MOMENT-CURVATURE RELATIONSHIP OF REINFORCED CONCRETE BEAMS
MOMENT-CURVATURE RELATIONSHIP OF REINFORCED CONCRETE BEAMS
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Date
1993-08
Authors
OKOLI, Obumneme Godwin
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Abstract
Rigorous analysis of reinforced concrete members loaded
into the inelastic range requires the knowledge of the
relationship between moment and curvature. This knowledge
is necessary for better evaluation of the deflections and
possible redistribution of bending moments after cracking
in statically indeterminate reinforced concrete members.
In this research work, a considerably simplified theory for
the analysis of moment-curvature relationship and hence
deflection of reinforced concrete beams in the cracking
stage is presented. The theory assumes concrete to have a
non-zero tensile capacity. The non-linear behaviour of
concrete in compression was accounted for by assuming a
parabolic stress-strain relationship. For the purpose of
this work, the stress-strain diagram of concrete in tension
was approximated by a bilinear curve.
These assumptions led to a third degree equation to
determine the position of the neutral axis according to the
equilibrium of internal forces. Having the position the
position of the position of the neutral axis, it was
possible to find the moments and the curvatures for an
assumed value of strain in the tensile reinforcement.
By increasing the value of the strain and repeating the
above procedure, we obtain the moment-curvature diagrams.
Good agreement was found between the results of this the and the experimental results of previous investigators.
To further confirm the validity the theory, six full sized
reinforced concrete beams grouped into two sets were
tested. The first set of beams have cross sectional
dimensions 300mm by 100mm and the second set has dimensions
100mm by 300mm. Each of the beams has total span 4.0m. All
the beams were reinforced with deformed bars of varying
diameters. Stirrups were provided throughout the length of
each beam.
It was found that results of the experiments were in good
agreement with the theory.
Description
being a report of research work submitted to the
Postgraduate School in partial fulfillment of the requirements
for the award of Doctor of Philosophy degree
in Ahmadu Bello University
Department of Building
Faculty of Environmental Design
Ahmadu Bello University
Zaria
Keywords
MOMENT-CURVATURE,, RELATIONSHIP,, REINFORCED,, CONCRETE,, BEAMS,