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 briges toconnect remote areas to urban areas. Mostthese structures are made of reinforced concrete (RC).
Reinforced concrete, asa structural 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). Inthe actual practice, structural designs if not all may have disregarded theimportance of the ductility in the designed structures which result to collapse.
One reason is that structural designers need to meet the requirements given tothem by the architects. A common scenario, structural designers are forced toreduce dimensions, the capacity may not be sacrificed but the ductility isaffected. Meeting ductile behaviour in the designs may be too complex for somestructural engineers. Contractors on the other hand can be blamed because theyfocus more on the practicality than safety. A learned structural designer shouldconsider the benefits of having structural elements behaving in a ductilemanner.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.
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 overallevaluation of the flexural capacity or strength and the flexural ductility. Thesecond part of the study is the plotting of the moment-curvature relationshipon a beam section, based on the control specimen. The analysis of the beamsection follows the Models for unconfined concrete and Models of differentgrades of steel. The flexural behavior of the beam is evaluated using the shapeof the moment-curvature diagram.FlexuralDuctility/Curvature DuctilityOneway of measuring the ductility of a beam is the determining of its curvature.
InRC flexural members, ductile failure is attained when steel has yielded beforeconcrete crushes. The yielding of steel occurs if it reaches and exceeds its specifiedyield strength. 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.
h d b BEAM SECTION BEFORE CRACKING As Figure 1a. Curvature in Reinforced Concrete Beam As’ ?cc ?s’ ?s < ?y ?cc ?ct ?s' ?s AFTER CRACKING ?cc ?s' ?s = ?y YIELDING ?cu =0.003 ?s' ?s > ?y ULTIMATE ?cr ?cr ?y ?u The calculation ofcurvature ? is given by the formula, in rad/mmwhere?cc is the strain of concrete at the extreme compression fiber and c is the depth of the compression block.As ductile behavior is followed, the rate of increase in the strain of steelmust be larger compared to that of the concrete. Thus, as the strain of steelincreases the depth of compression decreases which causes the increase in thecurvature of the beam.