible deflection according to the official standards was \(f = 85.2\) mm, or

\[ \frac{1}{1500}\,l \]

Dynamic test in 1915.

At a speed of \(v = 20\) km/hour, the vertical deflection ordinate was

\[ f = 32.5 \text{ mm, or } \frac{1}{3902}\,l \]

At a speed of \(v = 30\) km/hour, the vertical deflection ordinate was

\[ f = 33.0 \text{ mm, or } \frac{1}{3842}\,l \]

The horizontal deflection ordinate was \(\Delta = 3.5\) mm, or

\[ \frac{1}{36228}\,l \]

VI. Conclusion.

In view of all the above, on the basis of my personal acquaintance with the bridge in 1926, taking into account the history of the transportation of the bridge truss, relying on the data of the static and dynamic tests of the bridge truss, and considering the results of the mechanical testing and metallographic examination of the metal, I believe that the following conclusion may be reached.

It is not possible to establish precisely the true cause of the cracking of the bridge trusses. It remains only to make assumptions as to the causes of the failure, with a greater or lesser degree of probability. Apparently, among the various possible factors which, in one way or another, played a role in creating the conditions for the formation of cracks, the following should be placed first:

1. The reduced quality of the metal.
2. Impairment of the integrity of the truss during its transportation.

However, both of these factors require detailed consideration.

Quality of the metal. The quality of the metal may be judged, first, on the basis of the mechanical testing of the metal; second, on the basis of metallographic investigations of the metal; and third, on the basis of the results of the dynamic testing of the bridge.

Mechanical testing of the metal gave quite satisfactory results. Indeed: if we turn to the results of the mechanical testing, we see that the first six specimens, taken from angles, according to the tensile-test data and in accordance with the technical specifications of the NKPS, ed. 1924, satisfy the grade St. 3, used for bridges, and only the last two specimens, taken from plates,

satisfy the grade of St. 2 used for rivets. Thus, the results of the mechanical test give no indication of poor quality of the metal.

In judging the quality of the metal, the indications of the dynamic test of the bridge will be very valuable. The practice of bridge engineering has established that a dynamic test can indirectly indicate the general condition of a bridge. In the present case the results of the dynamic test proved satisfactory. From this one may conclude that the bridge trusses are in fairly good condition.

General results of the static and dynamic tests. Examination of the diagrams obtained in the dynamic tests, at different speeds of entry, with the regulators open and closed, gives in general a favorable picture. The influence of speeds was reflected rather weakly. Almost no oscillatory effect was observed. The outline of the diagrams was distorted only slightly and only at high speeds. All this is, to a sufficient degree, a favorable sign, indicating the smooth operation of the individual members of the bridge truss. The comparison of the dynamic coefficients also testifies to the same thing. They show almost complete independence from the speeds during the test and are close to unity.

The vertical stiffness of the trusses, according to the data of the static and dynamic tests, should be recognized as sufficient.

The greatest amplitude of lateral oscillations reached 7.5 mm, or

\[ \frac{1}{16920}\, l \]

in the plane of the upper chord at a train speed of \(V = 40\) km/hour. This amplitude proved to be less than the usual

\[ \frac{1}{15000}\, l. \]

The transverse stiffness of the structure, on the basis of both the static and the dynamic tests, may be recognized as sufficient.

A very important and interesting question is that of establishing the degree of aging of the bridge. In order to clarify the question connected with judging the span structure as a whole, one must turn to various factors.

A decrease in the monolithic character of the span structure, an increase in the mutual mobility of its members—what Prof. Streletsky calls an approach to a hinged scheme—can be established on the basis of the results of the static test of the bridge. Static indications of this phenomenon are a decrease in the camber and an increase in constructive corrections. In our case, during the testing of the bridge trusses, as has already been noted, the camber was preserved and no increase in constructive corrections was observed.

Thus, in view of the results of the static investigation, there would appear to be no grounds for asserting a decrease in the monolithic character of the span structure of both bridge trusses.

A very indicative sign would be an increase over time in the number of small teeth on the deflection and stress diagrams, and a general decrease in their smoothness. Unfortunately, this circumstance is difficult to verify in practice, since the small teeth depend to a significant extent on the condition of the track and the wheels of the rolling stock. Moreover, there is not always a practical possibility of comparing the diagrams now taken with those obtained many years ago.

Among the materials for judging the process of aging of a bridge, observations of forced and free vibrations must be included.

The amplitudes of vibration may change both in the direction of increase and in the direction of decrease. However, the science of bridge engineering is not yet in a position to give an exhaustive answer to the question posed, concerning the relation of the degree of aging of a bridge to the change in the amplitude of vibrations, since the relation is still unknown between the influence of aging of the metal and aging of the riveted joints. Aging of the metal should reduce the amplitude of vibrations, whereas aging of the riveted joints may also cause an increase in them. Usually, in practice, the question proves insoluble because it is impossible to possess reliable data on the initial dynamic vibrational properties of the metal and of the span structure as a whole. Not knowing the initial properties, we, of course, cannot draw a conclusion as to the direction in which the change has occurred.

As a bridge ages, the period of natural vibrations of the span structure, and together with it the critical speed of the train, should decrease somewhat. This occurs because the forces of internal friction, proportional to the rate of deformation, cause an increase in the period of vibrations. The forces of simple friction, however, do not affect the period. In the span structure, apparently, both kinds of friction are present. Therefore their increase, inevitably arising with the years, should cause a lengthening of the period of vibrations and a reduction of the critical speed of the train. This unfavorable circumstance theoretically deserves full attention, but unfortunately its practical use can be realized only after many years, and therefore is impracticable for us.

The most vivid and profound manifestation of the process of aging of a bridge should consist in a change in the character of the duration and the number of free vibrations of the span structure. It must be borne in mind that all the factors of aging act in one direction, and therefore the intensity of the results will manifest itself especially distinctly and vividly. The natural small vibration of any system does not depend on the cause that produced it, i.e., on the nature and character of the load, but depends only on the nature of the vibrating system itself. Considering the diagrams of the dynamic test of the trusses of our bridge, we cannot say that the number of free vibrations and the intense decrease of the amplitudes of each successive wave is declining, which would indicate considerable dimensions of decrepitude of the bridge. A free vibration that diminishes slowly and regularly testifies to the sufficient vitality of the bridge structure. In our case there are no sharply expressed violations of any regularity in the decrease of amplitude with the number of vibrations. And this would seem to indicate that the bridge truss has not yet become decrepit.

Metallographic investigation. The metallographic investigation shows that the iron consists chiefly of ferrite, and therefore it should have withstood these tests if there had not been in it harmful sulfurous and phosphorous inclusions and isolated inclusions of sulfurous manganese, discovered on the macro- and microsection, indicating a somewhat lowered quality of the metal. However, the results of the metallographic investigation do not give categorical indications of the degree of unsuitability of this metal in bridge engineering. Therefore, to draw any final conclusions based exclusively on the metallographic test alone would not be entirely correct and would not exhaust the whole internal substance of the question.

A very interesting and important question is whether, and if so to what extent, the overstresses that occurred during moving and transportation affected the integrity of the bridge trusses.

It would seem that, given the not very high quality of the metal, the overstresses should have affected the integrity of the truss especially noticeably. However, this has not only not been proved, but the facts even seem to suggest the opposite. In the inspection report for the transported bridge truss after strengthening and riveting in May 1915, there are not only no indications of defects, but, on the contrary, it is stated that the truss is in good condition. It is possible, of course, to point out fairly that documents of this kind cannot yet serve as proof in such a subtle, delicate matter as establishing the presence of hairline cracks in the comparatively small number of 52 pieces, scattered over the enormous area of two bridge trusses.

There are considerations of another kind as well. Examining the places where cracks are now observed, we see that such cracks are found in the upper chord, in the lower chord, in posts, and in diagonals. It is noteworthy that the number and size of these cracks do not agree—or, better said, do not correspond—with the magnitude of the stresses that, according to the calculation, were expected in the bridge trusses during its moving and transportation.

Crack No. 2, as has already been said, is located in the angle of the upper chord \(O_{9-11}\) of the right truss. The crack passes through the entire angle; the width of the crack is about 0.1 mm. Thus, apparently, this crack arose as a result of high stresses in the metal. However, we see that according to the calculations the stresses here could have been tensile \(+103.58\) kg per sq. cm and compressive \(-244.78\) kg per sq. cm. Thus the calculation indicates that the stresses here were very low and amounted to only about \(30\%\) of the permissible stresses. It is also unclear why only one angle was deformed in the form of a rupture, while the remaining angles and the vertical and horizontal plates remained undeformed and intact.

Crack No. 3 is in the angle of the upper chord \(O_{13-15}\) of the right truss. Its width reaches 0.3 mm. The crack passes through the entire angle. It must be assumed that here too, evidently, some very considerable forces acted. If we turn to the calculations of stresses in this truss member during its moving and transportation, we see that here there were tensile stresses \(+36.27\) kg per sq. cm and compressive stresses \(-179.81\) kg per sq. cm. In comparison with the preceding case the stresses were smaller, while the deformation turned out to be greater.

Considering cracks No. 4, No. 5, No. 7, No. 10, No. 11, No. 12, and No. 19, we see that they relate to the vertical posts \(S_{8-9}\), \(S_{20-21}\), \(S_{24-25}\), where the compressive stresses were very high, namely:

in post \(S_{2-9}\)	1624.10	kg per sq. cm
in post \(S_{12-13}\)	1328.62	” ” ” ”
in post \(S_{20-21}\)	1311.55	” ” ” ”
in post \(S_{24-25}\)	2211.35	” ” ” ”

Examination of the deformations expressed in the form of cracks indicates that here the cracks by no means always acquired a significant appearance. Sometimes they are barely noticeable. In some cases, despite the presence of high overstresses, there are even no cracks. Such is post \(S_{12-13}\), where the cracks involve only part of the leg of the angle and do not go deep.

are found. The stresses proved to exceed the permissible stress of the metal. In these cases there would seem still to be a formal basis for attributing all these cracks, in their origin, to the results of overstressing of the metal during the moving and transportation of the trusses.

But alongside these cracks we see many cracks in such places where the stress of the metal during moving and transportation was undoubtedly insignificant. The origin of such cracks is enigmatic.

Alongside the question of the origin of the cracks, an important question is the extent to which the presence of these cracks may affect the use of the bridge. The question of the bridge’s operation apparently presents nothing threatening. This very conclusion is suggested by the considerations that deformations were found exclusively only in the angle irons, and there was not a single observed case of cracks in the vertical or horizontal plates. The results of the static and dynamic tests state categorically that there is no threat whatever to the bridge trusses in service; the mechanical testing of the metal also gives positive results.