Advantages of design by analysis over design by formula in storage tanks

Today we look at the advantages of design by analysis.

When designing tanks, we are dealing with a type of structure that is typically susceptible to failure due to instability at the joint between the bottom and the first shell course; one of the most common failure modes in tank design, and the one that requires the most attention, is therefore compressive buckling. Consequently, to ensure correct tank behavior, it must be verified at the design stage that the stress state at the tank base, resulting from the combination of compressive stresses, hoop tensile stresses and high shear forces, is lower than the allowable buckling stress that leads to instability and collapse of the shell.

This verification can be carried out analytically or by using advanced simulation tools.

The main tank design standards include provisions for calculating the allowable buckling stress, as shown below:

• API 650, the US reference standard for tank design, defines the allowable buckling stress based on the theoretical buckling values of a cylindrical shell, reduced by various factors that account for the effect of internal pressure in the tank.

• Eurocode 8, the European reference standard with provisions for the seismic design of tanks, considers the elastic behavior of the tank in its equations to determine the allowable compressive stress at the tank base.
  
  

Comparing both formulations, the allowable stress defined in API 650 can be expected to be more restrictive than that of the Eurocode, since the latter does not account for elastic-plastic behavior in its formulation. However, these analytical methods have been shown to have certain limitations when calculating large-capacity tanks, and to yield very conservative designs. This is where advanced simulation plays a very important role in validating more complex and larger tanks, since finite element calculations help us gain a broader and more accurate understanding of their behavior and response to the different loads to which they are subjected.

Designing this type of tank with the advanced simulation tools available today at CADE results in significant material savings, as it enables much more efficient and optimized designs without requiring long computation times.

As the following chart shows, for small tanks (D<20m), the results obtained by analytical calculation according to API 650 and by finite element simulation are practically the same; however, in these small-diameter tanks there may be failure modes that go unnoticed with the analytical formulation but are detected in finite element calculations. On the other hand, as tank diameter increases, the discrepancy between the results of both methodologies grows, with design by analysis yielding more optimized results, a difference that is most noticeable in tanks with a diameter greater than 55m.