The beam using stress-strain models for concrete and

Philippines is one the countries in recent years, experiencing construction
boom due to economic growth and increasing population. At every corner,
residential buildings, low-rise, and high-rise structures are built to meet the
increasing demands of the populace such as dwellings and workplaces. Billions
of pesos are allotted for construction of roads, highways, and bridges to connect
remote areas to urban areas.  Most these
structures are made of reinforced concrete (RC). Reinforced concrete, as a
structural material have the advantages against other materials such as low
cost, availability, adaptability and environmental considerations. Due to the
rapid use of RC in building constructions, this designed buildings should
behave in the most desirable manner in response to the applied loads.

of the previous studies, the desired behavior of RC members especially on the
verge of collapse should be ductile in manner.  Ductility is defined as the ability to undergo
deformations without a substantial reduction in the flexural capacity of the
member (Park & Ruitong 1988). Ductility of reinforced structures is a
desirable property where resistance to brittle failure during flexure is
required to ensure structural integrity (Olivia& Mandal 2005).

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In the actual practice, structural
designs if not all may have disregarded the importance of the ductility in the
designed structures which result to collapse. One reason is that structural
designers need to meet the requirements given to them by the architects. A
common scenario, structural designers are forced to reduce dimensions, the
capacity may not be sacrificed but the ductility is affected. Meeting ductile behavior
in the designs may be too complex for some structural engineers. Contractors on
the other hand, can be blamed because they focus more on the practicality than
safety. A learned structural designer should consider the benefits of having structural
elements behaving in a ductile manner.

The first part the study is focused
on the theoretical-analytical calculation of the quantities in an RC beam using
stress-strain models for concrete and steel.  A Parametric study is being carried out by varying
the amount tensile reinforcement, varying the yield strength of steel, varying
the compressive strength of concrete and varying the dimensions as to how they affect
the overall flexural behavior. The flexural behavior refers to the overall evaluation
of the flexural capacity or strength and the flexural ductility.

The second part of the study is the
plotting of the moment-curvature relationship on a beam section, based on the
control specimen. The analysis of the beam section follows the Models for
unconfined concrete and Models of different grades of steel. The flexural
behavior of the beam is evaluated using the shape of the moment-curvature

Ductility/Curvature Ductility

One way of measuring the ductility
of a beam is the determining of its curvature. In RC flexural members, ductile
failure is attained when steel has yielded before concrete crushes. The
yielding of steel occurs if it reaches and exceeds its specified yield
strength. It is desired to have a ductile mode of failure in designing
structures for concrete is a brittle material. Brittle materials do not exhibit
substantial deformations before failure.

The effect of
curvature in the ductility of the beam is shown in Fig. 1a. The presented figure is based on the typical strain
diagram of the RC beam at crack initiation, flexural yielding, and ultimate
state. The strain diagrams are all linear in nature to conform to the basic
assumption in flexure analysis that plane sections before bending remain plane
after bending. The figure shows that the depth of compression block increases
with slight increase in the strain of concrete in the compression side as the
analysis progresses from initial to the ultimate stage. Also, the intensity of
the curvature ? increases as the stage progresses.