ThePhilippines is one the countries in recent years, experiencing constructionboom due to economic growth and increasing population. At every corner,residential buildings, low-rise, and high-rise structures are built to meet theincreasing demands of the populace such as dwellings and workplaces. Billionsof pesos are allotted for construction of roads, highways, and bridges to connectremote areas to urban areas. Most thesestructures are made of reinforced concrete (RC). Reinforced concrete, as astructural material have the advantages against other materials such as lowcost, availability, adaptability and environmental considerations.
Due to therapid use of RC in building constructions, this designed buildings shouldbehave in the most desirable manner in response to the applied loads. Asof the previous studies, the desired behavior of RC members especially on theverge of collapse should be ductile in manner. Ductility is defined as the ability to undergodeformations without a substantial reduction in the flexural capacity of themember (Park & Ruitong 1988). Ductility of reinforced structures is adesirable property where resistance to brittle failure during flexure isrequired to ensure structural integrity (Olivia& Mandal 2005). In the actual practice, structuraldesigns if not all may have disregarded the importance of the ductility in thedesigned structures which result to collapse. One reason is that structuraldesigners need to meet the requirements given to them by the architects. Acommon scenario, structural designers are forced to reduce dimensions, thecapacity may not be sacrificed but the ductility is affected.
Meeting ductile behaviorin the designs may be too complex for some structural engineers. Contractors onthe other hand, can be blamed because they focus more on the practicality thansafety. A learned structural designer should consider the benefits of having structuralelements behaving in a ductile manner.The first part the study is focusedon the theoretical-analytical calculation of the quantities in an RC beam usingstress-strain models for concrete and steel. A Parametric study is being carried out by varyingthe amount tensile reinforcement, varying the yield strength of steel, varyingthe compressive strength of concrete and varying the dimensions as to how they affectthe overall flexural behavior.
The flexural behavior refers to the overall evaluationof the flexural capacity or strength and the flexural ductility. The second part of the study is theplotting of the moment-curvature relationship on a beam section, based on thecontrol specimen. The analysis of the beam section follows the Models forunconfined concrete and Models of different grades of steel. The flexuralbehavior of the beam is evaluated using the shape of the moment-curvaturediagram.FlexuralDuctility/Curvature DuctilityOne way of measuring the ductilityof a beam is the determining of its curvature. In RC flexural members, ductilefailure is attained when steel has yielded before concrete crushes. Theyielding of steel occurs if it reaches and exceeds its specified yieldstrength.
It is desired to have a ductile mode of failure in designingstructures for concrete is a brittle material. Brittle materials do not exhibitsubstantial deformations before failure. The effect ofcurvature in the ductility of the beam is shown in Fig. 1a. The presented figure is based on the typical straindiagram of the RC beam at crack initiation, flexural yielding, and ultimatestate.
The strain diagrams are all linear in nature to conform to the basicassumption in flexure analysis that plane sections before bending remain planeafter bending. The figure shows that the depth of compression block increaseswith slight increase in the strain of concrete in the compression side as theanalysis progresses from initial to the ultimate stage. Also, the intensity ofthe curvature ? increases as the stage progresses.