Property modifiers for slab/shell thin design

[abdallah hamdan]

as stated on the (ACI 318.2-14):3.1.1) "Elastic behavior shall be an acceptable basis for determining internal forces and displacements of thin shells. This behavior shall be permitted to be established by calculations based on an analysis of the uncracked concrete structure in which the material is assumed linearly elastic, homogeneous, and isotropic. Poisson’s ratio of concrete shall be permitted to be taken equal to zero."
can I design slab/check deflection using an etabs model without using property modifiers for all members or do I misunderstand this?

 

[centondollar]

A question to anyone else reading this thread: does the ACI actually allow to ignore the plate effect (also present in shells) of restricted expansion (Poisson's ratio is a part of plate stiffness equations, and it is what distinguishes a plate from a beam) in shell design? That doesn't seem to make any sense. With such an approach, shells/plate are modeled as as collection of curved beams/beams in two orthogonal directions - that is not how a plate or shell behaves!

To answer your question: what do you mean by "property modifiers"? The text you quoted seems to allow you to modify the property of shells in such a way that they become curved beams (zero Poisson's ratio). Furthermore, the text you quoted is obviously not applicable to all reinforced concrete shells - uncracked behavior is not always guaranteed with shells!

The correct (linear-elastic) way to perform any design of plates or shells is to follow the linearly elastic solution for internal forces, and to use appropriate methods for reducing stiffness in case the plate/shell/beam is expected to crack. Code provisions do not overrule basic principles of structural mechanics that your hand-calculations or FEM-models assume to be valid.

PS. Axisymmetric liquid storage tanks are some of the few RC shell structures that are usually designed to be uncracked (by prestressing the concrete shell), and for those, the uncracked section assumption is reasonable.

 

[abdallah hamdan]

thank you for your response
property modifiers represent the cracking behavior of structural elements , and my question is basically about modeling an uncracked structure (uncracked column, beam, shear wall, slab) when analyzing and designing (shells) based on the quoted text.
I agree with you that uncracked behavior is not always guaranteed with shells, so, where is the quoted text applicable? and can we also guarantee the uncracked behavior of shells other than liquid storage tanks?

 

[centondollar]

I am not very familiar with ACI, but the most straightforward answer to your main question is that you cannot assume that the structure is uncracked just because it is a shell - regardless of what an ACI chapter says about it. If you wish to prevent cracking, you must ensure that the cross-sectional stresses do not exceed the tensile strength of concrete; this can be achieved by limiting shell geometry (e.g., a dome with restrictions on width-to-height ratio) or by introducing prestressing. For a general shell (no axisymmetry, non-uniform load), ensuring an uncracked cross-section is very difficult.

Furthermore, I wish to emphasize that modeling a shell (or slab) with zero Poisson's ratio is incorrect, because a basic concept of shells and plates (2D objects) is that Poisson expansion is restricted, resulting in a higher stiffness than for a beam. Illustrating the relevance of Poisson's ratio for the isotropic case:

a beam: bending stiffness = EI = E*(b*h^3)/12

a plate: bending stiffness = D = E*t^3/(12*(1-v^2)) , where v = Poisson's ratio

The shell is simply a stiffer plate (initial curvature increases stiffness and capacity), and from the above two equations, a difference of (approximately, depending on material) 20% in stiffness - in favor of the plate - can be observed.

This advice applies to modelling with FEM or performing hand-calculations. You may, of course, calculate an extremely conservative deflection approximation by neglecting the shell stiffness and instead using a beam model, but this should be done using the internal forces received from elastic theory (which includes non-zero Poisson's ratio), because elastic theory is what correctly predicts the distribution of internal forces.

 

[abdallah hamdan]

thank you for your clarification