Tracing non-linearities in the load bearing behavior of structural membranes: Typical shapes and load cases investigated towards European standardization

Ann-Kathrin Goldbach; Kai-Uwe Bletzinger

doi:10.3934/acse.2024001

Article Contents

2024, Volume 2, Issue 1: 1-9. Doi: 10.3934/acse.2024001

This issue Previous Article Next Article Shape-adaptive climate loading of tensile surface structures

Tracing non-linearities in the load bearing behavior of structural membranes: Typical shapes and load cases investigated towards European standardization

Ann-Kathrin Goldbach^1, , and
Kai-Uwe Bletzinger^1,

1.
Technical University of Munich, Chair of Structural Analysis, Arcisstr. 21, 80333 Munich, Germany

^*Corresponding author: Ann-Kathrin Goldbach
^*Corresponding author: Ann-Kathrin Goldbach

web page: https://www.cee.ed.tum.de/st

Received: January 2024

Early access: March 2024

Published online: March 2024

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Abstract

One of the prevalent challenges in the design, numerical analysis,, and verification of structural membranes lies in the non-linearity of their load-response curves. Structural analysis has to be performed with a geometrically non-linear approach due to the interaction of form and forces, and thus a linear extrapolation or combination of analysis results is not possible. The appropriate modeling of the environmental impacts (such as wind and snow) also has a significant influence on the analysis results. Furthermore, non-linear material behavior can be of interest. The resulting load-response curves (e.g. stresses and deformations) are typically non-linear and their interpretation towards the underlying safety requirements is not straight forward. In addition, the prestress also has a major influence on membranes' structural behavior. However, the current European regulations for the proof of the limit states (ULS and SLS) of any building require a simplified categorization of the structural behavior. This research investigates the load-bearing behavior of typical re occurring membrane shapes in the context of current verification requirements. Typical load cases are applied and the structural behavior is shown under consideration of the mentioned non-linearities.

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Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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Figure 1. Characterization of non-linearity according to EC 0 [3] and resulting design regulations

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Figure 2. Typical membrane shapes, adapted from [6]

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Figure 3. Principal stresses developing under snow and wind suction load for four typical membrane shapes undergoing load controlled geometrically non-linear structural analysis. Adapted from [6]

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Figure 4. Principal stresses under snow and wind suction load for the hypar at different prestress levels undergoing load controlled geometrically non-linear structural analysis. Adapted from [6]

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Figure 5. Staged analysis scheme: mounting and loading steps to be considered as consecutive actions

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Figure 6. Dimensioning points $ f_{Ed} $ computed from principal stresses for a hypar under snow load. Linear extrapolations of an origin (grey : zero, black : level of prestress) to the effect of characteristic action $ E(q_k) $ depicted as dashed lines, and the design effects of action are indicated by black and grey points

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