Concrete slabs designed with finite element methods:
modelling parameters, crack analyses and reinforcement design

University essay from Luleå/Väg- och vattenbyggnad

Abstract: Concrete slabs are today usually designed by traditional hand calculation
methods. Powerful numerical calculation methods like the Finite Element
Method (FEM) are not recommended in design handbooks for design of slabs,
see e.g. Hillerborg et al (1990),(1996). In contrary, its distribution of
reinforcement is considered to be unsuitable for practical use. Most
FE-programs are also more adapted for analyses than for design.

SKANSKA IT Solutions in Malmö, Sweden, has developed a FE-based design
program called FEM-Design. The program handles e.g. FE-analyses and design
of frames, trusses, beams, shear walls and plates. In this report the
program is checked and improved regarding the crack analysis, the calculated
effects of actions and the design of reinforcement. Another importent issue
discussed is the extreme-value problem of moments in centre of interior
columns/walls in flat slab floors.

The models used are checked regarding influence of mesh density, element
types, column widths and modelling of column stiffness. The FE-analyses show
that the mesh density and the modelling of the column stiffness mainly
affects the size of the support moments, whereas the field moments are
almost independent of all modelling parameters. Fem-Design's automatically
generated mesh gave good results with respect to the size of the support
moments. However, the result of moment distribution or actually the
reinforcement distribution could be improved by distributing the column
stiffness over one plate element. The multi spring concept is also suggested
for interior walls wider than 0.2 m.

The iterative crack analysis is compared with Abaqus/Explicit
smeared cracks and an experimental test, McNiece (1978). FEM-Design's crack
analysis is found to be adequate for design, despite that the crack
propagation differs quite much in comparison with Abaqus. FEM-Design's
load-displacement curve shows better agreement with the experimental test.
The difference depends on the implemented crack theory i.e. when a crack is
considered to be a crack.

The distribution of design moments for a simple flat slab floor are compared
with designs by two hand calculation methods, the strip method and the yield
line theory. The comparison shows that FEM-Design's design moments or
actually the required reinforcements have to be chosen at certain points and
redistributed by a design method.

A FE-based design method is developed with respect to the capabilities of
FEM-Design and FE-analyses performed with the traditionally distributed
reinforcement. Comparisons between the three methods show that the FE-based
reinforcement design method (FED) distributes less total amount of
reinforcement than the two traditional methods with respect of both bending-
and final design.

The thesis concludes that FE-analyses can be used to get a practical
reinforcement design in concrete slabs - if the reinforcement like for
other methods are redistributed in appropriate areas/strips. This is in
contradiction to statements by Hillerborg et al (1990), (1996).
Finally, FEM-Design has proven to give reliable analyses and designs, for
tested cases. Actually, there are very few drawbacks with the use of a
FE-based design, especially since FEM-Design's plate module is found to be a
very user-friendly design tool. However, three improvements/implementations
are suggested to make the program even better:

• A distributed stiffness (the multi spring concept) to model interior
• A more available and clear input check option.
• A distribution method for reinforcement.

The distribution method (FED), proposed in the thesis is suggested as one
suitable method to implement, because it combines FE-theory with theories
behind traditional design methods.