History and documentation

Structural Analysis of Historic Construction – D’Ayala & Fodde (eds)© 2008 Taylor & Francis Group, London, ISBN 978-0-415-46872-5

Construction and structural behavior of Vladimir Suchov’s Nigres tower

M. Beckh & R. BarthelDepartment of structural design, Munich Technical University, Munich, Germany

A. KutnyiDepartment of architectural history, building archeology, heritage conservation, Munich Technical University,Munich, Germany

ABSTRACT: From 1927–1929, the renown Russian engineer Vladimir Grigorevic Suchov (1853–1939)designed and built several towers for the Nigres power transmission line. As one of the last and most refinedhyperboloid steel lattice towers, they represent the culmination of his lifelong quest in the development andoptimization of this structural system.

1 INTRODUCTION

Suchov designed and built the first hyperboloid steellattice tower for the All-Russian exhibition in NizhniyNovgorod in the year 1896. The 25.6 m tall structurewith a bottom diameter of 11 m and a top diameter of4.3 m consisted of 80 straight steel angles and inter-mediate horizontal ring elements. The extremely lightand filigree structure served as a water tower combinedwith a viewing platform and attracted the attention ofthe engineering community and public alike.

In the following years, his invention gainedwidespread circulation throughout Russia due to itscost-effectiveness and structural stability in compari-son to other tower structures. Suchov standardized thebuilding type and constructed more than hundred tow-ers with varying heights and proportions for differentpurposes. The tallest structure of this kind is the 150 mtall Sabolovka radio tower in Moscow, built between1920 and 1922.

At the end of the same decade, from 1927–1929,Suchov built six power transmission line towers atthe Oka river, about 100 km southwest of NizhnyNovgorod (fig. 1). The four smaller ones were com-posed of three, the two taller ones of five hyperboloids,reaching 130.2 m in height. With their structural clar-ity, extreme lightness, and simple detailing, thesetowers mark the high point of Suchov’s advancementof hyperbolic lattice structures.

Five of the six towers have been dismantled sincethey became out of use more than ten years ago. Onlyone of the two 130.2 m tall structures is still existenttoday. This remaining structure was recently severelydamaged when 16 of the 40 elements in the lower partof the first drum were cut out by looters. The missingelements will be substituted in the fall of 2007.

Figure 1. The two tall Nigres transmission towers at the Okariver, photo taken by Igor Kazus in 1989 (Graefe 1990).

2 THE NIGRES TOWERS

2.1 Construction and geometry

The structure consists of five hyperboloids sectionswith decreasing diameters (34.0 m, 25.8 m, 19.4 m,14.0 m, 10.0 m, 6.0 m) stacked upon each other. Thesections are 24.9 m tall, except for the highest one,which measures 24.3 m. The three transmission lineswere supported at 128.0 m. With the trussed outriggerat the top, the structure reaches an overall height of130.2 m.

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Figure 2. Plan view of the 5 hyperboloid sections.

The first three drums are made of 40 members (steelangles), the fourth and fifth one of 20 members. Thus,the first, second and third hyperboloids are dividedin plan in 9◦ segments, whereas the two upper onesare divided in 18◦. In plan view, the angle ϕ betweenthe lower and upper end of each vertical expresses thetwisting of the hyperboloid. The angle ϕ is constant forthe three lowest sections (36◦) and becomes more pro-nounced towards the top of the structure (54◦ and 72◦).Due to the rather subtle twisting of the verticals onlythe two upper sections display the typical “waisted”hyperboloid form. The two sets of inversely runningverticals intersect each other 4 times in the lowest threesections and the highest one, and 3 times in the fourthsections. (See fig. 2).

Between the hyperboloid segments, horizontal lat-tice girders act as stiffening elements (See fig. 3) Thetwo sets of inversely arranged verticals are slightlyoffset and joined with two rivets at each “intersec-tion”. The 10 mm distance between the faces of thesteel angles is hereby bridged with a shim plate.

Each drum is stiffened by ten horizontal ring ele-ments, spaced 2.26 m on centre vertically. The con-nections between the verticals and the horizontal ringelements do not coincide to allow for more simpleconnection details. (fig. 4)

The connection between the brackets, which arecantilevering of the verticals, and ring elements isbolted. All other connections of the structure (e.g.

Figure 3. View of the steel structure from inside with thelattice girders, which separate the hyperboloid sections.

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Figure 4. Steel structure of the first hyperboloid section,showing the slightly offset verticals and the horizontal ringelements. The vertical to the right has been cut by looters.

Table 1. Steel sizes of the structure according to the originalconstruction documents.

Drum Verticals Ring elements Lattice girder

First L120 × 120 × L80 × 80 × 10 L100 × 100 × 1212 (40) − 240 mm

Second L100 × 100 × L75 × 75 × 8 L90 × 90 × 912 (40) − 200 mm

Third L100 × 100 × L75 × 75 × 8 L75 × 75 × 810 (40) − 200 mm

Fourth L100 × 100 × L60 × 60 × 6 L75 × 75 × 812 (20) − 200 mm

Fifth L100 × 100 × L50 × 50 × 6 L75 × 75 × 810 (20) − 10 mm

between verticals and the lattice girder, of membersat the outrigger, at splices, et cetera) are riveted.

2.2 History of the assembly

The construction of the two five-tiered towers startedin spring 1928. The first drum was constructed withhelp of an inner wooden scaffolding, which supportedthe structure at certain locations. By mid March, the

Figure 5. Assembly of the structure using the telescopemethod. (Graefe, 1990).

erection of the second drum started. Unlike in thecase of the neighbouring three-tiered towers, whichwere built conventionally with an assembly platformon top of each hyperboloid, a new construction methodwas used for the subsequent upper drums. Here, thetelescope method was employed, which had alreadyproven efficient in the erection of the Sabolovka towera few years earlier. (See fig. 5)

The subsequent sections were assembled inside theshaft. Their feet were pulled towards the center witha wooden corset. Five wooden derricks located at theupper lattice girder of the last drum then lifted the nextsection to the top. Once the section had reached itsintended height, the mountings were slowly released.Then the feet were bent outwards to the ring and wereconnected at their final position.

The construction of one drum element needed aboutsix to eight weeks. The towers were completed in1930. The employed telescope method explains whySuchov designed the lower sections without a real“necking”, even though it would have been structurallyadvantageous.

3 SUCHOV’S STRUCTURAL ANALYSIS

Suchov’s original calculations for the tower resurfacedin the town archive of Nishni Novgorod in 2007. The10 page typewritten structural analysis comprises load

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assumptions, steel member design as well as the designof the riveted connections and the foundations.

Referring to load combinations given by theRussian building code, Suchov states that the high-est forces in the tower are caused if “the transmissionlines aren’t ruptured, no ice build-up exists, and thewind pressure is 250 kg/m2”.

The design wind pressure of 250 kg/m2 – constantover the height of the structure – is used to calculatethe resulting forces on the different hyperboloid sec-tions and at the base. This design pressure is appliedon all the vertical members, using their unprojectedlength times the width of the steel angles as thereference area.

To account for wind shielding at the sides of the ringelements, Suchov uses the following formula with thediameter D and the width of the steel angle b to cal-culate the resulting horizontal wind force on one ring.

The resulting overturning moment of the tower is com-puted as 7384.21 tm; the self weight of the towerincluding the weight of the power lines is 144.26 t.

The forces on the verticals are calculated for eachsection with the z following equation:

with the overturning moment M, 2n the number ofverticals, and the radius of the considered ring r.

Hence, the highest forces in the first section due todead load and wind are:

This load is used to design the verticals in the firsthyperboloid. As buckling length, the distance betweenthe support and the connection between the verticalsand the first horizontal ring is used. Suchov argues thatthe connections provide enough torsional restraint, sothat column buckling of the L – shaped vertical willnot occur around the principal but the strong axis. Theallowable maximum compressive stress is computedwith the following formula:

with slenderness ratio λ = lc/i. In this manner, theverticals of the first section are designed.(E.g. L120×120×12 with iy =3.65 cm,A=27.54 cm2

This procedure is repeated with the respective over-turning moments to design the L-shaped verticals ofthe higher hyperboloid sections.

Finally, the riveted connections of the first verti-cal of each section are designed. The combined shearand bearing pressure appears to be at the maximum800 kg/cm2 for 7/8 inch rivets. 7/8, 3/4 and 5/8 inchrivets are used for the connections according to thecalculations.

In addition, the calculations entail the design ofanchor bolts, the steel members at the top, the stabil-ity against overturning of the structure as well as thedesign of the concrete foundation. There is no struc-tural design of ring elements or lattice girders includedin the original calculations. (Suchov 1927)

4 NEW ANALYSIS

4.1 Structural model

The structural analysis model is based on the sizesand dimensions given in Suchov’s original construc-tion drawings. For the calculations, the FEM programRStab was used. The structure was modelled in thefollowing way:

– In order to minimize the number of nodes, the slightoffset between the two sets of inversely runningverticals is only included in the first hyperboloidsection. This is due to the fact that the first section ismore susceptible to buckling (Compare fig. 6). In thehigher sections, the joints of all vertical hyperboloidshell members are in one plane, thus neglecting theslight offset.

– Verticals are joined at each intersection of thehyperboloid shell with fixed connections.

– All the horizontal ring elements and lattice girdersare joined with moment-released connections to theverticals.

Material testing showed that the historic steelhas similar mechanical properties to S 235 (fy =235 N/mm2, E = 210000 N/mm2), which was used inthe structural model.

4.2 Wind loads

Wind loads were based on the DIN 1055-4. Thecode calls for the wind velocity measured 10 m aboveground with an exceeding probability of 1/50. Onlythe 5 year wind velocity was available for the local-ity of the tower. Based on various reference material(Schueller 1981), the wind velocity was extrapolatedrather conservatively with the factor 1.39. The result-ing reference velocity pressure for 50 years was thusdetermined as 0.32 KN/m2.

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Table 2. Resulting wind pressures c∗f q(ze) on the steel

members according to DIN 1055-4.

hu ho ze q(ze) q(ze)∗ 1.84Drum [m] [m] [m] [KN/m2] [KN/m2]

First 0 24.9 15 0.632 1.16Second 24.9 49.8 40 0.909 1.67Third 49.8 74.7 65 1.053 1.94Fourth 74.7 99.6 90 1.139 2.10Fifth 99.6 123.9 114 1.205 2.22Outrigger 124.0 130.2 127 1.237 2.28

Taking reduction ratios for angular sections intoaccount, cf is ascertained as 1.84. The velocity pres-sure z meters above grade level is in midland areas:

Wind pressures were applied to all the members,taking their flange width times length as the referencearea. Unlike in Suchov’s original calculations, wherethe wind pressure on the horizontal rings is reduced, noreduction factor was applied to account for shieldingof the members. Even though there certainly will occursome shielding on the sides of the ring elements, nocode regulation could be found that was applicable tothis specific geometry.

4.3 Stability

To assess the ultimate bearing load of the tower, itwas critical to study its stability behaviour. Therefore,a geometrical non-linear stability analysis had to beperformed. For that reason, it was essential to findsuitable imperfection shapes.

Following recommendations by Graf, the imperfec-tion shape of grid shell structures should be deter-mined by scaling the first eigen-value mode shapeunder ultimate load. The first oscillation period wasdetermined in the modal analysis as 1.02 seconds.

In the case of a tower-like structure, the eigen-valuemode shapes are obviously extremely from the buck-ling shape of the perfect geometry. The structure ofthe first hyperboloid section proved to be the mostcritical. The buckling shape shows six evenly aroundthe perimeter line distributed bulges, which are con-fined to the lower half of the section. This bucklingshape of the perfect geometry was scaled and imposedon the structure as the imperfection shape. The max-imum deformation was selected rather conservativelyas 150 mm, a deformation considered to be visible tothe naked eye.

According to DIN 18800-2, the stiffness of struc-tures susceptible to buckling has to be reduced by

Figure 6. Buckling shape, based on the perfect geometry.The plan view shows the first hyperboloid section only.

dividing the E-modulus of elasticity by the coefficientγM = 1.1. The load increase factor of the imperfectgeometry was determined as 4.39, compared to 4.87 ofthe perfect geometry. This is a rather modest decreasecompared to other grid shell geometries.

Hyperboloids and some other anticlastic formedshells are typically less sensitive to imperfections, due

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Table 3. Comparison of forces in the first hyperboloidsection under different loadings.

Maximum Maximum Maximumnormal normal bendingforces in forces in moment inverticals of lowest lowest lattice

Load case/ the lowest lattice girder, aroundcombination drum girder strong axis.

LC 1 −30 KN 20 KN –LC 2 −42 KN 29 KN –LC 3 −393 KN −245 KN 11 KNm

+309 KN +303 KNLC4 −132 KN −39 KN 3 KNm

+48 KN +99 KNLC 5 −281 KN −169 KN 7 KNm

+219 KN +212 KNLC 6 −246 KN −131 KN 8 KNm

+167 KN +184 KN

to the stabilizing effect of the interaction of compres-sion and tension forces of the two main parabolas.(Gioncu 1992, Graf 2002).

4.4 Load cases

The subsequent load cases/combinations were exam-ined, in which the wind was applied perpendicular tothe direction of the transmission lines, in the followingcalled x-direction (fig. 7). For the analyses, the loadfactors 1.35 for dead load, and 1.5 for live loads wereapplied.

The self weight of the tower was deter-mined as 1090 KN. The resultant wind forcesin x-direction for the tower structure itself are1.5 × 1002 KN = 1503 KN for the 50 year wind, com-pared to 1239 KN as calculated by Suchov. Althoughthe base shears are quite similar, the overturningmoments are significantly higher if the modern codeis applied, due to the vertical distribution of windpressures. The forces in the members of the firsthyperboloid section under different load cases aresummarized in table 3.

LC 1: self weight of the towerLC 2: self weight of the tower including the

transmission line, factoredLC 3: like LC 2 plus 50-year wind load in

x-direction, factoredLC 4: like LC 2 plus 24% of the 50-year wind

in x-direction, factoredLC 5: Self weight including transmission line

plus wind load in x-direction accordingto the original calculations of Suchov.

LC 6: Current condition without transmissionlines. Self weight of the tower plus5-year wind in x-direction, factored.

Figure 7. Deformed shape of the tower under self weightand wind load in x-direction, displaying larger deformationsat the transition between the different hyperboloid sections.

4.5 Structural behaviour

4.5.1 Under self weightUnder self weight, all verticals are subjected evenlyto compression forces, whereas the lattice girders are

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Figure 8. Transition between first and second hyperboloidsection. From top to bottom: Structure, followed by qualita-tive contours of deformation, normal force distribution, andbending moments of the lattice girder.

subjected to tension forces. This is caused by the dif-ferently inclined verticals above and below each latticegirder. The outward thrust is thus balanced by thelattice girder.

The ring elements are not subject to any forces.Theysimply act as bracing elements for the verticals.

4.5.2 Under self weight and horizontal wind loadin x-direction

The tower displays a remarkably high bending stiff-ness. The horizontal deformation of the structureunder unfactored wind load is 340 mm, resulting ina deflection ratio of l/388.

Under self weight and wind load, the structure dis-plays a tube-like load bearing behaviour. All verticalsare subjected to normal forces. Predictably, the verti-cals at the front face are under tension and the ones atthe rear face under compression. At the “sides”, ver-ticals are alternating under tension or compression,

depending on their twisting angle. This imposes a ver-tical distortion of the lattice girder at the end of eachsection.

The discontinuity of the verticals between the dif-ferent hyperboloid sections results in a decrease ofthe shear stiffness, causing large deformations in theseareas.The lattice girders are subject to linearly increas-ing compression forces on the front face and tensionforces on the opposite side, thus balancing the normalforces of the inclined verticals below.

The bending action of the tower causes the latticegirder to ovalize, thereby inducing bending momentsaround the strong axis of the member. (fig. 8) In addi-tion, the girders are even more affected by the push-pull action of the sidewise verticals, acting around theirweak axis. The ring elements adjacent to the latticegirders get affected by the distortion in this area aswell, causing overstress due to bending.

Based on the current analysis and load assump-tions, the structure would not be adequate to sustainthe 50-year wind, due to buckling of the verticals inthe first section. The structure including transmissionlines would only satisfy code requirements if the fac-tored wind loads are reduced by 76%. Even the currentcondition without the transmission lines would not besufficient to sustain the 5-year wind.

Despite of some minor local overstressing, almostall other members of the structure are suitable (loadcase 3).

5 CONCLUSION

The buckling behaviour and wind load assumptions ofthe structure will have to be investigated more deeply,as the results are not in line with the 80 year life span ofthe tower. One critical point is the lack of the 50-yearwind velocity at the locality of the tower. Shieldingof members in an open circular framework is anotherissue that requires further research. The disregard ofany reduction factor for shielding (due to the lackof suitable specifications) certainly effectuates a tooconservative assessment of the structural safety of thetower.

Despite of these unanswered questions, it is intrigu-ing to comprehend the structural behaviour of thesemulti-storeyed hyperboloid lattice towers. The time-less elegance, ingenuity and courage that the NIGREStower exhibits still have a humbling effect on thebeholder.

ACKNOWLEDGEMENTS

The authors are part of a joint European-Russianresearch group, which is led by Rainer Graefe, insti-tute of architectural theory and history, Universität

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Innsbruck, in cooperation with Rainer Barthel, MuratGappoev, Uta Hassler, Alexander Kolesov, Igor Molev,Manfred Schuller, and Tatjana Vinogradova.

REFERENCES

De Vries, P. 1999. Morphology and structural behaviour ofthe hyperbolic lattice. In: 4. International colloquium onstructural morphology. Delft: University of Technology.

DIN 18800. 1990. Stahlbauten.DIN 1055-4. 2005. Einwirkungen auf Tragwerke –

Windlasten.

Gioncu, N.B. 1992. Instability behaviour of single layer retic-ulated shells. In: International journal of space structures.Vol.7. No 4.

Graefe, R. 1990. Die Kunst der sparsamen Konstruktion.Stuttgart: Deutsche Verlags Anstalt.

Graf, J. 2002. Entwurf und Konstruktion vonTranslationsnet-zschalen. Stuttgart: Verlag Grauer.

Schueller, G. 1981. Einführung in die Sicherheit und Zuver-lässigkeit von Tragwerken. Berlin: Verlag Ernst und Sohn.

Suchov, G.1927. Structural calculations of a 128 m tall tower.city archive of Nizhniy Novgorod.

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