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GRILLAGE ANALYSIS OF COMPOSITE CONCRETE PARTIAL INTERACTION

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GRILLAGE ANALYSIS OF COMPOSITE CONCRETE SLAB ON
STEEL BEAMS WITH PARTIAL INTERACTION
Prof. Dr. Husain M. Husain
1
, Dr. Ali N. Attiyah
2
and Jenan Niamah Yasser
3
ABSTRACT: The present study is concerned with the behavior of a composite structure
made up of a concrete slab connected to steel beams in two directions by shear connectors by
taking into consideration the linear action of shear connectors in the force-slip relationship.
The grillage or grid framework method as simplified method of analysis is used in this study
to study slip, deflection and stresses caused by moments from applied normal loads. A
method is suggested to derive the required section rigidities (the flexural and torsional
rigidities) of the grillage members from the composite action of the individual grillage
composite members. Design charts are constructed for estimating the percentage decrease in
flexural rigidity of each composite member with partial shear connection. It was found for a
composite structure analyzed by grillage members, the effective width of each member should
be used to calculate the flexural rigidity of that member. Also Poisson’s ratio effect was
included in the calculation of the flexural rigidities of the grillage members. Effect on
deflections by transverse shearing forces was found to be small and thus it can be neglected
(percentage differences is less than 11.8 %).
1. Introduction
Each different building material has a special prominent quality which distinguishes it
from other materials. There is no material that can provide all the structural
requirements. This is the reason of using different materials that can be arranged in an
optimum geometric configuration, with the aim that only the desirable property of
each material will be utilized by virtue of its designated position. The structure is then
known as a composite structure, and the relevant method of building as composite
construction.
The composite concrete slab-on-steel beam structure consists of three major structural
elements, namely a reinforced concrete slab resting on longitudinal and transverse
steel beams, which interact, compositely with the slab by means of mechanical shear
connectors. The analysis of composite beams and their behavior assuming linear and
nonlinear material and shear connector behavior has been in general based on an
approach initiated by Newmark, Siess and Viest in 1951
[1]
. The equilibrium and
compatibility equations for an element of the beam were reduced to a single second
1) University of Tikreet , College of Engineering , Civil Department.
2) University of Kufa , College of Engineering , Civil Department.
3) University of Kufa , College of Engineering , Civil Department.

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order differential equation in terms of either the resultant axial force in the (concrete)
flange or the interface slip. Solution for the axial force or the interface slip was
substituted back into the basic equilibrium and compatibility equations, which could
then be solved to give the displacements and the strains throughout the beam. That
approach was initially based on linear material and shear connector behavior.
In the method suggested for the present study, the composite structure is idealized as a
grillage, the grillage mesh is assumed to be coincident with the center-lines of the
main steel beams. The concrete slab and the steel beams are assumed to behave in the
elastic range and the force- slip behavior of the shear connectors is linear. To use the
T-beam approach, the concept of the effective width is used which refers to a fictitious
width of the slab that when acted on by the actual maximum stress the slab would
have the same static equilibrium effect as the existing variable stress. The effective
width is affected by various factors, such as the type of loading, the boundary
conditions at the supports and the ratio of beam spacing to span B/L
[2]
.
Johnson (1975)
[3]
proposed a partial interaction theory for simply supported composite
beams, in which the analysis was based on elastic theory. Kennedy, Grace, and
Soliman (1989)
[4]
presented an experimental study that was conducted on three
composite bridge models each subjected to one- vehicle load. Jasim (1994)
[5]
presented a method of analysis which depended on elastic theory. In that analysis he
adopted same assumptions of Newmark
[1]
.
2. Assumptions of the Grillage Analogy
The grillage analogy involves the representation of effectively a three- dimensional
composite structure by a two- dimensional assemblage of discrete one- dimensional
interconnected beams in bending and torsion. In analysis, the following assumptions
are introduced:
1- Concrete and steel are linearly elastic materials. The concrete slab is assumed
to be able to sustain sufficient tension such that no tensile cracks develop in
this part. The distribution of strains through the depth of each component is
linear.
2- The longitudinal and transverse steel beams are assumed rigidly connected
(welded connections).

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GRILLAGE ANALYSIS OF COMPOSITE CONCRETE SLAB ON STEEL BEAMS WITH PARTIAL INTERACTION Prof. Dr. Husain M. Husain1, Dr. Ali N. Attiyah2 and Jenan Ni’amah Yasser3 ABSTRACT: The present study is concerned with the behavior of a composite structure made up of a concrete slab connected to steel beams in two directions by shear connectors by taking into consideration the linear action of shear connectors in the force-slip relationship. The grillage or grid framework method as simplified method of analysis is used in this study to study slip, deflection and stresses caused by moments from applied normal loads. A method is suggested to derive the required section rigidities (the flexural and torsional rigidities) of the grillage members from the composite action of the individual grillage composite members. Design charts are constructed for estimating the percentage decrease in flexural rigidity of each composite member with partial shear connection. It was found for a composite structure analyzed by grillage members, the effective width of each member should be used to calculate the flexural rigidity of that member. Also Poisson’s ratio effect was included in the calculation of the flexural rigidities of the grillage members. Effect on deflections by transverse shearing forces was found to be small and thus it can be neglected (percentage differences is less than 11.8 %). 1. Introduction Each different building material has a special prominent quality which distinguishes ...
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