5.1 Shape and static loading

A biogas plant should be watertight. The gasholder must be gaslight. For this reason a biogas plant must have no cracks. But structures of masonry or concrete always crack. One can try to keep the cracks small. And one can determine the position where the cracks are to arise.

Cracks always arise where the tensile stresses are highest. Tensile stresses arise from tensile forces, flexure, displacements, settling and temperature fluctuations. When mortar or concrete sets, shrinkage cracks also form.

Stresses are high where the "external" forces are high. "External" forces are earth pressure, dead weight and applied load. Stresses are highest where the "internal" forces are highest. "Internal" forces are flexural, normal, gravitational and torsional forces.

The "external" forces can be reduced by favourable shaping of the structure. The liquid pressure and earth pressure are less in a low biogas plant. This is because both depend directly on the height (see Figure 57).

The "internal" forces can also be reduced by favourable shaping of the structure. If the "external" forces can act in one direction only, high "internal" forces arise. If, however, the "external" forces can be distributed in a number of directions, small "internal" forces arise. This is the case with all curved surfaces or "shells" (see Figure 16).

Fig. 16: Shape and load-bearing capacity Slabs will support a heavier load than beams for a given thickness of material. A curved shell supports more than a flat slab. A shell cuned in more than one dimension supports more than a shell of simple curvature. Curved structural components are more rigid; the stresses are smaller in them. Just imagine how thick the shell of a hen's egg would have to be if it were shaped like a cube!

Cracks arise where stresses are high. Particularly high stresses - "peak stresses" - arise at points where the stress pattern is disturbed.

Such disturbances occur at edges, angles, corners and under concentrated, applied or other loads. Disturbances arise along the line of intersection of surfaces. Cracks form at these points due to peak stresses.

Peak stresses always arise at the edges of angular structures. For this reason the gas space of a fixed-dome plant must never be angular.

Cracks arise owing to tensile stresses. If a component is under compression, it is free from cracks. The gas space of a fixed-dome plant should therefore always be under pressure at every point.

The liquid pressure of the fermentation slurry is directed outwards. The earth pressure is directed inwards. If the two forces balance reliably, the load on the structure is relieved. In a vaulted shape' the external loading is obtained even if the earth is stiff and cracked owing to drought (Figure 17-19).

Fig. 17: Same volume - different shape Different shapes have different stress patterns under the same load (a and b). The round shape has lower stresses. The angular shape has high stresses and many stress peaks. Different shapes are often loaded differently. In a vaulted shape, the loads acting in different directions are more reliably balanced than with a vertical wall (c and d).

Fig. 18: Pattern of stresses in a fixed-dome plant of masonry construction Top: empty; bottom: filled and with maximum gas pressure. The peak stresses shown are those resulting from the first approximation calculation. In practice they are reduced by deformation (with or without cracking). Positive (+) tensile stresses do not occur in the gas space.

Fig. 19: Cracks in the gas space of a fixed-dome plant Angular gas spaces must on no account be used (a)! The transition from the roof arch to the wall must never be at a higher level than the lowest slurry line (b). Inlet and outlet penetrations must never be situated in the gas space (c). The gas space must remain undisturbed. Only the entry hatch at the top is allowed, because it can easily be checked.

A round shape is always a good shape, Because a round shape has no corners. Because its load pattern is more favourable. And because it uses less material. A round shape is often easier to build than an angular one (see Section 5.3). The rounder the better!