PriMera Scientific Engineering (ISSN: 2834-2550)

Research Article

Volume 9 Issue 4

The Bella Curve and Load Bearing Capacity towards Wind

Rune Brincker*

September 30, 2026

DOI : 10.56831/PSEN-09-297

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Abstract

In this paper we are considering linear elasticity theory to model the maximum horizontal force on a building that can only carry compression stresses from the gravity load, such as masonry and unreinforced concrete buildings. To solve this problem, we define two simple dimensionless geometrical quantities and define a corresponding plot between the two quantities that we denote the Bella Curve. This curve can be used to provide an estimate of the moment arm of the normal force to withstand the above mentioned maximum horizontal force so that we still have compression stress in all load bearing walls. We illustrate the principle on classical beam sections and then also demonstrate how the principle can be applied to provide an estimate of safety towards wind for the Danish high rise building from Bellahøj and for the 670-year-old Giotto Bell Tower in Italy.

References

  1. Dansk Ingeniørforening. “DS 411: Normer for Bygningskonstruktioner, Beton- og jernbetonkonstruktioner”. Dansk Ingeniørforening (1949).
  2. Byskov E. “Elementær Teori for Plane Bjælker”. Department of Civil Engineering, Aalborg University, Institut for Bygningsteknik, Aalborg Universitet Nr. U0503 (2005).
  3. Ribbeler RC. “Statics and Mechanics of Materials”. Prentice Hall (2004).
  4. Jensen BC., et al. “Teknisk Ståbi”. 25th ed. Akademisk Forlag (2022).
  5. Eurocode Applied Steel Tables. “Eurocode Applied Steel Tables”.
  6. Statens Byggeforskningsinstitut. “Bellahøjhusbygger”. Statens Byggeforskningsinstitut, Studie Nr. 15. I kommission hos Teknisk Forlag, København (1955).
  7. Dominia AS Rådgivende Ingeniører. “Bellahøj I+II Betonundersøgelser” (2012).
  8. Jørgen Nielsen Rådgivende Ingeniører. “Granskning af konstruktionsundersøgelser vedrørende bygningsstabilitet” (2021).
  9. Jens-Peter Madsen ApS Rådgivende Ingeniører. “Bygningsstabilitet for SAB I og SAB II Granskningsnotat” (2023).
  10. Lacanna A., et al. “Seismic wave dispersion in high-rise historical building by interferometric analysis: The case history of Giotto’s Bell Tower”.
  11. “Eurocode 2: Design of Concrete Structures - Part 1-1: General Rules and Rules for Buildings”. Section 11, Eq. (11.2).
  12. “DSEN 1991-1-4 DK NA2024: Nationalt anneks til Eurocode 1: Last på bygværker – Del 1-4: Generelle laster – Vindlast”. Social- og Boligstyrelsen (2024).