Optimization of the Stiffening Configuration of Axially Compressed Steel Silos on Local Supports

Research project:

Optimization of the Stiffening Configuration of Axially Compressed Steel Silos on Local Supports

Researchers involved:
-    Arne Jansseune (former PhD researcher)
-    Jan Belis (supervisor)
-    Wouter De Corte (supervisor)




Silos are used in agricultural and food industry, in mining and industrial processes (e.g. concrete plants) to temporarily store large volumes of powdered, granular, or bulk materials between successive transports and production processes, as buffer, etc. One of the advantages of upward silos is that they require a relatively small floor space compared to the large volumes.


The focus of the doctoral thesis is on steel silos with a circular planform (most frequently used for metal silos), composed by welding together curved panels, and placed in an elevated position by means of a small number of local support columns. The elevated position frequently is preferred because of the necessity to discharge the silo contents (by gravity) into a transporting system.
Given that such silo structures are discretely supported and are for the most part exposed to vertical compression caused by friction between the bulk material and the silo wall, axial peak stresses are locally introduced in the silo wall above the discrete supports. These disadvantageous stress concentrations cause premature failure of the silo wall, either by plastic yielding, by elastic buckling, or a combination of both phenomena.

Two possible solutions are to either engage the (rectangular) support columns over a short distance or to provide (U-shaped) longitudinal stiffeners above the support columns. While the first type is used for light silos and the second type for intermediate to large silos, both configurations have in common that, along the attached height of the engaged column/longitudinal stiffener, the ground reaction force is transferred more gradually into the silo wall by shear. Consequently, the axial stresses are better distributed in circumferential direction and the disadvantageous stress concentrations are reduced, resulting in a significant increase of the failure load.

Problem statement

As a result of the substantial vertical compressive loading on the shell wall, the decisive design state for such thin-walled structures are the buckling limit state for relatively thin-walled silos) and the plastic limit state (for relatively thick-walled silos). However, not in the relevant European normative documents (EN 1993-1-6, 2007; EN 1993-4-1, 2007) nor in the recommendations of the European Convention for Constructional Steelwork (ECCS, 2008), there are currently calculation rules available for the design of locally supported stiffened cylindrical steel silos subjected to meridional compression. These documents only provide a general applicable framework and methodology with general concepts, rules, guidelines, and commentary. The design methods are (i) the stress design approach, (ii) the MNA/LBA approach, and (iii) the GMNIA approach.

Due to the presence of very local stress concentrations, the first method yields in a very conservative prediction of the elasto-plastic strength, making this method unsuitable.

The third design method is relatively complex, because a relatively complex shell calculation (GMNIA) must be performed, including geometrical and material non-linearity. Furthermore, during the entire design process, several important decisions have to be taken such as the choice of an appropriate geometric (equivalent) imperfection shape, the failure criterion, etc. as a result of which the results largely depend on the designer’s experience. Moreover, this powerful finite element software is required which is not available in every design office.

For the second method, two relatively simple numerical shell analyses (i.e. MNA and LBA) must be performed from which the elasto-plastic strength can be estimated on the basis of interaction (or buckling) parameters. However, these interaction parameters for meridional compression are currently missing in the normative document for locally supported stiffened cylindrical steel silos (EN 1993-1-6, 2007). Instead, the Eurocode proposes that the designer (i) makes an own appropriate conservative choice for the interaction parameters (by comparing the current problem with similar buckling problems), (ii) switches to the more complex GMNIA approach (i.e. the third method), or (iii) uses the default interaction parameters mentioned in the Eurocode for uniformly compressed unstiffened cylindrical steel silos (EN 1993-1-6, 2007; ECCS, 2008). In other words, none of the proposed alternatives seem to provide a satisfactory answer to the lack of interaction parameters.

The use of these buckling parameters for other types of silos is remarkable, and is based on the assumption that it is difficult to imagine that there are situations which are more unfavorable and more imperfection sensitive than the unstiffened cylinder shells under uniform axial compression. The design rule study (See Research - part 2) aimed to see whether or not the above assumption is true for locally supported stiffened steel silos with a distinctive non-uniform axial stress distribution in circumferential direction.

Research - part 1

The first main objective was to obtain a better understanding of the failure behaviour of locally supported steel silos subjected to axial compression. In order to achieve this goal, a numerical model was developed and validated against experimental results, a number of extensive parametrical studies were performed to explore the failure behaviour, and finally the most optimal stiffening configuration was determined.

Using the finite element package Abaqus and the programming language Python, a parameterized finite element model was prepared suitable for a wide range of geometries. The FE model was validated by confronting the numerical results with experimental results obtained from destructive tests of a limited number of well-chosen geometries. From this confrontation, it was concluded that the numerical model was able to make a reliable assessment of the failure load for pure axial compression.

To gain new insights into the structure, the validated model was used to conduct several parametrical studies to map the influence of a change in geometry on the failure behaviour. The key geometric parameters are, as expected, the wall thickness of the silo, the degree of support along the bottom of the silo wall, and the cross-section of the engaged columns and the U-shaped longitudinal stiffeners. Next, the most optimal configuration was determined for the engaged columns and the U-shaped longitudinal stiffeners, to maximize the failure load with a minimal increase of material.

During fabrication of a relatively thin-walled silo, small (geometrical) imperfections are inevitable in the silo wall, such as the presence of small deviations and irregularities in the vicinity of the welds. As a result of these imperfections, the failure load of a real imperfect silo will be significantly smaller than for a theoretically perfect silo, as a result of which these imperfections certainly must be taken into account during silo design. Therefore, an imperfection sensitivity study was performed to estimate the negative influence of location, amplitude, and orientation of different imperfection shapes on the failure load.

Based on the above results, a representative choice was made for all parameters (geometry, material, and imperfections) for the design rule study (part 2).

Research - part 2

Capacity or buckling curves were developed for a wide range of geometries using different types of shell analyses (i.e. LBA, MNA, GN(I)A, GMN(I)A) and an inward weld depression type A was chosen as imperfection shape. These results showed that, surprisingly, a relatively good agreement was found between the numerical results and the existing buckling curves, despite the difference in shell type mentioned above.

Most important publications:

  • Jansseune, A., De Corte, W., Vanlaere, W., and Van Impe, R. (2012). Influence of the cylinder height on the elasto-plastic failure of locally supported cylinders. Steel and Composite Structures, 12(4): 291-302.
  • Jansseune, A., De Corte, W., and Van Impe, R. (2013). Column-supported silos: Elasto-plastic failure. Thin-Walled Structures, 73(0): 158-173.
  • Jansseune, A., De Corte, W., and Belis, J. (2015). Elastic failure of locally supported silos with U-shaped longitudinal stiffeners. KSCE Journal of Civil Engineering, 19(4): 1041-1049.
  • Jansseune, A., W. De Corte and J. Belis (2016). Optimal stiffening configuration for locally supported cylindrical silos: Engaged columns. Journal of Constructional Steel Research, 119(0): 17-29.
  • Jansseune, A., W. De Corte and J. Belis (2016). Imperfection sensitivity of locally supported cylindrical silos subjected to uniform axial compression. International Journal of Solids and Structures, 96(): 92-109.
  • Jansseune, A., W. De Corte and J. Belis (2016). Elasto-plastic failure of locally supported silos with U-shaped longitudinal Stiffeners. Engineering Failure Analysis 70(0): 122-140.

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