Matthias Beckh - Hyperbolic Structures: Shukhovs Lattice Towers - Forerunners of Modern Lightweight Construction

1. Foreword
2. Introduction
3. Building with hyperbolic lattice structures
4. Geometry and form of hyperbolic lattice structures
5. Structural analysis and calculation methods
   1. 3 Relationship between the rotation angle and the position of the throat circle or waist
      a Waist below the top ring
      b Waist coincident with the top ring
      c Waist above the top ring
   2. 14 Load-displacement characteristics of systems with stress problems
      a System with increasing stiffness, e.g. a membrane-supported plate under transverse load
      b System with decreasing stiffness, e.g. a stretched rubber band
      c Combination of a and b, e.g. a very flat, not-too-thin shell, in the case of stress problems, reaching the materials ultimate strength determines the ultimate load of the structure.
6. Relationships between form and structural behaviour
   1. 6 Variant 2 (RU = 5.0 m, IR = 10, n = 24)
      a Load capacities shown in relation to , linear calculation
      b Load capacities shown in relation to , non-linear calculation
      c Relationships between load capacities for perfect and imperfect geometries, non-linear calculation
      d Load capacities shown in relation to , stiff intermediate ring connections, linear calculation
   2. 14 Variant 2 (RU = 5.0 m; KF = 1.0; IR = 24):
      a Number of intermediate rings (IR) to load capacity
      b Number of IR to load capacity/mass ratio
   3. 15 Variant 2 (RU = 5.0 m; IR = 10; n = 12):
      a Load capacities shown in relation to intermediate ring size, KF = 1.0
      b Load capacities shown in relation to intermediate ring size, KF = 2.0
   4. 19 Variant 2: Load capacities shown in relation to with 5 % horizontal load
      a RU = 3.0 m; IR = 10; n = 24
      b RU = 5.0 m; IR = 10; n = 24
   5. 21 Variant 3 (RU = 5.0 m; = 60)
      a Load capacities shown in relation to the number of vertical member pairs
      b Load capacity/mass ratio shown in relation to the number of vertical members
   6. 26 Water tower, Nizhny Novgorod (RUS) 1896
      a Finite-element models
      b Buckling shapes, non-linear, vertical load (l.) and vertical and horizontal load (r.)
      c Summary of geometry, cross sections and loads
      d Load-displacement diagram (L-D diagram)
   7. 27 Water tower, Mykolaiv (UA) 1907
      a Finite-element models
      b Buckling modes, non-linear, vertical load (l.) and vertical and horizontal load (r.)
      c Summary of geometry, cross sections and loads
      d Load-displacement diagram
   8. 28 Water tower, Tyumen (RUS) 1908
      a Finite-element models
      b Buckling modes, non-linear, vertical load (l.) and vertical and horizontal load (r.)
      c Summary of geometry, cross sections and loads
      d Load-displacement diagram
   9. 29 Water tower, Dnipropetrovsk (UA) 1930
      a Finite-element models
      b Buckling modes, non-linear, vertical load (l.) and vertical and horizontal load (r.)
      c Summary of geometry, cross sections and loads
      d Load-displacement diagram (as built)
7. Design and analysis of Shukhovs towers
   1. 2 Elevated water tanks
      a Maisons-Lafitte near Paris (F) 1850
      b Halle an der Saale (D) 1868
      c For the French Midi-Ouest railway (F) ca. 1865
   2. 26 Water tower in Yaroslavl (RUS) 1911
      a First page of Shukhovs design calculations
      b Photograph ca. 1911
      c Blueprint (different to the built version)
   3. 28 Water tower, Dnipropetrovsk (UA) 1930
      a Elevation and plan
      b Photograph of the collapsed tower
8. NiGRES tower on the Oka
   1. 2 NiGRES tower on the Oka, Dzerzhinsk (RUS) 1929
      a Gaps in the loadbearing structure
      b Repairs carried out in 2008
   2. 9 Details of the support points
      a Rendering
      b Exploded view
   3. 10 Connections of the members to the intermediate ring
      a Rendering
      b Condition 2011
   4. 16 Loads and deformations at the first main ring under load case 2 (horizontal wind load in accordance with DIN 1055-4)
      a Forces on the main rings from the vertical members
      b Normal and tangential force components
      c Resulting normal force distribution
      d Vertical bending moments
      e Horizontal bending moments
      f Deformed shape
   5. 19 Distortion of two meshes with the adjoining main ring under horizontal wind load, 50 magnification
      a First main ring with trapezoidal meshes (transition from first to second segment)
      b Third main ring with triangular meshes (transition from third to fourth segment)
   6. 20 Modelling of the node points and bearings
      a Actual condition
      b Drawing of finite-element model
   7. 21 Stress ratio v /vRd
      a LCC 1: Self-weight and wind unfactored
      b LCC 2: Self-weight and wind with safety factors
      c LCC 3: Self-weight and 40 % of the full wind loads in accordance with DIN 1055-4, with safety factors, conductors not present
9. Rsum
10. Towers in comparison

Matthias Beckh

English language edition first published 2015
2015 by John Wiley & Sons, Ltd

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Originally published in the German language as Hyperbolische Stabwerke. uchovs Gittertrme als Wegweiser in den modernen Leichtbau
By Matthias Beckh
Published with laminated folded brochure cover in 2012
By Edition DETAIL Institut fr international Architektur-Dokumentation, Munich

This English edition was translated by Raymond D. Peat, Alford, Aberdeenshire (GB).