The city of Deir ez-Zor is located in the northeast of the Syrian Arab Republic on the right bank of the Euphrates River, but part of it is located within the island in the middle of the river, where the river forks into two branches before entering the city, one large and the other small branch. The main attraction of this city was and is the so-called “suspension bridge of Deir ez-Zor” or “French bridge”. This bridge is a hybrid of a cable-stayed and suspension bridge built over the Euphrates River in six years (1925–1931) at a time when Syria was under the French mandate and connects the right and left banks of the above-mentioned river. Until 1980, it was used as a road bridge and a pedestrian bridge, but after that it was used exclusively as a pedestrian bridge in order to preserve it for future generations due toits architectural value to the country.

This pedestrian bridge is one of two bridges of the Gisklard system model built in Syria by the French Army, along with the Suvar Bridge on the Khabur River. The bridge was built according to the system of the French cable-stayed suspension bridge design engineer Albert Victor Hippolyte Leon Gisclard (Fig. 1a), the author of the bridge design was the French cable-stayed suspension bridge design engineer Gaston Leinekugel Le Cocq (Fig. 1b), who was the representative of the construction company “Arnodin”. This construction company belonged to Ferdinand Joseph Arnodin [11], who was also an engineer, industrialist and head of the above-mentioned construction company of the same name (Fig. 1c). Albert Gisklard died in 1909 in the south of France as a result of a catastrophe during load tests at the end of the construction of the railway cable-stayed suspension bridge “Pont de Cassagne”, which was later named after him “Pont Gisclard” [11–13].

The cable-stayed suspension bridge of Deir ez-Zor (Fig. 2) consists of four main pylons and two side anchor pylons located on the right and left banks of the Euphrates River. The bridge consists of five spans, three main spans of 112.50 m each and two side spans of34.62 m each, i.e. (34.62 + 3 × 112.5 + 34.62). The total length of the spans of the bridge according to the project is 406.74 m. The width of the bridge, including sidewalks, is 3.5 meters, and excluding sidewalks is 2.7 m, the width of each of the two sidewalks is 40 cm. The total width of the bridge is 3.9 m. The weight of the bridge is approximately 390 tons. The stiffening girder is steel I-shaped form. The distinctive features of this bridge are the radial-stay trusses and the middle cable attachment node, which are the “hallmark” of the Gisklard system [11–13].

The plan, section, and some stages of the construction of this bridge are shown in Figures 3–9, namely the beginning of construction in 1925, the construction process, load tests and the opening of the bridge in 1931, the modern view of the bridge in the XXI century, and photographs of the destroyed bridge after 2013 as a result of the war (Fig. 10–11).

During the hostilities in Syria, the bridge described above was damaged and destroyed (Fig. 10–11) in May 2013.

In the first half of the XX century, several bridges were designed and built by Gisklard's colleague Gaston Leinekugel Le Cocq, and Ferdinand Arnodin's construction company according to the Gisklard system. For example, a cable-stayed suspension bridge similar to the cable-stayed suspension bridge of Deir ez-Zor, but with an improved radial cable-stayed truss, the cable-stayed suspension bridge “Puente Colgante de Santa Fe” in the city of Santa Fe in Argentina (Fig. 12–13).

In general, suspension and cable-stayed bridges have similar schemes, but they also differ in the way of supporting the stiffening girder called a deck on which the roadway is located. The main difference between suspension bridges and cable-stayed bridges is that in suspension bridges, the roadbed is supported by suspenders or, in other words, vertical cables attached to the main load-bearing cables stretched from above along the entire length of the bridge, and in cable-stayed bridges, the roadbed is supported by cable stays attached directly to the pylons.

In suspension bridges (Fig. 14), the stiffening girder is supported by a curvilinear thread (cable or chain), stretched through the tops of the pylons, the ends of which are fixed at the ends in the shore anchor supports of the bridge, and vertical suspenders [8–10].

In cable-stayed bridges (Fig. 15), the stiffening girder is supported by inclined rectilinear cables fixed on pylons [8][9][14–17][19]. These cables are called “cable stays”. They are fixed on the pylons in several ways (Fig. 16). The system is called radial if the cable stays are fixed at one point on the top of the pylon (fan system), and if they are fixed on the pylon at several points along its height and are parallel to each other, then this system of cable stays arrangement is called "harp".

Figures 14 and 15 illustrate the differences between typical suspension and cable-stayed bridges, respectively. Figures 14 and 17 clearly illustrate the differences between a typical suspension and a cable-stayed suspension bridge built according to the Gisclard system [6] with a radial-stayed truss (Fig. 17). The scheme of a bridge with a radial-stay truss, built according to the Gisklard system, is a prototype of modern cable-stayed bridges. This truss is a distinctive feature of the projects of the bridge design engineer Albert Gisklard along with the middle cable attachment node (Fig. 18).

The load distributions in suspension and cable-stayed bridges are somewhat different from each other. The load [17] distribution scheme for both types of bridges is shown in Figure 19.

The following technique is designed to increase the rigidity of cable-stayed and suspension bridges by connecting the tops of the pylons with the help of an additional element in the form of a tightening of the so-called stiffening cable (Fig. 20–21). In addition, the use of a stiffening cable in the structures of the bridge superstructures reduces the consumption of material for the anchor supports of the bridges.

The cable must be able to resist large displacements; The cable needs to withstand the thrust caused by a temporary load; Temperature effects create additional stresses in the entire structure and in the cable and adversely affect its operation; When loading only one span, the cable works most efficiently. To increase rigidity, reduce cable sagging, and eliminate temperature deformations, that is, to increase the efficiency of its operation, immediately upon installation, it is pre-stretched by the amount of thrust arising from the temporary load. It should be noted that the cable in a loaded span works as a spacer, and in unloaded spans, it maintains its same tension without deforming. In a rectilinear cable, elastic deformations occur, which means that the deflections of the loaded span and the displacements of the pylon tops are small.

In the cable-stayed suspension bridge of the city of Deir ez-Zor, which was built according to the above-mentioned Gisklard system, its designer applied measures to increase rigidity, namely, stiffening cables were added (Fig. 22).

In the truss shown in Figure 23, each of the nodes, 1, 2, 3, 5, 6, 7, except for the middle node, that is, the “O” node is suspended only from the nearest pylon and is suspended from the adjacent truss node from the side of the second pylon. In the scheme under consideration, the influence lines are illustrated in Figure 23. Each cable stay is subject only to tensile forces, the condition for the cable stays to work in tension should be so that the top cable truss chords of one half-span (half-span are both sides of the “O” node) are located on a straight line with by the upper radial cable stay of the other half-span (Gisklard system). The disadvantage of this scheme is the high position of the “O” node, the large length of the vertical suspenders and high pylons.

To restore or strengthen the bridge (Fig. 24), it is necessary to make some calculations. For example, to calculate the stiffening girder [3][4], cable stays, anchor cables, pylons [6][10]. As an example, the algorithms for calculating the cable stays and their cross-sectional area are given below.

When calculating the bridge, we use the following known values (Fig. 24): L – the size of the main span; d – panel, that is, the distance between the points of attachment of the cable stays on the stiffening girder; Xi – the distance from the pylon to the point of attachment of the cable stay on the stiffening girder; hп – the height of the pylon; Вп – the width of the pylon; p, q – the intensity of the permanent and temporary load, respectively; α1 – the angle No. 1 of inclination of the anchor cable (anchor cable stay) to the horizon;N1 – the force No. 1 in the anchor cable stay No. 1 (anchor cable No. 1); α4 – the angle No. 4 of inclination of the cable stay to the horizon; N4 – the force No. 4 in the cable stay No. 4; Nп – the force in the pylon.

To determine the main forces NB in the cable stays, it is advisable to use the methodology proposed by professor V.K. Kachurin [6]:

(1)

Or in general

(2)

Where:

 – the distance from the pylon (to which the cable stay is attached) to the point of its attachment on the stiffening girder, expressed in fractions of the main span (Fig. 24).

n – the number of cable stays in the main span.

(3)

It should be noted that the cross section for the longest cable stays is assigned greater than for the rest of the cable stays by at least 30 to 50 %.

According to the strength condition, can be obtained from the following expression:

(4)

Where: Run – is the temporary tear resistance of the cable (brittle fracture), accepted for factory-made cables in the range of 1200–1800 MPa (1000–2400 MPa).

Since the territory of Syria is seismically hazardous with many earthquakes of varying intensity and frequency composition [1][2][14][18], which have occurred over the centuries, after the restoration of the cable-stayed suspension bridge of Deir ez-Zor, measures should be taken to protect it from wind [7] and seismic vibration [5][20] to ensure the safety of the bridge. Vibration reduction in cable-stayed suspension bridges can be achieved with tuned mass dampers, abbreviated (TMD), or with tuned mass magnetorheological dampers, abbreviated (TMD-MR DAMPER). Such damping systems have been studied by scholars W.J. Wu and S.C.S. Cai. The basic concept of cable vibration control with the TMD-MR damping system is shown in Figure 25, where the cable mass and the mass of the TMD-MR system are denoted m1 and m2 respectively. The MR damper provides adjustable damping and stiffness.

A sketch of the proposed TMD-MR system that can be used for cable-stayed suspension bridges, including the cable-stayed suspension bridge of the city of Deir ez-Zor in Syria, is shown in Figure 26. It should be noted that when MR dampers are not used or removed, the TMD-MR damper system, actually turns into a conventional vibration damper, i.e. TMD without a damping element. Although the TMD usually has a damping element, the TMD component is hereinafter deliberately referred to as the case without a damping element to distinguish it from the TMD-MR damper, which consists of tuned mass dampers (TMD) and magnetorheological dampers (MR) components.

This TMD-MR damping system is designed to be installed on a cable, and the concept of vibration suppression is shown in Figure 26. Cable vibrations are caused by excitations from the interaction of the pylon, bridge deck, wind-rain-cable, or their combinations. Characteristics of cable vibrations can be obtained in the spectral diagram, which is processed according to accelerometer data (Fig. 26). Multiple peaks in the spectral diagram are assumed and should be expected, since cable vibration excitations can be single frequency, multi frequency, or random. The frequency of the TMD-MR system will be tuned to the frequency corresponding to the most significant resonant vibration i.e. highest peak (Fig. 27) or other target frequency along with adjustment of its location and damping ratio to dampen vibration as effectively as possible.

The cable-stayed suspension bridge of the city of Deir ez-Zor, which is an architectural monument and part of the history of Syria, deserves a better fate, so every effort must be made to restore it and subsequently strengthen this unique object with seismic. For this, some calculations were given as an example that can be used to restore the bridge deck, cable-stays, pylons, pylon piers or abutments.

To protect the cable-stays from vibration, it is necessary to take into account their vibrations caused by excitations from the interaction of the pylon, bridge deck, wind-rain-cable or their combinations. The cable-stays are susceptible to external disturbances due to their own low damping. Due to the peculiarities of their location, the effectiveness of vibration reduction by mechanical dampers cannot be fully exploited, therefore, it is proposed to use magnetorheological (MR) liquid dampers with tuned or adjustable mass (TMD), which combine the convenience of installing TMD and the adjustability of MR dampers. Such an MR-TMD damper can be mounted anywhere on the cable. Scholars in different parts of the world, such as W.J. Wu, S.C.S. Cai, G.E. Valdebenito, A.C. Aparicio and others have experimentally demonstrated the good effect of such a damper to reduce or suppress cable vibration during periodic excitation. The effectiveness of vibration reduction is affected by the ratio between the excitation frequency, the frequency of the cable and the frequency ofthe damper, taking into account this, the damper frequency is adjusted. This combination of dampers can also be used in power transmission lines.

Since it is important to preserve the original appearance and authenticity of the cable-stayed suspension bridge in the city of Deir ez-Zor in Syria, the use of the TMD-MR damper system is the most suitable to reduce vibration, of course, during or after the restoration of the bridge.