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Equivalent frame Re: A structural engineering journal

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Roger,

My FE program is correct and so if my EF program for the calculation of the moments and shears in a slab and moments in a column and they both produce the same overall results as confirmed by Michael Bryson. I was not talking about the calculation of column reactions and neither were you but the reactions in the columns are correct for each case being analyzed.

The main point of all of this is that the appropriate analysis method be used to match the design approach being used.

If the slab is going to be designed as two-way following the elastic distribution of moments in the slab then FE gives the best results (especially for irregular support layouts) but EF gives results which, when combined with experience and logic, can be used to estimate design actions for column strips and middle strips as is done for reinforced concrete slab design.

If the slab is going to be designed as one-way banded, then it must be analyzed in the same way. For rectangular grids of supports it does not really matter which analysis method is used (FE or EF) for the ultimate design of the slab as both methods will give similar results, but it will affect the distributions of loads to supporting elements such as beams and columns and so EF gives the better results as it ignores effects from supports etc outside the frame being analyzed and matches the design approach best.

For irregular supported slabs, it is essential that the analysis be based on the same logic as the design. For ultimate strength design, a one-way action is being assumed as the failure mechanism so the analysis must be based on the same method. Otherwise, the distribution of actions within the slab from the analysis will be different to the way it is being assumed to act in design based on those actions and could produce misleading results. A further complication arises in the checking of service moments which are still based on an elastic distribution of the moments etc and should therefore be based on a FE analysis taking into account distribution of the moments across the slab.

The reason for the difference is that, at service, the slab is still elastic or nearly elastic and the moments will follow approximately the elastic two-way distributions.of moments and shears. Forcing the slab to then act as a one-way slab at failure results in a different analysis being needed. For loadings in between those causing elastic effects and those causing failure effects, the distributions are also in between and cannot be estimated logically unless you have an FE program which allows for cracking of concrete automatically. This is the problem with forcing a slab to act differently from the basic elastic action that it wishes to follow and that is what is happening with banded two-way slabs. This is partly why ACI318 limits the service stresses (but not harshly enough in my opinion) in such slabs.

At 11:14  20/11/00 -0500, you wrote:
Gil Brock wrote:

>>Roger,

In what way is the equivalent frame method "very conservative". A finite
element analysis results in the same total moments in a panel in each
direction as an equivalent frame analysis for a rectangular grid of
columns. This also shows that the total load needs to be carried in both
directions. The difference from a FE analysis is that it gives an elastic
distribution of those moments across the width of the panel and will also
show the distribution of moments for irregularly placed columns. The total
design moments in a panel, however, are the same from the 2 approaches for
the rectangular grid of columns.<<

The equivalent frame method is "very conservative" because it analyzes the
panels as one-way slabs in each direction, with each carrying the total
load.  Therefore, the shear forces in the panel at the column lines in
direction 1 have to equal the total load on the panel.  Similarly, the shear
forces in the panel at the column lines in direction 2 also have to equal the
total load on the panel.  Therefore, the total resisting shear on a panel is
equal to twice the load on the panel, a gross violation of statics.

There is nothing in the equivalent frame method that I have seen that
considers consistent deformation, one of the requirements of a two-way slab
or statically indeterminate system.

I cannot tell you why your FE program gives you the same results as the
equivalent frame method.  If the shear forces at all 4 panel edges total
twice the total load on the panel, I would suspect that the FE program was
written as an equivalent frame program and marketed as an FE program.

A. Roger Turk, P.E.(Structural)
Tucson, Arizona




Regards  Gil Brock
Prestressed Concrete Design Consultants Pty. Ltd.
5 Cameron Street Beenleigh Qld 4207 Australia
Ph +61 7 3807 8022              Fax +61 7 3807 8422
email:  gil(--nospam--at)raptsoftware.com
webpage:        http://www.raptsoftware.com/